Dislocation pile-ups in bicrystals within continuum dislocation theory

International Journal of Plasticity

Volumn 24, Issue 11, 2008, Pages 2125-2147

  Kochmann, D M ^a   Le, K C ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

A. Dislocations; A. Microstructures; A. Twinning; B. Crystal plasticity; Bicrystal

Indexed keywords

ALLOYS; BICRYSTALS; DEFORMATION; EPITAXIAL GROWTH; INTERNET PROTOCOLS; NUCLEATION; PHASE BOUNDARIES; PILES; PLASTICS; POWDERS; SEDIMENTATION; SINGLE CRYSTALS; SOLUTIONS; STRAIN HARDENING;

ANALYTICAL SOLUTIONS; BAUSCHINGER EFFECT (BE); BI CRYSTALS; CRYSTAL PLASTICITY (CP); DISLOCATION (MOBILITY); DISLOCATION NETWORK (DN); DISLOCATION NUCLEATION; DISLOCATION THEORY; EVOLUTION (CO); GENERAL SOLUTIONS; PILE UPS; PILE-UPS; PLASTIC DISTORTIONS; SIZE EFFECTS; SLIP PLANES; SLIP SYSTEMS; UNI-AXIAL EXTENSION; WORK-HARDENING;

DISLOCATIONS (CRYSTALS);

EID: 48749114897     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2008.03.007     Document Type: Article

References (57)

