The Activation Volume for Shear

Becker (1925) and Mott and Nabarro (1948) gave different expressions for the dependence of activation energy on stress 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 non-linearity 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. We then consider the influence of the sharpness of the dependence of the strain rate on the applied stress. Following Clough and Simmons (1975), we observe that the activation volume under a general stress is a tensor, representing the volume integral of the strain, which occurs during the process of activation. 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 activation.