An Energy Criterion for the Onset of Shear Localization in Thermal Viscoplastic Materials, Part II: Applications and Implications

Necessary and/or sufficient conditions for the onset of shear flow localization in thermal viscoplastic materials were derived by Shawki (1994) through the analysis of a one-dimensional model of dynamic simple shear with velocity-controlled boundaries. In the former work, an energy-based viewpoint of localization allows for the association of the positive rate of change of the total kinetic energy of the absolute perturbations with the onset of shear strain localization. Here, we derive explicit conditions for the onset of shear localization without the need to obtain exact linear solutions. Explicit localization conditions are then applied to a number of empirical constitutive descriptions of material response. The effects of inertia, heat conduction, thermal softening, strain hardening, and strain rate sensitivity as regards the onset of shear localization are thoroughly discussed. Furthermore, the validity of conclusions based on a constant homogeneous solution is quantified together with the validity of conclusions based on a quasi-static approximation. Moreover, we examine the inadequacy of the notion of asymptotic stability for shear localization in the presence of heat conduction effects. A critical wavelength threshold is derived, for a general description of material response, below which perturbations will not grow. This threshold may also serve as a lower bound for shear band thickness.