Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading

International Journal of Plasticity

Volumn 26, Issue 7, 2010, Pages 939-956

  Mohr, Dirk ^a,b   Dunand, Matthieu ^a,b   Kim, Keun Hwan ^b,c  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^b Massachusetts Institute of Technology Cambridge   (United States)

^c POSCO   (South Korea)

Author keywords

Dual phase steel; Finite strain; Multi axial testing; Plasticity; TRIP steel

Indexed keywords

AXIAL LOADS; HIGH STRENGTH STEEL; PLASTICITY; STEEL TESTING; STRESS-STRAIN CURVES;

ADVANCED HIGH STRENGTH STEEL; DUAL-ACTUATOR SYSTEMS; DUAL-PHASE STEEL; FINITE STRAIN; NON-ASSOCIATED PLASTICITY; QUADRATIC FORMULATION; STRESS-STRAIN RESPONSE; TRIP-STEEL;

PLASTICITY TESTING;

EID: 77955170975     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2009.11.006     Document Type: Article

References (60)

1. Abaqus, Reference Manuals, vol. 6.4-1, Abaqus Inc, 2003.
2. T. Angel Formation of martensite in austenitic stainless steels, Effect of deformation, temperature and composition Journal of the Iron and Steel Institute 1954 165
3. M. Banu, M. Takamura, T. Hama, O. Naidim, C. Teodosiu, and A. Makinouchi Simulation of springback and wrinkling in stamping of a dual phase steel rail-shaped part J. Mater. Processing Technology 173 2006 178 184
4. F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, S.H. Choi, F. Pourboghrat, E. Chu, and D.J. Lege Plane stress yield function for aluminum alloy sheets Int. J. Plast. 19 2003 1297
5. F. Barlat, J.M. Ferreira Duarte, J.J. Gracio, A.B. Lopes, and E.F. Rauch Plastic flow for non-monotonic loading conditions of an aluminum alloy sheet sample Int. J. Plast. 19 2003 1215
6. J.F.W. Bishop, and R. Hill A theory of the plastic distortion of a polycrystalline aggregate under combined stresses Philos. Mag 1951 42
7. J.P. Boehler, S. Demmerle, and S. Koss A new direct biaxial testing machine for anisotropic materials Exp. Mech. 34 1994 1 9
8. G.B. Broggiato, F. Campana, and L. Cortese The Chaboche nonlinear kinematic hardening model: calibration methodology and validation Meccanica 43 2 2008 115 124
9. M. Brünig Numerical simulation of the large elastic-plastic deformation behavior of hydrostatic stress-sensitive solids Int. J. Plast. 15 1999 1237 1264
10. M. Brünig, and H. Obrecht Finite elastic-plastic deformation behaviour of crystalline solids based on a nonassociated macroscopic flow rule Int. J. Plast. 14 1998 1189 1208
11. Cao, J., Lee, W., Cheng, H.S., Seniw, M., Wang, H.P, Chung, K., 2008. Experimental and numerical investigation of combined isotropic-kinematic hardening behavior of sheet metals. Int. J. Plast., doi:10.1016/j.ijplas.2008. 04.007.
12. J. Casey, and T.D. Sullivan Pressure dependency, strength-differential effect, and plastic volume expansion in metals Int. J. Plast. 1 1985 39 61
13. J.L. Chaboche A review of some plasticity and viscoplasticity constitutive theories Int. J. Plast. 24 10 2008 1642 1693
14. P.C. Chakraborti, and M.K. Mitra Microstructure and tensile properties of high strength duplex ferrite-martensite (DFM) steels Mater. Sci. Eng. A 466 2007 123 133
15. P. Chen, and M. Koc Simulation of springback variation in forming of advanced high strength steels J. Mater. Process. Technol. 190 2007 189 198
16. V. Cvitanic, F. Vlak, and Z. Lozina A finite element formulation based on non-associated plasticity for sheet metal forming Int. J. Plast. 24 2008 646 687
