JEC COMPOSITES MAGAZINE - Issue #90 - June/July 2014 - 50

damage
force Y is defined based on the pure contributions YI, YII and
YIII, in order to represent the global effect of the loading:

Here, a is equal to 1. In [9], a single damage variable d is used
to represent the damage, assuming that damage is damage,
whatever may be the influencing mode. Details can be found in
[5,9].
With the cohesive elements approach, a coarser mesh can be
used compared to VCE. Moreover, the crack propagation is
simulated in a natural way as it is related to the local loss of
mechanical properties of the material assigned to the interface.
For instance in pure mode loading, once the energy below
the curve of Figure 6 (which is directly linked to the fracture
toughness) is dissipated, damage is equal to 1 and the interface
is locally broken. With LMS Samtech Samcef , defining zerothickness interface elements in an existing mesh is a very simple
task. Consequently, there is no inconvenient associated to the
meshing process. Using the cohesive laws of Figure 6 requires
more parameters compared to VCE. However, this is no more
an issue today as the procedure to identify these parameters is
available at the coupon level based on, for instance, the DCB
and ENF tests as explained in [1].

Fig. 7: Location of the cracks in the composite element submitted to a pull test

size needed to obtain accurate results [5]. It then comes that
elements of an in-plane size of about 0.5mm are used in the
zones of interest. Two elements are used along each ply thickness; that is, multi-layer elements are not used. A very large
number of contact elements (14,186) is defined in the model
(Figure 9). It is indeed essential to avoid ply penetration in
order to obtain physical and accurate results. A given value of
the vertical load is imposed on the upper face, via rigid body
elements. A linear static analysis is conducted. The evolution of
the failure criterion (1) for these initial cracks is also provided.
It is clear from Figure 10 that 3D effects appear in the problem,
even if a simple pull test is conducted. Indeed, not only mode I
but also mode II are present in the problem and their magnitude is of the same order (mode III is not represented). The
results of Figure 10 indicate that the cracks at the noodle loca-

Fig. 6: Possible constitutive laws in the interface

Application
The test case is illustrated in Figure 7. It is a laminated composite element made of carbon/epoxy skin and stiffener,
supported at its edges along direction 1 and submitted to a
pull test. Initial delaminations (i.e. initial cracks) are defined
between each ply in the middle region of the structure, on a
square zone, as well as at the noodle location. Thus, 83 initial
crack fronts are taken into account in the structure (Figure 7).
The initial cracks are modelled by double nodes. Solid shell
elements are used. The laminates are made up of plies oriented
at 0°, 90°, 45° and -45°. The dimensions, stacking sequences,
number of plies and base material properties are not reported
here, for confidentiality reasons. Simulation is used here as
a predictive tool, and the physical and virtual test results are
finally compared in order to estimate the efficiency of the finite
element software.
First, VCE is used to detect the most dangerous cracks in the
problem. The model of Figure 8 includes 1,028,080 degrees
of freedom. Refinements are defined in the vicinity of the
crack fronts in order to satisfy the requirements on the mesh

50 jec composites magazine / No90 June - July 2014

Fig. 8: Finite element model for VCE

Fig. 9: Deformation of the element and ply penetration avoided thanks to contact
elements

JEC COMPOSITES MAGAZINE - Issue #90 - June/July 2014

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