A novel approach for anisotropic hardening modeling. Part I: Theory and its application to finite element analysis of deep drawing

International Journal of Plasticity

Volumn 25, Issue 12, 2009, Pages 2383-2409

  Rousselier, G ^a   Barlat, F ^b,c   Yoon, J W ^b  

^a PSL RESEARCH UNIVERSITY   (France)

^b ALCOA TECHNICAL CENTER   (United States)

^c Pohang University of Science and Technology (POSTECH)   (South Korea)

Author keywords

Aluminum alloy; Anisotropic hardening; Finite element method; Polycrystalline model; Sheet forming

Indexed keywords

ADDITIONAL HARDENING; ANISOTROPIC HARDENING; COMPUTATION TIME; CPU TIME; CRYSTALLOGRAPHIC ORIENTATIONS; EXPERIMENTAL DATABASE; EXPERIMENTAL MEASUREMENTS; EXPERIMENTAL TEST; FINITE ELEMENT ANALYSIS; FINITE ELEMENT CALCULATIONS; INITIAL ANISOTROPY; LOADING DIRECTION; MACROSCOPIC MODEL; MATERIAL SCIENCE; METALLIC MATERIAL; MICROSCOPIC SCALE; NONPROPORTIONAL LOADING; PARAMETER CALIBRATION; PHYSICAL MECHANISM; PLASTIC BEHAVIOR; POLYCRYSTALLINE MODEL; POLYCRYSTALLINE MODELS; SHEET FORMING; SIMPLE SHEAR; SLIP SYSTEM; STRESS-STRAIN; TEXTURE EVOLUTIONS; TRANSVERSE STRAIN; YIELD LOCI;

ALUMINA; ALUMINUM; ALUMINUM ALLOYS; ANISOTROPY; CURVE FITTING; DEEP DRAWING; DRAWING (FORMING); HARDENING; LOADING; MODELS; POLYCRYSTALLINE MATERIALS; SINGLE CRYSTALS; STRAIN;

FINITE ELEMENT METHOD;

EID: 70350123740     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2009.04.002     Document Type: Article

References (85)

1. Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. Report RD/B/N731, Central Electricity Generating Board, Berkeley, UK.
2. Aretz H. A simple isotropic-distortional hardening model and its application in elastic-plastic analysis of localized necking in orthotropic sheet metal. Int. J. Plasticity 24 (2008) 1457-1480
3. Asaro R.J., and Needleman A. Texture development and strain hardening in rate dependent polycrystal. Acta Metall. 33 (1985) 923-953
4. 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 (2001) 513-536
5. Barbe F., Forest S., and Cailletaud G. Intergranular and intragranular behavior of polycrystalline aggregates. Part 2: Results. Int. J. Plasticity 17 (2001) 537-563
6. Barlat F., Lege D.J., and Brem J.C. A six-component yield function for anisotropic materials. Int. J. Plasticity 7 (1991) 693-712
7. Barlat F., Brem J.C., and Liu J. On crystallographic texture gradient and its mechanical consequence in rolled aluminum-lithium sheet. Scripta Metall. Mater. 27 (1992) 1121-1126
8. Barlat F., Chung K., and Richmond O. Strain rate potential for metals and its application to minimum work path calculation. Int. J. Plasticity 9 (1993) 51-63
9. Barlat F., Brem J.C., Yoon J.W., Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi S.-H., and Chu E. Plane stress yield function for aluminum alloy sheets - Part 1: Theory. Int. J. Plasticity 19 (2003) 1297-1319
10. Barlat F., Aretz H., Yoon J.W., Karabin M.E., Brem J.C., and Dick R.E. Linear transformation-based anisotropic yield functions. Int. J. Plasticity 21 (2005) 1009-1039
11. Barlat F., Yoon J.W., and Cazacu O. On linear transformations of stress tensors for the description of plastic anisotropy. Int. J. Plasticity 23 (2007) 876-896
12. Benallal A., and Marquis D. Constitutive equations for non-proportional cyclic elasto-viscoplasticity. J. Eng. Mater. Technol. 109 (1987) 326-336
13. Benallal A., Le Gallo P., and Marquis D. An experimental investigation of cyclic hardening of 316 stainless steel and 2024 aluminium alloy under multiaxial loadings. Nucl. Eng. Des. 114 (1989) 345-353
14. Berveiller M., and Zaoui A. An extension of the self-consistent scheme to plastically-flowing polycrystals. J. Mech. Phys. Solids 26 (1979) 325-344
15. Besson J., and Foerch R. Large scale object-oriented finite element code design. Comput. Meth. Appl. Mech. Eng. 142 1-2 (1997) 165-187
16. Bishop J., and Hill R. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Philos. Mag. 42 (1951) 414-427
17. Bishop J., and Hill R. A theoretical derivation of the plastic properties of a polycrystalline face-centered metal. Philos. Mag. 42 (1951) 1298-1307
18. Bocher L., Delobelle P., Robinet P., and Feaugas X. Mechanical and microstructural investigations of an austenitic stainless steel under non-proportional loadings in tension-torsion and external pressure. Int. J. Plasticity 17 (2001) 1491-1530
19. Bron F., and Besson J. A yield function for anisotropic materials - application to aluminum alloys. Int. J. Plasticity 20 (2004) 937-963
20. Cailletaud, G., 1987. Une approche micromécanique phénoménologique du comportement inélastique des métaux. PhD thesis, Paris University, Paris 6.
21. Cailletaud G. A micromechanical approach to inelastic behavior of metals. Int. J. Plasticity 8 (1992) 55-73
22. Cailletaud G., Kaczmarek H., and Policella H. Some elements on the multiaxial behavior of 316 L stainless steel at room temperature. Mech. Mater. 3 (1984) 333-347
23. Cailletaud G., and Pilvin P. Utilisation de modèles polycristallins pour le calcul par éléments finis. Revue européenne des éléments finis 3 (1994) 515-541
24. Cailletaud G., and Sai K. A polycrystalline model for the description of ratchetting: effect of intergranular and intragranular hardening. Mater. Sci. Eng. A 480 (2008) 24-39
25. Cazacu O., Plunkett B., and Barlat F. Orthotropic yield criterion for hexagonal close packed metals. Int. J. Plasticity 22 (2006) 1171-1194
26. Chaboche J.L. Viscoplastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. Acad. Polon. Sci. Sér. Sci. Tech. XXV 1 (1977) 33-39
27. Chaboche J.L. A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plasticity 24 (2008) 1642-1693
28. Chaboche J.L., and Rousselier G. On the plastic and viscoplastic constitutive equations - Parts I and II. J. Pressure Vessel Technol. 105 (1983) 153-164
29. Choi Y., Han C.-S., Lee J.K., and Wagoner R.H. Modeling multi-axial deformation of planar anisotropic elasto-plastic materials, Part I: Theory. Int. J. Plasticity 22 (2006) 1745-1764
