A Dislocation Pile-Up Computation for Adiabatic Shear Banding

Abstract

ABSTRACTA model is presented for computing the temperature increase associated with the formation of an adiabatic shear band. The hypothesis is that the heating is supplied by the difference in energy of a pile-up of n dislocations and the energy of n individual dislocations. The heating is assumed to occur within a volume determined by the grain size (i.e. slip band length) and an effective thermal length determined by the dislocation velocity. The model predicts increases in temperature with increasing shear modulus (G), increasing numbers of piled up dislocations (n), increasing Burgers vector (b), increased grain size (d), and increased dislocation velocity (vd). Increasing temperature is also predicted with decreasing heat capacity (c*) and thermal diffusivity (α) as would be expected. The model was applied to low carbon steel for which considerable data are available. Application to low carbon steel gives a temperature increase of about 1400K. The implied result that untempered martensite should be observed after adiabatic shear banding is in agreement with examples cited in the literature. Further investigation into the dynamics of pile-up release and the associated heat transfer mechanisms is discussed.