Institute of Fundamental Technological Research

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.

The main objective of the present paper is the discussion of the influence of the evolution of the substructure of single crystal on the shear band localization phenomena. A constitutive model of an inelastic crystal within the thermodynamic framework of the rate type covariance constitutive structure with internal state variables is developed. Thermomechanical couplings are considered and internal heating generated by the rate of internal dissipation is described. It has been proved that the description of a rate independent adiabatic single slip process in elasto-plastic single crystal is reduced to one fundamental evolution equation for the Kirchhoff stress tensor. Using the analysis of acceleration waves the necessary condition for a localized plastic deformation region to be formed is obtained. The criteria for adiabatic shear band localization are presented in an exact analytical form. Numerical estimations for the critical hardening modulus rate and the direction of the macroscopic shear band are given. The influence of various effects on shear band localization criteria is investigated. It has been found that the influence of the dislocation substructure is combined with the thermomechanical coupling and leads to distinct synergetic effect. The possibility of deviation from the Schmid rule of the critical resolved shear stress is also investigated. Comparison of the numerical results with available experimental data is presented.