Computational Methods for Debonding in Composites

110 C. Schuecker and H.E. Pettermann
damage model assumptions, the exact formulation of the constitutive equations as
well as identification procedures for the model parameters see [22, 24, 25].
5.4 Laminate Behavior
In order to apply the combined damage/plasticity model to the analysis of multidirectional
laminates, the model is implemented in combination with classical
lamination theory extended for plastic strains (e.g. [5]). In the following, model
predictions are compared to experimental data to assess the model’s capabilities of
capturing laminate behavior under various loading conditions.
5.4.1 Influence of Curing Stresses on Shear Behavior
In this section, the combined damage/plasticity model is used to investigate the
effect of curing stresses on the shear response derived from two different experimental
test methods reported in [11]. One method is a torsion test of a hoop-wound
tube which yields the shear stress–shear strain relation of a UD laminate under inplane
simple shear. The other method is to derive the non-linear shear response via
lamination theory from tests on ±45 laminates under stress ratio σxx/σyy = −1
leading to in-plane simple shear in each layer. Since the individual plies experience
only shear stresses in both experiments, there should be no difference between the
non-linear shear responses derived by either test method. Both of these methods
were used in [11] to determine the shear response of the glass fiber/epoxy material
E-glass/MY750 (see Table 5.1). The experimental results are shown in Fig. 5.7
denoted as ‘exp. UD’ and ‘exp. laminate’. One difference between the two curves
is related to the fracture process. Fracture of the UD specimen is the result of a
single matrix crack, while a laminate can continue to carry load well after the individual
plies have cracked. But also prior to cracking, the non-linear behavior is not
the same as the curves from the laminate tests exhibit significantly higher strains
beyond σ12 ≈ 40 MPa. A possible explanation for this discrepancy are residual curing
stresses due to the production process which are expected to exist in the ±45
laminate but not in the UD specimens.
The results of analyses employing the proposed damage/plasticity model are also
displayed in Fig. 5.7. Damage parameters for the glass fiber/epoxy material have
been identified previously in [24] and are listed with the other material data in
Table 5.1. The non-linearity predicted for a UD laminate is caused by plasticity
only and the corresponding curve is labeled as ‘model UD’ in Fig. 5.7. It is a perfect
fit to the corresponding experimental curve, since the experimental data is the same
as that used for parameter identification in Fig. 5.3, left. The curve predicted for the
biaxial laminate test without consideration of residual stresses (‘model laminate’)
also follows the same curve up to the onset of damage and then continues with an