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Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

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Abstract

An inverse analysis methodology to simultaneously identify the parameters of various anisotropic yield criteria together with isotropic work-hardening models of metal sheets is outlined. This identification makes use of results of the cruciform biaxial test, i.e., the evolution of the force during the test, for the two axes of the sample, and the major and minor strain distributions along both axes, at a given moment during the test. Based on a study of the sensitivity of the constitutive parameters to the biaxial tensile test results, the inverse identification consists on a procedure that sequentially minimises the gap between experimental and numerical results. Each step of the sequence uses a distinct cost function according to the type of results to be minimised, using a gradient-based optimisation algorithm, the Levenberg-Marquardt method. The inverse methodology allows for the identification of constitutive parameters of complex constitutive models. This sequential identification strategy is compared to a strategy based on a single cost function, involving all parameters and type of results, which has lower performance.

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References

  1. Hill R (1948) A theory of yielding and plastic flow of anisotropic metals. Proc R Soc London 193:281–297. doi:10.1098/rspa.1948.0045

    Article  MathSciNet  MATH  Google Scholar 

  2. Barlat F, Lege DJ, Brem JC (1991) A 6-component yield function for anisotropic materials. Int J Plast 7:693–712. doi:10.1016/0749-6419(91)90052-Z

    Article  Google Scholar 

  3. Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41:1859–1886. doi:10.1016/0022-5096(93)90073-O

    Article  MATH  Google Scholar 

  4. Cazacu O, Barlat F (2001) Generalization of Drucker’s yield criterion to orthotropy. Math Mech Solids 6:613–630. doi:10.1177/108128650100600603

    Article  MATH  Google Scholar 

  5. Bron F, Besson J (2004) A yield function for anisotropic materials. Application to aluminium alloys. Int J Plast 20:937–963. doi:10.1016/j.ijplas.2003.06.001

    Article  MATH  Google Scholar 

  6. Vegter H, van den Boogaard AH (2006) A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states. Int J Plast 22:557–580. doi:10.1016/j.ijplas.2005.04.009

    Article  MATH  Google Scholar 

  7. Plunkett B, Cazacu O, Barlat F (2008) Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals. Int J Plast 24:847–866. doi:10.1016/j.ijplas.2007.07.013

    Article  MATH  Google Scholar 

  8. Aretz H, Barlat F (2013) New convex yield functions for orthotropic metal plasticity. Int J Non-Linear Mech 51:97–111. doi:10.1016/j.ijnonlinmec.2012.12.007

    Article  Google Scholar 

  9. Yoshida F, Hamasaki H, Uemori T (2013) A user-friendly 3D yield function to describe anisotropy of steel sheets. Int J Plast 45:119–139. doi:10.1016/j.ijplas.2013.01.010

    Article  Google Scholar 

  10. Voce E (1948) The relationship between stress and strain for homogeneous deformation. J Inst Metals 74:537–562

    Google Scholar 

  11. Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1:1–18. doi:10.1016/0022-5096(52)90002-1

    Article  Google Scholar 

  12. Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauschinger effect. GEGB report RD/B/N 731

  13. Geng L, Wagoner RH (2000) Springback analysis with a modified hardening model. SAE paper No. 2000-01-0768 SAE Inc. 10.4271/2000-01-0768.

  14. Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149–88. doi:10.1016/0749-6419(86)90010-0

    Article  MATH  Google Scholar 

  15. Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int J Plast 18:661–686. doi:10.1016/S0749-6419(01)00050-X

    Article  MATH  Google Scholar 

  16. Barlat F, Gracio JJ, Lee MJ, Rauch EF, Vincze G (2011) An alternative to kinematic hardening in classical plasticity. Int J Plast 27:1309–1327. doi:10.1016/j.ijplas.2011.03.003

    Article  MATH  Google Scholar 

  17. Ponthot J-P, Kleinermann J-P (2006) A cascade optimization methodology for automatic parameter identification and shape/process optimization in metal forming simulation. Comput Methods Appl Mech Engrg 195:5472–5508. doi:10.1016/j.cma.2005.11.012

    Article  MATH  Google Scholar 

  18. Oliveira MC, Alves JL, Chaparro BM, Menezes LF (2007) Study on the influence of work-hardening modeling in springback prediction. Int J Plast 23:516–543. doi:10.1016/j.ijplas.2006.07.003

