Slip transfer across grain and phase boundaries

A simple geometrical model is presented with the aim to connect measured distributions of orientation relationships between adjacent grains in single and dualphase brasses and the efficiency of grain and phase boundaries as dislocation obstacles. From the orientation relationships a slip transfer number is evaluated from the angle between the slip plane normals and the angle between the slip directions of the grain neighbors. Taking into account the different stacking fault energy and the different hardness of α-phase brass and β-phase brass and using reasonable limiting conditions for the above angles the result of the calculations is the same as obtained from the Hall-Petch analysis of the yield stress: phase boundaries are stronger dislocation obstacles than grain boundaries.