Mesoscopic description of martensitic phase transformations mediated by dislocations using the Landau-Ginzburg theory

Dislocations in crystals induce incompatibility between elastic strains. We show how this can be related to the densities of crystal dislocations in individual slip systems and how the incompatibility causes nonlocal coupling with elastic strains in the evolving microstructure. The order parameter and thus the corresponding stress fields develop long-range tails that correspond to the superposition of elastic stress fields of individual dislocations. Hence, the stress field of any distribution of dislocations in an arbitrarily anisotropic medium can be calculated just by minimizing the free energy. The corresponding continuous field of Peach-Koehler forces is then employed in a Fokker-Planck equation for the dynamics of the dislocation density. This approach represents a simple self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density.