1. business and industrial
2. chemicals industry
3. plastics and polymers

i
OPTIMAL DESIGN AND CHARACTERIZATION OF PLANTAIN
FIBER REINFORCED POLYESTER MATRICES
BY
OKAFOR, EMEKA CHRISTIAN
REG. NO.: 2010377002P
DEPARTMENT OF INDUSTRIAL/PRODUCTION ENGINEERING,
NNAMDI AZIKIWE UNIVERSITY, AWKA
2014
ii
TITLE PAGE
OPTIMAL DESIGN AND CHARACTERIZATION OF PLANTAIN
FIBER REINFORCED POLYESTER MATRICES
BY
OKAFOR, EMEKA CHRISTIAN
REG. NO.: 2010377002P
A DISSERTATION SUBMITTED TO THE DEPARTMENT OF
INDUSTRIAL/PRODUCTION ENGINEERING, FACULTY OF
ENGINEERING AND TECHNOLOGY, NNAMDI AZIKIWE
UNIVERSITY, AWKA. IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE AWARD OF
DOCTORATE DEGREE IN DESIGN AND
MANUFACTURING.
2014
iii
APPROVAL PAGE
This dissertation titled “optimal design and characterization of plantain fiber
reinforced polyester matrices” by Okafor, Emeka Christian with registration
number 2010377002P meets the requirements for the award of doctorate
degree in industrial/production engineering; it is approved for its contribution
to knowledge and literary presentation by:
Okafor, Emeka Christian
………………….
…………………..
(Student)
Sign
Date
Prof. C. C Ihueze
………………….
…………………..
(Supervisor)
Sign
Date
Dr. Harold Godwin
………………….
…………………..
(Head of Department)
Sign
Date
Prof. P. K Igbokwe
(Dean, Faculty of Engineering)
………………….
Sign
…………………..
Date
Prof. O. L Anike
(Dean, SPGS)
………………….
Sign
…………………..
Date
External Examiner
………………….
Sign
…………………..
Date
iv
DEDICATION
This dissertation is dedicated to God Almighty and Lovers of peace worldwide.
v
ACKNOWLEDGEMENTS
Special thanks to my supervisor, Professor Christopher Chukwutoo Ihueze
for his enthusiastic support, encouragement and understanding throughout my
study at Nnamdi Azikiwe University. He allowed me to work independently but
was always available when his advice was needed. His professional experience and
extensive contacts have contributed greatly to this research work. The support and
encouragements received from the Head, Department of Industrial Production
Engineering, Dr. Harold Godwin is gratefully acknowledged.
I would like to thank all administrative and lab staff especially Mr. S.
Oluwagbemiga Alayande of Obafemi Awolowo University (OAU) Ile-Ife for his
valuable suggestions and guidance in the FTIR measurements and Mr. Szentes
Adrienn of University of Pannonia for his discussions and contributions during
NAD testing.
Grateful appreciation is made to my friends and colleagues (Enyi Louis,
Okechukwu Ezeanyika, Chika-Edu Mgbemena) who have made my experience at
UNIZIK enjoyable and worthwhile. I would like to thank the academic staff of
department of industrial production engineering for their cooperation.
OKAFOR, EMEKA CHRISTIAN
2014
vi
ABSTRACT
This study involved design and manufacture of a natural fiber based composite at
optimal levels of factor combinations to achieve maximum strength. A plan of
experiments based on the Taguchi technique was performed to acquire data in a
controlled way. Taguchi Robust Design, Response Surface Methodology and
Finite Element Methods were applied to optimize the tensile strength, flexural
strength and Brinell hardness of plantain fibers reinforced composite (PFRC).
These properties were determined for empty fruit bunch fibers (EFBF) and pseudo
stem fibers (PSF) of the plantain plant. Tensile, flexural, Brinell hardness and
impact tests were conducted on replicated samples of the two types of plantain
fibers reinforced polyester (PFRP) using Archimedes principles in each case to
determine the volume fraction of fibers. The Taguchi robust design technique was
applied for the greater-the-better to obtain the highest signal-to-noise ratio
(SNratio) for the quality characteristics (strengths) in the determination of
optimum factor control levels which were then used to optimize the mechanical
properties of PFRP applying response surface method (RSM) of Design-expert 8
software. The Finite element method was applied in the computation of stress
distribution and prediction of material failure zones. The morphology of the
composites were examined by scanning electron microscopy (SEM) while the
Fourier transform infrared spectroscopy (FTIR) was used in identifying chemical
bonds and composition of materials for plantain fiber and composites. The
Nitrogen adsorption/desorption isotherm (NAD) studies established influences of
fibers modification on the properties studied. The yield strength, tensile strength,
flexural strength, Brinell hardness and impact strength of the plantain empty fruit
bunch fibers reinforced composites (PEFBFRC) were found to be 33.69MPa,
41.68MPa, 46.31MPa, 19.15N/mm2 and 158.01KJ/m2 respectively while those for
the plantain pseudo stem fibers reinforced composite (PPSFRC) were 29.24MPa,
34.76MPa, 45.94MPa, 18.59N/mm2 and 158.01KJ/m2 respectively. The PEFBFRC
with average light absorbance peak of 45.47 was found to have better mechanical
properties than the PPSFRC with average light absorbance peak of 45.77.
vii
TABLE OF CONTENTS
APPROVAL PAGE
iii
DEDICATION
iv
ACKNOWLEDGEMENTS
v
ABSTRACT
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xiv
LIST OF FIGURES
xxii
LIST OF SYMBOLS
xxviii
CHAPTER ONE
1
INTRODUCTION
1
1.1.
Background of the study
1
1.2
Statement of the problem
6
1.3
Aim and objectives of the study
8
1.4
Relevance of the study
9
1.5
Scope and limitation
11
1.6.
Justification for application of Taguchi Method in Composites design
12
CHAPTER TWO
15
LITERATURE REVIEW
15
2.1.
Conceptual framework
15
2.2
Backgrounds of plantain fiber
19
2.3
Structure and Properties of Cellulose Fibers
21
2.4
Extraction and ratting of Cellulose Fibers
24
viii
2.5
Mechanisms of Surface Modifications of Cellulose Fibers
2.6
Theories and Application of Taguchi design of experiments
27
in composites parameter Design
40
2.7
Theory and Principles of Response Surface Methodology (RSM)
45
2.8
Response Surface Methodology (RSM) and Robust Design
52
2.9
Failure theories and limit stress prediction in multiaxial stress state
54
2.10
Finite Element Analysis (FEA) and application in Composite Modelling
60
2.11 Properties of Composites and factors affecting strengths
65
2.12 Summary of literature review
73
CHAPTER THREE
77
METHODOLOGY
77
3.1
Materials
77
3.2
Experimentation
82
3.2.1 Fiber extraction and Retting
82
3.2.2 Alkali treatment
83
3.2.3 Silane treatment
83
3.2.4 Acetylation
84
3.2.5 Process Variables and modeling
84
3.2.6 Composites modulus
86
3.2.7 Random modulus of composite
97
ix
3. 2.8 Poisson’s ratio for plantain fibers
88
3.2.9 Fiber orientation and fiber stress distribution in loading
off the fiber axis
3.3
89
Design and optimization techniques
91
3.3.1 Design for composite manufacture
91
3.3.2 Determination of fiber quantity through
Archimedes principle
3.3.3 Mould design for various mechanical tests
96
3.3.4 Yielding of composite materials
102
3.3.5 Preparation of composites
105
3.3.5.1
3. 4
93
Basic Processing Steps
106
Material testing and characterization
107
3. 4.1 Flexural Test
107
3.4.2 Tensile Test
109
3.4.3 Brinell hardness evaluation
111
3.4.4 Impact test
111
x
3.5
Optimization of process variables
115
3.5.1 Application of Taguchi Robust design
115
3.5.2 Application of Response Surface Methodology (RSM)
119
3.5.2.1 Power Law Model for the Nonlinear Responses
of Experimental Data:
3.5.2.2Formation of Power Law Model
119
121
3.5.2.3 Implementation of Response Surface
Methodology (RSM)
3.5.3 Analysis of displacement and stress distributions of PFRP
3.5.3.1 Finite Element Analysis (FEA)
3.5.4 Non destructive testing and microscopic characterization
124
126
126
139
3.5.4.1
Scanning Electron Microscope (SEM)
3.5.4.2
Fourier Transform Infra Red Spectroscopy (FTIR) 141
3.5.4.3
Nitrogen Adsorption and Desorption Isotherms (NAD) 142
CHAPTER FOUR
145
DATA ANALYSIS AND DISCUSSIONS
145
4.1
145
Experimental Design and Parameter Optimization: Tensile Strength
139
xi
4.1.1 Taguchi experimental design based on the L9 (33) design
145
4.1.2 Response surface optimization of tensile strength based
on power law model
4.1.2.1
Curve fitting and linearization of experimental responses
4.1.2.2
Evaluation of Tensile Strength of Plantain Empty Fruit
Bunch (EFB) Fiber Reinforced Composites
4.1.2.3
155
156
Evaluation of Tensile Strength of plantain pseudo
stems (PPS) Fiber Reinforced Composites
4.2
154
167
Experimental Design and Parameter Optimization: Flexural Strength 172
4.2.1 Taguchi experimental design based on the L9(33) design
172
4.2.2 Response surface optimization of flexural strength based on power law
model
181
4.2.2.1
Curve fitting and linearization of experimental responses
181
4.2.2.2
Evaluation of Flexural Strength of PEFB Fiber Reinforced
Composites
183
4.2.2.3
Evaluation of Flexural Strength of plantain pseudo
stem (PPS) Fiber Reinforced Composites
4.3
192
Experimental Design and Parameter Optimization: Hardness Strength 197
4.3.1 Taguchi experimental design based on the L9(33) design
197
4.3.2 Response surface optimization of hardness strength based
on power law model
4.3.2.1
4.3.2.2
Brinell Hardness Strength of Plantain EFB Fibre Reinforced
Composites
Brinell Hardness Strength of Plantain PPS Fibre Reinforced
207
208
xii
Composites
216
4.4
Charpy Impact Test Results
221
4.5
Optimally designed plantain fiber reinforced composite sample and
specification
227
4.5.1 Finite Element Modelling of optimally designed plantain
fiber reinforced composites
4.5.2 Composites in tension
4.5.1.1
244
Estimation of transverse and longitudinal
stresses of composite at failure
4. 6
229
Failure predictions with stress theories and
specification for safety
4.5.1.2
227
246
4.5.3 Composites in flexure
247
Microscopic Characterization of Plantain Fibers and Composites
258
4.6.1 Fourier Transform Infrared (FTIR) Spectroscopy
259
4.6. 2 Nitrogen Adsorption/Desorption Isotherm (NAD)
265
4.6.3. Morphology mechanism of composites
269
xiii
CHAPTER FIVE
275
CONCLUSIONS, CONTRIBUTION TO KNOWLEDGE AND
RECOMMENDATIONS
275
5.1
Conclusions
275
5.2
Contribution to knowledge
280
5.2.1 Publications from research findings
283
5.3.
284
Recommendations for Future Research
REFERENCES
286
APPENDIX I
321
FOURIER TRANSFORM INFRARED (FTIR) DATA
321
APPENDIX II
323
NITROGEN ADSORPTION AND DESORPTION CHARACTERISTICS
OF UNTREATED PLATAIN FIBER
323
APPENDIX III
332
NITROGEN ADSORPTION AND DESORPTION
CHARACTERISTICS OF TREATED PLATAIN FIBER
332
xiv
LIST OF TABLES
Table 2.1
Properties of some natural fibers used for composites
Table 3.1:
Plantain fiber parameters determined by Archimedes principle 81
Table 3.2:
Theoretical volume of mould and volume of composite
for sample replicates
Table 3.3:
100
Brinell hardness test mold design variables for pseudo stem fiber
reinforced polyester composite
Table 3.9:
100
Brinell hardness test mold design variables for empty fruit
bunch fiber reinforced polyester composite
Table 3.8:
99
Tensile test mold design variables for pseudo stem fiber
reinforced polyester composite
Table 3.7:
99
Tensile test mold design variables for empty fruit bunch fiber
reinforced polyester composite
Table 3.6:
98
Flexural test mold design variables for pseudo stem fiber
reinforced polyester composite
Table 3.5:
97
Flexural test mold design variables for empty fruit bunch fiber
reinforced polyester composite
Table 3.4:
18
101
Impact test mold design variables for empty fruit bunch fiber
reinforced polyester composite
Table 3.10: Impact test mold design variables for pseudo stem fiber
101
xv
reinforced polyester composite
102
Table 4.1: Experimental outlay and variable sets for mechanical properties
145
Table 4. 2: Applicable Taguchi Standard Orthogonal array L9
146
Table 4. 3: Experimental design matrix for tensile test using
composite made from plantain pseudo-stem fiber
(ASTM-638)
147
Table 4. 4: Experimental design matrix for tensile test using
composite made from plantain empty fruit bunch
(ASTM-638)
148
Table 4. 5: Evaluated quality characteristics, signal to noise ratios and
orthogonal array setting for evaluation of
mean responses of PEFB
149
Table 4. 6: Response table for SN ratio and mean tensile strength of plantain
empty fruit bunch fiber reinforced composites based on Larger is
better quality characteristics
149
Table 4. 7: Response table for SN ratio and mean tensile strength of plantain
pseudo stem fiber reinforced composites based on Larger is better
quality characteristics
Table 4.8:
150
Optimum setting of control factors and expected optimum strength of
composites
154
xvi
Table 4.9:
Linearization data for power law model response of PEFB
155
Table 4.10: Linearization data for power law model response of PPS
156
Table 4.11: Factors for response surface study
157
Table 4.12: Matrix of central composite design for optimization of
power law model response of tensile strength of PEFB composites
157
Table 4.13: Analysis of variance (ANOVA) for RSM optimization
of PEFB tensile strength
Table 4.14: Goodness of fit and regression statistics
159
159
Table 4.15: Experimental design matrix of central composite design for
optimization of power law model response of tensile
strength of PPS composites
167
Table 4.16: Analysis of variance (ANOVA) for RSM optimization
of PPS tensile strength
169
Table 4.17: Experimental design matrix for flexural test using composite made
from plantain empty fruit bunch fiber (ASTM D-790M)
173
Table 4.18: Evaluated quality characteristics, signal to noise ratios and
orthogonal array setting for evaluation of mean responses of PEFB
173
Table 4.19: Average responses obtained for Volume fraction (A)
at levels 1, 2, 3 within experiments 1 to 9
174
xvii
Table 4.20: Average responses obtained for Aspect Ratio (B) at levels 1, 2, 3
within experiments 1-9
174
Table 4.21: Average responses obtained for fiber orientation (C) at levels 1, 2, 3
within experiments 1-9
174
Table 4.22: Response Table for flexural strength of plantain empty fruit bunch
fiber reinforced composites based on Larger is better quality
characteristics
176
Table 4.23: Experimental design matrix for flexural test using composite made
from pseudo-stem plantain fiber (ASTM D-790M)
178
Table 4.24: Response Table for flexural strength of plantain empty fruit bunch
fiber reinforced composites based on Larger is better quality
characteristics
179
Table 4.25: Optimum setting of control factors and expected optimum strength of
composites
180
Table 4.26: Linearization table for power law model response of PEFB
182
Table 4.27: Linearization table for power law model response of PPS
182
Table 4.28: Experimental design matrix of central composite design for
optimization of power law model response of flexural strength of
PEFB composites
183
xviii
Table 4.29: Analysis of variance (ANOVA) for RSM optimization of PEFB
flexural strength
Table 4.30: Goodness of fit and regression statistics
184
185
Table 4.31: Experimental design matrix of central composite design for
optimization of power law model response of tensile strength of PPS
composites
192
Table 4.32: Analysis of variance (ANOVA) for RSM optimization of PPS flexural
strength
Table 4.33: Goodness of fit and regression statistics
193
194
Table 4.34: Experimental Design Matrix for Hardness Test Using
Composite Made from Plantain Pseudo Stem Fibers
198
Table 4.35: Evaluated quality characteristics, signal to noise ratios and
orthogonal array setting for evaluation of mean responses of PPS
198
Table 4.36: Average responses obtained for Volume fraction (A) at levels 1, 2, 3
within experiments 1- 9.
199
Table 4.37: Average responses obtained for Aspect Ratio (B) at levels 1, 2, 3
within experiments 1-9
200
Table 4.38: Average responses obtained for fiber orientation (C) at levels 1, 2, 3
within experiments 1-9
200
xix
Table 4.39: Summary of responses and ranking for hardness strength of plantain
pseudo stem fiber reinforced composites based on Larger is better
quality characteristics
201
Table 4.40: Experimental Design Matrix for Hardness Test Using
Composite Made from Plantain Empty Fruit Bunch Fibers
203
Table 4.41: Summary of responses and ranking for hardness strength of plantain
empty fruit bunch fibers reinforced composites
Table 4.42: Signal to noise ratio response for hardness strength
205
206
Table 4.43: Optimum setting of control factors and expected optimum strength of
composites
207
Table 4.44: Experimental design matrix of central composite design for
optimization of power law model response of hardness strength of
PEFB composites
208
Table 4.45: Analysis of variance (ANOVA) for RSM optimization of PEFB
hardness strength
Table 4.46: Goodness of fit and regression statistics
210
210
Table 4.47: Experimental design matrix of central composite design for
optimization of hardness strength of PPS composites
216
Table 4.48: Analysis of variance (ANOVA) for RSM optimization of PPSFRC
tensile strength
217
xx
Table 4.49: Goodness of fit and regression statistics
218
Table 4.50: Experimental results of impact tests on plantain EFB fiber reinforced
composites
221
Table 4.51: Experimental results of impact tests on pseudo stem
fiber composites
222
Table 4.52: Construction of sample geometry
231
Table 4.53: Mechanical Properties of Plantain Fibers and polyester resin
234
Table 4.54: Composites elastic modulus with empirical equations
235
Table 4.55: Isotropic material properties for finite element analysis
238
Table 4.56: Summary of FEA results for PEFBFRC-50% 90O (10) sample settings
at selected nodes
241
Table 4.57: FEA results for PPSFRC-50% 90O (10) sample settings at selected
nodes
243
Table 4.58: Computed limit stresses for plantain fiber reinforced composites 244
Table 4.59: Evaluated mechanical properties of plantain fibers and
plantain fibers reinforced polyester composites
245
Table 4.60: Stress transformation for composites orientation stresses
246
Table 4.61: key point structure for the flexural model
249
Table 4.62: Summary of FEA results of flexural model settings
at selected nodes
256
xxi
Table 4.63: Summary results of strengths optimization for plantain fibers
reinforced polyester matrix composites
257
Table 4.64: NAD Summary Report for untreated plantain fiber
267
Table 4.65: NAD Summary Report for treated plantain fiber
268
xxii
LIST OF FIGURES
Figure 2.1:
Structural constitution of natural fiber cell
23
Figure 2.2:
Chemical reaction sequence of silane treatment
33
Figure 2.3:
Hypothetical Scheme of reaction of coupling agent
with natural fibers
Figure 2.4:
34
Schematic of the acetylation of hydroxyl groups
from fibers
38
Figure 2.5:
Parameter diagram of a product
42
Figure 2.6:
Fiber tensile stress and shear stress variation along the length of
a fiber embedded in a continuous matrix and subjected to a
tensile force in the direction of fiber orientation
69
Figure 2.7:
Effect of fiber length on fiber tensile stress
69
Figure 2.8:
Schematic representations of the changes in fiber
orientation occurring during flow
Figure 2.9:
70
Typical relationships between tensile strength and fiber volume
fraction for fiber reinforced composites.
71
Figure 3.1:
Basic raw materials
77
Figure 3.2:
The plantain plant
78
Figure 3.3:
Traditional usage of plantain fiber
79
Figure 3.4:
Depiction of fiber types
80
Figure 3.5:
Stressed single thin composite lamina
91
Figure 3.6:
Typical schematic diagram for hand lay-up technology
106
Figure 3.7:
Schematic illustration of three-point bending test
108
xxiii
Figure 3.8:
Plantain fiber reinforced composites sample and sample setup
mounted in Hounsfield tensometer for flexural tests
109
Figure 3.9:
Straight-sided tensile specimen.
110
Figure 3.10:
Tensile test set up.
110
Figure 3.11:
Schematics of Charpy tester
112
Figure 3.12:
The Taguchi methodology implementation scheme
115
Figure 3.13:
Subdivision of plate into triangular elements
126
Figure 3.14:
ZEISS Scanning Electron Microscope
140
Figure 3.15:
FT-IR 8400S spectrophotometer by Shimadzu
142
Figure 3.16:
BET Surface Area Analyzer
143
Figure 4.1:
Main effect plots for means-PEFBFRC
151
Figure 4.2: Main effect plots for signal-noise ratio-PEFBFRC
151
Figure 4.3:
Main effect plots for means-PPS
152
Figure 4.4:
Main effect plots for signal-noise ratio-PPS
152
Figure 4.5:
Depiction of standard error of design as a function of control
factors
158
Figure 4.6:
Residual plots normal distribution of data
162
Figure 4.7:
Contour plot depiction of interaction effects of factors
164
Figure 4.8
Depiction of response surface of and interaction effects of
factors
Figure 4.9:
165
Cube plot depiction of EFB composite optimum strength 166
Figure 4.10: Overlay plot depiction of optimal values for PEFB composite 166
xxiv
Figure 4.11:
optimal values for PPS composite
171
Figure 4.12:
Main effect plots for signal-noise ratio-PEFB
175
Figure 4.13:
Main effect plots for means ratio-PEFB
176
Figure 4.14: Percentage contribution of parameters on flexural strength
177
Figure 4.16:
Main effect plots for signal-noise ratio-PPSFRC
178
Figure 4.17:
Main effect plots for means-PPSFRC
179
Figure 4.18:
Residual plots indicating normal distribution of data Results of
plantain empty fruit bunch fiber reinforced composites
Optimization
187
Figure 4.19:
Contour plot depiction of interaction effects of factors
189
Figure 4.20:
Depiction of response surface of and interaction effects of
factors
Figure 4.21:
190
Cube plot depiction of EFB composite optimum strength 191
Figure 4.22: Overlay plot depiction of optimal values for PEFB composite 191
Figures 4.23:
Optimization graphics showing the optimal
factors and function PPS
195
Figure 4.24: Overlay plot depiction of optimal values for PPS composite
196
Figure 4.25:
Main effect plots for signal-noise ratio-PPS
202
Figure 4.26:
Main effect plots for means-PPSFRC
202
Figure 4.27:
Main effect plots for signal-noise ratio-PEFBFRC
203
Figure 4.28:
Main effect plots for means ratio-PEFBFRC
204
Figure 4.29:
Residual plots normal distribution of data
212
xxv
Figure 4.30:
Design Expert8 contour plot depiction of interaction
effects of factors
213
Figure 4.31: 3D plot of response surface of and interaction effects of factors 214
Figure 4.32:
Cube plot depiction of EFB composite optimum strength
214
Figure 4.33: Overlay plot depiction of optimal values for PEFB composite
215
Figure 4.34: Overlay plot depiction of optimal values for PPS composite
220
Figure 4.35:
Variation of impact strength with notch tip radius for different
fiber loading
224
Figure 4.36:
Variation of impact strength with notch depth.
225
Figure 4.37:
Variation of impact strength with impact angle
226
Figure 4.38:
Produced sample of an optimally designed plantain fiber
reinforced composite sample (150×19.05×3.2 mm) and
replicate FEM model
226
Figure 4.39:
Applicable PLANE82 2-D 8-Node Structural Solid
230
Figure 4.40:
Positions of Nodes and Key points for the test specimen 231
Figure 4.41:
The unmeshed tensile model.
232
Figure 4.42:
Meshed Model of the Rectangular Shaped specimen
233
Figure 4.43: Tensile test model with loading and Boundary Conditions
234
Figure 4.44:
Depiction of PPSFC transverse modulus computed with
empirical equations
Figure 4.45:
236
Depiction of PEFBFRC transverse modulus computed with
empirical equations
236
xxvi
Figure 4.46:
Plane strain analysis for PEFBFRC showing stress distribution in xdirection with a maximum stress of 38.781MPa
Figure 4.47:
Plane strain analysis for PEFBFRC resulting to a displacement of
0.264681 mm
Figure 4.48:
239
239
Plane strain analysis for PEFBFRC resulting
to strain of 0.003525
240
Figure 4.49:
Vector plots for PEFBFRC showing degree of freedom
241
Figure 4.50:
Plane strain analysis for PPSFRC showing distribution of applied
stress in x-direction with a maximum stress of 35.283MPa
242
Figure 4.51:
Vector plot for PPSFRC depicting degree of freedom.
243
Figure 4.52:
SOLID45 3-D Structural Solid.
248
Figure 4.53:
Unmeshed FEA model of after extrusion.
250
Figure 4.54:
Meshed Model showing the Rectangular Shaped elements and node
numbers
Figure 4.55:
252
Meshed FEA model with the applied loads and boundary
conditions.
Figure 4.56: A refined mesh obtained with 3000 elements and 4983 nodes
252
253
Figure 4.57: Flexural stress distribution for PEFB fiber reinforced composites in
MPa
253
Figure 4.58: Flexural stress distribution for PPS fiber reinforced composites in
MPa
254
Figure 4.59: x-directional deformation of the EFB flexural specimen in mm 255
xxvii
Figure 4.60: y-directional deformation of the EFB flexural specimen in mm 253
Figure: 4.61: Vector plot depiction of degree of freedom for EFB
256
Figure 4.62:
FTIR spectra of untreated plantain EFB fiber.
261
Figure 4.63:
FTIR spectra of Treated Plantain Empty Fruit Bunch Fibers 262
Figure 4.64:
FTIR spectra of Plantain Stem fiber Reinforced Composites 263
Figure 4.65:
FTIR spectra of Plantain EFB fiber Reinforced Composites
Figure 4.66:
Plot of adsorption and desorption of nitrogen isotherms for
untreated plantain fiber
Figure 4.67:
272
300 and 500 magnifications of SEM depiction of flaws in PPSFRC
of 90, 50, 10 composition
Figure 4.71:
271
X-ray relative abundance versus amount energy released for
PEFBFC of 90, 50, and 10 compositions
Figure 4.70:
268
100 and 500 magnifications of SEM depiction of flaws in PEFBFC
of 90, 50, 10 composition
Figure 4.69:
266
Plot of adsorption and desorption of nitrogen isotherms for treated
plantain fiber
Figure 4.68:
264
273
X-ray relative abundance versus amount energy released for PPSFC
of 90, 50, 10 composition
273
xxviii
LIST OF SYMBOLS
A
=
Area of Element
ad
=
The notch dept (mm)
=
Coefficient of power law model
=
Designations for power law exponents, i = 1,2, …m
Aopt
=
Value of response at optimum setting of factor A
AVR
=
Average value of responses of factor
b
=
Width of the specimen (mm)
α
Bop t
=
Linear Coefficient of Thermal Expansion
=
Angle of fall (Deg.)
=
Angle of rise (Deg.)
=
Value of response at optimum setting of factor B
=
Strain Displacement Matrix
=
Transpose Matrix of
=
Thermal Strain
=
Value of response at optimum setting of factor C
=
Node Displacement Matrix (Degree of Freedom Matrix)
(DOF)R
=
Degree’s of freedom
d
=
Nodal Displacement Vector
Cop t
xxix
=
Modulus Matrix (MPa)
=
Diameter of the ball (mm)
=
Diameter of the indentation (mm)
e
=
Strain vector (elastic strain)
E
=
Elastic Modulus
EV
=
Expected response,
=
Thermal strain
=
Longitudinal Modulus of Composites (MPa)
=
Transverse Modulus of Composites (MPa)
=
Modulus of Composites (MPa)
=
Modulus of Fibre (MPa)
=
Kinetic energy of the pendulum
=
Modulus of Matrix (MPa)
=
Potential energy of the pendulum
εij
F
=
Surface elongation at break
=
The nth element strain
=
Thermal Load Vector
=
the maximum load (N),
=
Nodal Force Vector
xxx
=
True response function
=
Shear Modulus of Composites (MPa)
=
Body Force Per Unit Volume
=
Thickness of the specimen (mm)
=
Element Stiffness
=
Linear elastic stress concentration factor
=
Stiffness
=
Thickness of Element
L
=
Span (mm)
LV
=
Number of factor levels
=
Mass of Resin (g)
=
Mass of composite specimen (g)
h
K
=
Mass of plantain fibers (g)
=
Mass of fibers determined using a digital balance (g)
=
Mass of matrix (g)
MSD
=
Mean standard deviation
Nr
=
the notch radius (mm)
=
Shape Function Matrix
xxxi
σij
=
Stress (MPa)
=
The nth element stress
=
Stress parallel to the fiber axis or longitudinal stress
=
Stress perpendicular or transverse to the fiber axis or the
transverse stress.
Pn
R
=
Variance
=
Flexural stress (MPa)
=
Tensile strength (MPa)
=
x directional normal stress (MPa)
=
y directional normal stress (MPa)
=
z directional normal stress (MPa)
=
Number of factors
=
Density of plantain fibers (Kg/m3)
=
Density of matrix (Kg/m3)
=
Correlation Coefficient
=
Pendulum arm
xxxii
s
=
Coefficient of Determination
=
Stress vector
SNratio
=
Signal-to-noise ratio
=
Shear Yield strength (MPa)
=
Uniaxial ultimate stress in compression (MPa)
=
Uniaxial ultimate stress in tension (MPa)
=
Yield stress of material (MPa)
=
Sample Variation
[ ]
=
The stress transformation matrix
T
=
Temperature Rise
=
Shear stress (MPa)
max
µ
V
Vd
=
Maximum shear stress (MPa)
=
Tensile modulus (MPa)
=
Poisson’s ratio
=
The Poisson’s ratio of matrix material.
=
Element Volume
=
=
Water displaced
Volume of resin (mm3)
xxxiii
=
Volume of Resin (mm3)
=
Volume of composite specimen (mm3)
=
Volume of fibres of a measurable mass determined through
application of Archimedes principle (mm3)
W
Volume fraction of fibers (%)
=
Volume of matrix (mm3)
=
Matrix volume fraction (%)
=
,
The defection (mm)
,…,
=
( , )
y
=
Independent variables
=
Designation for control factor variables
=
Nodal Coordinates of elements
=
=
Response variable
Shear strain
CHAPTER ONE
INTRODUCTION
1.1.
Background of the study
An increased interest in the use of agricultural residues and by-products
from agro-industries in reinforcing polymer matrices has been growing in the
recent years. Natural fibers offer some advantages over woody biomass, since they
are available in large quantities as residual and inexpensive agricultural waste
(Widsten and Kandelbauer, 2008). The plantain pseudo stem and empty fruit bunch
fibers of this study are agricultural by-products that can be utilized as
reinforcement for composite materials.
The use of lignocellulosic fiber reinforced composites for structural and
building materials has been explored and consideration has been given to a wide
variety of fiber sources (Widsten and Kandelbauer, 2008). Plantain is one of the
staples in most West African countries including Nigeria; it is consumed by almost
every tribe. The crop is grown in almost every region. It is estimated that about 70
million people in West and Central Africa derive more than a quarter of their food
energy requirement from plantain (Health Technology Assessment, 1990). Plantain
has an export potential because apart from its huge consumption in Nigeria, it is
also consumed in most parts of Africa. Therefore, as the demand for composites
increases in many applications, more seismic resistant structures have placed high
1
emphasis on exploration of new and advanced materials that not only decrease
dead weight but also absorb the shock and vibration through tailored
microstructures. Unlike conventional materials (e.g., steel), the properties of
composite materials can be designed considering the structural aspects. The design
of a structural component using composites involves both material and structural
considerations. Composite properties (e.g. stiffness, thermal expansion, etc.) can be
varied continuously over a broad range of values under the control of the designer.
Careful selection of reinforcement type and combination therefore enables finished
product characteristics to be tailored to almost any specific engineering
requirement while maintaining optimal strength (Wallenberger and Weston, 2004).
Plantain production in Africa is estimated at more than 50% of worldwide
production (FAO, 1990). Nigeria is one of the largest plantain producing countries
in the world (FAO, 2006). Plantain was then chosen for this study in terms of its
abundance and availability as it is estimated that over 15.07 million ton of plantain
is produced every year in Nigeria (Ahmed, 2004). Furthermore, plantain grows to
its mature size in only 10 months, whereas wood takes a minimum of 10years
(Xiaoya et al., 1998). This study utilized plantain empty fruit bunch fibers and
plantain pseudo stem fibers as reinforcement for polyester matrix; a composite
which can be defined as a physical mixture of two or more different materials, has
properties that are generally better than those of any one of the constituting
materials. It is necessary to use combinations of materials to solve problems
2
because any one material alone cannot do so at an acceptable cost or performance
(Samuel et al., 2012).
In recent years, polymeric based composite materials are being used in many
applications, such as automotive, sporting equipments, marine, electrical,
industrial, construction and household appliances, etc. Polymeric composites have
high strength and stiffness, light weight, and high corrosion resistance (Wang and
Sun, 2002). Furthermore, with the growing global energy crisis and ecological
risks, natural fiber reinforced polymer composites and applications in design of
equipment subjected to different loading conditions have attracted more research
interests due to their potential of serving as alternative for synthetic fibers
composites (Bledzki et al., 2002; Mishra et al., 2004). There has been a growing
interest in utilizing natural fibers as reinforcements in polymer composite for
making low cost construction materials in recent years. Natural fiber are
prospective reinforcing materials and their uses until now have been more
traditional than technical; they have long served many useful purposes but the
utilization of the fibers as reinforcement in polymer matrix took place quite
recently (Joseph et al. 1999).
Studies have also shown that composite materials have advantage over other
conventional materials due to their higher specific properties such as tensile,
impact and flexural strengths, stiffness and fatigue characteristics, which enable
structural design to be more versatile (Sastra et al., 2005). Due to their many
3
advantages they can be manufactured in many forms for use in the aerospace
industry, in a large number of commercial mechanical engineering applications,
such as machine components; internal combustion engines; automobiles; thermal
control and electronic packaging; railway coaches and aircraft structures; drive
shafts, tanks, brakes, pads, pressure vessels and flywheels; process industries
equipment requiring resistance to high-temperature corrosion, oxidation, and wear;
dimensionally stable components; sports and leisure equipment; marine structures;
and biomedical devices (Kutz, 2000).
Mechanical property data and information on the usage of plantain fibers in
reinforcing polymers is scarce in the literature; although, many studies had been
carried out on natural fibers like kenaf, bamboo, jute, hemp, coir, sugar palm and
oil palm (Arib et al. 2006; Khairiah & Khairul, 2006; Lee et al., 2005; Rozman et
al., 2003). The reported advantages of these natural resources include low weight,
low cost, low density, high toughness, acceptable specific strength, enhanced
energy recovery, recyclability and biodegradability (Lee et al. 2005; Myrtha et al.
2008; Sastra et al. 2005).
Natural fiber can be divided into five different types which are leaf, bast,
fruit, grass or cranes and seed (Khairiah & Khairul 2006; Wollerdorfer & Bader
1998) and plantain belongs to leaf family. While failure characteristics of fiber
reinforced composite materials subjected to different loading conditions have been
investigated extensively in past years (Plati and Williams, 1975; Rozman et al.,
4
2003; Ferit et al., 2011), optimal design and characterization of plantain fiber
reinforced composites have remained elusive. This current research interest
therefore focuses on studies of parameters and factors that can improve strength of
composites in particular and specification of safe stresses for plantain fiber
reinforced composite application in general using combined tools of design of
experiment (DOE) and finite element analysis (FEA).
For many simple engineering structures subjected to static or dynamic
loading, computational and analytical models can be employed to provide realistic
approximations of the physical failure processes under investigation. Similarly, in
studies on composite, finite element analysis (FEA) and Design of Experiment
(DOE) have become powerful tools for the numerical solution of a wide range of
engineering problems. Complex problems can be modeled with relative ease with
the advances in computer technology and Computer Aided Design (CAD) systems.
Several computer programmes are available that facilitate the use of finite element
analysis techniques (e.g ANSYS). These programmes that provide streamlined
procedures for prescribing nodal point locations, element types and locations,
boundary constraints, steady and/or time-dependent load distributions, are based on
finite element analysis procedures (Frank and Walter., 1989). Finite element
analysis is therefore based on the method of domain and boundary discretisation
which reduces the infinite number of unknowns defined at element nodes. It has
two primary subdivisions; the first utilizes discrete element to obtain the joint
5
displacements and member forces of a structural framework, while the second uses
the continuum elements to obtain approximate solutions to heat transfer, fluid
mechanics and solid mechanics problems (Portela and Charafi, 2002). On this
premise, this research targets the application of discrete element in modelling
plantain fiber reinforced composite material under different loading conditions.
This research therefore utilizes the complementary roles of both numerical analysis
and design of experiment to optimally design and characterize the plantain fiber
reinforced composites.
1.2
Statement of the problem
The scientific world is facing a serious problem of developing new,
advanced technologies and methods to treat solid wastes, particularly nonnaturally-reversible polymers. The processes to decompose those wastes are
actually not cost-effective and will subsequently produce harmful chemicals.
Consequently, reinforcing polymers with natural fibers is a better alternative. Also,
contemporary challenges in designing for new materials cut across the traditional
lines of engineering and science; methods of modern manufacturing engineering
rely on the mix of competence, knowledge and resources, effective testing and
model building. A developing country like Nigeria has neither the resources nor
the know-how to embark on high-technology steel processes. As a result, there is
need for an alternative that relies on manpower with minimal amount of tooling.
Plantain fiber reinforced composite materials can be considered as alternatives for
6
metal alloys used in low weight bearing product manufacturing and construction
because of the very little initial capital investment involved.
However, different kinds of variations exist everywhere and anytime in
material development processes and reducing these variations is one of the most
important tasks for a design engineer. The complex response of composite
materials coupled with high costs and limited amount of data from mechanical
testing has lead to experimental characterization of composites becomes expensive
and time consuming. Similarly, because accurate analytical models are also limited
to specific cases and require extensive material characterization, it follows that
composite characterization and experimental investigation should be preceded with
an optimal design of experiment. In order to address these issues, Taguchi design
of experiment and Response Surface Method (RSM) were utilized in this research
to optimize the strengths of plantain fiber reinforced composite. The problem of
this study therefore is to develop a new class of composite materials and establish a
design criterion (Model) that will predict the parameters of failure (displacement
and stress) using numerical technique of finite element method (FEM) and design
of experiment (DOE) in a way to design and manufacture a natural fiber based
composite at optimal levels of factor combination to achieve maximum strength.
Nowadays, the application of polymer composites as engineering materials
is fast becoming a state of the art, it follows that the ability of the engineer to
design the characteristics of polymer composites is an important advantage;
7
therefore in order to meet a special target of engineering application, e.g.
concerning one or several measurable material properties, polymer composites
should be designed by selecting the correct quantity of composition (using
Archimedes principle) and choosing the appropriate manufacturing process
(informed by Taguchi orthogonal array), this is because poor combination of
composites formulation variables during manufacturing can cause reduction in
strength of materials, introduce several stress initiation points and shorten the life
time of engineering composite structures; there is also a need to provide realistic
information on the stress distribution within elements of such composite materials
and assessment of failure zones using Finite Element Method, this stress
information is very important in predicting failures using appropriate failure
theories.
1.3
Aim and objectives of the study
The aim of this study is to optimally design and characterize plantain fiber
based polymer composites so as to establish their usefulness as reinforcing
materials in polymer matrix. The objectives of this study therefore include:
 Determination of the quantity of fibers and the subsequent volume fraction
of fibers for plantain fiber reinforced polyester resin;
 Application of robust design in the selection of optimal factors for PFRP;
 Application of Response Surface Methodology (RSM) for the determination
of interaction effects of control variables as related to responses of PFRP
8
 Analysis of displacement and stress distributions of PFRP during flexural
and tensile loading (using Finite Element Method);
 Non destructive testing of plantain fibers using Fourier transform infrared
(FTIR) spectroscopy to establish bond types;
 Investigation of the morphology mechanism of composites to rationalize its
atomic components (using scanning electron microscope);
 Determination of the adsorption and desorption characteristics of plantain
fibers before and after modification using Nitrogen Adsorption/desorption
isotherm (NAD) to ascertain influence of fiber treatment.
1.4
Relevance of the study
Nowadays, ecological concern has resulted in a renewed interest in natural
materials and issues such as recyclability and environmental safety are becoming
increasingly important for the introduction of new materials and products.
Environmental legislation as well as consumer pressure are all increasing the
demand on manufacturers of materials and end-products to consider the
environmental impact of their products at all stages of their life cycle, including
ultimate disposal, via a ‘from cradle to grave’ approach. At this moment ‘ecodesign’ is becoming a philosophy that is applied to more and more materials and
products. In view of all this, an interesting environmentally friendly alternative for
the use of glass fibers as reinforcement in engineering composites are natural fibers
(Morton and Hearle, 1975). These natural fibers including plantain fibers are
9
renewable, nonabrasive and can be incinerated for energy recovery since they
possess a good calorific value unlike glass fiber. Moreover, they give less concern
with safety and health during handling of fiber products. In addition, they exhibit
excellent mechanical properties, especially when their low price and density (1.4
g/cm3) in comparison to E-glass fiber (2.5 g/cm3) is taken into account (Clemons et
al., 1997). Although these fibers are abundantly available, especially in developing
countries such as Nigeria, Bangladesh and India, most applications are still rather
conventional, i.e. ropes, matting, carpet backing and packaging materials. Hence,
also in the economic interests of developing countries, there is an urgent need for
advanced studies to identify new application areas for these natural fibers
(Satyanarayana et al., 1981; Chawla and Bastos, 1979).
More recently, developments shifted to thermoplastic matrix composites
(Kuruvila et al., 1993; Selzer, 1994; Sanadi et al, 1995; Mieck et al., 1995;
Herrera-Franco and Aguilar-Vega, 1997; Clemons et al., 1997). This research
becomes very relevant as it adds to already existing researches on application of
polyester matrix through development of plantain fiber reinforced polyester
composite. In this era when mathematical models are also becoming increasingly
important in design and manufacturing; by developing computational models for
plantain fiber reinforced composites responses in terms of the design variables,
future research in this area can easily leverage on these to predict the success of
their designs, a method that they can find to be accurate and repeatable. In
10
addition, the conventional optimization process may not give an indication of the
interactive effects between any two factors in a multi-variable system; Response
surface methodology (RSM) of this study can avoid the limitations of conventional
methods and is commonly used in many fields. The main purpose of RSM is to
check the optimum operational conditions for a given system or to determine a
region that satisfies the operational specifications (Montgomery, 2001). It might
then be possible to obtain a second-order polynomial prediction equation to
describe the experimental data obtained at some particular combination of input
variables. This research work therefore becomes more useful as the FEM
procedures developed therein can be extended to the analysis of displacement and
stress distribution in irregular shaped continuum whose boundary conditions are
specified.
1.5
Scope and limitation
This study was limited to optimal design and characterization of plantain
fiber reinforced polyester. Meanwhile, finite element analysis and Design of
experiments are the basic optimization tools utilized. In material modeling,
composite material is modeled as an isotropic material. Fundamental experimental
studies yield understanding of physical and mechanical behavior of plantain fiber
reinforced composite that provides the foundation for analytical methods to predict
limit stresses in multiaxial stress states and tools to design and manufacture
optimal composite structures.
11
Thus, to achieve the study objectives, the following scopes have been recognized:
 Manufacturing of plantain fiber reinforced polyester composite for various
mechanical tests using American Society of Testing and Materials (ASTM)
specifications in the mould design and preparing samples for experiment
based on the variable combinations provided in Taguchi design of
experiment.
 Optimization of plantain fiber reinforced composite strengths through
Response Surface Methodology.
 Analysis of the stress distributions in the composite according to the step
and dimension using Finite element method.
 Utilization of relevant Microscopic approaches (SEM, FTIR and NAD) to
characterize the plantain fibers and composites.
