A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model

International Journal of Plasticity

Volumn 23, Issue 9, 2007, Pages 1540-1554

  Wang, H ^a   Hwang, K C ^a   Huang, Y ^b   Wu, P D ^c   Liu, B ^a   Ravichandran, G ^d   Han, C S ^e   Gao, H ^f  

^a TSINGHUA UNIVERSITY   (China)

^b University of Illinois at Urbana Champaign   (United States)

^c MCMASTER UNIVERSITY   (Canada)

^d CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^e North Dakota State University   (United States)

^f Brown University   (United States)

Author keywords

Constitutive behavior; Crystal plasticity; Strain gradient; Taylor dislocation model

Indexed keywords

DISLOCATIONS (CRYSTALS); HARDENING; MATHEMATICAL MODELS; PLASTIC DEFORMATION; PLASTICITY; STRESS ANALYSIS;

CONSTITUTIVE BEHAVIORS; CRYSTAL PLASTICITY; STRAIN GRADIENTS; TAYLOR DISLOCATION MODELS;

SINGLE CRYSTALS;

EID: 34248637033     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2007.01.004     Document Type: Article

References (35)

1. Abu Al-Rub R.K., and Voyiadjis G.Z. A physically based gradient plasticity theory. International Journal of Plasticity 22 (2006) 654-684
2. Acharya A., and Bassani J.L. Lattice incompatibility and a gradient theory of crystal plasticity. Journal of the Mechanics and Physics of Solids 48 (2000) 1565-1595
3. Arsenlis A., and Parks D.M. Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density. Acta Materialia 47 (1999) 1597-1611
4. Asaro R.J., and Rice J.R. Strain localization in ductile single crystals. Journal of the Mechanics and Physics of Solids 25 (1977) 309-338
5. Ashby M.F. The deformation of plastically non-homogeneous alloys. Philosophical Magazine 21 (1970) 399-424
6. Busso E.P., and Cailletaud G. On the selection of active systems in crystal plasticity. International Journal of Plasticity 21 (2005) 2212-2231
7. Cleveringa H.H.M., van der Giessen E., and Needleman A. Comparison of discrete dislocation and continuum plasticity predictions for a composite material. Acta Materialia 45 (1997) 3163-3179
8. Cleveringa H.H.M., van der Giessen E., and Needleman A. Discrete dislocation simulations and size dependent hardening in single slip. Journal de Physique IV 8 (1998) 83-92
9. Cleveringa H.H.M., van der Giessen E., and Needleman A. A discrete dislocation analysis of bending. International Journal of Plasticity 15 (1999) 837-868
10. Cleveringa H.H.M., van der Giessen E., and Needleman A. A discrete dislocation analysis of residual stresses in a composite material. Philosophical Magazine A 79 (1999) 893-920
11. Gao H., and Huang Y. Geometrically necessary dislocation and size-dependent plasticity. Scripta Materialia 48 (2003) 113-118
12. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity, Part I: theory. Journal of the Mechanics and Physics of Solids 47 (1999) 1239-1263
13. Gurtin M.E. A gradient theory of single-crystal viscoplasticity that account for geometrically necessary dislocations. Journal of the Mechanics and Physics of Solids 50 1 (2002) 5-32
14. Han C.S., Gao H.J., Huang Y., and Nix W.D. Mechanism-based strain gradient crystal plasticity - I. Theory. Journal of the Mechanics and Physics of Solids 53 (2005) 1188-1203
15. Han C.S., Gao H.J., Huang Y., and Nix W.D. Mechanism-based strain gradient crystal plasticity - II. Analysis. Journal of the Mechanics and Physics of Solids 53 (2005) 1204-1222
16. Hill R. Generalized constitutive relations for incremental deformation of metals crystals by multislip. Journal of the Mechanics and Physics of Solids 14 (1966) 95-102
17. Hill R., and Rice J.R. Constitutive analysis of elastic-plastic crystal at arbitrary strain. Journal of the Mechanics and Physics of Solids 20 (1972) 401-413
18. Huang Y., Gao H., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity, Part II: analysis. Journal of the Mechanics and Physics of Solids 48 (2000) 99-128
19. Huang Y., Xue Z., Gao H., Nix W.D., and Xia Z.C. A study of micro-indentation hardness tests by mechanism-based strain gradient plasticity. Journal of Materials Research 15 (2000) 1786-1796
20. Huang Y., Qu S., Hwang K.C., Li M., and Gao H. A conventional theory of mechanism-based strain gradient plasticity. International Journal of Plasticity 20 (2004) 753-782
21. Ma Q., and Clarke D.R. Size-dependent hardness of silver single crystals. Journal of Materials Research 10 (1995) 853-863
22. McElhaney K.W., Vlassak J.J., and Nix W.D. Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. Journal of Materials Research 13 (1998) 1300-1306
23. Menzel A., and Steinmann P. On the continuum formulation of higher gradient plasticity for single and polycrystals. Journal of the Mechanics and Physics of Solids 48 (2000) 1777-1796
24. Nye J. Some geometrical relations in dislocated crystals. Acta Metallurgica et Materialia 1 (1953) 153-162
25. Peirce D., Asaro R.J., and Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Materialia 30 (1982) 1087-1119
26. Qu S., Huang Y., Pharr G.M., and Hwang K.C. The indentation size effect in the spherical indentation of iridium: a study via the conventional theory of mechanism-based strain gradient plasticity. International Journal of Plasticity 22 (2006) 1265-1286
27. Shi M.X., Huang Y., Gao H., and Hwang K.C. Non-existence of separable crack tip field in mechanism-based strain gradient plasticity. International Journal of Solids and Structures 37 (2000) 5995-6010
28. Shi M., Huang Y., Jiang H., Hwang K.C., and Li M. The boundary layer effect on the crack tip field in mechanism-based strain gradient plasticity. International Journal of Fracture 112 (2001) 23-41
29. Shu J.Y., and Fleck N.A. The prediction of a size effect in micro-indentation. International Journal of Solids Structures 35 (1998) 1363-1383
30. Shu J.Y., and Fleck N.A. Strain gradient crystal plasticity: size-dependent deformation of bicrystals. Journal of the Mechanics and Physics of Solids 47 2 (1999) 297-324
31. Smyshlyaev V.P., and Fleck N.A. The role of strain gradients in the grain size effect for polycrystals. Journal of the Mechanics and Physics of Solids 44 4 (1996) 465-495
32. Stelmashenko N.A., Walls M.G., Brown L.M., and Milman Y.V. Microindentations on W and Mo oriented single crystals - an SEM study. Acta Metallurgica et Materialia 41 (1993) 2855-2865
33. Taylor G.I. The mechanism of plastic deformation of crystals, Part I - Theoretical. Proceedings of the Royal Society of London. Series A 145 (1934) 362-387
34. Taylor G.I. Plastic strain in metals. Journal of Institute of Metals 62 (1938) 307-325
35. Taylor G.I. Analysis of plastic strain in a cubic crystal. In: Lessels J.M. (Ed). Stephen Timoshenko 60th Anniversary Volume (1938), Macmillan, New York 218-224