Ab initio electronic structure calculations of the ideal strength of Fe, Co, Ni, and Cr under isotropic tension were performed using the linear muffin-tin orbital method in the atomic sphere approximation. Magnetic ordering was taken into account by means of a spin-polarized calculation. Two approximations for the exchange-correlation term were employed: namely, the local (spin) density approximation and the generalized gradient approximation. Computed values of equilibrium lattice parameters, bulk moduli, and magnetic moments were compared with available experimental data. The stability of the ground-state structure in the tensile region was assessed via comparison of its total energy and enthalpy with those of some other structures. No instabilities were found before reaching the inflection point on the total energy versus volume curve and the stress related to this point was therefore considered to be the ideal strength.

Critical shear stress under the superimposed hydrostatic and uniaxial normal stress conditions of C, Si, Ge, and SiC is evaluated by ab initio density functional theory calculations to investigate the response of ideal shear strength (ISS) to superimposed normal stresses in covalent crystals. We find a substantial difference in the responses of ISS to normal stress among the covalent crystals examined; e.g., hydrostatic compression increases the ISS of C but decreases that of Si, Ge, and SiC. The ISS is mostly a highly nonlinear and anisotropic function of normal stress. The results thus indicate that normal stresses can significantly affect the critical shear stress, which is crucial to interpreting experimental observations of crystal deformation, e.g., dislocation nucleation in nanoindentation.

Elastic response and strength of perfect crystals is calculated for triaxial loading conditions from first principles. The triaxial stress state is constituted by uniaxial tensile stress and superimposed transverse biaxial stresses. The maximum uniaxial tensile stress is evaluated as a function of the transverse stresses. Results for eight crystals of cubic metals and two orientations (⟨110⟩ and ⟨111⟩) of the primary loading axis are presented and compared with data for ⟨100⟩ direction of loading. Obtained results show that, within a studied range of biaxial stresses, the maximum tensile stress monotonically increases with increasing biaxial tensile stress for most of the studied metals. Within a certain range, the dependence can be mostly approximated by a linear function.