1. Acharya A., and Bassani J.L. Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48 (2001) 1565-1595
2. Aifantis E.C. The physics of plastic deformation. Int. J. Plasticity 3 (1987) 211-247
3. Aifantis K.E., Soer W.A., De Hosson J.T.M., and Willis J.R. Interfaces within strain-gradient plasticity: theory and experiments. Acta Mater. 54 (2006) 5077-5085
4. Aifantis K.E., and Willis J.R. The role of interfaces in enhancing the yield strength of composites and polycrystals. J. Mech. Phys. Solids 53 (2005) 1047-1070
5. Allain K.E., Chateau J.P., and Bouaziz O. A physical model of the twinning-induced plasticity effect in a high manganese austenitic steel. Mater. Sci. Eng. A 387 (2004) 143-147
6. Ashby M.F. The deformation of plastically non-homogeneous materials. Philos. Mag. 21 (1970) 399-424
7. Ashmawi W.M., and Zikry M.A. Prediction of grain-boundary interfacial mechanisms in polycrystalline materials. J. Eng. Mater. Technol.: Trans. ASME 124 (2002) 88-96
8. Ball J.M., and James R.D. Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100 (1987) 13-52
9. Bilby B.A., Bullough R., and Smith E. Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proc. R. Soc. A 231 (1955) 263-273
10. Berdichevsky V.L. Homogenization in micro-plasticity. J. Mech. Phys. Solids 53 (2005) 2457-2469
11. Berdichevsky V.L. On thermodynamics of crystal plasticity. Scripta Mater. 54 (2006) 711-716
12. Berdichevsky V.L. Continuum theory of dislocations revisited. Cont. Mech. Thermodyn. 18 (2006) 195-222
13. Berdichevsky V.L., and Le K.C. Dislocation nucleation and work hardening in anti-planed constrained shear. Cont. Mech. Thermodyn. 18 (2007) 455-467
14. Berdichevsky V.L., and Sedov L.I. Dynamic theory of continuously distributed dislocations. Its relation to plasticity theory. J. Appl. Math. Mech. (PMM) 31 (1967) 989-1006
15. Capolungo L., Spearot D.E., Cherkaoui M., et al. Dislocation nucleation from bicrystal interfaces and grain boundary ledges: relationship to nanocrystalline deformation. J. Mech. Phys. Solids 55 (2007) 2300-2327
16. Carstensen C., Hackl K., and Mielke A. Non-convex potentials and microstructures in finite-strain plasticity. Proc. R. Soc. Lond. A 458 (2002) 299-317
17. Clayton J.D., McDowell D.L., and Bammann D.J. Modeling dislocations and disclinations with finite micropolar elastoplasticity. Int. J. Plasticity 22 (2006) 210-256
18. Cosserat E., and Cosserat F. Théorie Des Corps Déformables (1909), Hermann, Paris
19. Dillon O.W., and Perzyna P. A gradient theory of materials with memory and internal changes. Arch. Mech. 24 (1972) 727-747
20. Ericksen J.L. Equilibrium of bars. J. Elasticity 5 (1975) 191-201
21. Eringen A.C. Nonlocal polar elastic continua. Int. J. Eng. Sci. 10 (1972) 1-16
22. Evers L.P., Parks D.M., Brekelmans W.A.M., and Geers M.G.D. Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation. J. Mech. Phys. Solids 50 (2002) 2403-2424
23. Fleck N.A., and Hutchinson J.W. A reformulation of strain-gradient plasticity. J. Mech. Phys. Solids 49 (2001) 2245-2271
24. Fox N. On the continuum theory of dislocations and plasticity. Quart. J. Mech. Appl. Math. 21 (1968) 67-75
25. 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
26. Govindjee S., Mielke A., and Hall G.J. The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis. J. Mech. Phys. Solids 51 (2003) 1-26
27. Green A.E., and Rivlin R.S. Simple forces and stress multipoles. Arch. Rat. Mech. Anal. 16 (1964) 325-353
28. Groma I., Csikor F.E., and Zaiser M. Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51 (2003) 1271-1281
29. Gurtin M.E. On a framework for small-deformation viscoplasticity: free energy, microforces, strain gradients. Int. J. Plasticity 19 (2003) 47-90
30. Gurtin M.E., and Anand L. A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part II: Finite deformations. Int. J. Plasticity 21 (2005) 2297-2318
31. Gurtin M.E., Anand L., and Suvrat P.L. Gradient single-crystal plasticity with free energy dependent on dislocation densities. J. Mech. Phys. Solids 55 (2007) 1853-1878
32. Han C.S., Gao H.J., Huang Y.G., and Nix W.D. Mechanism-based strain gradient crystal plasticity. I: Theory. J. Mech. Phys. Solids 53 (2005) 1188-1203
33. Han C.S., Gao H.J., Huang Y.G., and Nix W.D. Mechanism-based strain gradient crystal plasticity. II: Analysis. J. Mech. Phys. Solids 53 (2005) 1204-1222
34. Hirth J.P., and Lothe J. Theory of Dislocations. second ed. (1982), Krieger Publishing Company, Malabar, FL
35. Hochrainer, T., Zaiser, M., 2005. Fundamentals of a continuum theory of dislocations. In: SMPRI 2005.
36. Huang Y., Hwang Q.S., Li K.C., and Gao H. A conventional theory of mechanism-based strain gradient plasticity. J. Mech. Phys. Solids 20 (2004) 753-782
37. 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
38. Kochmann, D.M., Le, K.C., in press. Plastic deformation of bicrystals within continuum dislocation theory. J. Math. Mech. Solids. doi:10.1177/1081286507087322.
39. Kondo, K., 1952. On the geometrical and physical foundations of the theory of yielding. In: Proceedings of the Second Japan Congr. Appl. Mech., pp. 41-47.
40. Kröner E. Kontinuumstheorie der Versetzungen und Eigenspannungen (1958), Springer, Berlin
41. Kuroda M., and Tvergaard V. Studies of scale dependent crystal viscoplasticity models. J. Mech. Phys. Solids 54 (2006) 1789-1810
42. Lardner R.W. Dislocation dynamics and the theory of the plasticity of single crystals. Z. Angew. Math. Phys. 20 (1969) 514-529
43. Le, K.C., Sembiring, P., in press. Plane constrained shear of single crystals within continuum dislocation theory. Arch. Appl. Mech. doi:10.1007/s00419-007-0187-1.
44. Le, K.C., Sembiring, P., accepted for publication. Plane-constrained shear of a single crystal strip with two active slip-systems. J. Mech. Phys. Solids.
45. Louchet F., Weiss J., and Richeton T. Hall-Petch law revisited in terms of collective dislocation dynamics. Phys. Rev. Lett. 97 7 (2006)
46. Needleman A., and Van der Giessen E. Discrete dislocation and continuum descriptions of plastic flow. Mater. Sci. Eng. A (2001) 1-13
47. Nye J.F. Some geometrical relations in dislocated crystals. Acta Metall. 1 (1953) 153-162
48. Ortiz M., and Repetto E.A. Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47 (1999) 397-462
49. Ortiz M., Repetto E.A., and Stainier L. A theory of subgrain dislocation structures. J. Mech. Phys. Solids 48 (2000) 2077-2114
50. Shu J.Y., and Fleck N.A. Strain gradient crystal plasticity: size-dependent deformation of bicrystals. J. Mech. Phys. Solids 47 (1999) 297-324
51. Shu J.Y., Fleck N.A., Van der Giessen E., and Needleman A. Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity. J. Mech. Phys. Solids 49 (2001) 1361-1395
52. Spearot D.E., Jacob K.I., and McDowell D.L. Dislocation nucleation from bicrystal interfaces with dissociated structure. Int. J. Plasticity 23 (2007) 143-160
53. Spearot D.E., Tschopp M.A., Jacob K.I., and McDowell D.L. Tensile strength of 〈 1 0 0 〉 and 〈 1 1 0 〉 tilt bicrystal copper interfaces. Acta Mater. 55 (2007) 705-714
54. Teodosiu, C., 1969. A dynamic theory of dislocations and its application to the theory of elastic-plastic continuum. Fundamental Aspects of Dislocation Theory. NBS Special Publication 317. US Government Printing Office, Gaithersburg, pp. 837-876.
55. Truesdell C., and Toupin R.A. The classical field theories. Handbuch, der Physik, Band III/I (1960), Springer, Berlin
56. Tschopp M.A., Tucker G.J., and McDowell D.L. Structure and free volume of 〈 1 1 0 〉 symmetric tilt grain boundaries with the E structural unit. Acta Mater. 55 (2007) 3959-3969
57. Volokh K.Y., and Trapper P. A simple theory of strain gradient plasticity based on stress-induced anisotropy of defect diffusion. Int. J. Plasticity 23 (2007) 2085-2114