THEORY OF COBLE CREEP FOR IRREGULAR GRAIN STRUCTURES

Coble creep occurs by the diffusion of matter along grain boundaries. Under the action of an externally applied stress, matter diffuses from grain boundaries in compression to those in tension. Individual grains elongate and macroscopic creep ensues. To date, Coble creep has been derived only for simple periodic grain structures. In this work we show how to solve the Coble creep problem for irregular, two-dimensional grain structures consisting of straight grain boundary segments connected by triple points. Since the normal stress distributions at the grain boundaries are represented by cubic polynomials, 4n(gb) constants have to be determined for a two-dimensional grain structure consisting of n(gb) grain boundary segments. We show how the corresponding system of 4n(gb) equations can be set up for freely chosen boundary conditions at the grain boundary-surface intersections. Several calculated examples with clusters consisting of 25 grains illustrate the power of the technique.