A statistical theory of creep in polycrystalline materials

Abstract

Estimates for the properties of creeping polycrystals, which exhibit a power-law dependence of the stress on the strain-rate, are derived in the framework of statistical continuum theory. A creep modulus is obtained which incorporates n-point statistics for the spatial coherence of lattice orientation. For uniform boundary conditions and statistically homogeneous microstructures the modulus is shown to have local character. A hierarchy of mean field approximations enables estimates for the evolution of n-point statistical measures of the microstructure. Numerical implementation of the theory for isotropic face-centered-cubic polycrystals, incorporating two-point statistics of lattice orientation, results in substantial softening of the tensile reference stress relative to the Taylor-like uniform strain-rate upper-bound and the self-consistent estimate. Comparisons of the initial flow for the tensile axis show that estimates incorporating two-point statistics reduce the rate of rotation of the tensile axis over a significant area-fraction of the stereographic projection.