Grain boundary- and triple junction-induced martensitic transformations: A phase-field study of effects of grain boundary width and energy

Abstract

An original thermodynamically consistent large strains-based general multiphase phase-field (PF) approach of Ginzburg–Landau type is developed for studying the grain boundary (GB)- and triple junction (TJ)-induced martensitic transformations (MTs) in polycrystalline materials at the nanoscale considering the structural stresses within the interfaces. In this general PF approach, N+1 order parameters are used for describing the austenite (A)↔martensite (M) transformations and N(>1) martensitic variants and other M order parameters are used to describe M(>1) grains in the polycrystalline samples. Neglecting the kinetics of the GBs and TJs and assuming a uniform temperature of the sample, the system of coupled mechanics and Ginzburg–Landau equations for the order parameters related to MTs is derived. Distinct energies for the GBs in austenitic and martensitic phases due to their structural rearrangement are considered by using variable energy for the GB regions as a function of the order parameter related to the A↔M transformation and misorientations. The strong effects of the austenitic GB width (size-effect), the difference of GB energies of two phases, and applied strains on heterogeneous nucleation of the phases and their subsequent growth are explored in bicrystals with a symmetric planar tilt GB during the forward and reverse transformations. A rich plot for the temperatures of transformations between A, premartensite (the intermediate states between A and M), and M in a bicrystal is plotted for varying austenitic GB width exhibiting a strong GB size effect. The TJ energy and the energy and width of the adjacent GBs are also shown to significantly influence the nucleation and microstructures using the tricrystals having three symmetric planar tilt GBs meeting at 120° dihedral angles. The elastic and structural stresses across the interfaces are plotted, which is essential for understanding the role of GBs and TJs in material failure. The plausible reasons for the nonintuitive behaviour of the GBs on martensite nucleation observed in experiments and atomistic studies are explained.