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Journal ArticleDOI

Measurement of resistance curves in the longitudinal failure of composites using digital image correlation

15 Nov 2010-Composites Science and Technology (Elsevier)-Vol. 70, Iss: 13, pp 1986-1993

AbstractThis paper presents a new methodology to measure the crack resistance curves associated with fiberdominated failure modes in polymer–matrix composites. The 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 numerical simulation of fracture in composite materials. The proposed method is based on the identification of the crack tip location using 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 Finite Element based methods for compact tension carbon–epoxy specimens. However, it is also shown that, while the Digital Image Correlation based technique mitigates the problems resulting from Finite Element based data reduction schemes applied to compact compression tests, the delamination that accompanies the propagation of a kink-band renders compact compression test specimens unsuitable to measure resistance curves associated with fiber kinking.

Topics: Digital image correlation (56%), Composite laminates (52%), Fracture toughness (51%), Delamination (51%), Finite element method (51%)

Summary (2 min read)

1. Introduction

  • Sophisticated kinematic representations of failure mechanisms [8,9], and cohesive elements to deal with delamination [10,11], the accurate prediction of intralaminar fracture mechanisms still presents several challenges.
  • While this assumption is valid under smallscale bridging conditions, the shape of the cohesive law plays a fundamental role in the prediction of fracture under large-scale bridging conditions [12].
  • To account for these different failure mechanisms, a combined linear-exponential softening law for fiber tensile fracture has been proposed [5,6], and it was 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 [13].
  • In addition, the experimental determination of the exact location of the tip of a kink-band is even more difficult than for the CT specimens.
  • An automatic algorithm that post-processes the full-field data provided by the DIC system during the CT and CC tests is used to detect the crack tip location and to establish the R-curve from the surface measurements of the displacement and strain fields.

2. Identification of the crack tip location

  • The algorithm used to identify the crack tip location in the CT and CC test specimens is based on the work of Grégoire [19].
  • The contour integral J, which is defined along a region where the material is linear-elastic, is therefore used to calculate the crack resistance curve of the CC and CT test specimens.
  • The same happens with the sum of the thicknesses of the all the 90 plies.
  • To simplify the calculations, the simple rectangular contour shown in Fig. 6 is selected.
  • The differentials dx1 and dx2 are taken as the differences between the centers of adjoining subsets, measured along the corresponding axes.

4.1. Configuration of the test specimens

  • The material used in this work is unidirectional carbon-fiber reinforced epoxy Hexcel IM7-8552.
  • The elastic properties of IM7-8552, measured in a previous investigation [18], are shown in Table 1. E1 and E2 are the longitudinal and transverse.
  • The specimens were finally machined to their final geometry, shown in Fig. 7 (CT specimen), and in Fig. 8 (CC specimen).
  • In the set-up, the optical system was positioned perpendicular to the surface of the specimen mounted into the testing machine (Fig. 9).
  • The facet step (i.e., the distance between adjacent facets) can also be set either for controlling the total number of measuring points over the region of interest, or for enhancing the spatial resolution by slightly overlapping adjacent facets.

4.2. Compact tension

  • The load was measured using the 100 kN load cell, and the displacement was measured using the linear variable differential transformer (LVDT) connected to the hydraulic actuator of the test machine.
  • Fig. 12 shows a good correlation between the FEM and DIC data reduction methods.
  • This means that the fracture process zone that bridges the crack has a minor effect on the displacement and strain fields in the regions where the Finite Element model computes the J-integral.
  • Fig. 13 shows the R-curves obtained from the three CT tests.
  • Fig. 13 also shows the mean value of the fracture process zone, 3.4 mm, and the mean values of the initial fracture toughness and that corresponding to steady-state crack propagation, 97.8 kJ/m2 and 133.3 kJ/m2 respectively.

