Modelling microstructure evolution in engineering materials

In this paper we describe a general thermodynamically consistent variational principle for the rate of evolution of microstructure, which considers the competition between energy dissipation and the rate of change of Gibbs free energy of the system. We describe how numerical and approximate analytical procedures can be developed from the variational principle. Two examples are presented which demonstrate the utility of the approach: the kinetics of precipitate growth in an elastically strained body and the influence of an elastic strain on interdiffusion in a two-component system. Within these examples we pay particular attention to the effect of changes of elastic stored energy on the evolution process. The sensitivity of the morphology of growing phases to the ratio of the driving forces arising from elastic and chemical considerations is explored.