1.6
Justification for application of Taguchi Method in Composites design
The quality of any composite material is influenced by various processing
parameters. Among these parameters, there must be one or two that have the most
influence. It has been realized that the full economic and technical potential of any
manufacturing process can be achieved only while the process is run with the
optimum parameters. One of the most important optimization processes is Taguchi
method (Hu, 1998). Taguchi technique is a powerful tool for the design of high
quality material and systems (Taguchi and Konishi, 1987; Taguchi, 1993). It
provides a simple efficient and systematic approach to optimize design for
12
performance, quality and cost. Taguchi parameter design can optimize the
performance characteristics through the setting of design parameters and reduce
the sensitivity of the system performance to source of variation (Roy, 1990; Ross,
1988). The Taguchi approach enables a comprehensive understanding of the
individual and combined effect from a minimum number of simulation trials. This
technique is multi-step process which follows a certain sequence for the
experiments to yield an improved understanding of product or process performance
(Basavarajappa et al., 2007).
Taguchi method is a statistical tool used for the design of experiments
(DOE) which can be effectively utilized to optimize the strengths of plantain fiber
reinforced composites; it involves various steps of planning, conducting and
evaluating results of orthogonal array experiments to determine the optimum levels
of usage parameters under very noisy environment (Feriti et al., 2011). The major
goal is to maintain the variance in the results even in the presence of noise inputs
to make robust process against all variations. It focuses on optimizing quality
characteristics (strengths) most economically for a manufacturing process.
Taguchi’s methodology involves use of specially constructed tables called
“orthogonal array” (OA) (Noordin et al., 2004) which require very few number of
experimental runs. It has been successfully used in the various areas of
manufacturing industries (Feriti et al., 2011). This dissertation will implement
Taguchi's Design of Experiment methodology and technique in respect of plantain
13
fiber reinforced composites design and manufacturing to find the optimal levels of
parameters affecting the mechanical properties of the composite following step by
step procedure applicable for DOE (Dobrzañski and Domagala, 2007).
14
CHAPTER TWO
LITERATURE REVIEW
2.1
Conceptual framework
The recognition of the potential weight savings that can be achieved by
using the advanced composites, which in turn means reduced cost and greater
efficiency was responsible for growth in the technology of fiber reinforcements,
matrices and fabrication of composites (Gaurav and Gaurav, 2012). Composite
materials are emerging chiefly in response to unprecedented demands from
technology due to rapidly advancing activities in aircraft, aerospace and
automotive industries. The most widely used concept of composites has been
stated by Jartiz (1965) as multifunctional material systems that provide
characteristics not obtainable from any discrete material; they are cohesive
structures made by physically combining two or more compatible materials,
different in composition, characteristics and sometimes in form. Kelly (1967)
reported that composites should not be regarded simply as a combination of two
materials; he upheld that the combination has its own distinctive properties. In
terms of strength to resistance, to heat or some other desirable quality, a composite
material is expected to be better than either of the constituting components alone or
radically different from either of them.
Beghezan (1966) suggests that composites are compound materials which
differ from alloys by the fact that the individual components retain their
15
characteristics but are so incorporated into the composite as to take advantage only
of their attributes and not of their short comings, so as to obtain improved
materials. Van-Suchetclan (1972) explains composite materials as heterogeneous
materials consisting of two or more solid phases, which are in intimate contact
with each other on a microscopic scale; they can be also considered as
homogeneous materials on a microscopic scale in the sense that any portion of it
will have the same physical property. According to George (1999), a composite
material is considered to be one that contains two or more distinct constituents with
significantly different macroscopic behavior and a distinct interface between each
constituent, it has characteristics that are not depicted by any of the individual
components in isolation. There are two basic types of fibers applicable in
composites manufacturing, this includes natural fibers and synthetic fibers;
available literature indicates that researchers have studied composites based on
these fibers (Chand and Rohatgi, 1994; Franco and Gonzalez, 2005).
Compared with synthetic fibers, the advantages of using natural fibers in
composites are their low cost, low density, unlimited availability, biodegradability,
renewability and recyclability (Joseph et al., 2002; Espert et al., 2002; Li et al.,
2000; Bedzki and Gassan, 1999). Some studies suggest that natural fibers have the
potential to replace glass fibers in polymer composite materials (Gassan and
Bledzki, 2002). For example, vehicle interior parts such as door trim panels made
from natural fiber-polypropylene (PP) and exterior parts such as engine and
16
transmission covers from natural fiber-polyester resins are already in use
(Panthapulakkal and Sain, 2007).
The facts that composites in general can be custom tailored to suit individual
requirements, have desirable properties in corrosive environment provide higher
strength at a lower weight and have lower life-cycle costs has aided in their
evolution (Abdalla et al., 2008). It provides a good combination in mechanical
property, thermal and insulating protection. Binshan et al., (1995) observed that
these qualities in addition to the ability to monitor the performance of the material
in the field via embedded sensors give composites an edge over conventional
materials. Plantains are plants producing fruits that remain starchy at maturity
(Marriot and Lancaster, 1983; Robinson, 1996) and need processing before
consumption. Generally, all plant-derived cellulose fibers are polar and hydrophilic
in nature, mainly as a consequence of their chemical structure; table 2.1 shows
some properties of some natural fibers available. So far, the utilisation of sisal,
jute, coir and baggase fibers has found many successful applications and plantain
fiber needs to be explored for possible application in reinforcement of polymer.
Thermosets such as polyester is largely non-polar and hydrophobic; therefore the
incompatibility of the polar cellulose fibers and the non-polar matrix leads to poor
adhesion, which then results in a composite material with poor mechanical
properties (Maldas and Kokta, 1994). Nevertheless, these drawbacks can be
overcome by fiber treatment (Hu and Lim, 2005).
17
Plantain production in Africa is estimated at more than 50% of worldwide
production (FAO, 1990). Nigeria is one of the largest plantain producing countries
in the world (FAO, 2006). Plantain fibers can be obtained easily from the plants
which are rendered as waste after the fruits have been harvested; therefore plantain
fibers can be explored as a potential reinforcement for polymer matrices.
Table 2.1 Properties of some natural fibers used for composites
Fiber
Cellulose
Lignin
UTS
Elongation
2
content
content
(MN/m )
Max. (%)
(%)
(%)
Banana
64
5
700-780
3.7
Sisal
70
12
530-630
5.1
Pineapple
85
12
360-749
2.8
Coir
37
42
106-175
47
Talipot
68
28
143-263
5.1
Polymer
40-50
42
180-250
2.8
Source: Panthapulakkal and Sain (2007).
Elastic
Modulus
27-32
17-22
24-35
3-6
10-13
4-6
Many investigations have been made on the potential of the natural fibers as
reinforcements for composites and in several cases the results have shown that the
natural fiber composites own good stiffness but most times the composites do not
reach their optimal strength (Oksman and Selin, 2003); it was then realized that the
full economic and technical potential of any composite manufacturing process can
be achieved only while the formulation process is run with the optimum parameter
combinations. One of the most important optimization processes is design of
experiments (Hu, 1998); the approach enables a comprehensive understanding of
the individual and combined effects of factors from a minimum number of
18
simulation trials. This technique is a multi-step process which follows a certain
sequence for the experiments to yield an improved understanding of composites
performance (Basavarajappa et al., 2007).
2.2
Backgrounds of plantain fiber
Chimekwene et al., (2012) studied the mechanical properties of a new series
of bio-composite involving plantain empty fruit bunch as reinforcing material in an
epoxy based polymer matrix and found an optimal tensile strength of 243N/mm2
from the woven roving treated fiber reinforced composites at a fiber volume
fraction
of
40%.
Fabrication
of plantain
fiber
reinforced
low-density
polyethylene/polycaprolactone composites has been reported recently by Sandeep
and Misra (2007). When the quantity of plantain fibers is increased, tensile and
flexural properties of the Resol matrix resin (Joseph et al. 2002) is also increased.
Addition of plantain fibers to brittle phenol formaldehyde resin makes the matrix
ductile.
The interfacial shear strength indicates a strong adhesion between the
lignocellulosic plantain fibers and the phenol formaldehyde resin (Ali et al. 2003).
In general, the natural fiber that is nowadays disposed off as an unwanted waste
might be seen as a recyclable potential alternative to be used in polymeric matrice
composite material (Satynarayana et al., 1987; Venkataswamy et al., 1987; Calado
et al., 2000). The plantain plant is a multivalent fiber producer; its fibers can be
extracted from any part of the plant including the long leaf sheet, empty fruit bunch
19
and the pseudo-stem (Venkataswamy et al., 1987). Historically, plantain plant
fibers have been used as a cordage crop to produce twine, rope and sackcloth.
Plantains are a member of the banana family; they are starchy, low in sugar
and are cooked before serving as it is unsuitable raw. It is used in many savory
dishes somewhat like potato would be used and is very popular in Western Africa
and the Caribbean countries. It is usually fried or baked; Plantains are native to
India but are grown most widely in tropical climates. Sold in the fresh produce
section of supermarkets and open markets, they usually resemble green bananas
but ripe plantains may be black in color. This vegetable (plantain) can be eaten and
tastes different at every stage of development; the interior color of the fruit will
remain creamy, yellowish or lightly pink. When the peel is green to yellow, the
flavor of the flesh is bland and its texture is starchy. As the peel changes to brown
or black, it has a sweeter flavor and more of a banana aroma, but still keeps a firm
shape when cooked.
The plantain averages about 65% moisture content and the banana averages
about 83% moisture content (Calado et al., 2000). Since hydrolysis, the process by
which starches are converted to sugars, acts fastest in fruit of higher moisture
content it converts starches to sugars faster in bananas than it does in plantains. A
banana is ready to eat when the skin is yellow whereas a plantain is not ready to eat
"out of hand" until hydrolysis has progressed to the point where the skin is almost
black. Plantains have been grown in scattered locations throughout Anambra state
20
in recent time; the State can be considered a marginal area for plantain production;
they are available year round in the local markets and supermarkets.
Many people confuse plantains with bananas, although they look a lot like
green bananas and are close relatives, plantains are very different. They are
starchy, not sweet, and they are used as a vegetable in many recipes, especially in
Latin America and Africa. Plantains are longer than bananas and they have thicker
skins. They also have natural brown spots and rough areas. According to Leslie
(1976), it is cultivated throughout the tropics; Akinyosoye (1991) reported that the
plant is cultivated primarily for its fruits and to a lesser extent for the production of
fibers. It is also believed to be an ornamental plant. The plantain grows up to a
height of about 2-8m with leaves of about 3.5m in length; the stem which is also
called pseudo stem produces a single bunch of plantain before dying and replaced
by new pseudo stem. The fruit grows in hanging cluster on the empty fruit bunch
(EFB), with about ten fruits to a tier and 3-20 tiers to a bunch. The fruit is
protected by its peel which is discarded as waste after the inner fleshy portion is
eaten; plantain pseudo stem fibers and empty fruit bunch fibers were used
comparatively in this study as reinforcement in polyester matrices.
2.3
Structure and Properties of Cellulose Fibers
According to Eichhorn et al., (2001) and ASTM D123-52, Cellulose fibers
can be classified according to their origin and grouped into
21
Leaf: abaca, cantala, curaua, date palm, henequen, pineapple, sisal, banana;
plantain;
Seed: cotton; bast: flax, hemp, jute, and ramie;
Fruit: coir, kapok, oil palm;
Grass: alfa, bagasse, bamboo; and
Stalk: straw (cereal).
The natural fibers like bast and leaf (the hard fibers) types are the most
commonly used in composite applications (Williams and Wool, 2000; Torres and
Diaz, 2004); other plant fibers also used are cotton, jute, hemp, flax, ramie, sisal,
coir, henequen and kapok. The largest producers of sisal in the world are Tanzania
and Brazil. Henequen is produced in Mexico whereas abaca and hemp in
Philippines. Nigeria is one of the largest producers of plantain (FAO, 1990).
Hemicellulose found in these natural fibers is believed to be a compatibilizer
between cellulose and lignin (Kalia et al., 2009). The cell wall in a fiber is not a
homogenous membrane as shown in Figure 2.1 (Rong et al., 2001). Natural fibers
can be considered as composites of hollow cellulose fibrils held together by a
lignin and hemicellulose matrix (Jayaraman, 2003). Each fiber has a complex,
layered structure consisting of a thin primary wall which is the first layer deposited
during cell growth encircling a secondary wall. The secondary wall is made up of
22
three layers and the thick middle layer determines the mechanical properties of the
fiber. The middle layer consists of a series of helically wound cellular micro fibrils
formed from long chain cellulose molecules, the angle between the fiber axis and
the micro fibrils is called the micro fibrillar angle and the characteristic value of
microfibrillar angle varies from one fiber to another (Jayaraman, 2003).
Figure 2.1: Structural constitution of natural fiber cell (Rong et al., 2001)
The amorphous matrix phase in a cell wall is very complex and consists of
hemicellulose, lignin, and in some cases pectin. The hemicellulose molecules are
hydrogen bonded to cellulose and act as cementing matrix between the cellulose
23
microfibrils, forming the cellulose–hemicellulose network, which is thought to be
the main structural component of the fiber cell (Kalia et al., 2009).
The reinforcing efficiency of natural fiber is related to the nature of cellulose
and its crystallinity. The main components of natural fibers are cellulose (acellulose), hemicellulose, lignin, pectins, and waxes (Nevell and Zeronian, 1985).
2.4
Extraction and retting of Cellulose Fibers
A process called retting is employed to extract fiber from plants. This
process involves the action of bacteria and moisture on plants to dissolve and rot
away cellular tissues, gummy substances, cellular tissues and pectin surrounding
the fiber bundles in the plant. Once the surrounding tissue and other substances are
dissolved and they fall away, the fiber can then be easily separated from the stem.
Previous researches have focused on finding alternative methods for retting natural
fibres. Attempts was made to develop both enzymatic (Akin et al., 2000; Akin et
al., 1999; Belberger et al., 1999; Henriksson et al., 1997; Henriksson et al., 1998;
Ramaswamy et al., 1994) and chemical/physical (Belberger et al., 1999; Das, Sen
and Sen, 1976; Henriksson et al., 1998; Kundu et al., 1996; Morrison et al., 1996;
Ramaswamy et al., 1993; Ramaswamy et al., 1994) methods, and combined
chemical and enzymatic retting (Belberger et al., 1999; Ramaswamy et al., 1994)
has also been suggested (Henriksson et al., 1998). Chemical/physical retting
consist of treatments such as boiling in Sodium Hydroxide (Morrison et al., 1996),
boiling in sodium hydroxide in the presence of sodium sulphite (Kundu et al.,
24
1996; Ramaswamy et al., 1993) boiling in sodium hydroxide in the presence of
Sodium Bisulphite (Ramaswamy et al., 1994) boiling in Sodium hydroxide in the
presence of sodium chloride, EDTA and Sodium Sulphite (Kundu et al., 1996),
boiling in Sodium hydroxide in the presence of EDTA (Kundu et al., 1996),
boiling in Sodium hydroxide after soaking in Hydrochloric (Das, Sen and Sen,
1976) and boiling in Oxalic Acid at high pH (Henriksson et al., 1998) and steam
explosion (Nebel, 1995). In this study, water retting was chosen over enzymatic
and Chemical/physical retting because it is relatively cheap and produces high
quality fibers, water retting is done either with the help of water or with the help of
dew.
Dew retting: Dew retting process is used in areas where water resources are
scarce; for this process to be effective, the night-time dew should be quite heavy
and the daytime temperature should be warm. In the dew retting process, the
harvested plant stalks are spread out evenly on grassy surfaces. Here the sun, air,
dew and the natural decaying process involving bacteria produce fermentation and
as a result the cellular fleshy matter surrounding the fiber in the stalks falls away.
Depending upon the existing climatic conditions, this process could take two to
three weeks. Dew retted fiber can easily be distinguished from water retted fiber
due to its darker color. As compared to water retted fiber, dew retted fiber is poorer
in quality.
25
Double water retting: The preferred method of retting is double water
retting as it yields superior quality fiber. In this method, bundles of the plant stalks
are submerged in water. The time duration for the plants to remain submerged in
water should be carefully monitored. If the submerging time allowed is not
enough, the separation process becomes very difficult and so the yield is affected.
On the other hand, if the submerging time allowed is too much, the quality is
affected and the extracted fiber is weak.
Trial and error methods have resulted in a process known as double retting.
In this process, plant stalks are retted in water for a lesser time than optimum,
taken out and dried for a long time and then they are retted again. The fiber
extracted after this process is generally of a very superior quality.
Stagnant water retting: Another method employed is natural water retting,
stagnant or slow moving water like ponds and bogs are used for this. The stalk
bundles are dropped into the water and are weighted down with stones or logs. The
submerging time is decided depending upon the temperature of the water and the
mineral content of the water. The submerging time allowed varies between 10 days
to two weeks.
Tank water retting: Tank retting is yet another method used for retting
fiber yielding plant stalks. Control can be exercised over water conditions and thus
the quality of fiber obtained is better and more consistent. Tanks constructed for
the purpose are used for submerging plant stalks. Water is changed after the initial
26
eight hours of submerging. This aids the retting process, as a lot of waste and
toxins are removed along with this water. The waste water that is removed is
treated and then used as liquid fertilizer as it is rich in chemicals.
2.5
Mechanisms of Surface Modifications of Cellulose Fibers
According to Kalia et al., (2009), the shortcomings associated with natural
fibers have to be overcome before using them in polymer composites. The most
serious problem with natural fibers is its hydrophilic nature, which causes the fiber
to swell and ultimately rotting takes place through attack by fungi. Natural fibers
are hydrophilic as they are derived from lignocellulose, which contains strongly
polarized hydroxyl groups. These fibers, therefore, are inherently incompatible
with hydrophobic thermoplastics, such as polyester. The major limitations of using
these fibers as reinforcements in such matrices include poor interfacial adhesion
between polar-hydrophilic fiber and nonpolar-hydrophobic matrix. Moreover,
difficulty in mixing because of poor wetting of the fiber with the matrix is another
problem that leads to composites with weak interface (John and Anandjiwala,
2008).
In order to develop composites with better mechanical properties and
environmental performance, it becomes necessary to increase the hydrophobicity
of the cellulose fibers and to improve the interface between matrix and fibers. Lack
of good interfacial adhesion, low melting point and poor resistance towards
27
moisture make the use of plant cellulose fiber in reinforcing composites less
attractive; however, pretreatments of these cellulose fibers can clean the fiber
surface, chemically modify the surface, stop the moisture absorption process, and
increase the surface roughness (Kalia et al., 2008; Kalia et al., 2009).
An in-depth account of modification of cellulosic fibers has been reported by
Belgacem and Gandini (1995), surface modifications include (i) physical
treatments, such as solvent extraction; (ii) physico-chemical treatments, like the
use of corona and plasma discharges (Morales et al., 2006) or laser, g-ray, and UV
bombardment; and (iii) chemical modifications, both by direct condensation of the
coupling agents onto the cellulose surface and by its grafting by free-radical or
ionic polymerizations. The common coupling agents used are silanes, isocyanates
and titanate-based compounds (George et al., 1998; Joly et al., 1996). Several
research activities have been conducted to improve fiber adhesion properties with
the matrix through chemical treatments. The following are reviews of different
chemical treatments relevant to this study and their effects on composite
properties.
Alkali Treatment (Mercerization): Alkali treatment leads to the increase in
the amount of amorphous cellulose at the expense of crystalline cellulose.
According to Kabir (2012), natural fibers absorb moisture due to the presence of
hydroxyl groups in the amorphous region of cellulose, hemicellulose and lignin
28
constituents. The following reaction takes place as a result of alkali treatment (Li et
al., 2007; Mwaikambo and Ansell, 2002; Sreenivasan et al., 1996).
iber − OH + NaOH → iber − O Na + H O
(2.1)
During alkali treatment, alkalised groups (NaO-H) react with these hydroxyl
groups (-OH) of the fiber and produce water molecules (H-OH) which are
consequently removed from the fiber structure. Then the remaining alkalised
groups (Na-O-) react with the fiber cell wall and produce Fiber-cell-O-Na groups
(John & Anandjiwala, 2008).
The important modification occurring here is the removal of hydrogen
bonding in the network structure; this involves the treatment of fibers with 5 - 25%
solutions of Sodium hydroxide for some hours (Remzi, 2010). The fibers are rinsed
a number of times after it has been subjected to sodium hydroxide in a continuous
process; good results are obtained through proper saturation and complete washing
(Marjory, 1966; Corbman, 1983).
Wang et al. (2003) reported that mercerization being an alkali treatment
process follows a standard definition as proposed in ASTM D1965, it is the
process of subjecting a cellulose fiber to an interaction with a fairly concentrated
aqueous solution of strong base, to produce great swelling with resultant changes
29
in the fiber structure, dimension, morphology and mechanical properties (Bledzki
and Gassan, 1999).
These chemical activities reduce the moisture related hydroxyl groups
(hydrophilic) and thus improve the fibers hydrophobicity. Treatment also takes out
a certain portion of hemicellulose, lignin, pectin, wax and oil coverings (weak
boundary layer) from the cellulose surface (Mwaikambo et al., 2007; Ray et al.
2001). As a result, cellulose microfibrils are exposed to the fiber surface;
consequently, treatment changes the orientation of the highly packed crystalline
cellulose order, forming an amorphous region (Kabir, 2012). This amorphous
region of cellulose can easily mix with matrix materials and form strong interface
bonding which results in greater load transfer capacity of the composites. Alkaline
treatment also separates the elementary fibers from their fiber bundles by removing
the covering materials, thus increasing the effective surface area of fibers for
matrix adhesion and improving the fiber dispersion within the composite. Treated
fiber surfaces become rougher which can further improve fiber-matrix adhesion by
providing additional fiber sites for mechanical interlocking (Joseph, et al. 2003).
Mechanical and thermal behaviours of the composite are improved significantly by
this treatment. However, too high of alkali concentration can cause an excess
removal of covering materials from the cellulose surface, which results in
weakening or damage to the fiber structure (Lee, 2009; Wang, et al. 2003).
30
As reported in most literature, natural fiber chemical constituent consists of
cellulose and other non cellulose constituent like hemicellulose, lignin, pectin and
impurities such as wax, ash and natural oil (Khalil et al., 2006; Abdul et al., 2010).
This non cellulose material could be removed by appropriate alkali treatments,
which affect the tensile characteristic of the fiber (Sreenivasan et al., 1996; Gassan
and Bledzki, 1999). Mercerization was found to change fiber surface
morphologies, and the fiber diameter was reported to be decreased with increased
concentration of sodium hydroxide (Mwaikambo and Ansell, 2006). Mercerization
treatment also results in surface modifications leading to increased wettability of
coir fiber polyester resin as reported by Prasad et al (1983). It is reported that
alkaline treatment has two effects on the henequen fiber: (1) it increases surface
roughness, resulting in better mechanical interlocking; and (2) it increases the
amount of cellulose exposed on the fiber surface, thus increasing the number of
possible reaction sites (Valadez-Gonzalez et al., 1999). Consequently, alkaline
treatment has a lasting effect on the mechanical behavior of natural fibers
especially on their strength and stiffness.
Silane Treatment: Alkali treatment followed by silane treatment, Silane is
an inorganic compound with chemical formula SiH4. It is a colourless, flammable
gas with a sharp, repulsive smell, somewhat similar to that of acetic acid. Silane is
of practical interest as a precursor to elemental silicon. It may also refer to many
compounds
containing
silicon,
such
as
trichlorosilane
(SiHCl3)
and
31
tetramethylsilane (Si(CH3)4) (Kreiger, Shonnard and Pearce, 2013); silane
treatment of natural fibres is among the simplest and cheapest methods used to
improve composite interfaces. While surface treatments remain necessary to
improve natural fibres/plastics bonds, the majority of these treatments use
expensive equipment, complex treatment methods and expensive chemicals
(Zafeiropoulos, et al., 2002). Some silane coupling agents are expensive in their
concentrated form, but they are cost effective because they can be diluted with
large volumes of water before treatments (Dijon, 2002; Pickering et al., 2003;
Thamae and Baillie, 2007).
Organosilanes are the main groups of coupling agents for cellulose fiber
reinforced polymers. In fact, they are employed successfully to mineral fillers and
fibers such as glass (Wambua, 2003), silica (Sae-Oui, 2003), alumina, mica and
talc (Denac, 1999). According to Zafeiropoulos, et al., (2002), most of the silane
coupling agents can be represented by the following formula:
R-(CH2)n – Si(OR)3
(2.2)
where n=0-3 OR is the hydrolysable alkoxy group such as amine, mercapto, vinyl
group, and R the functional organic group such as methyl, ethyl or isopropyl group
attached to silicon by an alkyd bridge (Zafeiropoulos, et al., 2002).
The general mechanism of how alkoxysilanes form bonds with the fiber
surface which contains hydroxyl groups is shown in figure 2.2. Silane-coupling
32
agents that are widely used on fibers to form stable covalent bonds to both the
mineral surface and the resin; they are potentially suitable for use on cellulosic
fibers (Pothan et al., 2000). This involves a tightening up of the polymer structure
through increased crosslinking and increase in rigidity (Heinze et al., 1996).
Silane-coupling agents usually improve the degree of cross-linking in the interface
region and offer a perfect bonding. Agrewal et al., (2000) reported that among the
various coupling agents, silane-coupling agents were found to be effective in
modifying the natural fiber-matrix interface. Efficiency of silane treatment was
high for the alkaline pre-treated fibers than for the untreated fiber because more
reactive site can be generated for silane reaction.
Figure 2.2: Chemical reaction sequence of silane treatment (Karnani, 1997)
33
Also Sreekala, et al., (2000) reported that during the condensation process,
one end of silanol reacts with the cellulose hydroxyl group (Si-O-Cellulose) and
the other end reacts (bond formation) with the matrix (Si-Matrix) functional group
as shown in figure 2.3.
Figure 2.3. Hypothetical scheme of reaction of coupling agent with natural
fibers (Sreekala, et al., 2000).
This co-reactivity provides molecular continuity across the interface of the
composite; it also provides the hydrocarbon chain that restrains the fiber swelling
into the matrix (George et al., 1998; Wang, et al. 2003). As a result, fiber matrix
adhesion improves and stabilizes the composite properties (Li et al., 2007); natural
fibers exhibit surface micro-pores and silane couplings act as surface coatings to
penetrate the pores. In this case, silane coating is used as a mechanical interlocking
material for the fiber surface.
34
During the silane treatment, hydroxyl groups on the fiber surface are
covered by silane molecules. Due to this, hydroxyl groups that are present in
hemicellulose and lignin constituents cannot absorb the atmospheric moisture; as a
result, moisture absorption capacity of the treated fibers is reduced.
The
mechanism of adhesion of the silane on to the fiber has been represented by Pothan
et al., (1997) as follows:
=
=
(
−
−
(
) + 3
) +
→
−
=
→
−
=
−
(
(
) + 3
(2.3)
) −
(2.4)
Pothan et al., (1997) also observed that in the presence of moisture, the
silanol reacts with -OH groups attached to the glucose units of the cellulose
molecule in the cell wall thereby bonding itself to the cell wall by further rejection
of water.
Ethanol/water mixtures were most frequently employed reaction medium for
silane reactions (Pickering et al., 2003); Fernanda et al (1999) employed methanol
without water as the reaction medium for 3 different silanes but they could not
obtain significant improvements in mechanical properties for polypropylene-wood
fiber composites. 1% solution of three aminopropyl trimethoxy silane in a solution
of acetone and water (50/50 by volume) for 2h was reportedly used to modify the
flax surface by Van De Weyenberg (2003).
35
Rong et al. (2001) soaked sisal fiber in a solution of 2% aminosilane in 95%
alcohol for 5min at a pH value of 4.5–5.5 followed by 30min air drying for
hydrolyzing the coupling agent. Silane solution in water and ethanol mixture with
concentration of 0.033% and 1% was also carried out by Valadez-Gonzalez et al.
(1999) and Agrawal et al. (2000) respectively to treat henequen and oil-palm
fibers, they modified the short henequén fibers with a silane coupling agent in
order to find out its deposition mechanism on the fiber surface and the influence of
this chemical treatment on the mechanical properties of the composite. It was
shown that the partial removal of lignin and other alkali soluble compounds from
the fiber surface increases the adsorption of the silane coupling-agent whereas the
formation of polysiloxanes inhibits this process.
Seki (2009) investigated the effect of alkali (5% NaOH for 2 hours) and
silane (1% oligomeric siloxane with 96% alcohol solution for an hour) treatments
on flexural properties of jute-epoxy and jute-polyester composites. For jute-epoxy
composites, silane over alkali treatments showed about 12% and 7% higher
strength and modulus properties compared to the alkali treatment alone; similar
treatments reported around 20% and 8% improvements for jute-polyester
composites (Seki, 2009). Sever et al. (2010) applied different concentrations
(0.1%, 0.3% and 0.5%) of silane (γ-Methacryloxy-propyl-trimethoxy-silane)
treatments on jute fabrics polyester composites. Tensile, flexural and interlaminar
shear properties were investigated and compared with the untreated samples. The
36
results for the 0.3% silane treated sample showed around 40%, 30% and 55%
improvements in tensile, flexural and interlaminar shear strength respectively.
Silane treated fiber composites provided better tensile strengths than the alkali
(only) treated fiber composites (Valadez-Gonzalez et al., 1999).
Van De Weyenberg (2003) observed that these chemicals are hydrophilic
compounds with different groups appended to silicon such that one end will
interact with matrix and the other end can react with hydrophilic fiber, which act as
a bridge between them.
Acetylation of Natural Fibers: To introduce plasticization to cellulosic
fibers, acetylation of natural fibers is a well-known esterification method-A
chemical reaction resulting in the formation of at least one ester product (Rowell,
1991). Acetylation is originally applied to cellulose to stabilize the cell walls
against moisture, environmental degradation and improve dimensional stability
(Andersson and Tillman, 1989; Hill et al., 1998; Murray, 1998; Ebrahimzadeh,
1997;
Flemming
et
al.,
1995).
Pretreatment
of
fibers
with
acetic
anhydride substitutes the polymer hydroxyl groups of the cell wall with acetyl
groups, modifying the properties of these fibers so that they become hydrophobic
(Hill et al., 1998). Fiber hydroxyl groups that react with the reagent are those of
lignin and hemicelluloses (amorphous material), whereas the hydroxyl groups of
cellulose (crystalline material) which are being closely packed with hydrogen
37
bonds, prevent the diffusion of reagent and thus results in very low extents of
reaction (Rowell, 1998).
During the treatment process, Bledzki, et al. (2008) reported that the acetyl
group (CH3CO-) reacts with the hydroxyl groups (-OH) that are present in the
amorphous region of the fiber and remove the existing moisture, thus reducing the
hydrophilic nature of the fiber. The hydroxyl groups that react are those of the
minor constituents of the fiber, i.e. lignin and hemicelluloses, and those of
amorphous cellulose (Sjorstrom, 1981). Typical acetylation reaction as reported by
Fifield et al., (2005) is shown in figure 2.4.
Figure 2.4: Schematic of the acetylation of hydroxyl groups from fibers
(Fifield et al., 2005).
In general, treatment provides rough fiber surface topography that gives
better mechanical interlocking with the matrix (Lee et al., 2009; Kabir, 2012).
Treatment also improves the fiber dispersion in to the matrix and thus enhances
dimensional stability of the composite. Fibers can be acetylated with and without
an acid catalyst to graft the acetyl groups onto the cellulose surface, however,
38
acetic acid does not react sufficiently with the fibers; as a result, it is necessary to
use a catalyst to speed up the acetylation process. Acetic anhydrides, pyridine,
sulphuric acid, potassium and sodium acetate etc. are commonly used catalysts for
the acetylation process. The reagent then reacts with hemicellulose and lignin
constituents and removes them from the fiber, resulting in the opening of cellulose
surface to allow reaction with the matrix molecules.
It has been demonstrated that acetylation could reduce the water uptake of
acetylated-kenaf-UPE composites by about 50% (Bledzki and Gassan, 1999).
However, the acetylation did not result in significant increase in the strengths of
the composites (Bledzki and Gassan, 1999). The hydroxyl groups in the crystalline
regions of the fiber are closely packed with strong inter chain bonding, and are
inaccessible to chemical reagents. The acetylation of the -OH group in cellulose is
represented by Mwaikambo and Ansell (2002) as shown below:
(2.5)
Acetylation has been shown to be beneficial in reducing moisture absorption
of natural fibers. Reduction of about 50% of moisture uptake for acetylated jute
fibers and of up to 65% for acetylated pine fibers has been reported in the literature
(Bledzki and Gassan, 1999). Acetylation has also been found to enhance the
interface in flax/polypropylene composites (Zafeiropoulos et al., 2002).
39
Mwaikambo and Ansell (2002) used acetic acid and acetic anhydride to treat
hemp, flax, jute and kapok fibers. Rowell et al., (2000) investigated acetic
anhydride treatment on different types of natural fibers to analyze the effects of
equilibrium moisture content. They reported improved moisture resistance
properties of the treated fibers. This was due to the removal of hemicellulose and
lignin constituents from the treated fiber. Mishra, et al. (2003) used an acetic
anhydride treatment (with glacial acetic acid and sulphuric acid) on an alkali pretreated (5% and 10% NaOH solution for an hour at 30°C) sisal fiber and reported
improved fiber matrix adhesion of the final composites. Bledzki, et al. (2008)
studied different concentrations of acetyl treatment on flax fiber and reported 50%
higher thermal properties. Moreover, 18% acetylated flax fiber polypropylene
composites showed 25% higher tensile and flexural properties as compared to the
untreated fiber composites.
2.6
Theories and Application of Taguchi design of experiments in
composites parameter Design
The Taguchi technique is a powerful tool for the design of high quality
systems (Amar and Mahapatra, 2009; Basavarajappa and Chandramohan, 2005;
Chauhan et al., 2009; Ross, 1993; Roy, 1990). The Taguchi approach to
experimentation provides an orderly way to collect, analyze, and interpret data to
satisfy the objectives of the study. In the design of experiments, one can obtain the
maximum amount of information for a specific amount of experimentation.
40
Taguchi parameter design can optimize the performance characteristics through the
setting of design parameters and reduce the sensitivity of the system performance
to the source of variation (Roy, 1990; Basavarajappa et al., 2007).
Taguchi’s methods focus on the effective application of engineering
strategies rather than advanced statistical techniques (Singh et al., 2002; Mavruz
and Ogulata, 2010). Taguchi views the design of a product or process as a threephase program:
1. System design: This phase deals with the conceptual level, involving creativity
and innovative research. Here, one looks for what each factor and its level should
be rather than how to combine many factors to obtain the best result in the selected
domain (Park and Ha, 2005).
2. Parameter design: At this level, once the concept is established, the nominal
values of the various dimensions and design parameters need to be set. The
purpose of parameter design is to investigate the overall variation caused by noise
when the levels of the control factors are allowed to vary widely; quality
improvement can be achievable without incurring much additional cost, this
strategy is obviously well suited to the production floor (Park and Ha, 2005;
Taguchi et al., 2005).
P-Diagram of figure 2.5 is a must for every development project; it is a way
of succinctly defining the development scope. In this context, a process to be
optimized has several control factors which directly decide the target value of the
41
output, the optimization then involves determining the best control factor values so
that the output is at the target value. First the designer identifies the signal (input)
and response (output) associated with the design concept.
Next is to consider the parameters/factors that are beyond the control of the
designer which are called noise factors, the noise is shown to be present in the
process but should have no effects on the output. Outside temperature,
opening/closing of windows and number of occupants are examples of noise
factors. Parameters that can be specified by the designer are called control factors.
The factors like volume fraction, aspect ratio etc are examples of control factors in
composites design.
NOISE (x)
PROCESS
OR
PRODUCT
OUT PUT (y)
CONTROL FACTORS (z)
Figure 2.5 Parameter diagram of a product (Taguchi et al., 2005).
The job of the designer is to select appropriate control factors and their
settings so that the deviation from the ideal optimum strength is at a minimum
level. Such a design is called a minimum sensitivity design or a robust design. It
can be achieved by exploiting nonlinearity of the products/material. The Robust
42
Design method prescribes a systematic procedure for minimizing design sensitivity
and it is called Parameter Design.
An overwhelming majority of product failures and the resulting field costs
and design iterations come from ignoring noise factors during the early design
stages. The noise factors crop up one by one as surprises in the subsequent product
delivery stages causing costly failures and band-aids. These problems are avoided
in the Robust Design method by subjecting the design ideas to noise factors
through parameter design. The result of using parameter design followed by
tolerance design is successful products at low cost.
3. Tolerance design: This phase must be preceded by parameter design activities;
with a successfully completed parameter design and an understanding of the effect
that the various parameters have on performance, efforts can be focused on
reducing and controlling variation in the critical few dimensions; this is used to
determine the best tolerances for the parameters (Park and Ha, 2005; Zeydan,
2008). Taguchi methodology for optimization can be divided into four phases:
planning, conducting, analysis and validation. Each phase has a separate objective
and contributes towards the overall optimization process (Khosla et al., 2006; Roy,
2001).
Design of Experiment (DOE) therefore is a body of statistical techniques for
the effective and efficient collection of data for a number of purposes. Of all the
available design of experiment tool, Taguchi method and Response Surface
43
Methodology became popular in manufacturing due to their ease of nature.
Moreover the result predicted using Taguchi is well compared with other methods;
Taguchi method divides all problems into two categories - STATIC or
DYNAMIC. In Static problems, the optimization is achieved by using three Signalto-Noise ratios (smaller-the-better, larger-the-better and nominal-the-best). In
Dynamic problems, the optimization is achieved by using two Signal-to-Noise
ratios (Slope and Linearity). Taguchi’s orthogonal arrays provide an alternative to
standard factorial designs; factors and interactions are assigned to the array
columns via linear graphs. Kilickap (2010) investigated the effect of cutting
parameter in drilling of glass fiber reinforced composite using Taguchi method;
optimum drilling parameter was then predicted using signal-noise ratio.
Amar et al. (2006) studied the erosion behavior of glass fiber composite
using Taguchi method. The study indicated that erodent size, fiber loading,
impingement angle and impact velocity are the significant factors in a declining
sequence affecting the wear rate. Furthermore, studies revealed that Taguchi
method provides a simple, systematic and efficient methodology for the
optimization of the control factors. Tsao and Hocheng (2004) used Taguchi tool to
determine the delamination associated with various types of drill; comparison of
experimental and analytical shows the analytical method has the error of 8%.
Mohana et al. (2007) carried out the delamination analysis of glass fiber
reinforced composite with reference to specimen thickness, cutting speed and feed.
44
Signal-noise ratio was calculated using Mean Square Deviation. The optimal
parameters for peel up delamination are the feed rate (50 mm/min-Level1), the
cutting speed (1200 rpm-Level 3), drill tool diameter (6 mm-Level 2) and the
material thickness at (12 mm-Level 4). Similarly, the optimum parameters for push
down delamination are the feed rate (50 mm/min - level 1), the cutting speed
(600rpm - level 1), drill tool diameter (10 mm - level3), and the material thickness
(10 mm - level 3). Alok and Amar (2010) analyzed the wear behavior of red mud
polymer composite; in this study, the Taguchi’s experimental design method was
used to identify and select optimal design control factors.
2.7
Theory and Principles of Response Surface Methodology (RSM)
Design of Experiments (DOE) is useful for characterizing complex systems
and processes; statistical statements can be established about the system; a related
branch of DOE – Response Surface Methodology (RSM) – characterizes the
system performance, allowing for optimization activities to be made (Box et al.,
1987; Myers et al., 1995). The consideration of fiber reinforced composites as an
alternative engineering material has attracted considerable attention from many
researchers, the mechanical strengths of composites has been found to depend on
various parameters; successful operating performance of fiber reinforced
composites therefore depends on the selection of suitable design variables and
conditions (Anklin et al., 2006). Thus it is important to determine the operating
design parameters at which the response (strength) reaches its optimum. The
45
optimum could be either a maximum or a minimum of a function of the design
parameters. One of the methodologies for obtaining the optimum results is
response surface methodology (RSM). Performance optimization requires many
tests but the total number of experiments required can be reduced depending on the
experimental design technique. It is essential that an experimental design
methodology is very economical for extracting the maximum amount of complex
information while saving significant experimental time, material used for analyses
and personnel costs (Montgomery, 2009).
The classical method for the optimization of medium and cultural conditions
involves one variable at a time, while keeping the other parameters at fixed levels.
This method is generally time consuming and requires a considerable number of
experiments to be carried out and does not include interactive effects among the
variables (Dey et al., 2001). Response surface methodology (RSM) is the most
widely used statistical technique for bioprocess optimization (Francis et al., 2003;
Liu et al., 2003). It can be used to evaluate the relationship between a set of
controllable experimental factors and observed results. The interaction among the
possible influencing parameters can be evaluated with limited number of
experiments (Francis et al., 2003). It has been successfully employed for
optimization in many bioprocesses (Dey et al., 2001; Francis et al., 2003; Liu et al.,
2003).
46
This methodology is actually a combination of statistical and mathematical
techniques and it was primarily proposed by Box and Wilson (1951) to optimize
operating conditions in the chemical industry. RSM has been further developed
and improved during the past decades with applications in many scientific realms.
Myers et al., (1989) and Myers (1999) present reviews of RSM in its basic
development period and a comparison of different response surface meta models
with different applications is given by Rutherford et al (2006). A comprehensive
description of RSM theory can be found in (Myers and Montgomery, 2002;
Montgomery, 2009). Apart from chemistry and other realms of industry, RSM has
also been introduced into the reliability analysis and model validation of
mechanical and civil structures (Lee and Kwak, 2006; Gavin and Yau, 2008). This
methodology has been widely employed in many applications such as design
optimization, response prediction and model validation. But so far the literature
related to its application in design and manufacturing of plantain fiber reinforced
composites is scarce.
Response surface methodology (RSM) is widely used for multivariable
optimization studies in several chemical and biotechnological processes such as
optimization of media, process conditions, catalyzed reaction conditions,
oxidation, production, fermentation, etc., (Chang et al, 2006; Wang and Lu, 2005;
Su et al, 2004; Kristo et al, 2003; Lai et al, 2003; Beg et al, 2002). The objective of
47
this work therefore was to find out the optimum process parameters for improved
plantain fiber reinforced composites strengths using response surface methodology.
The most extensive applications of RSM are in the particular situations
where several input variables potentially influence some performance measure or
quality characteristic of the process. Thus performance measure or quality
characteristic is called the response. The input variables are sometimes called
independent variables, and they are subject to the control of the design engineer.
This dissertation will concentrate on statistical modeling to develop an appropriate
approximating model between the response y and independent variables
,
,…,
If all variables are assumed to be measurable, the response surface
can be expressed in a general relationship as
=
(
,
,...,
)+
;
where the form of the true response function
(2.1)
is unknown and perhaps very
complicated, and ε is a term that represents other sources of variability not
accounted for in
. Usually ε includes effects such as measurement error on the
response, background noise, the effect of other variables and so on. Usually ε is
treated as a statistical error, often assuming it to have a normal distribution with
mean zero and variance
. Then
48
( )=
=
[
(
,
,
The variables
,...,
,...,
)] +
( )=
(
,...,
);
(2.2)
in equation 2.2 are usually called the natural
variables, because they are expressed in the natural units of measurement, such as
%, mm, Degree, etc. The goal is to optimize the response variable y. An important
assumption is that the independent variables are continuous and controllable by
experiments with negligible errors. The task then is to find a suitable
approximation for the true functional relationship between independent variables
and the response surface (Taguchi, 1987). For the case of two independent
variables, the first order model is
=
+
+
;
(2.3)
The form of the first-order model is sometimes called a main effects model,
because it includes only the main effects of the two variables x1 and x2. If there is
an interaction between these variables, it can be added to the model easily as
follows:
=
+
+
+
;
(2.4)
This is the first-order model with interaction. Adding the interaction term
introduces curvature into the response function. Often the curvature in the true
response surface is strong enough that the first-order model (even with the
49
interaction term included) is inadequate. A second-order model will likely be
required in these situations. For the case of two variables, the second-order model
is
=
+
+
+
+
+
;
(2.5)
This model would likely be useful as an approximation to the true response
surface in a relatively small region. The second-order model is widely used in
response surface methodology for several reasons:
1. The second-order model is very flexible. It can take on a wide variety of
functional forms, so it will often work well as an approximation to the true
response surface.
