A Peierls analysis of the critical stress for transmission of a screw dislocation across a coherent, sliding interface

The resistance of interfaces and grain boundaries to dislocation transmission is a fundamental quantity that often serves to control strength in plastically deforming polycrystals and multiphase materials. This manuscript extends the standard continuum view of the transmission process, in which a Volterra or Peierls dislocation interacts with a non-slipping interface. The extensions in this work are to use a modified Peierls description of the dislocation on the incoming and outgoing slip planes and to let the interface slip according to a simple, periodic constitutive relation, so that the interface can store and emit dislocation content during the transmission process. The analysis is restricted to a screw dislocation oriented parallel to the interface, with incoming and outgoing slip planes that are normal to the interface, and with Burgers vectors that are the same on each side of the interface. The last restriction is characteristic of coherent interfaces. The results show that the critical stress for transmission can be increased dramatically by decreasing the elastic shear modulus and unstable stacking fault energy of the interface. In such cases, a significant portion of the dislocation core can become stored in the interface during the transmission process, so that the critical transmission step is to extract the core from the interface. The peak stress for dislocation transmission across interfaces is contrasted for slipping and non-slipping cases.