Abstract
A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments.
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Lloyd, D.J., Particle reinforced aluminum and magnesium metal matrix composites. International Materials Reviews, 1994, 39(1): 1–45.
Ma, Q., and Clarke, D.R., Size dependent hardness of silver single crystals. Journal of Materials Research, 1995, 10(4): 853–863.
McElhaney, K.W., Vlassak, J.J. and Nix, W.D., Determination of indenter tip geometry and indentation contact area for depth-sening indentation experiments, Journal of Materials Research, 1998, 13(5): 1300–1306.
Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson. J.W., Strain gradient plasticity: theory and experiment. Acta Metallurgica et Materialia, 1994, 42(2), 475–487.
Stölken, J.S. and Evans, A.G., A microbend test method for measuring the plasticity length scale, Acta Materialia, 1998, 46(14): 5109–5115.
Fleck, N.A. and Hutchinson, J.W., A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids, 1993, 41(12): 1825–1857.
Wei, Y.G. and Hutchinson, J.W., Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 1997, 45(8): 1253–1273.
Chen, S.H. and Wang, T.C., Finite element solutions for plane strain mode I crack with strain gradient effects. International Journal of Solids and Structures, 2002, 39(5): 1241–1257.
Fleck, N.A. and Hutchinson, J.W., Strain Gradient Plasticity. Advances in Applied Mechanics, 1997, 33: 295–361.
Nix, W.D. and Gao, H., Indentation size effects in crystalline materials: a law for strain plasticity. Journal of the Mechanics and Physics of Solids, 1998, 46(3): 411–425.
Gao, H., Huang, Y., Nix, W.D. and Hutchinson, J.W., Mechanism-based strain gradient plasticity — I. Theory. Journal of the Mechanics and Physics of Solids, 1999, 47(6): 1239–1263.
Gao, H., Huang, Y., Nix, W.D. and Hutchinson, J.W., Mechanism-based strain gradient plasticity — II. Analysis. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 99–128.
Bažant, Z.P. and Milan, Jirasek., Nonlocal integral formulations of plasticity and damage: survey of progress. Journal of Engineering Mechanics, 2002, 128(11): 1119–1149.
Chen, S.H and Wang, T.C., Strain gradient theory with couple stress for crystalline solids. European Journal of Mechanics A-Solids, 2001, 20(5): 739–756.
Qiu, X.M., Development and Applications of Mechanism Based Strain Gradient Plasticity. Doctor thesis. Beijing: Tsinghua University, 2001 (in Chinese).
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Project supported by the National Natural Science Foundation of China (Nos. 10672165 and 10732050) and KJCX2-YW-M04.
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Yi, D., Wang, T.C. & Chen, S. New strain gradient theory and analysis. Acta Mech. Solida Sin. 22, 45–52 (2009). https://doi.org/10.1016/S0894-9166(09)60089-6
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DOI: https://doi.org/10.1016/S0894-9166(09)60089-6