Computational Methods for Debonding in Composites

5 Combined Damage/Plasticity Model for Laminates 101
Fig. 5.1 Shear stress–shear strain response of a symmetric ±45 laminate under uniaxial tension
including unloading/reloading loops showing the evolution of shear modulus and residual strains
[28]
can be observed under shear loading [8,10,30]. Furthermore, it has been found that
fiber reinforced epoxy under transverse compression fails in an inclined plane due to
shear stresses and that shear bands form in these planes prior to cracking [3]. Therefore,
it is likely that the residual strains are a result of matrix plasticity. Irrespective
of the actual mechanisms behind the residual strains, it is clear that an approach
other than elastic/brittle damage mechanics is necessary to capture these strains in a
model.
In the present work, a ply-level plasticity model for plane stress states that is
able to capture the residual strains is presented. The plasticity model is combined
with a damage model for brittle matrix failure that has previously been proposed
by the authors [22, 24, 25]. Based on available experimental data, the combined
damage/plasticity model assumes that stiffness degradation due to damage is related
to the onset of matrix cracking at first ply failure (FPF). Consequently, damage
accumulation only occurs in plies embedded in a multi-axial laminate close to the
FPF load. The non-linearity of embedded plies prior to damage onset and all nonlinearity
in a single ply or UD laminate is due to plastic shear strains predicted by
the proposed plasticity model.
Note that the objective of the combined damage/plasticity model is to predict
residual strains and stiffness degradation. Hysteresis loops like the ones shown in
Fig. 5.1 during unloading and reloading, which could be the result of viscous effects,
are neglected in this study.