On the relative accuracy of power law analyses for uniaxial low stress steady state high homologous temperature deformation

Abstract

If the mathematical operations are correct, uniaxial low stress, steady state high homologous temperature creep and steady state structural Superplasticity phenomena can be well described by a ‘power law’ that relates the applied stress to the strain rate of deformation (Padmanabhan et al., 2015). Isothermal dislocation creep, which exhibits no grain size dependence, displays a linear log strain rate – log stress relationship till there is a change in the rate controlling mechanism. In contrast, during grain-size dependent, isothermal steady state structural superplastic flow, even within narrow strain rate ranges the slope changes, notwithstanding the presence of the same rate controlling mechanism. In both the phenomena the stress exponent, n, decreases with increasing temperature even for a constant rate controlling mechanism (Padmanabhan, 1973). Four analytical methods, differing in details, are based on the power law equation, viz., a procedure used by experimental scientists, its improved variant, a method in vogue in rheology and a procedure due to Padmanabhan et al., 2015. By examining experimental data pertaining to many systems, it is demonstrated that the method of rheology does not follow the tenets of Dimensional Analysis and that the scatter in the predictions is the maximum for this case. The method of experimental scientists ignores the temperature dependence of the stress exponent and this leads to significant discrepancies between the measured and predicted properties. When mathematics is correct and the relevant physical situation is taken into account, the other two methods, i.e. the improved method of the experimental scientists and that of Padmanabhan et al., 2015, lead to similar results, but the latter analysis is more accurate because of its better normalizing procedure. It is also simpler. A missing detail in the earlier paper (Padmanabhan et al., 2015), viz., estimation of the grain-size exponent of the strain rate predicted for isothermal, steady state structural superplastic flow in terms of the Buckingham Pi Theorem is also furnished here.