Kinetic Monte Carlo Modeling of Martensitic Phase Transformation Dynamics
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Martensitic transformation is, on the one hand, a pervasive deformation mechanism in both structural and functional materials, and on the other hand, a first-order phase transition that is diffusionless. The transformation from one crystal structure to another takes place by a volumetric change and a large shear. As a result, modeling of the martensitic transformation process requires an integration of thermodynamic, kinetic, and mechanical considerations. Moreover, the transformation process is intrinsically stochastic. Not only is there a competition between nucleation and propagation modes, but there are also competitions among different ways of transformation and different regions for transformation. In this chapter, an integrated thermodynamic and Kinetic Monte Carlo (KMC) treatment of martensitic transformation is presented. Modeling martensitic transformation as a unit process, the free energy function for potential transformation of each unit is determined. Stress and strain distributions are predicted by the Finite Element method after each unit transformation and are incorporated in the free energy function. A KMC algorithm that incorporates the free energy function in the rate formula is invoked to select a unit to transform and advance the time. The modeling formulation is described in detail, so is the simulation algorithm. Examples of transformation dynamics modeled by this method will be shown.
Y. Chen acknowledges the support from the US National Science Foundation with award number DMR-1352524.
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