Mode I intralaminar crack-growth
toughness of 90º layers of glass fiberreinforced polymers
Davi Montenegro1, Francesco Bernasconi, Markus Zogg1, Paolo Ermanni2,
Rafael Libanori3, André Studart3
Madrid, April 8th, 2015
1Innovative
Composite Structures, Inspire AG, Switzerland
Department of Mechanical and Process Engineering, ETH Zurich, Switzerland
3Complex Materials, Department of Materials, ETH Zurich, Switzerland
2CMAS-Lab,
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Davi Montenegro / April-8th-2015 / 1
Contents





Introduction
Quasi-static characterization
DCB tests
SENB tests
Conclusions
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Introduction
Characterization
DCB
SENB
Conclusions
Introduction – Motivation
 Fracture mechanics-based design of components
requires determination of the fracture toughness
FRPs
Source: Adapted from Harris (2003) Fatigue in Composites, ch. 26., Woodhead Publishing Ltd.
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Introduction
Characterization
DCB
SENB
Conclusions
Introduction – Literature
 Fracture toughness of FRPs is normally assessed by means
of tests with double cantilever beam specimens + LEFM
(linear-elastic fracture mechanics) concepts*
 Current standards restricted to 0º laminates (e.g. ISO 15024)
Fiber direction
Source: Manshadi et al. (2014) Comp. Part A 61, pp.43.
*Laksimi et al. (1991) CST 41 / Sorensen and Jacobsen (1998) Comp. Part A 29 / Sun et al. (2006) Comp. Str. 15.
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Introduction
Characterization
DCB
SENB
Conclusions
Introduction – Initial damage
 Initial damage in cross-ply laminates loaded under tension
is mode I cracking in the 90º layers (transverse cracking)*
Cross-ply
σ
σ
0º
90º
0º
Cracks
*Lim and Hong (1989) J. Comp. Mat. 23 / McCartney (1998) CST 58.
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Introduction
Characterization
DCB
Conclusions
SENB
Introduction – Initial damage
 Transverse cracking is observed under quasi-static and
fatigue loading*
Quasi-static
Tension/tension fatigue
σ
σ
0º
90º
0º
.
.
. ... .. .. .. . . .. .. .
.
. .. ... . .. .. .. .. .
.
.
.
.
.. . . .
.. . .
. .. .. . .
. . .
σ
.. .. .. . . . . . .. . . . . .. .
. . . . . . . .
.
.. .. .. . . . . . .. . . . . .. .
. . . . . . . .
.
0º
90º
0º
.
.
. .
.
. ... .. .. .. . . .. .. . . . . .. .. .. . . .. .. .
.
. .. ... . .. .. .. .. . . .. .. .. . .. .. .. .
.
.
.
.
.
.
.
.
*Berthelot and Le Corre (1999) Comp. Part B 30.
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σ
. .
.
.. .. .. . .. . .. . . . .
. .. . . .. . . .. .. .. .
. . .
.
Characterization
Introduction
SENB
DCB
Conclusions
Introduction
 Know-how gaps
 mode I fracture toughness of 90º FRP layers
σ
σ
Driving force
 Crack-growth toughness (R-curve) (Not only crackinitiation*)
Crack size
 NLEFM
(nonlinear-elastic
fracture mechanics)
Source: Launey and
Ritchie (2009) Adv.
Mat. 21
*Canal et al. (2012) CST 72.
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Introduction
Characterization
DCB
SENB
Conclusions
Introduction
 Goal
 To quantify the mode I crack-growth toughness of 90º
GFRP layers taking into account inelastic effects
 Approach
 Quasi-static mechanical characterization
 Tests with DCB specimens
 Tests with SENB specimens + NLEFM
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Contents





