Thermal activation under shear

Becker in 1925 and Mott and Nabarro in 1948 gave different expressions for the stress dependence of activation energy for shear in the limit when the stress approaches that at which plastic deformation can occur without thermal activation. We show that, when allowance is made for the inevitable elastic nonlinearity in the activated state, Becker's model leads to the same dependence as that of Mott and Nabarro. This limiting expression is likely to be valid in many, but not all, processes of thermally activated plastic deformation. Following Clough and Simmons, we explore definitions of activation volumes under a general stress that are tensors and represent the volume integral of the strain which occurs during the process of activation. We then consider the influence of the sharpness of the dependence of the strain rate on the applied stress. Activation of plastic deformation at one site sheds loads on to other sites which may then activate athermally, producing a multiplication factor which is itself stress dependent and may diverge before the applied stress reaches that at which activation occurs without thermal assistance.