Microstructure evolution in three-dimensional inhomogeneous elastic media
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23/6/03
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Microstructure Evolution in Three-Dimensional Inhomogeneous Elastic Media XIAOFAN LI, JOHN LOWENGRUB, QING NIE, VITTORIO CRISTINI, and PERRY LEO A new, three-dimensional boundary integral method is used to study the evolution of an isolated precipitate growing by diffusion in an infinite, elastic matrix. An adaptive surface mesh[23] is used to accurately and efficiently discretize the precipitate boundaries in three dimensions. The model accounts for diffusion, surface energy, interface kinetics and elastic energy, which are coupled through a modified Gibbs–Thomson boundary condition at the precipitate-matrix interface. The precipitate and matrix phases are taken to have different elastic-stiffness tensors, and there is a mismatch strain between the phases. Both isotropic and anisotropic elasticity are investigated. In this article, the coarsening and growth of a single precipitate are simulated under various conditions. For isotropic elasticity, coarsened shapes are found to be consistent with the equilibrium-shape analysis of Johnson and Cahn.[29] Growth shapes are found to become rapidly nonlinear and to develop regions of high curvature. In elastically anisotropic systems, coarsened shapes are found to be consistent with the equilibrium-shape calculations of Mueller and Gross.[7,8] Simulations of coarsening in which the cubic axes of the precipitate are different from those of the matrix suggest that there may be more than one local minima in the energy, so that the observed shapes depend on the growth path. Finally, nonconvex precipitate morphologies are seen for the growth of soft Ni3Al precipitates in a Ni matrix, consistent with experimental observations. In the case of a hard Ni3Si precipitate grown under the same conditions, we find self-similar growth of a convex shape.
I. INTRODUCTION
THE macroscopic properties of multiphase materials depend on their microstructure. In many metal alloys, this microstructure consists of individual precipitates embedded coherently in a continuous matrix phase. Such microstructures can result from a diffusional phase transformation in which a thermodynamically stable phase is driven from equilibrium by a sudden lowering of temperature. It is now established that microstructure evolution during phase transformations is influenced by the elastic fields generated by the transformation. There has been long-standing interest in simulating the diffusional evolution of these microstructures, with the ultimate aim of controlling them to achieve desired alloy properties. Much of the numerical work in simulating phase transformations has been restricted to two-dimensional domains. However, there has been an increasing body of work performed in three dimensions. Simulations in three dimensions of phase transformations have been primarily based on either diffuse-interface methods (e.g., References 1 through 3) or the discrete-atom method.[4,5] In these methods, microstructure evolution is mimicked through the evolution of a XIAOFAN LI is with the Depart
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