30. Darrieulat M., and Montheillet F. A texture based continuum approach for predicting the plastic behaviour of rolled sheet. Int. J. Plasticity 19 (2003) 517-546
31. Diard O., Leclercq S., Rousselier G., and Cailletaud G. Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity. Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries. Int. J. Plasticity 21 (2005) 691-722
32. Duchêne, L., 2003. FEM study of metal sheets with a texture based, local description of the yield locus. PhD thesis, Liège University.
33. Erieau P., and Rey C. Modeling of deformation and rotation bands and of deformation induced grain boundaries in IF steel aggregate during large plane strain compression. Int. J. Plasticity 20 (2004) 1763-1788
34. Eshelby J. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241 (1957) 376-396
35. Flores P., Duchêne L., Bouffioux C., Lelotte T., Henrard C., Pernin N., Van Bael A., He S., Duflou J., and Habraken A.M. Model identification and FE simulations: effect of different yield loci and hardening laws in sheet forming. Int. J. Plasticity 23 (2007) 420-449
36. Gotoh M. A theory of plastic anisotropy based on a yield function of fourth order (plane stress state) - I/II. Int. J. Mech. Sci. 19 505-512 (1977) 513-520
37. Grytten F., Holmedal B., Hopperstad O.S., and Borvik T. Evaluation of identification methods for YLD2004-18p. Int. J. Plasticity 24 (2008) 2248-2277
38. Guan Y., Pourboghrat F., and Barlat F. Finite element modeling of tube hydroforming of polycrystalline aluminum alloy extrusions. Int. J. Plasticity 22 (2006) 2366-2393
39. Haddadi H., Bouvier S., Banu M., Maier M., 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 (2006) 2226-2271
40. Habraken A.M., and Duchêne L. Anisotropic elasto-plastic finite element analysis using a stress-strain interpolation method based on a polycrystalline model. Int. J. Plasticity 20 (2004) 1525-1560
41. Hill R. Constitutive dual potential in classical plasticity. J. Mech. Phys. Solids 35 (1987) 23-33
42. Hoc T., and Forest S. Polycrystal modeling of IF-Ti steel under complex loading path. Int. J. Plasticity 17 (2001) 65-85
43. Hoc T., Crépin J., Gélébart L., and Zaoui A. A procedure for identifying the plastic behavior of single crystals from the local response of polycrystals. Acta Mater. 51 (2003) 5477-5488
44. Holmedal B., Van Houtte P., and An Y. A crystal plasticity model for strain-path changes in metals. Int. J. Plasticity 24 (2008) 1360-1379
45. Hu Z., Rauch E.F., and Teodosiu C. Work-hardening behavior of mild steel under stress reversal at large strains. Int. J. Plasticity 8 (1992) 839-856
46. Karafillis A.P., and Boyce M.C. A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids 41 (1993) 1859-1886
47. Kim D., Barlat F., Bouvier S., Rabahallah M., Balan T., and Chung K. Non-quadratic anisotropic potentials based on linear transformation of plastic strain rate. Int. J. of Plasticity 23 (2008) 1380-1399
48. 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 (2008) 2298-2334
49. Korkolis Y.P., and Kyriakides S. Inflation and burst of aluminum tubes. Part II: An advanced yield function including deformation-induced anisotropy. Int. J. Plasticity 24 (2008) 1625-1637
50. Kowalczyk K., and Gambin W. Model of plastic anisotropy evolution with texture-dependent yield surface. Int. J. Plasticity 20 (2004) 19-54
51. Kröner E. Zur plastischen Verformung des Vielkristalls. Acta Metall. 9 (1961) 155-161
52. Kuroda M., and Tvergaard V. Use of abrupt strain path change for determining subsequent yield surface: illustrations of basic idea. Acta Mater. 47 (1999) 3879-3890
53. Kuroda M., and Tvergaard V. A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity. J. Mech. Phys. Solids 49 (2001) 1239-1263
54. Kuwabara T. Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations. Int. J. Plasticity 23 (2007) 385-419
55. Ladévèze, P., 1980. Sur la théorie de la plasticité en grandes déformations. Technical report, ENS Cachan, Novembre 1980.
56. Lebensohn R.A., 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 (1993) 2611-2624
57. Lopes A.B., Barlat F., Gracio J.J., Ferreira Duarte J.F., and Rauch E.F. Effect of texture and microstructure on strain hardening anisotropy for aluminum deformed in uniaxial tension and simple shear. Int. J. Plasticity 19 (2003) 1-22
58. Méric L., Poubanne P., and Cailletaud G. Single crystal modeling for structural calculations - Part I: Model presentation. J. Eng. Mater. Technol. 113 (1991) 162-170
