Computational Methods for Debonding in Composites

142 F.P. van der Meer and L.J. Sluys
constitutive models are incorporated that give a complete description of the local
process from initial elastic behavior to complete loss of integrity.
For intraply failure, numerous theories exist that provide criteria to evaluate the
stresses inside a ply, either based on the different failure modes [7, 9, 17] or defined
as polynomial interaction between stress components [11, 24]. However, not much
is known on what happens inside a ply after such a criterion has been violated, even
though this information is necessary to predict redistribution of stresses and ultimate
failure of the laminate. We have used an interactive criterion and extended it with a
new softening plasticity model for the simulation of progressive failure.
For interply failure, models for the nonlinear material behavior are available
in literature. The interface can be modeled with interface (or decohesion) elements
[4,12,14,21,25,30], thin volume elements [27], or embedded discontinuities
incorporated through the partition of unity method [18]. Here, we have used interface
elements with a constitutive law developed by Turon et al. [25] to capture the
onset and growth of delamination cracks.
The outline of this paper is as follows. First, the softening orthotropic material
model for intraply failure is presented. Next, the delamination model is described.
And finally, the performance of the framework combining the two models is exemplified.
7.2 Softening Orthotropic Plasticity
The single expression failure criteria for orthotropic materials by Hoffman [11] and
Tsai and Wu [24] may be written in tensor notation (cf. [19]):
f (σ)= 1
σ · Pσ + σ · p − 1 (7.1)
2
where σ is the stress in Voigt notation, and the components of matrix P and vector
p are computed from the uniaxial strength parameters. Every stress state for
which f ≤0 is considered admissible. For the generalized Von Mises version of the
Tsai Wu criterion, P and p are defined as
⎡
2
1 − √
F1tF1cF2tF2c − ⎤
1 0 0 0
⎢
⎢−
⎢
⎢−
P = ⎢
⎣
√
F1tF1c
F1tF1cF2tF2c
√ 1
2 −
F1tF1cF2tF2c F2tF2c
1
F2tF2c
√ 1 −
F1tF1cF2tF2c
1
2
F2tF2c F2tF2c
1
0 0 0
F2 4
0 0 0 0 1
F2 6
0 0 0 0 0 1
F2 6
⎥
0 0 0 ⎥
0 0 0 ⎥
0 0 ⎥
0 ⎥
⎦
(7.2)