On dissipative gradient effect in higher-order strain gradient plasticity: the modelling of surface passivation
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RESEARCH PAPER
On dissipative gradient effect in higher‑order strain gradient plasticity: the modelling of surface passivation Fenfei Hua1,2 · Dabiao Liu1,2 Received: 20 January 2020 / Revised: 21 April 2020 / Accepted: 22 May 2020 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The phenomenological flow theory of higher-order strain gradient plasticity proposed by Fleck and Hutchinson (J. Mech. Phys. Solids, 2001) and then improved by Fleck and Willis (J. Mech. Phys. Solids, 2009) is used to investigate the surfacepassivation problem and micro-scale plasticity. An extremum principle is stated for the theory involving one material length scale. To solve the initial boundary value problem, a numerical scheme based on the framework of variational constitutive updates is developed for the strain gradient plasticity theory. The main idea is that, in each incremental time step, the value of the effective plastic strain is obtained through the variation of a functional in regard to effective plastic strain, provided the displacement or deformation gradient. Numerical results for elasto-plastic foils under tension and bending, thin wires under torsion, are given by using the minimum principle and the numerical scheme. Implications for the role of dissipative gradient effect are explored for three non-proportional loading conditions: (1) stretch-passivation problem, (2) bendingpassivation problem, and (3) torsion-passivation problem. The results indicate that, within the Fleck–Hutchinson–Willis theory, the dissipative length scale controls the strengthening size effect, i.e. the increase of initial yielding strength, while the surface passivation gives rise to an increase of strain hardening rate. Keywords Strain gradient plasticity · Dissipative length scale · Passivation · Size effect · Non-proportional loading
1 Introduction A number of experiments at small scales have revealed that metallic materials display significant size effects related to plastic deformation involving plastic strain gradients [1–10]. It is well known that conventional (local) plasticity theories cannot capture the experimentally observed change in the mechanical behavior with diminishing size. One way to predict size effects in polycrystalline metals is to introduce gradient effects in the governing equations. To date, various strain gradient theories of isotropic plasticity have been developed, mainly based on the relationship between geometrically necessary dislocations (GNDs) and the gradient of plastic strain [11, 12], see for example, Aifantis [13], Fleck and Hutchinson [14, 15], Fleck and Willis [16, 17], * Dabiao Liu [email protected] 1
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China
2
Gudmundson [18], Gudmundson and Dahlberg [19], Gurtin and Anand [20, 21], Gurtin [22], Nix and Gao [23], Gao et al. [24]
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