Temperature dependent phase field dislocation dynamics model

In this work, we present a three-dimensional phase field-based formulation for simulating the temperaturedependent motion of discrete dislocations in crystals. For demonstration, this thermal phase field dislocation dynamics method is applied to study pyramidal-type dislocations in three exemplar hexagonal close packed materials, Mg, Ti, and Zr. Pyramidal-type dislocations are well known for temperature sensitivity and influence on the yield strength of these metals. Calculations include the predictions of activation stress, dislocation velocity, and dislocation nucleation over temperature ranges from 0 K to up to half the melting temperatures of these metals. We show that pyramidal slip is glissile, but the activation stress and stacking fault widths are asymmetric with respect to forward/backward glide. The stress to initiate glide reduces logarithmically with homologous temperature. The role of temperature in Frank-Read source operation is shown to decrease the size and time of first loop formation. The analysis identifies a master inverse relationship for the dislocation loop nucleation rate with homologous temperature followed by all three metals.