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Mechanical design of a heterogeneous test for material parameters identification

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Abstract

The main goal of this work is to design virtually a heterogeneous test, with appropriate specimen shape and boundary conditions, which leads to an inhomogeneous strain field promoting the mechanical behavior characterization of thin metallic sheets under several strain paths and strain amplitudes. Finite element simulations were carried out with a virtual material, described by an anisotropic yield criterion (Yld2004-18p) associated to a mixed hardening law. The material parameters were derived from a large experimental database of quasi-homogeneous classical tests. A shape and boundary conditions optimization process was developed based on a quantitative indicator rating the strain field information and used as a cost function for guiding the test design. A heterogeneous test showing a butterfly shape was obtained, with strain states ranging from simple shear to plane strain tension. In addition, the designed heterogeneous test was used to determine the material parameters of the aforementioned constitutive model. The reliability of this identified material parameters set was then assessed and compared with the one coming from the experimental database composed by the quasi-homogeneous classical tests.

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References

  1. Andrade-Campos A, Thuillier S, Pilvin P, Teixeira-Dias F (2007) On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models. Int J Plast 23:1349–1379

    Article  MATH  Google Scholar 

  2. Carbonnière J, Thuillier S, Sabourin F, Brunet M, Manach PY (2009) Comparison of the work hardening of metallic sheets in bending-unbending and simple shear. Int J Mech Sci 51:122–130

    Article  Google Scholar 

  3. Zang SL, Thuillier S, Port AL, Manach PY (2011) Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension. Int J Mech Sci 53:338–347

    Article  Google Scholar 

  4. 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

    Article  Google Scholar 

  5. Hosford WF (2007) R.M. Mechanics and Metallurgy, Cambridge University Press, Caddell, Metal Forming

    Google Scholar 

  6. Aretz, H, Keller, S (2011) On the Non-Balanced Biaxial Stress State in Bulge-Testing, in: Steel research international, Special edition: 10th international conference on technology of plasticity, ICTP, pp 738–743

  7. Choung JM, Cho SR (2008) Study on true stress correction from tensile tests. J Mech Sci Technol 22:1039–1051

    Article  Google Scholar 

  8. Lubineau G (2009) A goal-oriented field measurement filtering technique for the identification of material model parameters. Comput Mech 44:591–603

    Article  MATH  Google Scholar 

  9. Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7:693–712

    Article  Google Scholar 

  10. Hill RG (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A 193:281–297

    Article  MathSciNet  MATH  Google Scholar 

  11. Hosford, WF (1979) On yield loci of anisotropic cubic metals, In: 7th North American Metalworking Conference (NMRC), Dearborn, pp 191–197

  12. Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transfomation-based anisotropic yield functions. Int J Plast 21:1009–1039

    Article  MATH  Google Scholar 

  13. Bron F, Besson J (2004) A yield function for anisotropic materials application to aluminum alloys. Int J Plast 20:937–963

    Article  MATH  Google Scholar 

  14. 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

    Article  MATH  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. Soare, S (2007) On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet metal forming, in, University of Florida

  17. Grédiac M (2004) The use of full-field measurement methods in composite material characterization: interest and limitations. Compos Part A 35:751–761

    Article  Google Scholar 

  18. Grédiac, M, Hild, F (2013) Full-field measurements and identification in solid mechanics, ISTE and John Wiley & Sons

  19. Belhabib S, Haddadi H, Gaspérini M, Vacher P (2008) Heterogeneous tensile test on elastoplastic metallic sheets: comparison between FEM simulations and full-field strain measurements. Int J Mech Sci 50:14–21

    Article  MATH  Google Scholar 

  20. 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

    Article  MATH  Google Scholar 

  21. Haddadi H, Belhabib S (2012) Improving the characterization of a hardening law using digital image correlation over an enhanced heterogeneous tensile test. Int J Mech Sci 62:47–56

    Article  Google Scholar 

  22. Pottier T, Vacher P, Toussaint F (2011) Contribution of heterogeneous strain field measurements and boundary conditions modelling in inverse identification of material parameters. Eur J Mech A Solids 30:373–382

