This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure modes in polymer-matrix composites. These crack resistance curves not only characterize the fracture toughness of the material, but are also the basis for the identification of the parameters of the softening laws used in the analytical and numerical simulation of fracture in composite materials. The method proposed is based on the identification of the crack tip location by the use of Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the proposed methodology yield crack resistance curves similar to those obtained using FEM-based methods in compact tension carbon-epoxy specimens. However, it is also shown that the Digital Image Correlation based technique can be used to extract crack resistance curves in compact compression tests for which FEM-based techniques are inadequate

Bessa, Miguel A.

Camanho, Pedro P.

Catalanotti, Giuseppe

Davila, Carlos G.

Lopes, Claudio S.

Xavier, Jose C.

NASA Technical Reports Server

RESISTANCE CURVES IN THE TENSILE AND COMPRESSIVE LONGITUDINAL FAILURE OF
COMPOSITES
Pedro P. Camanho ', Giuseppe Catalanotti' ,Carlos G. Dávila 2, Claudio S. Lopes ' ,
Miguel A. Bessa ' , José C. Xavier3
1DEMec, Faculdade de Engenharia, Universidade do Porto,
Rua Dr. Roberto Frias, 4200-465 Porto, Portugal-
E-mail: pcamanho@fe.up.pt
2NASA Langley Research Center, Hampton VA, USA
3Universidade de Trás-os-Montes e Alto Douro, Portugal
ABSTRACT
This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure
modes in polymer-matrix composites. These crack resistance curves not only characterize the fracture toughness of the
material, but are also the basis for the identification of the parameters of the softening laws used in the analytical and
numerical simulation of fracture in composite materials. The method proposed is based on the identification of the
crack tip location by the use of Digital Image Correlation and the calculation of the J-integral directly from the test data
using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the
proposed methodology yield crack resistance curves similar to those obtained using FEM-based methods in compact
tension carbon-epoxy specimens. However, it is also shown that the Digital Image Correlation based technique can be
used to extract crack resistance curves in compact compression tests for which FEM-based techniques are inadequate.
KEY WORDS: Intralaminar fracture toughness; R-curve; composite laminates; digital image correlation.
1. INTRODUCTION
Despite the significant advances in the analysis models
for the prediction of fracture in composite materials,
such as advanced failure criteria and associated damage
models, sophisticated kinematic representations of
fracture mechanisms, and cohesive elements to deal
with delamination, the accurate prediction of
intralaminar fracture mechanisms, acting at the ply
level, still presents several challenges.
The majority of existing models to predict intralaminar
fracture of polymer-based composite materials
reinforced by carbon fibers are based on softening
constitutive models [1]. The shape of the softening law,
e.g., linear, exponential or other, is generally assumed
to be inconsequential for the prediction of fracture.
While this assumption is valid under small-scale
bridging conditions, the shape of the cohesive law plays
a fundamental role in the prediction of fracture under
large-scale bridging conditions, where the process zone
length may be large relative to other length scales in the
problem [2]. When crack propagation includes different
energy dissipation mechanisms that act over different
length scales, the nature of these mechanisms must be
accounted for in the cohesive law.
Several failure mechanisms including fiber tensile
fracture, fiber-matrix pull-out and matrix cracking are
present when a crack propagates in a plane
perpendicular to the fiber direction. To account for
these different failure mechanisms, the authors have
proposed in a previous paper a combined linear-
exponential softening law for fiber tensile fracture [3],
and demonstrated that a simple linear softening law is
unable to predict the load-displacement relation
obtained in a cross-ply Compact Tension (CT) test
specimen, while a bi-linear softening law provides an
accurate prediction [4].
For longitudinal compression, the definition of the
parameters used in the softening law related to the fiber
kinking failure mechanisms is based on the
experimental determination of the crack resistance
curve (R-curve) of the Compact Compression (CC) test
specimen [5]. However, the CC test specimen presents
several problems that are yet to be resolved: the
tractions that are transferred along a kink band render
the numerical calculation of the J-integral using the
Finite Element Method (FEM) inaccurate [5]. In
addition, the experimental determination of the exact
location of the tip of a kink band is difficult.
Therefore, the objective of this paper is to address these
problems by using an alternative method that is based
on the use of the Digital Image Correlation (DIC)
technique. An automatic algorithm that post-processes
the data obtained from the DIC system is used to detect
https://ntrs.nasa.gov/search.jsp?R=20100012825 2019-08-30T09:18:33+00:00Z
the crack tip location and to establish the R-curve from
the surface measurements of the displacement field.
2. CONFIGURATION OF THE TEST
SPECIMENS
Grégoire [7], which identifies a discontinuity inside a
pattern based on the observed displacement field. The
procedure was modified to enable the identification of
crack tips in carbon-epoxy CT and CC test specimens,
and implemented in a MATLAB [8] code which
provides the following information:
The material used is the carbon-fiber reinforced epoxy
IM7-8552 provided by Hexcel composites. Average
values of the material properties of IM7-8552, measured
in a previous investigation [6], are shown in Tables 1
and 2.
Table 1. Elastic properties of IM7-8552
	