Introduction
Quasi-static characterization
DCB tests
SENB tests
Conclusions
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Introduction
Characterization
DCB
SENB
Conclusions
Quasi-static characterization
d
 3-point-bending
h
 Matrix (SikaDur300 [epoxy]): ISO 178
 GFRP (E-glass + matrix): ISO 14125
 Resin transfer molding
L
 Cure: 2h @ 80ºC + 3h @ 125ºC; P = 2.5 bar
 Calculation of σ and ε accounted for large displacements
3FL
σ=
2bh 2
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2

d


 
 dh  
1
6
3
+
−

 
 2 
L
 
 L 



h d
d 
d 
ε=
 6 − 24.37   + 62.17  
L L
L
L
Davi Montenegro / April-8th-2015 / 10
3
5



Introduction
Characterization
DCB
SENB
Conclusions
Quasi-static characterization
 Laminate is considerably more stiff and more brittle than
the matrix, as usual
 Matrix presents considerable inelastic deformation
Stress (MPa)
120
100
80
Matrix
60
Tg , matrix ≅ 80o C
(DSC)
10.28 ± 0.75 GPa
GFRP
GFRP E2,=
90º
=
v
52.1 ± 1.1%
40
20
0
Ematrix
= 3.26 ± 0.02 GPa
f
0
2
4
6
8
Strain (%)
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Contents





Introduction
Quasi-static characterization
DCB tests
SENB tests
Conclusions
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Introduction
Characterization
DCB
SENB
Conclusions
DCB tests




Hinges with a0 = 50 mm and a0 = 30 mm
Aluminum substrate*
Test speed: 0.05 mm/min
160 x 20 x 4 mm3
Fibers
Hinge
Adhesive layer
*Reeder et al. (2004) Comp. Part A 35.
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Characterization
Introduction
DCB
SENB
Conclusions
DCB tests
 Specimens showed early failure probably due to
excessive bending stresses in the cantilever arms
 New attempt with smaller initial crack length was also
not successful
Force (N)
20
Hinge 30mm away
from crack tip
Early failure
Tip of the
initial crack
10
Hinge 50mm away
from crack tip
0
95mm
4 mm
0
5
10
Displacement (mm)
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Introduction
Characterization
DCB
SENB
Conclusions
DCB tests
• Aluminum substrates (thickness: 1mm) were glued onto
the surfaces of the specimens as a means to further stiffen
them  early failure was avoided, however the cracks
were deflected
Crack deflection
Crack deflection
Force (N)
30
Aluminum
substrates
20
10
0
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Delamination
substrate-specimen
0
5
10
15
Displacement (mm)
Tip of the
initial crack
Davi Montenegro / April-8th-2015 / 15
4 mm
Introduction
Characterization
DCB
SENB
Conclusions
DCB tests
 Crack deflection probably caused by tensile stresses in
the x-direction of the specimen around the crack tip
y
x
 Ideal situation: specimen configuration where the stresses
acting in the desired crack propagation direction are
minimized  single edge-notched beam (SENB)
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Contents





