Effect of constitutive equations on qualitative behavior of solutions in the vicinity of bi-material interfaces at large plastic strains

Abstract

The main objective of the present paper is to compare, by means of a problem permitting a closed-form solution, qualitative behavior of solutions based on three models of strain hardening plasticity and two models of viscoplasticity. The elastic portion of the strain tensor is neglected. The study focuses on the solution behavior near frictional interfaces. The solution behavior essentially depends on the model chosen. Such features of the solutions as nonexistence and singularity are emphasized. The key constitutive parameter that divides all the models considered into two groups is the saturation stress. In particular, under certain conditions no solution satisfying the regime of sticking exists for the models that involve the saturation stress. Qualitative comparison with numerous experimental observations is made. It is concluded that models with a saturation stress, including the models considered in the present paper, may be capable of describing the generation of a narrow layer of severe plastic deformation in the vicinity of frictional interfaces.