(456f) Analysis of Elastic Stability and Structural Response of Cubic Crystals under Uniaxial Loading
The theoretical strength of a material is determined by the highest stress that a bulk single perfect crystal of the material can withstand under specified mechanical loading. Predicting this limit of strength of crystalline solids requires systematic analyses of the crystals' elastic stability taking all the relevant parameters into account. At given temperature, the structural response of a crystal to a specified mode of applied mechanical loading will become unstable beyond a critical stress level. This large-strain mechanical deformation may lead to fracture of the crystal. Determining the onset of elastic instability and analyzing the structural response of the crystalline solid beyond the instability onset is a topic of major interest in the mechanics of crystalline materials.
In this presentation, elastic stability analyses are performed systematically for face-centered cubic (fcc) metallic crystals subjected to hydrostatic tension. The computations involved are based on isothermal isostress molecular-dynamics (MD) simulations according to the Lagrangian formulation of Parrinello and Rahman. In the simulations, interatomic interactions are expressed by classical force fields that have been fitted to experimental elastic moduli of metals and yield large-strain nonlinear elastic behavior in excellent qualitative agreement with more sophisticated atomistic models and with experiment. We find that the computed pressure-volume relations over the entire loading range at different temperatures are described satisfactorily by the Birch-Murnaghan equation of state. We examine in detail geometric, mechanical, energetic, and kinetic characteristics of elastic instabilities that are triggered as the tensile load increases. Elastic moduli are computed as functions of temperature and stress according to canonical strain fluctuation formulae; these are implemented through canonical MD simulations at the strain state determined by the isostress MD simulations. The elastic moduli are used in rigorously derived criteria for the assessment of crystal elastic stability.
Results are presented for the structural response to hydrostatic tension of several model crystals that have an fcc lattice structure at equilibrium. In all cases, it is demonstrated that the observed instabilities are thermally activated and associated with a vanishing or diminishing bulk modulus and that the instability causes the fracture of the fcc crystal. In addition, the temperature dependence is calculated of the critical stress that marks the instability onset and of the thermal activation enthalpy barrier that should be overcome for the fracture process to take place beyond the instability onset. We find that the critical stress and the activation enthalpy are monotonically decreasing and monotonically increasing functions of temperature, respectively, and that the enthalpy barrier vanishes completely as the temperature is lowered to absolute zero. The MD simulation results at low temperature are in excellent agreement with the predictions of stability criteria according to ?static? elastic stability theory. Introduction of structural defects, such as nanovoids, into the crystal affects the instability onset significantly. Specifically, the critical tension required to cause the imperfect (defective) crystal fracture is lowered at each temperature. Furthermore, it is demonstrated that in the imperfect crystal, fracture is initiated at the defects of the lattice structure (heterogeneous nucleation) and proceeds through decohesion and voiding. Under the continuously applied hydrostatic tension, the void grows and causes the failure of the crystal.