Introduction
Quasi-static characterization
DCB tests
SENB tests
Conclusions
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Introduction
Characterization
DCB
SENB
Conclusions
SENB tests
 ASTM E1820  test method for measuring the fracture
toughness JIC and R-curves of metallic materials
 J is the nonlinear strain-energy release rate
 J = G under linear-elastic
conditions
*
 Method was used before for
heterogeneous materials*
*Source: Ritchie (2011), Nature Materials 10, DOI: 10.1038/NMAT3115
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Introduction
Characterization
SENB
DCB
Conclusions
SENB tests
 Compliance method
 Specimens: 30 x 5 x 2.5 mm3
 Load cycles with small displacement increments:
stable crack propagation
Matrix
GFRP 90o
Matrix
Force (N)
40
30
20
10
0
0.0
GFRP 90º
0.1
0.2
0.3
LLD (mm)
0.4
LLD: Load-line displacement
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Introduction
Characterization
DCB
SENB
Conclusions
SENB tests
 Compliance method
 Compliance ‘C’ used to calculate crack length ‘a’
a
= 0.997 − 3.58U − 1.51U 2 − 110U 3 + 1232U 4 − 4400U 5
W
=
U
(
)
FC + 1
−1
 Calibration factor ‘F’ with initial crack length*
*Launey et al. (2010) Acta Biomaterialia 6, pp.1505
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Introduction
Characterization
SENB
DCB
Conclusions
SENB tests
 Data reduction
Strain-energy =
J J el + J in
release rate
=
J
Fitting
Effective stress
K=
IR
1.9 Apl
K I2
+
E ' b (W − a )
J= C1( ∆a + δ )
C2
K=
IR , C
J ⋅ E ' intensity factor
J IC ⋅ E ' Critical effective
J in
=
β 100 ⋅
J
∆acorr
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stress intensity factor
Contribution of
inelastic part
Introduction
Characterization
SENB
DCB
Conclusions
SENB tests
0.4
0.3
0.2
0.1
0.0
0 200 400 600 800
2.5
2.0
1.5
1.0
0.5
0.0
0 100 200 300 400 500 600 700
Crack extension (µm)
KIR (MPa.m1/2)
J-integral (kJ/m2)
 Results
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 100 200 300 400 500 600 700
Crack extension (µm)
 Laminate is much less tough than the matrix; higher difference in J
than KIR because of the difference in the elastic moduli
 Resistance to damage propagation rises in the range of crack
extensions obtained
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Introduction
Characterization
SENB
DCB
Conclusions
SENB tests
 Results
 JIC values obtained according to ASTM E1820
JIC [kJ.m-2]
KIR,C [MPa.m1/2]
This work
Canal et al.*
E-glass/
MTM-57
2.15
E-glass/
SikaDur300
2.0
1.5
1.42
F
1.27
F
Fmax
1.0
d
d
0.5
0.0
K IR ,C = J IC E '
0.18
Matrix
Matrix
GFRP90º
GFRP
1.27MPa m
*Canal et al. (2012) CST 72.
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K Ic = f ( Fmax )
1.8MPa m
Characterization
Introduction
DCB
SENB
Conclusions
SENB tests
 Inelastic contribution to the total crack-driving force
accounted for up to 73% in the GFRP and 38% in the matrix
β = Jin / J (%)
80
60
40
20
0
0
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200
400
600
Crack extension (µm)
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Contents





Introduction
Quasi-static characterization
DCB tests
SENB tests
Conclusions
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Introduction
Characterization
DCB
SENB
Conclusions
Conclusions
 The DCB specimen was not suited for assessing the
mode I fracture toughness of 90º GFRP layers
 The mode I intralaminar crack-growth toughness of 90º
GFRP layers was successfully quantified with SENB
specimens and concepts of NLEFM
 The method allows to determine full crack-resistance
curves (thus not only a value of fracture toughness at the
onset of crack propagation)
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Introduction
Characterization
DCB
SENB
Conclusions
Conclusions
 R-curves were obtained for a commercial epoxy resin
and for 90º GFRP lamina
 The contribution of the inelastic part Jin to the total crackdriving force J to the accounted for up to 73% in the
GFRP during crack propagation
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Thank you for your attention!
Q&A
Davi Melo Montenegro
Innovative Composite Structures, ICS
Inspire AG
Technoparkstr. 1
PFA H23
CH-8005 Zürich
Switzerland
+41 44 632 73 67
[email protected]
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Dr. Markus Zogg
Team Leader ICS
Inspire AG
Technoparkstr. 1
PFA H21
CH-8005 Zürich
Switzerland
+41 44 632 33 79
[email protected]
References
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[2]
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[5]
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Davi Montenegro / April-8th-2015 / 29
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References
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K. Koester, J. Ager III and R. Ritchie, "The true toughness of human cortical bone measured with realistically
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[15]
F. Barthelat and H. Espinosa, "An experimental investigation of deformation and fracture of nacre-mother of
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