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Out-of-plane Testing Procedure for Inverse Identification Purpose: Application in Sheet Metal Plasticity

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Abstract

Many recent works in inverse identification of constitutive parameters have pointed to the need of tests which exhibit heterogeneous strain paths. The present study details a new testing procedure based on out-of-plane motion capture by Stereo-Image Correlation (SIC). With the original test proposed hereby, a unique sample is deformed on a tensile machine along two perpendicular tensile directions, two perpendicular shear directions and one expansion area. The choice of the sample shape is discussed along with the stereo imaging device, 3D reconstruction and measurement uncertainties. The test sample is made from a sheet of commercially pure titanium. A Finite-Element updating inverse method is applied in order to identify six parameters of an anisotropic plastic constitutive model. Results show that this new testing procedure allows every constitutive parameter of the model to be identified from one and only one test.

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References

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

    Article  MATH  Google Scholar 

  2. Ferron G, Makkouk R, Morreale J (1994) A parametric description of orthotropic plasticity in metal sheets. Int J Plast 10(5):431–449

    Article  MATH  Google Scholar 

  3. Barlat F, Becker RC, Hayashida Y, Maeda Y, Yanagawa M, Chung K, Brem JC, Lege DJ, Matsui K, Murtha SJ, Hattori S (1997) Yielding description for solution stenghtened aluminum alloys. Int J Plast 13:385–401

    Article  Google Scholar 

  4. Cazacu O, Barlat F (2003) Application of the theory of representation to describe yielding of anisotropic aluminum alloys. Int J Eng Sci 41(12):1367–1385

    Article  Google Scholar 

  5. Hu W (2007) A novel quadratic yield model to describe the feature of multi-yield-surface of rolled sheet metals. Int J Plast 23:2004–2028

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Avril S, Bonnet M, Bretelle AS, 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 

  8. Kajberg J, Lindkvist G (2004) Characterization of materials subjected to large strains by inverse modeling based on in-plane displacement fields. Int J Solids Struct 41:3439–3459

    Article  MATH  Google Scholar 

  9. Pannier Y (2006) Identification de paramètres élastoplastiques par des essais statiquement indéterminés : mise en œuvre expérimentale et validation de la méthode des champs virtuels. PhD thesis, Ecole National Supérieure des Arts et Métiers, France

  10. Belhabib S, Haddadi H, Gaspérini M, Vacher P (2007) Heterogeneous tensile test on elastoplastic metallic sheets: comparison between FEM simulations and full-field strain measurements. Int J Mech Sci 50:14–21

    Article  Google Scholar 

  11. Molimard J, Le Riche R, Vautrin A, Lee JR (2005) Identification of the four orthotropic plate stiffnesses using a single open-hole tensile test. Exp Mech 45:404–411

    Article  Google Scholar 

  12. Meuwissen MHH (1998) An inverse method for mechanical characterization of metal. PhD thesis, Eindhoven University of Technology, Netherlands

  13. Cooreman S (2008) Identification of the plastic material behaviour through full-field displacement measurements and inverse methods. PhD thesis, Vrije Universitet Brussel, Belgique

  14. Kuwabara T, Kuroda M, Tvergaard V, Nomura K (2000) Use of abrupt strain path change for determining subsequent yield surface: experimental study with metal sheets. Acta Mater 48:2071–2079

    Article  Google Scholar 

  15. Lecompte D, Smits A, Sol H, Vantomme J, Van Hemelrijck D (2007) Mixed numerical-experimental technique for orthotropic parameter identification using biaxial tensile test on cruciform specimens. Int J Solids Struct 44:1643–1656

    Article  Google Scholar 

  16. Promma N, Raka B, Grédiac M, Toussaint E, LeCam J-B, Balandraud X, Hild F, Application of the virtual fields method to mechanical (2009) characterization of elastomeric materials. Int J Solids Struct 46:698–715

    Article  MATH  Google Scholar 

  17. Guélon T, Toussaint E, Le Cam J-B, Promma N, Grédiac M (2009) A new characterisation method for rubber. Polym Test 28(7):715–723

    Article  Google Scholar 

  18. Bruno L, Felice G, Pagnotta L, Poggialini A, Stigliano G (2008) Elastic characterization of orthotropic plates of any shape via static testing. Int J Solids Struct 45:908–920

    Article  MATH  Google Scholar 

  19. Chamekh A, BelHadjSalah H, Hambli R, Gahbiche A (2006) Inverse identification using the bulge test and artificial neural networks. J Mater Process T echnol 177(1–3):307–310

    Article  Google Scholar 

  20. Ghouati O, Gelin JC (2001) A finite element-based identification method for complex metallic material behaviours. Comput Mater Sci 21:57–68

    Article  Google Scholar 

  21. Forestier R (2004) Développement d’une méthode d’identifcation de paramètres matériaux par analyse inverse couplée avec un modèle éléments-finis 3D. PhD thesis, Ecole Nationale Supérieure des Mines de Paris

  22. Garcia D, Orteu JJ, Penazzi L (2002) A combined temporal tracking and stereo-correlation technique for accurate measurement of 3D displacements: application to sheet metal forming. J Mater Process Technol 125–126:736–742

