The dynamics of dislocation pile-up formation with a non-linear stress-velocity relation for dislocation motion

The time dependent formation of single-ended dislocation pile-ups by the sequential emission of individual dislocations from a stress-activated source is considered. While in a previous paper a linear stress-velocity relation for dislocation motion was employed, a power law relation of the form V=Kσ m is used here. It is found that the times required for the essential completion of pile-up formation increase greatly with increasing values of m and, in some instances (e.g. body-centred cubic metals), it is rarely completed. In addition, the calculations permit the phenomenon of delayed yielding to be examined. The results are found to be in qualitative agreement with pertinent experimental observations.