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

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 9, 2007, Pages 1879-1898

  Ohno, Nobutada ^a   Okumura, Dai ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Crystal plasticity; Dislocations; Elastic plastic material; Metallic material; Strengthening and mechanisms

Indexed keywords

DISLOCATIONS (CRYSTALS); GRAIN SIZE AND SHAPE; PLASTIC FLOW; POLYCRYSTALLINE MATERIALS; POLYCRYSTALS; SHEAR STRESS; VISCOPLASTICITY; YIELD STRESS;

DISLOCATION CELL SIZE; GEOMETRICALLY NECESSARY DISLOCATIONS; POLYCRYSTALLINE METALS; SELF-ENERGY; SLIP GRADIENT;

STRESS ANALYSIS;

EID: 34347396143     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.02.007     Document Type: Article

References (46)

1. Acharya A., and Bassani J.L. Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48 (2000) 1565-1595
2. Aifantis E.C. On the microstructural origin of certain inelastic models. ASME J. Eng. Mater. Technol. 106 (1984) 326-330
3. Anand L., Gurtin M.E., Lele S.P., and Gething C. A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results. J. Mech. Phys. Solids 53 (2005) 1789-1826
4. Ashby M.F. Deformation of plastically non-homogeneous materials. Philos. Mag. 21 (1970) 399-424
5. Bassani J.L. Incompatibility and a simple gradient theory of plasticity. J. Mech. Phys. Solids 49 (2001) 1983-1996
6. Berveiller M., and Zaoui A. An extension of the self-consistent scheme to plastically-flowing polycrystals. J. Mech. Phys. Solids 26 (1979) 325-344
7. 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.
8. Fleck N.A., and Hutchinson J.W. Strain gradient plasticity. Adv. Appl. Mech. 33 (1997) 295-361
9. Fleck N.A., and Hutchinson J.W. A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49 (2001) 2245-2271
10. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42 (1994) 475-487
11. Frederiksson P., and Gudmundson P. Size-dependent yield strength of thin films. Int. J. Plasticity 21 (2005) 1834-1854
12. Frost H.J., and Ashby M.F. Deformation-mechanism Maps (1982), The Plasticity and Creep of Metals and Ceramics. Pergamon, Oxford
13. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids 47 (1999) 1239-1263
14. Gudmundson P. A unified treatment of strain gradient plasticity. J. Mech. Phys. Solids 52 (2004) 1379-1406
15. Gurtin M.E. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48 (2000) 989-1036
16. Gurtin M.E. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50 (2002) 5-32
17. Gurtin M.E., and Anand L. A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: small deformations. J. Mech. Phys. Solids 53 (2005) 1624-1649
18. Gurtin M.E., and Needleman A. Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector. J. Mech. Phys. Solids 53 (2005) 1-31
19. Han C.-S., Gao H., Huang Y., and Nix W.D. Mechanism-based strain gradient crystal plasticity-I. Theory. J. Mech. Phys. Solids 53 (2005) 1188-1203
20. Hirth J.P., and Lothe J. Theory of Dislocations. seond ed. (1982), Wiley, New York
21. Huang J.Y., Zhu Y.T., Jiang H., and Lowe T.C. Microstructures and dislocation configurations in nanostructured Cu processed by repetitive corrugation and straightening. Acta Mater. 49 (2001) 1497-1505
22. Huang Y., Gao H., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity-II. Analysis. J. Mech. Phys. Solids 48 (2000) 99-128
23. Hutchinson J.W. Elastic-plastic behaviour of polycrystalline metals and composites. Proc. R. Soc. London A 319 (1970) 247-272
24. Kashyap B.P., and Tangri K. On the Hall-Petch relationship and substructural evolution in type 316L stainless steel. Acta Metall. Mater. 43 (1995) 3971-3981
25. Kimura, H., 2002. Perspectives on Strengths of Materials, revised ed. AGNE Gijutsu Center, Tokyo (in Japanese).
26. Kröner E. Kontinuumstheorie der versetzungen und eigenspannungen (1958), Springer, Berlin
27. Kröner E. Zur plastischen verformung des vielkristalls. Acta Metall. 9 (1961) 155-161
28. Kuroda M., and Tvergaard V. Studies of scale dependent crystal viscoplasticity models. J. Mech. Phys. Solids 54 (2006) 1789-1810
29. Lin T.H. Analysis of elastic and plastic strains of a face-centered cubic crystal. J. Mech. Phys. Solids 5 (1957) 143-149
30. Lloyd D.J. Deformation of fine-grained aluminum alloys. Metal Sci. 14 (1980) 193-198
31. Menzel A., and Steinmann P. On the continuum formulation of higher gradient plasticity for single and polycrystals. J. Mech. Phys. Solids 48 (2000) 1777-1796
32. Meyers M.A., Mishra A., and Benson D.J. Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51 (2006) 427-556
33. Nicola L., Van der Giessen E., and Gurtin M.E. Effect of defect energy on strain-gradient predictions of confined single-crystal plasticity. J. Mech. Phys. Solids 53 (2005) 1280-1294
34. Nye J.F. Some geometrical relations in dislocated crystals. Acta Metall. 1 (1953) 153-162
35. Ohashi T. Finite-element analysis of plastic slip and evolution of geometrically necessary dislocations in fcc crystals. Philos. Mag. Lett. 75 (1997) 51-57
36. Ohashi T., Kawamukai M., and Zbib H. A multiscale approach for modeling scale-dependent yield stress in polycrystalline metal. Int. J. Plasticity 23 (2007) 897-914
37. Ohno, N., Kametani, R., Okumura, D., 2007. Effect of GND self-energy on yield behavior of thin foils subject to bending, in preparation.
38. 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.
39. {ring operator} C. Acta Metall. 20 (1972) 569-579
40. Takahashi H., Motohashi H., Tokuda M., and Abe T. Elastic-plastic finite element polycrystal model. Int. J. Plasticity 10 (1994) 63-80
41. Taylor G.I. Plastic strain in metals. J. Inst. Met. 62 (1938) 307-324
42. Thompson A.W. Effect of grain size on work hardening in nickel. Acta Metall. 25 (1977) 83-86
43. Thompson A.W., and Baskes M.I. The influence of grain size on the work hardening of face-centered cubic polycrystals. Philos. Mag. 28 (1973) 301-308
44. Tomota Y., Lukas P., Harjo S., Park J.-H., Tsuchida N., and Neov D. In situ neutron diffraction study of IF and ultra low carbon steels upon tensile deformation. Acta Mater. 51 (2003) 819-830
45. Tsuji N., Ito Y., Saito Y., and Minamino Y. Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing. Scr. Mater. 47 (2002) 893-899
46. Yu C.Y., Kao P.W., and Chang C.P. Transition of tensile deformation behaviors in ultrafine-grained aluminum. Acta Mater. 53 (2005) 4019-4028