A multiscale strength model for extreme loading conditions

Abstract

We present a multiscale strength model in which strength depends on pressure, strain rate, temperature, and evolving dislocation density. Model construction employs an information passing paradigm to span from the atomistic level to the continuum level. Simulation methods in the overall hierarchy include density functional theory, molecular statics, molecular dynamics, dislocation dynamics, and continuum based approaches. Given the nature of the subcontinuum simulations upon which the strength model is based, the model is particularly appropriate to strain rates in excess of 104 s−1. Strength model parameters are obtained entirely from the hierarchy of simulation methods to obtain a full strength model in a range of loading conditions that so far has been inaccessible to direct measurement of material strength. Model predictions compare favorably with relevant high energy density physics (HEDP) experiments that have bearing on material strength. The model is used to provide insight into HEDP experimental observations and to make predictions of what might be observable using dynamic x-ray diffraction based experimental methods.

A multi-scale strength model with phase transformation

“…The strength model for the α phase is just as in [1]. The γ phase model uses the same functional forms with the following exceptions.…”

“…Here we present a phase-aware strength model that addresses some of these issues for the α/γ (BCC/rhombohedral) phase transformation in vanadium. The model builds from a recently developed multi-scale strength model for the α phase [1]. A new strength model is developed for the γ phase and the α and γ strength models are combined into a unified multi-phase strength capability.…”

“…Within each phase, the strength response depends on pressure, temperature, strain rate, and descriptors of dislocation density. These strength models target comparatively high strain rates in a range over which experiments provide valuable validation data but do not provide data appropriate to the construction of phenomenological models [2,1], motivating the use of a multi-scale approach with information passing to span from the atomistic level to the continuum level.…”

“…with τ * (v, θ ) and τ p (p) as in [1]. The multiplication kinetics of the short-b dislocations are modeled using the form in [1], and the long-b dislocation density can be approximated by using a scale factor:ρ b L = r b Lρ b S .…”

“…The multiplication kinetics of the short-b dislocations are modeled using the form in [1], and the long-b dislocation density can be approximated by using a scale factor:ρ b L = r b Lρ b S . Material parameters are given in Table 1 and in [1]. …”