4.3. Compact compression

  • A non-linear response is observed in the load–displacement relation before the peak load is attained.
  • The reason for this fact is that the FEM-based calculation of the J-integral does not account for the contact and load transfer across the band of the kinked fibers.
  • On the other hand, the DIC-based method uses the actual displacement and strain fields on the surface of the specimen, provided that the contours selected do not include delaminated regions, thus resulting in an improved R-curve.
  • Delamination associated with the propagation of the kink-band from the initial notch was also observed in the CC tests.
  • In addition, the presence of delamination invalidates the assumption of a two-dimensional crack, and of constant strain through the thickness of the laminate (assumption used in Eq. (6)).

5. Conclusions

  • This paper presents a new method to measure the crack resistance curves in CT and CC test specimens manufactured using cross-ply CFRP composite laminates.
  • The method was implemented in a ”Matlab” code that obviates the need of any complex pre- and post-processing of the test data, either based on FEM or standard data reduction methods, and enables the real-time generation of R-curves during a test.
  • The mean value of the associated cohesive zone is 3.4 mm.
  • The DIC-based method is an improvement over FE-based data reduction methods because it is based on the actual displacement field on a pre-defined contour that does not include delaminated regions.
  • The values computed for the fracture toughness using the CC specimen do not account for the energy dissipated by the delamination that accompanied the propagation of the kink-band.

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Measurement of resistance curves in the longitudinal failure of composites
using digital image correlation
G. Catalanotti
a
, P.P. Camanho
a,
*
, J. Xavier
b
, C.G. Dávila
c
, A.T. Marques
a
a
DEMec, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
b
CITAB/UTAD, Engenharias I, Apartado 1013 5001, 801 Vila Real, Portugal
c
NASA Langley Research Center, Hampton, VA, USA
article info
Article history:
Received 7 April 2010
Received in revised form 16 July 2010
Accepted 22 July 2010
Available online 1 August 2010
Keywords:
A. Polymer–matrix composites (PMCs)
B. Fracture toughness
abstract
This paper presents a new methodology to measure the crack resistance curves associated with fiber-
dominated failure modes in polymer–matrix composites. The crack resistance curves not only character-
ize the fracture toughness of the material, but are also the basis for the identification of the parameters of
the softening laws used in the numerical simulation of fracture in composite materials. The proposed
method is based on the identification of the crack tip location using 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 Finite Element based methods for compact tension
carbon–epoxy specimens. However, it is also shown that, while the Digital Image Correlation based tech-
nique mitigates the problems resulting from Finite Element based data reduction schemes applied to
compact compression tests, the delamination that accompanies the propagation of a kink-band renders
compact compression test specimens unsuitable to measure resistance curves associated with fiber
kinking.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Despite the significant advances in the analysis models for the
prediction of fracture in composite materials such as advanced fail-
ure criteria and associated damage models [1–7], sophisticated
kinematic representations of failure mechanisms [8,9], and cohe-
sive elements to deal with delamination [10,11], the accurate pre-
diction of intralaminar fracture mechanisms still presents several
challenges.
The majority of existing models for intralaminar fracture of
polymer-based composite materials reinforced by carbon-fibers
are based on softening constitutive models [7]. The shape of the
softening law is often assumed to be inconsequential for the pre-
diction of fracture, provided that it is defined as a function of the
fracture toughness. 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 [12]. When crack propagation includes differ-
ent energy dissipation mechanisms that act over different length
scales, the nature of these mechanisms must be appropriately
accounted 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, a combined
linear-exponential softening law for fiber tensile fracture has been
proposed [5,6], and it was 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 [13]. The
definition of the parameters used in the softening law related to
the fiber-dominated failure mechanisms is based on the experi-
mental determination of the crack resistance curve (R-curve) of
the Compact Tension (CT) and Compact Compression (CC) test
specimens proposed by Pinho [14]. However, these test specimens
present some problems that are yet to be resolved.
Laffan et al. [15] performed a detailed investigation of the dif-
ferent data reduction methods available for the measurement of
the ply fracture toughness associated with mode I fiber tensile fail-
ure and concluded that the data reduction methods based on Finite
Elements (e.g. by using the J-integral [16]) eliminate errors that
occur in the compliance calibration method, which result from
the differentiation of a fitted curve. Based on a detailed comparison
of the area method, the J-integral/Virtual Crack Closure Technique,
the ASTM E399 [17] standard, the compliance calibration and the
modified compliance calibration methods, the authors concluded
0266-3538/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compscitech.2010.07.022
* Corresponding author. Tel.: +351 225081753; fax: +351 225081315.
E-mail address: pcamanho@fe.up.pt (P.P. Camanho).
Composites Science and Technology 70 (2010) 1986–1993
Contents lists available at ScienceDirect
Composites Science and Technology
journal homepage: www.elsevier.com/locate/compscitech

