Modeling the Diffusion-Controlled Growth of Needle andplate-Shapedprecipitates
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Modeling the Diffusion-Controlled Growth of Needle and Plate-Shaped Precipitates Z. Guo and W. Sha, Metals Research Group, School of Civil Engineering, Queen’s University of Belfast, UK ABSTRACT Various theories have been developed to describe the diffusion-controlled growth of precipitates with shapes approximating needles or plates. The most comprehensive one is due to Ivantsov, Horvay and Cahn, and Trivedi (HIT theory), where all the factors that may influence the precipitate growth, i.e. diffusion, interface kinetics and capillarity, are accounted for within one equation. However, HIT theory was developed based on assumptions that transformation strain/stress and interfacial free energy are isotropic, which are not true in most of the real systems. An improved growth theory of precipitates of needle and plate shapes was developed in the present study. A new concept, the compression ratio, was introduced to account for influences from the anisotropy of transformation strain/stress and interfacial free energy on the precipitate morphology. Experimental evidence supports such compression effect. Precipitate growth kinetics were quantified using this concept. The improved HIT theory (IHIT theory) was then applied to study the growth of Widmanstatten austenite in ferrite in Fe-C-Mn steels. The calculated results agree well with the experimental observations. INTRODUCTION Various theories have been developed to describe the diffusion-controlled growth of precipitates with shapes approximating needles or plates [1], among which the most comprehensive one is due to Trivedi [2-4], based on work by Ivantsov [5,6] and Horvay and Cahn [7] (in this paper referred to as HIT theory). In this theory, the needle is assumed to be in the form of a paraboloid of revolution and the plate a parabolic cylinder, figure 1. The solutions obtained for specified conditions are shape-preserving when the tip radius ρ is several times the critical radius value ρc and in this context they allow rigorously for changes in capillarity and interface kinetics as the curvature of the interface varies along the parabolic surfaces. However, HIT theory was developed based on many assumptions [2,3]. For modelling the growth of precipitate needles or plates by diffusion of solute in solid-solid phase transformations, HIT theory assumes the transformation strain/stress, interfacial free energy, and interfacial kinetic coefficient to be independent of crystallographic orientation, i.e. they are assumed to be isotropic. Unfortunately, such assumptions are generally unjustified for the precipitation process in steels, although in most solid-solid phase transformations the interface kinetics effect can be safely neglected [8]. Interfacial free energy reflects the degree of mismatch between precipitates and parent phase, which is usually anisotropic, and so is the transformation strain/stress. Recent improvement was made to account for the influence from the anisotropy of the transformation strain/stress and interfacial free energy on the precipitate morpholog
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