Theoretical strength of a perfect crystal in a state of simple shear

Abstract

A theoretical study was made of the lattice stability or theoretical strength of fcc crystals subjected to a particular mode of simple unconstrained shear. Numerical calculations were made for crystals with two-body exponentially attractive and exponentially repulsive interatomic interactions. The results of calculations were not very sensitive to the detailed nature of the atomic potentials, providing that the theoretical values of the stress-free elastic moduli ${C}_{11}$ and ${C}_{12}$ and lattice parameter of the crystal were kept invariant when the detailed nature of the atomic potentials was changed. The results exhibited a variety of interesting behaviors, including the existence of two distinct nonintersecting branches of equilibrium solutions, one of which was a closed path, and both of which contained regions in which the crystal was stable and in which the crystal was unstable. The numerical values of stress and strain at the onset of lattice instability compared well with experimental values of maximum stresses and strains which have been observed for fine metallic whiskers, reinforcing the belief that both the theoretical and the experimental values of stress and strain at failure are quite close to the "theoretically ultimate" values.