that the modified compliance calibration method using an effective
crack length was the most appropriate data reduction scheme be-
cause it provides consistent results and it does not require an opti-
cally measured crack length [15].
The Finite Element based method developed by Pinho et al.
[14,15] consists in the generation of a set of shell Finite Element
models of the CT specimen with variable crack lengths that are
used to calculate the corresponding values of the J-integral for a
unit load. Equipped with this information, it is possible to correlate
the experimental results, load and crack length, to the J-integral
calculated using Finite Elements, and to generate the correspond-
ing R-curve. However, Finite Element based methods have the
additional difficulty of requiring a numerical model and an opti-
cally measured crack length.
For the case of the CC tests, there are additional difficulties: the
tractions that are transferred along a kink-band render the numer-
ical calculation of the J-integral using the Finite Element Method
(FEM) inaccurate. In addition, the experimental determination of
the exact location of the tip of a kink-band is even more difficult
than for the CT specimens.
Therefore, the objective of this paper is to address these prob-
lems by using an alternative method to measure the R-curves
based on the Digital Image Correlation (DIC) technique. An auto-
matic algorithm that post-processes the full-field data provided
by the DIC system during the CT and CC tests is used to detect
the crack tip location and to establish the R-curve from the surface
measurements of the displacement and strain fields.
2. Identification of the crack tip location
The algorithm used to identify the crack tip location in the CT
and CC test specimens is based on the work of Grégoire [19]. Con-
sidering Fig. 1, M and N are two points in the reference image, d(x)
is the displacement of the images, and M
*
and N
*
are the two points
in the deformed image that are separated by a geometric or mate-
rial discontinuity.
An auxiliary function that identifies a discontinuity in the dis-
placement field, M o N, is defined as:
M o N ¼ M
N
!
MN
!
ð1Þ
Eq. (1) can be re-written in terms of the displacements as:
M o N ¼kdðNÞdðMÞk ð2Þ
Using (1), the presence of a discontinuity in a pattern ABCD (Fig. 2)
is identified in a facet P with the help of the following function:
KðPÞ¼maxðA o C; B o DÞ
maxðkdðCÞdðAÞk; kdðDÞdðBÞkÞ ð3Þ
Eq. (3) quantifies the displacement discontinuity inside the pattern,
and Fig. 2 shows that this equation is able to detect a displacement
jump associated with a crack, independently of the orientation of
the crack within the pattern. To identify whether a pattern is dam-
aged or undamaged a threshold value is associated to this function.
It is assumed that the threshold applied is proportional to the mean
value of the function K(P) along the facet; therefore, the threshold
function K
T
(P) is:
KðPÞ P
a
K ) K
T
ðPÞ¼1 ð4aÞ
KðPÞ <
a
K ) K
T
ðPÞ¼0 ð4bÞ
KðPÞ¼NaN ) K
T
ðPÞ¼1 ð4cÞ
where K is the mean value of K(P) inside the image,
a
is the thresh-
old value, and NaN indicates that the information it is not available
(not a number). Fig. 3 shows a typical relation between the mea-
sured crack length of a CT specimen and the time for several values
of the parameter
a
. A small value of
a
,
a
= 2, was chosen to prevent
loosing information in vicinity of the crack tip.
Thus, the function K
T
(P) represents a mask over the region of
interest indexing the following regions:
K
T
(P) = 1 are the region where a discontinuity is present but the
material is not completely damaged. This happens at the crack
tip;
K
T
(P) = 0 corresponds to the region where the material is
undamaged;
Fig. 1. Points M and N before and after crack propagation.
Fig. 2. Different position of the discontinuity with respect to a given pattern.
G. Catalanotti et al. / Composites Science and Technology 70 (2010) 1986–1993
1987

