Numerical simulation of the large elastic–plastic deformation behavior of hydrostatic stress-sensitive solids

Abstract

The present paper deals with the numerical simulation of the large elastic–plastic deformation and localization behavior of metals which are plastically dilatant and sensitive to hydrostatic stresses. The model is based on a generalized macroscopic theory taking into account macroscopic as well as microscopic experimental data obtained from tests with iron based metals. It shows that hydrostatic components may have a significant effect on the onset of localization and the associated deformation modes, and that they generally lead to a notable decrease in ductility. The continuum formulation relies on the mixed-variant metric transformation tensor which leads to the definition of an appropriate logarithmic strain measure. Its rate is additively decomposed into elastic and plastic as well as isochoric and volumetric strain rate tensors. Particular attention is focused on the formulation of a generalized I1–J2 yield criterion to describe the effect of the hydrostatic stress on the plastic flow properties in metals. In contrast to classical theories of metal plasticity, the evolution of the plastic part of the strain rate tensor is determined by a non-associated flow rule based on a plastic potential function which is expressed in terms of stress invariants and kinematic parameters. Numerical analyses of the elastic–plastic deformation and localization behavior of hydrostatic stress-sensitive metals will demonstrate the influence of the constitutive description on critical strains as well as on localization behavior.