Phase Transformation of Ni-Ti Shape Memory Alloy Investigated by Multi-Phase-Field Method and Microscopic Data

Multi-phase-field (MPF) method which is capable of using several phase-field variables is applied to simulate martensitic transition in micro-scale Ni-Ti shape-memory alloy (SMA). By modeling Ni-Ti SMA specimen in MPF simulation assuming only three major variants of martensite crystal in monoclinic structure, the detailed manner of forming martensite variants and interaction between them are observed. We adjust several free energy (densities) usually used for the phase-field functional to Ni-Ti SMA properties, e.g. chemical free energy, elastic strain energy, gradient energy, and double-well potential energy. Especially in the formulation of elastic strain energy, to express austenite (cubic)-to-martensite (monoclinic) transition of Ni-Ti alloy, microscopic parameter available from experimental result for lattice mismatch between austenite and martensite is brought into free energy functional. We discuss the different growth of martensite variants depending on initial condition for martensite nucleus, in which some arbitrary area in the computation domain is provided with random number. It is confirmed that a martensite variant with a positive lattice mismatch (i.e. the direction of larger edge in monoclinic unit) grows preferentially in the case of tensile loading in that direction. In compression, a variant with the most negative mismatch in the compressive direction grows strongly. The starting time of loading is sometimes a factor for the resulted variant structures. We found that, once a lamellae structure is formed, the relation between direction of further loading and that of lamellae interface plane dominates the resulted structural combination of variants.