Analysis of the influence of the substructure of a crystal on shear band localization phenomena of plastic deformation

摘要

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.