Ab initio calculations of ideal strength and lattice instability in W-Ta and W-Re alloys

Abstract

An important theoretical criterion to evaluate the ductility of metals with a body-centered cubic (bcc) lattice is the mechanical failure mode of their perfect crystals under tension along $\ensuremath{\langle}100\ensuremath{\rangle}$ directions. When the tensile stress reaches the ideal tensile strength, the pure W crystal fails by a cleavage fracture along the ${100}$ plane so that it is intrinsically brittle. To discover the strategy to improve its ductility, we performed density functional theory and density functional perturbation theory calculations to study the ideal tensile strength and the lattice instability under $\ensuremath{\langle}100\ensuremath{\rangle}$ tension for both W-Ta and W-Re alloys. Anisotropic linear elastic fracture mechanics (LEFM) theory and Rice's criterion were also applied to analyze the mechanical instability at the crack tip under $\ensuremath{\langle}100\ensuremath{\rangle}$ tension based on the competition between cleavage propagation and dislocation emission. The results show that the intrinsic ductility can be achieved in both W-Ta and W-Re, however, by different mechanisms. Even though W-Ta alloys with low Ta concentrations are still intrinsically brittle, the intrinsic ductility of W-Ta alloys with high Ta concentrations is promoted by elastic shear instability before the cleavage failure. The intrinsic ductility of W-Re alloys is produced by unstable transverse phonon waves before the cleavage failure, and the corresponding phonon mode is related to the generation of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}{\overline{2}11}$ dislocation in bcc crystals. The ideal tensile calculations, phonon analyses, and anisotropic LEFM examinations are mutually consistent in the evaluation of intrinsic ductility. These results bring us physical insights on the ductility-brittle mechanisms of W alloys under extreme stress conditions.