A binary-tree based model for rate-independent polycrystals

International Journal of Plasticity

Volumn 26, Issue 1, 2010, Pages 42-64

  Mahesh, Sivasambu ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Binary tree; Crystal plasticity; Numerical algorithms; Texture modeling

Indexed keywords

CAUCHY STRESS; COPPER POLYCRYSTALS; CRYSTAL PLASTICITY; DEVIATORIC PART; EXPERIMENTAL DATA; GOVERNING EQUATIONS; LINEAR COMBINATIONS; LINEAR CONSTRAINTS; LINEAR PROGRAMS; MACROSCOPIC RESPONSE; MECHANICAL RESPONSE; NUMERICAL ALGORITHMS; OBJECTIVE FUNCTIONS; PLANAR INTERFACE; PLANE STRAIN COMPRESSION; PLANE-STRAIN; POLYCRYSTALLINE AGGREGATES; TEXTURE MODELING;

BINARY TREES; DEFORMATION; LAGRANGE MULTIPLIERS; LARGE SCALE SYSTEMS; PLASTICITY; POLYCRYSTALS; SIMULATORS; TEXTURES;

AGGREGATES;

EID: 70350714180     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2009.05.002     Document Type: Article

References (80)

1. Aernoudt, E., Van Houtte, P., Leffers, T., 1993. Plastic deformation and fracture of materials. In: Materials Science and Technology: A Comprehensive Treatment, vol. 6, VCH, New Yorek, pp. 89-136 (Chapter: Deformation and Textures of Metals at Large Strains).
2. Amirkhizi A.V., and Nemat-Nasser S. A framework for numerical integration of crystal elasto-plastic constitutive equations compatible with explicit finite element codes. Int. J. Plasticity 23 10-11 (2007) 1918-1937
3. Arsenlis A., Barton N.R., Becker R., and Rudd R.E. Generalized in situ adaptive tabulation for constitutive model evaluation in plasticity. Comput. Methods Appl. Mech. Eng. 196 (2006) 1-13
4. Asaro R., and Lubarda V. Mechanics of Solids and Materials (2006), Cambridge University Press, Cambridge
5. Asaro R.J., and Needleman A. Overview 42. Texture development and strain-hardening in rate dependent polycrystals. Acta Metall. 33 6 (1985) 923-953
6. Ashby M.F. The deformation of plastically non-homogeneous materials. Philos. Mag. 21 170 (1970) 399
7. Barbe F., Decker L., Jeulin D., and Cailletaud G. Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model. Int. J. Plasticity 17 4 (2001) 513-536
8. Barton N.R., Knap J., Arsenlis A., Becker R., Hornung R.D., and Jefferson D.R. Embedded polycrystal plasticity and adaptive sampling. Int. J. Plasticity 24 2 (2008) 242-266
9. Beaudoin A.J., Mathur K.K., Dawson P.R., and Johnson G.C. Three-dimensional deformation process simulation with explicit use of polycrystal plasticity models. Int. J. Plasticity 9 7 (1993) 833-860
10. Beaudoin A.J., Dawson P.R., Mathur K.K., and Kocks U.F. A hybrid finite element formulation for polycrystal plasticity with consideration of macrostructural and microstructural linking. Int. J. Plasticity 11 5 (1995) 501-521
11. Bishop J.F.W., and Hill R. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Philos. Mag. 42 327 (1951) 414-427
12. Chin G.Y., and Mammel W.L. Generalization and equivalence of the minimum work (Taylor) and maximum work (Bishop-Hill) principles of crystal plasticity. Trans. AIME 245 (1969) 1211
13. Cormen T.H., Leiserson C.E., and Rivest R.L. Introduction to Algorithms (1990), MIT press, Cambridge, MA
14. Dantzig G.B. Linear Programming and Extensions (1963), Princeton University Press, Princeton, NJ
15. Engler O., Crumbach M., and Li S. Alloy-dependent rolling texture simulation of aluminium alloys with a grain-interaction model. Acta Mater. 53 8 (2005) 2241-2257
16. Fleck N.A., Ashby M.F., and Hutchinson J.W. The role of geometrically necessary dislocations in giving material strengthening. Scripta Mater. 48 (2003) 179-183
17. Franciosi P., and Zaoui A. Multislip in FCC crystals: a theoretical approach compared with experimental data. Acta Metall. 30 (1982) 1627-1637
18. Fuh S., and Havner K.S. A theory of minimum plastic spin in crystal mechanics. Proc. Roy. Soc. Lond. A 422 (1989) 193-239
19. Ganapathysubramanian S., and Zabaras N. Modeling the thermoelastic-viscoplastic response of polycrystals using a continuum representation over the orientation space. Int. J. Plasticity 21 1 (2005) 119-144
20. Garmestani H., Lin S., Adams B.L., and Ahzi S. Statistical continuum theory for large plastic deformation of polycrystalline materials. J. Mech. Phys. Solids 49 3 (2001) 589-607
21. Gil Sevillano J., Houtte P.V., and Aernoudt E. Geometical models for polycrystal deformation and texture prediction. Prog. Mater. Sci. 25 2-4 (1980) 272-341
22. Guan Y., Pourboghrat F., and Barlat F. Finite element modeling of tube hydroforming of polycrystalline aluminum alloy extrusions. Int. J. Plasticity 22 12 (2006) 2366-2393
