  An original thermodynamically consistent large strains-based multiphase
phase-field (PF) approach of Ginzburg-Landau type is developed for studying the
grain boundary (GB)-induced martensitic transformations (MTs) in
polycrystalline materials at the nanoscale considering the structural stresses
within the interfaces. In this general PF approach, N independent order
parameters are used for describing the austenite (A)<->martensite (M)
transformations and N(>1) martensitic variants, and another M independent order
parameters are considered for describing M(>1) grains in the polycrystalline
samples. The change in the GB energy due to its structural rearrangement during
MTs is considered using variable energy for the GB(s) as a function of the
order parameter related to the A<->M transformation. A rich plot for the
temperatures of transformations between the A, premartensite, and M in a
bicrystal with a symmetric planar tilt GB are plotted for the varying
austenitic GB width. The strong effects of the parameters, including the
austenitic GB width, change in GB energy due to MTs, GB misorientation, applied
strains, and sample size on heterogeneous nucleation of the phases and the
subsequent complex martensitic microstructures evolution are explored in
various bicrystals with symmetric or asymmetric planar or circular tilt GBs
during the forward and reverse transformations. The triple junction (TJ) energy
and the energy and width of the adjacent GBs are also shown to strongly
influence the nucleation and microstructures using the tricrystals having three
symmetric planar tilt GBs. The compatibility of the microstructures across the
GBs is studied. The elastic and structural stresses across the GBs and TJ
regions are plotted, which is essential for understanding the role of GBs and
TJs in materials failure.
