Towards an accurate description of the anisotropic behaviour of sheet metals under large plastic deformations: Modelling, numerical analysis and identification

International Journal of Plasticity

Volumn 22, Issue 12, 2006, Pages 2226-2271

  Haddadi, H ^a   Bouvier, S ^a   Banu, M ^b   Maier, C ^b   Teodosiu, C ^a  

^a CNRS   (France)

^b DUNAREA DE JOS UNIVERSITY OF GALATI   (Romania)

Author keywords

Anisotropic behaviour; Large strains; Sensitivity study; Strain path changes; Strategy of identification

Indexed keywords

ANISOTROPY; DISLOCATIONS (CRYSTALS); MICROSTRUCTURE; NUMERICAL ANALYSIS; PLASTIC DEFORMATION; POLYCRYSTALLINE MATERIALS;

ANISOTROPIC BEHAVIOR; LARGE STRAINS; STRAIN-PATH CHANGES; STRATEGY OF IDENTIFICATION;

SHEET METAL;

EID: 33748790680     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2006.03.010     Document Type: Article

References (96)

1. 3DS report, 2001. Selection and identification of elastoplastic models for the materials used in the benchmarks. 18-Months Progress Report, Inter-regional IMS contract "Digital Die Design Systems (3DS)", IMS 1999 000051.
2. Alves, L., 2003. Numerical simulation of the sheet metal forming process. Mechanical modelling and numerical methods. Ph.D. Thesis of the University of Minho, Portugal.
3. Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. GEGB Report RD/B/N731, Berkeley Nuclear Laboratories.
4. Bacroix B., Genevois P., and Teodosiu C. Plastic anisotropy in low carbon steels subjected to simple shear with strain path changes. Eur. J. Mech. A 13 5 (1994) 661-675
5. Bacroix B., and Hu Z. Texture evolution induced by strain path changes in low carbon steel sheets. Met. Mater. Trans. A 26 (1995) 601-613
6. Barlat F., and Lian J. Plastic behaviour and stretchability of sheet metals. Part I : a yield function for orthotropic sheet under plane stress conditions. Int. J. Plasticity 5 (1989) 51-66
7. Barlat F., Becker R.C., Hayashida Y., Maeda Y., Yanagawa M., Chung K., Brem J.C., Lege D.J., Matsui K., Murtha S.J., and Hattori S. Yielding description for solution strengthened aluminium alloy. Int. J. Plasticity 13 (1997) 385-401
8. Bassani J.L. Yield characterization of metals with transversely isotropic plastic properties. Int. J. Mech. Sci. 19 (1977) 651-660
9. Bay B., Hansen N., and Kuhlmann-Wilsdorf D. Deformation structures in lightly rolled pure aluminium. Mater. Sci. Eng. A 113 (1989) 385-397
10. Beaudoin A.J., Mathur K.K., Dawson P.R., and Johnson G.C. Three-dimensional deformation process simulation with explicit use of polycrystalline plasticity models. Int. J. Plasticity 9 (1993) 833-866
11. Bouvier, S., Gardey, B., Haddadi, H., Teodosiu, C., 2006. Characterization of the strain-induced plastic anisotropy of rolled sheets by using sequences of simple shear and uniaxial tensile tests. J. Mater. Proc. Tech. in press.
12. Bouvier S., Alves J.L., Oliveira M.C., and Menezes L.F. Modelling of anisotropic work-hardening behaviour of metallic materials subjected to strain-path changes. Comp. Mater. Sci. 32 (2005) 301-315
13. Bouvier, S., Alves, J.L., Menezes, L.F., Oliveira, M., 2005b. Characterizing the plastic anisotropy and its effect on sheet metal forming simulation. In: Oňate, E., Owen, D.R.J. (Eds.), Proceedings of the VIII International Conference on Computational Plasticity Complas VIII, Barcelone, Spain.
14. Bucher A., Görke U.-J., and Kreißig R. A material model for finite elasto-plastic deformations considering a substructure. Int J. Plasticity 20 (2004) 619-642
15. Cailletaud, G., Pilvin, P., 1994. Identification and inverse problems related to the material behaviour. In: Proceedings of the 2nd International Symposium on Inverse Problems, ESIP94, 2-4 November, Paris, France, pp. 79-86.
16. Cashform report, 2001. An accurate plasticity model of texture, strain-path induced anisotropy and forming limits for computer-aided sheet metal forming. Final Technical Report, Cashform Brite-Euram Contract No. BRPR-CT97-0492.
17. Cazacu O., and Barlat F. Generalization of Drucker's yield criterion to orthotropy. Math. Mech. Solids 6 (2001) 613-630
18. Chaboche, J.L., Dang Van K., Cordier, G., 1979. Modelisation of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the Transactions on 5th SMIRT, Berlin, p. L11/3.
