Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations

Acharya, 2000, Lattice incompatibility and a gradient theory of crystal plasticity, J. Mech. Phys. Solids, 48, 1565, 10.1016/S0022-5096(99)00075-7 Aifantis, 1984, On the microstructural origin of certain inelastic models, ASME J. Eng. Mater. Technol., 106, 326, 10.1115/1.3225725 Anand, 2005, A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results, J. Mech. Phys. Solids, 53, 1789, 10.1016/j.jmps.2005.03.003 Ashby, 1970, Deformation of plastically non-homogeneous materials, Philos. Mag., 21, 399, 10.1080/14786437008238426 Bassani, 2001, Incompatibility and a simple gradient theory of plasticity, J. Mech. Phys. Solids, 49, 1983, 10.1016/S0022-5096(01)00037-0 Berveiller, 1979, An extension of the self-consistent scheme to plastically-flowing polycrystals, J. Mech. Phys. Solids, 26, 325, 10.1016/0022-5096(78)90003-0 Budiansky, B., Wu, T.T., 1962. Theoretical prediction of plastic strains of polycrystals. In: Proceedings of the Fourth US National Congress of Applied Mechanics, pp. 1175–1185. Fleck, 1997, Strain gradient plasticity, Adv. Appl. Mech., 33, 295, 10.1016/S0065-2156(08)70388-0 Fleck, 2001, A reformulation of strain gradient plasticity, J. Mech. Phys. Solids, 49, 2245, 10.1016/S0022-5096(01)00049-7 Fleck, 1994, Strain gradient plasticity: theory and experiment, Acta Metall. Mater., 42, 475, 10.1016/0956-7151(94)90502-9 Frederiksson, 2005, Size-dependent yield strength of thin films, Int. J. Plasticity, 21, 1834, 10.1016/j.ijplas.2004.09.005 Frost, 1982 Gao, 1999, Mechanism-based strain gradient plasticity—I, Theory. J. Mech. Phys. Solids, 47, 1239, 10.1016/S0022-5096(98)00103-3 Gudmundson, 2004, A unified treatment of strain gradient plasticity, J. Mech. Phys. Solids, 52, 1379, 10.1016/j.jmps.2003.11.002 Gurtin, 2000, On the plasticity of single crystals: free energy, microforces, plastic-strain gradients, J. Mech. Phys. Solids, 48, 989, 10.1016/S0022-5096(99)00059-9 Gurtin, 2002, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, J. Mech. Phys. Solids, 50, 5, 10.1016/S0022-5096(01)00104-1 Gurtin, 2005, A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: small deformations, J. Mech. Phys. Solids, 53, 1624, 10.1016/j.jmps.2004.12.008 Gurtin, 2005, Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector, J. Mech. Phys. Solids, 53, 1, 10.1016/j.jmps.2004.06.006 Han, 2005, Mechanism-based strain gradient crystal plasticity—I, Theory. J. Mech. Phys. Solids, 53, 1188, 10.1016/j.jmps.2004.08.008 Hirth, 1982 Huang, 2001, Microstructures and dislocation configurations in nanostructured Cu processed by repetitive corrugation and straightening, Acta Mater., 49, 1497, 10.1016/S1359-6454(01)00069-6 Huang, 2000, Mechanism-based strain gradient plasticity—II, Analysis. J. Mech. Phys. Solids, 48, 99, 10.1016/S0022-5096(99)00022-8 Hutchinson, 1970, Elastic–plastic behaviour of polycrystalline metals and composites, Proc. R. Soc. London A, 319, 247, 10.1098/rspa.1970.0177 Kashyap, 1995, On the Hall–Petch relationship and substructural evolution in type 316L stainless steel, Acta Metall. Mater., 43, 3971, 10.1016/0956-7151(95)00110-H Kimura, H., 2002. Perspectives on Strengths of Materials, revised ed. AGNE Gijutsu Center, Tokyo (in Japanese). Kröner, 1958 Kröner, 1961, Zur plastischen verformung des vielkristalls, Acta Metall., 9, 155, 10.1016/0001-6160(61)90060-8 Kuroda, 2006, Studies of scale dependent crystal viscoplasticity models, J. Mech. Phys. Solids, 54, 1789, 10.1016/j.jmps.2006.04.002 Lin, 1957, Analysis of elastic and plastic strains of a face-centered cubic crystal, J. Mech. Phys. Solids, 5, 143, 10.1016/0022-5096(57)90058-3 Lloyd, 1980, Deformation of fine-grained aluminum alloys, Metal Sci., 14, 193, 10.1179/msc.1980.14.5.193 Menzel, 2000, On the continuum formulation of higher gradient plasticity for single and polycrystals, J. Mech. Phys. Solids, 48, 1777, 10.1016/S0022-5096(99)00024-1 Meyers, 2006, Mechanical properties of nanocrystalline materials, Prog. Mater. Sci., 51, 427, 10.1016/j.pmatsci.2005.08.003 Nicola, 2005, Effect of defect energy on strain-gradient predictions of confined single-crystal plasticity, J. Mech. Phys. Solids, 53, 1280, 10.1016/j.jmps.2005.02.001 Nye, 1953, Some geometrical relations in dislocated crystals, Acta Metall., 1, 153, 10.1016/0001-6160(53)90054-6 Ohashi, 1997, Finite-element analysis of plastic slip and evolution of geometrically necessary dislocations in fcc crystals, Philos. Mag. Lett., 75, 51, 10.1080/095008397179741 Ohashi, 2007, A multiscale approach for modeling scale-dependent yield stress in polycrystalline metal, Int. J. Plasticity, 23, 897, 10.1016/j.ijplas.2006.10.002 Ohno, N., Kametani, R., Okumura, D., 2007. Effect of GND self-energy on yield behavior of thin foils subject to bending, in preparation. Okumura, D., Higashi, Y., Sumida, K., Ohno, N., 2007. A homogenization theory of strain gradient single-crystal plasticity and its finite element discretization. Int. J. Plasticity, in print. Staker, 1972, The dislocation cell size and dislocation density in copper deformed at temperatures between 25 and 700∘C, Acta Metall., 20, 569, 10.1016/0001-6160(72)90012-0 Takahashi, 1994, Elastic–plastic finite element polycrystal model, Int. J. Plasticity, 10, 63, 10.1016/0749-6419(94)90054-X Taylor, 1938, Plastic strain in metals, J. Inst. Met., 62, 307 Thompson, 1977, Effect of grain size on work hardening in nickel, Acta Metall., 25, 83, 10.1016/0001-6160(77)90249-8 Thompson, 1973, The influence of grain size on the work hardening of face-centered cubic polycrystals, Philos. Mag., 28, 301, 10.1080/14786437308217454 Tomota, 2003, In situ neutron diffraction study of IF and ultra low carbon steels upon tensile deformation, Acta Mater., 51, 819, 10.1016/S1359-6454(02)00473-1 Tsuji, 2002, Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing, Scr. Mater., 47, 893, 10.1016/S1359-6462(02)00282-8 Yu, 2005, Transition of tensile deformation behaviors in ultrafine-grained aluminum, Acta Mater., 53, 4019, 10.1016/j.actamat.2005.05.005