Inverse Problems in Stochastic Modeling of Mixed-Mode Power-Law and Diffusional Creep for Distributed Grain Size

Abstract

We seek to develop analytical methods through which the high-temperature deformation behavior of polycrystals can be explained in terms of the statistical distribution of the grain size. Changes in the stress exponent and grain size exponent with the strain rate are related to mixed-mode deformation in which the large grains deform by power-law creep and the small grains by diffusional creep. Two results are obtained. The first is an expression (Eq. [13]) that relates the experimental values of the power-law exponent and the grain size exponent to the values predicted from the classical models for uniform grain size. This equation is independent of the standard deviation of the grain size distribution, the average grain size, and the temperature. In a second result, it is shown that measurements of the change in the stress exponent with the strain rate can be analyzed to estimate the standard deviation and the median value of the grain size. The possible significance of these results is tested against experiments on the superplastic deformation of aluminum, drawn from the literature.