We simulate the diffusional evolution of microstructures produced by solid state diffusional transformations in elastically stressed binary alloys in two dimensions. The microstructure consists of arbitrarily shaped precipitates embedded coherently in an infinite matrix. The precipitate and matrix are taken to be elastically isotropic, although they may havedifferentelastic constants (elastically inhomogeneous). Both far-field applied strains and mismatch strains between the phases are considered. The diffusion and elastic fields are calculated using the boundary integral method, together with a small scale preconditioner to remove ill-conditioning. The precipitate-matrix interfaces are tracked using a nonstiff time updating method. The numerical method is spectrally accurate and efficient. Simulations of a single precipitate indicate that precipitate shapes depend strongly on the mass flux into the system as well as on the elastic fields. Growing shapes (positive mass flux) are dendritic while equilibrium shapes (zero mass flux) are squarish. Simulations of multiparticle systems show complicated interactions between precipitate morphology and the overall development of microstructure (i.e., precipitate alignment, translation, merging, and coarsening). In both single and multiple particle simulations, the details of the microstructural evolution depend strongly on the elastic inhomogeneity, misfit strain, and applied fields.
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It is a pleasure to thank L. Greengard, R. James, R. Kohn, D. Meiron, M. Shelley, T. Shield, and P. Voorhees for interesting discussions. We also thank P. Voorhees for sending us his anisotropic, homogeneous elasticity solver. This work was supported in part by the Minnesota Supercomputer Institute, the McKnight Foundation (J.S.L.), the National Science Foundation through Grants CMS-9503393 (P.H.L.) and DMS-940004310 (J.S.L.). A large part of this work is contained in the Ph.D. thesis of H.-J. Jou in the department of Aerospace Engineering and Mechanics at the University of Minnesota.