K
T
(P)=1 represents the region where the material is com-
pletely damaged and no information is available using digital
image correlation.
Fig. 4 shows the K
T
function computed for a CT carbon speci-
men. It can be observed that the function takes the value K
T
=0
for the undamaged material points, K
T
= 1 in the regions where
the material is completely fractured, and K
T
= 1 at the crack tip.
The spatial resolution of the K
T
function is defined by the size of
the subsets used in the DIC method.
3. Experimental determination of the J-integral
Having defined an automatic way to quantify the crack length
that does not require any visual inspection, we propose a new
method to evaluate the J-integral and to measure the crack resis-
tance curve based on the surface displacement and strain fields ob-
tained from the DIC technique.
For a surface S
0
that surrounds the crack and that includes the
edges of the cohesive zone that bridges the crack, the conservation
integral, I, can be defined as:
I ¼
1
h
Z
S
0
wn
1
@u
@x
1
t

dS ¼ 0 ð5Þ
where h is the total thickness of the laminate, w the strain energy
density, u the displacement field and t the traction vector x
1
is an
axis aligned with the crack growth direction and n
1
is the Cartesian
coordinate of the unit vector normal to the contour in the x
1
axis.
Taking the contour represented in Fig. 5, defined by
C
S
C
+
S
C
0
S
C
, and taking into account that n
1
= 0 and t
= t
+
on C
and C
+
, Eq. (5) results in:
1
h
Z
h
0
Z
C
wn
1
@u
@x
1
t

dS þ
Z
D
T
0
t dD

dx
3
¼
1
h
Z
h
0
Z
C
0
wn
1
@u
@x
1
t

dS

dx
3
ð6Þ
where
D
T
is the displacement jump at the beginning of the cohesive
zone.
The two terms on the LHS of the previous equation are used to
account for the energy-dissipating mechanisms acting on the cohe-
sive zone:
J
coh
¼
1
h
Z
h
0
Z
D
T
0
t dDdx
3
ð7Þ
and for the energy-dissipating mechanisms acting on the crack tip:
J
tip
¼
1
h
Z
h
0
Z
C
wn
1
@u
@x
1
t

dS

dx
3
ð8Þ
It is clear from Eq. (6) that the contribution of the mechanisms act-
ing at the crack tip and along the cohesive region for the total en-
ergy dissipation can be computed from a contour integral that
encompasses a region away from the crack tip, i.e. J
tip
+ J
coh
= J, with:
J ¼
1
h
Z
h
0
Z
C
0
wn
1
@u
@x
1
t

dS

dx
3
ð9Þ
The contour integral J, which is defined along a region where the
material is linear-elastic, is therefore used to calculate the crack
resistance curve of the CC and CT test specimens. The CT and CC
specimens are manufactured using a cross-ply configuration,
[90/0]
ns
. For these specimens, the J-integral reads:
250 300 350 400 450
25
30
35
40
45
50
time [s]
crack length [mm]
α=0.5
α=1
α=2
α=3
α≥ 5
Fig. 3. Relation between the crack length and time for different values of
a
.
Fig. 4. KT function.
1988 G. Catalanotti et al. / Composites Science and Technology 70 (2010) 1986–1993

