Phase-field modeling of diffusion controlled phase transformations
Abstract: Diffusion controlled phase transformations are studied bymeans of the phase-field method. Morphological evolution ofdendrites, grains and Widmanst\"atten plates is modeled andsimulated.Growth of dendrites into highly supersaturated liquids ismodeled for binary alloy solidification. Phase-field equationsthat involve both temperature and solute redistribution areformulated. It is demonstrated that while at low undercoolingheat diffusion does not affect the growth of dendrites, i.e.solidification is nearly isothermal, at high cooling rates thesupersaturation is replaced by the thermal undercooling as thedriving force for growth.In experiments many crystals with different orientationsnucleate. The growth of randomly oriented dendrites, theirsubsequent impingement ant formation of grain boundaries arestudied in two dimensions using the FEM on adaptive grids.The structure of dendrites is determined by growthconditions and physical parameters of the solidifying material.Effects of the undercooling and anisotropic surface energy onthe crystal morphology are investigated. Transition betweenseaweeds, doublons and dendrites solidifying out of puresubstance is studied and compared to experimental data. Two-and three-dimensional simulations are performed in parallel onadaptive and uniform meshes.A phase-field method based on the Gibbs energy functional isformulated for ferrite to austenite phase transformation inFe-C. In combination with the solute drag model, transitionbetween diffusion controlled and massive transformations as afunction of C concentration and temperature is established byperforming a large number of one dimensional calculations withreal physical parameters. In two dimensions, growth ofWidmanstaetten plates is governed by the highly anisotropicsurface energy. It is found that the plate tip can beapproximated as sharp, in agreement with experiments.Keywords:heat and solute diffusion, solidification,solid-solid phase transformation, microstructure, crystalgrowth, dendrite, grain boundary, Widmanstaetten plate,phase-field, adaptive mesh generation, FEM.
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