The ideal tensile and shear strengths of binary $\beta$-phase Ti${}_3$Nb alloys have been investigated using ab initio density functional calculations. The binary alloy is considered as an approximant to the multifunctional Ti-Nb-Ta-Zr-O alloy known as “gum metal,” which displays high strength, low elastic modulus, high yield strain, and very good ductility. This alloy has been reported to deform elastically until the stress approaches the ideal tensile strength. Our calculations have been performed for an optimized chemical decoration of the body-centered cubic (bcc) structure of the $\beta$ phase. Previous work has demonstrated that this model yields elastic constants in very good agreement with those measured for gum metal specimens and leads to a reasonably accurate description of the martensitic transformations between the bcc $\beta$, the orthorhombic ${\alpha }^{\prime \prime }$ and the hexagonal $\omega$ phases [Lazar et al., Phys. Rev. B 84, 054202 (2011)]. The simulations of the response to tensile and shear loading have been performed for large supercells which account also for the different orientations of the -Nb-Nb- chains characteristic for the $\beta$-phase structure relative to the direction of the applied load. The energy-strain and stress-strain curves are found to be very different from those reported for all bcc metals. Under uniaxial $\langle 100\rangle$ loading we find an ideal tensile strength of 2.4 GPa, the upper limit to the tensile stress arising from a shear instability of the structure. Under uniaxial $\langle 110\rangle$ load we calculate an ideal tensile strength of 2.2 or 2.8 GPa, depending on the orientation of the -Nb-Nb- chains relative to the loading direction. For a realistic multidomain structure the ideal strength is expected to correspond to the average of these values. An ideal strength of 2.6 GPa under $\langle 110\rangle$ loading is roughly the same as under $\langle 100\rangle$ load, despite a considerable anisotropy of the tensile moduli. For $\left\{211\right\}\langle 111\rangle$ shear we calculate an ideal shear strength of 1.6 GPa, again as an average over different possible shearing directions relative to the Nb-Nb bonds. For the $\left\{110\right\}\langle 110\rangle$ shear system we find a lower strength of 0.9 GPa. The structures reached at the stress maximum under $\langle 100\rangle$ uniaxial tension and $\left\{211\right\}\langle 111\rangle$ shear are identical, and since the maximal shear stress is much lower than the tensile stress, the alloy will fail by shear even under strictly uniaxial tension. The values of the ideal tensile and shear strengths are significantly low, even in comparison with those calculated for bcc V and Nb with very small shear moduli and approach the values reported for gum metal alloys.

• Received 17 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.024122