Atomic pattern formation at the onset of stress-induced elastic instability: Fracture versus phase change

Abstract

A systematic theoretical study is presented of the stress-induced structural response of initially cubic single crystals to uniaxial [100] loading based on elastic stability analysis and isostress molecular-dynamics simulations through a classical description of interatomic interactions in model metallic crystals. Special emphasis is placed on the study of the atomic pattern formation characteristics in the crystal's structural response to loading at and beyond the onset of elastic instability. The instability is reached at a rigorously defined critical stress level that occurs in association with the vanishing of a shear modulus, i.e., when ${C}_{22}∕{C}_{23}\ensuremath{-}1=0$, where ${C}_{rs}$ are stress-dependent elastic moduli. Although the atomic mechanism for the onset of instability is invariant, two divergent atomic processes are found to occur beyond the onset of instability, depending on subtle differences in the elastic properties of the crystals. Our analyses and simulations of a crystal model with the relatively small initial value of ${C}_{22}∕{C}_{23}\ensuremath{-}1=0.41$ (based on the elastic moduli of copper) reveal an inhomogeneous structural transformation mechanism, through the creation of individual rotating domains that lead to formation of a new hexagonal single crystal without loss of strength. This theoretical result is consistent with what is known experimentally for metals with relatively small values of $({C}_{22}∕{C}_{23}\ensuremath{-}1)$, e.g., certain copper alloys and the alkali metals, which can undergo various cubic-to-hexagonal structural transformations. However, a crystal model based on the elastic moduli of nickel, with the larger initial value of ${C}_{22}∕{C}_{23}\ensuremath{-}1=0.73$, fails to exhibit domain rotation beyond the onset of elastic instability and, as a result, the initial destabilization of the crystal structure then leads to fracture.