J ¼
1
h
Z
C
0
X
n
0
Z
h
0
0
w
0
n
1
@u
@x
1
t
0

dS
"
þ
X
n
90
Z
h
90
0
w
90
n
1
@u
@x
1
t
90

dS
#
dx
3
ð10Þ
where n
0
, n
90
are the number of 0° and 90° plies, respectively, and h
0
,
h
90
are the thickness of each 0° and 90° ply, respectively. w
0
, w
90
are
the strain energy densities in the 0° and 90° plies, respectively.
In the laminates used in this work, the sum of the thicknesses of
the all the 0° is equal to half of the laminate thickness. The same
happens with the sum of the thicknesses of the all the 90° plies.
Taking these facts into account, and assuming linear elasticity
along the contour
C
0
shown in Fig. 5 and that the strain tensor is
constant through the thickness of the CT and CC test specimens,
the previous equation yields:
J ¼
1
2
Z
C
0
1
2
r
0
þ
r
90

n
1
:
e
r
0
þ
r
90

n
@u
@x
1

dS ð11Þ
where
r
0
and
r
90
are respectively the stress fields in the 0° and 90°
plies. Defining the laminate average stress as
r ¼
1
2
ðr
0
þ r
90
Þ, Eq.
(11) is written in matrix notation as:
J ¼
1
2
Z
C
0
r
fg
e
fg
T
n
1
2
@u
@x
1

T
r
½
nfg
!
dS ð12Þ
The method proposed in this work consists in determining each
term of the previous equation using the displacement and strain
fields provided by the DIC system, which are collected in the vectors
{u} and {
e
}, respectively. The first step consists in defining a contour.
To simplify the calculations, the simple rectangular contour shown
in Fig. 6 is selected.
The calculation of the terms used in (12) is performed as
follows:
Average stresses, f
r
g. The average stresses are computed from
the transformed stiffness matrices of the 0° and 90° plies, ½
C
0
and ½
C
90
respectively, as f
r
1
2
ð½C
0
þ½C
90
Þf
e
g.
Differentials dx
1
, dx
2
and dS. The differentials dx
1
and dx
2
are
taken as the differences between the centers of adjoining sub-
sets, measured along the corresponding axes. The differential
dS is the Euclidian norm of dx
1
and dx
2
.
Vectors normal to the contour, {n}. These vectors are directly
defined by the simple contour sub-divisions shown in Fig. 6,
taking the following forms: {1,0,0}
T
on C
3
, {0,1, 0}
T
on C
4
,
{1,0,0}
T
on C
1
, and {0,1,0}
T
on C
2
.
Derivative of the displacement field,
@u
@x
1
no
. This vector is calcu-
lated using the central difference method applied in three
adjoining subsets:
@u
@x
1

D
u
D
x
1

¼
u
iþ1
u
i1
2
D
x
1

ð13Þ
Having calculated all the terms required in Eq. (12), the J-inte-
gral is computed from the summation of all discrete contributions
of each subset, which are calculated as previously explained.
This method was implemented in a Matlab [20] script that
generate an R-curve automatically by assigning to each measured
crack length its corresponding value of the J-integral.
4. Experimental tests
4.1. Configuration of the test specimens
The material used in this work is unidirectional carbon-fiber
reinforced epoxy Hexcel IM7-8552. The elastic properties of
IM7-8552, measured in a previous investigation [18], are shown
in Table 1.
E
1
and E
2
are the longitudinal and transverse Young’s modulus
respectively, G
12
is the shear modulus, and
t
12
is the major
Poisson’s ratio.
The pre-impregnated plies were laid-up in an [90/0]
8s
configu-
ration proposed in [14] and cured according to Hexcel’s specifica-
tions. The resulting plates were cut using a diamond-coated disk
to their nominal overall dimensions, which are based on the work
of Pinho et al. [14]. The specimens were finally machined to their
final geometry, shown in Fig. 7 (CT specimen), and in Fig. 8 (CC
specimen). The holes for the load introduction pins shown in Figs.
7 and 8 were cut using tungsten carbide drills while clamping the
specimens between two sacrificial carbon–epoxy plates. This pro-
cedure prevents delamination at the entrance and exit of the drill.
The CT and CC tests were conducted using a servo-hydraulic
MTS 312.31 test machine with a load capacity of 250 kN. The tests
were performed using a 100 kN load cell and at controlled speed of
2 mm/min. Fig. 9 shows the set-up used during one CT tests. The
test specimen was previously sprayed with a white and black ink
to generate a random and contrasted distribution of granular spots,
as required by the DIC system. The average size of the granular
spots was suitable with regard to the resolution necessary for the
measurement of the energy release rate.
Fig. 5. Conservation integral.
Fig. 6. Contour used for the calculation of the J-integral.
Table 1
IM7-8552 ply elastic properties.
Property Mean value
E
1
(GPa) 171.42
E
2
(GPa) 9.08
G
12
(GPa) 5.29
t
12
0.32
G. Catalanotti et al. / Composites Science and Technology 70 (2010) 1986–1993
1989