23. Gurtin M.E. An Introduction to Continuum Mechanics (1981), Academic Press, New York
24. Haddadi H., Bouvier S., Banu M., Maier C., and Teodosiu C. Towards an accurate description of the anisotropic behaviour of sheet metals under large plastic deformations: modelling, numerical analysis and identification. Int. J. Plasticity 22 12 (2006) 2226-2271
25. Havner K.S. A discrete model for the prediction of subsequent yield surfaces in polycrystalline plasticity. Int. J. Solids Struct. 7 (1971) 719-730
26. Havner K.S. Finite Plastic Deformation of Crystalline Solids (1992), Cambridge University Press, Cambridge
27. Héripré E., Dexet M., Crépin J., Gélébart A.R.L., Bornert M., and Caldemaison D. Coupling between experimental measurements and polycrystal finite element calculations for micromechanical study of metallic materials. Int. J. Plasticity 23 9 (2007) 1512-1539
28. Hill R. Discontinuity relations in mechanics of solids. In: Sneddon I.N., and Hill R. (Eds). Progress in Solid Mechanics vol. 2 (1961), Springer, Berlin 247-278
29. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13 (1965) 89-101
30. Hill R. Generalized constitutive relations for incremental deformation of metal crystals by multislip. J. Mech. Phys. Solids 14 2 (1966) 95-102
31. Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 (1967) 79-95
32. Hirsch J., and Lucke K. Mechanism of deformation and development of rolling textures in polycrystalline FCC metals: I. Description of rolling texture in homogeneous CuZn alloys. Acta Metall. 36 11 (1988) 2863-2882
33. Hirsch J., and Lucke K. Mechanism of deformation and development of rolling textures in polycrystalline FCC metals: II. Simulation and interpretation of experiments on the basis of Taylor-type theories. Acta Metall. 36 11 (1988) 2883-2904
34. Honneff H., and Mecking H. A method for the determination of the active slip systems and orientation changes during single crystal deformation. Proceedings of the Fifth International Conference on the Textures of Materials vol. 1 (1978), Springer, Berlin 265-275
35. Hosford W.F. The Mechanics of Crystals and Textured Polycrystals (1993), Oxford University Press, New York
36. Hutchinson J.W. Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A 348 1652 (1976) 101-127
37. Kalidindi S.R., and Duvvuru H.K. Spectral methods for capturing crystallographic texture evolution during large plastic strains in metals. Acta Mater. 53 13 (2005) 3613-3623
38. Kalidindi S.R., Bronkhorst C.A., and Anand L. Crystallographic texture evolution in bulk deformation processing of FCC metals. J. Mech. Phys. Solids (1992) 537-569
39. Kalidindi S.R., Duvvuru H.K., and Knezevic M. Spectral calibration of crystal plasticity models. Acta Mater. 54 7 (2006) 1795-1804
40. Kim J.H., Lee M.-G., Barlat F., Wagoner R.H., and Chung K. An elasto-plastic constitutive model with plastic strain rate potentials for anisotropic cubic metals. Int. J. Plasticity 24 12 (2008) 2298-2334
41. Knezevic M., Kalidindi S.R., and Fullwood D. Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals. Int. J. Plasticity 24 (2008) 1264-1276
42. Kocks U.F., Tomé C.N., and Wenk H.R. Texture and Anisotropy (1998), Cambridge University Press, Cambridge
43. Kröner E. Zur plastischen verformung des vielkristalls. Acta Metall. 9 (1961) 155-161
44. Lebensohn R. Modeling the role of local correlations in polycrystal plasticity using viscoplastic self-consistent schemes. Model. Simul. Mater. Sci. Eng. 7 (1999) 739-746
45. Lebensohn R.E., and Tomé C.N. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall. Mater. 41 9 (1993) 2611-2624
46. Lebensohn R., Ühlenhut H., Hartig C., and Mecking H. Plastic flow of γ-TiAl-based polysynthetically twinned crystals: micromechanical modeling, and experimental validation. Acta Mater. 46 13 (1998) 4701-4709
47. Lebensohn R.A., Turner P.A., Signorelli J.W., Canova G.R., and Tomé C.N. Calculation of intergranual stresses based on a large strain visoplastic self-consistent polycrystal model. Model. Simul. Mater. Sci. Eng. 6 (1998) 447-465
48. Lee E.H. Elastic-plastic deformation at finite strains. J. Appl. Mech. 36 (1969) 1-6
49. Lee C.S., and Duggan B.J. Studies on the sharpness of simulated deformation textures. Scripta Metall. Mater. 28 1 (1993) 121-126
50. Lee B.J., Ahzi S., and Parks D.M. Bicrystal-based modeling of plasticity in FCC metals. J. Eng. Mater. Technol. 124 1 (2002) 27