E1T (GPa)	 E1C (GPa)	 E2 (GPa)	 G12 (GPa)	 u12
171.4	 150	 9.1	 5.3	 0.3
where E 1 and E2 are, respectively, the ply longitudinal
and transverse modulus, G 12 is the ply shear modulus,
and u 12 is the ply major Poisson ratio.
Table 2. Strengths of IM7-8552 (MPa)
	
XT	 XC	 YT	 YT	 SL
	
2326	 1200	 62	 200	 92
where XT and XC are respectively the ply longitudinal
tensile and compressive strength, YT and YC are,
respectively, the ply transverse tensile and compressive
strengths, and SL is the ply shear strength.
The pre-impregnated plies were laid-up in an [90/0] 8s
configuration and cured according to Hexcel’s
specifications. The resulting plates were cut using a
diamond-coated saw to their nominal overall
dimensions. The specimens were finally machined to
their final geometry, shown in Figure 1. The holes for
the load introduction points were cut using tungsten –
carbide drills and by clamping the specimens between
to sacrificial carbon-epoxy plates. This procedure
prevents the test specimens from delamination at the
entrance and exit of the drill.
ft* j^ftil..] n uJru	 ME) 0,(4- ll	 a
Figure 1. Geometry of the CT and CC test specimens
(after Pinho [5]).
3. IDENTIFICATION OF THE CRACK TIP
LOCATION
The accurate measurement of the crack location is
performed by post-processing the information obtained
by the DIC system. The function K(P) proposed by
• K(P)=0 - no discontinuity (bulk material).
• K(P)=-1 - discontinuity (crack).
• K(P)=1 - crack tip.
Figure 2 shows the result of the application of the
MATLAB algorithm during the crack propagation stage
of a CT specimen. The exact location of the crack tip is
identified and quantified by the location where K(P)=1.
This procedure obviates the need for the visual
identification of the crack tip, which is prone to human
errors, especially in the case of the CC test specimen.
K(P)
Figure 2. Identification of the crack tip location in a CT
test specimen.
4. EXPERIMENTAL DETERMINATION OF
THE J-INTEGRAL
A new method to evaluate the J-integral and to measure
the crack resistance curve based on the surface
displacement and strain fields obtained from a Digital
Image Correlation (DIC) system is proposed.
The digital image correlation ARAMIS software
developed by GOM [9] was used in this work. This
measurement system is equipped with an 8-bit Baumer
Optronic FWX20 camera (resolution of 1624x1236
pixels, pixel size of 4.41im and sensor format of 1/1.8'')
coupled with a Schneider-Kreuznach Componar-S
50mm f/2.8 lenses. Using DIC, several matrices
containing the in-plane displacement and strain fields
are obtained; these fields are the basis for the
calculation of the J-integral.
For the cross-ply laminate used here, and assuming that
there is no bending of the specimen, the J-integral can
be defined using classical lamination theory as:
(1)
where the stress tensor, collected in {^}, is averaged
through-the-thickness of the laminate and t corresponds
to the laminate thickness.
The contour selected to calculate the J-integral from the
DIC system is shown in Figure 3.
Figure 3. Contour used to calculate the J-integral
4.1. Calculation of the stresses.
The stresses are computed from the homogenized
stiffness matrix as: rJ=LCls} , where {e} is the strain
matrix calculated at a given position by the DIC.
4.2. Calculation of dx1, dx2, and ds.
The differentials dx 1 and dx2 are taken as the
differences between the centers of adjoining macro-
pixel windows, measured along the corresponding axes.
The differential ds is the Euclidian norm of dx 1 and dx2 .
4.3. Calculation of { c 1^,
This vector is directly defined by the simple contour
sub-divisions shown in Figure 3, taking the following
forms: {1,0,0} T on C3 , {0,1,0} T on C4 , {-1,0,0} T on C 1 ,
and {0,-1,0} T on C2 .
4.4. Calculation of
L
This vector is calculated using the central difference
method applied in three adjoining macro-pixels. Having
calculated all the terms required in equation (1), the J-
integral is computed from the summation of all discrete
contributions of each macro-pixel, which are calculated
using equation (1) with the relevant terms calculated as
explained in the previous points. This methodology was
implemented in a MATLAB program that enables the
automatic generation of the R-curve by assigning to