19. Chaboche J.L., and Rousselier. On the plastic and viscoplastic constitutive equations. Parts I and II. ASME J. Pressure Vessel Technol. 105 (1983) 153-165
20. Chum B.K., Kim H.Y., and Lee J.K. Modeling the Bauschinger effect for sheet metals. Part II: applications. Int. J. Plasticity 18 (2002) 597-616
21. Chung K., and Shah K. Finite element simulations of sheet metal forming for planar anisotropic metals. Int. J. Plasticity 8 (1992) 453-476
22. Christodoulou N., Woo O.T., and MacEwen S.R. Effect of stress reversals on the work hardening behaviour of polycrystalline copper. Acta Metall. 34 (1986) 1553-1562
23. Cleveland R.M., and Ghosh A.K. Inelastic effects on springback in metals. Int. J. Plasticity 18 (2002) 769-785
24. Cordebois, J.P., Boucher, M., 1990. A new approach of elastic domain evolution. Theoretical and applied aspects. In: S.K. Ghosh (Ed.), Proceedings of the International Conference on Development in Forming Technology, p. 1.
25. Dafalias Y.F. Plastic spin: necessity or redundancy?. Int. J. Plasticity 14 (1998) 909-931
26. Dirras G.F., Biget M.P., and Rey C. On the microstructural evolution of cold-rolled Al + 5at.% Mg. Scr. Met. Mater. 33 n°5 (1995) 755-760
27. Dirras, G., Chauveau, T., Garnier, A.P., 1999. Dislocations patterning and texture development under monotonic and Bauschinger shear tests on the 6016-T4 aluminium alloy. In: Bilde-Sørensen, J.B., Carstensen, J.V., Hansen, N., Juul Jensen, D., Lefers, T., Pantleon, W., Pedersen, O.B., Winther, G., Roskilde, Danmark (Eds.), Proceedings of the 20th Risø.
28. Dogui, A., 1989. Plasticité anisotrope en grandes déformations. Ph.D. Thesis, University of Lyon, France.
29. Gardey B., Bouvier B., and Bacroix B. Correlation between the macroscopic behaviour and the microstructural evolutions during large plastic deformation of a dual phase steel. Metall. Mater. Trans. A 36 (2005) 2937-2945
30. Garnier, A.P., Dirras, G., Teodosiu, C., 1998. Analysis of the dislocation substructure development of the aluminium alloys 6016 and 5182 at large strains. 12th Months Progress Report, Brite-Euram European contract Cashform BRPR-CT97-0492.
31. Gau J.-T., Gray L.K., and Kinzel L. A new model for springback prediction in which the Bauschinger effect is considered. Int. J. Mech. Sci. 43 (2001) 1813-1832
32. Ghosh A.K., and Backofen W.A. Strain-hardening and instability in biaxially stretched sheets. Metall. Trans. 4 (1973) 1113-1123
33. Ghosh A.K. A physically-based constitutive model for metal deformation. Acta Metall. 28 (1980) 1443-1465
34. Haddadi, H., 1999. Incorporation of the simple shear and the off-axis tensile tests in an identification software. Internal LPMTM Report.
35. Hasegawa T., Yakou T., and Karashima S. Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium. Mater. Sci. Eng. A 20 (1975) 267-276
36. Häusler O., Schick D., and Tsakmakis C. Description of plastic anisotropy effects at large deformations - Part II the case of transverse isotropy. Int. J. Plasticity 20 (2004) 199-223
37. Hill R. The Mathematical Theory of Plasticity (1950), Clarendon Press, Oxford
38. Hill R. Constitutive modeling of orthotropic plasticity in sheet metals. J. Mech. Phys. Sol. 38 (1990) 405-417
39. Hoc T., and Forest S. Polycrystal modelling of IF-Ti steel under complex loading path. Int. J. Plasticity 17 (2001) 65-85
40. 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
41. Huang X., and Hansen N. Grain orientation dependence of microstructure in aluminium deformed in tension. Scr. Metall. 37 1 (1997) 1-7
42. Ishigaki H. In: Koistinen D.P., and Wang N.-M. (Eds). Mechanics of Sheet Metal Forming: Material Behavior and Deformation Analysis (1978), Plenum Press, New York, London 315
43. Kalidindi S.R., Bronkhorst C.A., and Anand A. Crystallographic texture evolution in bulk deformation processing of metals. J. Mech. Phys. Solid 40 (1992) 537-569
44. Karafillis A.P., and Boyce M.C. A general anisotropic yield criterion using bounds and transformation weighting tensor. J. Mech. Phys. Solids 41 n° 12 (1993) 1859-1886
45. Kocks U.F., Hasegawa T., and Scattergood R.O. On the origin of cell walls and of lattice misorientations during deformation. Scr. Metall. 14 4 (1980) 449-454