    Article  MATH  Google Scholar 

  19. Chaparro BM, Thuillier S, Menezes LF, Manach PY, Fernandes JV (2008) Material parameters identification: Gradient-based, genetic and hybrid optimization algorithms. Comput Mater Sci 44:339–346. doi:10.1016/j.commatsci.2008.03.028

    Article  Google Scholar 

  20. Rabahallah M, Balan T, Bouvier S, Bacroix B, Barlat F, Chung K, Teodosiu C (2009) Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction. Int J Plast 25:491–512. doi:10.1016/j.ijplas.2008.03.006

    Article  MATH  Google Scholar 

  21. Pottier T, Toussaint F, Vacher P (2011) Contribution of heterogeneous strain field measurements and boundary conditions modelling in inverse identification of material parameters. Eur J Mech A-Solid 30:373–382. doi:10.1016/j.euromechsol.2010.10.001

    Article  MATH  Google Scholar 

  22. Andrade-Campos A, de Carvalho R, Valente RAF (2012) Novel criteria for determination of material model parameters. Int J Mech Sci 54:294–305. doi:10.1016/j.ijmecsci.2011.11.010

    Article  Google Scholar 

  23. Rossi M, Pierron F (2012) Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields. Comput Mech 49:53–71. doi:10.1007/s00466-011-0627-0

    Article  MATH  Google Scholar 

  24. Pottier T, Vacher P, Toussaint F, Louche H, Coudert T (2012) Out-of-plane testing procedure for inverse identification purpose: application in sheet metal plasticity. Exp Mech 52:951–963. doi:10.1007/s11340-011-9555-3

    Article  Google Scholar 

  25. Xiao-qiang LI, De-hua HE (2013) Identification of material parameters from punch stretch test. Trans Nonferrous Met Soc China 23:1435–1441. doi:10.1016/S1003-6326(13)62614-X

    Article  Google Scholar 

  26. Kim J-H, Barlat F, Pierron F, Lee M-G (2014) Determination of anisotropic plastic constitutive parameters using the virtual fields method. Exp Mech 54:1189–1204. doi:10.1007/s11340-014-9879-x

    Article  Google Scholar 

  27. Avril S, Bonnet M, Bretelle A-S, Grédiac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48:381–402. doi:10.1007/s11340-008-9148-y

    Article  Google Scholar 

  28. Green DE, Neale KW, MacEwen SR, Makinde A, Perrin R (2004) Experimental investigation of the biaxial behaviour of an aluminum sheet. Int J Plast 20:1677–1706. doi:10.1016/j.ijplas.2003.11.012

    Article  MATH  Google Scholar 

  29. Cooreman S, Lecompte D, Sol H, Vantomme J, Debruyne D (2008) Identification of mechanical material behavior through inverse modeling and DIC. Exp Mech 48:421–433. doi:10.1007/s11340-007-9094-0

    Article  MATH  Google Scholar 

  30. Prates PA, Oliveira MC, Fernandes JV (2014) A new strategy for the simultaneous identification of constitutive laws parameters of metal sheets using a single test. Comp Mater Sci 85:102–120. doi:10.1016/j.commatsci.2013.12.043

    Article  Google Scholar 

  31. Schmaltz S, Willner K (2014) Comparison of different biaxial tests for the inverse identification of sheet steel material parameters. Strain. doi:10.1111/str.12080

    Google Scholar 

  32. Zhang S, Leotoing L, Guines D, Thuillier S, Zang SL (2014) Calibration of anisotropic yield criterion with conventional tests or biaxial test. Int J Mech Sci 85:142–151. doi:10.1016/j.ijmecsci.2014.05.020

    Article  Google Scholar 

  33. Khalfallah A, Bel Hadj Salah H, Dogui A (2002) Anisotropic parameter identification using inhomogeneous tensile test. Eur J Mech A-Solid 21:927–942. doi:10.1016/S0997-7538(02)01246-9

    Article  MATH  Google Scholar 

  34. Schmaltz S, Willner K (2013) Material parameter identification utilizing optical full-field strain measurement and digital image correlation. J Jap Soc Exp Mech 13:120–125. doi:10.11395/jjsem.13.s120

