Derivation of Polycrystal Creep Properties From the Creep Data of Single Crystals

Abstract

A method developed for calculating the polycrystal stress-strain-time relation from the creep data of single crystals is shown. Slip is considered to be the sole source of creep deformation. This method satisfies, throughout the aggregate, both the condition of equilibrium and that of continuity of displacement as well as the creep characteristics of single crystals. A very large three-dimensional region is assumed to be filled with innumerable identical cubic blocks, each of which consists of 64 cube-shaped crystals of different orientations. This region is assumed to be embedded in an infinite elastic isotropic medium. This infinite medium is subject to a uniform loading. The average stress and strain of a cubic block at the center of the region is taken to represent the macroscopic stress and strain of the polycrystal. This method is self-consistent and considers the heterogeneous interaction effect of the creep deformation of all slid crystals. The macroscopic stress-strain-time relations of the polycrystal were calculated for three tensile loadings, one radial loading, and two nonradial loadings of combined tension and torsion. The numerical results given by the present theory agree well with those predicted by the so-called “Mechanical Equation of State.” The creep strain components calculated by the present theory for the case of a constant tensile loading followed by an additional constant tensile loading are found to be considerably higher than those predicted by von Mises and Tresca’s theories. These results agree well qualitatively with experimental results.