2. It is easy to estimate the parameters (the β’s) in the second-order model. The
method of least squares can be used for this purpose.
3. There is considerable practical experience indicating that second-order models
work well in solving real response surface problems.
In general, the first-order model is
=
+
+
+. . . +
(2.6)
And the general second-order model is
=
+
+
+
(2.7)
50
In some infrequent situations, approximating polynomials of order greater
than two are used. In some cases, the first four terms of the above equation can
satisfactorily predict the response, i.e. quadratic terms are not necessary. In most
cases, the second-order model is adequate for well-behaved responses. This
empirical model is called a ‘response surface model’.
As mentioned above, the first requirement for RSM involves the design of
experiments to achieve adequate and reliable measurement of the response of
interest. To meet this requirement, an appropriate experimental design technique
has to be employed. The experimental design techniques commonly used for
process analysis and modeling are the full factorial, partial factorial and central
composite designs (CCD). A full factorial design requires at least three levels per
variable to estimate the coefficients of the quadratic terms in the response model
(Box and Wilson, 1951). A partial factorial design requires fewer experiments than
the full factorial design. However, the former is particularly useful if certain
variables are already known to show no interaction (Box and Hunter, 1961). An
effective alternative to factorial design is CCD, originally developed by Box and
Wilson (1951) and improved upon by Box and Hunter (Box and Hunter, 1957).
CCD gives almost as much information as a three-level factorial, requires many
fewer tests than the full factorial design and has been shown to be sufficient to
describe the majority of steady-state process responses (Srinivasan et al., 2012).
Hence in this study, it was decided to use CCD design of Response Surface
51
Method in determination of interaction effects of control variables as related to
responses of PFRP.
2.8
Response Surface Methodology (RSM) and Robust Design
RSM is an important branch of experimental design. RSM is a critical
technology in developing new material and optimizing their performance. The
objectives of quality improvement, including reduction of variability and improved
process and product performance, can often be accomplished directly using RSM.
It is well known that variation in key performance characteristics can result in poor
process and product quality. During the 1980s (Taguchi, 1986; Taguchi, 1987)
considerable attention was given to process quality and methodology was
developed for using experimental design, specifically for the following:
1. For designing or developing products and processes so that they are robust to
component variation.
2. For minimizing variability in the output response of a product or a process
around a target value.
3. For designing products and processes so that they are robust to environment
conditions.
Robust means that the material or product performs consistently on target
and is relatively insensitive to factors that are difficult to control. Professor Genichi
Taguchi (Taguchi, 1986; Taguchi, 1987) used the term Robust Parameter Design
(RPD) to describe his approach to this important problem. Essentially, robust
52
parameter design methodology prefers to reduce process or product variation by
choosing levels of controllable factors (or parameters) that make the system
insensitive (or robust) to changes in a set of uncontrollable factors that represent
most of the sources of variability. Taguchi referred to these uncontrollable factors
as noise factors. RSM also assumes that these noise factors are uncontrollable in
the field, but can be controlled during process development for purposes of a
designed experiment.
Interactions are part of the real world. In Taguchi's arrays, interactions
are confounded and difficult to resolve. However the RSM technique seemed
to have an edge over the Taguchi technique in terms of significance of interactions
and square terms of parameters. However, in the some paper (Iqbal and Khan,
2010; Srinivasan et al., 2012), authors concluded that the time required for
conducting experiments using RSM technique was almost twice that needed for the
Taguchi methodology. In another study, Teng and Xu (2007) initially optimized
whole cell lipase production in submerged fermentation using the Taguchi method.
The optimum condition determined by the Taguchi methodology was used as a
center point in the RSM, this further optimization using RSM was reported to have
improved the lipase production.
Considerable attention has been focused on the methodology advocated by
Taguchi and a number of flaws in his approach have been discovered; however, the
framework of response surface methodology easily incorporates many useful
53
concepts in his philosophy (Myers & Montgomery, 2002). There are also two other
full-length books on the subject of RSM (Box and Draper, 1987; Khuri and
Cornell, 1996). The response surface methodology (RSM) accounts for possible
interaction effects between variables. If adequately used, this powerful tool can
provide the optimal conditions that improve a process (Haaland, 1989). With this
kind of approach, it is possible to create response surfaces that allow the ranking of
each variable according to its significance on the studied responses.
Therefore, with reduced time and experimental effort, it may be possible to
predict what composites formulation condition that will produce a desired or
optimum strength (Box et al., 1978; Myers and Montgomery, 1995; CanteriSchemin, et al., 2005; Soares, et al., 2005).
2.9
Failure theories and limit stress prediction in multiaxial stress state
High cost of synthetic fibers and health hazards of asbestos fiber have really
necessitated the exploration of natural fibers (Agbo, 2009; Brahmakumar et al.,
2005). Consequently, natural fibers have always formed wide applications from the
time they gained commercial recognition (Samuel et al., 2012). The use of a
reliable multiaxial or even biaxial experimental data to validate failure theories is
the critical step in the evolution and efficient usage of composite materials (Hinton
et al., 2004). “Multiaxial” and biaxial testing of composites was studied in (Chen
and Matthews, 1993), but a careful examination of Olsson (2011) submissions
clarifies that “multiaxial” solely refers to various combinations of in-plane loads.
54
Relevant literatures related to composite design and analysis of multi-axial
stresses were thus reviewed and applied in the study of limiting stresses of Plantain
fiber reinforced polyester matrix composites (PFRP). A designer is always
interested in the estimation of failure stresses of material he/she wants to employ in
a design. Crawford (1998) reported the rule of mixtures equation, the Halpin-Tsai
equation and the Brintrup equation for the estimation of composite modulus found
in almost all the strength of materials and mechanical design tests are relevant
equations for the prediction of failure of engineering materials.
Many factors must be considered when designing fiber reinforced
composites (Derek, 1891). These factors include volume fraction of fibers, aspect
ratio of fiber and fiber orientation in matrix, etc. Although a multiaxial stress state
can be a biaxial or triaxial stress state, in practice, it is difficult to devise
experiments to cover every possible combination of critical stresses because each
test is expensive and a large number is required. Therefore a theory is needed that
compares the normal and shear stresses
,
,
,
,
and
with the
uniaxial stress for which experimental data are relatively easy to obtain (Hamrock
etal., 1999).
Experimental results from the World Wide Failure Exercise (WWFE)
(Hinton and Soden, 2002; Soden et al., 2002) indicate that the (admittedly scarce)
data on fiber tensile failure under bi- or multi-axial stress states does not seem to
55
invalidate the maximum stress criterion. This review will include four important
failure theories, namely (1) maximum shear stress theory, (2) maximum normal
stress theory, (3) maximum strain energy theory, and (4) maximum distortion
energy theory. According to Hamrock et al., (1999), the following are the
important common features for all the theories.
 In predicting failure, the limiting strength (Syp or Sut or Suc) values obtained
from the uniaxial testing are used.
 The failure theories have been formulated in terms of three principal normal
stresses (σ1, σ 2, σ3) at a point. For any given complex (axial) state of stress
(σx, σy, σz, τxy, τyz, τzx), we can always find its equivalent principal normal
stresses (σ1, σ2, σ3). Thus the failure theories in terms of principal normal
stresses can predict the failure due to any given state of stress.
 The three principal normal stress components σ 1, σ 2 and σ 3, each which can
comprised positive (tensile), negative (compressive) or zero value.
 When the external loading is uniaxial, that is σ1= a positive or negative real
value, σ2= σ3=0, then all failure theories predict the same result as that has
been determined from regular tension/compression test.
A good knowledge of the principal stresses on the element of material
enables the designer to apply the appropriate theory of failure for the material of
his design (Hinton and Soden, 2002). Some of the failure theories are discussed as
follows:
56
Maximum shear stress theory (MSST) [aka Tresca yield criterion]:
This theory postulates that failure will occur in a material or machine
part if the magnitude of the maximum shear stress (max) in the part
exceeds the shear strength (yp) of the material determined from
uniaxial testing.
The maximum-shear-stress theory (MSST) was first proposed by Coulomb
(1773) but was independently discovered by Tresca (1868) and is therefore often
called the 'Tresca yield criterion. His observations led to the MSST. Experimental
evidence verifies that the MSST is a good theory for predicting the yielding of
ductile materials, and it is a common approach in design.
If σ1, σ2, & σ3, are the three principal normal stresses from applied loading,
then from Mohr circle, the maximum shear stress in the part is, max = Maximum of
the following three quantities | σ 1- σ2|/2 , | σ2- σ3|/2 , and | σ3- σ 1|/2
In uniaxial testing of the part material, the tensile stress was Syp during
yielding. In this case σ1 = σyp, σ2= σ3=0. Thus, again from Mohr circle, shear
strength yp = Syp/2.
This theory postulates, that failure will occur when,
max = yp or max of [|σ1-σ2|/2, | σ2-σ3|/2, and |σ3-σ1|/2] = Syp/2 Dividing both side by
2, max of [|σ1-σ2|, | σ2-σ3|, and | σ3-σ1|] = Syp
Using a design factor of safety Nfs, the theory formulates the design equation
57
as, Max of [|σ1- σ2|, | σ2- σ3|, and | σ3- σ1|] should be less than or equal to Syp/Nfs
Note: Instead of the above formulation, it is easier to find the actual max from
Mohr circle, and then use the following design equation max = Syp/2Nfs
The Maximum distortion energy theory (DET) [aka von Mises criterion]:
This theory is also known as shear energy theory or von MisesHencky theory. This theory postulates that failure will occur when the
distortion energy per unit volume due to the applied stresses in a part
equals the distortion energy per unit volume at the yield point in
uniaxial testing.
The total elastic energy due to strain can be divided into two parts. One part
causes change in volume, and the other part causes change in shape. Distortion
energy is the amount of energy that is needed to change the shape. Derivation of
the distortion energy equation can be found in the textbook. Comparing distortion
energy for an applied stress (S1, S2, S3) and an applied stress (Syp, 0, 0) and using
a factor of safety, the following design equation is obtained.
S12+ S22+ S32 - S1S2 - S2S3 - S3S1
< (Syp/Nfs)2
The maximum normal stress theory (MNST):
This theory postulates that failure will occur in a machine part if the
maximum normal stress in the part exceeds the normal strength of
the material as determined from uniaxial testing.
This theory caters for brittle materials and we have learnt that brittle
58
materials behave differently in compression and tension tests. In compression
test it fails when the compressive stress reaches Suc, the ultimate compressive
strength of the material and in tensile test it fails when the tensile stress reaches
Sut, the ultimate tensile strength of the material. Also generally the magnitude of
Suc is larger than Sut for brittle materials.
As the three principal stresses at a point in the part σ1, σ2 or σ3 may be
comprised of both tensile and compressive stresses, when this theory is applied, we
need to check for failures both from tension and compression. Thus according to
this theory, the safe design condition for brittle material can be given by:
The maximum tensile stress should be less than or equal to Sut/Nfs
and The magnitude of the maximum compressive stress should be less
than Suc/Nfs
Maximum strain energy theory (MSET):
This theory postulates that failure will occur when the strain energy
per unit volume due to the applied stresses in a part equals the strain
energy per unit volume at the yield point in uniaxial testing.
Strain energy is the energy stored in a material due elastic deformation,
which is, work done during elastic deformation. Work done per unit volume =
strain x average stress. During tensile test, stress increases from zero to Syp,
that is average stress = Syp/2. Elastic strain at yield point = Syp/E, where E is
the modulus of elasticity. Strain energy per unit volume during uniaxial
59
tension = average stress x strain = Syp2/2E
When the applied stress is (S1, S2, S3) then it can be shown (Harmrock etal.,
1999; Shigley and Mischke, 1989) that the strain energy stored in the part = [S12+
S22+ S32 - 2 (S1S2 + S2S3 + S3S1)]/2E, where  is Poisson’s ratio. Thus according
to this theory, the safe design condition can be given by comparing the two strain
energies with a factor of safety:
[S12+ S22+ S32 - 2 ( S1S2 + S2S3 + S3S1 )] < (Syp/Nfs)2
2.10 Finite Element Analysis (FEA) and application in Composite Modelling
Finite Element Method (FEM) is a numerical method of structural analysis
(Jovanovic and Filipovic, 2005). The basic idea of this method is a physical
discretization of a continuum; this implies dividing accounted domain (some
structures) or material into a finite number of small dimensions and simple shapes,
which makes up a mesh of so-called “'finite elements”'. The finite elements are
connected by common nodes, so that they make the original structure. Mesh
generation is the division of a certain area on nodes and finite elements.
Commercial software packages (e.g ANSYS) have an in-built automatic division
of the areas for the purpose of obtaining faster as well as qualitative solutions; this
is of big importance in large or very complex engineering tasks (Montemurro et al.,
1993). Theoretically viewed, the discussed domain has infinite degrees of freedom.
With this method, such a real system is replaced by the model, which has a finite
number of degrees of freedom.
60
At certain conditions the loads act only in certain points of finite element,
which are called nodes; on the basis of well-known displacements in nodes,
determination of stresses in nodes can be done as well as in other points of finite
elements, which enabled stress-strain analysis of structures to be carried out
(Ritter, 2004). The FEM is used to find out: stresses and deformations in the
complex and unusually shaped components; conditions of fluid flow around
buildings; heat transfer through gases and in other applications. A complete model
takes into account geometry components, used materials, load conditions,
boundary conditions and other significant factors. Appropriate use of FEM permits
that component is tested before it is made; consecutive iterations of that part would
be modified, in order to attain the minimum weight with supply of an adequate
strength (Bathe, 1982).
The main advantage of Finite Element Analysis (FEA) in composites
modeling through computer use is the possibility of simulations, in that way, the
behaviour of structures in real working conditions is examined. The investigated
model replaces the real construction with certain accuracy (Ritter, 2004).
Sometimes it was necessary to create a physical model to examine its properties.
Today, most of the work on the design is done in virtual environment (Jovanovic
and Filipovic, 2005).
The finite element method is the dominant discretization technique in
structural mechanics. It was originally an extension of matrix structural analysis,
61
developed by structural engineers. The FEM has been used in every field, where
differential equations define the problem (Montemurro et al., 1993). The process
implementation of the FEM, based on solving differential equations, is leading to
the residue method (Galerkin method) or to the variation methods (principle of
virtual work, the principle of minimum potential energy). It can be said that the
FEM solution process consists of the following steps:
 Divide structure into piece elements with nodes (discretization/meshing);
 Connect (assemble) the elements at the nodes to form an approximate
system of equations for the whole structure (forming element matrices);
 Solve the system of equations involving unknown quantities at the nodes;
 Calculate desired quantities (e.g., strains and stresses) at selected elements.
Finite Element Analysis is an accurate and flexible technique to predict the
performance of a structure, mechanism or process under in-service or abused
loading conditions using leading software such as ANSYS®, ABAQUS®, LISA®,
AUTODESK®, MOLDFLOW®, DEFORM® and PLAXIS® etc. It is a numerical
method for analyzing complex structural and thermal problems.
Fiber reinforced composites consist of fiber and matrix phases and the
mechanical behavior of the composites are much determined by the fiber and
matrix properties. When finite element analysis is used, the material is modeled
using certain assumptions and analyzed for mechanical properties with finite
element method software. Some of the assumptions used in the FEA have been
62
identified in literature (Bayat and Aghdam , 2012; Igor et al., 2012; Leandro et al.,
2012; Antoine, 2010; Elsayed et al., 2012; Behzad and Sain, 2007).
1. Fibers are not porous
2. The material property for all the constituents are attributed as isotropic material
for both the volumes.
3. Fibers are uniform in properties
4. Inter phase bonding is maintained between fibers and matrix
5. Perfect bond exists between fiber and matrix and no slippage
6. Fibers are arranged in unidirectional manner and perfectly aligned
FEA has traditionally been associated with validating designs before
committing to manufacture. However, it is now also commonly used early in a
design process to try out new concepts and optimize before any physical
prototypes are made and tested. Benefits include:

Increased innovation, as FEA encourages the designer to think creatively at
less risk

Optimum rather than acceptable designs, resulting in better performance and
reduced material costs, as FEA enables the designer to run multiple
scenarios quickly and cheaply.

Improved understanding and control of operating envelopes, leading to
higher quality and robustness, as FEA provides detailed performance
information difficult to obtain from physical tests.
63

Reduced development cost and lead time, with pass/fail physical tests
replaced by virtual design iterations, as FEA models are generally quicker to
build than prototypes and test equipment.
FEA requires selection of appropriate elements of suitable size and
distribution (the FEA mesh). A displacement function and material property are
associated with each finite element. Boundary conditions and loading define
behaviour of each node and these are expressed in matrix notations (Hodzic and
Stachurski, 2001; Huang and Bush, 1997).
FEA modelling scheme: The composite containing aligned short fibers
could be modelled as a regular uniform arrangement; the model included the fiber,
the matrix and the fiber-matrix interface (Houshyar et al., 2009; Abraham et al.,
2007; Izer and Bárány, 2007). Boundary conditions can be applied as an imposed
displacement on all boundary nodes to obtain the equivalent in-plane stiffness
properties (Kang and Gao, 2002). Such models give detailed stress distributions
around and within the fiber once the actual strains have been determined (Shati et
al., 2001). Equivalent properties can be used in a global model, the problem is then
solved and the stresses at any point are computed.
The boundary conditions for the model include fixing one end of the model
in all its three or two degrees of freedom and applying an axial load to the free end.
The contribution of each element of the composite model needs to be taken into
64
consideration; micromechanical approach utilizing the rule of mixture (Krenchel,
1964; He and Porter, 1988), Brintrup and Halpin-Tsai (Ibarra et al., 1995)
equation, which is an empirical expression containing a geometric fitting parameter
obtained by fitting with the numerical solution of formal elasticity theory.
Ultimately, these physics has been coupled together as an input in ANSYS
multiphysics software; FEA combines a model in the form of microstructures with
fundamental material properties such as elastic modulus or coefficient of thermal
expansion of the constitutive phases as a basis for understanding material
behaviour. Solutions are stress and strain data for each node in the system and they
are summarized according to the usual criteria (Shati et al., 2001; Kang and Gao,
2002; Hodzic and Stachurski, 2001; Huang and Bush, 1997).
The objective of this current research is to apply FEM in the analysis of the
deformation and stress distributions of plantain empty fruit bunch (PEFB) fibers
reinforced composites and plantain pseudo stem (PPS) fiber reinforced composite
materials during tensile and flexural loading apart from experimental testing. FEM
has been applied as a design validating tool before committing to manufacture.
2.11 Properties of Composites and factors affecting strengths
The primary effect of fiber reinforcement on the mechanical properties of
composites included increased modulus, increased strength with good bonding at a
high fiber content, decreased elongation at rupture, increased hardness even with
relatively low fiber content, and possible improvements in cut, tear, and puncture
65
resistance. The properties of short-fiber reinforced composites depended on the
fiber aspect ratio (AR), fiber length, fiber content, fiber dispersion, fiber
orientation and fiber-matrix adhesion. There are many other factors to be
considered when designing with composite materials, according to Baiardo et al.
(2004); Brader and Hill, (1993); Nando, and Gupta, (1996), the mechanical
properties of fiber reinforced composites are expected to depend on (i) the intrinsic
properties of matrix and fibers, (ii) aspect ratio, content, length distribution and
orientation of the fibers in the composite, and (iii) fiber–matrix adhesion that is
responsible for the efficiency of load transfer in the composites.
A crucial parameter for the design with composites is the fiber content, as it
controls the mechanical and thermo-mechanical responses. The strength and
stiffness of a composite can increase to a point with increasing the volume content
of reinforcements. However, if the volume content of reinforcements is too high
there will not be enough matrices to keep them separate, and they can become
tangled. Similarly, the fiber length is a very important parameter which affects the
various properties of composite material. Therefore, in order to obtain the favoured
material properties for a particular application, it is important to know how the
material performance changes with the fiber content, fiber aspect ratio and fiber
orientation under specific loading conditions.
Studies to understand the influence of these factors on cellulose-based
composites have been carried out and reported in the literature by many
66
investigators such as Gatenholm et al. (1993) and Sain and Kokta (1991). Some of
these factors studied will be briefly described in this section.
Length: The fibers can be either long or short. Long fibers provide many benefits
over short fibers. These include impact resistance, low shrinkage, improved surface
finish and dimensional stability. However, short fibers have few flaws and
therefore have higher strength.
Shape: The most common shape of fibers is circular because handling and
manufacturing them is easy. Hexagon and square shaped fibers are possible but
their advantages of strength and high packing factors do not outweigh the difficulty
in handling and processing.
Material: The material of the fiber directly influences the mechanical performance
of a composite. Fibers are generally expected to have high elastic modulus and
strengths. This expectation and cost have been key factors in graphite, aramids and
glass dominating the fiber market for composites.
Fiber aspect ratio: Many researchers reported that fiber loading and fiber
structure, such as length and ratio of fiber length to width (aspect ratio), also affect
the overall properties of biocomposites (Stark and Rowlands 2003; Klyosov 2007;
Migneault et al. 2008; Mengeloğlu and Karakuş 2008; Bouafif et al. 2009). Other
researchers have indicated that increasing the aspect ratio provides higher tensile
and flexural strength, and a greater modulus for WPCs (Stark and Rowlands 2003).
67
Zárate, Aranguren and Reboredo (2003) examined the influence of fiber volume
fraction and aspect ratio in resol–sisal composites, an optimum for the fiber length
as well as for the fiber volume fraction was found. The improvement of the
properties occurred up to a length of about 23 mm, they concluded that the use of
longer fibers lead to reduced properties because they tended to curl and bend
during processing. Fiber aspect ratio, i.e. the length to diameter ratio of fibers, is a
critical parameter in a composite. Figure 2.6 shows how variations in fiber stress
and shear stress at the fiber/matrix interface occur along the fiber length
(Gatenholm, 1997). The effect of fiber length on fiber stress, which is commonly
used to define critical fiber length, is shown in Figure 2.7 (Gatenholm, 1997).
During processing, fibers, such as glass and carbon fibers, are often broken into
smaller fragments (Nando and Gupta, 1996). This may potentially make them too
short to be useful for reinforcement (Nando and Gupta, 1996).
However, cellulose fibers are flexible and resistant to fracture during
processing can be expected (Lee et al., 2004). This enables the fibers to maintain a
desirable fiber aspect ratio after processing. (Nando and Gupta, 1996; Lee et al.,
2004).
68
Figure 2.6. Fiber tensile stress and shear stress variation along the length of a
fiber embedded in a continuous matrix and subjected to a tensile force in the
direction of fiber orientation (Gatenholm, 1997).
Figure 2.7 Effect of fiber length on fiber tensile stress (Gatenholm, 1997).
Fiber orientation: Fibers oriented in one direction give very high stiffness and
strength in that direction. Fiber orientation is an important parameter that
influences the mechanical behavior of fiber reinforced composites (Brader and
69
Hill, 1993; White, 1996). This is because the fibers in such composites are rarely
oriented in a single direction which is necessary for the fibers to offer maximum
reinforcement effects; as a result, the degree of reinforcement in a short-fiber
composite is found to be strongly dependent on the orientation of each individual
fiber with respect to the loading axis (Brader and Hill, 1993). In these operations,
the polymer melt will undergo both elongational or extensional flow and shear
flow (Clyne and Hull, 1996). The effect of these flow processes on the fiber
orientation is illustrated in Figure 2.8.
Figure 2.8 Schematic representations of the changes in fiber orientation
occurring during flow. a) Initial random distribution, b) rotation during shear
flow, and c) alignment during elongational flow (Clyne and Hull, 1996).
Fiber volume fraction: Like other composite systems, the properties of short-fiber
composites are also crucially determined by fiber concentration. Variation of
composite properties, particularly tensile strength, with fiber content can be
70
predicted by using several models such as the ‘Rule of Mixtures’ (Figure 2.9)
which involves extrapolation of matrix and fiber strength to fiber volume fractions
of 0 and 1.
Figure 2.9 Typical relationships between tensile strength and fiber volume
fraction for fiber reinforced composites (Bigg, 1996).
At low fiber volume fraction, a drastic decrease in tensile strength is usually
observed. This has been explained with dilution of the matrix and introduction of
flaws at the fiber ends where high stress concentrations occur, causing the bond
between fiber and matrix to break (Bigg, 1996). At high fiber volume fraction, the
matrix is sufficiently restrained and the stress is more evenly distributed. This
results in the reinforcement effect outweighing the dilution effect (Nando and
71
Gupta, 1996; Bigg, 1996). As the volume fraction of fibers is increased to a higher
level, the tensile properties gradually improve to give strength higher than that of
the matrix. The corresponding fiber volume fraction in which the strength
properties of the composite cease to decline with fiber addition, and begin to again
to improve, is known as the optimum or critical fiber volume fraction, (Nando and
Gupta, 1996; Bigg, 1996).
For short-fiber composites to perform well during service, the matrix must
be loaded with fibers beyond this critical value (Nando and Gupta, 1996). At very
high fiber volume fraction, the strength again decreases due to insufficient matrix
material (Nando and Gupta, 1996; Bigg, 1996). Thomas et al. (1997) investigated
the mechanical behavior of pineapple leaf fiber-reinforced polyester composites as
a function of fiber loading, fiber length, and fiber surface modification; they found
that tensile strength and modulus to increase linearly with fiber content.
The impact strength was also found to follow the same trend. But in the case
of flexural strength, there was a leveling off beyond 30 % fiber content. A
significant improvement in the mechanical properties was observed when treated
fibers were used to reinforce the composite (Bigg, 1996).
72
2.12 Summary of literature review
This chapter has provided an exhaustive review of research works on fibers
reinforced polymer composites as reported by various scholars; the surveys reveal
the following knowledge gap in the research reported so far:
 Though much work has been done on a wide variety of natural fibers for
polymer composites, very little has been reported on the reinforcing
potential of plantain fiber in spite of its abundant availability; research on
plantain fibers based polyester composites is very rare and in fact no study
has been found particularly on polyester based plantain fiber reinforced
composites. Despite the fact that a number of avenues are being established
for utilization and disposal of agro wastes, there is still no report available in
the existing literature on the use of wastes like plantain empty fruit bunch
and plantain pseudo stem fibers in polyester composites. Against this
background, the present research work has been undertaken with an aim to
explore the usefulness of plantain fibers as reinforcing materials in polyester
matrices and to establish their limit strengths.
 Based on the literature survey performed, venture into this research was
amply motivated by the fact that a little research has been conducted to
obtain the optimal levels of control parameters that yield the optimum
strength of plantain fibers reinforced polyester composites. A suitable
optimization technique or algorithm can be chosen based on the output
73
performance of the optimization technique and the best one can be selected
to maximize the production efficiency. This is possible only by evaluating
the performance of different algorithm. No such performance evaluation is
conducted throughout the literature. Majority of the works are concentrating
only on particular method or technique. This has been rectified by
comparatively employing different set of algorithms in this work (Taguchi
approach, RSM and FEA).
 Though many investigators have proposed a number of models to predict
strengths of polymer composites (It is mostly one factor at a time evaluation
of influence), none of them have considered combined influence of
formulation variables as factors influencing the strength of plantain fibers
reinforced polyester matrices; as a result, no specific model based on fiber
orientation, aspect ratio and volume fraction has so far been developed. In
the present study, Response Surface Methodology (RSM) was identified and
thus applied to develop computational models of the responses in terms of
the design variables and identify the optimal setting of factors affecting the
strengths of plantain fibers reinforced composites.
 The studies indicate the importance in analyzing the problem and efforts
done to improve the performance of the production or design system even
under disturbed conditions. Researchers are responsible to conceive new and
74
improved analytical tools to solve a problem. When a new tool is available
the problem should be re-examined to find better and more economical
solutions. In recent years, the evolution of Computer Aided Designs and
Finite Element Analysis have been gaining more importance and giving
promising results in industrial applications. This issue motivates the
application of such methodology in analyzing and validating experimental
results of this study to enhance quality and economy. ANSYS finite element
analysis is an alternative approach to solving the prevailing equations of a
structural problem; this computer aided approach involves modelling the
material using finite elements consisting of interconnected nodes and/or
boundary lines and/or surfaces that are directly or indirectly linked with
other elements via interfaces.
 Out of the four theories of failure reviewed, only the maximum normal stress
theory (MNST) predicts failure for brittle materials. The rest of the three
theories are applicable for ductile materials. Out of these three, the distortion
energy theory (DET) provides most accurate results in majority of the stress
conditions. The strain energy theory (SET) needs the value of Poisson’s ratio
of the part material which is often not readily available. The maximum shear
stress theory (MSST) is conservative. However, for simple unidirectional
normal stresses all theories are equivalent, which means all theories will
75
give the same result. This study utilizes DET, MSST, and MNST in
prediction of the yield stresses for plantain fiber reinforced composites.
 In general, after reviewing the existing literature on natural fiber composites,
particularly leaf fibers (abaca, cantala, curaua, date palm, henequen,
pineapple, sisal, etc) composites, efforts were made to understand the basic
reason for the growing composite industry; the conclusions drawn from this
are that the success of combining natural fibers with polymer matrices
results in the improvement of mechanical properties of the composites
compared with the matrix materials. These composite fibers are cheap,
nontoxic, can be obtained from renewable sources and are easily recyclable.
Moreover, despite their low strength, they can lead to composites with high
specific strengths because of their low density.
76
CHAPTER THREE
MATERIALS AND METHODS
Mixed method of research was applied through experimentation, modelling
and optimization techniques to optimally design and characterize plantain fiber
reinforced polyester (PFRP).
3.1
Materials
Composite structures are composed of fibrous materials held in place by a
matrix system. They drive most of their unique characteristics from the reinforcing
fibers. Fabricating a composite part is simply a matter of placing and retaining
fibers in the direction and form that is required to provide specified characteristics
while the part perform its design function. The basic raw materials used in
fabricating the composites of this study are as shown in figure 3.1, and consists of
polyester, hardener, mould releasing agent and plantain fiber.
Figure 3.1. Basic raw materials
77
Fiber: Plantain empty fruit bunch fibers and plantain pseudo stem fibers used was
obtained from a local plantation in Anambra state. Plantain plant is one of the main
sources of food in the southern region of Nigeria, it is also a major source of fibers,
and the people refer to the fiber as “elili jioko”. Conventionally, they use it to make
rope and mats. The fibers obtained from this plant are whitish in color, in average
0.5 m to 1 m long and it is a strong fiber. In this study, the plantain fiber was used
as reinforcement; figure 3.2 depicts a plantation of plantain plants.
PLANTAIN EMPTY
FRUIT BUNCH
PLANTAIN PSEUDO
STEM
Figure 3.2. The plantain plant
78
Using plantain fiber and the other parts of the plantain plant, the Anambra
people prepare mats for different purposes depending on the size of the mat as
shown in figure 3.3. Most of the time the mat is used to decorate their house
specially the floor. This material is strong and costs less in price than synthetic
fibers; as a result this material was selected to reinforce composites for engineering
application.
(a)
(b)
Figure 3.3. Traditional usage of plantain fiber (a) Unfinished processing mat
(b) Trimmed piece of mat used in floor covering.
The plantain fibers were chopped using grinder model Retch into lengths
ranging from 10mm to 40 mm. Figure 3.4 depicts the plantain empty fruit bunch
and plantain pseudo stem fibers, the fibers were extracted from empty fruit bunch
and pseudo stem sections of plantain plant using double water rating process. The
empty fruit bunch fibers look finer than pseudo stem fibers.
79
(a) Plantain pseudo stem fiber
Figure 3.4. Depiction of fiber types
(b) Plantain EFB Fiber
Resin: Polyester resin purchased from Ajasa-Onitsha, Anambra state, with density
of about 1.15 g/cm3 was used as the matrix. The resin is an unsaturated polyester
with brand name of TOPAZ – 2100 AT manufactured by NCS Resins South
Africa. TOPAZ – 2100 AT is a medium viscosity thixitropic unsaturated polyester
resin based on Isophthalic acid. It exhibits good mechanical and electrical
properties together with good chemical resistance compared to general purpose
resins. It has superior chemical resistance towards most mineral and organic acids,
solvents and oils.
Polyester (thermoset) resin was chosen for this study instead of
thermoplastic resin because it is a room temperature liquid resin and is easy to
work with, also beyond ease of manufacturing, polyester resins can exhibit
excellent properties at a low raw material cost, it also has the following benefits:
good handling characteristics, low viscosity and versatility, good mechanical
80
strength, good electrical properties, good heat resistance, cold and hot molding and
flame resistant with fire proof additive.
Hardener (catalyst): Polyester resin is cured by adding a catalyst, which causes a
chemical reaction without changing its own composition. The catalyst initiates the
chemical reaction of the unsaturated polyester and its monomer ingredient from
liquid to a solid state. When used as a curing agent, catalysts are referred to as
catalytic hardeners. Proper care was taken while handling the catalysts as they can
cause skin burning and permanent eye damage.
The curing agent applied for the liquid resin is hardener with brand name of
BUTANOX M-50 Manufactured by AKZO NOBEL Company. The product has a
density of 1180 Kg/m3 and viscosity of 0.51 Pasca-Second at of 20oC. The
chemical nomenclature of the hardener is Methyl Ethyl Ketone peroxide in
Dimethyl phthalate. It is common to use the ratio of catalyst to resin between 2% 5% based on their mass. Most of the time the ratio depends on the weather
condition and it is also known that too much catalyst usually result in brittle
material so care was taken. However, in this study 2% was used as the ratio
between catalysts to resin; and the mixture was stirred for two minutes using rod
like material.
Quantity of resin and fiber required: The ratio of the resin to the composites
formulation can be determined through experience. But for this study the quantity
81
of resin and fiber required was determined by utilizing the Archimedes principle to
obtain the volume of fiber required and then determining the volume of resin from
relevant equations.
3.2
Experimentation
Fiber treatment first with Alkali next with Silane and finally with Acetylene
has reportedly led to strong covalent bond formation and there are evidences of
marginal strength enhancement after the treatment process, the treatments
improved the Young's modulus of the fibers and improve fiber matrix adhesion of
the final composites (Bledzki and Gassan, 1999; Zafeiropoulos et al., 2002;
Mwaikambo & Ansell, 2002; Rowell et al., 2000; Mishra, et al., 2003; Bledzki, et
al., 2008). Fiber modification is carried out to clean the fiber surface, chemically
modify the surface, stop the moisture absorption process, and increase the surface
roughness (Kalia et al., 2008; Kalia et al., 2009).
3.2.1 Fiber extraction and Retting: The process involves steeping and keeping
the stems submerged in water for 7 days by weighing down with cement blocks
such that the immersion is about 10-15 cm from top. The softening of fibers took
place due to action of the enzyme released by the bacteria acting on the stem and
empty fruit bunch (EFB). The fibers are removed from the pseudo stem and EFB
by hand; the stems are then stripped one by one. The person after breaking the
lower end of the stalk gets free end of the fibers, grasps the other end of the stalk
with his left hand and removes the fibers in strips by running up the thumb and
82
first finger of the right hand between it and the stalk. Finally, the fibers were
washed again with deionised water and dried at room temperature for about 15
days; the dried fibers were designated as untreated fibers.
3.2.2 Alkali treatment: Generally, the first step in chemical treatment is usually
the alkali treatment of all the fiber samples and this causes changes in the crystal
structure of cellulose. The important modification occurring at this level is the
removal of hydrogen bonding in the network structure. The fibers were soaked in a
5% sodium hydroxide (NaOH) solution for 4hours to activate the hydroxyl (–OH)
groups of the cellulose and lignin in the fiber so that they would effectively react
with silane in the succeeding treatment. Sreekala et al. (2000) indicated that a 430% sodium hydroxide solution has produced the best effects on natural fiber
properties. The fibers were then thoroughly washed and dried.
3.2.3 Silane treatment: Coupling agents are usually employed in order to increase
compatibility between fiber and matrix and to decrease hyrophilicity of fibers
(Wambua, 2003); from this point of view, silane coupling agents were used as
suitable candidates to alter incompatibility between fiber and matrix. Silane
coupling agents are silicon-based chemicals that contain two types of reactivity
(inorganic and organic) in the same molecule.
Methyl-phenyl-dimethoxysilane was dissolved in a solution of water and
methanol solution (alcohol: water = 60: 40). The solution was mixed using a
mechanical mixer for 30 minutes at room temperature for hydrolysis reaction of
83
silane coupling agent to take place; according to Kalia et al. (2009) the silane
coupling agent will act as an interface between inorganic substrate (plantain fibers)
and organic material (polyester resin) to couple the two dissimilar materials.
Finally the fibers were added to the solution and left for 45 minutes under agitation
for condensation and chemical bonding of silanes and cellulose fibers. Treated
fibers were then washed to remove excess coupling agents.
3.2.4 Acetylation: Pre-treated plantain fibers were soaked in acetic acid for one
hour and subsequently treated with acetic anhydride solution containing a few
drops of concentrated sulphuric acid for 5 min, they were then filtered and washed
several times to remove residual acetic anhydride and then dried. Li et al., (2007)
reported that this is an esterification method which should stabilize the cell walls,
especially in terms of humidity absorption and consequent dimensional variation.
3.2.5 Process Variables and modeling:
System and Parameter Design of this study was preceded by an extensive
review of literature regarding factors influencing the strength of natural fiber
reinforced composites (Baiardo et al. 2004; Lee et al., 2004; Zárate, Aranguren and
Reboredo, 2003; Stark and Rowlands 2003; Klyosov 2007; Migneault et al. 2008;
Mengeloğlu and Karakuş 2008; Bouafif et al. 2009). The experimental process
variables used in this study were volume fraction (%), Fiber orientation (Deg.) and
fiber aspect ratio while the response variables used are discussed in the materials
84
testing and characterization section. The nominal values of the three design
parameters were set choosing low medium high levels.
Volume fraction: The presence of plantain fiber would make the composite better
in terms of mechanical properties, cost, renewability and biodegradability. Fiber
loadings used were 10% (A1), 30% (A2) and 50% (A3) fiber content by volume in
the composites following the nominal values of low-medium-high levels.
Aspect ratio: In fiber technology, the ratio of length to diameter of a fiber is
aspect ratio (AR), in this study AR values used were 10 (B1), 25(B2) and 40 (B3)
Fiber orientation: Fiber orientation is another important parameter that influences
the mechanical behavior of fiber composites (Brader and Hill, 1993; White, 1996).
This is because the fibers in such composites are rarely oriented in a single
direction (Brader and Hill, 1993), which is necessary for the fibers to offer
maximum reinforcement effects; fibers were matted in a unidirectional order and
cut to the requisite angle during sample preparation. Fiber orientation values used
were 30Deg (C1), 45Deg (C2) and 90Deg (C3). These orientations were ensured in
the matrix by first matting the fibers, flat unidirectional arrangements of the fibers
were matted using polyvinyl acetate as the bonding agent; they were arranged to a
thickness of 1.2mm and dried at room temperature for 72 hours before formation
of the composites.
85
3.2.6 Composites modulus
Since composites are weaker in directions perpendicular to fibers direction
(transverse direction) and stronger in directions parallel to the fibers axis, most
longitudinal properties of unidirectional fibers composites are evaluated by
equation from rule of mixtures; such properties includes, the
longitudinal
modulus, tensile strength of composite, density of composite, Poisson’s ratio of
composite, shear modulus, thermal conductivity of composite etc.(Crawford,
1998). The mechanical properties of fibers and polyester resins of this study are
presented in table 4.53. The longitudinal modulus of unidirectional fiber
composites can be estimated using the rule of mixture equation as reported by
Crawford (1998).
=
+
(3.1 )
Generally the fibers are dispersed at random on any cross section of the
composite and so the applied force will be shared by the fibers and matrix but not
necessarily equally as assumed in the rule of mixtures equation for transverse
modulus expressed by Crawford (1998) as
1
=
=
+
(3.2)
+
(3.3)
86
Other inaccuracies also arise due to mis-match of the Poisson’s ratios for the
fibers and matrix; these issues led to the use of some empirical equations to
estimate composite modulus. One of these is the Halphin-Tsai equation which is
expressed by Halpin (1976) as
=
1+2
1−
(3.4 )
Where
=
⁄
−1
⁄
+2
Another alternative equation for the modulus of composite is the Brintrup equation
which is expressed as
′
=
1−
+
′
(3.5 )
Where
′
=
⁄(1 −
) and
is the Poisson’s ratio of matrix material.
3.2.7 Random modulus of composite
The rule of mixture alone is inadequate in calculating the modulus of fiber
reinforced composites, this is because the rule of mixture states that the modulus of
a unidirectional fiber composite is proportional to the volume fraction of the
materials in the composite. The study therefore considered the propositions of Hull
87
(1981) for predicting the modulus of elasticity which varies with direction because
of inclination of the fibers as expressed in equation (3.6).
=
=
+
=
=3
⁄8 + 5
Where E1 is the longitudinal modulus while
⁄8
(3.6 )
is regarded as the transverse
modulus of the aligned fiber composite and is determined according to equations
(3.3), (3.4) and (3.5). On this premise, the shear modulus of the composite is then
determined according to Hull (1981) using:
=
1
8
+
1
4
(3.7)
While the Poisson’s ratio of plantain fiber reinforced composites is estimated with
=
2
−1
(3.8)
This is because the dispersions of fibers in the cross section of unidirectional
composites it at random (Crawford 1998).
3. 2.8 Poisson’s ratio for plantain fibers
Belyaev (1979) reported that the lateral strain is 3to 4 times less than axial
strain, ie
+4
=
(3.9)
88
Where
is the axial or longitudinal strain and
is the lateral or transverse strain.
The coefficient of lateral deformation or Poisson’s ratio is expressed as
=
(3.10)
The Poisson’s ratio is therefore the slope obtained by plotting lateral strain
against axial strain. The slope of
plotted on vertical axis and
experimental strain on the horizontal axis gives Poisson’s ratio of fibers as 0.20 for
both PEFBF and PPSF. These are used with the rule of mixtures equation to
compute the respective composites Poisson’s ratio in the fibers direction
(Crawford, 1998). This equation can be expressed as
=
+
(3.11)
3.2.9 Fiber orientation and fiber stress distribution in loading off the fiber axis
This is for the analysis of composites with fibers inclined or oriented with
respect to the axial or longitudinal direction of the composite. It applies to situation
where the applied loading axis does not coincide with the fiber axis. The first step
in the analysis of this situation is the transformation of the applied stresses on the
fiber axis following the methods of Benham et al., (1987), such that by referring to
figure 3.5, it may be seen that
=
+
+2
and
can be resolved into x, y axes as follows:
( 3.12)
89
=
+
=−
−2
(3.13 )
+
+
(
−
)
( 3.14)
Where
= stress parallel to the fiber axis or longitudinal stress,
= stress perpendicular
or transverse to the fiber axis or the transverse stress.
By putting equations (3.12)-( 3.14) in matrix form,
2
−2
( −
=
−
Where c =
(3.15)
)
and s =
Equation (3.15) can also be expressed as
{ }
= [ ]{ }
(3.16)
Where [ ] is called the stress transformation matrix. Similar transformations may
be made for the strains so that
1
2
=[ ] 1
2
(3.17)
Finite element analysis is very useful in the computation of the stresses
distribution within the global axes. It is only when these stresses
and
and
90
are known that computation of the transverse and directional properties such as
and
,
can be evaluated. Therefore finite element analysis was carried out in an
effort to determine stresses
and
and
1
2
y
Global
axes
x
Figure 3.5: Stressed single thin composite lamina
3.3
Design and optimization techniques
3.3.1 Design for composite manufacture
The volume of composites and moduli are evaluated following derivations
from the rule of mixtures and empirical relations and by writing
=
=
=
1−
+
(3.18)
(3.19)
91
=
=
=
(3.20)
These relations are used in determining the quantity of fibers and resin
needed for composition.