46. Korbel A., and Martin P. Microstructural events of macroscopic strain localization in prestrained tensile specimen. Acta Metall. 36 9 (1988) 2575-2586
47. Kuroda M. Interpretation of the behaviour of metals under large plastic shear deformations: comparison of macroscopic predictions to physically based predictions. Int. J. Plasticity 15 (1999) 1217-1236
48. Langlois L., and Berveiller M. Overall softening and anisotropy related with the formation and evolution of dislocation microstructures. Int. J. Plasticity 19 5 (2003) 599-624
49. Leffers, T., 1991. Microstructures, textures and deformation patterns at large strains. In: Teodosiu, C., Raphanel, J., Sidoroff, F. (Eds.), Proceedings of the Mecamat'91.
50. Lewandowska M. Dependence of the deformation microstructure of aluminium alloys on the strain path. Mater. Chem. Phy. 81 2-3 (2003) 555-557
51. Li K.P., Carden W.P., and Wagoner R.H. Simulation of springback. Int. J. Mech. Sci. 44 (2002) 103-122
52. Lian J., Barlat F., and Baudelet B. Plastic behavior and stretchability of sheet metals. Part II: Effect of yield surface shape on sheet forming limit. Int. J. Plasticity 5 (1989) 131-147
53. Lopes A.B., Rauch E.F., and Gracio J.J. Textural vs. structural plastic instabilities in sheet metal forming. Acta Mater. 47 N°3 (1999) 859-866
54. McDowell, D.L., Moosbrugger, J.C., 1987. A generalized rate-dependent bounding surface model. In: ASME PVP Division, Fall Conference, Knoxville, TN, October 21-23.
55. McDowell D.L. Stress state dependence of cyclic ratcheting behaviour of two rail steels. Int. J. Plasticity 11 (1995) 397-421
56. Mandel J. Définition d'un repère privilégié pour l'étude des transformations anélastiques du polycristal. J. Méc. Théor. Appl. 1 (1982) 7
57. Mathur K.K., and Dawson P.R. On modelling the development of crystallographic texture in bulk forming processes. Int. J. Plasticity 5 (1989) 69-94
58. Mazilu P., and Meyers A. Yield surface description of isotropic materials after cold prestrain. Ingenieur Archiv. 55 (1985) 213-220
59. Mecking H., and Kocks U.F. Kinetics of flow and strain-hardening. Acta Metall. 29 (1981) 1865-1875
60. Menezes, L.F., Thuillier, S., Manach, P.Y., Bouvier, S., 2002. Influence of work hardening models on the numerical simulation of a reverse deep drawing process. In: Khan A.S., Lopez-Pamies O. (Eds.) Proc. Plasticity 2002, 9th Int. Symp. Plas., Plasticity, Damage and Fracture at Macro, Micro and Nano Scales, Aruba, Netherlands, pp. 331-333.
61. Menzel A., Ekh M., Runesson K., and Steinmann P. A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage. Int. J. Plasticity 21 (2005) 397-434
62. Moreton D.N., Moffat D.G., and Parkinson D.B. The yield surface behaviour of pressure vessel steels. J. Strain Anal. 16 (1981) 127
63. Mróz Z. On the description of anisotropic work-hardening. J. Mech. Phys. Solids 15 (1967) 163-175
64. Nesterova, E.V., Teodosiu, C., Bacroix, B., 1999. TEM investigation of an IF and Bake-hardened steels. LPMTM Internal Report.
65. Nesterova E.V., Bacroix B., and Teodosiu C. Experimental observation of microstructure evolution under strain-path changes in low-carbon IF steel. Mater. Sci. Eng. A 309-310 (2001) 495-499
66. Nesterova E.V., Bacroix B., and Teodosiu C. Microstructure and texture evolution under strain-path changes in low-carbon interstitial-free steel. Metall. Trans. A 32 (2001) 2527-2538
67. Ohno N., and Wang J.-D. Nonlinear kinematic hardening rule with critical state of dynamic recovery, Part I: formulation and basic features for ratchetting behaviour. Int. J. Plasticity 9 (1993) 375-390
68. Peeters B., Kalidindi S.R., Van Houtte P., and Aernoudt E. A crystal plasticity based work-hardening/softening model for b.c.c. metals under changing strain paths. Acta Mater. 48 (2000) 2123-2133
69. Peeters B., Hoferlin E., Van Houtte P., and Aernoudt E. Assessment of crystal plasticity based calculation of the plastic spin of polycrystalline metals for FE implementation. Int. J. Plasticity 17 (2001) 819-836
70. Rauch E.F., and G'Sell C. Flow localization induced by a change in strain path in mild steel. Mater. Sci. Eng. A 111 (1989) 71-80
71. Rauch E.F., and Schmitt J.H. Dislocation substructures in mild steel deformed in simple shear. Mater. Sci. Eng. A 113 (1989) 441-448
