Analysis of the influence of various effects on criteria for adiabatic shear band localization in single crystals

The paper aims at the investigation of the influence of various effects on criteria for shear band localization in inelastic single crystals. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. Particular attention is focussed on the analysis of the effects as follows: (i) spatial covariance and plastic spin; (ii) thermomechanical coupling; (iii) non-Schmid; (iv) evolution of substructure; (v) nondissipative thermal term; (vi) cooperative phenomena (synergetic). The theory of thermoviscoplasticity of inelastic single crystals is presented within a framework of the rate type covariance constitutive structure with a finite set of the internal state variables. By assuming that the mechanical relaxation time is equal to zero the thermo-elasto-plastic (rate independent) response of single crystals is accomplished. An adiabatic inelastic flow process of the single crystal is formulated and investigated. Symmetric double slip and single slip processes are considered. The formulation of macroscopic adiabatic shear bands is investigated. The criteria for adiabatic shear band localization for a single slip process are presented in exact analytical form. For a symmetric double slip process these criteria are estimated numerically. The discussion of the influence of various effects is presented, and the comparison of the results obtained with available experimental observations is given.