A unification of finite deformation $J_2$ Von-Mises plasticity and quantitative dislocation mechanics

Abstract

We present a framework which unifies classical phenomenological $J_2$ and crystal plasticity theories with quantitative dislocation mechanics. The theory allows the computation of stress fields of arbitrary dislocation distributions and, coupled with minimally modified classical ($J_2$ and crystal plasticity) models for the plastic strain rate of statistical dislocations, results in a versatile model of finite deformation mesoscale plasticity. We demonstrate some capabilities of the framework by solving two outstanding challenge problems in mesoscale plasticity: 1) recover the experimentally observed power-law scaling of stress-strain behavior in constrained simple shear of thin metallic films inferred from micropillar experiments which all strain gradient plasticity models overestimate and fail to predict; 2) predict the finite deformation stress and energy density fields of a sequence of dislocation distributions representing a progressively dense dislocation wall in a finite body, as might arise in the process of polygonization when viewed macroscopically, with one consequence being the demonstration of the inapplicability of current mathematical results based on $\mathrm{\Gamma }$-convergence for this physically relevant situation. Our calculations in this case expose a possible `phase transition' - like behavior for further theoretical study. We also provide a quantitative solution to the fundamental question of the volume change induced by dislocations in a finite deformation theory, as well as show the massive non-uniqueness in the solution for the (inverse) deformation map of a body inherent in a model of finite strain dislocation mechanics, when approached as a problem in classical finite elasticity.

arXiv commentarXiv admin note: text overlap with arXiv:2004.04201

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• Integrated Experiment and Simulation Co-Design: A Key Infrastructure for Predictive Mesoscale Materials Modeling
• Vector Field Models for Nematic Disclinations
• How useful are formal hierarchies? A case study on averaging dislocation dynamics to define meso-macro plasticity