Multi-scale phase field approach to martensitic transformations

Because of its flexibility in treating complex geometries and topological changes, the phase field method has been used widely in modeling microstructural evolution during various phase transformations, grain growth and, most recently, plastic deformations. We review formulations and applications of the method in the context of martensitic transformations (MTs). Examples are chosen to illustrate the capabilities of the method at both mesoscopic and microscopic length scales. At the mesoscopic level we present simulation predictions on structural configurations of critical nuclei generated by homogeneous nucleation through Langevin thermal fluctuations under large undercooling, formation of herringbone structures by autocatalytic growth, and microstructural evolution and transformation hysteresis in a polycrystalline alloy under uniaxial stresses. At the microscopic level we discuss new developments in phase field model of dislocation dissociation and core structure and phase field model of mislocation—a new elementary defect introduced to describe the initiation and growth of martensite.