Where
= volume fraction of fibers,
and volume fraction,
= actual volume of fibers related to composition
= volume of composite related having mold characteristics
and approximately equal to volume of mould for a specific test,
= volume of a
measurable mass of fiber determined through application of Archimedes principle,
= volume of resin or matrix material,
= mass of fibers determined using a
digital balance.
From equation (3.18)
=
(3.21)
and from equation (3.20)
=
=
(3.22)
Next is to determine the mass of resin for specific composition of a certain volume
fraction by the expression,
=
+
By knowing the density of resign as
(3.23)
, the mass of resin for making a composite
of a particular volume fraction can be expressed as
92
=
(3.24)
=
(3.25)
is determined with expected number of replicate samples and the depth of the
mould as specified by ASTM standard in mind. Remember also that for a
particular volume fraction, computations of
,
and
are made.
3.3.2 Determination of fiber quantity through Archimedes principle
Archimedes principle states that when a body is totally or partially immersed
in a fluid, the upthrust (difference between weight of body in air and weight of
body in fluid) on it is equal to the weight of fluid displaced. The fluid density can
be used to evaluate the volume of fluid displaced which is the same as the volume
of body immersed; the strength of FRP classically was reported to depend greatly
on volume fraction of fibers.
Calculations of volume of plantain fiber is achieved following the
derivations from rule of mixtures based on the procedures of Jones (1998) and
Barbero (1998) and implementation of Archimedes principles in the determination
of volume of fiber.
=
+
(3.26)
=
(3.27)
=
(3.28)
93
=
+
(3.29)
=
=
=
(3.30)
(3.31)
+
1−
(3.32)
Where
= Mass of composite specimen, (g);
Mass of Resin, (g);
= Mass of plantain fiber, (g);
= Density of plantain fiber, (g/m3);
(g/m3);
= Volume of composite specimen, (mm3);
(mm3);
= volume of resin;
=
= Density of Resin,
= Volume of Resin,
= volume fraction of fiber.
Because the calculation of the volume of an irregular object (such as
plantain fiber) from its dimensions is a mirage by traditional method, such a
volume can be accurately measured based on steps below. It follows from the
Archimedes principle that the volume of the displaced fluid is equal to the object
volume (Acott, 1999). The following steps lead to the estimation of a given volume
of fibers:
Step 1: The mass of a sizable quantity of plantain fiber lump (mf) sample is
determined using digital METLER(R) balance (Precision: 0.0001g) and then
a water tight container (Cs) for which its density and mass is known or
94
previously determined, is used to contain the fiber ensuring that the water
tight container is completely filled with plantain fiber.
Step 2: A measuring cylinder was then filled with about 100 ml of water.
Step 3: Errors due to parallax were avoided by viewing the meniscus from a 0/180
degree angle, that is hold it up to eyes and then take the water volume
measurement from the base of the curved water meniscus.
Step 4: The water volume from Step 3 is recorded and denoted as (V0)
Step 5: The object is then placed into the cylinder. The water level will rise, noting
that the object must be completely covered with water.
Step 6: Step 3 is repeated and denoting the new water level as V1.
Step 7: The volume V0 (Step 4) is subtracted from V1 (Step 6) to calculate the
volume of the object, such that
Volume of object = V1-V0
But the volume of water displaced (Vd) = [volume of fiber (Vf)] + [volume of
container (Cs)]
Therefore
=
–
( )
(
)
(3.33)
95
Step 8: Finally the density of plantain fiber is determined by dividing the fiber
mass (Step 1) by its volume (Step 7), the values obtained are shown in table
3.1.
Table 3.1: Plantain fiber parameters determined by Archimedes principle
Mf2 (g)
Vf2 (mm3)
PEFB fiber
20.670
58364.8
381.966
PSTEM fiber
20.397
53364.8
354.151
FIBER SOURCE
Density Kg/m3
3.3.3 Mould design for various mechanical tests
The ASTM standards for various mechanical tests are presented in table 3.2
such that the volume of composite is computed by considering a mould size of
300×300×12 (LWB) that is suitable for both flexural, tensile, Brinell hardness and
Charpy impact tests, the composite volume is designed with specifications of table
3.2.
96
Table 3.2: Theoretical volume of mould and volume of composite for sample
replicates
Test
Standard
Specification for sample
Volume of
Volume of
)
(mm×mm×mm)
composite
mould(
(
)
Flexural
ASTM
300×19.05×3.175 (LWB)
300× 300×12
300×300×3.175
D790-10
=1080000
= 285750
Tensile
ASTM
150×19.05×3.2 (LWB)
300×300×12
300×300×3.2
D638-10
=1080000
=288000
Brinell
ASTM
25×25×10 (LWB)
300×300×12
300×300×10
Hardness
E10-12
=1080000
= 900000
Charpy
ASTM
55×10×10 (LWB)
300×300×12
300×300×10
impact
A370
=1080000
= 900000
The volume of fibers
is computed by equation (3.21) so that by
considering a particular volume fraction say
= 0.10, and flexural testing
standard
= 0.1 ∗
= 0.1 ∗ 285750 = 28575mm
The mass of fibers
is given in equation (3.22) so that by considering the
parameters determined by Archimedes principle,
= 58.3648
= 58364.8
,
= 20.670 , for plantain empty fruit
bunch fibers and by putting values in equation (3.22).
=
=
20.670
58364.8
28575mm = 10.1184g
The volume of resin is computed from equation (3.19) so that
=
1−
=
1 − 0.1
28575mm = 257175mm
0.1
97
Next is to determine the mass of resin for specific composition of a certain
volume fraction by using equation (3.23) and by knowing the density of resin as
, the mass of resin for making a composite of a particular volume fraction has
been expressed in equation (3.25).
was determined with the knowledge of
replicate samples and the depth of the mould as specified by ASTM standard in
mind. The mass of resin is then evaluated with equation (3.25) so that by knowing
the density of polyester resin as 1200kg/m3
=
= 257175mm ∗ 1200kg/m3 = 308.61g
The actual density of resin must be sourced from the manufacturer’s
catalogue. Similar computations are made for volume fractions of 0.20, 0.30, 0.40,
0.50, 0.60, 0.70 and 0.80 and summarized as in table 3.3-3.10.
Table 3.3: Flexural test mould design variables for empty fruit bunch fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
28575
10.12
257175
308.61
285750
0.2
57150
20.24
228600
274.32
285750
0.3
85725
30.36
200025
240.03
285750
0.4
114300
40.48
171450
205.74
285750
0.5
142875
50.60
142875
171.45
285750
0.6
171450
60.72
114300
137.16
285750
0.7
200025
70.84
85725
102.87
285750
0.8
228600
80.956
57150
68.58
285750
98
Table 3.4: Flexural test mould design variables for pseudo stem fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
28575
10.92
257175
308.61
285750
0.2
57150
21.84
228600
274.32
285750
0.3
85725
32.77
200025
240.03
285750
0.4
114300
43.69
171450
205.74
285750
0.5
142875
54.61
142875
171.45
285750
0.6
171450
65.53
114300
137.16
285750
0.7
200025
76.45
85725
102.87
285750
0.8
228600
87.38
57150
68.58
285750
Table 3.5: Tensile test mould design variables for empty fruit bunch fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
28800
10.20
259200
311.04
288000
0.2
57600
20.40
230400
276.48
288000
0.3
86400
30.60
201600
241.92
288000
0.4
115200
40.80
172800
207.36
288000
0.5
144000
50.99
144000
172.8
288000
0.6
172800
61.20
115200
138.24
288000
0.7
201600
71.40
86400
103.68
288000
0.8
230400
81.60
57600
69.12
288000
99
Table 3.6: Tensile test mould design variables for pseudo stem fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
28800
11.01
259200
311.04
288000
0.2
57600
22.02
230400
276.48
288000
0.3
86400
33.02
201600
241.92
288000
0.4
115200
44.03
172800
207.36
288000
0.5
144000
55.04
144000
172.8
288000
0.6
172800
66.05
115200
138.24
288000
0.7
201600
77.06
86400
103.68
288000
0.8
230400
88.06
57600
69.12
288000
Table 3.7: Brinell hardness test mould design variables for empty fruit bunch
fiber reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
90000
31.88
810000
972
900000
0.2
180000
63.75
720000
864
900000
0.3
270000
95.62
630000
756
900000
0.4
360000
127.49
540000
648
900000
0.5
450000
159.37
450000
540
900000
0.6
540000
191.24
360000
432
900000
0.7
630000
223.12
270000
324
900000
0.8
720000
254.99
180000
216
900000
100
Table 3.8: Brinell Hardness test mould design variables for pseudo stem fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
90000
34.40
810000
972
900000
0.2
180000
68.80
720000
864
900000
0.3
270000
103.20
630000
756
900000
0.4
360000
137.60
540000
648
900000
0.5
450000
171.99
450000
540
900000
0.6
540000
206.39
360000
432
900000
0.7
630000
240.79
270000
324
900000
0.8
720000
275.19
180000
216
900000
Table 3.9: Impact test mould design variables for empty fruit bunch fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
90000
31.87
810000
972
900000
0.2
180000
63.75
720000
864
900000
0.3
270000
95.62
630000
756
900000
0.4
360000
127.49
540000
648
900000
0.5
450000
159.37
450000
540
900000
0.6
540000
191.24
360000
432
900000
0.7
630000
223.12
270000
324
900000
0.8
720000
254.99
180000
216
900000
101
Table 3.10: Impact test mould design variables for pseudo stem fiber
reinforced polyester composite
Vfr
Vf (mm3)
Mf (g)
VR (mm3)
MR (g)
Vc (mm3)
0.1
90000
34.40
810000
972
900000
0.2
180000
68.80
720000
864
900000
0.3
270000
103.20
630000
756
900000
0.4
360000
137.60
540000
648
900000
0.5
450000
171.99
450000
540
900000
0.6
540000
206.39
360000
432
900000
0.7
630000
240.79
270000
324
900000
0.8
720000
275.19
180000
216
900000
3.3.4 Yielding of composite materials
The stresses applied to the material in service are not expected to exceed the
ultimate strength of material usually provided in a materials data sheet. If an
isotropic material is subjected to multi-axial stresses such as
,
and
then
the situation is slightly more complex. However, there are well established
procedures for predicting failure, if
,
and
question of ensuring that neither of these exceeds
below
are applied, it is not only a
. At values of
,
and
there can be a plane within the material where the stress reaches
and this will initiate failure.
The stresses acting on the three principal planes of a stressed material
element need to be known before yielding can be predicted for a general case of
102
engineering material. The classical relation for predicting the three principal
stresses in a triaxially stressed state is expressed in Harmrock etal. (1999) and
Shigley and Mischke (1989) as
−
+
+
+2
+
−
+
+
−
−
−
−
= 0
−
−
( 3.34)
Solving for the three roots of this equation gives the value of the three principal
stresses as
, and
,
≥
where
≥
.
The principal shear stresses are determined with the relations
−
2
=
,
=
−
2
,
=
−
2
( 3.35)
A good knowledge of the principal stresses on the element of material
enables the designer to apply the appropriate theory of failure for the material of
his design. Some of the failure theories are the Maximum shear stress theory
(MSST), the distortion energy theory (DET), and the maximum normal stress
theory (MNST).
The maximum shear stress theory (MSST) also remembered as Tresca yield
criterion is well suited in predicting failure of ductile materials. This Tresca yield
criterion is expressed as
−
=
≥
2
(3.36 )
103
Where
is the yield stress of material, for design purposes, the failure relation
can be modified to include a factor of safety (n):
=
(3.37)
−
The distortion energy theory (DET) also known as the von Mises criterion,
postulates that failure is caused by the elastic energy associated with shear
deformation. The von Mises stress is expressed as
=
1
√2
(
−
) +(
−
) +(
−
)
(3.38)
≥
(3.39)
=
(3.40)
Thus DET predicts failure if
=
( 3.41)
The maximum normal stress theory (MNST) states that failure occurs at the
ultimate stress of the material. This can be expressed as
≥
,
≥
(3.42)
Where
= uniaxial ultimate stress in tension,
104
= uniaxial ultimate stress in compression,
= safety factor
3.3.5 Preparation of composites
Flat unidirectional arrangements of the previously determined volume of
fibers as per required volume fraction were matted using polyvinyl acetate as the
bonding agent. They were arranged to a thickness of 1.2mm and dried at room
temperature for 72 hours. The composite manufacturing method adopted for this
study based on open molding Hand Lay-up processing technology in which the
plantain fiber reinforcement mat is saturated with resin, using manual rollout
techniques of Clyne and Hull (1996) to consolidate the mats and removing the
trapped air. A mild steel mold of dimensions (300×300×12) mm was used for
casting the composites in a matching group of 10%, 30% and 50% volume
fractions, 300, 450, 900 fiber orientation and 10, 25, 40 mm/mm aspect ratio based
on orthogonal array matrix of this study. First, the mould was polished and then a
mould-releasing agent (Polyvinyl alcohol) was applied on the surface to facilitate
easy removal of the composite from the mold after curing. Initially, polyester and
hardener were mixed to form a matrix and then the plantain fiber reinforcement
was placed on the top. A roller is used to impregnate the fiber with the resin.
Another resin and reinforcement layer may be applied until a suitable thickness
builds up. This is called hand lay-up process because the reinforcement is placed
manually; though this process requires little capital, it is labor intensive.
105
This process requires less capital investment and expertise and is therefore
easy to use. The schematic diagram for standard hand lay-up process is shown in
figure 3.6, where the thickness of the composite part is built up by applying a
series of reinforcing layers and liquid resin layers. A roller is used to squeeze out
excess resin and create a uniform distribution of the resin throughout the surface.
By the squeezing action of the roller, homogeneous fiber wetting is obtained. The
part is then cured at room temperature for 24 hours and, once solidified; it is
removed from the mold.
Figure 3.6: A typical schematic diagram for hand lay-up technology
3.3.5.1
Basic Processing Steps
The major processing steps in the hand lay-up technology include:
1. The mold was cleaned and prepared for use.
2. Release agent (Polyvinyl alcohol) was applied to the mold.
106
3. Liquid polyester resin was then applied to the mold.
4. The plantain fiber reinforcement layer was placed on the mold surface and then
it is impregnated with resin.
5. Using brush, resin was uniformly distributed over the laminate and consolidation
made between the laminate and the mold.
6. The part was allowed to cure at room temperature.
3. 4
Material testing and characterization
The manufactured composite was left to cure for 15(360 hours) days at
standard laboratory atmosphere prior to preparing specimens and performing
mechanical tests. The appropriate American Society for Testing and Materials
(ASTM) standards was followed while preparing the specimens for test. At least
three replicate specimens were tested and the results presented as an average of
tested specimens, the tests were conducted at a laboratory atmosphere of 290C.
3. 4.1 Flexural Test: An experimental investigation was carried out to determine
the ultimate breaking load of the composites subjected to bending. The composites
were tested in 3-point bending using Hounsfield Monsanto Tensometer. The
plantain stem and empty fruit bunch fibers reinforced composites were prepared
for flexural test as per ASTM D790M.
107
Figure 3.7. Schematic illustration of three-point bending test
Tests were carried out in Hounsfield tensometer model –H20 KW with
magnification of 4:1 and 31.5kgf beam force. The cross head speed is 1 mm/min.
Each specimen was loaded to failure. A beam subjected to bending moment and
shear force undergoes certain deformations. The material of the member offers
resistance or stresses against these deformations. The stresses introduced by
bending moment are called bending stresses. In a beam, the bending moment is
balanced by a distribution of bending stress. The top side is under compression
while the bottom surface is under tension. The mid-plane contains the neutral layer
which is neither stretched nor compressed and is subjected to zero bending stress.
The line of intersection of the neutral layer with the cross-section of the beam is
called as the neutral axis.
108
Figure 3.8: Plantain fiber reinforced composites sample setup mounted in
Hounsfield tensometer for flexural tests
The flexural properties were determined using equations (3.43) to (3.45):
=
6 ℎ
=
=
4 ℎ
3
2 ℎ
( 3.43)
( 3.44)
( 3.45)
3.4.2 Tensile Test: The basic principle adopted for tensile test is transformation of
tension force from the machine to the grips and from the grips, the shear stress are
transferred to both side of the tab length. From the tab lengths, the shear stress is
uniformly distributed to the gage length (see fig. 3.9).
Replicate samples of
plantain fiber reinforced polyester matrix were therefore subjected to tensile tests
using Hounsfield Monsanto Tensometer. The plantain stem and empty fruit bunch
fiber reinforced composites were prepared for tensile test in according to ASTM
109
D638. Tests were carried out in Hounsfield Tensometer model –H20 KW. Each
specimen was loaded to failure.
Figure 3.9: Straight-sided tensile specimen.
A gage length can be defined as the longitudinal length of the predicted failure
region.
Figure 3.10: Tensile test set up.
The tensile properties were determined using equations (3.46) to (3.48):
110
=
−
∗ 100
( 3.46)
=
=
( 3.47)
( 3.48)
.ℎ
3.4.3 Brinell hardness evaluation: Replicate samples of plantain fiber reinforced
polyester matrix were subjected to hardness tests using Hounsfield Monsanto
Tensometer. The plantain stem and empty fruit bunch fiber reinforced composites
were prepared for hardness test in according to Brinell hardness. The Brinell
hardness tests were conducted as per ASTM Standard E 10, with a ball indenter of
2 mm diameter, a test load of 122.32 kg is applied on the specimens for 30sec.
The Brinell hardness number (Hb) is an important surface mechanical
property and it’s known as a resistance of the material to deformation (Calister,
1999), it is calculated for the composites using the equation( 3.49). The large size
of indentation and possible damage to test-piece limits its usefulness (Calister,
1999).
=
( 3.49)
2
−(
−
)
3.4.4 Impact test: The ability of a material to withstand accidental knocks can
decide its success or failure in a particular application (Crawford, 1998). Impact
111
test was conducted to determine impact toughness of plantain fibers reinforced
composites by measuring the work required to fracture the test specimen under
impact. Although impact tests cannot directly predict the reaction of a material to
real life loading; instead, the results are used for comparison purposes. In this test
the pendulum is raised up to its starting position (height Ho) and then it is allowed
to strike the notched specimen fixed in a vice. The pendulum fractures the
specimen spending a part of its energy.
Initial position
Of the hammer
End of
The swing
Ho
PFRP
Specimen
Ho
H
H
PFRP
Specimen
Figure 3.11. Schematics of Charpy tester
=
(1 −
=
(1 –
Where
)
(3.50)
)
= Angle of fall,
(3.51)
=
Angle of rise, R =Pendulum arm
After the fracture the pendulum swings up to a height H. Before the mass
(m) is released, the potential energy will be:
=
(3.52)
112
After being released, the potential energy will decrease and the kinetic energy will
increase. At the time of impact, the kinetic energy of the pendulum:
=
(3.53)
And the potential energy:
=
(3.54)
The velocity of impact (v) is derived based on the understanding that E
k
= E p,
leading to:
= (2
)
/
(3.55)
=
=
ℎ
(1 −
=
ℎ
)
=
(3.56)
(1 −
=
=
)
(
(3.57)
−
) (3.58)
The linear elastic stress concentration factor k is given by
= 1+2
/
(3.59)
Where: Nr = the notch radius (mm) and ad = the notch dept (mm), Kt = stress
concentration factor (SCF).
Impact tests on specimens were performed by using Charpy methods as per ASTM
A370. Crawford (1998) noted that the impact energy measured is only for relative
comparison and does not give the accurate toughness of the material. For accurate
measurement of toughness, various correction factors like geometrical and kinetic
113
energy correction factors are to be considered (Plati and Williams, 1975). Impact
strength are normally quoted as
Impact Strength =
( /
)
(3.60)
Where
Cross sectional area at the notched section = (sample thickness × notch dept)
Stress due to impact =
(N/m2)
(3.61)
Experimental Procedure: To conduct the impact test:
1. The specimens were prepared according to stated standard.
2. The specimen was carefully positioned in the anvil. And the proper
position of the impact head (striking edge) and the height the
pendulum was set.
3. The specimen was then secured on the anvil.
4. Next the pendulum was set in raised position with the pointer on
upper limit of the scale.
5. Precaution: no attempt was made to stop the pendulum manually.
6. Finally, the pendulum was released and results recorded.
114
3.5
3.5.1
Optimization of process variables
Application of Taguchi Robust design
The Taguchi Robust design methodology shown in figure 3.12 was adopted
in this research. The Taguchi approach is a form of Design of Experiment (DOE)
with special application principles because for most experiments carried out in the
industry, the difference between the DOE and Taguchi approach is in the method
of application (Roy, 2001).
IDENTIFY THE
FACTORS
SELECT AN APPROPRIATE
ORTHOGONAL ARRAY
CONDUCT THE
EXPERINMENTS
(OA)
IDENTIFY THE LEVELS OF
EACH FACTOR
ASSIGN THE FACTORS
TO COLUMNS OF THE OA
DETERMINATION OF
EXPECTED RESPONSE
AND VALIDATION
ANALYSE THE DATA,
DETERMINE THE
OPTIMAL LEVELS
Figure 3.12. The Taguchi methodology implementation scheme, adapted from
Chen et al (1996).
Taguchi method is therefore applied as a technique for designing and
performing experiments to investigate processes where the output depends on
many factors (variables, inputs) without having tediously and uneconomically run
of the process using all possible combinations of values, such that using a
systematically chosen combinations of variables it is possible to separate their
individual effects (Lochner and Matar, 1990).
In Taguchi methodology, the
desired design was finalized by selecting the best performance under given
115
conditions. The tool used in the Taguchi method is based on the orthogonal array
(OA). OA is the matrix of numbers arranged in columns and rows (Sharma et al,
2005). The Taguchi method employs a generic signal-to-noise (S/N) ratio to
quantify the present variation. These S/N ratios are meant to be used as measures
of the effect of noise factors on performance characteristics. S/N ratios take into
account both amount of variability in the response data and closeness of the
average response to target. There are several S/N ratios available depending on
type of characteristics: smaller is better, nominal is best and larger is better
(Lochner and Matar, 1990; Syrcos, 2003).
In the present work, the influence of three process parameters as are studied
using L9 (33) orthogonal design (Zhu and Schmauder, 2003). Three parameters
each at three levels would require Taguchi’s factorial experiment approach to 9
runs only, offering a great advantage over the classical method of experimentation.
The signal-to-noise (S/N) ratio measures the sensitivity of the quality
characteristics being investigated to those external influencing factors (noise
factors) not under control in a controlled manner. The (S/N) ratio combines the
mean level of the quality characteristics and the variance around the mean into a
single metric. The aim of any experiment is always to determine the highest
possible (S/N) ratio of the results. A high value of (S/N) ratio implies that the
signal is much higher than the random effects of the noise factors. Process
116
operation consistent with highest (S/N) ratio always yields optimum quality with
minimum variance.
From material strength point of view there are three categories of quality
characteristics using (S/N) ratio and the method of calculating the S/N ratio
depends on whether the quality characteristic is smaller-the-better, larger-thebetter, or nominal-the-best (Taguchi et al., 2005; Roy, 2001; Palanikumar, 2006;
Ross, 1996).
Lower is better (flaws, trapped air etc.).
(S/N) ratio = −10
1
(3.62)
Higher is better (tensile, flexural, Brinell hardness etc).
(S/N) ratio = −10
(
)
(
)=
(3.63)
Where
1
1
(3.64)
Nominal is best (dimension, humidity etc.).
(S/N) ratio = 10
(3.65)
Where n is the number of experiments in the orthogonal array and yi the ith
are value measured. y2 is the average of data observed and s2 is the variation.
Detailed information about the Taguchi method can be found in many articles
117
(Taguchi et al., 2005; Roy, 2001; Ross, 1996). According to the rule that degree of
freedom for an orthogonal array should be greater than or equal to sum of chosen
quality characteristics, (DOF) was calculated by equation (3.66)
(
)
= P ∗(
– 1)
(3.66)
(DOF)R = degree’s of freedom, Pn = number of factors, LV = number of factor
levels
(DOF)R = 3(3 – 1) = 6
Therefore, since total DOF of the orthogonal array (OA) should be greater
than or equal to the total DOF required for the experiment, an L9 orthogonal array
was selected and applied; the selection of orthogonal array depends on three items
in order of priority, viz, the number of factors, number of levels for the factors and
the desired experimental solution or cost limitation. A total of 9 experiments were
performed based on the run order generated by the Taguchi model.
MSD of equation 3.64 is the mean square deviation from the largest value of
the quality characteristics. It is the statistical quantity that reflects the deviation
from the target value. The expressions for the MSD are different for different
quality characteristics. For larger is better, the inverse of each large value becomes
a small value and again, the unstated target value is zero for all three expression; in
general, the smallest magnitude of MSD is being sought (Roy, 1990). The S/N
ratio for maximum (tensile, flexural and Brinell hardness) comes under larger is
118
better characteristic, which can be calculated as logarithmic transformation of the
loss function (Ross, 1993).
3.5.2 Application of Response Surface Methodology (RSM)
3.5.2.1 Power Law Model for the Nonlinear Responses of Experimental Data:
It is a frequent experience in engineering design and experimentation to be
interested in determining whether there is a relation between two or more
variables. Regression analysis is a statistical technique for establishing such
relations. It establishes a functional relationship between variables when one
values (independent variables) and the responses (dependent variable) is
established. The simplest case of regression analysis is linear relationship between
independent variable x and the dependent variable y; the mathematical model for
the population is
=
+
(3.67)
+
In which yi and xi are the ith observation variables (experimental responses)
respectively. α and β are the populate values of the intercept and slope regression
respectively, coefficients
is the error.
The sample equation is
=
+
(3.68)
119
In which
is the predicted value of the depending variable, a and b are the
sample estimates of the regression coefficients. In most cases a linear functional
responses depends on more than one variable that in many research we employ
multiple linear regression model conventionally expressed as
=
+
+
+ ⋯+
+ .
(3.69)
Solution of regression model involves minimization of regression model’s
sum of squares of residuals. Also in many cases functional relationship with
independent factors are never linear that nonlinear regression is employed (Dieter,
2000) in modeling experimental data. A second order non linear regression model
with independent variables is given as
=
+
+
+
+
(3.70)
+
Similarly a second order model with three independent factors can be expressed as
=
+
+
+
+
+
+
+
+
+
(3.71)
Such nonlinear model is needed to detect nonlinearity and second-order
effects within population of data. However, the computational difficulties
associated with nonlinear regression analysis sometimes can be avoided by using
simple transformations that convert a problem that is nonlinear into one that can be
handled by simple linear regression analysis. According to Chapra and Canale
120
(1998) the nonlinear model can be transformed by employing the power law
model,
= a
…
(3.72)
Notably, multiple linear regression has additional educational utility in the
derivation of power equation of equation (3.72). To fit power law model of
equation (3.72) to experimental data using linear regression approach, the power
law equation is transformed by taking its logarithm to yield,
Log y = Loga + a Log
+ a
+ ⋯ + a Log
(3.73)
where the value of a = Antilog
For three independent factors of fiber volume fraction (A), Aspect ratio (B), and
fiber orientation (C) equation (3.73) reduces to
Log y = Loga + a Log
+ a
+ a Log
(3.74)
And in tandem with (3.72) equation (3.74) becomes
= a
3.5.2.2
(3.75)
Formation of Power Law Model: By employing the linearized form
of power law equation (3.74) such that if the experimental observations are
represented by
then the residual r is represented as
r = y − Log y
121
= y − (Log α + α Log A + Log α B + α Log C )
r =[
− (Log
+
Log A +
Log B +
Log ]
and
r =S =
[
− (Loga + a LogA + a LogB + a LogC )]
By minimizing residual sum of square as in (Ihueze, 2005, Ihueze, 2007) and
taking partial derivatives with respect to unknown constants, Loga
∂S
= −2
∂Loga
∂S
= −2
,
,
a and a
(y − Loga − a LogA − a LogB − a LogC )
(3.76)
(y − Loga − a LogA − a LogB − a LogC )LogA
(3.77)
∂S
= −2
∂a
(y − Loga − a LogA − a LogB −
)
(3.78)
∂S
= −2
∂a
(y − Loga − a LogA − a LogB −
)
(3.79)
The coefficients yielding the minimum sum of squares of the residuals are
obtained by setting the partial derivatives equal to zero and expressing in matrix
form as
log
+
log A + a
log B + a
log C =
y
(3.80)
122
log a
log A + a
log A + a
log a
log B + a
log A log B + a
log
log
log
+
log A log B + a
log
log B + a
+
log
log
log A log C =
log A y
(3.81)
log B log C =
log B y
(3.82)
+
log
=
log
(3.83)
By putting (3.80) – (3.83) matrix form
⎡
⎢∑
⎢∑
⎢
⎣∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
⎤
⎥
⎥
⎥
⎦
The solution of matrix system of (3.84) gives values for
∑
⎡
∑
=⎢
⎢∑ Log
⎣ ∑ Log
−
⎤
⎥ (3.84)
⎥
⎦
and
which represents the unknowns of equation (3.75).
So far efforts have been made to establish a power law model that represents
the nonlinear responses of an experimental parameter. Notably, complex
engineering problems can be analyzed to give multiple regression equation that
describes either a linear or a nonlinear behavior; the equation gives the response in
terms of the several independent variables of the problem. If the responses are
plotted as a function of
,
, etc, a response surface is obtained; this Response
123
Surface Method is a powerful procedure that employs factorial analysis to
determine the optimum operating condition (Dieter, 2000). Since a design seeks
for an optimal outcome, this study adopted the power law model in the
implementation of RSM to optimize the response of interest. The two objectives of
RSM are:
 To determine with one experiment where to move in the next experiment so
as to continually seek out the optimal point on the response surface
 To determine the equation of the response surface near the optimal point.
The response surface methodology can be applied with the design expert 8
software employing the central composite design and optimal response. RSM starts
by initially performing a fit of multiple linear regression model to data and finally
fitting nonlinear regression model when optimum is reached.
3.5.2.3 Implementation of Response Surface Methodology (RSM): In the
practical application of RSM it is necessary to develop an approximating model for
the true response surface. The underlying true response surface is typically driven
by some unknown physical mechanism. The approximating model is based on
observed data from the process or system and is an empirical model. Multiple
regression techniques were useful for building the types of empirical models
required in RSM. Applications of RSM were sequential in nature and are
implemented in three phases.
124
Phase 1: At first some ideas are generated concerning which factors or variables
are likely to be important in response surface study. It is usually called a screening
experiment. The objective of factor screening is to reduce the list of candidate
variables to a relatively few so that subsequent experiments will be more efficient
and require fewer runs or tests. The purpose of this phase is the identification of
the important independent variables.
Phase 2: The study determined if the current settings of the independent variables
result in a value of the response that is near the optimum. This phase of RSM
makes considerable use of the first-order model and an optimization technique
called the method of steepest ascent (descent).
Phase 3: Phase 3 begins when the process is near the optimum. At this point the
study wants a model that will accurately approximate the true response function
within a relatively small region around the optimum. Because the true response
surface usually exhibits curvature near the optimum, a second-order model (or
perhaps some higher-order polynomial) was used. Once an appropriate
approximating model has been obtained, this model may be analyzed to determine
the optimum conditions for the process. This sequential experimental process is
performed within some region of the independent variable space called the
operability region or experimentation region or region of interest.
125
3.5.3 Analysis of displacement and stress distributions in PFRP
3.5.3.1 Finite Element Analysis (FEA)
The analysis of stress within a body implies the determination at each point
of the body of the magnitudes of stress components. In other words, it is the
determination of the internal distribution of stresses. A finite element model of the
plantain fiber reinforced polyester was basically formed by subdividing the sample
into triangular sub regions as shown in figure 3.13, each of these forms a single
triangular element which is a finite segment having a cross sectional area A and
Young’s modulus E. The triangles have straight sides and are defined by nodal
points at their vertices. The triangle vertices are defined by nodes 1, 2 and 3 with
coordinates ( ,
), ( ,
) and ( ,
).
,
3
y, v
,
1
2
1.0
,
x, u
Figure 3.13.
Subdivision of plate into triangular elements
In the derivation of Finite element models, numerical approach of linear
interpolation and principles of virtual work are employed. The principle states that
126
the total virtual work done by all the forces acting on a system in static equilibrium
is zero for a set of infinitesimal virtual displacements from equilibrium. The virtual
work is thus the work done by the virtual displacements, which can be arbitrary,
provided they are consistent with the constraints of the system. The finite element
method is probably the most commonly used numerical analysis technique in
mechanical engineering design and usually applied in the finite element stress
analysis. Interpolation function relates displacement of a point in the element to its
geometry and contributes to the system of equations of those terms needed to
evaluate displacement of all the modes in the model (Ihueze, 2005). The steps
involved in finite element analysis according to Astley (1992) and Ihueze (2005)
includes:
 Element definition (element topology): types of element to be used are
decided and nodes defined, properties such as, elastic modulus, E, poisson’s
ratio µ and density of element ρ are defined for the element, it may have
triangular, beam, rod, bar, rectangular, curvilinear and quadrilateral
elements. For this study linear triangular elements are employed
 Interpolation of elements displacement: The displacement field within the
element is interpolated using values of displacement at the nodes. These are
ordered
sequentially
for
the
model;
Interpolation
functions
are
approximations to the behavior of an element.
127
Astley (1992) and Ihueze (2005) expressed the general interpolation polynomial
adapted in the finite element modeling as;
=
+
+
Where
to
y+
+
+
+⋯
(3.85)
are polymonial coefficients or shape constants when applied to
finite elements. (x,y) are nodal coordinates for two-dimensional elements. Number
of constants or coefficients equals number of element nodes and equals number of
polynomial expressions to solve for
. For two-dimensional triangular elements i
= 1, 2 and 3. When displacement of nodal points is assumed to be linear, the
general polynomial expression (3.85) reduces to.
=
+
+
(3.86)
So for a triangular element having u and v components of displacement (two
degrees of freedom), the horizontal and vertical components of displacement can
be predicted with the following polynomials.
=
+
+
=
+
+
-
,
(3.87)
(3.88)
are arbitrary constants related to element geometry and called shape
constants. On assumption of linear displacement when u and v are associated with
128
the nodal points (
, ), (
, ), (
, ), a relationship for the displacements at
each node is expressed as:
+
+
+
+
+
+
+
+
+
+
+
+
=
=
=
=
=
=
(3.89)
Equation (3.89) Shows that the numbers of unknown polynomial coefficient
are equal to the numbers of nodes defining the topology of the element; for
triangular element of 3 nodes, the designer have
and
and
,
,
for
,
,
,
,
to interpolate
,
,
. Equation (3.89) expressed in matrix form
gives
⎡
⎢
⎢
⎢
⎢
⎣
1
⎡
⎤
1
⎢
⎥
⎥ = ⎢1
⎥
⎢0
⎥
⎢0
⎦
⎣0
0
0
0
0
0
0
0 0 0
⎤
0 0 0 ⎡
⎥⎢
0 0 0⎥ ⎢
1
⎥⎢
⎥⎢
1
⎦⎣
1
⎤
⎥
⎥
⎥
⎥
⎦
(3.90)
Equation (3.90) is obtained by evaluating the interpolation polynomial at
each node and equating to the nodal displacements to form the system of
equations. Equation (3.90) marks the beginning of the formulation for the stiffness
of an element (Ihueze, 2005); it is a kind of shape function matrix and forms the
basis for generating the stiffness matrix for each element and eventually the whole
129
model. The boundary conditions which define a load case are in terms of specified
displacements of particular nodes and a system of applied forces. The stiffness
relates the reaction forces at each node with the displacements to form a system of
equations which can be solved by appropriate methods.
Formulation of element Shape function: The solution of (3.90) for shape
constants by crammers rule leads to the establishment of the shape function, so
representing equation 3.86 for nodes 1, 2, 3 in matrix form gives.
u
u
u
1 x
= 1 x
1 x
(3.91)
By determinant rule
det v
=
1
1
1
−
=
det
det
=
1
1
−
=
+
1
1
+
(3.92)
=
−
−
+
+
−
130
= (x
−x
) u + (x
det
=
(
−
)
+(
−
)
+(
det
=
(
−
)
+(
−
)
+ (
det
)u + (x
−x
)u
−x
(3.93)
Similarly
−
−
)
(3.94)
)
(3.95)
From row 2 of coefficient matrix,
det v = −
=
1
1
−
+x b +
1
1
−
c
(3.96)
From row 3 of coefficient matrix,
det v =
=
det
det
det
det
−
−x b +
, det
1
1
c
, and det
=
=
=
1
1
+
(3.97)
can now be reduced as
+
+
+
+
+
+
(3.98)
And by crammers rule
131
=
det
det v
=
1
(
det v
=
=
=
det
1
(
=
det v
det v
+
(
)
+
+
+
+
(3.99)
)
(3.100)
)
+
(3.101)
Combining equation (3.99) through (3.101) and rearranging grouping terms, gives
the u component of displacement as.
=
=
( , )
+
+
det v
+
( , )
+
+
+
+
det v
( , )
+
+
+
det v
(3.102)
Similarly, for v components of displacement
=
( , )
+
( , )
+
( , )
(3.103)
The shape function can then be expressed as
( , ) =
1
(
det v
+
+
)
(3.104)
Where i = 1,2,3
132
Equations (3.102) and (3.103) define displacement field interpolation within
each element in terms of its nodal (triangular vertices) variables. The universal
nature of elemental shape relationship (shape function matrix) is thus presented in
a matrix form by combination of (3.102) and (3.103) as
( , )
0
=
( , )
0
( , )
0
0
( , )
0
( , )
⎡
⎢
0
⎢
( , ) ⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎥
⎦
(3.105)
Equation 3.105 can be expressed as
(3.106)
=
Where
= (A column vector containing the displacement component at a point)
=
= (a shape matrix whose components are the shape functions of the element)
=
( , ),
( , ),
( , )
= (column vector containing the nodal displacements)
⎡
⎢
= ⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎥
⎦
133
= the superscript signifying a matrix or vector quantity which relates to a
particular element rather than to the system as a whole.
Evaluation of Strain-Displacement Matrix: The two dimensional strains,
and
,
are expressed in terms of nodal displacements using the knowledge of
(3.105) and (3.106) and applying the solid mechanics definition of strain.
=
=
+
+
,
(3.107)
=
=
+
+
,
(3.108)
=
+
=
+
+
,+
+
+
,
(3.109)
Rewriting these equations in matrix form, we obtain
⎡
= ⎢⎢ 0
⎢
⎣
0
0
0
0
0 ⎡
⎤⎢
⎥⎢
⎥⎢
⎥
⎦⎢
⎣
⎤
⎥
⎥
⎥
⎥
⎦
(3.110)
Evaluating equation 3.110 with equation 3.104 gives
=
b
0
c
b
0
c
b 0 0 0
0 c c c
c b b b
⎡
⎢
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎥
⎦
(3.111)
134
Equation (3.111) can be expressed as
=
=
(3.112)
And
= Strain displacement matrix and since all of the components of
are
constants, the strains are constant throughout the element by virtue of
(3.112). The element is for this reason frequently referred to as the ‘constant
strain triangle’ (CST).
NB:
Represents a column vector containing the components of strain,
represents column vector containing the nodal displacemenand
represents
the strain displacement matrix whose component are derivatives of the shape
function.
Evaluation of Stress-Strain relationships (D-Matrix or Modulus matrix): In
Plane strain analysis, it is assumed that the out-of-plane strain
stresses
and
is zero; the shear
are also taken to be zero; this is suited for component long in
the z-direction (Astley, 1992). The stress-strain relation referred to as D-matrix is
then derived by rewriting the general statement of Hooke’s law for a Cartesian
state of stress, this gives
=
−
−
+
(3.113)
135
=
−
0=
−
−
−
+
(3.114)
+
(3.115)
And
=
(1 + )
(3.116)
The axial stress
may be eliminated from equation (3.113) and (3.114)
using equation (3.115) and the remaining equations inverted to give,
=
(1 − )
(1 + )(1 − 2 )
+
=
(1 − )
(1 + )(1 − 2 )
+
=
1−
1−
−
1+
1−
(3.117)
−
1+
1−
(3.118)
(3.119)
2(1 + )
By putting the stress and strain in column vectors s and e we have
=
[ −
]
(3.120)
Where
=
, =
The stress-strain matrix (
,
(1 + )
= (1 + )
0
(3.121)
) also called modules or property matrix is given as
136
=
(1 − )
(1 + )(1 − 2 )
1
⁄(1 − )
0
⁄(1 − )
1
0
0
0
1
(1 − 2 ) (1 − )
2
(3.122)
Note that the thickness of the element in the z direction is not always clearly
defined in the case of plane strain, since the theory apply in principle to bodies
which are in determinately long. A definite value is required in all element
integrals and is conveniently taken to be unity in the absence of other information;
the plane strain analysis of this study follows the approach of Asteley (1992).
Evaluation of Stiffness matrix: The stiffness matrix relates the reaction forces at
each point (node) with the displacement to form a system of equations which can
be solved by crammers rule, Gauss-Jordan or Choleski-LU decomposition method.
The computational relation for element stiffness matrix
=∫ (
is expressed thus:
)
(3.123)
For an element
=
V
(3.123)
=
element volume
=
element stiffness
Equivalent Nodal Forces: The nodal forces at the nodes are due to thermal load
and the nodal reaction due to temperature changes is expressed as
137
=
(3.124)
Following usual finite element formulation when the temperature change is
uniform over the element,
=
(3.125)
Where
A
=
thickness of element
=
Area of element
=
thermal load vector
The body force vector is estimated by
=∫ (
Where
)
(3.126)
= body force per unit volume
Assembly: To find the global equation system for the whole solution region, all the
element equations must be assembled. In other words local element equations for
all elements used in discretization should be combined. Element connectivities are
used for the assembly process; however, before solution boundary conditions
(which are not accounted in element equations) should be imposed. In theory, these
local element equations can be expanded as algebraic expression and simply added
138
together. However it is more practical and sensible to maintain the notation of
expression (3.105) and to extend it to the whole specimen. A simple algorithm
termed ‘assembly’ then emerges which performs the required summations as
shown in equation (3.128).
χ =
−
∑
χ =
,
,
−
+
(3.127)
+
(3.128)
are now the stiffness matrix, nodal force vectors and nodal
displacement vector for the assembled system respectively. The term
,
,
are
obtained by incrementing them one element at a time.
3.5.4 Non destructive testing and microscopic characterization
3.5.4.1
Scanning Electron Microscope (SEM)
The scanning electron microscope is essentially a large vacuum tube with
the sample placed inside. The electrons in the vacuum tube are generated from a
heated filament and driven by a high voltage to the sample, which is conductive or
which has been made conductive by coating with a conductive material. The SEM
generates an image of the sample from this electron beam. The Morphology of the
composites was therefore examined by using ZEISS Scanning Electron
Microscope.
139
Figure 3.14. ZEISS Scanning Electron Microscope (Sheda Science and
Technology Complex (SHESTCO), 2012)
The samples were coated with silver prior to examination under the electron
beam, the samples were then placed inside the Scanning Electron Microscope
(SEM) (Zeiss EVO MA10 Carl Zeiss SMT AG, Germany) and micrographs were
taken at a magnification of 100, 500 and 1000 µm. An operating voltage 30 KV
and magnification of 245X magnification are used. The computer-assisted
SEM/EDS analysis was performed on both plantain empty fruit bunch fiber
reinforced composites (PEFBFRC) and plantain pseudo stem fiber reinforced
composites (PPSFRC). The specific operational settings of Zeiss EVO MA10
restricted detection to 4000 particles and 28 elements: Sodium (Na), Magnesium
(Mg), Aluminum (Al), Silicon (Si), Sulfur (S), Chlorine (Cl), Calcium (Ca),
Titanium (Ti), Chromium (Cr), Manganese (Mn), Iron (Fe), Nickel (Ni), Copper
(Cu), Zinc (Zn), Bromine (Br), Strontium (Sr), Zirconium (Zr), Silver (Ag), Tin
(Sn), Antimony (Sb), Barium (Ba), Tungsten (W), Gold (Au) and Mercury (Hg).
