Multigrain phase-field simulation in ferroelectrics with phase coexistences: An improved phase-field model

Grain boundary-induced martensitic transformations: A phase-field study of nucleation, size-effect, triple junction-effect, microstructures, and compatibility at the nanoscale

“…The small strains-based multiphase phase-field approaches have been developed to study MTs in polycrystalline materials in [97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115]. The only PF model used for polycrystalline samples by Malik et al [116,117] considers a geometric nonlinear total strain, which was additively decomposed into inelastic and elastic parts.…”

“…8.2 of [118] and the references therein). Both concentration based [97][98][99][100][101][102][103][104][105][106][108][109][110][111][112][113][114][115] and transformation strains [98,102,103,111] based order parameters have been used for describing the A and the N variants M 1 M 2 , . .…”

“…However, the remaining papers for polycrystals cited here did not introduce any order parameter for describing the grains. A single constraint, which is the summation of all the order parameters (volume fraction) is equal to the unity, was used in [97,104,105].…”

“…It is to be mentioned that none of the existing papers on MTs in polycrystalline solids [15,81,[97][98][99][100][101][102][103][104][105][106][108][109][110][111][112][113][114][115][116][117] studied the role of the GB width on the temperature of nucleation of the phases and the subsequent microstructure evolution. The change in GB energy due to MTs, an important material parameter discussed above, is also yet to be incorporated to develop a robust model.…”

“…Furthermore, the role of the TJ energy on GB-induced MTs is not yet studied. The PF models in [15,[97][98][99][100][101][102][103][104][105][106][108][109][110][111][112][113][114][115] considered small strains, whereas the MTs usually involve large strains, and hence a large strains-based general PF model for MTs in polycrystals is yet to be developed. Recall that the only large strains-based model in [116,117] has issues with the kinematic model, as pointed out above.…”