Frank-Read source operation in six body-centered cubic refractory metals

Abstract

The Frank-Read (FR) source is a well-known intragranular dislocation source that plays an important role in size-dependent dislocation multiplication in metallic crystals. In this work, we extend a phase-field dislocation dynamics (PFDD) technique to study FR source operation on the {110}, {112}, and {123} slip planes in body-centered cubic (BCC) crystals. Here, the periodic lattice potentials for shearing across these planes used in PFDD simulations are provided by density functional theory (DFT) calculations for six BCC refractory metals, Cr, Mo, Nb, Ta, V, and W. The DFT calculations show that the group 6 elements (Cr, Mo, and W) have higher generalized stacking fault energies than the group 5 elements (Nb, Ta, and V). With PFDD, we focus on the effects of the GSFE curve shape, initial character angle, slip plane crystallography, and elastic anisotropy (measured by the Zener ratio, Ac) on the critical stresses to activate the FR source. For the same FR source of any character angle in the same metal, the critical stress on the {123} plane is lower than those on the {110} and {112} planes. It is also shown that elastic anisotropy decreases the critical stress when Ac < 1 and increases it when Ac > 1. We also find that in both Cr and Nb, which possess the lowest values of Ac among the six metals, elastic anisotropy causes the critical stress on {110} planes to achieve a local maximum for the mixed 45∘ oriented FR source.