Carbon (C), Potassium (K)
140
SEM/EDS were thus used to determine the surface elemental composition.
The typical sample size that can be accommodated within the chamber of the SEM
is a maximum of a few cubic centimeters. This small sample size necessitates the
sectioning of larger samples. For imaging purposes, the sample must be conductive
or made conductive by coating with a thin layer of gold. The EDS testing is
performed in accordance with ASTM E1508.
3.5.4.2
Fourier Transform Infra Red Spectroscopy (FTIR)
FT-IR 8400S spectrophotometer by Shimadzu was used to acquire IR
spectra of plantain fiber and composites. It has peak-to-peak signal/noise ratio of
20000:1. FTIR-8400S is combined with the IRsolution - a 32 bit high performance
FTIR software - to analyze the samples easily and securely. The untreated plantain
fibers, treated plantain fibers, plantain empty fruit bunch fiber reinforced
composites and plantain stem fiber reinforced composites were characterized by
the FTIR spectrometer based on ASTM E1252. FT-IR spectra are recorded in a
range of 4000 - 400 cm−1 at a resolution of 4 cm−1. The Purpose was to identify
the primary component of the plantain fiber reinforced composite and plantain
fibers material. Matching the unknown infrared spectrum to known spectra was
done manually from the plots.
This instrument transmits an infrared light through a sample and varies the
wavelength of the light as it records how much light is absorbed at each
wavelength. FTIR can identify the difference between materials which are made of
only carbon and hydrogen but have different types of bonds between the elements.
141
The results are typically plotted as a spectrum with frequency on the X-axis and
absorption on the Y-axis.
Figure 3.15. FT-IR 8400S spectrophotometer by Shimadzu (Redeemers
University (RUN), 2012)
3.5.4.3
Nitrogen Adsorption and Desorption Isotherms (NAD)
Determination of Nitrogen Adsorption and Desorption Isotherms was
performed as per ASTM D4222 - 03(2008) Standard Test Method. The test method
covers the determination of nitrogen adsorption and desorption isotherms of fibers
at the boiling point of liquid nitrogen. A static volumetric measuring system is
used to obtain sufficient equilibrium adsorption points on each branch of the
isotherm to adequately define the adsorption and desorption branches of the
isotherm.
142
Figure 3.16: BET Surface Area Analyzer (University of Pannonia, Veszprem,
Hungary, 2012).
Brunauer, Emmett and Teller (BET) surface area measurement techniques
was used to measure the surface area and porosity of plantain fibers. Molecules of
an adsorbate gas are physically adsorbed onto the particle surfaces, including the
internal surfaces of any pores, under controlled conditions within a vacuum
chamber. An adsorption isotherm is obtained by measuring the pressure of the gas
above the sample as a function of the volume of gas introduced into the chamber.
The linear region of the adsorption isotherm was then used to determine the
volume of gas required to form a monolayer across the available particle surface
area using BET theory.
BET theory aims to explain the physical adsorption of gas molecules on the
plantain fiber surface and serves as the basis for an important analysis technique
143
for the measurement of the specific surface area of the material. The concept of
the theory is an extension of the Langmuir theory, which is a theory for monolayer
molecular adsorption, to multilayer adsorption. The resulting BET equation is
expressed as:
1
=
−1
+
1
(3.129)
−1
and
are the equilibrium and the saturation pressure of adsorbates at the
temperature of adsorption,
units), and
is the adsorbed gas quantity (for example, in volume
is the monolayer adsorbed gas quantity.
is the BET constant,.
Equation (1) is an adsorption isotherm and can be plotted as a straight line with
on the y-axis and ∅ =
on the x-axis according to experimental results.
This plot is called a BET plot. The linear relationship of this equation is
maintained only in the range of 0.05 <
the y-intercept
quantity
< 0.35. The value of the slope
and
of the line are used to calculate the monolayer adsorbed gas
and the BET constant .
144
CHAPTER FOUR
DATA ANALYSIS AND DISCUSSION
4.1
Experimental Design and Parameter Optimization: Tensile Strength
4.1.1 Taguchi experimental design based on the L9 (33) design
In this section the tensile strengths of plantain fiber reinforced polyester
were investigated for optimum reinforcement combinations employing Taguchi
methodology. The signal to noise ratio and mean responses associated with the
dependent variables of this study are evaluated and presented. Traditional
experimentation on replicate samples of empty fruit bunch fiber reinforced
composite and plantain pseudo stem fiber reinforced composites were used to
obtain the value of quality characteristics using different levels of control factors as
in table 4.1.
Table 4.1: Experimental outlay and variable sets for mechanical testing
S/N
PROCESSING FACTORS
LEVEL
I
II
III
A: Volume fraction (%)
10
30
50
1
2
B: Aspect Ratio (lf/df)
10
25
40
3
C: Fiber orientations (Degree)
±30
±45
±90
Table 4.2 and table 4.3 show Taguchi DOE orthogonal array and Design
matrix implemented for the larger the better signal to noise ratio (SN ratio)
respectively.
145
Table 4.2: Taguchi Standard Orthogonal array L9
Experiment
Parameter
Parameter
Parameter
Number
1:A
2:B
3:C
1
1
1
1
1
2
2
2
1
3
3
3
2
1
2
4
2
2
3
5
2
3
1
6
3
1
3
7
3
2
1
8
3
3
2
9
Parameter
4:D
1
2
3
3
1
2
2
3
1
The tensile test signal-to-noise ratio for plantain empty fruit bunch fiber
reinforced polyester composite is calculated with (3.63) using values of various
experimental trials and presented as in table 4.3 so that for first experiment,
SNratio
= −10 × log
1
1
1
1
+
+
3 (19.24679487)
(21.79487179)
(20.52083333 )
= 26.21
Equation (3.64) is used in the computation of the mean standard deviation (MSD)
as recorded in table 4.3.
146
Table 4.3: Experimental design matrix for tensile test using composite made
from plantain pseudo-stem fiber reinforced polyester composite (ASTM-638)
A:
B:
C:
Expt. Volume Aspect
Fiber
No. fraction Ratio orientations
(%)
(lf/df)
(± degree)
1
2
3
4
5
6
7
8
9
10
10
10
30
30
30
50
50
50
10
25
40
10
25
40
10
25
40
30
45
90
45
90
30
90
30
45
Specimen replicates
tensile response (MPa)
Trial
#1
Trial
#2
Trial
#3
19.25
18.93
21.75
23.80
34.52
25.00
31.33
37.72
28.24
21.80
18.85
20.03
25.31
32.37
22.76
34.94
37.18
28.86
20.52
18.89
20.89
24.55
33.45
23.88
33.13
37.45
28.55
Mean
ultimate
tensile
response
(MPa)
20.52
18.89
20.89
24.55
33.45
23.88
33.13
37.45
28.55
MSD
SNratio
0.0024
0.0028
0.0023
0.0017
0.0009
0.0018
0.0009
0.0007
0.0012
26.21
25.52
26.38
27.79
30.48
27.54
30.38
31.47
29.11
Similarly, the tensile test signal-to-noise ratio for plantain pseudo-stem fiber
reinforced polyester composite is calculated with (3.63) using values of various
experimental trials and presented as in table 4.4 so that for first experiment,
SNratio
= −log
1
1
1
1
+
+
3 (31.63461538)
(23.22115385)
(27.42788462 )
= 28.56
Also, Equation (3.64) was utilized in the computation of the mean standard
deviation MSD as recorded in table 4.4.
147
Table 4.4: Experimental design matrix for tensile test using composite made
from plantain empty fruit bunch fiber reinforced polyester composite (ASTM638)
A:
Volume
fraction
(%)
B:
Aspect
Ratio
(lf/df)
C:
Fiber
orientations
(± degree)
Specimen replicates
tensile response
(MPa)
Trial Trial Trial
#1
#2
#3
Mean
ultimate
tensile
response
(MPa)
1
10
10
30
31.63 23.22 27.43
2
10
25
45
3
10
40
4
30
5
Expt.
No.
MSD
SNratio
27.43
0.0013
28.56
17.74 17.79 17.76
17.76
0.0031
24.99
90
21.75 23.13 22.44
22.44
0.0019
27.01
10
45
29.47 31.01 30.24
30.24
0.0010
29.61
30
25
90
39.90 41.11 40.51
40.50
0.0006
32.15
6
30
40
30
26.60 28.67 27.64
27.64
0.0013
28.82
7
50
10
90
40.14 34.54 37.34
37.34
0.0007
31.39
8
50
25
30
37.48 37.08 37.28
37.28
0.0007
31.43
9
50
40
45
30.85 32.28 31.56
31.56
0.0010
29.98
Taguchi approach uses a simpler graphical technique to determine which
factors are significant. Since the
experimental design is orthogonal it is possible
to separate out the effect of each factor. This is done by companioning the Taguchi
orthogonal matrix and the experimental responses as in table 4.5 and calculating
the average SN ratio (
) and mean (
) responses for every factor at each
of the three test levels as summarized in tables 4.6 and 4.7.
148
Table 4.5: Evaluated quality characteristics, signal to noise ratios and
orthogonal array setting for evaluation of mean responses of PEFB
Experiment Factor Factor Factor Mean ultimate
number
A
B
C
tensile response
(MPa)
1
1
1
27.43
1
1
2
2
17.76
2
1
3
3
22.44
3
2
1
2
30.24
4
2
2
3
40.50
5
2
3
1
27.64
6
3
1
3
37.34
7
3
2
1
37.28
8
3
3
2
31.56
9
SNratio
28.56
24.99
27.01
29.61
32.15
28.82
31.39
31.43
29.98
Figures 4.1 - 4.4 are the excel graphics for SN ratio and mean tensile
strength of plantain empty fruit bunch and pseudo stem fiber reinforced composites
based on Larger is better quality characteristics.
Table 4. 6: Response Table for SN ratio and mean tensile strength of plantain
empty fruit bunch fiber reinforced composites based on Larger is better
quality characteristics
Level
1
2
3
Delta
Rank
Signal –to- Noise Ratios
A:
B:
C:
Volume Aspect
Fiber
Fraction
Ratio Orientations
(%)
(lf/df)
(± degree)
26.85
29.85
29.60
30.19
29.52
28.19
30.93
28.60
30.18
4.08
1.25
1.99
1
3
2
Means of quality characteristic
A:
B:
C:
Volume
Aspect
Fiber
Fraction
Ratio
Orientations
(%)
(lf/df)
(± degree)
22.54
31.67
30.78
32.79
31.85
26.52
35.40
27.21
33.43
12.85
4.64
6.90
1
3
2
149
Table 4. 7: Response Table for SN ratio and mean tensile strength of plantain
pseudo stem fiber reinforced composites based on Larger is better quality
characteristics
Signal -to -Noise Ratios
Means of quality characteristics
Level
A:
B:
C:
A:
B:
C:
Volume Aspect
Fiber
Volume Aspect
Fiber
Fraction
Ratio Orientations Fraction
Ratio
Orientations
(%)
(lf/df)
(± degree)
(%)
(lf/df)
(± degree)
1
26.04
28.13
28.41
20.10
26.07
27.28
2
28.60
29.16
27.48
27.29
29.93
24.00
3
30.32
27.68
29.08
33.04
24.44
29.16
Delta
4.28
1.48
1.60
12.95
5.49
5.16
Rank
1
3
2
1
2
3
The average SN ratios and mean of means for the response tables are plotted
against test levels for each of the three control parameters. In tables 4.6 - 4.7 it is
found that factor A which is the volume fraction of fibers has a stronger effect on
SN ratios and mean of means than the other two control factors and hence more
significant than other two control factors. The response tables for means and SN
ratios show that the volume fraction has the highest contribution in the composite
tensile strength, followed with fiber orientation as depicted in figure 4.1 - 4.4.
150
40
35
Mean of means
30
25
20
A
15
B
C
10
5
0
0
1
2
3
4
factor levels-PEFBFRC
Figure 4.1: Main effect plots for means-PEFBFRC
31.5
31
30.5
SNratio
30
29.5
29
A: Volume Fraction (%)
28.5
B: Aspect Ratio (lf/df)
28
C: Fibre Orientations ± degree)
27.5
27
26.5
0
1
2
Factor levels-PEFBFRC
3
4
Figure 4.2: Main effect plots for signal-noise ratio-PEFBFRC
151
35
30
Mean of means
25
20
A
15
B
C
10
5
0
0
1
2
3
4
level of factors-PPS
Figure 4.3: Main effect plots for means-PPS
31
30.5
30
29.5
SNratio
29
28.5
A: Volume Fraction (%)
28
B: Aspect Ratio (lf/df)
27.5
C: Fibre Orientations ± degree)
27
26.5
26
25.5
0
1
2
3
4
Factor levels-PPS
Figure 4.4: Main effect plots for signal-noise ratio-PPS
152
Estimation of expected tensile responses based on optimum settings:
According to Radharamanan and Ansui (2001), the expected response is estimated
using the optimum control factor setting from the main effects plots; by employing
the response table for signal to noise ratio and the response table for mean, the
expected response model is as in the following equation:
EV = AVR + Aopt − AVR + Bopt − AVR + Copt − AVR + ⋯ + (nth
opt −
AVR)
Where, EV = expected response, AVR = average response, Aopt = mean value of
response at optimum setting of factor A, Bopt = mean value of response at optimum
setting of factor B, Copt = mean value of response at optimum setting of factor C, so
that for the empty fruit bunch and from figures 4.1 and 4.2 and table 4.6:
EVEFB Tensile = 30.2 + (35.4 − 30.2) + (31.85 − 30.02) + (33.43 − 30.2) =
40.28MPa
The expected responses is similarly computed for pseudo stem and presented in
table 4.8.
153
Table 4.8: Optimal setting of control factors and expected optimum strength
of composites
Control
Optimum Optimal
Expected optimum
Composite
factor
level
setting
strength
A
3
50
40.28 MPa
Empty fruit bunch
fiber reinforced
B
1
10
composites
C
3
90
A
3
50
38.51 MPa
Pseudo stem fiber
B
2
25
reinforced composites
C
3
90
4.1.2 Response surface optimization of tensile strength based on power law
model
Although Taguchi's approach towards robust parameter design as presented
in section 4.1.1 has introduced innovative techniques to obtain optimal parameter
setting for optimum tensile response, however, few concerns regarding this
philosophy have been identified. Some of these concerns are related to the absence
of the means to test for higher-order control factor interactions. For these reasons,
other approaches to carry out robust parameter design have been suggested which
includes RSM. The RSM technique has an edge over the Taguchi technique in
terms of significance of interactions and square terms of parameters. In this
section, the optimum condition determined by the Taguchi methodology was
considered in setting design points for the RSM. This further optimization using
RSM showed significant improvements in tensile response.
154
4.1.2.1
(a)
Curve fitting and linearization of experimental responses
Plantain Empty Fruit Bunch fiber reinforced composites (PEFB): The
multilinear regression equation of Plantain Empty Fruit Bunch fiber reinforced
composites (PEFB) is obtained through linearization of the power law model of
equation (3.75) using table 4.4 to obtain table 4.9 and expressing equation (3.74) as
Log yEFB = 1.05 + 0.297 log A - 0.102 log B + 0.085 log C
(4.1)
And also expressing equation (3.75) as
yEFB = 11.220*(A^0.297)*(B^- 0.102)*(C^0.085)
(4.2)
Table 4. 9: Linearization table for power law model response of PEFB
A B C PEFB TENSILE
log A
log B
log C
STRENGTH (y)
10 10 30
27.43
1
1
1.477
10 25 45
17.76
1
1.398
1.653
10 40 90
22.44
1
1.602
1.954
30 10 45
30.24
1.477
1
1.653
30 25 90
40.50
1.477
1.398
1.954
30 40 30
27.64
1.477
1.602
1.477
50 10 90
37.34
1.699
1
1.954
50 25 30
37.28
1.699
1.398
1.477
50 40 45
31.56
1.699
1.602
1.653
SUM TOTAL
12.528
12
15.250
(b)
log y
1.438
1.2496
1.351
1.481
1.607
1.441
1.572
1.571
1.499
13.211
Plantain Pseudo Stem fiber reinforced composites (PPS): The multilinear
regression equation of Plantain Pseudo Stem fiber reinforced composites (PPS) is
obtained through linearization of the power law model of equation (3.75) using
table 4.3 to obtain table 4.10 and expressing (3.74) as
155
Log yPPS = 0.865 + 0.300 log A - 0.0156 log B + 0.092 log C
(4.3)
And then expressing equation (3.75) as
yPPS = 7.328245331*(A^0.3)*(B^-0.0156)*(C^0.092)
Table 4.10: Linearization table for power law model response of PPS
A
B
C
STEM TENSILE
log A
log B
log C
STRENGTH (y)
10
30
20.521
1
1
1.477
10
25
45
18.886
1
1.398
1.653
10
40
90
20.889
1
1.602
1.954
10
10
45
24.551
1.477
1
1.653
30
25
90
33.445
1.4771
1.398
1.954
30
40
30
23.878
1.477
1.602
1.477
30
10
90
33.133
1.699
1
1.954
50
25
30
37.451
1.699
1.398
1.477
50
40
45
28.550
1.699
1.602
1.653
50
SUM TOTAL
12.528
12
15.254
4.1.2.2
(4.4)
log y
1.312
1.276
1.320
1.3901
1.524
1.3780
1.520
1.573
1.456
12.750
Evaluation of Tensile Strength of Plantain Empty Fruit Bunch
(EFB) Fiber Reinforced Composites
The power law model of equation (4.2) is used to establish the responses of
the central composite design of table 4.12 generated with the control factor levels
of table 4.11 using response surface methodology platform of Design expert8
software.
156
Table 4.11: Factors for response surface study
S/N
PROCESSING FACTORS
Low Level (-1)
High Level (+1)
1
A: Volume fraction (%)
10
50
2
B: Aspect Ratio (lf/df)
10
40
3
C: Fiber orientations (± degree)
30
90
Table 4.12: Matrix of central composite design for optimization of tensile
strength of PEFB composites
Std Run Block
Factor 1
Factor 2
Factor 3
Response 1
A:
B:
C:
PEFB
Volume
Aspect Ratio
Fiber
Tensile
fraction
(lf/df)
orientations
strength
(%)
(± degree)
(MPa)
12
1
Day 1
30
25
60
31.42
11
2
Day 1
30
25
60
31.42
7
3
Day 1
10
40
90
22.37
2
4
Day 1
50
10
30
37.85
1
5
Day 1
10
10
30
23.47
4
6
Day 1
50
40
30
32.87
10
7
Day 1
30
25
60
31.42
9
8
Day 1
30
25
60
31.42
3
9
Day 1
10
40
30
20.38
6
10 Day 1
50
10
90
41.56
5
11 Day 1
10
10
90
25.77
8
12 Day 1
50
40
90
36.08
20
13 Day 2
30
25
60
31.42
17
14 Day 2
30
25
90
32.53
15
15 Day 2
30
10
60
34.50
13
16 Day 2
50
25
60
36.57
18
17 Day 2
30
25
110
33.09
14
18 Day 2
64
25
60
39.29
16
19 Day 2
30
50
60
29.27
19
20 Day 2
30
25
60
31.42
157
The standard error of design describes the spread within the regression or
line of best fit while the standard deviation value of 0.22 presented in table 4.14
describes the spread around the mean of the predicted tensile strength values. The
standard error of design of the experiment was found to be of range 0.5 and 1.5
with optimum of about 0.5 as shown in figure 4.5 and this is found to vary
Std Error of Design
parabolically with volume fraction of fibers and aspect ratio of fibers.
0.000
0.200
0.400
0.600
0.800
10.00
1.000
40.00
18.00
34.00
26.00
28.00
34.00
22.00
42.00A:
16.00
B: B: Aspect Ratio (lf/df)
10.00
A: Volume fraction
50.00
Figure 4.5: Depiction of standard error of design as a function of control
factors
The table 4.13 Model F-value of 1241.73 implies the model is significant.
There is only a 0.01% chance that this large value could occur due to noise.Values
of "Prob > F" less than 0.0500 indicate model terms are significant. In this case A,
B, C, AB, AC, A2, B2, C2 are significant model terms. Values greater than 0.1000
indicate the model terms are not significant.
158
Table 4.13: Analysis of variance (ANOVA) for RSM optimization of PEFB
tensile strength
Source
Sum of
Df Mean
F
p-value
Decision
Squares
Square
Value
Prob > F
Block
Model
A: Volume fraction
B: Aspect Ratio
(lf/df)
C: Fiber orientations
AB
AC
BC
A^2
B^2
C^2
Residual
Lack of Fit
Pure Error
Cor Total
43.4205
528.1725
413.8312
49.25673
1
9
1
1
43.4205
58.68583
413.8312
49.25673
16.70956
1.97932
0.864861
0.07832
16.91943
2.211964
0.696279
0.425353
0.425353
0
572.0184
1
1
1
1
1
1
1
9
5
4
19
16.70956
1.97932
0.864861
0.07832
16.91943
2.211964
0.696279
0.047261
0.085071
0
1241.728
8756.212
1042.218
< 0.0001
< 0.0001
< 0.0001
353.5558
41.88023
18.2995
1.657162
357.9964
46.80272
14.73251
< 0.0001
0.0001
0.0021
0.2301
< 0.0001
< 0.0001
0.0040
Significant
From table 4.14 the "Pred R-Squared" of 0.9939 is in reasonable agreement
with the "Adj R-Squared" of 0.9984. "Adeq Precision" measures the signal to noise
ratio. A ratio greater than 4 is desirable. The ratio of 131.814 indicates an
adequate signal. This model can be used to navigate the design space.
Table 4.14: Goodness of fit and regression statistics
Std. Dev.
0.217397
R-Squared
0.999195
Mean
31.70755
Adj R-Squared
0.998391
C.V. %
0.685632
Pred R-Squared 0.99386
PRESS
3.245525
Adeq Precision
131.8135
159
The response surface models in terms of coded and actual factors are in
equations (4.5) and (4.6). Both models show that volume fraction has the highest
effect on the tensile response. Also interaction effects are shown to be significant;
both main and high order effects were also depicted.
Final Equation in Terms of Coded Factors:
PEFB Tensile strength = +31.43+7.04 * A-2.17* B+1.41 * C-0.50 * A * B+0.33*
A * C-0.099* B * C-1.51* A2+0.52* B2-0.31* C2
(4.5)
Final Equation in Terms of Actual Factors:
PEFB Tensile strength = +17.88566+0.58711* A-0.19727* B+0.077069* C1.65803E-003* A* B+5.47995E-004 * A* C-2.19876E-004* B * C-3.77483E003* A2+2.31076E-003* B2-3.40420E-004* C2
(4.6)
The residuals from the least squares fit play an important role in judging
model adequacy. By using Goodness of fit, regression statistics and constructing a
normal probability plot of the residuals, a check was made for the normality
assumption, as given in Table 4.14 and Figure 4.6, the normality assumption was
satisfied as the residual plot approximated along a straight line; the R-Squared
value indicates that 99.9% variation in strength was due to independent Variable,
only about 0.01% cannot be explained by the model, so it is concluded that the
empirical model is adequate to describe the material strenght by response surface.
160
Predicted vs. Actual
45.00
Predicted
40.00
35.00
2
4
30.00
25.00
20.00
20.00
25.00
30.00
35.00
40.00
45.00
Actual
(a)
Normal Plot of Residuals
99
Normal % Probability
95
90
80
70
50
30
20
10
5
1
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Internally Studentized Residuals
(b)
161
Externally Studentized Residuals
Externally Studentized Residuals
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
1
4
7
10
13
16
19
Run Number
(c)
Figure 4.6. a, b, c: Residual plots normal distribution of data
The graphics of figures 4.7, 4.8 and 4.9 show clearly the interaction effects
of factors, optimum level of factors as well as the optimum value of tensile
strength of PEFB composite. The contour plots of figure 4.7 as well as 3D plots of
figures 4.8 show the interaction effects of factors and the optimum value of tensile
strength as 41.680MPa and optimum combination of factors as 50%, 10mm/mm
and 90degree. The cube plot of figure 4.9 and overlay plot of figure 4.10 show also
the optimal value of tensile strength for optimum combination of factors.
162
PEFB Tensile strenght
40.00
B: B: Aspect Ratio (lf/df)
34.00
25
28.00
27.0447
30
35
22.00
37.8669
Prediction
Observed
X1
X2
16.00
41.6804
41.5628
40
50.00
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: A: Volume fraction
(a)
PEFB Tensile strenght
90.0 0
Prediction
Observed
X1
X2
84.0 0
C: C: Fibre orientations
78.0 0
41.6804
41.5628
50.00
90.00
40
72.0 0
66.0 0
60.0 0
30
27.0447
35
37.8669
54.0 0
48.0 0
25
42.0 0
36.0 0
30.0 0
10.00
18.00
2 6.00
34.00
42.00
50.00
A: A: Volume fraction
(b)
163
PEFB Tensile strenght
90.00
84.00
C: C: Fibre orientations
78.00
Prediction
Observed
X1
X2
40
41.6804
41.5628
10.00
90.00
72.00
39.1971
66.00
37.8669
60.00
35.9993
54.00
35
48.00
42.00
34.0541
36.00
33.3525
30.00
10.00
16.00
22.00
28.00
34.00
40.00
B: B: Aspect Ratio (lf/df)
(c)
Figure 4.7 a, b and c: contour plot depiction of interaction effects of factors
Design points above predicted value
Design points below predicted value
4 1 .6 8 0 4
PEFBTensile strenght
45
X1 = B: B: Aspect Ratio (lf/df) = 10.00
X2 = C: C: Fibre orientations = 90.00
40
35
30
25
20
40.00
90.00
84.00
78.00
72.00
66.00
60.00
54.00
48.00
42.00
36.00
C: C: Fibre orientations
30.00
34.00
28.00
22.00
B: B: Aspect Ratio (lf/df)
16.00
10.00
(a)
Design points below predicted value
41.6804
45
PEFB Tensile strenght
X1 = A: A: Volume fraction = 50.00
X2 = B: B: Aspect Ratio (lf/df) = 10.00
40
35
30
25
20
50.00
42.00
40.00
34.00
34.00
28.00
26.00
22.00
18.00
16.00
B: B: Aspect Ratio (lf/df)
10.00
A: A: Volume fraction
10.00
(b)
164
Design points above predicted value
Design points below predicted value
41.6804
PEFB Tensile strenght
45
X1 = A: A: Volume fraction = 50.00
X2 = C: C: Fibre orientations = 90.00
C: C:
40
35
30
25
20
90.00
84.00
78.00
72.00
66.00
60.00
54.00
48.00
42.00
Fibre orientations
36.00
30.00
50.00
42.00
34.00
26.00
18.00
10.00
A: A: Volume fraction
(c)
Figure 4.8 a, b and c: 3Depiction of response surface of and interaction effects
of factors
Figure 4.8 a-c show that the tensile strength increases with volume fraction
and that aspect ratio has least influence on the variability of tensile strength, it also
indicates that the tensile strength is optimum when volume fraction and fiber
orientation are at their maximum settings (50% and 90degree) and aspect ratio on
its lowest setting (10mm/mm). The tradeoffs can be seen from the overlay plot for
better understanding of the process, the designer can estimate from the overlay plot
of figure 4.10 that volume fraction should be at high level while fibers aspect ratio
is designated for at low level and fiber orientation should be around the upper
level.
165
Cube
PEFB Tensile strenght
22.4029
2
20.4287
B: B: Aspect Ratio (lf/df)
B+: 40.00
36.1477
32.8583
6
Prediction
25.9459
41.6804
41.6804
C+: 90.00
C: C: Fibre orientations
B-: 10.00
C-: 30.00
23.576
37.9953
A-: 10.00
A+: 50.00
A: A: Volume fraction
Figure 4.9: cube plot depiction of EFB composite optimum strength
Design-Expert® Software
Factor Coding: Actual
Overlay Plot
Overlay Plot
40.00
PEFB Tensile strenght
Design Points
34.00
X1 = A: A: Volume fraction = 50.00
X2 = B: B: Aspect Ratio (lf/df) = 10.00
Actual Factor
C: C: Fibre orientations = 90.00
B: B: Aspect Ratio (lf/df)
Std # 6 Run # 10
28.00
22.00
16.00
PEFB Tensile 41.6804
X1
50.00
X2
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: A: Volume fraction
Figure 4.10: overlay plot depiction of optimal values for PEFB composite
The highest tensile strength was predicted in plantain EFB fiber reinforced
composite with 50% fiber content and processed at low aspect ratio (x2 = 10) and
high fiber orientation (x3 = 900). Statistical analysis also showed that fiber volume
166
fraction was the most significant impact factor on the plantain EFB fiber reinforced
composite tensile strength. It can be seen that the tensile strength increased with
increasing fiber content. It is well known that the use of reinforcement, e. g. fiber
in a thermoplastic matrix, increases the bio composite tensile and flexural strength
and modulus (Herrera-Franco et al. 1997; Ota et al. 2005). For example, Joseph et
al., (1999b) observed that the tensile strength of sisal fiber-PP composites with
10% fiber increased only by 1.7%, 20% fiber increased by 4.2%, 30% fiber
increased by 5.7%, 40% fiber increased by 10.6% compared with pure PP.
4.1.2.3
Evaluation of Tensile Strength of plantain pseudo stems (PPS)
Fiber Reinforced Composites
Similar analysis using power law model as in PEFBFRC were implemented
with table 4.11 and summarized as in table 4.15. Equation (4.4) is used in the
computation of the responses of different factors combinations.
Table 4.15: Experimental design matrix of central composite design for
optimization of tensile strength of PPS composites
Std Run Block
Factor 1
Factor 2
Factor 3
Response 1
A:
B:
C:
PSTEM
Volume Aspect Ratio
Fiber
Tensile
fraction
(lf/df)
orientations
Strength
(%)
(± degree)
(MPa)
3
1
Day 1
10
40
30
18.88
7
2
Day 1
10
40
90
20.88
1
3
Day 1
10
10
30
19.29
11
4
Day 1
30
25
60
28.18
4
5
Day 1
50
40
30
30.59
2
6
Day 1
50
10
30
31.26
167
6
10
5
12
8
9
16
19
15
13
14
20
18
17
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Day 1
Day 1
Day 1
Day 1
Day 1
Day 1
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
50
30
10
30
50
30
30
30
30
10
64
30
30
30
10
25
10
25
40
25
50
25
40
25
25
25
25
25
90
60
90
60
90
60
60
60
60
60
60
60
110
30
34.584
28.18
21.34
28.18
33.84
28.18
27.87
28.18
27.97
20.27
35.31
28.18
29.81
26.44
From table 4.16, the Model F-value of 1264.814 implies the model is
significant. There is only a 0.01% chance that a "Model F-Value" this large could
occur due to noise. Values of "Prob > F" less than 0.0500 indicate model terms are
significant. In this case A, B, C, AB, AC, A2, B2, C2 are significant model terms.
Values greater than 0.1000 indicate the model terms are not significant.
168
Table 4.16: Analysis of variance (ANOVA) for RSM optimization of PPS
tensile strength
Source
Sum of
df Mean
F
p-value
Decision
Squares
Square
Value
Prob > F
Block
Model
A-Volume fraction
B- Aspect Ratio (lf/df)
C-Fiber orientations
AB
AC
BC
A^2
B^2
C^2
Residual
Lack of Fit
Pure Error
Cor Total
5.336959 1
454.5217 9
419.1538 1
0.548199 1
19.8978 1
0.036379 1
0.793325 1
0.001654 1
15.28438 1
0.005101 1
0.905749 1
0.359359 9
0.359359 5
0 4
460.218 19
5.336959
50.50241
419.1538
0.548199
19.8978
0.036379
0.793325
0.001654
15.28438
0.005101
0.905749
0.039929
0.071872
0
1264.814
10497.55
13.72943
498.3329
0.9111
19.86852
0.041414
382.7915
0.127748
22.68412
< 0.0001
< 0.0001
0.0049
< 0.0001
0.3648
0.0016
0.8433
< 0.0001
0.7290
0.0010
Significant
The response surface models in terms of coded and actual factors are in
equations (4.7) and (4.8). Both models show that volume fraction has the highest
effects on the tensile response. Also interaction effects are shown to be significant.
Final Equation in Terms of Coded Factors:
PSTEM Tensile Strength =+28.17+6.33* A-0.26* B+1.38* C-0.067* A * B+0.31*
A * C-0.014* B * C-1.35 * A2-0.026* B2-0.33* C2
(4.7)
Final Equation in Terms of Actual Factors:
PSTEM Tensile Strength =+12.65395+0.49286* A-2.66786E-003* B+0.074802*
C-2.24781E-004* A * B +5.24843E-004* A * C-3.19492E-005* B * C-3.37427E003* A2-1.15348E-004* B2-3.65071E-004*C2
(4.8)
169
Figure 4.11 shows the optimal factors combination for optimum tensile
strength of PPS composites; it is obvious that the graphical optimization allows
visual selection of the optimum formulation conditions according to certain
criterion. The result of the graphical optimization includes overlay plot (figure
4.11b), which is extremely practical for quick technical use in the workshop to
choose the values of the composites parameters that would achieve maximum
strength value for this type of material.
34.8189
36
X2 = B: Aspect Ratio (lf/df) = 10.00
PSTEM Tensile Strenght
PSTEM Tensile Strenght = 34.5845
34
32
30
28
26
24
22
20
40.00
50.00
34.00
42.00
28.00
34.00
22.00
B: Aspect Ratio (lf/df)
26.00
16.00
18.00
10.00
10.00
A: Volume fraction
(a)
170
Design-Expert® Software
Factor Coding: Actual
Overlay Plot
Overlay Plot
40.00
PSTEM Tensile Strenght
Design Points
Actual Factor
C: Fibre orientations = 90.00
B: Aspect Ratio (lf/df)
34.00
X1 = A: Volume fraction
X2 = B: Aspect Ratio (lf/df)
28.00
22.00
16.00
PSTEM Tensil 34.7605
X1
50.00
X2
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
(b)
Figure 4.11 a, b: optimal values for PPS composite
171
4.2
Experimental Design and Parameter Optimization: Flexural Strength
4.2.1 Taguchi experimental design based on the L9(33) design
In this study, the flexural strength of plantain fibers reinforced polyester was
investigated for optimum reinforcement combinations to yield optimal response
employing Taguchi methodology. The signal to noise ratio and mean responses
associated with the dependent variables of this study are evaluated and presented.
Designed experimentation on replicated samples of empty fruit bunch fiber
reinforced
polyester composite
were used to obtain the value of quality
characteristics of flexural strength using different levels of control factors as in
table 4.1. Table 4.17 show Taguchi DOE orthogonal array and Design matrix
implemented for the larger the better signal to nose ratio (SN ratio).
The flexural test signal-to-noise ratio for plantain empty fruit bunch fiber
reinforced polyester composite is calculated with equation (3.63) using values of
various experimental trials and presented as in table 4.17 so that for first
experiment,
SNratio
= −10 × log
1
1
1
1
+
+
3 (32.01172)
(31.64063)
(31.26953)
= 30.004
Also equation (3.64) was used in the computation of the mean standard
deviation MSD as recorded in table 4.17.
172
Table 4.17: Experimental design matrix for flexural test using composite
made from plantain empty fruit bunch fiber reinforced polyester composite
(ASTM D-790M)
Expt.
A:
No. Volume
fraction
(%)
1
2
3
4
5
6
7
8
9
10
10
10
30
30
30
50
50
50
B:
Aspect
Ratio
(lf/df)
10
25
40
10
25
40
10
25
40
C:
Specimen replicates
Mean
Flexural response
Flexural
Fiber
(MPa)
response
orientations Trial Trial Trial (MPa)
MSD S/N
(± degree)
#1
#2
#3
ratio
30
32.01 31.64 31.27
31.64 0.0009 30.00
45
20.41 22.656 21.53
21.53 0.0021 26.63
90
15.35 15.35 15.35
15.35 0.0042 23.72
45
38.86 35.94 37.40
37.40 0.0007 31.44
90
24.02 24.61 24.32
24.32 0.0017 27.72
30
21.50 25.00 23.25
23.25 0.0019 27.28
90
30.76 30.76 30.76
30.76 0.0010 29.76
30
34.96 35.35 35.16
35.16 0.0008 30.92
45
36.33 36.91 36.62
36.62 0.0007 31.27
Table 4.18: Evaluated quality characteristics, signal to noise ratios and
orthogonal array setting for computation of mean responses of PEFB
Experiment
Factor Factor Factor Mean ultimate tensile S/N ratio
number
A
B
C
response (MPa)
1
1
1
1
31.64
30.00
2
1
2
2
21.53
26.64
3
1
3
3
15.35
23.72
4
2
1
2
37.40
31.44
5
2
2
3
24.32
27.72
6
2
3
1
23.25
27.28
7
3
1
3
30.76
29.76
8
3
2
1
35.156
30.92
9
3
3
2
36.62
31.27
Since the
experimental design is orthogonal it is possible to separate out
the effect of each factor. This is done by looking at the control matrix of table 4.18
173
and calculating the average SN ratio (
) and mean (
) responses for each
factor at each of the three test levels following the methods of Ihueze et al., (2012).
Table 4.19: Average responses obtained for Volume fraction (A) at levels 1, 2,
3 within experiments 1 to 9
quality characteristics
Average of response for
Response value
Factor level
different experiments
( +
26.79
+ )⁄3
( +
22.84
+ )⁄3
( +
28.81
+ )⁄3
( +
28.32
+ )⁄3
( +
30.65
+ )⁄3
( +
34.18
+ )⁄3
Table 4.20: Average responses obtained for Aspect Ratio (B) at levels 1, 2, 3
within experiments 1-9
quality characteristics
Average of response for
Response value
Factor level
different experiments
( + + )⁄3
30.40
( + + )⁄3
33.27
( +
28.43
+ )⁄3
( +
27.00
+ )⁄3
( +
27.43
+ )⁄3
( +
25.07
+ )⁄3
Table 4.21: Average responses obtained for fiber orientation (C) at levels 1, 2,
3 within experiments 1-9
quality characteristics
Average of response for
Response value
Factor level
different experiments
( + + )⁄3
29.40
( + + )⁄3
30.02
( + + )⁄3
29.79
( + + )⁄3
31.85
( + + )⁄3
27.07
( + + )⁄3
23.48
174
This procedure is also followed in the computation of response for mean of
PPS and the results are presented in tables 4.22 and 4.24. Figures 4.12, 4.13, 4.16
and 4.17 are the excel graphics for SN ratio and mean tensile strength of plantain
empty fruit bunch and pseudo stem fiber reinforced composites based on Larger is
better quality characteristics.
The Figure 4.15 shows the effect of factors on the responses. Increasing the
fiber content increases the flexural strength of plantain empty fruit bunch fiber
reinforced composites. A maximum of 40.9 % contribution is attained in the
flexural strength as a result of increasing fiber volume fraction. It then follows that
fiber volume fraction is the prominent parameter followed by fiber orientation
(24.7 % contribution) and then aspect ratio contributing 23 %.
31
30.5
30
SN Ratio
29.5
29
A: Volume fraction (%)
28.5
B: Aspect Ratio (lf/df)
28
C:Fibre Orientations (± degree)
27.5
27
26.5
0
1
2
3
4
Factor levels-PEFB
Figure 4.12: Main effect plots for signal-noise ratio-PEFB
175
mean of means
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
C:Fibre Orientations (± degree)
A: Volume fraction (%)
B: Aspect Ratio (lf/df)
0
1
2
3
4
Factor levels-PEFB
Figure 4.13: Main effect plots for means ratio-PEFB
Table 4.22: Response Table for flexural strength of plantain empty fruit
bunch fiber reinforced composites based on Larger is better quality
characteristics
response
Signal to Noise Ratios
Means
Level
A:
B:
C:
A:
B:
C:
Volume Aspect
Fiber
Volume Aspect
Fiber
Fraction
Ratio Orientation
Fraction
Ratio
Orientations
(%)
(lf/df)
s
(%)
(lf/df)
± degree)
± degree)
1
26.79
30.40
29.40
22.84
33.27
30.02
2
28.81
28.43
29.79
28.32
27.00
31.85
3
30.65
27.43
27.07
34.18
25.07
23.48
Delta
3.86
2.98
2.72
11.34
8.19
8.38
Rank
1
2
3
1
3
2
Based on the main effects plot of signal to noise ratio of figure 4.12, the
optimum setting of composite parameters for the flexural strength of plantain
176
empty fruit bunch fiber reinforced polyester composites and percentage
contribution of each factor is compiles and presented in the graphics of figure 4.15.
45
40
level of factor contribution
35
30
25
20
15
10
5
0
% Contribution
Volume Fraction
(%)
Aspect Ratio (lf/df)
Fibre orientations
(± degree)
40.96004
23.3818
24.69386
Figure 4.14: Percentage contribution of parameters on flexural strength
The flexural test signal-to-noise ratio for plantain pseudo-stem fiber
reinforced polyester composite is calculated with (3.63) using values of various
experimental trials and presented as in table 4.23 so that for first experiment,
SNratio
= −log
1
1
1
1
+
+
(31.64063)
3 (32.01172)
(31.26953)
= 30.00
Similarly, Equation (3.64) was utilized in the computation of the mean standard
deviation MSD as recorded in table 4.23.
177
Table 4.23: Experimental design matrix for flexural test using composite
made from pseudo-stem plantain fiber reinforced polyester composite (ASTM
D-790M)
Expt.
A:
No. Volume
fraction
(%)
1
2
3
4
5
6
7
8
9
10
10
10
30
30
30
50
50
50
B:
Aspect
Ratio
(lf/df)
C: Fiber
orientations
(± degree)
10
25
40
10
25
40
10
25
40
30
45
90
45
90
30
90
30
45
Specimen replicates
Flexural response
(MPa)
Trial Trial Trial
#1
#2
#3
32.01 31.64 31.27
15.23 15.43 15.33
12.30 12.50 12.40
36.91 33.81 35.36
22.27 23.63 22.95
15.35 18.75 17.05
30.76 36.91 33.84
30.76 30.76 30.76
31.05 29.30 30.18
Mean
Flexural
response
(MPa) MSD
31.64
15.33
12.40
35.36
22.95
17.05
33.84
30.76
30.18
0.0009
0.0042
0.0065
0.0008
0.0019
0.0035
0.0008
0.0010
0.0011
31
30
29
SN Ratio
28
27
A: Volume fraction (%)
26
B: Aspect Ratio (lf/df)
C:Fibre Orientations (± degree)
25
24
23
0
1
2
3
Factor levels-PPSFRC
4
Figure 4.16: Main effect plots for signal-noise ratio-PPSFRC
178
S/N
ratio
30.00
23.712
21.87
30.95
27.21
24.55
30.52
29.76
29.57
36
34
32
mean of means
30
28
26
A: Volume fraction (%)
24
B: Aspect Ratio (lf/df)
22
C:Fibre Orientations (± degree)
20
18
16
0
1
2
3
4
Factor levels-PPSFRC
Figure 4.17: Main effect plots for means-PPSFRC
Table 4.24: Response Table for flexural strength of plantain empty fruit
bunch fiber reinforced composites based on Larger is better quality
characteristics
response
Signal to Noise Ratios
Means
A:
B:
C:
A:
B:
C:
Volume Aspect
Fiber
Volume Aspect
Fiber
Level
Fraction
Ratio Orientations Fraction
Ratio
Orientations
(%)
(lf/df)
(± degree)
(%)
(lf/df)
(± degree)
1
25.19
30.49
28.10
19.79
33.61
26.48
2
27.57
26.89
28.08
25.12
23.01
26.96
3
29.95
25.33
26.53
31.59
19.88
23.06
Delta
4.76
5.16
1.57
11.80
13.74
3.89
Rank
2
1
3
2
1
3
179
Estimation of expected flexural responses based on optimum setting:
The expected response of table 4.25 is estimated using the optimum control factor
setting from the main effects plots (Ross, 1988; Radharamanan and Ansui, 2001;
Phadke, 1989); by employing the response table for signal to noise ratio and the
response table for mean, the expected response model is as in equation 4.9:
EV = AVR + A
− AVR + B
− AVR + C
− AVR + ⋯ + (n
AVR)
−
(4.9)
Where
EV = expected response
AVR = average response
Aop t = mean value of response at optimum setting of factor A
Bopt = mean value of response at optimum setting of factor B
Copt = mean value of response at optimum setting of factor C
The expected responses are therefore computed and presented in table 4.25.