17. L. Delannay, I. Doghri, and O. Pierard Prediction of tension-compression cycles in multiphase steel using a modified incremental mean-field model Int. J. Solids Struct. 44 2007 7291 7306
18. L. Delannay, P. Jacques, and T. Pardoen Modelling of the plastic flow of trip-aided multiphase steel based on an incremental mean-field approach Int. J. Solids Struct. 45 2008 1825 1843
19. Dunand, M., Mohr, D., 2010. Hybrid experimental-numerical analysis of basic ductile fracture experiments for sheet metals. Int. J. Solids Struct., in press, doi:10.1016/j.ijsolstr.2009.12.011.
20. L. Durrenberger, J.R. Klepaczko, and A. Rusinek Constitutive modeling of metals based on the evolution of the Strain-Hardening rate J. Eng. Mater. Technol. 129 4 2007 550
21. L. Durrenberger, A. Molinari, and A. Rusinek Internal variable modeling of the high strain-rate behavior of metals with applications to multiphase steels Mater. Sci. Eng. A 478 2008 297 304
22. G. Ferron, and A. Makinde Design and development of a biaxial strength testing device J. Testing Eval. 16 1988 253 256
23. D.E. Green, K.W. Neale, S.R. MacEwen, A. Makinde, and R. Perrin Experimental investigation of the biaxial behaviour of an aluminum sheet Int. J. Plast. 20 2004 1677 1706
24. G.W. Greenwood, and R.H. Johnson The deformation of metals under small stresses during phase transformation A Proc. Roy. Soc. 283 1965 403
25. A.V. Hershey Plasticity of isotropic aggregate of anisotropic facecentered cubic crystals J. Appl. Mech. 21 1954 241 249
26. R. Hill A theory of the yielding and plastic flow of anisotropic metals Proc. Roy. Soc. London A193 1948 281 297
27. H. Huh, S.B. Kim, J.H. Song, and J.H. Lim Dynamic tensile characteristics of TRIP-type and DP-type steel sheets for an auto-body Int. J. Mech. Sci. 50 5 2008 918 931
28. P. Jacques, Q. Furnmont, A. Mertens, and F. Delannay On the sources of work hardening in multiphase steels assisted by transformation-induced plasticity Philos. Mag. A 81 7 2001 1789 1812
29. J.Y. Koo, and G. Thomas Thermal cycling treatments and microstructures for improved properties of Fe-0 12%C-0.5% Mn steels. Mater. Eng. Sci. 24 1976 187 198
30. T. Kuwabara, S. Ikeda, and T. Kuroda Measurement and analysis of differential work hardening in cold-rolled steel sheet under biaxial tension J. Mater. Process. Technol. 80-81 1998 517 523
31. T. Kuwabara Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations Int. J. Plast. 23 3 2007 385 419
32. O.G. Lademo, O.S. Hopperstad, and M. Langseth An evaluation of yield criteria and flow rules for aluminium alloys Int. J. Plast. 15 1999 191 208
33. F. Lecroisey, and A. Pineau Martensitic transformations induced by plastic deformation in the Fe-Ni-Cr-C system Metall. Trans. 3 1972 387 396
34. M.G. Lee, D. Kim, C. Kim, M.L. Wenner, R.H. Wagoner, and K. Chung Spring-back evaluation of automotive sheets based on isotropic-kinematic hardening laws and non-quadratic anisotropic yield functions Part II: characterization of material properties Int. J. Plast. 21 2005 883 914 (Pubitemid 40034579)
35. M.G. Lee, D. Kim, C. Kim, M.L. Wenner, R.H. Wagoner, and K.A. Chung practical two-surface plasticity model and its application to spring-back prediction Int. J. Plast. 23 2007 1189
36. Lee, W., Chung, K.-H., Kim, D., Kim, C., Okamoto, K., Wagoner, R.H., Chung, K., 2008. Experimental and numerical study on formability of friction stir welded TWB sheets based on hemispherical dome stretch tests, Int. J. Plast., doi:10.1016/j.ijplas.2008.08.005.
