Relation Between Yield Stress and Peierls Stress

It is often assumed that the Peierls stress of single dislocations can reflect accurately the macroscopic yield stress. Here, dislocation dynamics simulations show that the yield stress-to-Peierls stress (Y/P) ratio remains within a small range of approximate to 0.3 +/- 0.1, over a wide range of initial dislocation density, mobile dislocation fraction, and temperature which affects cross slip. This range of Y/P arises from the typical stress concentration ahead of dislocation pile-ups. The results explain why Y/P was observed to be around one-third in previous experiments.