A continuum description of dislocations in elastically nonlinear media: martensitic embryo formation

Abstract

Candidate sites for heterogeneous nucleation of martensite are constructed from two dislocation structures placed in a nonlinear, nonlocal elastic continuum. The resulting static strain fields of the dislocation arrays give rise to mesoscopic embryos of the product phase, which exhibit athermal behavior as the effective temperature of the system is changed. A high-potency dislocation array gives rise to a strained classical (sharp boundary) martensitic embryo at high temperatures, corresponding to the limit of metastability for the martensitic phase. This embryo grows rapidly with decreasing temperature, interacting with the system boundary before the transformation can occur. A low-potency dislocation gives rise to a more diffuse, nonclassical structure, which increases in strain amplitude and size with decreasing effective temperature, becoming metastable before finally triggering the transformation of the full system. Transformation occurs in the low-potency case when force is 61% of the driving force at the lattice instability, and the strain embryo achieves 80% of the transformation strain.