Micro-mechanics based fatigue modeling and
validation of the damage behavior of short wavy
fiber composites
Yasmine Abdin*, Atul Jain, Ignaas Verpoest, Stepan V. Lomov,
Department of Metallurgy and Materials Engineering,
KULeuven, Belgium
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
1
Short wavy steel fiber composites
•
Short steel fiber composites are novel
material combining outstanding properties of
stiffness and ductility.
•
Typically used for improved shielding
properties of polymers.
•
Processing of injection molded short steel
fiber composites leads to significant fiber
waviness.
VF 0.5%
VF 2%
Very dense and wavy
structures at low volume
fractions
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
2
Micro-Mechanics based fatigue model:
solution overview
Interfacing
•Ψ(L)
•Ψ(θ,φ)
•waviness
(MOSCO.Translate)
•For each segment i
•Xc(i), Yc(i), Zc(i)
•l(i)
•Θ(i), φ(i)
Geometrical Model
(MOSCO.GEO)
Geometrical model
• Modeling of an RVE of
wavy fiber with
described fiber
waviness, random
orientation, length
distribution
• Validation with microCT scans of real
samples
09/04/2015
Damage
•Ceff
•<σ(i)>, <ε(i)>
•Plasticity of matrix
•Plasticity of fibers
•Debonding
•Breakage
Micro-Mechanical
Model
(MOSCO.MICRO)
•Cyclic failure criteria
•Final output: cyclic
damage of composite
•Stiffness degradation
of composite
Fatigue MicroAnalyzer
(MOSCO.FAT)
Micro-mechanical elastic model
Damage model
Fatigue model
•Extension of Mori-Tanaka
solution to wavy fibers
•Validation needed for MicroMechanical model for:
-prediction of overall composite
effective response
-- prediction of the local stress
and strain states in inclusions
<σ(i)>, <ε(i)>
• Modeling and
validation of nonlinear plasticity
behavior of matrix
• Modeling and
validation of damage
of the wavy fiber
composite
• Modeling and
validation of
fatigue lifetime of
short fiber
composites based
on input of fatigue
life of constituents
Yasmine Abdin
COMPTEST 2015, Madrid
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Characterization and
modeling of geometry of
short steel fiber
composites
Geometrical characterization of short steel
fiber composites
Micro-CT characterization for determination of geometrical
parameters
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
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Micro-structural modeling of wavy fibers
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Yasmine Abdin
COMPTEST 2015, Madrid
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Micro-mechanical
modeling for static
properties of RFRC
Poly-Inclusion model
Aim:
• Model for extending mean field based
algorithms to wavy fibers.
• Validation of homogenized elastic properties
predicted by model.
• Validation of stress state in inclusions as a
significant parameter for modeling damage
analysis.
Transformation of a
wavy fiber into an
equivalent
ellipsoidal inclusion
system
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
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Poly-Inclusion model: Validation - 1
•
Good agreement of model predictions compared to full FEA simulations
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
9
Poly-Inclusion model: Validation - 2
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
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Non-linear quasi-static modeling
Matrix plasticity model
Debonding model
J2 plasticity model: secant
approach by Tandon and
Weng [1988]
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
d = percentage of
debonded points
γ = percentage of
debonded points
in tension
δ = percentage of
frictional sliding
interface
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Validation of micromechanical and damage
model for short steel fiber composites
• Using the same value of interface strength of GF-PA for the SF-PA samples lead to
overestimation of the stress-strain curves.
• It can then be concluded that the steel fibers exhibit weak interface strength with
the matrix.
