Strain gradient crystal plasticity effects on flow localization

International Journal of Plasticity

Volumn 23, Issue 8, 2007, Pages 1400-1416

  Borg, Ulrik ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Crystal plasticity; Shear band; Strain gradient plasticity

Indexed keywords

FINITE ELEMENT METHOD; GRADIENT METHODS; PLASTIC FLOW; PLASTICITY; SHEAR BANDS; SINGLE CRYSTALS; STRAIN MEASUREMENT;

CRYSTAL PLASTICITY; STRAIN GRADIENT PLASTICITY; STRAIN TENSIONS;

CRYSTAL MICROSTRUCTURE;

EID: 34247474852     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2007.01.003     Document Type: Article

References (29)

1. Abu Al-Rub R.K., and Voyiadjis G.Z. A physically based gradient plasticity theory. Int. J. Plast. 22 (2006) 654-684
2. Acharya A., and Bassani J.L. Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48 (2000) 1565-1595
3. Aifantis E.C. On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol. 106 (1984) 326-330
4. Ashby M.F. The deformation of plastically non-homogeous alloys. Philos. Mag. 21 (1970) 399-424
5. Borg U., Niordson C.F., Fleck N.A., and Tvergaard V. A viscoplastic strain gradient analysis of materials with voids or inclusions. Int. J. Solids Struct. 43 (2006) 4906-4916
6. Cheong K.S., Busso E.P., and Arsenlis A. A study of microstructural length scale effects on the behavior of fcc polycrystals using strain gradient concepts. Int. J. Plast. 21 (2005) 1797-1814
7. Fleck N.A., and Hutchinson J.W. Strain gradient plasticity. In: Hutchinson J.W., and Wu T.Y. (Eds). Advances in Applied Mechanics vol. 33 (1997), Academic Press, New York 295-361
8. Fleck N.A., and Hutchinson J.W. A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49 (2001) 2245-2271
9. 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
10. 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
11. Gudmundson P. A unified treatment of strain gradient plasticity. J. Mech. Phys. Solids 52 (2004) 1379-1406
12. Gurtin M.E. On the plasticity of single crystals: free energy, microforces, plastic strain gradients. J. Mech. Phys. Solids 48 (2000) 989-1036
13. Gurtin M.E. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50 (2002) 5-32
14. 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
15. 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
16. Han C.-S., Gao H., Huang Y., and Nix W.D. Mechanism-based strain gradient crystal plasticity - II: analysis. J. Mech. Phys. Solids 53 (2005) 1204-1222
17. Haque M.A., and Saif M.T.A. Strain gradient effect in nanoscale thin films. Acta Mater. 51 (2003) 3053-3061
18. Mikkelsen L.P. Necking in rectangular tensile bars approximated by a 2-d gradient dependent plasticity model. Eur. J. Mech. A/Solids 18 (1999) 805-818
19. Niordson C.F., and Redanz P. Size-effects in plane strain sheet-necking. J. Mech. Phys. Solids 52 (2004) 2431-2454
20. Niordson C.F., and Tvergaard V. Instabilities in power law gradient hardening materials. Int. J. Solids Struct. 42 (2005) 2559-2573
21. Nye J.F. Some geometrical relations in dislocated crystals. Acta Metall. 1 (1953) 153-162
22. Peirce D., Asaro R.J., and Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall. 30 (1982) 1087-1119
23. Peirce D., Asaro R.J., and Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metall. 31 (1983) 1951-1976
24. Rice J. Tensile crack tip fields in elastic-ideally plastic crystals. Mech. Mater. 6 (1987) 317-335
25. Shu J.Y., and Barlow C.Y. Strain gradient effects on microscopic strain field in a metal matrix composite. Int. J. Plast. 16 (2000) 563-591
26. Shu J.Y., and Fleck N.A. Strain gradient crystal plasticity: size-dependent deformation of bicrystals. J. Mech. Phys. Solids 47 (1999) 297-324
27. Sluys L.J., and Estrin Y. The analysis of shear banding with a dislocation based gradient plasticity model. Int. J. Solids Structures 37 (2000) 7127-7142
28. Stölken J.S., and Evans A.G. Microbend test method for measuring the plasticity length scale. Acta Mater. 46 (1998) 5109-5115
29. Tvergaard V., and Needleman A. Effects of nonlocal damage in porous plastic solids. Int. J. Solids Struct. 32 (1995) 1063-1077