The single-camera ARAMIS digital image correlation software
developed by GOM [21] was used. This measurement system is
equipped with an 8-bit Baumer Optronic FWX20 camera (resolu-
tion of 1624 1236 pixels, pixel size of 4.4
l
m and sensor format
of 1/1.8
00
) coupled with a Schneider–Kreuznach Componar-S
50 mm f/2.8 lens. For mobility and adaptability, the camera was
mounted on a tripod, which was positioned facing the testing ma-
chine. In the set-up, the optical system was positioned perpendic-
ular to the surface of the specimen mounted into the testing
machine (Fig. 9).
A laser pointer was used to facilitate a correct alignment. The
working distance (defined between the specimen’s surface and
the support of the cameras) was set in the range of 0.8 m. The lens
was adjusted to be in focus with regard to the surface of interest,
setting the lens aperture to f/2.8 in order to minimize the depth
of field. The aperture of the lens was then closed (f/11) to improve
the depth of field during testing. The shutter time was set to 1/20 s,
a value appropriate for the cross-head displacement rate used
during testing (2 mm/min), and the size of the camera unit cells
(4.4
l
m). The light source was finally adjusted in order to guaran-
tee an even illumination of the specimen’s surface and to avoid
over-exposition (i.e., the saturation of pixels over the field of
view).
The region of interest was set to approximately 20 20 mm
2
,
which defines a conversion factor of about 0.185 mm pixel
1
.In
the digital image correlation method, the displacement field is
measured by analyzing the geometrical deformation of the images
of the surface of interest, recorded before and after loading. For this
purpose, the initial (undeformed) image was mapped by square
facets (subsets), within which an independent measurement of
the displacement is calculated. Therefore, the facet size, on the
plane of the object, will characterize the displacement spatial res-
olution. The facet step (i.e., the distance between adjacent facets)
can also be set either for controlling the total number of measuring
points over the region of interest, or for enhancing the spatial res-
olution by slightly overlapping adjacent facets. Typically, a larger
facet size will improve the precision of the measurements but also
will degrade the spatial resolution [22]. Thus, a compromise must
be found according to the application to be handled. In this work, a
facet size of 15 15 pixels was chosen, attending to the size of the
region of interest, the optical system (magnification) and the qual-
ity of the granulate (average speckle size) obtained by the spray
paint. The facet step was also set to 15 15 pixels to avoid statis-
tically correlated measurements. The in-plane displacements were
then numerically differentiated in order to determine the strain
field need for the calculation of the J-integral using the procedure
previously presented.
A typical strain field obtained by ARAMIS [21] for the CT test
specimens is shown in Fig. 10.
4.2. Compact tension
A typical load–displacement relation obtained in the CT tests is
shown in Fig. 11. The load was measured using the 100 kN load
cell, and the displacement was measured using the linear variable
differential transformer (LVDT) connected to the hydraulic actua-
tor of the test machine. Three CT specimens were tested.
Fig. 7. Geometry of compact tension test specimen (after [14], dimensions in mm).
Fig. 8. Geometry of compact compression test specimen (after [14], dimensions in
mm).
Fig. 9. Compact tension test specimen and DIC system.
Fig. 10. Strain field obtained by ARAMIS:
e
yy
(x), with 0–y perpendicular to the
crack.
1990 G. Catalanotti et al. / Composites Science and Technology 70 (2010) 1986–1993

