Mechanism-based strain gradient crystal plasticity—I. Theory

Journal of the Mechanics and Physics of Solids - Tập 53 - Trang 1188-1203 - 2005
Chung-Souk Han1,2, Huajian Gao1, Yonggang Huang3, William D. Nix4
1Max Planck Institute for Metals Research, Heisenbergstr. 3, D-70569 Stuttgart, Germany
2Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
3Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801, USA
4Department of Materials Science and Engineering, , Stanford University, Stanford, CA, 94305, USA

Tài liệu tham khảo

Acharya, 2000, Lattice incompatibility and a gradient theory of crystal plasticity, J. Mech. Phys. Solids, 48, 1565, 10.1016/S0022-5096(99)00075-7 Acharya, 2003, Geometrically necessary dislocations, hardening, and a simple gradient theory of crystal plasticity, Scripta Mater., 48, 167, 10.1016/S1359-6462(02)00337-8 Aifantis, 1987, The physics of plastic deformation, Int. J. Plasticity, 3, 211, 10.1016/0749-6419(87)90021-0 Anand, 1996, A computational procedure for rate-independent crystal plasticity, J. Mech. Phys. Solids, 44, 525, 10.1016/0022-5096(96)00001-4 Arsenlis, 1999, Crystallographic aspects of geometrically necessary and statistically stored dislocation density, Acta Mater., 47, 1597, 10.1016/S1359-6454(99)00020-8 Arsenlis, 2003, Simulation on the growth of dislocation density during stage 0 deformation in BCC metals, Model. Simul. Mater. Sci. Eng., 11, 251, 10.1088/0965-0393/11/2/309 Cermelli, 2001, On the characterization of geometrically necessary dislocations in finite plasticity, J. Mech. Phys. Solids, 49, 1539, 10.1016/S0022-5096(00)00084-3 Cermelli, 2002, Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations, Int. J. Solids Struct., 39, 6281, 10.1016/S0020-7683(02)00491-2 Cleveringa, 1997, A discrete dislocation analysis of bending, Int. J. Plasticity, 15, 837, 10.1016/S0749-6419(99)00013-3 Courtney, 1990 Cuitino, 1992, Computational modelling of single crystals, Model. Simul. Mater. Sci. Eng., 1, 225, 10.1088/0965-0393/1/3/001 Evers, 2002, Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation, J. Mech. Phys. Solids, 50, 2403, 10.1016/S0022-5096(02)00032-7 Fleck, 1994, Strain gradient plasticity, Acta Metall. Mater., 42, 475, 10.1016/0956-7151(94)90502-9 Gao, 2001, Taylor-based nonlocal theory of plasticity, Int. J. Solids Struct., 38, 2615, 10.1016/S0020-7683(00)00173-6 Gao, 1999, Mechanism-based strain gradient plasticity—I. Theory, J. Mech. Phys. Solids, 47, 1239, 10.1016/S0022-5096(98)00103-3 Groma, 1997, Link between the microscopic and mesoscopic length-scale description of the collective behavior of dislocations, Phys. Rev. B, 56, 5807, 10.1103/PhysRevB.56.5807 Groma, 2003, Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater., 51, 1271, 10.1016/S1359-6454(02)00517-7 Guo, 2001, Taylor-based nonlocal theory of plasticity, Int. J. Solids Struct., 38, 7447, 10.1016/S0020-7683(01)00047-6 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 Han, C.-S., Gao, H., Huang, Y., Nix, W.D., 2004a. Mechanism-based strain gradient crystal plasticity—II. Analysis, submitted for publication. Han, 2004, On precipitate induced hardening in crystal plasticity, Int. J. Plasticity, 20, 1441, 10.1016/j.ijplas.2003.11.002 Hansen, 2001, Microstructural evolution and hardening parameters, Mater. Sci. Eng. A, 317, 3, 10.1016/S0921-5093(01)01191-1 Hirth, 1982 Huang, 2000, Mechanism-based strain gradient plasticity—II, Analysis. J. Mech. Phys. Solids, 48, 99, 10.1016/S0022-5096(99)00022-8 Huang, 2000, A study of microindentation hardness tests by mechanism-based strain gradient plasticity, J. Mater. Res., 15, 1786, 10.1557/JMR.2000.0258 Huang, 2004, A conventional theory of mechanism-based strain gradient plasticity, Int. J. Plasticity, 20, 753, 10.1016/j.ijplas.2003.08.002 