Micromechanical modelling of creep using distributed parameters

Abstract

Microstructural parameters such as diffusion coefficients and grain size usually have distributed values in a polycrystal. However, micromechanical constitutive equations for power-law creep and diffusional creep assume that these parameters are uniform. In this paper it is shown that the use of distributed parameters can lead to a transition from power-law creep to diffusional creep which is spread over several orders of magnitude in strain rate. It also leads to the generation of internal stress and anelasticity. Two specific cases, a bimodal distribution of grain size and a two phase structure, are analysed in detail. A graphical analytical technique which is developed can be extended to other distribution functions; but even the simple bimodal structures are relevant to engineering materials such as austenitic stainless steels and α-β titanium alloys. This paper primarily concerns steady state creep and includes a brief discussion on the transient problem. Further developments will be given in a subsequent paper.