Jump condition for GND evolution as a constraint on slip transmission at grain boundaries

Abstract

The jump condition at a possibly non-material interface for geometrically-necessary dislocation density in field dislocation mechanics (FDM) and its averaged approximation, phenomenological mesoscopic FDM (PMFDM), is derived. In the context of grain boundaries, the condition implies a tensorial constraint on all five grain boundary parameters, slip transmission at the boundary, possible grain boundary motion and dislocation nucleation/annihilation at the grain boundary. The jump condition is physically interpreted in special cases, and the importance of understanding dislocation motion at a boundary/interface as a flux across curves, and not surfaces, is emphasized.

Acknowledgments

I thank Vasily Bulatov for encouraging me to think about this problem. The financial support of the National Science Foundation through the CMU MRSEC, Grant no. DMR-0520425, is gratefully acknowledged.