59. Molinari A., Canova G.R., and Ahzi S. A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall. 35 (1987) 2983-2994
60. Pilvin, P., 1990. Approches multiéchelles pour la prévision du comportement anélastique des métaux. PhD thesis, Paris University, Paris 6.
61. Plunkett B., Cazacu O., and Barlat F. Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals. Int. J. Plasticity 24 (2008) 847-866
62. Portier L., Calloch S., Marquis D., and Geyer P. Ratchetting under tension-torsion loadings: experiments and modeling. Int. J. Plasticity 16 (2000) 303-335
63. Raabe D., and Roters F. Using texture components in crystal plasticity finite element simulations. Int. J. Plasticity 20 (2004) 339-361
64. Rabahallah M., Balan T., Bouvier S., Bacroix B., Barlat F., Chung K., and Teodosiu C. Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction. Int. J. Plasticity 25 (2009) 491-512
65. Rousselier, G., 2007. Procédé pour déterminer un modèle polycristallin destiné à représenter le comportement d'un matériau solide soumis à une sollicitation mécanique. Demande de brevet d'invention n° 07 03215 du 4 mai 2007.
66. Rousselier G., and Leclercq S. A simplified "polycrystalline" model for viscoplastic and damage finite element analyses. Int. J. Plasticity 22 (2006) 685-712
67. Rousselier, G., Barlat, F., 2008. Modeling of plastic anisotropy with reduced polycrystalline models. Application to aluminum alloys. In: Proceedings of ESAFORM 2008 Conference, MS04 Paper 17, Lyon, 23-25 April 2008.
68. Sai K., Cailletaud G., and Forest S. Micro-mechanical modeling of the inelastic behavior of directionally solidified materials. Mech. Mater. 38 (2006) 203-217
69. Soare S., Yoon J.W., and Cazacu O. On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming. Int. J. Plasticity 24 (2008) 915-944
70. Sobotka Z. Theorie des plastischen Fliessen von anisotropen Körpern. Z. Angew. Math. Mech. 49 (1969) 25-32
71. Takahashi H., Motohashi H., and Tsuchida S. Development of plastic anisotropy in rolled aluminium sheets. Int. J. Plasticity 12 (1996) 935-949
72. Taylor G.I. Plastic strain in metals. J. Inst. Met. 62 (1938) 307
73. Van Houtte P., and Van Bael A. Convex plastic potentials of fourth and sixth rank for anisotropic materials. Int. J. Plasticity 20 (2004) 1505-1524
74. Van Houtte P., Li S., Seefeldt M., and Delannay L. Deformation texture predictions: from the Taylor model to the Advanced Lamel model. Int. J. Plasticity 21 (2005) 589-624
75. 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 (2009) 332-360
76. Vincent L., Calloch S., and Marquis D. A general cyclic plasticity model taking into account yield surface distortion for multiaxial ratchetting. Int. J. Plasticity 20 (2002) 1817-1850
77. Wang J., Levkovitch V., Reusch F., Svendsen B., Huétink J., and van Riel M. On the modeling of hardening in metals during non-proportional loading. Int. J. Plasticity 24 (2008) 1039-1070
78. Wu P.D., MacEwen S.R., Lloyd D.J., Jain M., Tugcu P., and Neale K.W. On pre-straining and the evolution of material anisotropy in sheet metals. Int. J. Plasticity 21 (2005) 723-739
79. Yoon J.W., Yang D.Y., and Chung K. Elasto-plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials. Comput. Methods Appl. Mech. Eng. 174 (1999) 23-56
80. Yoon J.W., Yang D.Y., Chung K., and Barlat F. A general elasto-plastic finite element formulation based on incremental deformation theory for planar anisotropy and its application to sheet metal forming. Int. J. Plasticity 15 (1999) 35-68
81. Yoon J.W., Barlat F., Chung K., Pourboghrat F., and Yang D.Y. Earing predictions based on asymmetric nonquadratic yield function. Int. J. Plasticity 16 (2000) 1075-1104
82. Yoon J.W., Barlat F., Dick R.E., Chung K., and Kang T.J. Plane stress yield function for aluminum alloy sheets - Part II: FE formulation and its implementation. Int. J. Plasticity 20 (2004) 495-522
83. Yoon J.W., Barlat F., Gracio J.J., and Rauch E. Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets. Int. J. Plasticity 21 (2005) 2426-2447
84. Yoon J.W., Barlat F., Dick R.E., and Karabin M.E. Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function. Int. J. Plasticity 22 (2006) 174-193
85. Zamiri A., Pourboghrat F., and Barlat F. An effective computation algorithm for rate-independent crystal plasticity based on a single crystal yield surface with an application to hydroforming. Int. J. Plasticity 23 (2007) 1126-1147