Effect of uniaxial stress on coarsening of precipitate clusters
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INTRODUCTION
COARSENING, the growth of larger particles at the expense of smaller particles during the late stage of diffusional phase transformations, is well understood in stressfree materials and adequately described by the LSW theory[~,2~ and its modifications for higher volume fractions. [3-71 The LSW theory predicts the microstructure to remain self-similar and its average size scale to increase as the cube root of time. The modified theories extend its scope from the limit of zero volume fraction to finite volume fractions and find that the self-similarity and the exponent of the growth rate are maintained. They also find the rate constant to increase and the particle size distribution to broaden as the volume fraction increases. These theodes assume the reduction of interfacial surface and the energy associated with it to be the only driving force for the coarsening process. This in no longer the case when elastic stresses, due either to misfit strains or externally applied fields, are present in the coarsening system and result in a multitude of new phenomena observed in these systems. Examples are particle shape changes, particle splitting, inverse coarsening, the development of strong spatial correlations, and the deceleration of particle coarsening with increasing average particle volume, tS-l~] Stress effects are especially important in materials used in high-temperature structural applications, where the microstructure has to resist coarsening in the presence of service stresses. Nickel-based superalloys are, in particular, good examples for such alloys. The microstructures consist of highly correlated dispersions of Ni3AI(3") precipitates, aligned along the elastically soft (100) directions, in a nickel-rich matrix phase. The highly correlated microstructure and its ability to resist coarsening have been attributed in part to the misfit strain of the 3" precipitates. Recent theoretical investigations and computer simula-
WERNER HORT, Graduate Student, and WILLIAM C. JOHNSON, Professor, are with the Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903-2442. This article is based on representation made during TMS/ASM Materials Week in the symposium entitled "Atomistic Mechanisms of Nucleation and Growth in Solids," organized in honor of H.I. Aaronson's 70th Anniversary and given October 3-5, 1994, in Rosemont, Illinois. METALLURGICALAND MATERIALSTRANSACTIONS A
tions have studied the effect of misfit strain on microstructural evolution in two-phase alloys512-2~ However, theoretical studies investigating the influence of applied loads are either two-dimensional (2-D) Monte-Carlo simulations[21]or have been restricted to either the equilibrium shape of a single precipitate or the interaction of two precipitates, t1~ Since applied stresses might be used during processing to achieve certain microstructural features and are crucial for microstructural changes during high-temperature applications, a better understanding of the inter-relationship between mis
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