Crack initiation at twin boundaries due to slip system mismatch

What determines if a grain boundary acts as a crack initiation site during fatigue? The grain boundary defines a mismatch of slip systems, which strongly depends on the three-dimensional positions of the boundary plane. In the case of a coherent Σ3 twin boundary, the boundary plane, and thus the mismatch between the slip systems, is known for all possible combinations of active slip systems. Thus, the tendency for crack initiation can be reduced to a purely geometric calculation.