On shear band nucleation and the finite propagation speed of thermal disturbances

Abstract

This paper examines the onset of shear flow localization in thermal viscoplastic materials at high rates of loading while accounting for the finite speed of thermal wave propagation. It is well known that the Fourier's classical law of heat conduction implies that thermal disturbances travel with infinite speed. We introduce a modification to the classical Fourier law which renders a finite speed for thermal wave propagation. We then utilize the energy viewpoint of dynamic localization introduced in Shawki (Shawki, T. G. (1994). An energy criterion for the onset of shear localization in thermal viscoplastic materials, part I: Necessary and sufficient initiation conditions. ASME J. Appl. Mech.61, 530–537) and (Shawki, T. G. (1994). An energy criterion for the onset of shear localization in thermal viscoplastic materials, part II: Applications and implications. ASME J. Appl. Mech.61, 538–547) as well as a linear stability analysis to determine the necessary conditions for the onset of localization. An exact linear solution is obtained for adiabatic deformations of thermal viscoplastic materials with no strain dependence. A matched asymptotic expansion is obtained for the general case involving non-adiabatic deformations of the foregoing class of materials. The foregoing solutions illustrate the effect of finite speed of thermal wave propagation on localization initiation.