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 following a certain loading mode becomes unstable beyond a critical stress level. In spite of numerous studies aiming to determine the theoretical strength of crystals, identifying and analyzing the prevailing atomic mechanisms of a crystal's structural response beyond the onset of stress-induced instability remains a major challenge in materials mechanics.

In this presentation, we report results of systematic elastic stability analyses in bulk metallic crystals under uniaxial loading. These analyses are based on isostress molecular-dynamics (MD) simulations according to the Lagrangian formulation of Parrinello and Rahman and focus on crystals with a body-centered cubic (bcc) lattice structure at equilibrium. We examine in detail geometric, mechanical, energetic, and kinetic characteristics of instabilities in such crystals under uniaxial stress, placing special emphasis on the atomic pattern formation characteristics in the crystals' structural response to loading at and beyond the onset of elastic instability. In addition to the detailed monitoring of atomic-scale dynamics, we use canonical strain fluctuation formulae to calculate elastic moduli as functions of temperature and stress; these moduli are computed through canonical MD simulations at the strain state determined by the isothermal-isostress MD simulations and are used in rigorously derived criteria for the assessment of crystal elastic stability.

Results are presented for the elastic stability and structural response of cubic crystals subjected to [100] and [110] uniaxial loading from the equilibrium bcc phase. Born's criterion for the loss of structural stability is found to be applicable in most cases examined. Our analysis emphasizes bifurcations in the crystal structural response that are exhibited when the applied uniaxial load and/or the temperature are varied, as well as the atomic pattern formation characteristics beyond the instability onset. The MD simulations reveal the atomic-scale mechanisms that trigger the lattice instability and elucidate the atomic-scale dynamics that may lead to either structural change or crystal failure beyond the elastic instability. The structural response of a bcc crystal along the tetragonal path as the [100] and [110] uniaxial loading is gradually increased is discussed in detail. The MD simulations reveal that beyond the onset of the instability, bcc crystals under [100] and [110] loading exhibit certain similarities in their behavior with face-centered cubic (fcc) crystals under the same loading mode. Specifically, both bcc and fcc crystals lose stability by violation of the same stability criteria and, in both crystalline structures, loss of stability is accompanied by the same mechanisms of structural response (e.g., structural transformation to a hexagonal close-packed lattice structure). However, the stability criterion violated when a bcc crystal loses stability under tension coincides with that violated when an fcc crystal loses stabililty under compression and vice versa. In all of the cases studied, the observed instabilities are found to be associated with vanishing or diminishing elastic moduli combinations consistently with the theoretical stability criteria.

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