AN ENERGY CRITERION FOR THE ONSET OF SHEAR LOCALIZATION IN THERMAL VISCOPLASTIC MATERIALS .2. APPLICATIONS AND IMPLICATIONS

Necessary and/or sufficient conditions for the onset of shear flow loc alization in thermal viscoplastic materials were derived by Shawki (19 94) through the analysis of one-dimensional model of dynamic simple sh ear with velocity-controlled boundaries. rn the former work, an energy -based viewpoint of localization allows for the association of the pos itive rare of change of the total kinetic energy of the absolute pertu rbations with the onset of shear strain localization. Here, we derive explicit conditions for the onset of shear localization without the ne ed 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 s oftening, strain hardening, and strain rare sensitivity as regards the onset of shear localization are thoroughly discussed. Furthermore, th e 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 notio n of asymptotic stability for shear localization in the presence of he ar 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 she ar band thickness.