A phase field model was presented for the study of dislocation formation (coherency loss) in 2-phase binary alloys. In this model, the elastic energy density was a periodic function of the shear and tetragonal strains, which permitted the multiple formation of dislocations. The composition was coupled twofold to the elastic field: via lattice misfit and via the compositional dependence of the elastic moduli. By numerically integrating the dynamic equations in 2 dimensions, it was found that dislocations appeared in pairs in the interface region and grew into slips. One end of each slip glided preferentially into the softer region, while the other end remained trapped at the interface. Under uniaxial stretching in deep quenching, slips appeared in the softer region and did not penetrate into the harder domains, giving rise to a gradual increase in the stress with increasing applied strain in plastic flow.

Dislocation Formation in Two-Phase Alloys. A.Minami, A.Onuki: Physical Review B, 2004, 70[18], 184114 (10pp)