Analysis of anisotropy and plastic spin effects on localization phenomena
This paper presents a thorough investigation of the influence of anisotropy and plastic spin effects on the expressions of criteria for the formation of localized adiabatic shear bands. In order to fulfill this ambitious aim, a rather comprehensive theory of thermoplasticity is first set forth, including the influence of a set of internal variables and given in a covariant framework that allows for an invariant formulation of rate-type material evolution. The multiplicity of effects includes: plastic non-normality, plasticity-induced anisotropy (kinematic hardening), micro-damage mechanisms, thermomechanical couplings and, obviously, plastic spin. A particular constitutive law for the plastic spin is chosen after some discussion of the roles of various cooperative (synergetic) phenomena. As became standard, the necessary condition for the formation of localized plastic deformation is deduced from an acceleration-wave analysis (vanishing of the eigenvalues of instantaneous adiabatic acoustic tensor). More specific analytic forms of this criterion are obtained in two cases: the first case where plastic spin, spatial covariance, and kinematic hardenings are the most relevant effects viewed in an isothermal process developing in an undamaged solid; the second case where spatial covariance terms and plastic spin effects can be neglected in an adiabatic process in a damaged solid. The above-mentioned effects are examined with particular focus on synergetic (cooperative) ones. Both qualitative discussion and numerical estimation of the effects are given by way of conclusion. A rich bibliography completes the paper.
criteria for formation of localized adiabatic shear bands
scientific article; zbMATH DE number 1218490