Effect of nonlinear and noncollinear transformation strain pathways in phase-field modeling of nucleation and growth during martensite transformation

The phase-field microelasticity theory has exhibited great capacities in studying elasticity and its effects on microstructure evolution due to various structural and chemical non-uniformities (impurities and defects) in solids. However, the usually adopted linear and/or collinear coupling between eigen transformation strain tensors and order parameters in phase-field microelasticity have excluded many nonlinear transformation pathways that have been revealed in many atomistic calculations. Here we extend phase-field microelasticity by adopting general nonlinear and noncollinear eigen transformation strain paths, which allows for the incorporation of complex transformation pathways and provides a multiscale modeling scheme linking atomistic mechanisms with overall kinetics to better describe solid-state phase transformations. Our case study on a generic cubic to tetragonal martensitic transformation shows that nonlinear transformation pathways can significantly alter the nucleation and growth rates, as well as the configuration and activation energy of the critical nuclei. It is also found that for a pure-shear martensitic transformation, depending on the actual transformation pathway, the nuclei and austenite/martensite interfaces can have nonzero far-field hydrostatic stress and may thus interact with other crystalline defects such as point defects and/or background tension/compression field in a more profound way than what is expected from a linear transformation pathway. Further significance is discussed on the implication of vacancy clustering at austenite/martensite interfaces and segregation at coherent precipitate/matrix interfaces. A method for modeling complex changes in the crystal structures of solids is developed by researchers in the USA. Yunzhi Wang from the Ohio State University and his colleagues’ model provides a more accurate description of crystal structure rearrangement during a phase change known as martensitic transformation. Even though this structural evolution has be modeled successfully using the phase-field microelasticity theory, the existing models do not incorporate some the more complex nonlinear transformation pathways that have been seen when using atomistic simulations. Wang and co-workers now extended phase-field microelasticity theory to include these complex pathways. They show that configuration and activation energies of a critical nucleus of the martensitic phase differ significantly when such nonlinear coupling is considered. This model has applications to understanding structural transformations in metals and ceramics.