Nonlocal Linear Instability Drives the Initiation of Motion of Rational and Irrational Twin Interfaces

Twin boundaries play a central role in the functional behavior of martensitic materials, yet the mechanisms governing the initiation of their motion remain poorly understood for twins lying along irrational crystallographic directions. Here we present an atomistic investigation of the onset of motion of both rational and irrational twin interfaces in a two-dimensional model lattice with rectangular unit cells. Using quasistatic shear loading and full linear stability analysis, we show that the initiation of twin boundary motion is signaled by a nonlocal linear instability, marked by the vanishing of the lowest eigenvalue of the Hessian; the corresponding eigenmode predicts the atomic displacements that initiate motion. We find that irrational twin boundaries have significantly lower critical shear stress to initiate motion compared to rational twin boundaries. Further, we find that they display unusual mechanisms to initiate motion such as the formation of microtwins in directions orthogonal to the overall twin boundary. Finally, we compare various local measures against the nonlocal stability analysis, and find that the former do not capture that irrational twin boundaries initiate their motion at lower stresses compared to rational boundaries.