Simulation of phase‐transformations based on numerical minimization of intersecting Gibbs energy potentials

We present a novel approach for the simulation of solid to solid phase‐transformations in polycrystalline materials. To facilitate the utilization of a non‐affine micro‐sphere formulation with volumetric‐deviatoric split, we introduce Helmholtz free energy functions depending on volumetric and deviatoric strain measures for the underlying scalar‐valued phase‐transformation model. As an extension of affine micro‐sphere models [5], the non‐affine micro‐sphere formulation with volumetric‐deviatoric split allows to capture different Young's moduli and Poisson's ratios on the macro‐scale [1]. As a consequence, the temperature‐dependent free energy assigned to each individual phase takes the form of an elliptic paraboloid in volumetric‐deviatoric strain space, where the energy landscape of the overall material is obtained from the contributions of the individual constituents. For the evolution of volume fractions, we use an approach based on statistical physics–taking into account actual Gibbs energy barriers and transformation probabilities [2]. The computation of individual energy barriers between the phases considered is enabled by numerical minimization of parametric intersection curves of elliptic Gibbs energy paraboloids. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)