open access publication

Article, 2016

On modeling micro-structural evolution using a higher order strain gradient continuum theory

International Journal of Plasticity, ISSN 0749-6419, 1879-2154, Volume 76, Pages 285-298, 10.1016/j.ijplas.2015.08.008

Contributors

El-Naaman, S A (Corresponding author) [1] Nielsen, Kim Lau 0000-0002-0502-8008 [1] Niordson, Christian Frithiof 0000-0001-6779-8924 [1]

Affiliations

  1. [1] Technical University of Denmark
    2. [NORA names: DTU Technical University of Denmark; University; Denmark; Europe, EU; Nordic; OECD]

Abstract

Published experimental measurements on deformed metal crystals show distinct pattern formation, in which dislocations are arranged in wall and cell structures. The distribution of dislocations is highly non-uniform, which produces discontinuities in the lattice rotations. Modeling the experimentally observed micro-structural behavior, within a framework based on continuous field quantities, poses obvious challenges, since the evolution of dislocation structures is inherently a discrete and discontinuous process. This challenge, in particular, motivates the present study, and the aim is to improve the micro-structural response predicted using strain gradient crystal plasticity within a continuum mechanics framework. One approach to modeling the dislocation structures observed is through a back stress formulation, which can be related directly to the strain gradient energy. The present work offers an investigation of constitutive equations for the back stress based on both considerations of the gradient energy, but also includes results obtained from a purely phenomenological starting point. The influence of model parameters is brought out in a parametric study, and it is demonstrated how a proper treatment of the back stress enables dislocation wall and cell structure type response in the adopted framework.

Keywords

back stress, back stress formulation, behavior, cell structure, cells, considerations, constitutive equations, continuum, continuum mechanics framework, continuum theory, crystal, crystal plasticity, deformed metal crystals, discontinuation, discontinuous process, dislocation, dislocation structure, dislocation walls, distribution, distribution of dislocations, energy, equations, evolution, evolution of dislocation structures, experimental measurements, field quantities, formation, formulation, framework, gradient, gradient continuum theory, gradient crystal plasticity, gradient energy, influence, influence of model parameters, investigation, lattice, lattice rotation, measurements, mechanics framework, metal crystals, micro-structural behavior, micro-structural evolution, micro-structural response, model parameters, non-uniformity, parameters, parametric study, pattern formation, patterns, phenomenological starting point, plasticity, point, process, published experimental measurements, quantity, response, results, rotation, starting point, strain, strain gradient continuum theory, strain gradient crystal plasticity, stress, stress formulation, structure, study, theory, treatment, type response, wall

Funders

  • Danish Agency for Science and Higher Education

Data Provider: Digital Science

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