Time constant of logarithmic creep and relaxation

Abstract

Under certain conditions, the plastic extension of a sample subjected to a constant stress is to a good approximation proportional to the logarithm of the time. Similarly, if a sample is plastically strained and unloaded, there are changes in its length and hardness which vary logarithmically with time. For dimensional reasons, a logarithmic variation must involve a time constant tau characteristic of the process, so that the deformation is proportional to ln(t/tau). Two distinct mechanisms of logarithmic creep have been proposed, the work-hardening of a set of barriers to dislocation motion, all having the same activation energy, or the progressive exhaustion of the weaker barriers in a set which has a distribution of activation energies, these energies remain constant during the process of creep. It has been suggested that the experimentally observed value of tau can be used to decide which of the two mechanisms is operative. It is shown here that the work-hardening mechanism expresses tau in terms of parameters which are not easy to estimate, while, if the exhaustion mechanism operates, the observed value of tau is determined by the experimental conditions rather than by the parameters of the dislocation mechanism.