Damage model for anisotropic materials, and its application to analysis of stability and spallation

We use Bai's conservation equation for cracks, and Rice and Tracey's equation for the growth of a spherical void in an infinite medium to derive an evolution equation for damage in an anisotropic material. It is then used to delineate the instability strain in a thin anisotropic sheet deformed in a plane stress state of deformation, and obeying Hill's yield criterion. Assuming that strain- and strain-hardening, and thermal and damage softening of the material can be characterized by a relation similar to that proposed by Batra, the effect of various material parameters, and the anisotropy of the sheet on the instability strain has been quantified. It is found that only strain hardening and thermal softening exponents strongly influence the instability strain. The spallation strength, time to spallation, and the fragment size are also discussed.