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

• Published in: International journal of plasticity Vol. 76; pp. 111 - 129
• Main Authors: Luscher, D.J., Mayeur, J.R., Mourad, H.M., Hunter, A., Kenamond, M.A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2016
• Subjects: A. Dislocations; A. Dynamics; A. Shock waves; Advection-diffusion equation; B. Crystal plasticity; Crystals; Dislocations; Mathematical models; Plasticity; Residual stress; Shock loading; Transport; A. Dislocations; A. Shock waves; B. Crystal plasticity; A. Dynamics
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2015.07.007

We 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. •A framework for continuum modeling of crystal plasticity under shock loading is presented.•Dislocation density is included as a field variable and evolves in accordance with conservation principle.•The kinematic description includes an internal strain associated with long-range stresses caused by dislocation pile up.•Numerical simulations reinforce the utility of the proposed framework under various scenarios.