Crystal level continuum modelling of phase transformations: the α ↔ ϵ transformation in iron

We present a crystal level model for thermo-mechanical deformation with phase transformation capabilities. The model is formulated to allow for large pressures (on the order of the elastic moduli) and makes use of a multiplicative decomposition of the deformation gradient. Elastic and thermal lattice distortions are combined into a single lattice stretch to allow the model to be used in conjunction with general equation of state relationships. Phase transformations change the mass fractions of the material constituents. The driving force for phase transformations includes terms arising from mechanical work, the temperature dependent chemical free energy change on transformation, and the interaction energy among the constituents. Deformation results from both these phase transformations and elasto-viscoplastic deformation of the constituents themselves. Simulation results are given for the α to phase transformation in iron. Results include simulations of shock-induced transformation in single crystals and of compression of polycrystals. Results are compared with available experimental data.

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