60
2 VF%
50
40
Experimental VF2%
30
Model with strong interface
20
Model with weaker interface
10
0
0
09/04/2015
0,02
0,04
0,06
0,08
0,1
0,12
Yasmine Abdin
COMPTEST 2015, Madrid
0,14
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SEM quasi-static failed samples SF-PA
High percentage of debonding in all volume fractions due to weak interface
0.5VF%
4VF%
09/04/2015
2VF%
5VF%
Yasmine Abdin
COMPTEST 2015, Madrid
13
Validation of micromechanical and damage
model for short glass fiber composites -1
Stress-strain curves of SG-PP
200
180
• 0 degees coupon
• 30 wt% GF
• High orientation a11
= 0.823
• Long fibers
• Length distribution
Lognormal (6.9, 0.5)
160
140
Plasticity
Stress/MPa
120
Elastic
100
80
Platicity+damage
60
40
20
0
0
0,005
0,01
0,015
0,02
0,025
0,03
Strain
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
14
Validation of micromechanical and damage
model for short glass fiber composites -3
Stress-strain curves GF-PBT
200
180
160
Stress, MPa
140
120
Experimental
Plasticity + damage
100
Plasticity
Elastic
80
60
• 0 degees coupon
• 50 wt% GF
• High orientation a11
= 0.801
• Very short fibers
• Contant fiber length
40
20
0
0
09/04/2015
0,002
0,004
0,006
Strain
0,008
0,01
Yasmine Abdin
COMPTEST 2015, Madrid
0,012
0,014
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Fatigue Modelling of
short fiber composites
Micro-mechanics based Fatigue Model (FATIGUE
MICRO-ANALYZER)
S
matrix
interface
N
S
Fiber
• Geometrical model
(generator)
• Micro-mechanical
model
• Damage model
• Fatigue failure criteria
S
Short fiber composite
N
σmax
stress
N
Micro-mechanics based fatigue
model
σmin
time
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
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17
The Fatigue Model
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
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The Fatigue Model – Validation -1 GF-PP
80
S-N curve of SG-PP
Max Stress, MPa
70
60
50
Experimental
40
Model Slope = 0.05
Model Slope Int = 0.1
30
Model Slope int = 0
20
10
0
100
1000
10000
100000
Cycles to failure
35
1000000
Max Stress, MPA
30
25
20
Interface Slope = 0
15
Interface Slope = 0.506
10
Interface Slope =1.012
5
0
1
10
100
1000
10000
10000000
• 0 degees coupon
• 30 wt% GF
• High orientation a11
= 0.823
• Long fibers
• Length distribution
Lognormal (6.9, 0.5)
• Parametric study
shows the increased
effect of the fatigue
of interface on the
accurate prediction
of short fibers S-N
curves
Model results generated with using the
slope of critical interface strength vs. cycles
curve the same as that of S-N curve of matrix
100000 1000000 10000000
Cycles to failure
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
19
The Fatigue Model – Validation -2 GF-PBT
115
• 0 degees coupon
• 50 wt% GF
• High orientation a11
= 0.801
• Very short fibers
• Constant fiber
length
Stress, MPa
Tσ =
0-deg
Model
Model Slope =0
Model Slope = 0.138
20
10
100
1000
60
10000
Number of cycles
100000
1000000
Max Stress, MPa
50
Interface Slope = 0.069
Interface Slope = 0
Interface Slope =0.138
40
30
Model results generated with
using the slope of critical
interface strength vs. cycles
curve the same as that of S-N
curve of matrix
20
10
0
100
1000
10000
Cycles to failure
09/04/2015
100000
1000000
Yasmine Abdin
COMPTEST 2015, Madrid
20
Summary
• A geometrical model is developed for generation of RVE of
•
•
•
•
short wavy fibers.
A micro-mechanical modelling approach is validated for
extension of the mean-field model for short wavy fiber
composite systems.
Non-linear models developed for damage of short fiber
composites: straight and wavy.
A micro-mechanics based fatigue model is proposed based
on fatigue of constituents.
Validation of overall modelling approaches against
experimental findings.
09/04/2015
Yasmine Abdin
COMPTEST 2015, Madrid
21
Acknowledgment
The work has been funded by SIM-IWT“
ModelSteelComp” project
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Yasmine Abdin
COMPTEST 2015, Madrid
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Thank you!
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