Table 4.25: Optimum setting of control factors and expected optimum
strength of composites
Composite and
Control
Optimum
Expected
property
factor
setting
optimum strength
A
50
Empty fruit
B
10
42.4 MPa
bunch/flexural
C
45
A
50
Pseudo stem/flexural
B
10
41.16 MPa
C
30
180
4.2.2 Response surface optimization of flexural strength based on power law
model
Interactions are part of the real world. In Taguchi's arrays, interactions
are confounded and difficult to resolve. In consideration of this and other
limitations of Taguchi methodology, the RSM technique was identified to have an
edge over the Taguchi technique in terms of significance of interactions and square
terms of parameters. For this reason, the optimum condition determined by the
Taguchi methodology was considered in setting design points for the RSM. This
further optimization using RSM will improve the flexural response.
4.2.2.1
Curve fitting and linearization of experimental responses
The multilinear regression equation of PEFB is obtained through
linearization of the power law model of equation (3.75) using table 4.17 to obtain
table 4.26 and expressing equation (3.74) as
log yEFB = 1.85 + 0.266 log A - 0.247 log B - 0.269 log C
(4.10)
And then expressing equation (3.75) as
yEFB = 70.79457844*(A^0.266)*(B^- 0.247)*(C^- 0.269)
(4.11)
181
Table 4.26: Linearization table for power law model response of PEFB
A B
C PEFB Flexural
log A
log B
log C
log y
Strength
10 10 30
31.64
1
1
1.477
1.500
10 25 45
21.53
1
1.398
1.653
1.333
10 40 90
15.35
1
1.602
1.954
1.186
30 10 45
37.40
1.477
1
1.653
1.573
30 25 90
24.32
1.477
1.398
1.954
1.386
30 40 30
23.25
1.477
1.602
1.477
1.366
50 10 90
30.76
1.699
1
1.954
1.488
50 25 30
35.16
1.699
1.398
1.477
1.546
50 40 45
36.62
1.699
1.602
1.653
1.564
TOTAL
12.528
12
15.254
12.942
Similarly by linearization of response of PPS, the regression equation is
obtained by using table 4.23 for table 4.27 and expressing (3.74) as
log yPPS = 1.80 + 0.328 log A - 0.432 log B - 0.175 log C
(4.12)
And then expressing equation (3.75) as
yPPS = 63.095734*(A^0.328)*(B^- 0.432)*(C^- 0.175)
(4.13)
Table 4.27: Linearization table for power law model response of PPS
A
B C
Stem flexural
log A
log B
log C
log y
strength
10 10 30
31.64
1
1
1.477
1.500
10 25 45
15.33
1
1.398
1.653
1.186
10 40 90
12.40
1
1.602
1.954
1.094
30 10 45
35.36
1.477
1
1.653
1.549
30 25 90
22.95
1.477
1.398
1.954
1.361
30 40 30
17.05
1.477
1.602
1.477
1.232
50 10 90
33.84
1.699
1
1.954
1.529
50 25 30
30.76
1.699
1.398
1.477
1.488
50 40 45
30.18
1.699
1.602
1.653
1.480
TOTAL
12.528
12
15.254
12.417
182
4.2.2.2
Evaluation of Flexural Strength of PEFB Fiber Reinforced
Composites
The power law model of equation (4.11) is used to establish the response of the
central composite design of table 4.28 generated with the control factor levels of
table 4.11.
Table 4.28: Experimental design matrix of central composite design for
optimization of power law model response of flexural strength of PEFB
composites
Factor 2
Factor 3
Response 1
Std
Run Block Factor 1
A:
B:
C:
PEFBFRC
Volume
Aspect
Fiber
flexural
fraction
Ratio
orientations
Strength
(%)
(lf/df)
(± degree)
(MPa)
1
1
Day 1
10
10
30
29.62
4
2
Day 1
50
40
30
32.28
9
3
Day 1
30
25
60
26.260
12
4
Day 1
30
25
60
26.260
8
5
Day 1
50
40
90
24.02
7
6
Day 1
10
40
90
15.65
5
7
Day 1
10
10
90
22.04
11
8
Day 1
30
25
60
26.26
6
9
Day 1
50
10
90
33.82
10
10
Day 1
30
25
60
26.26
3
11
Day 1
10
40
30
21.04
2
12
Day 1
50
10
30
45.45
20
13
Day 2
30
25
60
26.26
16
14
Day 2
30
50
60
22.10
13
15
Day 2
50
25
60
30.08
14
16
Day 2
64
25
60
32.08
17
17
Day 2
30
25
10
42.52
18
18
Day 2
30
25
110
22.28
15
19
Day 2
30
10
60
32.93
19
20
Day 2
30
25
60
26.26
183
The statistical significance of the response model was checked and presented
in the analysis of variance of table 4.29; the Model F-value of 67.31 implies the
model is significant. There is only a 0.01% chance that a "Model F-Value" this
large could occur due to noise. Values of "Prob > F" less than 0.0500 indicate
model terms have significant effects on the response. In this case A, B, C, AB, A2,
B2, C2 are significant model terms. Values greater than 0.1000 indicate the model
terms are not significant.
Table 4.29: Analysis of variance
flexural strength
Source
Sum of
df
Squares
17.33943 1
Block
921.9101 9
Model
290.338 1
A-Volume
fraction
241.7287 1
B-Aspect Ratio
(lf/df)
329.0454 1
C-Fiber
orientations
8.010823 1
AB
5.996603 1
AC
3.87789 1
BC
20.132
1
A^2
15.23446 1
B^2
63.62945 1
C^2
13.69577 9
Residual
13.69577 5
Lack of Fit
0
4
Pure Error
952.9453 19
Cor Total
(ANOVA) for RSM optimization of PEFB
Mean
Square
17.33943
102.4345
290.338
F
Value
p-value
Prob > F
67.31351
190.7919
< 0.0001
< 0.0001
241.7287 158.849
< 0.0001
329.0454 216.228
< 0.0001
8.010823
5.996603
3.87789
20.132
15.23446
63.62945
1.521752
2.739153
0
0.0474
0.0784
0.1449
0.0054
0.0115
0.0001
5.264212
3.940592
2.548306
13.22949
10.01113
41.81329
significant
184
The precision of a model can be checked by the determination coefficient
(R2). The determination coefficient implies that the sample variation of 99.9% in
strength was attributed to the independent variables, and only about 0.1% of the
total variation cannot be explained by the model. Normally, a regression model
having an R2 value higher than 0.9 is considered to have a very high correlation. In
general, the closer the value of R (correlation coefficient) to 1, the better the
correlation between the experimental and predicted values. From table 4.30, "Pred
R-Squared" of 0.7997 is in reasonable agreement with the "Adj R-Squared" of
0.9707. "Adeq Precision" measures the signal to noise ratio. A ratio greater than 4
is desirable. “Adeq Precision” measures the signal to noise ratio, a ratio greater
than 4 is desirable, thus ratio of 34.134 indicates an adequate signal. This model
can be used to navigate the design space.
Table 4.30: Goodness of fit and regression statistics
Std. Dev.
1.233593
R-Squared
Mean
28.17456
Adj R-Squared
C.V. %
4.378394
Pred R-Squared
PRESS
187.4142
Adeq Precision
0.985362
0.970723
0.799687
34.13436
The coefficient of variation (CV) indicates the degree of precision with
which the treatments were compared. Usually, the higher the value of CV, the
lower the reliability of experiment is. Here, a lower value of CV (4.38) indicated a
better precision and reliability of the experiments. The response surface models in
terms of coded and actual factors are in equations (4.14) and (4.15). Both models
show that volume fraction has the highest influence on the flexural response. Also
185
interaction effects are shown to be significant. Both main and high order effects
were also depicted.
Final Equation in Terms of Coded Factors:
PEFBFRC flexural Strength =+26.28+5.90* A-4.80* B-4.92* C-1.00* A * B0.87* A * C+0.70* B * C-1.61* A2+1.34*B2+2.13* C2
(4.14)
Final Equation in Terms of Actual Factors:
PEFBFRC flexural Strength =+41.11223 + 0.70698* A- 0.61125* B-0.44324* C 3.33559E-003 * A*B - 1.44297E - 003* A * C+1.54718E-003 * B * C-4.03606E003* A2+5.97079E-003* B2+2.36603E-003* C2
(4.15)
The plots of figures 4.28 show that data are normally distributed and this
further validates the model above as both predicted and actual values falling on
line show that model is valid and data are normally distributed. Figure 4.19 is the
response surface method depiction of model predicted values and the value of
actual factor. All the data values falling in line shows normal distribution of data
and an approximate model error.
186
Predicted vs. Actual
50.00
Predicted
40.00
30.00
2
4
20.00
10.00
10.00
20.00
30.00
40.00
50.00
Actual
(a)
Normal Plot of Residuals
99
Normal %Probability
95
90
80
70
50
30
20
10
5
1
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Internally Studentized Residuals
(b)
Figure 4.18 a, b: Residual plots indicating normal distribution of data Results
of plantain empty fruit bunch fiber reinforced composites Optimization
187
The following graphics of figures 4.19, 4.20 and 4.21 show clearly the
interaction effects of factors, optimum level of factors as well as the optimum
value of flexural strength of PEFB composite having a power law model response.
Thirty seven experiments were conducted according to RSM central composite
design methods employing different factors combinations to optimize the quadratic
tensile response of PEFB composites and results presented as in the following
figures. The contour plots of figure 4.19 as well as 3D plots of figures 4.20 show
the optimum value of flexural strength as 46.32 MPa and optimum combination of
factors as 50%, 10mm/mm and 30 degree. The cube plot of figure 4.21 and overlay
plot of figure 4.22 show also the optimum value of flexural strength for optimum
combination of factors.
PEFBFRC flexural Strenght
40.00
34.00
B: Aspect Ratio (lf/df)
25
28.00
30
35
22.00
40
16.00
Prediction
X1
X2
46.3198
50.00
10.00 45
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
(a)
188
PEFBFRC flexural Strenght
90.00
84.00
25
78.00
C: Fibre orientations
72.00
66.00
30
60.00
54.00
35
48.00
42.00
36.00
Prediction 40 46.3198
X1
10.00
X2
30.00
45
30.00
10.00
16.00
22.00
28.00
34.00
40.00
B: Aspect Ratio (lf/df)
(b)
Figure 4.19 a and b: Contour plot depiction of interaction effects of factors
Design points above predicted value
Design points below predicted value
PEFBFRCflexural Strenght
46.3198
50
40
30
20
10
50.00
90.00
84.00
78.00
72.00
66.00
60.00
54.00
48.00
42.00
36.00
C: Fibre orientations
30.00
42.00
34.00
26.00
18.00
A: Volume fraction
10.00
(a)
189
PEFBFRCflexural Strenght
Design points above predicted value
Design points below predicted value
50
40
46.3198
30
20
10
40.00
90.00
84.00
78.00
72.00
66.00
60.00
54.00
48.00
42.00
36.00
C: Fibre orientations
30.00
34.00
28.00
22.00
16.00
B: Aspect Ratio (lf/df)
10.00
(b)
Figure 4.20 (a) and (b): 3Depiction of response surface of and interaction
effects of factors
Figure 4.20 a-b shows that the flexural strength increases with volume
fraction and that aspect ratio has least influence on the variability of flexural
strength and the flexural strength is optimum when volume fraction and Fiber
orientation are at their maximum setting (50% and 30degree) and aspect ratio on its
lowest setting (10mm/mm).
190
Cube
PEFBFRC flexural Strenght
15.0917
21.8034
B: Aspect Ratio (lf/df)
B+: 40.00
23.1527
33.3275
6
21.2963
Prediction
46.3198
X1
50.00
X2
10.00
X3
30.00
C+: 90.00
33.36
C: Fibre orientations
B-: 10.00
C-: 30.00
30.7929
46.3198
A-: 10.00
A+: 50.00
A: Volume fraction
Figure 4.21: Cube plot depiction of EFB composite optimum strength
Design-Expert® Software
Factor Coding: Actual
Overlay Plot
Overlay Plot
40.00
PEFBFRC flexural Strenght
Design Points
Actual Factor
C: Fibre orientations = 30.00
B: Aspect Ratio (lf/df)
34.00
X1 = A: Volume fraction
X2 = B: Aspect Ratio (lf/df)
28.00
22.00
16.00
PEFBFRC fle 46.3198
X1
50.00
X2
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
Figure 4.22: Overlay plot depiction of optimal values for PEFB composite
191
4.2.2.3
Evaluation of Flexural Strength of plantain pseudo stem (PPS)
Fiber Reinforced Composites
Similar analysis of power law model of equation (4.13) were also made with
table 4.11 and summarized as in table 4.31. Equation (4.13) is used in the
computation of the responses of different factors combinations generated with
settings of the control factors.
Table 4.31: Experimental design matrix of central composite design for
optimization of power law model response of tensile strength of PPS
composites
Factor 2
Factor 3
Response 1
Std Run Block Factor 1
A:Volume
B:Aspect
C:Fiber
PSTEM
fraction
Ratio
orientations
flexural
(%)
(lf/df)
(± degree)
Strength
(MPa)
10
1
Day 1
30
25
60
23.41
2
2
Day 1
50
10
30
46.43
11
3
Day 1
30
25
60
23.41
7
4
Day 1
10
40
90
12.41
1
5
Day 1
10
10
30
27.38
3
6
Day 1
10
40
30
15.05
5
7
Day 1
10
10
90
22.59
6
8
Day 1
50
10
90
38.30
8
9
Day 1
50
40
90
21.04
9
10 Day 1
30
25
60
23.41
4
11 Day 1
50
40
30
25.51
12
12 Day 1
30
25
60
23.41
18
13 Day 2
30
25
30
26.43
13
14 Day 2
50
25
60
27.68
15
15 Day 2
30
10
60
34.78
17
16 Day 2
30
25
30
26.43
19
17 Day 2
30
25
60
23.41
14
18 Day 2
64
25
60
29.96
20
19 Day 2
30
25
60
23.41
16
20 Day 2
30
50
60
17.32
192
Table 4.32: Analysis of variance (ANOVA) for RSM optimization of PPS
flexural strength
ANOVA for Response Surface Quadratic Model
Source
Sum of
df Mean
F
p-value
Squares
Square
Value
Prob > F
Block
4.608409 1 4.608409
Model
1112.099 9 123.5666 369.6861 < 0.0001
significant
A-Volume
364.5085 1 364.5085 1090.535 < 0.0001
fraction
B-Aspect Ratio
637.123 1 637.123
1906.142 < 0.0001
(lf/df)
C-Fiber
49.64004 1 49.64004 148.5129 < 0.0001
orientations
AB
30.6506 1 30.6506
91.70037 < 0.0001
AC
3.328791 1 3.328791 9.959065 0.0116
BC
4.229486 1 4.229486 12.65376 0.0061
A^2
15.98546 1 15.98546 47.82526 < 0.0001
B^2
61.18329 1 61.18329 183.048
< 0.0001
C^2
4.344031 1 4.344031 12.99646 0.0057
Residual
3.008226 9 0.334247
Lack of Fit
3.008226 4 0.752056
Pure Error
0
5 0
Cor Total
1119.716 19
from table 4.32, the Model F-value of 369.69 implies the model is
significant. There is only a 0.01% chance that "Model F-Value" this large could
occur due to noise. Values of "Prob > F" less than 0.0500 indicate model terms are
significant. In this case A, B, C, AB, AC, BC, A2, B2, C2 are significant model
terms. Values greater than 0.1000 indicate the model terms are not significant.
193
Table 4.33: Goodness of fit and regression statistics
Std. Dev.
0.578141
R-Squared
0.997302
Mean
25.58927
Adj R-Squared
0.994605
C.V. %
2.259311
Pred R-Squared
0.953612
PRESS
51.72747
Adeq Precision
78.96024
The "Pred R-Squared" of 0.9536 is in reasonable agreement with the "Adj
R-Squared" of 0.9946. "Adeq Precision" measures the signal to noise ratio. A ratio
greater than 4 is desirable. the ratio of 78.960 indicates an adequate signal. This
model can be used to navigate the desig space.
Final Equation in Terms of Coded Factors:
PSTEM flexural Strength =+23.32+6.66 * A-7.84 * B-2.43* C - 1.96 * A * B0.65* A * C+0.73* B * C-1.53* A2+2.82 * B2+1.19* C2
(4.16)
Final Equation in Terms of Actual Factors:
PSTEM flexural Strength =+35.96388+0.79045* A-1.04945* B-0.24727* C6.52459E-003* A * B-1.07510E-003 * A * C+1.61580E-003* B * C-3.82889E003* A2+0.012518 * B2+1.31756E-003* C2
(4.17)
The following graphics shows the optimum factors combinations for optimum
flexural strength of PPS composites
194
PSTEM flexural Strenght
40.00
15.924
B: Aspect Ratio (lf/df)
34.00
20
22.0877
28.00
2
28.0582
22.00
30
Prediction
46.0493
37.0434
Observed
46.4265
40
X1
50.00
X2
10.00
16.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
(a)
PSTEM flexural Strenght
50
C:
45
40
45.9959
35
30
25
20
90.00
84.00
78.00
72.00
66.00
60.00
54.00
Fibre orientations48.00
42.00
36.00
30.00
40.00
34.00
28.00
22.00
16.00
10.00
B: Aspect Ratio (lf/df)
(b)
Figures 4.23 a and b: Optimization graphics showing the optimal factors and
function PPS
195
Design-Expert® Software
Factor Coding: Actual
Overlay Plot
Overlay Plot
40.00
PSTEM flexural Strenght
X1 = A: Volume fraction
X2 = B: Aspect Ratio (lf/df)
B: Aspect Ratio (lf/df)
Actual Factor
C: Fibre orientations = 30.43
34.00
28.00
22.00
16.00
PSTEM flexura45.9418
X1
50.00
X2
10.02
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
Figure 4.24: Overlay plot depiction of optimal values for PPS composite
196
4.3
Experimental Design and Parameter Optimization: Brinell hardness
4.3.1 Taguchi experimental design based on the L9(33) design
In this section, the Brinell hardness characteristics of plantain fibers
reinforced polyester composites were investigated for optimum reinforcement
combinations to yield optimal response employing Taguchi methodology. The
signal to noise ratio and mean responses associated with the dependent variables of
the study were evaluated and presented. Designed experimentation on replicated
samples of empty fruit bunch and pseudo stem fiber reinforced
polyester
composite were used to obtain the value for quality characteristics of Brinell
hardness using different levels of control factors levels as in table 4.1. Using
equation 3.63 and equation 3.49 for the nine experiments conducted on plantain
empty fruit bunch fibers reinforced composites and plantain pseudo stem fibers
reinforced composites, the signal to noise ratio (SN Ratio) and mean square
deviation (MSD) were calculated and the results are presented in Tables 4.34 and
4.40.
197
Table 4.34. Experimental Design Matrix for Brinell hardness Test Using
Composite Made from Plantain Pseudo Stem Fibers Reinforced Polyester
Composite
Exp
No.
1
2
3
4
5
6
7
8
9
A:
Volume
fraction
(%)
10
10
10
30
30
30
50
50
50
B:
Aspect
Ratio
(lf/df)
C:
Fibers
orientations
(± degree)
10
25
40
10
25
40
10
25
40
30
45
90
45
90
30
90
30
45
Specimen replicates
Mean
Brinell Hardness
Brinell
-2
Response Nmm
Hardness
response
Trial Trial Trial (Nmm-2)
#1
#2
#3
18.14 18.04 18.09
18.09
18.54 18.61 18.57
18.57
18.14 18.06 18.09
18.10
18.06 17.27 17.68
17.67
18.23 18.92 18.61
18.59
16.25 16.22 16.24
16.24
18.23 18.14 18.18
18.18
17.68 18.92 18.39
18.33
18.06 18.23 18.14
18.14
MSD
SNratio
0.003
0.002
0.003
0.003
0.002
0.003
0.003
0.002
0.003
25.15
25.38
25.15
24.94
25.38
24.21
25.19
25.25
25.17
Table 4.35. Evaluated quality characteristics, signal to noise ratios and
orthogonal array setting for computation of mean responses of PPS
Exp
A
B C
Mean Brinell hardness
SNratio
No
response
(Nmm-2)
1
1 1
18.09
25.15
1
1
2 2
18.57
25.38
2
1
3 3
18.10
25.15
3
2
1 2
17.67
24.94
4
2
2 3
18.59
25.38
5
2
3 1
16.24
24.21
6
3
1 3
18.18
25.19
7
3
2 1
18.33
25.25
8
3
3 2
18.14
25.17
9
Taguchi approach uses a simpler graphical technique to achieve influence of
each factor and since the
experimental design is orthogonal it is possible to
separate out the effect of each factor. This is done by examining the control matrix
198
of table 4.35 and calculating the average SN ratio (
) and mean (
)
responses for each factor at each of the three test levels as outlined in table 4.363.38 based on the methods of Ihueze et al. (2012); the calculated responses for SN
ratio and mean as per each factor and level are tabulated in tables 4.39; the range
(Delta) is the difference between high and low response. The larger the (Delta)
value for a parameter, the larger the effect the variable has on the Brinell hardness
of the composites (Ross, 1993).
Table 4.36. Average responses obtained for Volume fraction (A) at levels 1, 2,
3 within experiments 1-9.
quality
Average of response for different
Response value
characteristics
experiments
Factor level
(
+
+
)⁄3
25.23
(
+
+
)⁄3
18.25
(
+
+
)⁄3
24.84
(
+
+
)⁄3
17.50
(
+
+
)⁄3
25.20
(
+
+
)⁄3
18.22
199
Table 4.37. Average responses obtained for Aspect Ratio (B) at levels 1, 2, 3
within experiments 1-9
quality characteristics
Average of response for
Response value
Factor level
different experiments
(
+
+
)⁄3
25.09
(
+
+
)⁄3
17.98
(
+
+
)⁄3
25.34
(
+
+
)⁄3
18.50
(
+
+
)⁄3
24.85
(
+
+
)⁄3
17.49
Table 4.38. Average responses obtained for fiber orientation (C) at levels 1, 2,
3 within experiments 1-9
quality characteristics
Average of response for
Response value
Factor level
different experiments
( + + )⁄3
24.87
( + + )⁄3
17.55
( + + )⁄3
25.16
( + + )⁄3
18.13
( + + )⁄3
25.24
( + + )⁄3
18.29
Table 4.39 shows the evaluated responses and their ranking for Brinell
hardness of plantain pseudo stem fiber reinforced composites based on Larger is
better quality characteristics for signal to noise ratio and mean values.
200
Table 4.39. Summary of responses and ranking for Brinell hardness of
plantain pseudo stem fiber reinforced composites based on Larger is better
quality characteristics
Signal to Noise Ratios
Level
A: Volume
B:Aspect
C:Fiber
fraction (%)
Ratio (lf/df)
Orientations
(± degree)
1
25.23
25.09
24.87
2
24.84
25.34
25.16
3
25.21
24.85
25.24
Delta
0.38
0.49
0.37
Rank
2
1
3
Means
Level
A: Volume
B:Aspect
C:Fiber
Fraction (%)
Ratio (lf/df)
Orientations
(± degree)
1
18.25
17.98
17.55
2
17.50
18.50
18.13
3
18.22
17.49
18.29
Delta
0.76
1.01
0.74
Rank
2
1
3
Figures 4.25 to 4.26 are the excel graphics for SN ratio and mean tensile
strength of plantain empty fruit bunch and pseudo stem fiber reinforced composites
based on Larger is better quality characteristics. Table 4.41 is the Response table
for Brinell hardness of plantain empty fruit bunch fiber reinforced composites
based on Larger is better quality characteristics for signal to noise ratio and
response mean values.
201
25.4
25.3
SN Ratio
25.2
25.1
A: Volume fraction (%)
B: Aspect Ratio (lf/df)
25
C:Fibre Orientations (± degree)
24.9
24.8
0
1
2
3
4
Factor levels-PPSFRC
Figure 4.25. Main effect plots for signal-noise ratio-PPS
18.6
mean of means
18.4
18.2
18
A: Volume fraction (%)
B: Aspect Ratio (lf/df)
17.8
C:Fibre Orientations (± degree)
17.6
17.4
0
1
2
3
4
Factor levels-PPSFRC
Figure 4.26: Main effect plots for means-PPSFRC
202
Table 4.40. Experimental Design Matrix for Brinell hardness Test Using
Composite Made from Plantain Empty Fruit Bunch Fibers Reinforced
Polyester Composite
Expt
No.
A:
Volume
fraction
(%)
1
2
3
4
5
6
7
8
9
10
10
10
30
30
30
50
50
50
B:
Aspect
Ratio
(lf/df)
C:
Fiber
orientations
(± degree)
10
25
40
10
25
40
10
25
40
Specimen replicates
Brinell hardness
Response (Nmm-2)
Trial
#1
18.23
18.54
17.27
18.23
18.23
15.37
18.54
18.54
18.54
30
45
90
45
90
30
90
30
45
Trial
#2
18.22
18.23
18.75
16.47
18.92
15.30
18.87
18.87
17.68
Mean
Brinell
Hardness
response
(Nmm-2)
Trial
#3
18.22
18.39
18.20
17.43
18.61
15.34
18.71
18.71
18.14
18.22
18.38
18.04
17.38
18.59
15.34
18.71
18.71
18.12
MSD
SNratio
0.0030
0.0029
0.0030
0.0033
0.0028
0.0042
0.0028
0.0028
0.0030
25.21
25.29
25.11
24.78
25.38
23.71
25.44
25.44
25.16
25.5
25.4
25.3
SN Ratio
25.2
25.1
25
A: Volume fraction (%)
24.9
B: Aspect Ratio (lf/df)
24.8
C:Fibre Orientations (± degree)
24.7
24.6
24.5
0
1
2
3
4
Factor levels-PEFBFRC
Figure 4.27. Main effect plots for signal-noise ratio-PEFBFRC
203
18.8
18.6
mean of means
18.4
18.2
18
A: Volume fraction (%)
17.8
B: Aspect Ratio (lf/df)
17.6
C:Fibre Orientations (± degree)
17.4
17.2
17
0
1
2
3
4
Factor levels-PEFBFRC
Figure 4.28. Main effect plots for means ratio-PEFBFRC
Figure 4.27 shows graphically the effect of the three control factors on
Brinell hardness of plantain empty fruit bunch fiber reinforced composites,
analysis of results gives the combination of factors resulting in maximum hardness
strength of the composites. From analysis of these results it is concluded that
factors combination A3B2C3 yields maximum hardness strength of the composites.
Table 4.41 clearly spelt out the influence of various control factors for
plantain empty fruit bunch fiber reinforced composites, the response of the S/N
ratio shows that the volume fraction (A) factor has major influence on Brinell
hardness of plantain fiber reinforced composites followed Aspect ratio and fiber
orientation.
204
Figure 4.28 depicts the variations of hardness strength of plantain empty
fruit bunch fiber reinforced polyester composites with all the three working
parameters. The hardness strength decreases for increasing values of volume
fraction up till level II (30%) before increasing towards level III (50%). But in the
case of aspect ratio, hardness strength increases up to the level II (25) and
afterwards its value decreases from level II to level III.
Table 4.41. Summary of responses and ranking for Brinell hardness of
plantain empty fruit bunch fibers reinforced composites
response
Signal to Noise Ratios
Level
A: Volume
B: Aspect
C: Fiber
Fraction (%)
Ratio (lf/df)
Orientations
(± degree)
1
25.20
25.14
24.79
2
24.62
25.37
25.07
3
25.35
24.66
25.31
Delta
0.72
0.71
0.52
Rank
1
2
3
response
Means
Level
A: Volume
B: Aspect
C: Fiber
Fraction (%)
Ratio (lf/df)
Orientations
(± degree)
1
18.22
18.10
17.42
2
17.10
18.56
17.96
3
18.51
17.17
18.44
Delta
1.41
1.39
1.02
Rank
1
2
3
205
Table 4.42. Signal to noise ratio response for Brinell hardness
Exp
No
EFB
hardness
strength
MSD
SN ratio
1
2
3
4
5
6
7
8
9
18.22
18.39
18.044
17.38
18.59
15.34
18.71
18.71
18.12
0.0030
0.0029
0.0030
0.0033
0.0028
0.0042
0.0028
0.0028
0.0030
25.21
25.29
25.11
24.78
25.38
23.72
25.44
25.44
25.16
Pseudo
stem
hardness
strength
18.09
18.57
18.10
17.67
18.59
16.24
18.18
18.33
18.14
MSD
SN ratio
0.0030
0.0028
0.0030
0.0032
0.0028
0.0037
0.0030
0.0029
0.0030
25.15
25.38
25.15
24.94
25.38
24.21
25.19
25.25
25.17
The response table for means of SN ratios shows that the volume fraction
has the highest contribution in influencing the composite hardness strength (36.89
%), followed with aspect ratio (33.60 %) and then fiber orientation (17.39 %).
Estimation of expected Brinell Hardness responses based on optimum
setting: The expected responses are computed following the procedures of
Radharamanan and Ansui (2001) such that the optimum setting of composites
parameters for the hardness strength of plantain empty fruit bunch and pseudo stem
fibers reinforced polyester composites are compiled utilizing equation 4.9 and
presented in table 4.43.
206
Table 4.43. Optimum setting of control factors and expected optimum
strength of composites
Composite and
Control
Optimum setting Expected optimum
property
factor
strength
Empty fruit bunch
A
50 %
19.63 N/mm2
/hardness
B
25
C
90Degrees
Pseudo stem/hardness
A
50 %
19.06 N/mm2
B
25
C
90Degrees
4.3.2 Response surface optimization of Brinell hardness based on power law
model
The Taguchi method has been criticized in the literature for difficulty in
accounting for interactions between parameters. The RSM technique has an
edge over the Taguchi technique in terms of significance of interactions and square
terms of parameters. For this reason the optimum condition determined by the
Taguchi methodology was considered in setting design points for the RSM. This
further optimization using RSM showed a significant improvement the hardness
response of plantain fiber reinforced composites.
By using the data in table 4.40 in conjunction with equation (3.74) we obtain
the linearization of responses of PEFBFRC as
log yEFB = 1.21 - 0.0013 log A - 0.0308 log B + 0.0534 log C
(4.18)
and using equation (3.75)
yEFB = 16.21810097*(A^- 0.0013)*(B^- 0.0308)*(C^0.0534)
(4.19)
207
Similarly, by using the data in table 4.34 in conjunction with equation (3.74)
we obtain the linearization of responses of PPSFRC as
log yPPS = 1.22 - 0.0073 log A - 0.0137 log B + 0.0359 log C
(4.20)
and using equation (3.75)
yPPS = 16.595869*(A^- 0.0073)*(B^- 0.0137)*(C^0.0359)
4.3.2.1
(4.21)
Brinell hardness of Plantain EFB Fiber Reinforced Composites
The power law model of equation (4.19) is used to establish the response of
the central composite design of table 4.44 generated with the control factor levels
of table 4.11 using response surface methodology platform of design Expert 8.
Table 4.44: Experimental design matrix of central composite design for
optimization of power law model response of Brinell hardness of PEFB
composites
Factor 1
Factor 2
Factor 3
Response 1
Std Run Block
A:Volume B:Aspect
C:Fiber
PEFBFRC
fraction
Ratio
orientations
Hardness
(%)
(lf/df)
(± degree)
Strength
(Nmm-2)
11
1
Day 1
30
25
60
18.10
3
2
Day 1
10
40
30
17.31
2
3
Day 1
50
10
30
18.02
6
4
Day 1
50
10
90
19.11
9
5
Day 1
30
25
60
18.20
7
6
Day 1
10
40
90
18.35
10
7
Day 1
30
25
60
18.20
4
8
Day 1
50
40
30
17.27
12
9
Day 1
30
25
60
18.20
208
1
5
8
20
15
16
14
13
18
19
17
10
11
12
13
14
15
16
17
18
19
20
Day 1
Day 1
Day 1
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
10
10
50
30
30
30
64
50
30
30
30
10
10
40
25
40
50
25
25
25
25
25
30
90
90
60
60
60
60
60
110
60
30
18.06
19.15
18.31
18.20
17.93
17.81
18.18
18.18
18.80
18.20
17.53
The Model F-value of 3100.41 as shown in table 6.2.5 implies that the
model is significant. There is only a 0.01% chance that "Model F-Value" this large
could occur due to noise. Values of "Prob > F" less than 0.0500 indicate model
terms are significant.
In this case A, B, C, BC, B2, C2 are significant model
terms. Values greater than 0.1000 indicate the model terms are not significant. If
there are many insignificant model terms (not counting those required to support
hierarchy), model reduction may improve your model.
209
Table 4.45: Analysis of variance (ANOVA) for RSM optimization of PEFB
Brinell hardness
Source
Sum of df
Mean
F
p-value
Squares
Square
Value
Prob > F
Block
0.043231 1
0.043231
Model
4.439919 9
0.493324
3100.407 < 0.0001 significant
A-Volume fraction 0.003249 1
0.003249
20.41915
0.0014
B-Aspect
Ratio 1.255496 1
1.255496
7890.441 < 0.0001
(lf/df)
C-Fiber orientations 3.009516 1
3.009516
18913.97 < 0.0001
AB
1.32E-06 1
1.32E-06
0.008305
0.9294
AC
2.49E-06 1
2.49E-06
0.015674
0.9031
BC
0.001038 1
0.001038
6.525498
0.0310
A^2
0.000407 1
0.000407
2.560296
0.1440
B^2
0.072953 1
0.072953
458.4905 < 0.0001
C^2
0.092306 1
0.092306
580.1208 < 0.0001
Residual
0.001432 9
0.000159
Lack of Fit
0.001432 5
0.000286
Pure Error
0
4
0
Cor Total
4.484582 19
From table 4.46, the "Pred R-Squared" of 0.9978 is in reasonable agreement
with the "Adj R-Squared" of 0.9994. "Adeq Precision" measures the signal to noise
ratio. A ratio greater than 4 is desirable. The ratio of 201.806 indicates an
adequate signal. This model can be used to navigate the design space.
Table 4.46: Goodness of fit and regression statistics
0.012614
Std. Dev.
R-Squared
18.16088
Mean
Adj R-Squared
0.069458
C.V. %
Pred R-Squared
0.009552
PRESS
Adeq Precision
0.999678
0.999355
0.997849
201.8056
The response surface models in terms of coded and actual factors are in
equations (6.5) and (6.6). Both models show that volume fraction has the highest
210
influence on the tensile response. Also interaction effects are shown to be
significant. Both main and high order effects were also depicted.
Final Equation in Terms of Coded Factors:
PEFBFRC Brinell hardness = +18.20 - 0.020*A -0.39*B+0.54*C+4.064E-004*
A*B-5.583E-004*A*C-0.011* B * C+7.410E-003* A2+0.099* B2-0.11* C2(4.22)
Final Equation in Terms of Actual Factors:
PEFBFRC Hardness Strength = +17.62843- 2.07601E-003*A0.046413*B+0.032704* C+1.35473E-006*A*B - 9.30561E-007* A * C 2.53167E-005* B * C+1.85256E-005* A2 + 4.40727E-004*B2 - 1.18029E004*C2
(4.23)
Normal Plot of Residuals
99
Normal %Probability
95
90
80
70
50
30
20
10
5
1
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Internally Studentized Residuals
(a)
211
Externally Studentized Residuals
Externally Studentized Residuals
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
1
4
7
10
13
16
19
Run Number
(b)
Figure 4.29: Residual plots normal distribution of data
The graphics of figures 4.30, 4.31 and 4.32 show clearly the interaction
effects of factors as a result of RSM, optimum level of factors as well as the
optimum value of Brinell hardness of PEFB composite having a power law model
response. Thirty two experiments were conducted according to RSM central
composite design methods employing different factors combinations to optimize
the quadratic tensile response of PEFB composites. The contour plots of figure
4.30 as well as 3D plots of figures 4.31 show the interaction effects of factors and
the optimum value of Brinell hardness as 19.1533 N/mm2 and optimum
combination of factors as 10%, 10mm/mm and 90degree. The cube plot of figure
212
4.32 and overlay plot of figure 4.33 show also the optimum value of Brinell
hardness for optimum combination of factors.
PEFBFRC Hardness Strength
90.00
84.00
78.00
Prediction
19
Observed
X1
X2
19.1533
19.1539
10.00
90.00
C: Fibre orientations
72.00
18.5
66.00
60.00
54.00
18
48.00
42.00
36.00
17.5
30.00
10.00
16.00
22.00
28.00
34.00
40.00
B: Aspect Ratio (lf/df)
PEFBFRC Hardness Strength
Figure 4.30. Design Expert8 contour plot depiction of interaction effects of
factors
19.5
19
19.1 471
18.5
18
17.5
17
50.00
42.00
40.00
34.00
34.00
28.00
26.00
22.00
B: Aspect Ratio (lf/df)
18.00
16.00
10.00
A: Volume fraction
10.00
(a)
213
PEFBFRC Hardness Strength
19.1509
19.5
19
18.5
18
17.5
17
40.00
90.00
84.00
78.00
72.00
66.00
60.00
54.00
48.00
42.00
36.00
C: Fibre orientations
30.00
34.00
28.00
22.00
16.00
B: Aspect Ratio (lf/df)
10.00
(b)
Figure 4.31: a-b 3D plot of response surface of and interaction effects of
factors
Cube
PEFBFRC Hardness Strength
18.354
B: Aspect Ratio (lf/df)
B+: 40.00
17.3029
18.3143
17.2654
Prediction
19.1509
X1 6
11.38
X2
10.00
X3
90.00
2
19.1533
19.1119
C+: 90.00
C: Fibre orientations
B-: 10.00
C-: 30.00
18.0566
18.0175
A-: 10.00
A+: 50.00
A: Volume fraction
Figure 4.32: Cube plot depiction of EFB composite optimum strength
214
Design-Expert® Software
Factor Coding: Actual
Overlay Plot
Overlay Plot
40.00
PEFBFRC Hardness Strength
Design Points
Actual Factor
C: Fibre orientations = 90.00
B: Aspect Ratio (lf/df)
34.00
X1 = A: Volume fraction
X2 = B: Aspect Ratio (lf/df)
28.00
22.00
16.00
PEFBFRC Ha 19.1533
X1
10.00
X2
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
Figure 4.33: Overlay plot depiction of optimal values for PEFB composite
215
4.3.2.2.
Brinell hardness of Plantain Pseudo Stem (PPS) Fiber Reinforced
Composites
Similarly, equation (4.21) is used in the computation of the responses of
different factors combinations as presented in table 4.47 settings for the control
factors.
Table 4.47: Experimental design matrix of central composite design for
optimization of Brinell hardness of PPS composites
Factor 1
Factor 2
Factor 3
Response 1
Std Run
Block
A:
B:
C:
PSTEMFRC
Volume
Aspect
Fiber
Hardness
fraction
Ratio
orientations
Strength
(%)
(lf/df)
(± degree)
(Nmm-2)
9
1
Day 1
30
25
60
17.94
8
2
Day 1
50
40
90
18.02
11
3
Day 1
30
25
60
17.94
3
4
Day 1
10
40
30
17.53
4
5
Day 1
50
40
30
17.33
1
6
Day 1
10
10
30
17.87
10
7
Day 1
30
25
60
17.94
6
8
Day 1
50
10
90
18.37
7
9
Day 1
10
40
90
18.24
5
10
Day 1
10
10
90
18.58
12
11
Day 1
30
25
60
17.94
2
12
Day 1
50
10
30
17.66
14
13
Day 2
64
25
60
17.85
13
14
Day 2
10
25
60
18.09
17
15
Day 2
30
25
30
17.50
20
16
Day 2
30
25
60
17.94
15
17
Day 2
30
10
60
18.17
16
18
Day 2
30
50
60
17.77
19
19
Day 2
30
25
60
17.94
18
20
Day 2
30
25
110
18.34
216
The F-value of 3753.57 as shown in table 4.48 implies the model is
significant. There is only a 0.01% chance that this large "Model F-Value" could
occur due to noise. Values of "Prob > F" less than 0.0500 indicate model terms are
significant. In this case A, B, C, A2, B2, C2 are significant model terms. Values
greater than 0.1000 indicate the model terms are not significant.
Table 4.48: Analysis of variance (ANOVA) for RSM optimization of PPSFRC
tensile strength
Source
Sum of df
Mean
F
p-value
Squares
Square
Value
Prob > F
Block
6.94E-05 1
6.94E-05
Model
1.786057 9
0.198451
3753.57
< 0.0001 significant
A-Volume fraction
0.120627 1
0.120627
2281.586 < 0.0001
B-Aspect Ratio (lf/df) 0.313263 1
0.313263
5925.179 < 0.0001
C-Fiber orientations 1.329578 1
1.329578
25148.12 < 0.0001
AB
8.02E-06 1
8.02E-06
0.151681
0.7060
AC
3.46E-05 1
3.46E-05
0.653988
0.4395
BC
9.03E-05 1
9.03E-05
1.708879
0.2235
A^2
0.008179 1
0.008179
154.6962 < 0.0001
B^2
0.01709 1
0.01709
323.2555 < 0.0001
C^2
0.044421 1
0.044421
840.1907 < 0.0001
Residual
0.000476 9
5.29E-05
Lack of Fit
0.000476 5
9.52E-05
Pure Error
0
4
0
Cor Total
1.786602 19
The "Pred R-Squared" of 0.9973 is in reasonable agreement with the "Adj RSquared" of 0.9995. "Adeq Precision" measures the signal to noise ratio. A ratio
greater than 4 is desirable. the ratio of 235.903 indicates an adequate signal. This
model can be used to navigate the design space.
217
Table 4.49: Goodness of fit and regression statistics
Std. Dev.
0.007271
R-Squared
0.999734
Mean
17.94829
Adj R-Squared
0.999467
C.V. %
0.040512
Pred R-Squared
0.997342
PRESS
0.004748
Adeq Precision
235.903
Final Equation in Terms of Coded Factors:
PSTEMFRC Brinell hardness = +17.94 - 0.11* A - 0.17* B + 0.36 * C +1.001E003* A * B - 2.079E-003 * A * C - 3.361E-003* B * C + 0.031* A2 + 0.045* B2 0.072 * C2
(4.24)
Final Equation in Terms of Actual Factors:
PSTEMFRC Brinell hardness = +17.57111 - 9.86022E-003* A - 0.021073* B
+0.021735* C+3.33736E-006* A * B - 3.46492E-006* A * C- 7.46796E-006 * B
* C + 7.70510E-005* A2 + 1.98011E-004* B2 -7.98077E-005 * C2
(4.25)
The 3D surface graphs and contour for the response is shown in figure 4.34
for formulation variables of the composites. The figure shows the effect of control
factors on the response. The curvilinear profile in the figure is in accordance with
the quadratic model fitted. The optimum value of Brinell hardness is obtainable
when the fiber orientation is somewhere at the highest level of the orientation
range experimented. The following graphics show the optimum factors
combinations for optimum Brinell hardness of PPS composites.
