Anomalies in the response of V, Nb, and Ta to tensile and shear loading: Ab initio density functional theory calculations

Ab initio density functional calculations of the response of V, Nb, and Ta to tensile and shear loading have been performed. We find that the behavior of all three metals of the V group under large strains differs considerably from that reported for the other body-centered cubic (bcc) transition metals (Mo, W, and Fe). Under unaxial < 100 > tensile loading, V and Nb undergo a bifurcation from a tetragonal to an orthorhombic deformation path, associated with a shear instability, before reaching the stress maximum. The bifurcation strongly reduces the ideal tensile strengths to 11.5 GPa for V and 12.5 GPa for Nb. For Ta the bifurcation point coincides with the stress maximum of 13.6 GPa along the tetragonal path so that the metal fails under tensile strain by shear and not by cleavage. The stress-strain curves calculated for the {110}< 111 > and {211}< 111 > slip systems are strongly asymmetric; the ideal shear strengths for both slip systems are 6.5 (5.5) GPa for V and 7.8 (6.0) GPa for Nb. Hence the ideal shear strengths are only half as large as for the bcc metals Mo and W, but much larger than expected on the basis for the low shear moduli of V and Nb. Ta shows a behavior intermediate between these two groups of metals, with a calculated ideal shear strength of 7.1 (6.5) GPa, in excellent agreement with the experimental estimate from nanoindentation experiments. The saddle-point structure determining the shear strength for both slip systems is a special body-centered-tetragonal structure. This structure is identical to the saddle-point structure identified on the orthorhombic deformation path under uniaxial tension. Hence also V and Nb will fail under uniaxial tension not by cleavage, but by shear.