Plastic deformation of bicrystals within continuum dislocation theory

Mathematics and Mechanics of Solids

Volumn 14, Issue 6, 2009, Pages 540-563

  Kochmann, D M ^a   Le, K C ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Bicrystal; Dislocation; Size effect; Threshold; Work hardening

Indexed keywords

ANALYTICAL SOLUTIONS; DISLOCATION; DISLOCATION NUCLEATION; DISLOCATION THEORY; NUMERICAL SOLUTION; PLANE STRAINS; SIZE EFFECT; SIZE EFFECTS; THRESHOLD; WORK HARDENING;

PLASTIC DEFORMATION; SIZE DETERMINATION; STRAIN HARDENING;

BICRYSTALS;

EID: 68149138322     PISSN: 10812865     EISSN: 17413028     Source Type: Journal    
DOI: 10.1177/1081286507087322     Document Type: Article

References (25)

1. Kondo, K., On the geometrical and physical foundations of the theory of yielding, in Proceedings of the 2nd Japan Congress on Applied Mechanics, pp. 41-47, 1952.
2. Nye, J.F., Some geometrical relations in dislocated crystals. Acta Metallica, 1, 153-162 (1953).
3. Bilby, B.A., Bullough, R. and Smith, E. Continuous distributions of dislocations - a new application of the methods of non-Riemannian geometry. Proceedings of the Royal Society of London A, 231, 263-273 (1955).
4. Kröner, E. Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer, Berlin, 1958.
5. Berdichevsky, V.L. and Sedov, L.I. Dynamic theory of continuously distributed dislocations. Its relation to plasticity theory. Journal of Applied Mathematics and Mechanics (PMM), 31, 989-1006 (1967).
6. Ortiz, M. and Repetto, E.A., Nonconvex energy minimization and dislocation structures in ductile single crystals. Journal of Mechanics and Physics of Solids, 47, 397-462 (1999).
7. Berdichevsky, V.L., Continuum theory of dislocations revisited. Continuum Mechanics and Thermodynamics, 18, 195-222 (2006).
8. Berdichevsky, V.L. Homogenization in micro-plasticity. Journal of Mechanics and Physics of Solids, 53, 2457-2469 (2005).
9. Berdichevsky, V.L. On thermodynamics of crystal plasticity. Scripta Materiala, 54, 711-716 (2006).
10. Shu, J.Y. and Fleck, N.A. Strain gradient crystal plasticity: size-dependent deformation of bicrystals. Journal of Mechanics and Physics of Solids, 47, 297-324 (1999).
11. Gao H., Huang Y., Nix W. D. and Hutchinson J. W. Mechanism-based strain gradient plasticity-I. Theory. Journal of Mechanics and Physics of Solids, 47, 1239-1263 (1999)
12. Acharya, A. and Bassani, J.L. Lattice incompatibility and a gradient theory of crystal plasticity. Journal of Mechanics and Physics of Solids, 48, 1565-1595 (2000).
13. Huang, Y., Hwang, Q.S., Li, K.C. and Gao, H. A conventional theory of mechanism-based strain gradient plasticity. International Journal of Plasticity, 20, 753-782 (2004).
14. Huang Y., Gao H., Nix W. D. and Hutchinson J. W. Mechanism-based strain gradient plasticity-II. Analysis. Journal of Mechanics and Physics of Solids, 48, 99-128 (2000)
15. Fleck, N.A. and Hutchinson, J.W. A reformulation of strain-gradient plasticity. Journal of Mechanics and Physics of Solids, 49, 2245-2271 (2001).
16. Han C.S., Gao H.J., Huang Y.G. and Nix W.D. Mechanism-based strain gradient crystal plasticity-I. Theory. Journal of Mechanics and Physics of Solids, 53, 1188-1203 (2005).
17. Han C.S., Gao H.J., Huang Y.G. and Nix W.D. Mechanism-based strain gradient crystal plasticity-II. Analysis. Journal of Mechanics and Physics of Solids, 53, 1204-1222 (2005).
18. Aifantis, K.E. and Willis, J.R. The role of interfaces in enhancing the yield strength of composites and polycrystals. Journal of Mechanics and Physics of Solids, 53, 1047-1070 (2005).
19. Aifantis, K.E., Soer, W.A., De Hosson J.T.M. and Willis, J.R. Interfaces within strain gradient plasticity: Theory and experiments. Acta Materiala, 54, 5077-5085 (2006).
20. Berdichevsky, V.L. and Le, K.C. Dislocation nucleation and work hardening in anti-planed constrained shear. Continuum Mechanics and Thermodynamics, 18, 455-467 (2007).
21. Le, K.C. and Sembiring, P. Analytical solution of plane constrained shear problem for single crystals within continuum dislocation theory. Archives on Applied Mechanics, in press (DOI 10.1007/s00419-007-0178-1).
22. Needleman, A. and Van der Giessen, E. Discrete dislocation and continuum descriptions of plastic flow. Material Science and Engineering, A309, 1-13 (2001).
23. Shu, J.Y., Fleck, N.A., Van der Giessen, E., Needleman, A., Boundary layers in constrained plastic flow: Comparison of nonlocal and discrete dislocation plasticity. Journal of Mechanics and Physics of Solids, 49, 1361-1395 (2001).
24. Allain, S., Chateau, J.P., Bouaziz, O., A physical model of the twinning-induced plasticity effect in a high manganese austenitic steel. Material Science and Engineering, A387, 143-147 (2004).
25. Le, K.C. and Sembiring, P. Plane constrained shear of single crystals with two active slip systems. Journal of the Mechanics and Physics of Solids, 56, 2541-2554.