Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions

Abstract

Please cite this article as: Luscher, D.J., Mayeur, J.R., Mourad, H.M., Hunter, A., Kenamond, M.A., Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions AbstractWe have developed a multi-physics modeling approach that couples continuum dislocation transport, nonlinear thermoelasticity, crystal plasticity, and consistent internal stress and deformation fields to simulate the single-crystal response of materials under extreme dynamic conditions. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. Nonlinear thermoelasticity provides a thermodynamically consistent equation of state to relate stress (including pressure), temperature, energy densities, and dissipation. Crystal plasticity is coupled to dislocation transport via Orowan's expression where the constitutive description makes use of recent advances in dislocation velocity theories applicable under extreme loading conditions. The configuration of geometrically necessary dislocation density gives rise to an internal stress field that can either inhibit or accentuate the flow of dislocations. An internal strain field associated with the internal stress field contributes to the kinematic decomposition of the overall deformation. The paper describes each theoretical component of the framework, key aspects of the constitutive theory, and some details of a one-dimensional implementation. Results from single-crystal copper plate impact simulations are discussed in order to highlight the role of dislocation transport and pile-up in shock loading regimes. The main conclusions of the paper reinforce the utility of the modeling approach to shock problems.

Velocity dependent dislocation drag from phonon wind and crystal geometry

“…Hence, many dislocation based material strength models require the dislocation drag coefficient B as one of their input parameters (typically determining the dislocation glide time between obstacles), see e.g. [1][2][3][4][5][6][7]. B is usually assumed to be a constant (or a constant over a simple "relativistic" factor) as a fist order approximation.…”

Dislocation drag from phonon wind in an isotropic crystal at large velocities

“…We note that drag is initially dominated by thermal effects at very low dislocation velocities, and that phonon wind becomes important only at velocities of the order of 1% transverse sound speed and higher.2 Many authors estimate the velocity dependence of the drag coefficient by means of "relativistic" factors ∝ 1/(1 − v 2 /c 2 ) m with different exponents m and a limiting (sound) speed c based on purely empirical arguments which lack a first-principles theoretical framework, see[3][4][5][6][7] and references therein.…”

Interaction of run-in edge dislocations with twist grain boundaries in Al-a molecular dynamics study

“…Such investigation represents a bottom-up nanoscale understanding of the dislocation-GB interactions, which can then be captured more accurately by the modelling efforts at micro-and meso-scales. Examples of such efforts include the molecular dynamics level [19,33,35,60], Discrete Dislocation Dynamics approach [82][83][84][85], crystal plasticity framework [86][87][88] and continuum description [89][90][91] of dislocation pile-ups in such cases can be described either explicitly using discrete approaches or implicitly using continuum approaches. In the discrete approach, the treatment of interaction forces among the piled-up dislocations leads to a set of nonlinear equations for their equilibrium positions [92].…”