    Article  MATH  Google Scholar 

  23. Tardif N, Kyriakides S (2012) Determination of anisotropy and material hardening for aluminium sheet metal. Int J Solids Struct 49:3496–3506

    Article  Google Scholar 

  24. Zhang S, Léotoing L, Guines D, Thuillier S, Zang S (2014) Calibration of anisotropic yield criterion with conventional tests or biaxial test. Int J Mech Sci 85:142–151

    Article  Google Scholar 

  25. Zhang S, Léotoing L, Guines D, Thuillier S (2015) Potential of the cross biaxial test for anisotropy characterization based on heterogeneous strain field. Exp Mech 55:817–835

    Article  Google Scholar 

  26. Pottier T, Vacher P, Toussaint F, Louche H, Coudert T (2011) Out-of-plane testing procedure for inverse identification purpose: application in sheet metal plasticity. Exp Mech:1–13

  27. Grédiac M, Pierron F, Avril S, Toussaint E (2006) The virtual fields method for extracting constitutive parameters from full-field measurements: a review. Strain 42:233–253

    Article  Google Scholar 

  28. Güner A, Soyarslan C, Brosius A, Tekkaya AE (2012) Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld2000-2D yield function. Int J Solids Struct 49:3517–3527

    Article  Google Scholar 

  29. Souto N, Thuillier S, Andrade-Campos A (2015) Design of an indicator to characterize and classify mechanical tests for sheet metals. Int J Mech Sci 101-102:252–271

    Article  Google Scholar 

  30. Simo JC (1988) A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Comput Methods Appl Mech Eng 66:199–219

    Article  MathSciNet  MATH  Google Scholar 

  31. Chaboche JL, Rousselier G (1983) On the plastic and viscoplastic constitutive equations, Parts I and II. Int J Press Vessel Pip 105:153–158

    Article  Google Scholar 

  32. Li H, Fu MW, Lu J, Yang H (2011) Ductile fracture: experiments and computations. Int J Plast 27:147–180

    Article  Google Scholar 

  33. Souto N, Andrade-Campos A, Thuillier S (2015) Material parameter identification within an integrated methodology considering anisotropy, hardening and rupture. J Mater Process Technol 220:157–172

    Article  Google Scholar 

  34. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the nelder-mead simplex method in low dimensions. SIAM J Optim 9:112–147

    Article  MathSciNet  MATH  Google Scholar 

  35. Souto, N, Andrade-Campos, A, Thuillier, S (2015) A numerical methodology to design heterogeneous mechanical tests, submitted for publication

  36. Andrade-Campos A (2011) Development of an optimization framework for parameter identification and shape optimization problems in engineering. Int J Manuf Mater Mech Eng 1:57–79

    Google Scholar 

  37. Levenberg K (1944) A method for the solution of certain problems in least squares. Q Appl Math 2:164–168

    Article  MathSciNet  MATH  Google Scholar 

  38. Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441

    Article  MathSciNet  MATH  Google Scholar 

  39. 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

    Article  Google Scholar 

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Acknowledgments

The authors would like to acknowledge the Région Bretagne (France) for its financial support. This work was also co-financed by the Portuguese Foundation for Science and Technology via project PTDC/EME-TME/118420/2010 and by FEDER via the “Programa Operacional Factores de Competitividade” of QREN with COMPETE reference: FCOMP-01-0124-FEDER-020465. One of the authors, N. Souto, was also supported by the grant SFRH/BD/80564/2011 from the Portuguese Science and Technology Foundation. All supports are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Centre for Mechanical Technology and Automation, GRIDS, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    N. Souto & A. Andrade-Campos

  2. Univ. Bretagne Sud, FRE CNRS 3744, IRDL, F-56100, Lorient, France

    N. Souto & S. Thuillier

Authors
  1. N. Souto
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  2. A. Andrade-Campos
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  3. S. Thuillier
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Correspondence to S. Thuillier.

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Souto, N., Andrade-Campos, A. & Thuillier, S. Mechanical design of a heterogeneous test for material parameters identification. Int J Mater Form 10, 353–367 (2017). https://doi.org/10.1007/s12289-016-1284-9

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  • DOI: https://doi.org/10.1007/s12289-016-1284-9

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