Hull, 1984 Hwang, 2002, A finite deformation theory of strain gradient plasticity, J. Mech. Phys. Solids, 50, 81, 10.1016/S0022-5096(01)00020-5 Hwang, 2003, Finite deformation analysis of mechanism-based strain gradient plasticity, Int. J. Plasticity, 19, 235, 10.1016/S0749-6419(01)00039-0 Kalidindi, 1992, Approximate procedure for predicting the evolution of crystallographic texture in bulk deformation processing of fcc metals, Int. J. Mech. Sci., 34, 309, 10.1016/0020-7403(92)90038-I Kok, 2002, A polycrystal plasticity model based on the mechanical threshold, Int. J. Plasticity, 18, 715, 10.1016/S0749-6419(01)00051-1 Kok, 2002, A finite element model for the Portevin–Le Chatelier effect based on polycrystal plasticity, Model. Simul. Mater. Sci. Eng., 10, 745, 10.1088/0965-0393/10/6/309 Kondo, 1952, On the geometrical and physical foundations of the theory of yielding, Proc. Jpn. Natl. Congr. Appl. Mech., 2, 41 Kröner, 1958, Der fundamentale Zusammenhang zwischen Versetzungsdichte und Spannungsfunktionen, Z. Phys., 142, 463, 10.1007/BF01375082 Ma, 1995, Size dependent hardness of silver single crystals, J. Mater. Res., 10, 853, 10.1557/JMR.1995.0853 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 Miehe, 2001, A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity, Int. J. Numer. Meth. Eng., 50, 273, 10.1002/1097-0207(20010120)50:2<273::AID-NME17>3.0.CO;2-Q Mott, 1952, A theory of work-hardening of metal crystals, Philos. Mag., 43, 1151, 10.1080/14786441108521024 Mura, 1987 Nix, 1998, Indentation size effects in crystalline materials, J. Mech. Phys. Solids, 46, 411, 10.1016/S0022-5096(97)00086-0 Nye, 1953, Some geometrical relations in dislocated solids, Acta Metall., 1, 153, 10.1016/0001-6160(53)90054-6 Oldroyd, 1950, On the formulation of rheological equations of state, Proc. R. Soc. London, 200A, 523, 10.1098/rspa.1950.0035 Regueiro, 2002, A nonlocal phenomenological anisotropic finite deformation plasticity model accounting for dislocation defects, J. Eng. Mater. Technol., 124, 380, 10.1115/1.1480410 Shi, 2000, Non-existence of separable crack tip field in mechanism-based strain gradient plasticity, Int. J. Solids Struct., 37, 5995, 10.1016/S0020-7683(99)00217-6 Shizawa, 1999, A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I, Int. J. Plasticity, 15, 899, 10.1016/S0749-6419(99)00018-2 Shizawa, 2001, A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors, Mater. Sci. Eng. A, 309, 416, 10.1016/S0921-5093(00)01630-0 Shu, 1998, The prediction of a size effect in micro-indentation, Int. J. Solids Struct., 35, 1363, 10.1016/S0020-7683(97)00112-1 Smyshlyaev, 1996, The role of strain gradients in the grain size effect for polycrystals, J. Mech. Phys. Solids, 44, 465, 10.1016/0022-5096(96)00009-9 Stainier, 2002, A micromechanical model of hardening, rate sensitivity and thermal softening, J. Mech. Phys. Solids, 50, 1511, 10.1016/S0022-5096(01)00114-4 Steinmann, 1996, Views on multiplicative elastoplasticity and the continuum theory of dislocations, Int. J. Eng. Sci., 34, 1717, 10.1016/S0020-7225(96)00062-6 Stölken, 1998, A microbend test method for measuring the plasticity length scale, Acta Metall., 46, 5109 Taylor, 1934, The Mechanism of Plastic Deformation of Crystals. Part I. Theoretical, Proc. R. Soc. London A, 145, 362, 10.1098/rspa.1934.0106 Teodosiu, 1982 Van der Giessen, 1995, Discrete dislocation plasticity, Model. Simul. Mater. Sci. Eng., 3, 689, 10.1088/0965-0393/3/5/008 Wood, 1971 Yefimov, 2001, Comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations, J. Phys. IV, 11, 103, 10.1051/jp4:2001513 Zhou, 1993, A modified model for simulating latent hardening during the plastic deformation of rate-dependent fcc polycrystals, Int. J. Plasticity, 9, 961, 10.1016/0749-6419(93)90061-T