Citations
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Journal ArticleDOI
Abstract: A comprehensive review of techniques for the experimental characterisation of the fracture toughness associated with the translaminar (fibre-breaking) failure modes of continuously reinforced laminated composites is presented. The collection of work relating to tensile failure reveals a varied approach in terms of specimen configuration, size and data reduction, despite the existence of an ASTM standard. Best practices are identified and suggestions for extending the scope of the current standard are made. Works on compressive failure are found to be less comprehensive. Measurement of the toughness associated with initiation of the failure mode in isolation has been achieved, but this review finds that significant research steps need to be taken before a resistance curve can be fully characterised.

152 citations


Journal ArticleDOI
Abstract: Despite the recent success of modeling progressive damage of open-hole fiber reinforced composites subjected to tension (OHT), it is still a challenging task to predict the strengths and the damage progression of open-hole composite laminates under compressive loading (OHC). Herein, we propose a progressive damage model for OHC based on our early model for OHT and apply it to study the size effects of OHC. In the proposed model, continuum shell elements are used to account for both in-plane and out-of-plane deformation and delamination is modeled using cohesive elements. A smeared crack model is used to model the progressive failure of composite plies. It is found that the proposed model can predict accurately the experimental strengths and damage patterns with the assumption that the translaminar fracture toughness for blocked plies increases. The different failure mechanisms of the sublaminate scaled laminates of the stacking sequence 45 / 90 / - 45 / 0 ms and the ply-level scaled laminates of stacking sequence 45 n / 90 n / - 45 n / 0 n s are found to be closely related to the in-plane shear stress of the central 0 ° ply block and the initiation of interface delamination.

108 citations


Cites background from "Measurement of resistance curves in..."

  • ...[20] reported a compressive translaminar fracture toughness of 47....

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  • ...The tensile fracture toughness in the fiber direction is regarded as a lamina property which can be measured using compact tension or four-point bending experiments [20–22]....

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Journal ArticleDOI
Abstract: The tensile strength of open-hole fibre reinforced composite laminates depends on in-plane, thickness and ply lay-up scaling. Translaminar (fibre direction) mode I fracture toughness has recently been experimentally determined to be thickness dependent. This paper presents a computational study of the tensile strength prediction of open-hole laminates using a cohesive zone model. To the authors’ knowledge, it is for the first time in the literature that the thickness-dependence of translaminar fracture toughness is accounted for in the numerical modelling of composites. The thickness size effect in the strength of open-hole composite laminates failed by pull-out is accurately predicted for the first time by a deterministic model. It is found that neglecting delamination in the numerical models will lead to mesh-dependency and over-estimation on the predicted strength. Smeared crack model with cohesive elements to model delamination is able to predict the correct failure mode; but it is found not suitable for accurate strength predictions for laminates failed by delamination.

98 citations


Journal ArticleDOI
Abstract: This paper describes and validates a new fully three-dimensional smeared crack model to predict the onset and propagation of ply failure mechanisms in polymer composites reinforced by unidirectional fibers. The failure criteria are used to predict not only the onset of the failure mechanisms but also the orientation of the fracture plane. This information is used in a smeared crack model for transverse cracking that imposes a linear softening relation between the traction acting on the fracture planes and the crack opening displacements. The longitudinal failure mechanisms are represented using bi-linear softening relations. The model is validated using off-axis compression tests performed in unidirectional specimens as well as using tensile tests in notched multidirectional laminates. A good correlation between experimental observations and numerical predictions is obtained.

