Strength of bcc crystals under combined shear and axial loading from first principles

Ab initio simulations of uniaxial tensile and compressive loading in 〈1 1 0〉 direction, 〈1 1 1〉{1 1 0} shear and their superposition in six perfect crystals of bcc metals are performed using a plane wave code working within the framework of density functional theory. Under uniaxial compression, the crystal lattice transforms along an orthorhombic path that connects two bcc states and goes through one or two states of tetragonal symmetry. Such structural transformations determine compressive strengths of bcc crystals. On the other hand, reaching the maximum tensile stress coincides with vanishing of the shear strength in lattice planes perpendicular to the loading axis. The theoretical shear strength is found to be a decreasing (increasing) function of the applied tensile (compressive) normal stress in most studied cases. One of potential applications of this particular result is a prediction of shear instabilities in crystal lattices during tensile tests. Estimated critical tensile stresses related to shear instabilities in Mo and W under 〈1 1 0〉 tension are lower than the computed maximum tensile stresses and somewhat higher than experimental values.