each crack length the corresponding value of the J-
integral.
5. COMPACT TENSION TESTS
The CT test was conducted using an MTS 312.31
testing machine with a load capacity of 250 kN. The
tests were performed using a load cell of 100 kN and
the speed of the machine used in the displacement
controlled test was 2mm/min. Figure 4 shows the set-up
used during the CT tests. The test specimen was
previously sprayed with a white ink to generate a
random distribution of points, as required by the DIC
system.
Figure 4. Compact tension test specimen and DIC
system.
Figure 5 shows the R-curves measured from the FEM
post-processing of the test results obtained by the
method proposed by Pinho et al. [4] and those obtained
by processing of the displacement and strain fields
measured by the DIC system. Figure 5 shows a good
correlation between the two techniques.
1200`, T^'^ yM .9 t y	 —i
^^ FEPA
[60',^	 ^	 ^C DiC
dc
Viso la 	 ^1
r14 1.
F
Figure 5. R-curves extracted from a CT specimen using
FEM and DIC.
The results show an initial fracture toughness of 92 J/m2
that steadily increases up to an average toughness of
146 J/m2 for a crack increment of 4mm. This R-curve
results from fiber bridging, as shown in Figure 6.
Figure 6. CT test specimen showing fiber bridging
6. COMPACT COMPRESSION TESTS
The CC tests were conducted with the same test
machine and speed as those used in the CT tests. As
previously explained, the FEM-based calculation of the
J-integral is not appropriate to the calculation of the R-
curve because it does not account for the contact and
load transfer across the kink band. Figure 7 shows that
the FEM-based and DIC-based R-curves differ
approximately by a factor of two. At large crack
increments (>11 mm.), the FEM-based solution yields
unrealistically high values of the fracture toughness that
could result in an unreliable softening law for the fiber
kinking failure mode.
IM
Figure
111 FE 11 I
Val zi
k
"'W"
7. R-curves extracted from a CC specimen
using FEM and DIC.
The initiation values of the fracture toughness are also
different: approximately 80 J/m2 for the DIC-based
solution and 100 J/m2 for the FEM-based solution. In
addition, the algorithm developed to detect the exact
location of the tip of the kink band was unable to yield
reliable results for kink band lengths between 2mm and
1 1mm. The reason for this uncertainty is the presence of
a delamination associated with the propagation of the
kink band, which pollutes the data in the vicinity of the
tip of the kink band.
Figure 8 shows the propagation of the kink band from
the initial notch and illustrates the difficulty in detecting
the exact location of the tip of the kink band by visual
inspection alone. Figure 8 also shows the delamination
that accompanies the propagation of the kink band.
Figure 8. CT test specimen showing the propagation of
a kink band.
7. CONCLUSIONS
The displacement and strain fields obtained using DIC
during the CT and CC tests of composite laminates may
serve as the basis for the rigorous determination of the
location of the crack or kink band tips and for the
automatic computation of the J-integral. The models
develop for these purposes were implemented in a
MATLAB code that obviates the need of any complex
pre-and post-processing, either based on FEM or
standard data reduction methods. In addition, the
proposed methodology can be used to generate R-
curves for CC tests. Some difficulties encountered in
the identification of the tip of the kink-band in the
presence of delamination still need to be addressed.
The carbon-epoxy material system used, IM7-8552,
shows an R-curve for fiber dominated failure modes
under tensile loads, where the fracture toughness
increases from 92 J/m2 to 146 J/m2. An even more
pronounced R-curve was obtained for fiber dominated
failure modes under compressive loads, where the
fracture toughness ranges from 80 J/m2 to
approximately 300 J/m2 for large kink band lengths.
ACKNOWLEDGEMENTS
The second author acknowledges the financial support
of the European Commission under Contract No.
MRTN-CT-2005-019198.
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Resistance Curves in the Tensile and Compressive Longitudinal Failure of Composites

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