A model for creep based on microstructural length scale evolution

This paper seeks to quantitatively link recovery and plastic deformation to develop a model for creep. A simple approach with one length scale coarsening equation is postulated in this paper to provide a descriptive and unified framework to understand recovery. We propose that recovery is a general dislocation-level coarsening process whereby the length scale,;, is refined by dislocation generation by plastic deformation and is increased concurrently by coarsening processes. Coarsening relations generally take the form: d(lambda(Mc)) = KR(T)dt where R(T) is the rate equation for the fundamental rate controlling step in coarsening, K a free constant, dt a time increment and m(c) is the coarsening exponent. Arguments are presented that m(c) should be in the range of 3-4 for dislocation or subgrain coarsening. The coarsening equation postulated is consistent with the compared data sets in the following ways: (i) temporal evolution of one length scale lambda; (ii) temperature dependence of recovery rate; (iii) adequacy of single parameter in the proper description of strength change. The coarsening equation is coupled with standard arguments for modeling plastic deformation. Combining these we can easily justify the form of the empirically derived Dorn creep equation: (gamma)/(D(T)) = B((tau)/(mu))(n) where the mobility of the recovering feature, R(T) should typically scale with self diffusivity, D(7), and the value of the steady-state creep exponent, n is 2 + m(c) - 2c where c is a constant related to dislocation generation that should be in the range of 0-0.5. Hence, this approach predicts creep as being controlled by self diffusion and that the steady-state stress exponent should be on the order of 4-6. All the parameters in the creep model can be estimated from non-creep data. Comparison with the reported steady-state creep data of pure metals shows good agreement suggesting recovery modeled as coarsening is a fundamental element in steady-state creep. (C) 2004 Elsevier B.V. All rights reserved.