72. Rauch E.F., and Thuillier S. Rheological behaviour of mild steel under monotonic loading conditions and cross-loading. Mater. Sci. Eng. A 164 1-2, 30 (1993) 255-259
73. Rauch E.F., and Thuillier S. Plasticity and unstable flow of mild steel. Arch. Metall. 38 (1993) 167-177
74. Rauch E.F., Gracio J.J., Barlat F., Lopes A.B., and Ferreira Duarte J. Hardening behavior and structural evolution upon strain reversal of aluminium alloys. Scr. Mater. 46 12 (2002) 881-886
75. Reis, A., Costa, N., Duarte, J.F., Santos, A., Barata da Rocha, A., 1999. Basic test case, 24th months periodic progress report. Cashform Brite-Euram European contract, An accurate plasticity model of texture, strain-path induced anisotropy, no. BRPR-CT97-0492.
76. Richard, V., Chauveau, T., Swiatnicki, W., 2000. TEM examination of the dislocation microstructure evolution in the Dual Phase 600 under various paths of deformation. Internal LPMTM-CNRS Report.
77. Schmitt J.H., Aernoudt E., and Baudelet B. Yield loci for polycrystalline metals without texture. Mater. Sci. Eng. 75 (1985) 13-20
78. Strauven Y., and Aernoudt E. Directional strain softening in ferritic steel. Acta Metall. 35 5 (1987) 1029-1036
79. Teodosiu C., and Hu Z. Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. In: Shen S.F., and Dawson P.R. (Eds). Proceedings of the NUMIFORM' 95 (1995), Balkema, Rotterdam 173-182
80. Teodosiu, C., Hu, Z., 1998. Microstructure in the continuum modelling of plastic anisotropy. In: Roskilde, Danemark (Eds.), Proceedings of the 19th Risø International Symposium on Modelling of Structures and Mechanics of Materials from Microscale to Product, pp. 149-168.
81. Thuillier S., and Rauch E.F. Development of microbands in mild steel during cross loading. Acta Metall. Mater. 42 (1994) 1973-1983
82. Tsakmakis C. Description of plastic anisotropy effects at large deformations - part I restrictions imposed by the second law and the postulate by il'iushin. Int. J. Plasticity 20 (2004) 167-198
83. Tugcu P., and Neale K.W. On the implementation of anisotropic yield functions into finite strain problems of sheet metal forming. Int. J. Plasticity 15 (1999) 1021-1040
84. Uemori T., Okada T., and Yoshida F. FE analysis of springback in hat-bending with consideration of initial anisotropy and the Bauschinger effect. Key Eng. Mater. 177-180 (1998) 497-502
85. Uemori T., Okada T., and Yoshida F. Simulation of springback in V-bending process by elasto-plastic finite element method with consideration of Bauschinger effect. Met. Mater. 4 (2000) 311-314
86. Uenishi, A., 2003. Thermodynamical behaviour of solution hardened interstitial free steels at high strain rates. Ph.D. Thesis, University Paris 13, France.
87. Uenishi A., and Teodosiu C. Constitutive modelling of the high strain rate behaviour of interstitial-free steel. Int. J. Plasticity 20 4-5 (2004) 915-936
88. Voyiadjis G.Z., and Abu Al-Rub R.K. Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity. Int. J. Plasticity 19 (2003) 2121-2147
89. Wagoner, R.H., Geng, L., Balakrishnan, V., 2000. Role of hardening law in springback. In: Proceedings of the 8th International Symposium on Plasticity and its Current Applications, Whistler, Canada, pp. 609-611.
90. Wallin M., and Ristinmaa M. Deformation gradient based kinematic hardening model. Int. J. Plasticity 21 (2005) 2025-2050
91. Wilson D.V., and Bate P.S. Influences of cell walls and grain boundaries on transient responses of an IF steel to changes in strain path. Acta Metall. Mater. 42 4 (1994) 1099-1111
92. Yoshida F. A constitutive model of cyclic plasticity. Int. J. Plasticity 16 (2000) 359-380
93. Yoshida F., and Uemori T. A model of large-strain cyclic plasticity describing the Bauschinger effect and work-hardening stagnation. Int. J. Plasticity 18 (2002) 661-686
94. 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 forming. Int. J. Plasticity 15 (1999) 35-67
95. Zhang, Z.T., Lee, D., 1995. Effect of process variables and material properties on the springback of 2D-draw bending parts. SAE Paper 950692, in SP-1067. Society of Automotive Sheet Engineers, Warrendale, PA, pp. 11-18.
96. Zhou Y., Jonas J.J., Szabo L., Makinde A., Jain M., and MacEwen S.R. Incorporation of an anisotropic (texture-based) strain-rate potential into three-dimensional finite element simulations. Int. J. Plasticity 13 (1997) 165-181