Understanding large-strain mechanical deformation and failure of crystalline solids requires analyses of elastic stability in order to determine the crystal's mechanical strength. At given temperature, the structural response of a crystal to applied mechanical loading under a certain loading mode becomes unstable beyond a critical stress level. A major challenge in materials mechanics is to predict the theoretical strength of crystals under various mechanical loading modes and to analyze and fundamentally understand the underlying atomic-scale mechanisms of the crystals' structural response beyond the onset of stress-induced instability.

In this presentation, we report results of systematic elastic stability analyses in body-centered cubic (bcc) crystals under uniaxial and hydrostatic loading. The bcc structure is not a close-packed one and, therefore, it tends to be less stable and with higher energy than that of the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures. Stress-induced bcc-to-fcc and bcc-to-hcp transitions have been observed experimentally in K, Rb, Cs, Ca, Sr, Tl, and Fe crystals and in Be, Mg, Ba, Tl, Ti, Zr, and Fe crystals, respectively. Parameters that affect the bcc crystal lattice stability under mechanical loading include the loading mode, the direction of loading, temperature, and the presence of defects (such as nanovoids and other lattice imperfections) in the crystal. We employ isostress-isothermal molecular-dynamics (MD) simulation to analyze systematically the structural response of the crystal, placing special emphasis on the atomic pattern formation characteristics during the structural transformation. Subsequently, we conduct isothermal-isostrain MD simulations in order to compute the elastic moduli through canonical strain fluctuation formulae and use them to assess the crystal's elastic stability rigorously, according to proper stability criteria.

Our analysis emphasizes the similarities and differences in the atomic pattern formation during the stress-induced structural transformations of bcc crystals and the bifurcations in the crystal structural response that are exhibited when the applied load and/or the temperature are varied. We find that a bcc crystal would transform readily to a more stable structure, rather than fail, under both uniaxial and hydrostatic loading. In most of the cases that we examined, the loss of structural stability is consistent with Born's criterion. The bcc structure transforms to a fcc one, when it follows the tetragonal path of Bain deformation, and when it is under very high uniaxial compressive stress. However, the bcc structure transforms to a hcp one at the points of bifurcation from the tetragonal path and when a shear-modulus instability occurs. The bcc-to-hcp transformation mechanism is governed by the shearing of alternate planes of the body-centered tetragonal (bct) structure; this produces the stacking sequence of the {0001} basal planes of the hcp phase. Finally, we find that the presence of nanovoids within the crystal generates heterogeneous nucleation sites for the shearing transformation mechanisms and enhances the likelihood of structural transformation; this heterogeneous nucleation of the new phase at the defect site lowers the overall critical stress levels for the transformation.