A continuum model for initiation and evolution of deformation twinning

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 6, 2009, Pages 987-1002

  Kochmann, Dennis M ^a   Le, Khanh C ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

A. Dislocations; A. Microstructures; A. Twinning; B. Crystal plasticity; C. Energy methods

Indexed keywords

A. DISLOCATIONS; A. MICROSTRUCTURES; A. TWINNING; B. CRYSTAL PLASTICITY; C. ENERGY METHODS;

CONTINUUM MECHANICS; DEFORMATION; MICROSTRUCTURE; PLASTICITY; REAL TIME SYSTEMS; SINGLE CRYSTALS; STRAIN; TITRATION;

DISLOCATIONS (CRYSTALS);

EID: 65049083605     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2009.03.001     Document Type: Article

References (62)

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 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
3. 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
4. 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
5. Ashby M.F. The deformation of plastically non-homogeneous materials. Philos. Mag. 21 (1970) 399-424
6. Baihe M., Keming F., and Weimin B. On the microstructure of graphite spherulites in cast irons by TEM and HREM. Acta Metall. Mater. 38 (1990) 2167-2174
7. Ball J.M., and James R.D. Fine phase mixtures as minimizers of energy. Arch. Ration. Mech. Anal. 100 (1987) 13-52
8. Bhattacharya K. Microstructure of Martensite (2003), Oxford University Press, Oxford
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. Botta W.J., Christian J.W., and Taylor G. Solution hardening and softening of Nb-Zr single-crystals. Philos. Mag. 57 (1988) 703-716
16. Bullough R. Deformation twinning in the diamond structure. Proc. R. Soc. London A 241 (1957) 568-577
17. Cahn R.W. Twinned crystals. Adv. Phys. 3 (1954) 363-445
18. Carstensen C., Hackl K., and Mielke A. Non-convex potentials and microstructures in finite-strain plasticity. Proc. R. Soc. London A 458 (2002) 299-317
19. Christian J.W., and Mahajan S. Deformation twinning. Progr. Mater. Sci. 39 (1995) 1-157
20. Cohen J.B., and Weertman J. A dislocation model for twinning in f.c.c. metals. Acta Metall. 11 (1963) 996
21. Ericksen J.L. Equilibrium of bars. J. Elasticity 5 (1975) 191-201
22. Farrell K., and Evans P.R.V. Some observations of mechanical twinning in polycrystalline Niobium. J. Less Common Met. 8 (1965) 222
23. Fleck N.A., and Hutchinson J.W. A reformulation of strain-gradient plasticity. J. Mech. Phys. Solids 49 (2001) 2245-2271
24. Frenkel J., and Kontorova T. On the theory of plastic deformation and twinning. Acad. Sci. USSR J. Phys. 1 (1939) 137-149
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. Gelfand I.M., and Fomin S.V. Calculus of Variations (2000), Dover Publications, New York
27. 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
28. Groma I., Györgyi G., and Kocsis B. Dynamics of coarse grained dislocation densities from an effective free energy. Philos. Mag. 87 8-9 (2007) 1185-1199
29. Hall E.O. Twinning (1954), Butterworths, London
30. 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
31. 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
32. Hirth, J.P., 1964. In: Reed-Hill, R.E., Hirth, J.P., Rogers, H.C. (Eds.), Deformation Twinning. Gordon & Breach, New York.
33. Hirth J.P., and Lothe J. Theory of Dislocations. second ed (1982), Krieger Publishing Company, Malabar, FL
34. Hochrainer, T., Zaiser, M., 2005. Fundamentals of a continuum theory of dislocations. In: SMPRI 2005.
35. 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
36. 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
37. Kaschner G.C., Tomé C.N., Beyerlein I.J., et al. Role of twinning in the hardening response of zirconium during temperature reloads. Acta Mater. 54 (2006) 2887-2896
38. Kaschner G.C., Tomé C.N., McCabe R.J., et al. Exploring the dislocation/twin interactions in zirconium. Mater. Sci. Eng. A 463 (2007) 122-127
39. Kochmann, D.M., Le, K.C., 2008a. Plastic deformation of bicrystals within continuum dislocation theory. J. Math. Mech. Solids, pre-published online 11 March 2008 (doi: 10.1177/1081286507087322).
40. Kochmann D.M., and Le K.C. Dislocation pile-ups in bicrystals within continuum dislocation theory. Int. J. Plasticity 24 (2008) 2125-2147
41. Kondo, K., 1952. On the geometrical and physical foundations of the theory of yielding. In: Proceedings of the 2nd Japan Congress of Applied Mechanics, pp. 41-47.
42. Kröner E. Kontinuumstheorie der Versetzungen und Eigenspannungen (1958), Springer, Berlin
43. Le K.C., and Berdichevsky V.L. Energy distribution in a neutral gas of point vortices. J. Stat. Phys. 104 3-4 (2001) 883-894
44. Le K.C., and Sembiring P. Plane constrained shear of single crystals within continuum dislocation theory. Arch. Appl. Mech. 78 (2008) 587-597
45. Le K.C., and Sembiring P. Plane-constrained shear of a single crystal strip with two active slip-systems. J. Mech. Phys. Solids 56 (2008) 2541-2554
46. Le K.C., and Stumpf H. A model of elastoplastic bodies with continuously distributed dislocations. Int. J. Plasticity 12 (1996) 611-627
47. Le K.C., and Stumpf H. On the determination of the crystal reference in nonlinear continuum theory of dislocations. Proc. R. Soc. London A 452 (1996) 359-371
48. Mahajan S. Nucleation and growth of deformation twins in Mo-35 at-percent Re alloy. Philos. Mag. 26 (1972) 161
49. Mahajan S. Interrelationship between slip and twinning in bcc crystals. Acta Metall. 23 (1975) 671-684
50. Meyers M.A., Vohringer O., and Lubarda V.A. The onset of twinning in metals: a constitutive description. Acta Mater. 49 (2001) 4025-4039
51. Narita N., and Takamura J.-I. Deformation twinning in f.c.c. and b.c.c. metals. In: Nabarro F.R.N. (Ed). Dislocations in Solids vol. 9 (1992), North-Holland, Amsterdam 135-190
52. Needleman A., and Van der Giessen E. Discrete dislocation and continuum descriptions of plastic flow. Mater. Sci. Eng. A 309-310 (2001) 1-13
53. Nye J.F. Some geometrical relations in dislocated crystals. Acta Metall. 1 (1953) 153-162
54. Ortiz M., and Repetto E.A. Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47 (1999) 397-462
55. Ortiz M., Repetto E.A., and Stainier L. A theory of subgrain dislocation structures. J. Mech. Phys. Solids 48 (2000) 2077-2114
56. Proust, G., Tomé, C.N., Jain, A., Agnew, S.R., 2009. Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31. Int. J. Plasticity 25, 861-880.
57. Reed-Hill R.E., and Abbashian R. Physical Metallurgy Principles. third ed (1994), PWS Publishing Company, Boston
58. Sedov L.I. Variational methods of constructing models of continuous media. Irreversible Aspects of Continuum Mechanics (1968), Springer, Wien, New York
59. 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
60. Skaland T., Grong O., and Grong T. A model for the graphite formation in ductile cast-iron solid state transformation reactions. Metall. Trans. A 24 (1993) 2347-2353
61. Siedersleben M.E., and Taylor G. Slip systems in bcc Li-Mg alloys. Philos. Mag. 60 (1989) 631-647
62. Venables, J.A., 1964. In: Reed-Hill, R.E., Hirth, J.P., Rogers, H.C. (Eds.), Deformation Twinning. Gordon & Breach, New York.