Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations |
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Authors: | Nobutada Ohno Dai Okumura |
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Institution: | Department of Mechanical Science and Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan |
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Abstract: | The higher-order stress work-conjugate to slip gradient in single crystals at small strains is derived based on the self-energy of geometrically necessary dislocations (GNDs). It is shown that this higher-order stress changes stepwise as a function of in-plane slip gradient and therefore significantly influences the onset of initial yielding in polycrystals. The higher-order stress based on the self-energy of GNDs is then incorporated into the strain gradient plasticity theory of Gurtin 2002. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50, 5-32] and applied to single-slip-oriented 2D and 3D model crystal grains of size D. It is thus found that the self-energy of GNDs gives a D-1-dependent term for the averaged resolved shear stress in such a model grain under yielding. Using published experimental data for several polycrystalline metals, it is demonstrated that the D-1-dependent term successfully explains the grain size dependence of initial yield stress and the dislocation cell size dependence of flow stress in the submicron to several-micron range of grain and cell sizes. |
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Keywords: | Dislocations Strengthening and mechanisms Crystal plasticity Elastic-plastic material Metallic material |
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