218
PSTEMFRC Hardness Strenght
40.00
18.1
B: Aspect Ratio (lf/df)
34.00
18.2
28.00
22.00
18.3
16.00
Prediction
X1 18.5
X2
18.4
18.5894
10.00
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
PSTEMFRC Hardness Strenght
(a)
1 8.586 4
18.6
18.4
18.2
18
17.8
17.6
17.4
40.00
90.00
84.00
78.00
72.00
66.00
60.00
54.00
48.00
42.00
36.00
C: Fibre orientations
30.00
34.00
28.00
22.00
16.00
B: Aspect Ratio (lf/df)
10.00
(b)
219
Design-Expert® Software
Factor Coding: Actual
Overlay Plot
Overlay Plot
40.00
PSTEMFRC Hardness Strenght
Design Points
Actual Factor
C: Fibre orientations = 90.00
B: Aspect Ratio (lf/df)
34.00
X1 = A: Volume fraction
X2 = B: Aspect Ratio (lf/df)
28.00
22.00
16.00
PSTEMFRC H18.5894
X1
10.00
X2
10.00
10.00
10.00
18.00
26.00
34.00
42.00
50.00
A: Volume fraction
(c)
Figure 4.34: Overlay plot depiction of optimal values for PPS composite
220
4.4
Charpy Impact Test Results
The Charpy impact test results for plantain empty fruit bunch fiber
reinforced composites and plantain pseudo stem fiber reinforced composites are
presented in tables 4.50 and 4.51. Charpy V-notch impact tests were conducted on
plantain empty fruit bunch and Pseudo stem fibers reinforced composites to
compare and provide information on their impact behavior. The lowest Charpy
absorbed energy was recorded in experiment number nine at notch dept of 2mm
and crosshead height of 1.75m for plantain pseudo stem specimens. The Charpy
Impact strength of experiment four and experiment one using plantain EFB fiber
reinforced composites and plantain pseudo stem fiber composites respectively was
observed at 158.01 kJ/m2. The impact strength values presented in this section may
be used for the initial selection purposes on the basis of their desired level of
toughness.
Table 4.50: Experimental results of impact tests on plantain EFB fiber
reinforced composites
Expt.
No
Notch
crosshead
Impactor
Impact
impact
Mean
Velocity
1/2
impact
dept
Height
weight
energy
angle
Impact
( 2 g a)
force
(mm)
(m)
(kg)
(joules)
(β)
strength
(m/s)
(N)
Impact
stress
(MPa)
(kJ/m2)
1
1
1.55
3.94
86.61
111.6
157.44
5.57
39.4
157.48
2
1
1.75
6.03
55.28
124
100.46
5.92
60.3
100.50
3
1
1.93
9.97
8.27
151
14.99
6.21
99.7
15.03
4
1.5
1.55
6.03
86.93
110
158.01
5.57
60.3
105.37
5
1.5
1.75
9.97
55.59
122.5
101.03
5.92
99.7
67.39
221
6
1.5
1.93
3.94
8.50
151.5
15.42
6.21
39.4
10.31
7
2
1.55
9.97
86.85
110.3
157.87
5.57
99.7
78.96
8
2
1.75
3.94
55.28
124
100.46
5.92
39.4
50.25
9
2
1.93
6.03
8.03
151.6
14.56
6.21
60.3
7.30
In some applications, impact performance may not be critical and only a
general knowledge of materials behavior in needed. In these circumstances, it
would be worthwhile to provide basic information using Charpy impact tests. The
purpose of the Charpy test in this study is to provide a comparative test to evaluate
the local impact energy absorption of plantain EFB and pseudo stem fibers
reinforced composites. The impact stress was determined as 158.05 MPa for
pseudo stem fiber composites and 157.48 MPa for plantain EFB fiber reinforced
composites.
Table 4.51: Experimental results of impact tests on pseudo stem fiber
composites
Expt.
No
Notch
crosshead
Impactor
Impact
impact
Mean
Velocity
1/2
impact
dept
Height
weight
energy
angle
Impact
( 2 g a)
force
(mm)
(m)
(kg)
(J)
(β)
strength
(m/s)
(N)
Impact
stress
(MPa)
(kJ/m2)
1
1
1.55
3.94
86.93
110.00
158.01
5.57
39.4
158.05
2
1
1.75
6.03
55.67
124.50
101.17
5.92
60.3
101.22
3
1
1.93
9.97
8.03
150.02
14.56
6.21
99.7
14.60
4
1.5
1.55
6.03
86.77
111.00
157.72
5.57
60.3
105.18
5
1.5
1.75
9.97
62.99
121.90
114.49
5.92
99.7
76.35
6
1.5
1.93
3.94
8.27
150.90
14.99
6.21
39.4
10.02
7
2
1.55
9.97
86.81
110.80
157.80
5.57
99.7
78.92
222
8
2
1.75
3.94
55.75
122.00
101.32
5.92
39.4
50.68
9
2
1.93
6.03
7.87
151.00
14.27
6.21
60.3
7.16
Earlier research results reported by Crawford (1998) validate the above
results as glass fiber/Polyester (GFRP) was reported to have tensile strength of
34MPa-520MPa at 0.42 volume fraction, while polyester resin has impact strength
of 2KJ/m2 chopped strand mat (CSM)/polyester composite has impact strengths in
the range of 50-80KJ/m2. Also Woven roving laminates have impact strengths in
the range of 100-150KJ/m2.
Figure 4.35 and figure 4.36 show the effect of the notch depth and the notch
tip radius on impact strength of various reinforcement combinations of PFRP
(volume fractions of 45%, 50%, 55% and 60%). In figure 4.35, the impact strength
was found to increase with increasing notch tip radius and decrease with increasing
notch depth (figure 4.36). This assertion was obeyed by most composites except
that with 60% volume fraction, with composite of 50% volume fraction showing
highest strength. The first important fact to be noted from figure 4.35 is that the use
of a sharp notch will rank the composite material in a different order to that
obtained using a blunt notch (Crawford, 1998). Figure 4.36 therefore gives a
convenient representation of the notch sensitivity of plantain fiber reinforced
composites. For example it may be seen that sharp notches are clearly detrimental
223
to all the materials tested (45%, 50%, 55%, and 60%) and should be avoided in any
IMPACT strength(KJ/m2)
good design.
180
160
140
120
100
80
60
40
20
0
45% Vol
50% Vol
55% Vol
60% Vol
0.9
1.1
1.3
1.5
1.7
1.9
2.1
Notch tip radius (mm)
Figure 4.35: Variation of impact strength with notch tip radius for different
fiber loading
In general, the impact test is used to measure directly the total energy needed
to break the test specimen by impact (Rajput, 2006). Charpy impact test was thus
used to evaluate the impact strength of the plantain fiber reinforced composites
specimens that have (1, 1.29 and 2) mm notch depth. The results of this test are
shown in Figure 4.36, which illustrates the effect of notch depth on the impact
strength values of plantain fiber reinforced composites plantain fiber reinforced
composites at different volume fractions. Figure 4.36 demonstrates the impact
strength of plantain fiber reinforced composites is highest when the notch depth
tends to zero, but when the notch depth increases gradually, the impact strength of
the composites will be decreased, this is related to the decrease of the cross-
224
sectional area of the material resulting to a decrease in the energy required to break
IMPACT strength(KJ/m2)
the sample and thus the impact will be decreased as well (Rajput, 2006).
180
160
140
120
100
80
60
40
20
0
45% Vol
50% Vol
55% Vol
60% Vol
0.9
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
2
2.1
Notch dept (mm)
Figure 4.36: Variation of impact strength with notch depth.
This severity of notch depth is quite understandable because as the resisting
cross sectional area reduces load bearing capacity will also reduce and hence the
reduction in impact toughness. The influence of impact angle on impact strength is
IMPACT strength (KJ/m2)
exhibited in figure 4.37 (a).
180
160
140
120
100
80
60
40
20
0
162.3104
114.5398
36.8687
100
105
110
115
120
125
130
135
140
145
150
impact angle (β) Deg.
(a)
225
IMPACT strength(KJ/m2)
180
160
140
120
100
80
60
40
20
0
162.3104
114.5398
36.8687
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
stress concentration factor (kt)
(b)
Figure 4.37 (a) and (b): Variation of impact strength with impact angle and
stress concentration factor
Three different notch lengths were converted to stress concentration factor
using Equation (3.59) and stress concentration factor was found to have a linear
relationship with impact strength and break energy of PFRP. Figure 4.38(b) shows
that as stress concentration factor increases, impact strength and break energy of
PFRP decreased.
226
4.5
Optimally designed plantain fiber reinforced composite sample and
specification
The optimal design characteristics of plantain fiber reinforced composites
were established for control factors set at 50% fiber volume fraction, 10 fiber
aspect ratio and 90O fiber orientation, these specifications was manufactured and
analysed using finite element method (FEM).
Figure 4.38: Produced sample of an optimally designed plantain fiber
reinforced composite sample (150×19.05×3.2 mm) and replicate FEM model.
This section explains in detail the geometry and material property of the
composite material, step wise procedure to develop the composites finite element
model, the boundary and loading conditions applied on the model.
4.5.1 Finite Element Modelling of optimally designed plantain fiber reinforced
composites
The experimental investigation of plantain fiber reinforced composites in
tension and flexure conducted on the specimens gave rise to several interesting
results. However since only a limited number of tests have been made on these
227
samples, proper validation of these results was of utmost importance. Hence a
finite element analysis (FEA) was conducted by simulating the conditions of the
tests. 2D and 3-D finite element model of plantain fiber reinforced composite was
developed and suitable material properties were assigned to validate the
experimental results of the previous sections. The established finite element
software ANSYS 11.0 Classic was used to develop the required finite element
models. Loads were applied as in the experimental tests to get numerical
verification of the results.
Finite element is a mathematical method which makes calculations by
dividing complex structures into very little elements. Finite Element (FE)
programme is a programme which puts forth the performance and possible fracture
loads of constructions into consideration in a virtual medium. The results can be
obtained as tables or graphics (Gabor et al., 2005). The solution of very complex
systems as geometrical scale or an equation can be made with FE programme.
Therefore, it can be used in the modelling of plantain fiber reinforced composites
effectively. In order to get the solution with FE pogramme, the following
procedures was carried out:
 First step is to put forth the physical model into consideration. The geometric
model of the specimen that will be modeled in two or three dimensional spaces
is formed by using graphical procedure interface of ANSYS 11.0 (FE
programme).
228
 Second step includes the introduction of material properties. For this reason, the
reinforced composites material element and factuality present in the library of
the programme are all suitable for the modeling. Moreover, element
formulation which is a suitable element type for rigid modeling is also present
in the library.
 Third step is the process for dividing (mesh) two or three-dimensional model
into elements.
 Final step, on the other hand, is the introduction of limit conditions, that is,
support conditions. After the completion of modelling process, the matrix
solution processor of ANSYS 11.0 is used in order to determine the rigidity
matrix that will be obtained with the programme as well as displacement matrix
as a product (Gabor et al., 2005).
4.5.2 Composites in tension
The finite element code ANSYS, Version 11.0, has been used. Its
composites model consists of material model to predict the failure of elastic
materials, applied to a two dimensional PLANE 82 element. The material is
capable of plastic deformation. The tension softening is determined by failure
surface. Tensile failure is defined by the maximum tensile stress criterion.
Element Type: The type of element to be used in the analysis influences the
exactness and accuracy of the results to a great extent. Literature review and
229
examination of peer researchers’ works (Akram and Arz, 2008; Stere and Baran,
2011; Nidhi and Veerendra, 2012) show that PLANE 82 element have been
conveniently used in the numerical analysis and optimization of fiber reinforced
composite subjected to tensile loading. A 2-D solid model of the actual test
specimen was therefore built using ANSYS 11.0 software package (ANSYS, 2006)
using the PLANE 82 element. PLANE 82 is an 8-node structural plane element
designed to model plane strain conditions (Zienkiewicz and Taylor, 2000). The
element is defined by 8 nodes having two degrees of freedom per node:
translations in the nodal x, and y directions. The X-direction corresponds to the
longitudinal direction of the test specimen and the loading direction. The Ydirection corresponds to the lateral direction of the test specimen. Figure 4.39
below shows a geometric model of a PLANE 82 element with its nodes positioned
at the appropriate places. A triangular-shaped element was formed by defining the
same node number for nodes K, L and O.
Figure 4.39. Applicable PLANE82 2-D 8-Node Structural Solid
230
Modeling and development of nodal points: The modeling of the sample
required the creation of key points at specific locations. The key points are created
by specifying an identity for each one of them and giving their respective coordinates as shown in table 4.40. Thus key points were created at the starting and
ending of the lines based on the specification of ASTM D638-10. Figure 4.40
below shows the skeleton of a rectangular specimen outlined by its key points at
the above mentioned location and the nodes.
Table 4.52. Construction of sample geometry
Key point number
x
1
0
2
20
3
130
4
150
5
150
6
130
7
20
8
0
y
0
0
0
0
19.05
19.05
19.05
19.05
z
0
0
0
0
0
0
0
0
Figure 4.40 Positions of Nodes and Key points for the test specimen
231
These key points are then connected with lines, such that the working area
can be generated based on the line created as shown in figure 4.41
Figure 4.41 the unmeshed tensile model.
Figure 4.41 shows the unmeshed model of tensile specimen in positive xplane. The modeling was followed by meshing of the area so far formed. The mesh
tool was used to actuate the areas required to be meshed. The size of each element,
the shape of each element and the type of mesh were given in the mesh tool. Figure
4.42. Shows a meshed model of the rectangular specimen indicating nodal position
of the elements. The meshing was done uniformly over the sample using a free
mesh; triangular shaped elements as described in figure 3.13 were used in the
meshing.
232
Figure 4.42 Meshed Model of the Rectangular Shaped specimen
The boundary conditions applied and the loading procedures are discussed in
the following section.
Model Restraints and Load Application: The rectangular model having
150×19.05×3.2 mm dimensions as per ASTM D638-10 is composed of two ends at
positive x-plane. A maximum load (P=2330N) was applied on the flat tabs area to
simulate the actual experimental process as shown in figure 4.43. The load is
parallel to the sample and is symmetric with respect to the centerline such that it
cannot create bending moments about the x, y, z-axes.
233
Figure 4.43. Tensile test model with loading and Boundary Conditions
Transverse modulus of composite: The mean value of modulus computations
from empirical equations of (3.3), (3.4) and (3.5) using data of tables 4.53 and are
presented in figures 4.44 and 4.45, the modulus E2 estimated for PPSFRC and
PEFBFRC composites
at 50% volume fraction of fibers are 6818 MPa and
7031MPa respectively.
Table 4.53: Mechanical Properties of Plantain Fibers and polyester resin
Property
Polyester resin
Density (g/cm3)
1.2 - 1.5 (1400 kilograms per cubic meter)
Young modulus (MPa)
2000 – 4500
Tensile strength (MPa)
40 - 9 0
Compressive strength (MPa)
90 -250
Tensile elongation at break (%)
2
Water absorption 24h at 20 °C
0.1 - 0.3
Flexural modulus (GPa)
11.0
Poisson's ratio.
0.37 – 0.38
Plantain Pseudo Stem Fibers
Young modulus (MPa)
23555
UTS (MPa)
536.2
Strain (%)
2.37
234
Density Kg/m3
Young modulus (MPa)
UTS (MPa)
Strain (%)
Density Kg/m3
381.966
Plantain Empty fruit bunch Fibers
27344
780.3
2.68
354.151
Table 4.54: Composites elastic modulus with empirical equations
EMPTY FRUIT BUNCH (EFB) FIBER REINFORCED COMPOSITES
SPECIMEN Vm
Vfr
E_Rule of E_Halphin- E_Brintrup
E2
CODE
Mixture
Tsai (MPa)
(MPa)
(MPa)
(MPa)
EFB0
1
0
3250
3250
3781.818 3427.273
EFB1
0.9
0.1
3564.044
3997.318
4138.424 3899.929
EFB2
0.8
0.2
3945.27
4868.707
4569.284 4461.087
EFB3
0.7
0.3
4417.821
5897.861
5100.285 5138.656
EFB4
0.6
0.4
5018.976
7131.891
5770.93 5973.932
EFB5
0.5
0.5
5809.505
8638.735
6644.647 7030.962
EFB6
0.4
0.6
6895.621
10520.11
7830.125 8415.284
EFB7
0.3
0.7
8481.228
12935.45
9530.464 10315.71
EFB8
0.2
0.8
11013.78
16149.7
12174.12 13112.53
PSEUDO STEM FIBER REINFORCED COMPOSITES
STEM 0
1
0
3250
3250
3781.818 3427.273
STEM1
0.9
0.1
3556.587
3956.431
4128.373 3880.464
STEM2
0.8
0.2
3927.042
4773.227
4544.851 4415.04
STEM3
0.7
0.3
4383.643
5728.441
5054.786 5055.623
STEM4
0.6
0.4
4960.393
6860.518
5693.614 5838.175
STEM5
0.5
0.5
5711.901
8223.59
6517.271 6817.587
STEM6
0.4
0.6
6731.775
9896.388
7619.539 8082.568
STEM7
0.3
0.7
8195.017
11998.01
9170.559 9787.863
STEM8
0.2
0.8
10471.04
14717.6
11514.41 12234.35
Figures 4.44 and 4.45 express the variation of transverse moduli of composites
with volume fraction of fibers while giving the average values of transverse moduli
at 50% volume fraction estimated with rule of mixtures, Brintrop and Halpin-Tai
equations as 6818MPa and 7031MPa respectively for PPSFC and PEFBFRC.
235
Modulus of Elasticity (MPa)
16000
14000
y = 15498x3 - 6085.x2 + 5941.x + 3386.
R² = 0.999
12000
10000
E_Rule of Mixture (MPa)
8000
E_Halphin-Tsai (Mpa)
6000
E_Brintrup (Mpa)
4000
E2 (Mpa)
2000
Poly. (E2 (Mpa))
0
0
0.2
0.4
0.6
0.8
1
Fiber Volume fraction Vfr
Figure 4.44: Depiction of PPSFC transverse modulus computed with
empirical equations
Therefore a computational model for evaluating the elastic modulus of
plantain pseudo stem fiber reinforced polyester matrix based material is expressed
as
= 15498
– 6085
+ 5941
+ 3386
(4.26)
Modulus of Elasticity (MPa)
18000
16000
y = 18727x3 - 8051.x2 + 6540.x + 3376
R² = 0.999
14000
12000
E_Rule of Mixture (MPa)
10000
E_Halphin-Tsai (Mpa)
8000
6000
E_Brintrup (Mpa)
4000
E2 (Mpa)
2000
Poly. (E2 (Mpa))
0
0
0.2
0.4
0.6
0.8
1
Fiber Volume fraction Vfr
Figure 4.45: Depiction of PEFBFRC transverse modulus computed with
empirical equations.
236
Through Figure 4.45 generated from predictions of Table 4.54 a cubic
polynomial equation relating elastic modulus and volume fraction was established
in this study for plantain EFBFRC as
= 18727
– 8051
+ 6540
+ 3376
(4.27)
Estimation of random modulus of composite: This is based on the rule of
mixtures assumptions and equation (3.6). The rule of mixture states that the
modulus of a unidirectional fiber composite is proportional to the volume fraction
of the materials in the composite. The modulus of elasticity varies with direction
because of inclination of the fibers such that the substantive modulus of elasticity
is computed as follows:
For plantain stem fiber reinforced composites, where
23555 MPa, 0.5, 2500 (MPa), 0.5 respectively thus
equation (3.6) of rule of mixtures, also
3332.835 (
) by equations (3.7) and
,
,
,
= 13027.5 (
= 9146.305 (
),
) by
=
equals 0.37 by equation (3.8).
For plantain empty fruit bunch fiber reinforced composites, where
,
=
,
,
= 27344 (MPa), 0.5, 2500(MPa), 0.5 respectively therefore
= 14922 (
= 9990.10 (
) by equation (3.6) of rule of mixtures, also
),
= 3622.99 (
) by equations (3.7) and
equals 0.38 by equation (3.8).
237
Table 4.55: Isotropic material properties for finite element analysis
PLANTAIN EFBFR COMPOSITES
Symbol
Label
Item
units
Value
E
EX
Elastic modulus (Young’s modulus)
MPa
9990.10
µ
NUXY
Poisson’s ratio
-
0.38
G
GXY
Shear modulus
MPa
3332.835
ρ
DENS
Mass density
Kg/m3
877.076
F
FX
Force
N
2330
α
ALPX
Coefficient of thermal expansion
C^-1
0
o
PLANTAIN PSFR COMPOSITES
E
EX
Elastic modulus (Young’s modulus)
MPa
9146.305
µ
NUXY
Poisson’s ratio
-
0.37
G
GXY
Shear modulus
MPa
3622.99
ρ
DENS
Mass density
Kg/m3
890.501
F
FX
Force
N
2067
α
ALPX
Coefficient of thermal expansion
C^-1
0
o
Orthogonal deformation results: The tensile strength distribution for the
PEFBFRC specimen is shown in Figure 4.46. The tensile strength obtained from
this analysis is 38.78 MPa and its optimal value from RSM is observed at 41.68
MPa.
238
Figure 4.46: Plane strain analysis for PEFBFRC showing stress distribution in
x-direction with a maximum stress of 38.781 MPa
Figure 4.47: Plane strain analysis for PEFBFRC resulting to a displacement of
0.264681 mm
239
Figure 4.47 and 4.48 exhibits the maximum displacement and strain for
PEFBFRC as 0.26mm and 0.004 respectively while figure 4.49 which is a vector
plot depiction of maximum degree of freedom as 0.27 for PEFBFRC.
Figure 4.48: Plane strain analysis for PEFBFRC resulting to strain of
0.003525
240
Figure 4.49: Vector plots for PEFBFRC showing degree of freedom
Table 4.56: Summary of FEA results for PEFBFRC-50% 90O (10) sample
settings at selected nodes
NODE
1
37.340
0.32030E-06
10.829
-0.43229E-06
0.0000
0.0000
2
37.340
0.13285E-06
10.829
0.16822E-06
0.0000
0.0000
4
37.340
-0.12616E-08
10.829
0.48565E-06
0.0000
0.0000
26
36.328
-0.47302E-01
10.522
0.14818
0.0000
0.0000
28
35.575
-0.38033E-01
10.306
0.19353E-01
0.0000
0.0000
30
38.772
1.0944
11.561
-1.9777
0.0000
0.0000
32
38.772
1.0944
11.561
1.9777
0.0000
0.0000
564
37.340
-0.35800E-06
10.829
0.65936E-06
0.0000
0.0000
565
37.340
-0.97078E-06
10.829
-0.20651E-05
0.0000
0.0000
241
ANSYS finite element orthogonal deformation results for PPSFRC at 50, 90,
10 sample settings: The tensile strength distribution for the specimen is shown in
Figure 4.50. The tensile strength obtained from this analysis is 35.28 MPa. Its
experimental value observed from RSM is 34.76 MPa. The variation in the two
values is noticed to be 1.5 % which is within the acceptable error range.
Figure 4.50: Plane strain analysis for PPSFRC showing distribution of applied
stress in x-direction with a maximum stress of 35.28 MPa
Figure 4.50 and table 4.57 shows the maximum orthogonal stress for PPSFC
as 35.28MPa while figure 4.51 is a vector depiction of maximum degree of
freedom for PPSFC as 0.25mm. Table 4.58 expresses the principal stresses for both
PEFBFRC and PPSFC and gives the yield stresses for PFRP as 33.69MPa and
29.24MPa for PEFBFRC and PPSFRC respectively.
242
Figure 4.51: Vector plot for PPSFRC depicting degree of freedom
Table 4.57: FEA results for PPSFRC-50% 90O (10) sample settings at selected
nodes
NODE
1
2
60
98
100
102
565
564
33.133
33.133
33.133
32.444
35.283
32.444
33.133
33.133
0.54789E-07
0.54265E-07
-0.21030E-08
-0.66660
6.0978
-0.66660
-0.15613E-06
-0.15509E-06
3.3133
3.3133
3.3133
3.1778
4.1381
3.1778
3.3133
3.3133
-0.71909E-07
0.71931E-07
-0.56613E-07
0.50614
0.31273E-07
-0.50614
-0.32084E-06
0.32077E-06
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
243
4.5.1.1
Failure predictions with stress theories and specification for safety
Computation of principal stresses is based on equation (3.34) and that of
tensile orthogonal stresses results of the FEA results. The idea behind the various
classical failure theories is that whatever is responsible for failure in the standard
tensile test will also be responsible for failure under all other conditions of static
loading (Shigley and Mischke, 1989); so that by putting the orthogonal stresses
results of nodes 30 and 100 of tables 9 and 10 in equation (3.34) the following
cubic equations for principal stresses for PEFBFRC and PPSFRC are obtained
− 51.4274
+ 503.3276 − 445.3387 = 0
(4.28 )
− 45.5183
+ 386.0238 − 890.3067 = 0
(4.29 )
The solution of equations 4.28 and 4.29 resulted to the principal stresses of
the composite as presented in tables 4.58 and 4.59. The failure yield stress
is
evaluated with equations (3.36), (3.38), and (3.42) and presented in table 4.58.
Table 4.58: Computed limit stresses for plantain fiber reinforced composites
Maximum
Yield stress
principal
Principal normal stress
shear stress
DET
MSST
MNST
( MPa)
(MPa)
Composites
(MPa)
(MP)
(MPa)
37.80 14.44 -0.82
19.31
33.69
38.62
37.80
PEFBFC
35.30 6.06
4.16
15.57
29.24
31.13
35.30
PPSFC
244
Table 4.59 shows that the tensile properties of PEFBFRC such as modulus
of composite and tensile strength of composite are higher than that of PPSFRC in
the fiber direction when the rule of mixtures equation is applied with the basic
properties of reinforcing fibers and matrix.
Table 4.59: Evaluated mechanical properties of plantain fibers and plantain
fibers reinforced polyester composites
Composites/fib
ers
PEFBF
PEFBFC
PPSF
PPSFC
,
Properties
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
780.30
410.15
536.20
288.10
37.3397
33.1330
33.69
29.24
27344
14922
23555
13027.5
7030.962
6817.175
9990.10
9146.305
0.37
0.38
0.20
0.29
(MPa)
G
(MPa)
1812.575
19.3100
1561.410
15.5700
11393.33
3622.99
9814.58
3332.835
are tensile strengths in the longitudinal and transverse directions
respectively. Figure 4.46 and table 4.56 show the orthogonal stresses with the
maximum value at node 30 for PEFBFRC.
In general, table 4.59 summarizes the basic physical and mechanical
properties of PFRP evaluated in this study while table 4.60 exhibits the composite
directional stresses. It was established that while the PEFBFRC carries 38.77MPa,
PPSFRC carries 35.28MPa stresses equivalent to the ultimate tensile strength of
the composites with respect to their transverse directions. Table 4.59 equally
reports the tensile strength of PEFBFRC in the fiber direction as 410.15MPa and
for PPSFRC as 288.10MPa. Chimekwene et al., (2012) studied on the mechanical
properties of a new series of bio-composite involving plantain empty fruit bunch as
reinforcing material in an epoxy based polymer matrix and found an optimal
245
tensile strength of 243N/mm2 from the woven roving treated fiber reinforced
composites at a fiber volume fraction of 40%.
4.5.1.2
Estimation of transverse and longitudinal stresses of composite at
failure
By using the values of the orthogonal stresses of tables 4.56 and 4.57 at nodes 30
and 100 the orthogonal stresses are transformed to composite axis and the
longitudinal and transverse stresses of the composites are evaluated and presented
as in table 4.60. It must be noted that composite failure stress determined during
tensile test is the ultimate strength of composite in the transverse direction while
the ultimate strength of composite in the longitudinal or in the direction of
alignment of fibers is that usually determined through the rule of mixtures. These
stresses aid the determination of occurrence of yielding.
Table 4.60: Stress transformation for composites orientation stresses
Orthogonal stresses
Composite orientation
stresses
Composites
PEFBFC
38.772
1.094
11.561 -1.977
0.000
0.0000
1.094
38.772
1.978
PPSFC
35.283
6.098
4.138
0.000
0.0000
6.098
35.283
0.000
0.000
Halpin-Hill Criterion is an empirical criterion that defines failure as occurring if
+
+
≥1
(4.30 )
246
By employing the values of tables 4.58 and 4.60 in equation (4.30) where
=
=
, equation (4.30) is evaluated for PEFBFRC and PPSFRC respectively
as
1.0944
410.15
+
38.772
37.3397
+
1.9777
19.3100
= 1.10
6.0978
288.10
+
35.283
33.1330
+
0.000
15.5700
= 1.13
Since the values of the computations of equation (4.30) gave 1.10 and 1.13 for
composites of PEFBF and PPSF and are more than unity (1), failure is likely to
occur and it is reasonable for yield stresses to be specified for the two materials.
4.5.3 Composites in flexure
This section specifically describes the finite element modeling and analysis
techniques used for simulating the flexural behavior of plantain fiber reinforced
composites. ANSYS 11.0 software is one of the most reliable and popular
commercial finite element method programs (Lawrence, 2007). The Flexural test
measures the force required to bend a beam under 3 point loading conditions and
the data is often used to select materials for parts that will support loads without
flexing. Flexural modulus is used as an indication of a material’s stiffness when
flexed.
247
Element type: The composite element type Solid 45 has been applied for three
point flexural test according to ASTM testing to determine the fracture toughness
of many materials, including composites (Gabor et al., 2005; Kim et al., 2010;
Stere and Baran, 2011; Mahzabin et al., 2012). For a linear elastic isotropic beam
in bending, the neutral axis is a hypothetical line demarking that half of the beam is
in compression and the other half is in tension.
The element is defined by eight nodes having three degrees of freedom at
each node: translations in the nodal x, y, and z directions. The element has
plasticity, creep, swelling, stress stiffening, large deflection, and large strain
capabilities (Gabor et al., 2005). The geometry, node locations, and the coordinate
system for this element are shown in Figure 4.52. The element is defined by eight
nodes.
Figure 4.52: SOLID45 3-D Structural Solid
248
Pressures may be input as surface loads on the element faces as shown by the
circled numbers on Figure 4.52. Positive pressures act into the element.
Modeling and meshing: The modeling of the sample required the creation of key
points at specific locations as previously described shown in section 4.5.1. These
key points are then connected with lines. The specimen geometry for 3 point bend
test as per ASTM D790-10 standards is shown in Figure 4.53 while the key points
are shown in table 4.61
Table 4.61 key point structure for the flexural model
Key point number
x
y
1
0
0
2
20
0
3
280
0
4
300
0
5
300
3.175
6
280
3.175
7
20
3.175
8
0
3.175
z
0
0
0
0
0
0
0
0
The model is then extruded along the z-direction to the required width of
19.05mm by sweeping all the lines along the reference axis. This extrusion of lines
about a reference creates the volume required for meshing. Figure 4.53 shows the
unmeshed model of a rectangular specimen after extrusion.
249
Figure 4.53: Unmeshed FEA model of after extrusion.
The modeling was followed by meshing of the models as shown in figure
4.54. The mesh tool was opened and the areas required to be meshed were selected.
The size of each element, the shape of each element and the type of mesh were
given in the mesh tool.
250
Figure 4.54 Meshed Model showing the Rectangular Shaped elements and
node numbers
Boundary conditions and loading: The problem was modeled as a three point
bending system, in three-point bending; the simply supported beam is supported on
two outer points, and deformed by driving the third central point downwards. The
maximum load is located at the centre, which are the same as those of the test
setup. The experimental conditions were closely simulated in order to obtain
accurate results. Figure 4.55 below shows a meshed FEA model with the applied
loads and boundary conditions.
251
Figure 4.55: Meshed FEA model with the applied loads and boundary
conditions.
The boundary conditions were specified as follows:
1. The simply supported beam is supported on two outer points; both ends of
the model were completely constrained in the rotational direction by fixing
all degrees of freedom.
2. The slender structural element was then subjected to an external load applied
perpendicular to an axis of the element.
Results and discussions: A refined mesh is obtained with 3000 elements and 3642
nodes which is shown in Fig: 4.56, the computer simulations of flexural test are
performed by choosing the ultimate loads (23.273N) recorded in the test.
252
Figure: 4.56. A refined mesh obtained with 3000 elements and 3642 nodes
Figure 4.57: Flexural stress distribution for PEFB fiber reinforced composites
in MPa
253
Figure 4.58: Flexural stress distribution for PPS fiber reinforced composites
in MPa
The x-directional deformation obtained by FEA of flexural test is 0.372 mm
as shown in Figure 4.59. While the y-directional deformation is 2.136 mm as
shown in Figure 4.60. The flexural stress distribution is shown in Figure 4.58. The
maximum flexural strength obtained by FE analysis is 48.23 MPa where as its
experimental value is 46.32 MPa. The variation is 4.12% which is within
acceptable error range; figure 4.60 shows the vector plot depiction of degree of
freedom.
254
Figure: 4.59. x-directional deformation of the EFB flexural specimen in mm
Figure: 4.60. y-directional deformation of the EFB flexural specimen in mm
255
Figure: 4.61. Vector plot depiction of degree of freedom for EFB
Table 4.62: Summary of FEA results of flexural model settings at selected
nodes
NODE
PEFB fiber reinforced composites
320
-0.53694E03
-0.10887E01
-0.39730E01
8.2836
321
15.495
-3.3482
-0.84852
-4.7579
322
22.033
0.16898
0.92659
-2.2260
323
21.573
-0.31560E-01
0.76652
-1.1387
-0.26816
1.8158
528
40.694
0.20597E-01
0.30080E-01
-1.4718
0.50063E-02
-1.2638
529
42.401
0.11660E-01
0.76797E-01
-1.4336
-0.94852E-02
-1.2127
0
44.384
0.96463E-01
0.14028
-1.4583
0.18910E-01
-1.0274
1
2
3
-0.14956E-02
-0.33002E-02
0.74156E-02
0.26709E-02
-0.25182E-02
-0.29490E-02
-0.54970E-02
0.15722E-01
0.30905E-02
-0.83602E-02
-0.44445E-02
-0.81978E-02
0.25030E-01
0.36628E-02
-0.17382E-01
4.1285
2.3414
4.9856
-0.50971
-2.5693
-0.78589
3.2514
-0.64964
2.7173
256
531
46.625
0.11487E-01
0.97561E-01
-1.0978
0.48989E-01
-0.75662
532
48.228
0.34167
0.60818
0.10874
0.57341
-0.96734E-01
3641
0.15950
0.62444
0.60233
0.46993E-01
0.18206
0.80558E-01
3642
4.4350
-1.0416
-0.72384
-1.5611
-0.13586
0.80054E-02
1
-0.16555
PPS fiber reinforced composites
-0.12796
-0.14394
-0.28695E-01
-0.11059E-01
-0.94933E-01
2
-0.42301
0.17557
-0.16105
-0.49859E-01
0.49535E-02
-0.26626
83
30.599
0.79873E-02
0.49187E-02
-1.3867
-0.98792E-02
-2.6014
84
35.632
0.27686
0.19807
-1.3879
-0.84510E-01
-2.5813
85
41.573
-0.20059
-0.69082E-01
-1.3717
0.95675E-01
-2.3689
86
46.865
3.0889
0.38311
-0.26491
-0.37913
-0.23063
87
44.403
-0.38683
-0.31298
0.88430
0.14811
1.8063
88
40.940
0.10834
0.30482E-01
0.95531
-0.26083E-01
1.8412
568
-0.31627E-01
-0.10222
-0.10832
-0.23528E-01
0.15402E-01
0.62638E-01
569
0.60568E-01
0.31635
0.43386E-02
-0.28643E-01
0.16796E-01
0.16590
570
0.90842
-0.77808
-0.89805E-01
0.26024E-01
0.18800E-02
-0.19990E-02
Table 4.63: Summary results of strengths optimization for plantain fibers
reinforced composites
Evaluated
Mechanical
property
Tensile
strength
(MPa)
Flexural
strength
(MPa)
Brinell
hardness
Taguchi method
(TM)
Empty
Pseudo
fruit
stem
bunch
Optimization scheme
Response surface
methodology (RSM)
Empty
Pseudo
fruit
stem
bunch
Finite Element
Analysis (FEA)
Empty
Pseudo
fruit
stem
bunch
40.28
38.51
41.6804
34.7605
38.781
35.283
42.4
41.16
46.3198
45.9418
48.228
46.865
19.63
19.06
19.1533
18.5894
2
( N/mm )
257
Tables 4.58, 4.59 and 4.63 for plantain fiber reinforced polyester composites
indicate discovery of plantain fibers as a potential reinforcement material, this is
because the results were comparable with a number of researches using leaf fibers
(Abaca, Cantala, Curaua, Date Palm, Henequen, Pineapple, Sisal, Banana etc) as a
reinforcement in polymer matrix.
Bisanda (1991) studied the mechanical
properties of sisal fiber/polyester composites and found the tensile strength at 50%
volume fraction to be 47.1MPa; Myrtha et al. (2008) reported that the flexural
strength of empty fruit bunch/polyester composites for longer fiber is 36.8 MPa
while for short fiber is 33.9 MPa both at 18 % volume fraction, also the
investigation on banana fiber reinforced polyester composites by Laly et al. (2003)
gave the optimum content of fiber at 40%. The result of the current study however,
is slightly higher than the results obtained by Myrtha et al. (2008) and Laly et al.
(2003).
4. 6
Microscopic Characterization of Plantain Fibers and Composites
The quality of plantain fiber and the manufactured composite used in this
study was evaluated (relatively) using several complementary microscopic
methods. The microscopy gives information on voids, fiber distribution and
compositions. The following evaluation methods are chosen to compare the
composite systems considered in this study, the unknown material is visually
inspected using scanning stereo microscopy to better understand morphology,
258
composition and homogeneity. These techniques which include Fourier Transform
Infrared (FTIR) Spectroscopy, Scanning Electron Microscopy (SEM) with Energy
Dispersive Spectroscopy (EDS) and Nitrogen Adsorption/Desorption Isotherm
(NAD) are discussed in greater detail below.
4.6.1 Fourier Transform Infrared (FTIR) Spectroscopy
Fourier Transform Infrared Spectroscopy (FTIR) works by exciting
chemical bonds with infrared light and is best for identification of organic
materials. The different chemical bonds in this excited state absorb the light energy
at frequencies unique to the various bonds. This activity is represented as a
spectrum (See figure 4.62 - 4.65). The spectrum is expressed as % transmittance
(%T) versus wave number (cm-1). The wave number of the peak tells what types of
bonds are present and the %T tells the signal strength. Low signal strength directly
affects the resolution of the peaks making sample size and preparation key for
acquiring a quality spectrum. The spectrum is essentially a “fingerprint” of the
compound that can be used to search against reference spectra from libraries for
the purpose of identification.
The FTIR spectroscopy measures the intensity of light absorbed or emitted
by a material at a particular wave length which is related to some functional groups
in the material. It must be recalled that low strength properties and water
absorption which are addressed by fibers modification limit the application of
natural fibers. The characteristic spectrum of plantain fibers and composites are
259
shown figures 4.62 - 4.65. There are irregular patterns of light intensity spectrum
of PFRP as depicted in figures 4.65 and 4.64. Figures 4.62 and 4.63 shows the
absorbance peaks in the regions of 472.58
PEFBF and 418.57
and 3774.82
and 3406.4
for untreated
for treated PEFBF showing that the
fibers are modified while figures 4.64 and 4.65 show the absorbance peaks in the
regions of 468.72
and 3435.34
for PEFBFRP and 464.86
and
3774.82
for PPSFRP. These correspond to ranges of 2966.62
and
3309.96
for PEFBFRP and PPSFRP respectively. Also this corresponds to
absorbance intensity ranges of 85.98 - 48.12 = 37.86 and 92.687- 82.311 = 10.376
for PEFBFRP and PPSFRP respectively showing the influence of fibers
modification on light absorption. These variations signify that the composites may
have similar properties but PPSFRP may be more porous than PEFBFRP.
260
Figure 4.62: FTIR spectra of untreated plantain EFB fiber.
As seen in figure. 4.62, the strong peak 3406.40 cm-1 is characteristic of
hydrogen-bonded –OH stretching vibration; the peak observed at 3406.40 cm-1 in
untreated plantain empty fruit bunch fibers indicates the presence of intermolecular
hydrogen bonding and tends to shift to higher absorbency values in treated fibers
as shown in figure 4.63, similar observations have been reported in earlier works
by Clemsons et al, (1992), Mallari et al, (1989) and Rowell et al, (1994).
261
The peak at 2920.32 cm-1 is due to CH stretching vibrations (Mital, 2000)
and the peak 1043.52 cm-1 is a characteristic of C-O- symmetric stretching
vibration in cellulose, hemicellulose and minor lignin contribution (Lu & Drazel,
2010).
Figure 4.63: FTIR spectra of Treated Plantain Empty Fruit Bunch Fibers
As can be seen in figure 4.63, the intensity of the peak around 3416.05 cm-1
which is evidence of OH band is increased after treatment of plantain fibers, this
increment according to Liu et al., (2012) may be due to part of hydrogen bond and
262
lignin that was broken during treatment, thus leading to increase in the amorphous
part in cellulose and release of more hydroxyl group.
Figure: 4.64: FTIR spectra of Plantain Stem fiber Reinforced Composites
The peak at about 2926.11 cm−1 in figure 4.64 is due to the C-H asymmetric
stretching from aliphatic saturated compounds. This stretching peak is
corresponding to the aliphatic moieties in cellulose and hemicelluloses (Liu et al.,
2012). An aromatic functional group (C–C stretch in ring) was observed from the
absorption band 1600.97 and 1492 cm–1.
263
Figure 4.65: FTIR spectra of Plantain EFB fiber Reinforced Composites
From figure 4.65, the peak at 2926.11 cm−1 is due to C-H symmetric
stretching. In the double bond region, a shoulder peak range at 1950.10 cm−1 in the
spectrums is assigned to the C=O stretching of the acetyl and uronic ester (Bledzki
et al., 2010).
264
4.6. 2
Nitrogen Adsorption/Desorption Isotherm (NAD)
Adsorption is defined as the adhesion of atoms or molecules of gas to a
surface. Adsorption should not be confused with absorption, in which a fluid
permeates a liquid or solid. The amount of gas adsorbed depends on the exposed
surface are but also on the temperature, gas pressure and strength of interaction
between the gas and solid. In BET surface area analysis, nitrogen is usually used
because of its availability in high purity and its strong interaction with most solids.
Because the interaction between gaseous and solid phases is usually weak, the
surface is cooled using liquid N2 to obtain detectable amounts of adsorption.
Known amounts of nitrogen gas are then released stepwise into the sample cell.
Relative pressures less than atmospheric pressure is achieved by creating
conditions of partial vacuum. After the saturation pressure, no more adsorption
occurs regardless of any further increase in pressure. Highly precise and accurate
pressure transducers monitor the pressure changes due to the adsorption process.
After the adsorption layers are formed, the sample is removed from the nitrogen
atmosphere and heated to cause the adsorbed nitrogen to be released from the
material and quantified. The data collected is displayed in the form of a BET
isotherm, which plots the amount of gas adsorbed as a function of the relative
pressure.
Figure 4.66 indicates that the sample show almost no hystereis and capillary
condensation of nitrogen occurs at relative pressure P/P0= 0.6~0.8, it presents a
plot of relative pressure vs volume adsorbed obtained by measuring the amount of
265
Nitrogen (N2) gas that adsorbs onto the plantain fiber (the 'sorbate') and the
subsequent amount that desorbs at a constant temperature.
VOLUME ADSORBED (cc/g STP)
1.6
1.4
1.2
1
0.8
VOL ADSORBED (cc/g STP)
0.6
VOL DISORBED (cc/g STP)
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
RELATIVE PRESSURE (P/P0)
Figure 4.66: Plot of adsorption and desorption of nitrogen isotherms for
untreated plantain fiber
All samples presented a typical reversible nitrogen adsorption/desorption
isotherm of type II (Rouquerol et al., 1994), having both curves nearly completely
identical; i.e almost no hystereis was observed, with 4.67 having negative
adsorption profile. Natural fibers exhibits adsorption isotherms close to that of
BET-type II (Bismarck et al., 2002).
The influence of fibers modification is clearly shown in figures 4.66 and
4.67, tables 4.64 and 4.65 show significant reduction of fibers specific surface area
with fiber modification, the BET surface areas of untreated plantain fiber and
treated plantain fiber were 0.3369 sq. m/g and 0.0493sq.m/g respectively. Also
266
shown are slight increases in pore area and pore volume with treatment. Similar
observation was made by Cordeiro, et al., (2011), they found for Agro-materials a
BET surface area value between 0.38 and 2.793sq. m/g. Similarly Ouajai and
Shanks (2006) obtained BET specific surface area for raw hemp at 0.334sq. m/g.