51. Leffers T. On the misfit between the grains in a deformed sachs polycrystal and its relation to the inhomogeneous deformation of real polycrystals. Scripta Metall. 9 (1975) 261-264
52. Leffers T. The shortcomings of the Taylor model in the description of the plastic deformation of real polycrystals. Proceedings of the Fifth International Conference on the Textures of Materials vol. 1 (1978), Springer, Berlin 277-287
53. Leffers T., and Christoffersen H. The importance of grain-to-grain interaction during rolling deformation of copper. Mater. Sci. Eng. (1997) 676-679
54. Logé R.E., and Chastel Y.B. Coupling the thermal and mechanical fields to metallurgical evolutions within a finite element description of a forming process. Comput. Methods Appl. Mech. 195 48-49 (2006) 6843-6857
55. Mahesh S. Deformation banding and shear banding in single crystals. Acta Mater. 54 17 (2006) 4565-4574
56. Mahesh S. A hierarchical model for rate-dependent polycrystals. Int. J. Plasticity 25 5 (2009) 752-767
57. Manonukul A., and Dunne F.P.E. High- and low-cycle fatigue crack initiation using polycrystal plasticity. Proc. Roy. Soc. Lond. A 460 2047 (2004) 1881-1903
58. Mathur K.K., and Dawson P.R. On modeling the development of crystallographic texture in bulk forming processes. Int. J. Plasticity 5 1 (1989) 67-94
59. Mika D.P., and Dawson P.R. Effects of grain interaction on deformation in polycrystals. Mater. Sci. Eng. A 257 1 (1998) 62-76
60. Molinari A., Canova G.R., and Ahzi S. A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall. 35 (1987) 2983-2994
61. Pan J., and Rice J.R. Rate-sensitivity of plastic flow and implications for yield-surface vertices. Int. J. Solids Struct. 19 11 (1983) 973-987
62. Pierce D., Asaro R.J., and Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Mater. 30 (1982) 1087-1119
63. Pierce D., Asaro R.J., and Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metall. 31 12 (1983) 1951-1976
64. Proust G., Tomé C.N., and Kaschner G.C. Modeling texture, twinning and hardening evolution during deformation of hexagonal materials. Acta Mater. 55 (2007) 2137-2148
65. Rice J.R. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19 6 (1971) 433-455
66. Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton, NJ
67. Sachs G. Zur Ableitung einer Fliessbedingung. Z. Ver. Dtsch. Ing. 72 (1928) 734-736
68. Saran M. Comparison of elastic-plastic and rigid-plastic implicit FEM simulations in sheet forming applications. J. Mater. Process. Technol. 27 1-3 (1991) 279-300
69. Taylor G.I. Plastic strain in metals. J. Inst. Met. 62 (1938) 307
70. Tomé C., Canova G.R., Kocks U.F., Christodoulou N., and Jonas J.J. The relation between macroscopic and microscopic strain hardening in fcc polycrystals. Acta Metall. 32 10 (1984) 1637-1653
71. Van Houtte P., and Aernoudt E. Solution of the generalized Taylor theory of plastic flow. I and II. Z. Metall. 66 (1975) 202-209
72. Van Houtte P., and Aernoudt E. Solution of the generalized Taylor theory of plastic flow. III. Applications. Z. Metall. 66 (1975) 303-306
73. Van Houtte P., Delannay L., and Samajdar I. Quantitative predictions of the cold-rolling texture in low-carbon steel by means of the LAMEL model. Texture Microstruct. 31 3 (1999) 104-119
74. Van Houtte P., Delannay L., and Kalidindi S.R. Comparison of two grain interaction models for polycrystal plasticity and deformation texture prediction. Int. J. Plasticity 18 3 (2002) 359-377
75. Van Houtte P., Li S., and Engler O. Modelling deformation texture of aluminium alloys using grain interaction models. Aluminium 80 (2004) 702-706
76. Van Houtte P., Li S., Seefeldt M., and Delannay L. Deformation texture prediction: from the Taylor model to the advanced lamel model. Int. J. Plasticity 21 3 (2005) 589-624
77. Van Houtte P., Kanjarla A.K., Van Bael A., Seefeldt M., and Delannay L. Multiscale modelling of the plastic anisotropy and deformation texture of polycrystalline materials. Eur. J. Mech. A 25 4 (2006) 634-648
78. Van Houtte P., Yerra S.K., and Van Bael A. The facet method: a hierarchical multilevel modelling scheme for anisotropic convex plastic potentials. Int. J. Plasticity 25 2 (2009) 332-360
79. Wang Z.Q., Beyerlein I.J., and LeSar R. Plastic anisotropy in fcc single crystals in high rate deformation. Int. J. Plasticity 25 1 (2008) 26-48
80. Zhang F., Bower A.F., Mishra R.K., and Boyle K.P. Numerical simulations of necking during tensile deformation of aluminum single crystals. Int. J. Plasticity 25 1 (2008) 49-69