93 citations


Journal ArticleDOI
Dongyup Shin1, Hee Chul Kim1, Jung-Ju Lee1
Abstract: The damage behavior of an aluminum–composite hybrid beam under three point bending loading was investigated by a finite element analysis (FEA). An aluminum square hollow section beam wrapped by four plies of unidirectional carbon fiber reinforced plastic (CFRP) with a designed stacking sequence was investigated. Nonlinear elasto-plasticity and progressive damage mechanics were applied for aluminum and CFRP, respectively. Hashin’s damage initiation criteria and energy based damage evolution were applied. Delamination and debonding were modeled by a cohesive zone model defined by the traction separation law and an energy based damage evolution scheme. For a numerical analysis, material properties of the aluminum, failure characteristics of the CFRP laminate, and adhesion between the aluminum and CFRP were measured experimentally. The FEA showed that stress was concentrated at the edges under the loading nose. It was observed that the lay-up sequence of the laminates strongly influenced the performance. At low bending loading, failure of CFRP and delamination over a small area just below the loading nose occurred. As the load increased, the interface between aluminum and CFRP was debonded. Plastic buckling of aluminum and bending collapse behavior of the hybrid beam then occurred upon further loading. Overall performance of the hybrid beam represented by load–displacement curves with respect to the stacking sequence of the laminate was compared with experimental results. The FEA showed good agreement with the experimental results.

73 citations


References
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Journal ArticleDOI
James R. Rice1
Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

7,005 citations


Journal ArticleDOI
Abstract: A realistic failure analysis of structural members made of FRP composites requires consideration of the non-linear stress/strain relationships. In laminate design and for determination of safety factors of FRP structural members, there is a strong need for fracture criteria and degradation models which are simple enough for application in common engineering problems while still being in good agreement with physical reality. It is essential to distinguish between fibre failure and inter-fibre failure by separate failure criteria. A recent success was the introduction of inter-fibre failure criteria which model the brittle failure behaviour of composites very realistically. These not only provide realistic stresses to failure, but also indicate the crack direction, which is an extremely important piece of information when evaluating the likely effect of fracture. After crack initiation, the stiffnesses of the affected plies degrade gradually with increasing load, until fibre fracture in one ply provokes ultimate failure of the laminate. Also, an inclined wedge-shaped inter-fibre crack can lead to ultimate failure. From now on, the risk of fracture caused by these phenomena can be evaluated. The determination of the fracture angle which is the key for this evaluation is derived in the present paper.

1,333 citations


Journal ArticleDOI
Abstract: A thermodynamically consistent damage model is proposed for the simulation of progressive delamination in composite materials under variable-mode ratio. The model is formulated in the context of Damage Mechanics. A novel constitutive equation is developed to model the initiation and propagation of delamination. A delamination initiation criterion is proposed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. The formulation accounts for crack closure effects to avoid interfacial penetration of two adjacent layers after complete decohesion. The model is implemented in a finite element formulation, and the numerical predictions are compared with experimental results obtained in both composite test specimens and structural components.

714 citations


"Measurement of resistance curves in..." refers background in this paper

  • ...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 [1–7], sophisticated kinematic representations of failure mechanisms [8,9], and cohesive elements to deal with delamination [10,11], the accurate prediction of intralaminar fracture mechanisms still presents several challenges....

    [...]


Journal ArticleDOI
Abstract: This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.

613 citations


Journal ArticleDOI
Abstract: A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.

604 citations


"Measurement of resistance curves in..." refers background in this paper

  • ...To account for these different failure mechanisms, a combined linear-exponential softening law for fiber tensile fracture has been proposed [5,6], and it was 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 [13]....

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Q1. What are the contributions in "Measurement of resistance curves in the longitudinal failure of composites using digital image correlation" ?

This paper presents a new methodology to measure the crack resistance curves associated with fiberdominated failure modes in polymer–matrix composites.