ON SHEAR-BAND NUCLEATION AND THE FINITE PROPAGATION SPEED OF THERMAL DISTURBANCES

This paper examines the onset of shear dow localization in thermal vis coplastic materials at high rates of loading while accounting for the finite speed of thermal wave propagation. It is well known that the Fo urier's classical law of heat conduction implies that thermal disturba nces travel with infinite speed. We introduce a modification to the cl assical Fourier law which renders a finite speed for thermal wave prop agation. We then utilize the energy viewpoint of dynamic localization introduced in Shawki (Shawki, T. G. (1994). An energy criterion for th e 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 o nset of shear localization in thermal viscoplastic materials, part II: Applications and implications. ASME J. Appl. Mech. 61, 538-547) as we ll as a linear stability analysis to determine the necessary condition s for the onset of localization. An exact linear solution is obtained for adiabatic deformations of thermal viscoplastic materials with no s train dependence. A matched asymptotic expansion is obtained for the g eneral case involving non-adiabatic deformations of the foregoing clas s of materials. The foregoing solutions illustrate the effect of finit e speed of thermal wave propagation on localization initiation.