A general phase-field framework for predicting the structures and micromechanical properties of crystalline defects

Highlights: • A phase-field framework is provided to bridge defect structures to properties. • Model input can be solely determined by atomistic calculations. • The predicted stress field of defects can be directly used in mesoscopic analysis. This work provides a phase-field simulation framework that bridges the structure of defects (e.g., dislocations and grain boundaries (GBs)) to their characteristic properties, such as stresses and energies. The validity of the current methodology is examined first by predicting the stress field of a single infinitely long screw dislocation using both the analytical solutions based on anisotropic elasticity and the current phase-field framework. The well-known stress singularity associated with the dislocation core in the former method has been effectively avoided in the latter. The framework is then applied to predicting the dislocation network of {0 0 0 1} twisted GB in Mg, which is found to consist of triangular-shaped regions of stacking faults and perfect crystals separated by partial dislocations. This prediction is consistent with some existing atomistic simulations and the underlying formation mechanism is analyzed rigorously using the displacement field predicted by our model, revealing the energy minimization process via the dissociation of a $〈11\overline{2}0〉/3$ screw dislocation into a pair of $〈1100〉/3$ screw dislocations. Based on the structure prediction, the associated stress field is further simulated, which provides critical information in evaluating the interaction of GBs and other crystalline defects such as impurities and dislocations.