Analysis of soft impingement in nonisothermal precipitation
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e effects of soft impingement on precipitation are considered. A physically realistic analytical treatment of soft impingement has been developed for solid-state precipitation in a nonisothermal heating/cooling process following the basic assumptions (i.e., a two-stage transformation including site saturation of nucleation, isotropic growth and linear approximation for a concentration gradient in front of the precipitate/matrix interface). Furthermore, both one- and three-dimensional precipitations have been described using a compact expression which is analogous to Zener’s model but with a temperaturedependent growth coefficient. A detailed description for the model parameters has been given for the model application. Good agreement with published experimental data, for example, the decomposition of austenite in a 0.038–0.30wt%Mn plain carbon steel, has been achieved. I. INTRODUCTION
For most age-hardening metallic alloys (e.g., precipitation from supersaturated solid solution and crystallization of amorphous alloys), nonisothermal precipitation plays a key role. Actually, the nonisothermal characteristic can be either imposed by constraints on the process route or may be the optimal pathway to the desired properties.1 For a transformation consisting of nucleation and growth, generally two impingement modes may occur, that is, hard impingement considering only the geometric factor, and soft impingement involving a compositional change (or solute redistribution).2 When hard impingement prevails, an approach to treat diffusion-controlled growth under nonisothermal reactions was proposed based on the concept of classical Johnson–Mehl–Avrami (JMA) kinetics.3–9 To date, several works for modeling soft impingement in the nonisothermal case were carried out, for example, Cahn10 developed an approach that modeled nonisothermal transformations by application of the additivity rule. Sieurin and Sandstro¨m developed a quasi-stationary model,11 Wen and Simmon12 developed an explicit nucleation phase field method, and Kampmann and Wagner13 developed a mean field model. Most of the above models used for soft impingement in the nonisothermal precipitation are numerical. For example, Wen and Simmon12 explored the formation of bimodal distributions under continuous cooling conditions and simulated the realistic microstructure subjected to overlapping diffusion fields; Kampmann and Wagner13 accounted for the nonlinear contribution to the particlea)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0434
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J. Mater. Res., Vol. 24, No. 12, Dec 2009
size distribution and predicted the formation of g0 precipitation in Ni-based superalloys. However, a clear (physically realistic) relationship between the transformed fraction and the temperature upon nonisothermal precipitation could not be achieved using the above numerical models. The aim of this work is therefore to develop an analytical (soft impingement) model for nonisothermal precipitation and to show its application. Two difficultie
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