    Google Scholar 

  35. Güner A, Soyarslan C, Brosius A, Tekkaya AE (2012) Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld 2000–2D yield function. Int J Solids Struct 49:3517–3527. doi:10.1016/j.ijsolstr.2012.05.001

    Article  Google Scholar 

  36. Kim J-H, Barlat F, Pierron F, Lee M-G (2014) Determination of anisotropic plastic constitutive parameters using the virtual fields method. Exp Mech 54:1189–1204. doi:10.1007/s11340-014-9879-x

    Article  Google Scholar 

  37. Ghouati O, Gelin JC (1998) Identification of material parameters directly from metal forming processes. J Mater Process Technol 80–81:560–564. doi:10.1016/S0924-0136(98)00159-9

    Article  Google Scholar 

  38. Ghouati O, Gelin JC (2001) A finite element-based identification method for complex metallic material behaviours. Comput Mater Sci 21:57–68. doi:10.1016/S0927-0256(00)00215-9

    Article  Google Scholar 

  39. Marquardt DW (1963) An algorithm for least squares estimation of non-linear parameters. J Soc Ind Appl Math 11:431–441. doi:10.1137/0111030

    Article  MathSciNet  MATH  Google Scholar 

  40. Güner A, Yin Q, Soyarslan C, Brosius A, Tekkaya AE (2011) Inverse method for identification of initial yield locus of sheet metals utilizing inhomogeneous deformation fields. Int J Mater Form 4:121–128. doi:10.1007/s12289-010-1009-4

    Article  Google Scholar 

  41. Oliveira MC, Alves JL, Menezes LF (2008) Algorithms and strategies for treatment of large deformation frictional contact in the numerical simulation of deep drawing process. Arch Comput Method Eng 15:113–162. doi:10.1007/s11831-008-9018-x

    Article  MathSciNet  MATH  Google Scholar 

  42. Hosford WF (1972) A generalized isotropic yield criterion. J Appl Mech -T ASME 39:607–9. doi:10.1115/1.3422732

    Article  Google Scholar 

  43. Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. J Appl Mech -T ASME 16:349–357

    MathSciNet  MATH  Google Scholar 

  44. Prates PA, Oliveira MC, Fernandes JV (2014) On the equivalence between sets of parameters of the yield criterion and the isotropic and kinematic hardening laws. Inter J Mater Form 1–11. doi:10.1007/s12289-014-1173-z

  45. Chaparro BM (2006) Comportamento plástico de materiais metálicos: identificação e optimização de parâmetros. Dissertation, University of Coimbra

  46. Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transformation-based anisotropic yield function. Int J Plast 21:1009–1039. doi:10.1016/j.ijplas.2004.06.004

    Article  MATH  Google Scholar 

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Acknowledgments

This research work is sponsored by national funds from the Portuguese Foundation for Science and Technology (FCT) via the projects PTDC/EME–TME/113410/2009 and PEst-C/EME/UI0285/2013 and by FEDER funds through the program COMPETE – Programa Operacional Factores de Competitividade, under the project CENTRO-07-0224-FEDER-002001 (MT4MOBI). One of the authors, P.A. Prates, was supported by a grant for scientific research from the Portuguese Foundation for Science and Technology (SFRH/BD/68398/2010). All supports are gratefully acknowledged.

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Authors and Affiliations

  1. CEMUC—Department of Mechanical Engineering, University of Coimbra, Rua Luís Reis Santos, Pinhal de Marrocos, 3030-788, Coimbra, Portugal

    P. A. Prates, M. C. Oliveira & J. V. Fernandes

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  1. P. A. Prates
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  2. M. C. Oliveira
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  3. J. V. Fernandes
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Correspondence to P. A. Prates.

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Highlights

•Inverse identification strategy based on a single cruciform tensile test.

•Simultaneous identification of yield criterion and work-hardening law parameters.

•Sequential parameter identification procedure, using distinct cost functions.

•Load evolution and principal strains at a single load step, for both axes are used.

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Prates, P.A., Oliveira, M.C. & Fernandes, J.V. Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy. Int J Mater Form 9, 547–571 (2016). https://doi.org/10.1007/s12289-015-1241-z

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  • DOI: https://doi.org/10.1007/s12289-015-1241-z

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