Also Cordeiro et al. (2012) obtained the surface area of raw cellulose fibers
ranging between 0.81 and 1.19sq. m/g and after treatment the modified fibers
showed values for the surface area in the range of 0.48 and 0.96sq. m/g.
Table 4.64: NAD Summary Report for untreated plantain fiber
AREA
Bet surface area:
0.3369 sq. m/g
Single point surface area at P/Po 0.2188:
0.3079sq.m/g
BJH cumulative desorption surface
0.2765 sq.m/g
Area of pores between 17.0000 and
3000.0000 a diameter:
Micro pore area:
0.0030 sq. m/g
VOLUME
Single point total pore volume pores
0.001126 cc/g
Less than 1316.8137 a diameter at P/Po 0.9852:
BJH cumulative desorption pore volume
0.002098 cc/g
Of pores between 17.0000 and
3000.0000 a diameter:
Micro pore Volume:
-0.000014 cc/g
PORE SIZE
Average pore diameter (4V/A by BET):
133.6502 A
BJH desorption average pore diameter
303.5635 A
(4V/A):
267
0.5
VOL ADSORBED (cc/g STP)
0.4
0.3
0.2
VOL ADSORBED (cc/g STP)
0.1
VOL DISORBED (cc/g STP)
0
0
0.2
0.4
0.6
0.8
1
1.2
-0.1
-0.2
-0.3
RELATIVE PRESSURE (P/Po)
Fig 4.67: Plot of adsorption and desorption of nitrogen isotherms for
treated plantain fiber
Porous structure parameters are summarized in tables 4.64 and 4.65. From
table 4.65, the value of micro pore area occurrence of 0.3302sq. m/g for treated
fibers suggests that the observed fibrous samples exhibited almost no pores inside
the single fibers.
Table 4.65: NAD Summary Report for treated plantain fiber
AREA
Bet surface area:
Langmuir surface area:
Single point surface area at P/Po 0.2191
Micro pore area:
VOLUME
Micro pore volume:
0.0493sq.
0.0618sq.
0.0552sq.
0.3302sq.
m/g
m/g
m/g
m/g
0.000148
cc/g
268
4.6.3. Morphology mechanism of composites
The morphology mechanism of composites was established using Scanning
Electron Microscopy (SEM) with Energy Dispersive Spectroscopy (EDS), in
addition to having the capability to identify the surface elemental composition of
materials, particles, and contaminants, the SEM is ideal for imaging and the
features revealed can be used to determine the mode of failure and clues to the
cause of failure (i.e. in support of a failure analysis), the electrons generate x-rays
from the surface of the materials in the sample. The x-rays emitted from the sample
was interpreted using energy dispersive spectroscopy (EDS) to determine of which
elements (atoms) the surface of the sample is composed, and the elemental
composition of the features on the sample (see figures 4.69 and 4.71).
The SEM micrographs depictions of x-ray intensity and the associated
energies of atoms of an element are shown in figures 4.69-4.71. The elements of
the composites structures are clearly shown as well as the energies released during
the bombardment of the atoms. Figure 4.69 shows the highest intensity of X-ray
and lower energy difference for atoms of elements of PEFBFRC, while figures
4.71 show lower intensity of X-ray and higher energy releases for atoms of
PPSFRC. These characteristics may be linked to the reasons while PEFBFRC have
the higher strength. The presence of voids in the composites due to hand lay-up
technology could also contribute higher degradation rates in composites.
269
The strengths of the composites are linked to the number of the elements
found in the depictions of figure 4.69 and figure 4.719. It is very clear that figure
4.69 contains more elements than figure 4.71. The electronic configuration of these
elements atoms favors different types of bonding which contributes to the strength
of the composites. Figures 4.71 shows the presence of more atomic energy
abundance for oxygen atom (O) in composite of PPSFRC, this is also confirmed
with SEM micrograph of figure 4.70 as shown with many surface flaws as pores.
Porosity decreases the strength of composites as they constitute stress initiation
points. This may be the reason why PPSFC composites have less strength than
PEFBFC.
Both samples of PPSFRC and PEFBRC of figures 4.68 and 4.70 show
porosity flaws and shrinkage flaws which are stress raisers that contribute to the
untimely failure of composites. It may be difficult to state which of the two types
of composites has the highest qualities since the method of composition may
influence the results of tests. However the rule of mixtures results which are based
on the properties of the fibers, the resin and the orientation of the fibers show with
the tensile tests results that PEFBFRC has the highest tensile strength and yield
strength as depicted in table 4.58 and 4.59. In general, the design of unidirectional
fibers composite will be based on the on the properties of composites as related to
the transverse direction.
270
Figure 4.68: 100 and 500 magnifications of SEM depiction of flaws in
PEFBFC of 90, 50, 10 composition
From the Energy dispersive X-ray spectroscopy (EDS) analyses of figure
4.69, the plantain EFB fiber/polyester interface was found to be rich in aluminum
(Al) along with the presence of Argon (Ar). Also the incidence of Silicon (Si) and
Magnesium (Mg) is consistent with the location of the plantain fiber. SEM and
EDS analyses confirmed that the boundary of fiber–matrix transition zone have
excellent adhesion. The impregnation of fibers within the polymer showed better
strength enhancement.
271
Figure 4.69: X-ray relative abundance versus amount of energy released for
PEFBFC of 90, 50, and 10 compositions
The result also show that plantain EFB fibers reinforced polyester
composites contain higher percentage content of some elements of Carbon (C) and
Manganese (Mn) including Magnesium (Mg) at varying quantities. This
composition may be ascribed to the improved mechanical properties and resilience
of treated plantain EFB fibers composites.
272
Figure 4.70: 300 and 500 magnifications for SEM depiction of flaws in
PPSFRC of 90,50,10 composition
In all samples, the characteristics of polyester-matrix and reinforcing
plantain fibers were identified with the help of EDS analysis performed during
SEM observations, these spectra shows a composite with homogeneous
composition on the surface.
Figure 4.71: X-ray relative abundance versus amount energy released for
PPSFC of 90, 50, 10 composition
273
From figure 4.71 showing an EDS spectrum performed at a micro region of
the fiber-matrix surface, the spectrum reveals that the composite is essentially
composed of carbon (C), oxygen (O), Chlorine (Cl), Calcium (Ca) and Potassium
(K) in different proportions. From the result, it is observed that surface treatment
process involving the alkali and saline resulted in the prominent improvement in
carbon content. The improvement in the carbon content in the plantain STEM
fibers composites has effect on the strength properties, the elements of plantain
stem fiber and polyester were detected by the EDS analysis.
274
CHAPTER FIVE
CONCLUSIONS, CONTRIBUTION TO KNOWLEDGE AND
RECOMMENDATIONS
5.1
Conclusions
In this dissertation, integrated robust design and optimization of plantain
fiber reinforced composites was studied as an effective method to improve quality
in product design and manufacturing. Taguchi robust parameter design works on
the control factors and noise factors to optimize the response and minimize the
variability transmitted from the internal and external noise factors. The goal of
parameter design is to fulfill the requirements of the quality characteristics or the
responses. Response surface methodology is used in system design and modeling
of the new material. The final optimum solutions are obtained through RSM and
validated using Finite Element Analysis (FEA).
It was shown that the RSM is superior to Taguchi approach because of its
ability to handle interaction effects and it provides a better fit for robust design
problems, a finite element model was created to obtain the stiffness of Plantain
fiber reinforced composites. The results of finite element method were compared
with empirical solution. From experimental results for plantain pseudo-stem fiber
reinforced polyester composite and plantain empty fruit bunch fiber reinforced
polyester composite as shown in figures 4.8, 4.10 and 4.11, including the solution
275
of finite element analysis as shown in figure 4.46 and figure 4.58, there is a good
agreement with numerical and experimental results. In general, the plantain EFB
fiber reinforced polyester composites have better tensile properties than the
plantain pseudo stem fiber reinforced polyester composite; this may be due to
higher hemi-cellulose content of the plantain pseudo stem than that of plantain
EFB fiber because hemicelluloses has a random, amorphous structure with little
strength (Kalia et al., 2009).
Therefore, in line with the set objectives of this study, the mechanical
properties of plantain fiber reinforced polyester matrix composite (PFRP) was
optimally designed and characterized and the following are the key findings:
1. Determination of fiber volume fraction of fibers for empty fruit bunch fibers
(EFBF) and pseudo stem fibers (PSF) of the plantain plant was done using
Archimedes principles, the study therefore concludes from table 3.1 that
plantain EFBF of mass 20.670g occupies a volume of 58364.8mm3 with a
density of 381.966 Kg/m3, while plantain PSF of mass 20.397g occupies a
volume of 53364.8mm3 with a density of 354.151Kg/m3
2. The optimal control factors for PFRP were determined for volume fraction of
fiber(A), aspect ratio of fiber(B) and fiber orientation(C) as 50%, 10 and
90degree respectively as shown in table 4.8. furthermore, from tables 4.6 - 4.7,
276
the study concludes that factor A has a stronger significant effect and the
highest contribution to composite strength than the other two control factors.
3. The tensile, flexural, Brinell hardness and impact response of the plantain
empty fruit bunch fibers reinforced composites (PEFBFRC) were found to be
41.68MPa[figure 4.10], 46.31MPa[figure 4.22], 19.15N/mm2 [figure 4.33]and
158.01KJ/m2[table 4.50] respectively while those for the plantain pseudo stem
fibers reinforced composite (PPSFRC) were
34.76MPa[figure 4.11],
45.94MPa[figure 4.24], 18.59N/mm2 [figure 4.34] and 158.01KJ/m2 [table
4.51] respectively.
The table 4.13 model F-value of 1241.73 implies that the response model is
significant. There is only a 0.01% chance that this large value could occur due
to noise. In this case factors A, B, C, AB, AC, A2, B2, C2 are significant model
terms, hence the response of this study was found to follow a polynomial model
of the form:
=
+
+
+
+
+
+
+
+
+
capturing main effects, interaction effects and second–order effects of
combinations of factors. In general, the optimal response models of this study
generated through design expert8 software for tensile, flexural and Brinell
hardness are presented in equations 4.6, 4.8, 4.15, 4.17, 4.23 and 4.25 in terms
of actual factors. The main effects of factors show that volume fraction has the
277
highest effects in the variability of the quality characteristics of the response
under investigation for PFRP. The interaction effects of control factors as
depicted in the models were found to be minimal, hence the design is
considered robust and the models are optimum models.
4. The analysis of displacement and stress distributions of PFRP was done using
Finite Element Method, Figure 4.47 and 4.48 exhibits the maximum
displacement in tension and strain for PEFBFRC as 0.26mm and 0.004
respectively with maximum degree of freedom of 0.27. Figure 4.50 and table
4.57 shows the maximum orthogonal stress for PPSFC as 35.28MPa while
figure 4.51 is a vector depiction of maximum degree of freedom for PPSFC as
0.25mm. Table 4.58 expresses the principal stresses for both PEFBFRC and
PPSFC and gives the yield stresses for PFRP as 33.69MPa and 29.24MPa for
PEFBFRC and PPSFRC respectively. The x-directional deformation obtained
by FEA of flexural test is 0.372 mm as shown in Figure 4.59. While the ydirectional deformation is 2.136 mm as shown in Figure 4.60. The flexural
stress distribution is shown in Figure 4.58 and the maximum flexural stress was
found to be 48.23 MPa.
5. Non destructive testing of plantain fibers was performed using Fourier
transform infrared (FTIR) spectroscopy and comparing figures 4.64 and 4.65,
the study found that PEFBFRP with average light absorbance peak of 45.47
278
have better mechanical properties than the PPSFRP with average light
absorbance peak of 45.77.
6. Investigation of the morphology mechanism of composites was performed
using scanning electron microscope and the study concludes from the Energy
dispersive X-ray spectroscopy (EDS) analyses of figure 4.69-4.70 that
PEFBFRP interface is rich in aluminum (Al) along with the presence of Argon
(Ar) while Figures 4.71 shows the presence of more atomic energy abundance
for oxygen atom (O) in composite of PPSFRC, this is also confirmed with SEM
micrograph of figure 4.70 as shown with many surface flaws as pores. Porosity
decreases the strength of composites as they constitute stress initiation points
and this may be the reason why PPSFC composites have less strength than
PEFBFC because the electronic configuration of these elements atoms favors
different types of bonding which contributes to the strength of the composites,
the SEM and EDS analyses therefore confirmed that the boundary of fiber–
matrix transition zone have excellent adhesion. The impregnation of fibers
within the polymer showed better strength enhancement.
7. The adsorption and desorption characteristics of plantain fibers before and after
modification was established using Nitrogen Adsorption/desorption isotherm
(NAD) and the study found a significant reduction of fibers specific surface
area and adsorbed volume of Nitrogen gas with fiber modification [figures
4.66-4.67, tables 4.64-4.65], the BET surface areas of untreated plantain fiber
279
and treated plantain fiber were found to be 0.3369 sq. m/g and 0.0493sq.m/g
respectively. Also shown are slight increases in pore area and pore volume with
treatment.
5.2
Contribution to knowledge.
This study has contributed in no small measure by leading to the
development of new class of natural fibers reinforced composites and optimization
of their mechanical properties; it has established some general rules in terms of
Archimedes principles application in determination of fiber volume fraction and
appropriate ASTM standard in mould design, reducing the manufacturing process
sensitivity to variation by ensuring that optimal formulation variable conditions are
used in composites manufacturing and consequently producing a robust final
component with the highest performances achievable.
Available literature showed various methods for determination of fiber
volume fraction which includes resin burn-out methods, chemical matrix digestion,
densities methods, ultrasonic non destructive testing and acid digestion methods,
however, these methods cannot be conformed to specification for a robust design
process; the present study therefore devised Archimedes principles which was
successfully applied in the designing and manufacturing of composites prior to
analysis of mechanical properties; In general, experimental investigation on
plantain fiber reinforced polyester composites has led to successful development of
predictive models for its strengths.
280
The application of Finite Element techniques have been utilized to validate
the properties of plantain fiber reinforced composites; the finite element analysis
(FEA) applied in the optimal design for flexural strength of plantain fibers
reinforced polyester matrix suggests that the composite sample subjected to
48.228MPa will deflect 14.569mm within its elastic limit [see figure 4.57]. This
study has therefore demonstrated that two predictive models; one based on RSM
and the other on Finite Element Method approach well reflect the effects of various
factors on the strength of plantain fiber reinforced composites. A number of
contributions have therefore been made to the knowledge of plantain fiber
reinforced composites in this regard.
Taguchi and RSM applied in the design have led to the evaluation of the
optimal control factors and mechanical properties; with this study upgraded our
existing knowledge about the mechanical properties and established plantain fiber
reinforced composites as new materials applicable under different loading
conditions. The results indicated that the mechanical properties have a strong
association with the composites characteristic, the properties are greatly dependent
on reinforcement combination and the composite having plantain fibers volume
fraction of 0.5% has been recommended in design. The overall analysis has
provided basic mechanical data required for design of composite materials without
expensive and time consuming experimentation. In particular, the specification of
important plantain fiber reinforced composites properties and establishment of
281
limit stresses for plantain fiber reinforced composites remains a valuable
contribution that will be of immense use to designer intending to use plantain
fibers reinforced composites.
This study established an integrated Design of Experiment (DOE) based
approach for the finding out the significant forming parameters during the
fabrication of plantain fiber based composites which provides efficient guide lines
for manufacturing engineers. Therefore from the present study, it is evident that the
establishment of optimal combination of forming parameters is very beneficial for
manufacturing of plantain fibers reinforced composites with better tensile, flexural
and Brinell hardness. Thus modeling and optimization of reinforcement
combinations for the tensile strength of plantain fiber reinforced polyester matrix
composites (PFRP) has shown that the volume fraction has the highest influence
on the tensile response while specifying the composition range that gives the
optimum strength for the composites. Comparing the mechanical characteristics of
plantain reinforcement material with other natural fibers, this study established that
plantain empty fruit bunch and pseudo stem fibers can be used for the production
of composites and this can turn natural wastes into industrial wealth. This can also
solve the problem of disposal of plantain trunks and empty fruit bunches.
282
5.2.1 Publications from research findings
Above all, the following contributions were made through publication in
reputable journals.
C. C. Ihueze, E. C. Okafor and A. J. Ujam (2012). Optimization of Tensile
Strengths Response of Plantain Fibers Reinforced Polyester Composites
(PFRP) Applying Taguchi Robust Design. Innovative Systems Design and
Engineering. (2012). 3(7), 64-76.
C. C. Ihueze, E. C. Okafor and S.C. Nwigbo (2013). Optimization of Hardness
Strengths Response of
Plantain Fibers Reinforced Polyester Matrix
Composites (PFRP) Applying Taguchi Robust Design. International Journal
of Engineering (IJE). 26(1), 1-12.
C. C. Ihueze and E. C. Okafor and C. I. Okoye (2013). Natural fibers composites
design and characterization for limit stress prediction in multiaxial stress
state.
Journal
of
King
Saud
University-Engineering
Sciences.
DOI:10.1016/j.jksues.2013.08.002.
C. C. Ihueze, E. C. Okafor, and P.K. Igbokwe (2014). Modeling and Optimization
of Reinforcement Combinations for the Tensile Strength of Plantain Fiber
Reinforced Polyester Matrix Composites (PFRP). International Journal of
Advanced Manufacturing Technology (Springer).
283
C. C. Ihueze, E. C. Okafor and S. O. Ezeonu (2014). Optimal Design for
Flexural Strength of
Plantain Fibers Reinforced Polyester Matrix (PFRP).
Journal of Materials Science & Technology.
C. C. Ihueze , E. C. Okafor, O. D. Onukwuli (2014). Application of Power Law
Model and Response Surface Methodology to Optimize the Hardness
Strength of
Plantain Fibers Reinforced Polyester Matrix Composites
(PFRP). Journal of Engineering and Technology Management.
5.3.
Recommendations for Future Research
By careful review of scientific literature, several unresolved problems were
found; the results of the research work introduced in this dissertation offers
answers for them, but during the examinations some other new questions were
born. Time and scope of this Ph.D. dissertation limited the investigation of those
problems; in this research, it was assumed that the noise variables are independent,
so the interactions among the noise variables are not included in the response
surface model. In real applications, the lack of attention in adequately dealing with
these potential interactions may lead to critical mistakes. Therefore, dependence
among the noise variables should be investigated further. For complex systems,
Latin hypercube design and other space-filling designs could be researched further
to improve the design modeling and analysis of plantain fiber reinforced
composites. This research used Taguchi method and response surface methodology
to solve robust design problems on the material design and manufacturing only.
284
Further research can extend to other areas, such as financial implications,
environmental studies, supply chain, service industry, and so on.
In the case of the materials considered in this study, the current study
suggests that robust composites can be designed with plantain fibers.
Consequently, the systems may not be useful in long term implications in which
the natural fibers would be expected to degradation due to chemical and
mechanical interactions between the fibers and matrix materials. Further work is
clearly needed to extensively study the chemical interactions between the fiber and
matrix materials; the long term effects of exposure to natural weathering (with
moisture and heat) should also be explored to provide insights into how
environmental exposure can degrade the mechanical properties of composites.
Other factors influencing the strengths of composites can also be of future research
interest for plantain fiber reinforced composites.
Nevertheless, the current results are important since they suggest the
potential for the future development of robust and affordable composite materials
for use in manufacturing and the future development of affordable housing in the
world utilizing plantain fibers reinforced composites. It is also recommended that
reinforcement combinations which improve the response of PFRP such as volume
fraction (50%) aspect ratio of fibers (10) and fiber orientation (90degree) should be
encouraged.
285
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APPENDIX I
FOURIER TRANSFORM INFRARED (FTIR) DATA
FTIR Data for Untreated Plantain Empty Fruit Bunch Fibers
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Peak
Intensity
472.58
518.87
561.3
599.88
669.32
775.41
875.71
898.86
1043.52
1159.26
1269.2
1332.86
1384.94
1415.8
1502.6
1600.97
1643.41
2360.95
2920.32
3302.24
3346.61
3406.4
72.68
71.12
69.05
69.11
68.84
87.65
84.41
81.23
20.73
45.91
65.8
57.07
46.06
37
59.67
48.86
42.85
76.73
50.6
23.44
20.01
18.92
Corr.
Inte
0.92
3.25
0.95
1.19
4.01
2.17
6.16
7.21
46.39
11.23
1.42
0.43
1.86
1.47
2.9
0.76
2.03
7
13.39
0.29
0.34
0.32
Base (H)
480.29
526.58
565.16
607.6
682.82
788.91
885.36
918.15
1143.83
1193.98
1288.49
1334.78
1388.79
1419.66
1508.38
1602.9
1647.26
2397.6
2997.48
3304.17
3350.46
3412.19
Base
(L)
470.65
503.44
551.66
586.38
665.46
763.84
860.28
885.36
920.08
1143.83
1249.91
1288.49
1346.36
1388.79
1496.81
1575.89
1635.69
2349.38
2600.13
3032.2
3304.17
3400.62
Area
Corr.Are
1.23
3.03
2.09
3.32
2.41
1.3
1.28
2.31
91.17
12.66
6.83
9.91
12
11.73
2.48
7.69
4.16
3.99
68.34
111.93
30.84
8.33
0.01
0.16
0.03
0.09
0.12
0.14
0.27
0.57
51.57
1.76
0.18
0.27
-0.05
0.05
0.12
0.44
0.15
0.67
9.15
0.26
0.2
0.04
Area
Corr.Are
0.32
1.29
1.05
4.25
2.05
0.05
0.06
0.02
0.19
0.05
FTIR Data for Treated Plantain Empty Fruit Bunch Fiber
1
2
3
4
5
Peak
Intensity
418.57
518.87
597.95
669.32
719.47
86.15
79.15
72.77
69.07
79.67
Corr.
Inte
4.29
1.22
0.65
5.59
1.43
Base (H) Base (L)
420.5
522.73
601.81
698.25
736.83
414.71
509.22
594.1
663.53
713.69
321
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
898.86
1058.96
1111.03
1159.26
1236.41
1323.21
1371.43
1427.37
1626.05
1759.14
2332.02
2360.95
2887.53
3230.87
3385.18
3416.05
3774.82
79.33
32.31
41.26
48.96
69.91
64.28
63.76
63.65
69.6
89.9
78.68
73.09
67.75
46.96
32.19
31.88
90.02
8.07
19.81
1.43
9.66
1.1
4.06
1.38
2.88
0.55
0.5
0.48
10.23
1.2
0.38
0.9
0.37
2.59
918.15
1105.25
1141.9
1192.05
1249.91
1340.57
1375.29
1437.02
1627.97
1763
2333.94
2397.6
2895.25
3232.8
3390.97
3421.83
3780.6
862.21
918.15
1107.18
1143.83
1217.12
1286.56
1361.79
1419.66
1624.12
1757.21
2281.87
2349.38
2798.8
3115.14
3367.82
3412.19
3770.96
FTIR Data for Plantain Stem fiber Reinforced Composites
Peak
Intensity Corr.
Base (H) Base (L)
Inte
1
464.86
82.311
3.351
470.65
451.36
2
542.02
68.098
12.845
586.38
524.66
3
605.67
82.114
3.053
615.31
594.1
4
700.18
11.386
63.321
717.54
673.18
5
744.55
35.027
44.183
810.13
719.47
6
846.78
74.891
5.568
862.21
812.06
7
910.43
61.148
4.336
920.08
862.21
8
993.37
34.195
0.934
995.3
922
9
1041.6
18.059
1.724
1045.45 997.23
10
1068.6
9.262
9.636
1091.75 1047.38
11
1122.61 10.081
11.421
1195.91 1093.67
12
1259.56 7.562
3.962
1273.06 1197.83
13
1284.63 7.875
4.536
1348.29 1274.99
14
1377.22 27.294
19.89
1417.73 1350.22
15
1452.45 23.316
37.18
1481.38 1419.66
16
1492.95 35.041
36.047
1508.38 1481.38
17
1581.68 50.069
14.391
1589.4
1558.54
18
1600.97 40.414
20.108
1616.4
1589.4
4
58.69
12.04
12.15
4.97
9.38
2.56
3.28
0.6
0.26
3.67
4.21
12.25
29.48
11.2
4.76
0.39
1
16.97
0.57
1.71
0.11
0.77
0.07
0.22
0.01
0
-0.16
0.98
0.22
0.17
0.18
0.02
0.07
Area
Corr.Are
1.336
7.724
1.677
18.223
23.446
4.97
9.137
22.791
29.253
38.786
85.352
66.383
55.326
28.489
22.265
6.831
6.029
7.759
0.197
2.415
0.198
12.454
15.189
0.625
0.201
0.202
0.979
6.68
19.707
5.285
2.8
6.905
8.653
2.949
1.185
1.936
322
19
20
21
22
23
24
25
26
27
28
1728.28
1874.87
1950.1
2343.59
2360.95
2926.11
3026.41
3228.95
3441.12
3774.82
2.656
86.296
85.419
79.329
76.442
34.232
43.104
57.6
45.692
92.687
66.787
2.469
1.768
3.985
8.07
28.46
18.043
0.561
0.088
2.221
1830.51
1890.3
1967.46
2349.38
2397.6
2997.48
3045.7
3232.8
3443.05
3780.6
1670.41
1869.08
1942.38
2281.87
2349.38
2760.23
3012.91
3149.86
3439.19
3770.96
92.782
1.281
1.622
4.763
3.787
63.797
9.076
17.74
1.311
0.276
69.688
0.175
0.145
0.692
0.767
22.365
2.068
0.225
0.002
0.059
FTIR Data for Plantain EFB Fiber Reinforced Composites
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Peak
Intensity
468. 72
540.09
603.74
700.18
744.55
848.71
910.43
1041.6
1068.6
1122.61
1259.56
1284.63
1377.22
1452.45
1581.68
1600.97
1728.28
1950.1
2332.02
2360.95
2926.11
3026.41
3435.34
85.98
72.87
83.09
17.85
40.95
79.43
65.62
21.77
13.6
14.92
11.58
12.56
29.69
27.49
49.95
43.17
6.37
85.64
78.22
73.38
37.42
46.21
48.12
Corr.
Inte
2.75
8.48
5.15
62.62
45.08
4.89
3.71
2
10.06
12.59
5.7
1.85
20.04
33.82
13.61
18.79
55.81
1.85
0.48
9.53
25.54
16.37
0.8
Base (H)
Base (L)
Area
Corr.Are
474.5
553.59
615.31
717.54
810.13
862.21
920.08
1045.45
1091.75
1192.05
1278.85
1348.29
1417.73
1479.45
1589.4
1616.4
1811.22
1992.53
2333.94
2397.6
2997.48
3045.7
3448.84
461
503.44
588.31
673.18
719.47
812.06
885.36
952.87
1047.38
1093.67
1193.98
1280.78
1348.29
1419.66
1558.54
1589.4
1683.91
1942.38
2281.87
2349.38
2681.14
3012.91
3421.83
0.76
4.52
1.76
15.15
18.52
3.7
5.38
40.58
33.07
68.08
63.13
40.58
27.67
20.43
6.48
7.23
73.38
2.92
3.65
4.25
66.36
8.49
8.5
0.07
0.88
0.3
10.69
13.22
0.49
0.3
0.99
5.26
14.9
5.63
-1.7
6.89
7.52
1.31
1.7
49.2
0.25
-0.17
0.91
18.18
1.81
0.11
323
APPENDIX II
NITROGEN ADSORPTION AND DESORPTION CHARACTERISTICS OF
UNTREATED PLATAIN FIBER
Table A1. Untreated plantain fiber NAD analysis log
RELATIVE PRESSURE
VOL.
ELAPSED
PRESSURE
(mmHg)
ADSORBED
TIME
(cc/g STP)
(HR:MN)
0:21
0.0104
7.861
0.0209
0:23
0.0335
25.392
0.0417
0:26
0.0680
51.612
0.0603
0:27
0.0912
69.195
0.0681
0:28
0.1142
86.623
0.0700
0:30
0.1371
104.051
0.0787
0:32
0.1589
120.599
0.0805
0:34
0.1789
135.752
0.0837
0:35
0.1989
150.956
0.0850
0:37
0.2188
166.005
0.0905
0:39
0.2687
203.861
0.0920
0:40
0.3678
279.054
0.0957
0:42
0.4673
354.558
0.0992
0:44
0.5668
430.062
0.0935
0:46
0.6662
505.462
0.0971
0:48
0.7560
573.571
0.1064
0:51
0.8165
619.546
0.1278
0:52
0.8571
650.316
0.1513
0:54
0.8921
676.646
0.1871
0:56
0.9219
699.445
0.2444
0:58
0.9420
714.701
0.3205
1:00
0.9683
734.663
0.4776
1:02
0.9852
747.489
0.7277
1:04
0.9950
754.884
1.3162
1:09
0.9982
757.314
2.3314
1:15
0.9856
747.747
1.3719
1:19
0.9704
736.215
0.9262
1:23
0.9514
721.786
0.6360
1:26
SATURATION
PRESS
(mmHg)
758.814
324
0.9389
0.9276
0.9222
0.9136
0.9046
0.8899
0.8747
0.8596
0.8400
0.8199
0.8000
0.7703
0.7403
0.7006
0.6508
0.6008
0.5507
0.5005
0.4311
0.3806
0.3499
0.2999
0.2499
0.1997
0.1397
712.322
703.686
699.601
693.084
686.206
675.088
663.555
652.074
637.181
621.925
606.624
584.328
561.573
531.475
493.671
455.764
417.754
379.640
326.994
288.725
265.401
227.494
189.587
151.473
105.964
0.4971
0.4174
0.3779
0.3389
0.3010
0.2588
0.2229
0.1932
0.1667
0.1516
0.1331
0.1252
0.1167
0.1126
0.1098
0.1065
0.1088
0.1109
0.1115
0.1109
0.1068
0.1070
0.1039
0.1006
0.0899
1:29
1:31
1:34
1:37
1:40
1:43
1:45
1:48
1:51
1:53
1:56
1:58
2:01
2:03
2:06
2:08
2:10
2:12
2:14
2:16
2:18
2:20
2:22
2:26
2:27
325
1.6
VOLUME ADSORBED (cc/g STP)
1.4
1.2
1
0.8
VOL ADSORBED (cc/g STP)
0.6
VOL DISORBED (cc/g STP)
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
RELATIVE PRESSURE (P/P0)
Figure A1. Plot of adsorption and desorption of nitrogen isotherms for
untreated plantain fiber
BET SURFACE AREA ANALYSIS
Table A2. Analysis log for BET surface
0.3369 +/- 0.0062 sq. m/g
BET SURFACE AREA:
12.588930 +/- 0.234207
SLOPE:
0.332498 +/- 0.034993
Y–INTERCEPT:
38.861664
C:
0.077391 cc/g STP
VM:
CORRELATION COEFFICIENT: 9.9948IE-01
Table A3. Analysis table for bet surface
RELATIVE PRESSURE VOL ADSORBED(cc/g
STP)
0.0680
0.0603
0.0912
0.0681
0.1371
0.0787
0.1789
0.0837
0.2188
0.0905
1/{VA(Po/P - 1)}
1.211288
1.474384
2.018407
2.601811
3.093641
326
3.2
y = 12.58x + 0.332
R² = 0.999
3
BET TRANSFORMATION (Y = 1/{VA(Po/P - 1)}
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
RELATIVE PRESSURE (‫ = ﻼ‬P/P0)
Figure A2. BET plot for untreated plantain empty fruit bunch fiber
Table A4. Micro pore Analysis Report summary for untreated plantain fiber
MICROPORE VOLUME:
MICROPORE AREA:
EXTERNAL SURFACE AREA:
SLOPE:
Y – INTERCEPT:
CORRELATION COEFFICIENT:
-0.000014 cc/g
0.0030 sq. m/g
0.3339 sq. m/g
0.021589 +/-0.008883 +/9.69245E-01
0.002238
0.009361
327
Table A5. Micro pore Analysis table for untreated plantain fiber
Relative pressure
0.0104
0.0335
0.0680
0.0912
0.1142
0.1371
0.1589
0.1789
0.1989
0.2188
0.2687
0.3678
0.4673
0.5688
0.6662
Statistical
thickness,(nm)
0.263
0.304
0.341
0.361
0.379
0.395
0.410
0.423
0.436
0.449
0.481
0.547
0.620
0.706
0.815
Vol adsorbed (cc/g stp)
0.0209
0.0417
0.0603
0.0681
0.0700
0.0787
0.0805
0.0837
0.0850
0.0905
0.0920
0.0957
0.0992
0.0935
0.0971
Thickness Values Used In the Least-Squares And Analysis Were Between 0.350
and 0.500mm
t = [13.9900/(0.0340 – log(P/Po))]0.500 Surface Area Correction Factor is 1.000.
0.12
Vol adsorbed (cc/g stp)
0.1
0.08
0.06
0.04
0.02
0
0
0.2
0.4
0.6
0.8
1
thickness (nm)
Figure A3. t – Plot of untreated plantain fiber
328
Table A6. BJH Desorption Pore Distribution Report for untreated plantain
fiber
Pore
Average Incremental Cumulative dV/dD pore dV/dlog
diameter
diameter pore volume Pore
volume
(D)pore
range (nm) (nm)
(cc/g)
volume
(cc/g-nm)
volume
(cc/g)
(cc/g)
134.4- 66.2 79.1
0.000751
0.000751
1.1002E-05 2.4397E-03
66.2- 40.7 47.5
0.000493
0.001244
1.9335E-05 2.3330E-03
40.7- 32.5 35.7
0.000239
0.001482
2.9239E-05 2.4545E-03
32.5- 27.5 29.6
0.000136
0.001618
2.7058E-05 1.8657E-03
27.5- 25.6 26.5
0.000068
0.001687
3.6492E-05 2.2312E-03
25.6- 23.1 24.2
0.000066
0.001753
2.6170E-05 1.4673E-03
23.1- 20.9 21.9
0.000064
0.001817
2.9444E-05 1.4922E-03
20.9- 18.2 19.3
0.000069
0.001886
2.4927E-05 1.1204E-03
18.2- 16.0 16.9
0.000058
0.001944
2.6192E-05 1.0276E-03
16.0- 14.2 15.0
0.000047
0.001991
2.7183E-05 9.4339E-04
14.2- 12.4 13.2
0.000039
0.002030
2.1938E-05 6.7240E-04
12.4- 11.0 11.6
0.000017
0.002047
1.1814E-05 3.1854E-04
11.0- 9.9
10.4
0.000026
0.002073
2.2632E-05 5.4351E-04
9.9 -7.4
7.9
0.000002
0.002075
9.6692E-07 1.9136E-05
7.4 -1.8
1.9
0.000023
0.002098
4.1070E-06 3.7283E-05
0.0025
Pore volume (cc/g)
0.002
0.0015
0.001
0.0005
0
0
20
40
60
80
100
Pore diameter (nm)
Figure A4. Cumulative Desorption Pore Volume Plot for untreated plantain
fiber
329
4.00E-05
3.50E-05
Pore volume (cc/g)
3.00E-05
2.50E-05
2.00E-05
1.50E-05
1.00E-05
5.00E-06
0.00E+00
0
10
20
30
40
50
60
70
80
Pore diameter (nm)
Figure A5. dV/dD desorption pore volume plot for untreated plantain fiber
3.00E-03
Pore volume (cc/g)
2.50E-03
2.00E-03
1.50E-03
1.00E-03
5.00E-04
0.00E+00
0
-5.00E-04
10
20
30
40
50
60
70
80
Pore diameter (nm)
Figure A6. dV/dlog (D) desorption pore volume plot for untreated plantain
fiber
330
Table A7. NAD Summary Report for untreated plantain fiber
AREA
BET SURFACE AREA:
0.3369 sq. m/g
SINGLE POINT SURFACE AREA AT P/Po 0.2188:
0.3079sq.m/g
BJH CUMULATIVE DESORPTION SURFACE
0.2765 sq.m/g
AREA OF PORES BETWEEN 17.0000 AND
3000.0000 A DIAMETER:
MICROPORE AREA:
0.0030 sq. m/g
VOLUME
SINGLE POINT TOTAL PORE VOLUME PORES
0.001126 cc/g
LESS THAN 1316.8137 A DIAMETER AT P/Po 0.9852:
BJH CUMULATIVE DESORPTION PORE VOLUME
0.002098 cc/g
OF PORES BETWEEN 17.0000 AND
3000.0000 A DIAMETER:
MICROPORE VOLUME:
0.000014 cc/g
PORE SIZE
AVERAGE PORE DIAMETER (4V/A BY BET):
133.6502 A
BJH DESORPTION AVERAGE PORE DIAMETER
303.5635 A
(4V/A):
331
APPENDIX III
NITROGEN ADSORPTION AND DESORPTION CHARACTERISTICS OF
TREATED PLATAIN FIBER
Table A8. Treated plantain empty fruit bunch fiber NAD analysis log
RELATIVE PRESSURE
VOL
ELAPSED
SATURATION
PRESSURE
(mmHg)
ADSORBED
TIME
PRESSURE
(cc/g STP)
(HR:MN)
(mmHg)
0:21
752.350
0.0104
7.861
0.0114
0:23
0.0336
25.289
0.0209
0:25
0.0682
51.301
0.0262
0:27
0.0912
68.626
0.0276
0:28
0.1144
86.054
0.0242
0:30
0.1372
103.223
0.0253
0:32
0.1591
119.720
0.0253
0:33
0.1791
134.769
0.0206
0:35
0.1991
149.818
0.0173
0:37
0.2191
164.816
0.0162
0:39
0.2690
202.361
0.0039
0:40
0.3683
277.089
-0.0173
0:42
0.4678
351.972
-0.0458
0:44
0.5673
426.804
-0.0719
0:46
0.6668
501.687
-0.1024
0:48
0.7565
569.175
-0.1226
0:50
0.8171
614.788
-0.1354
0:52
0.8577
645.300
-0.1438
0:54
0.8927
671.623
-0.1438
0:56
0.9228
694.826
-0.1472
0:58
0.9431
709.582
-0.1392
1:00
0.9705
730.216
-0.1221
1:02
0.9885
743.765
-0.0782
1:03
1.0001
752.458
0.4170
1:10
0.9774
727.371
-0.0668
1:12
0.9667
717.391
-0.1096
1:15
0.9536
715.942
-0.1308
1:18
0.9515
711.754
-0.1462
1:21
332
0.9460
0.9393
0.9323
0.9244
0.9145
0.9045
0.8897
0.8747
0.8597
0.8398
0.8198
0.7999
0.7701
0.7208
0.6804
0.6305
0.5804
0.5308
0.4803
0.4300
0.3799
0.3300
0.2799
0.2296
0.1797
0.1197
706.737
701.462
695.515
688.066
680.569
669.451
658.125
646.851
631.854
616.857
601.859
579.467
542.335
511.978
474.433
436.681
399.033
361.384
323.581
285.881
248.284
210.583
172.780
135.235
90.088
90.088
-0.1515
-0.1625
-0.1686
-0.1749
-0.1818
-0.1830
-0.1896
-0.1914
-0.1957
-0.1903
-0.1919
-0.1913
-0.1817
-0.1678
-0.1578
-0.1456
-0.1294
-0.1152
-0.1035
-0.0932
-0.0803
-0.0722
-0.0631
-0.0545
-0.0519
-0.0557
1:24
1:27
1:30
1:33
1:35
1:38
1:41
1:44
1:46
1:49
1:52
1:54
1:57
1:59
2:02
2:04
2:06
2:08
2:10
2:12
2:14
2:16
2:18
2:20
2:22
2:24
2:25
752.453
333
0.5
VOL ADSORBED (cc/g STP)
0.4
0.3
0.2
VOL ADSORBED (cc/g STP)
0.1
VOL DISORBED (cc/g STP)
0
0
0.2
0.4
0.6
0.8
1
1.2
-0.1
-0.2
-0.3
RELATIVE PRESSURE (P/Po)
Figure A7. Plot of adsorption and desorption of nitrogen isotherms for
treated plantain fiber
Table A9. Analysis log for bet surface
BET SURFACE AREA:
SLOPE:
Y–INTERCEPT:
C:
VM:
CORRELATION
COEFFICIENT:
0.0493 +/- 0.0079 sq. m/g
93. 166389+/-13.940501
-4.826078+/-2.085208
-18.304783
0.011320 cc/g STP
9.68019E-01
Table A10. Analysis table for BET surface
RELATIVE
PRESSURE
0.0682
0.0912
0.1372
0.1791
0.2191
VOL ADSORBED(cc/g 1/{VA(Po/P - 1)}
STP)
0.0262
2.797614
0.0276
3.641820
0.0253
6.278889
0.0206
10.596526
0.0162
17.286150
334
BET TRANSFORMA\TION [1/{VA(Po/P - 1)}]
20
18
16
14
12
10
8
6
4
2
0
0
0.05
0.1
0.15
0.2
0.25
RELATIVE PRESSURE (P/Po)
Figure. A8. BET plot for untreated plantain empty fruit bunch fiber
Table A11. Analysis table for LANHUIR SURFACE AREA REPORT
BET SURFACE AREA:
SLOPE:
Y–INTERCEPT:
C:
VM:
CORRELATION
COEFFICIENT:
0.0618+/-0.0062 sq. m/g
70.406898 +/-9.522094
-3.077311+/-1.424303
-22.879358
0.014203 cc/g STP
9.73644E-01
Table A12. Analysis table for LANHUIR surface
RELATIVE
VOL ADSORBED 1/{VA*(Po/P}
PRESSURE
(cc/g STP)
0.0682
0.0262
2.606851
0.0912
0.0276
3.309633
0.1372
0.0253
5.417429
0.1791
0.0206
8.698388
0.2191
0.0162
13.499356
335
Table A13. Micro pore Analysis Report summary for treated plantain fiber
MICROPORE VOLUME:
MICROPORE AREA:
EXTERNAL SURFACE AREA:
SLOPE:
Y – INTERCEPT:
CORRELATION COEFFICIENT:
0.000148 cc/g
0.3302 sq. m/g
-0.2809 sq. m/g
-0.018161 +/-0.003070
0.095739 +/-0.009361
-9.23945E-01
Table A14. Micro pore Analysis table for treated plantain fiber
Relative pressure
0.0104
0.0336
0.0682
0.0912
0.1144
0.1372
0.1591
0.1791
0.1991
0.2191
0.2690
Statistical
thickness,(A)
2.635
3.046
3.414
3.609
3.787
3.950
4.100
4.233
4.363
4.492
4.812
Vol adsorbed
STP)
0.0114
0.0209
0.0262
0.0276
0.0242
0.0253
0.0253
0.0206
0.0173
0.0162
0.0039
(cc/g
THICKNESS VALUES USED IN THE LEAST-SQUARES AND ANALYSIS
WERE BETWEEN 0.350 AND 0.500mm t = [13.9900/(0.0340 – log(P/Po))]0.500
SURFACE AREA CORRECTION FACTOR IS 1.000.
336
0.03
Vol adsorbed (cc/g STP)
0.025
0.02
0.015
0.01
0.005
0
2
2.5
3
3.5
4
4.5
5
Statistical thickness,(A)
Figure A9. t – Plot of treated plantain fiber
------------------------------------------------------------------No sufficient data for BJH Desorption Pore Distribution Report for treated
plantain fiber, at least 2 desorption point is required !
------------------------------------------------------------------Table 15. NAD Summary Report for treated plantain fiber
AREA
BET SURFACE AREA:
LANGMUIR SURFACE AREA:
SINGLE POINT SURFACE AREA AT P/Po 0.2191:
MICROPORE AREA:
VOLUME
MICROPORE VOLUME:
0.0493sq.
0.0618sq.
0.0552sq.
0.3302sq.
m/g
m/g
m/g
m/g
0.000148
cc/g
337