Determining the onset of elastic instability and analyzing the structural response of crystalline solids beyond the instability onset is a topic of major interest in materials mechanics over a broad class of industrial applications from aerospace to microelectronics. Predicting this limit of strength of crystalline solids requires systematic analyses of the crystals' elastic stability taking all the relevant parameters into account.  At any given temperature, the structural response of a crystal to a specified mode of applied mechanical loading will become unstable beyond a critical stress level. 

In this presentation, we report results of a coarse-molecular dynamics (CMD) approach to approximating an effective free-energy landscape of the stressed crystalline solids under uniaxial loading and analyzing their stability and stress-induced polymorphic transitions.  In CMD, coarse-grained information is estimated on-the-fly from many short and properly initialized independent replica molecular-dynamics (MD) simulations.  The method is based on the description of the evolution of the probability density, P(y,t), approximated by the Fokker-Planck equation, where y(t) is an appropriate coarse-grained observable that describes the state of the system under investigation.  The method has been demonstrated to be efficient and accurate in determining the onset of structural transitions in condensed matter, such as melting and pressure-induced polymorphic transitions. In our study, CMD analyses are performed systematically for metallic crystals with a face-centered cubic (fcc) structure at equilibrium subjected to [100] uniaxial loading. The corresponding short MD simulations are based on isothermal-isostress MD according to the Lagrangian formulation of Parrinello and Rahman.  Our CMD approach is used to explore a broad range of values of a properly chosen coarse variable. In this analysis, among several options, we have chosen as a coarse variable the stretch along the loading direction, l₁, which provides a good metric for the deformation of a crystal under uniaxial loading.

By exploring the coarse-variable space, we capture all the possible states of a model metallic crystal, a Morse model for Cu, including fcc, body-centered cubic (bcc), and hexagonal close-packed (hcp) lattice structures.  We construct the underlying effective free-energy landscape for every value of the bifurcation parameter (applied uniaxial stress) and construct a comprehensive bifurcation diagram, which includes stable and unstable states, as well as previously unknown branches in comparison with bifurcation diagrams constructed based on lattice-statics analyses. Furthermore, the stability of each branch and the location of “the next stable branch” at the onset of instability also are identified clearly, resulting in the first comprehensive dynamic stability diagram of cubic crystals at finite temperature. Our results also explain why sometimes defects such as stacking faults get introduced into a structure during a transformation mechanism.