The yield stress of materials exhibiting work‐hardening and thermal softening can reach a maximum, at which they are unstable to further strain. Deformation then localizes as shear bands. This critical strain has been calculated using parameters for the Steinberg‐Guinan strength model. A simple model to predict the onset of shear‐banding in the impact of flat‐ended rods on plates produces results consistent with known experiments in steel/Ti‐6Al‐4V, using the calculated critical strain. Conduction effects can modify the critical strain by reducing the rate of thermal softening, introducing a dependence on strain rate. The magnitude of the conduction effects caused by a microstructure of spherical grains in a matrix and by solitary inclusions is estimated. Comparison with experiments indicates that the rate‐dependence is consistent with conduction between the phases of the Ti‐6Al‐4V microstructure.