    Article  Google Scholar 

  23. Coudert T (2005) Reconstruction tridimensionnelle du volume intérieur d’une chaussure: évaluation du chaussant. PhD thesis, Université de Savoie

  24. Vacher P, Dumoulin S, Morestin F, Mguil-Touchal S (1999) Bidimensional strain measurement using digital images. Proc Inst Mech Eng 213:811–817

    Google Scholar 

  25. Sutton MA, Yan JH, Tiwari V, Schreier WH, Orteu JJ (2008) The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt Lasers Eng 46:746–757

    Article  Google Scholar 

  26. Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11:431–441

    Article  MathSciNet  MATH  Google Scholar 

  27. De Almeida O, Lagattu F, Brillaud J (2008) Analysis by a 3D DIC technique of volumetric deformation gradients: application to polypropylene/EPR/talc composites. Compos, Part A 39:1210–1217

    Article  Google Scholar 

  28. Haddadi H, Belhabib S (2008) Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Opt Lasers Eng 46:185–196

    Article  Google Scholar 

  29. Pan B, Xie H, Gao J, Asundi A (2008) Improved speckle projection profilometry for out-of-plane shape measurement. Appl Opt 47:5527–5533

    Article  Google Scholar 

  30. Pan B, Lu Z, Xie H (2010) Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation. Opt Lasers Eng 48:469–477

    Article  Google Scholar 

  31. Chambard J-P, Jaminion S, Tazeroualti M, Galerne C, Hild F (2009) 3D displacement field measurement by digital image correlation - metrological study and application to composite structures. In: Comptes Rendus des JNC 16 – Toulouse

  32. Garcia D (2001) Mesure de formes et de champs de déplacements tridimensionnels par stéréo-corrélation d’images. PhD thesis, Institut National Polytechnique de Toulouse

  33. Fazzini M (2009) Développement de méthodes d’intégration des mesures de champs. PhD thesis, Université de Toulouse, France

  34. Toussaint F, Tabourot L, Ducher F (2008) Experimental and numerical analysis of the forming process of CP titanium scoliotic instrumentation. J Mater Process Technol 197:10–16

    Article  Google Scholar 

  35. Haddadi H, Bouvier S, Banu M, Maier C, Teodosiu C (2006) Towards an accurate description of the anisotropic behaviour of sheet metals under large plastic deformations: modelling, numerical analysis and identification. Int J Plast 22:2226–2271

    Article  MATH  Google Scholar 

  36. Le Port A, Toussaint F, Arrieux R (2009) Finite element study and sensitivity analysis of the deep-drawing formability of commercially pure titanium. Int J Mater Form 2:121–129

    Article  Google Scholar 

  37. Boissière R (2008) Effet de la température sur les capacités de mise en forme d’alliages de magnésium corroyés. PhD thesis, INP Grenoble, Université de Savoie, France

  38. Pottier T (2010) Identification paramétrique par recalage de modèles éléments finis couplée à des mesures de champs cinématiques et thermiques. PhD thesis, Université de Savoie, France

  39. Kleinermann J-P (2000) Identification paramétrique et optimisation des procédés de mise en forme par problème inverse. PhD thesis, Université de Liège, Belgique

  40. Gelin JC, Ghouati O, Paquier P (1998) Modelling and control of hydroforming processes for flanges forming. Ann CIRP 47(1):213–216

    Article  Google Scholar 

  41. Harth T, Schwan S, Lehn J, Kollmann FG (2004) Identification of material parameters for inelastic constitutive models: statistical analysis and design of experiments. Int J Plast 20:1403–1440

    Article  MATH  Google Scholar 

  42. Amiot F, Hild F, Roger J-P (2007) Identification of elastic property and loading fields from full-field displacement measurements. Int J Solids Struct 44:2863–2887

    Article  MATH  Google Scholar 

  43. Nakamura T, Liu Y (2007) Determination of nonlinear properties of thermal sprayed ceramic coatings via inverse analysis. Int J Solids Struct 44:1990–2009

    Article  MATH  Google Scholar 

  44. 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/Solids 30:372–382

    Article  Google Scholar 

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Authors and Affiliations

  1. Chiang Mai University, Faculty of Engineering, Department of Mechanical Engineering, Chiang Mai, 50200, Thailand

    T. Pottier

  2. Laboratoire SYMME, Université de Savoie, Polytech’Annecy-Chambéry BP, 80439, 74944, Annecy le Vieux Cedex, France

    P. Vacher & F. Toussaint

  3. Laboratoire de Mécanique et Génie Civil, Université Montpellier II, pl. E. Bataillon, 34095, Montpellier Cedex, France

    H. Louche

  4. SINTEF Materials and Chemistry, Trondheim, Norway

    T. Coudert

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  1. T. Pottier
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  2. P. Vacher
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  3. F. Toussaint
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  4. H. Louche
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  5. T. Coudert
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Correspondence to T. Pottier.

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Pottier, T., Vacher, P., Toussaint, F. et al. Out-of-plane Testing Procedure for Inverse Identification Purpose: Application in Sheet Metal Plasticity. Exp Mech 52, 951–963 (2012). https://doi.org/10.1007/s11340-011-9555-3

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  • DOI: https://doi.org/10.1007/s11340-011-9555-3

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