Phase field study of precipitate rafting under a uniaxial stress M P Gururajan and T A Abinandanan Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012 INDIA Abstract We examine rafting of two-phase microstructures under a uniaxial applied stress, a process in which a mismatch in elastic moduli (elastic inhomogeneity) plays a central role. For this purpose, we have used a phase field model of an elastically inhomogeneous alloy; elastic stress and strain fields are calculated using a method adapted from the homogenization literature. We have characterized the efficiency of the resulting iterative algorithm based on Fourier transforms. Our simulations of rafting in two-dimensional systems show that rafting (unidirectionally elongated microstructures) is promoted when the precipitate phase is softer than the matrix and when the applied stress has the same sign as the eigenstrain. They also show that migration (for both hard and soft precipitates) and coalescence (for soft precipitates) have significant contributions to rafting. Key words: phase field modelling, microstructure, homogenisation, rafting, elastic stress effects 1 Introduction Elastic stresses arise during solid state phase transformations due to a lattice parameter mismatch between the participating phases. In addition, there may also be externally applied stresses. These stresses have a marked influence on the evolution of microstructures [1–4]. While some of these stress effects may be explained or rationalised by assuming that the phases have the same elastic moduli, other effects arise primarily due to a mismatch in elastic moduli (elastic inhomogeneity) of the phases. Examples of the latter include rafting in Ni-base superalloys [5], phase inversion [6], and instabilities in thin solid films [7]. This paper is on rafting; preliminary results for phase inversion and thin film instabilities were presented in [8]. Preprint submitted to Elsevier Science 21 March 2007