JEC COMPOSITES MAGAZINE - Issue #100 - Special JEC Asia - October 2015 - 65

Fig. 2: Resulting nonlinear resin response as a function of shear strain (left: shear stress, middle: resin damage, right: plastic shear strain)

proprietary damage initiation law has been derived based on the
assumption that fibre micro-buckling is dependent on compressive fibre strain, effective resin stiffness (including resin plasticity
and damage) and out-of-plane strains (compressive out-of-plane
strains are assumed to inhibit micro-buckling and tensile strains
are assumed to promote micro-buckling). The resin is assumed to
have an elasto-plastic behaviour, with linear elastic behaviour up to
the point where the material starts to plastically deform. Both resin
damage and plasticity are assumed to depend on the in-plane resin
von Mises stress.
Mesh dependency
When a material becomes damaged, part of the material can no
longer carry any loads, so that the effective stiffness of the material decreases. Analyses with such softening behaviour normally
show a high mesh dependency (giving different results for different
mesh densities). Two different techniques are used to alleviate this
problem: the Hillerborg's fracture energy proposal (Hillerborg et
al., 1976) is used for the tensile failure of the fibres and a non-local
method (e.g. Pijaudier-Cabot and Bazant, 1987) is used for the
compression failure of the fibres. In the non-local method, the
local strain that determines the damage initiation is replaced by a
non-local strain. When modelling failure in composites, next to
alleviating mesh dependency there is another reason to use a nonlocal method. For micro-buckling of the fibres to occur, high strains
or stresses should be present over a certain length of the fibre. As
the non-local method uses an average strain over a certain area, it
will automatically filter out very local strain peaks.
Delaminations
Another important failure mechanism in composites is delamination. Mode 1 delaminations are assumed to occur due to excessive
tensile out-of-plane stresses alone. The initiation and growth of
Mode 2 delaminations in composites is mainly governed by transverse shear stresses. However, compressive out-of-plane stresses
are known to inhibit the initiation and growth of Mode 2 delaminations while tensile out-of-plane stresses are known to promote
the initiation and growth of Mode 2 delaminations (Lecuyer and
Engrand, 1992). The above assumptions are used to derive new
cohesive failure laws.

Fig. 3. Top: force-displacement graph of peel test; bottom: force-displacement
graphs of ILS3 3-point bending test (blue=no damage; red=failed)

Implementation in Abaqus and general model description
The material model was implemented in Abaqus/Standard 6.14-3
using the UMAT and USDFLD user subroutines. Each ply was
modelled as a separate element layer. The layers were tied together
using cohesive surfaces (including damage initiation and growth).
Boundary conditions were chosen such that they mimic the test
conditions most accurately.
Determination of unknown material parameters
A composite material consisting of a combination of a quasi-UD
No100 October 2015 /

jec composites magazine 65

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #100 - Special JEC Asia - October 2015