Chapter 6 - Damage and plasticity in metals

Abstract

This chapter discusses the development of a constitutive model for anisotropic continuum damage mechanics using finite strain plasticity. The formulation is given in spatial coordinates, and incorporates both isotropic and kinematic hardening. The von Mises yield criterion is modified to include the effects of damage through the use of the hypothesis of elastic energy equivalence. A modified elasto-plastic stiffness tensor that includes the effects of damage is derived within the framework of the proposed model. This chapter explains how the model can be used in conjunction with other damage-related yield functions. In particular, Gurson's yield function is incorporated in the theory proposed in the chapter. This yield function is derived based on the presence of spherical voids in the material. Numerical implementation of the proposed model includes the finite element formulation where an updated Lagrangian description is used. The problem of crack initiation is solved for a thin elasto-plastic plate with a center crack that is subjected to inplane tension.