37. S.B. Lin, and J.L. Ding Experimental study of the plastic yielding of rolled sheet metals with the cruciform plate specimen Int. J. Plast. 11 5 1995 583 604
38. R.W. Logan, and W.F. Hosford Upper bound anisotropic yield locus calculations assuming <1 1 1>-pencil glide Int. J. Mech. Sci. 22 1980 419 430
39. A. Makinde, L. Thibodeau, and K.W. Neale Development of an apparatus for biaxial testing using cruciform specimens Exp. Mech. 32 1992 138 144
40. Mohr, D., Dunand, M., in preparation. Optimized specimen for the fracture testing of advanced high strength steels under combined normal and shear loading.
41. D. Mohr, and J. Jacquemin Large deformation of anisotropic austenitic stainless steel sheets at room temperature: multi-axial experiments and phenomenological modeling J. Mech. Phys. Solids 56 10 2008 2935 2956
42. D. Mohr, and M. Oswald A new experimental technique for the multi-axial testing of advanced high strength steel sheets Exp. Mech. 48 1 2008 65 77
43. W. Müller, and K.J. Pöhlandt New experiments for determining yield loci of sheet metal Mater. Process. Technol. 60 1996 643 648
44. G.B. Olson, and M. Cohen Kinetics of strain-induced martensitic nucleation Metall. Trans. 6A 1975 791 795
45. R. Padmanabhan, A.J. Baptista, M.C. Oliveira, and L.F. Menezes Effect of anisotropy on the deep-drawing of mild steel and dual-phase steel tailor-welded blanks J. Mater. Process. Technol. 184 1-3 2007 288 293
46. I. Papatrianatfillou, M. Agoras, N. Aravas, and G. Haidemenopoulos Constitutive modeling and finite element methods for TRIP steels Comput. Methods Appl. Mech. Eng. 195 2006 5094 5114
47. P. Ponte Castaneda New variational principles in plasticity and their application to composite materials J. Mech. Phys. Solids 40 1992 1757 1788
48. A. Rusinek, and J.R. Klepaczko Experiments on heat generated during plastic deformation and stored energy for TRIP steels Mater. Design 30 1 2009 35 48
49. J.C. Simo, and T.J.R. Hughes Computational Inelasticity 1998 Springer Berlin
50. W.A. Spitzig, and O. Richmond The effect of pressure on the flow stress of metals Acta Metall. 32 1984 457 463
51. T.B. Stoughton A non-associated flow rule for sheet metal forming Int. J. Plast. 18 2002 687 714
52. T.B. Stoughton, and J.W. Yoon A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming Int. J. Plast. 20 2004 705 731
53. T.B. Stoughton, and J.W. Yoon On the existence of indeterminate solutions to the equations of motion under non-associated flow Int. J. Plast. 24 2008 583 613
54. R.G. Stringfellow, D.M. Parks, and G.B. Olson A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels Acta Metall. Mater. 40 7 1992 1703 1716
55. H.W. Swift Plastic instability under plane stress J. Mech. Phys. Solids 1 1952 1 76
56. V. Tarigopula, O.S. Hopperstad, M. Langseth, and A.H. Clausen Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes Eur. J. Mech. A/Solids 27 2008 764 782
57. S. Turteltaub, and A.S.J. Suiker Transformation-induced plasticity in ferrous alloys J. Mech. Phys. Solids 53 2005 1747 1788
58. J. Wang, V. Levkovitch, F. Reusch, B. Svendsen, J. Huetink, and M. Van Riel On the modeling of hardening in metals during non-proportional loading Int. J. Plast. 24 2008 1039 1070
59. X.C. Wei, R.Y. Fu, and L. Li Tensile deformation behavior of cold-rolled TRIP-aided steels over large range of strain rates Mater. Sci. Eng. A 465 2007 260 266
60. F. Yoshida, T. Uemori, and K. Fujiwara Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain Int. J. Plast. 18 2002 633 659