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Mechanical characterization of anisotropic elasto-plastic materials by indentation curves only

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Abstract

Anisotropy, usually orthotropy, arises in structural materials, particularly metals, due to production processes like laminations and concerns primarily parameters which govern the plastic behavior. Identification of such parameters is investigated here by a novel approach with the following features: experimental data provided by indentation curves only (not by imprint geometry); indenter shape with elliptical cross-section derived from classical conical or spherical shape and optimized by sensitivity analyses; indentation test repeated in near places after indenter rotation; deterministic inverse analyses centered on discrepancy function minimization and made computationally economical by an ‘a priori’ model reduction procedure.

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References

  1. Tabor D (1951) The hardness of metals. Clarendon Press, Oxford

    Google Scholar 

  2. Mott BW (1957) Microindentation hardness testing. Butterworths, London

    Google Scholar 

  3. Bolzon G, Maier G, Panico M (2004) Material model calibration by indentation, imprint mapping and inverse analysis. Int J Solids Struct 41:2957–2975

    Article  MATH  Google Scholar 

  4. Bocciarelli M, Bolzon G, Maier G (2005) Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping. Mech Mater 37:855–868

    Article  Google Scholar 

  5. Vlassak J, Nix WD (1994) Measuring the elastic properties of anisotropic materials by means of indentation experiments. J Mech Phys Solids 42:1223–1245

    Article  ADS  Google Scholar 

  6. Jorgensen O, Giannakopoulos AE, Suresh S (1998) Spherical indentation of composite laminates with controlled gradients in elastic anisotropy. Int J Solids Struct 58:505–513

    Google Scholar 

  7. Swadener JG, Pharr GM (2001) Indentation of elastically anisotropic half-spaces by cones and parabolas of revolution. Philos Mag A 81:447–466

    Article  ADS  Google Scholar 

  8. Vlassak J, Ciavarella M, Barber JR, Wang X (2003) The indentation modulus of elastically anisotropic materials for indenter of arbitrary shape. J Mech Phys Solids 51:1701–1721

    Article  ADS  MATH  Google Scholar 

  9. Swadener JG, Rho J-Y, Pharr GM (2001) Effect of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone. J Biomed Mater Res 57:108–112

    Article  Google Scholar 

  10. Hengberger S, Enstoem J, Peyrin F, Zysset P (2003) How is the indentation modulus of bone related to its macroscopic elastic response? A validation study. J Biomech 36:1503–1509

    Article  Google Scholar 

  11. Yonezu A, Kuwahara Y, Yoneda K, Hirakata H, Minoshima K (2009) Estimation of anisotropic plastic properties using single spherical indentation-an FEM study. Comput Mater Sci 47:611–619

    Article  Google Scholar 

  12. Yonezu A, Tanaka M, Kusano R, Chen X (2013) Probing out-of-plane anisotropic plasticity using spherical indentation: a numerical approach. Comput Mater Sci 79:336–344

    Article  Google Scholar 

  13. Nakamura T, Gu Y (2007) Identification of elastic-plastic anisotropic parameters using instrumented indentation and inverse analysis. Mech Mater 39:340–356

    Article  Google Scholar 

  14. Bocciarelli M, Maier G (2007) Indentation and imprint mapping method for identification of residual stresses. Comput Mater Sci 39:381–392

    Article  Google Scholar 

  15. Buljak V, Maier G (2012) Identification of residual stresses by instrumented elliptical indentation and inverse analysis. Mech Res Commun 41:21–29

    Article  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  17. Lubliner J (2008) Plasticity theory. Dover Publications, New York

    MATH  Google Scholar 

  18. Jirasek M, Bazant Z (2002) Inelastic Analysis of Structures. Wiley, London

    Google Scholar 

  19. Abaqus (2006) Standard, Theory and User’s manuals, Release 6.7, Simulia Inc., Providence, RI 02909, USA

  20. Matlab (2002) User’s guide and optimization toolbox, release 6.13, The Math Works Inc., USA

  21. Nocedal J, Wright SJ (2006) Numerical optimization. Springer, New York

    MATH  Google Scholar 

  22. Buljak V (2012) Inverse analysis with model reduction – Proper Orthogonal Decomposition in structural mechanics. Springer, Berlin

    Book  Google Scholar 

  23. Jolliffe IT (1986) Principal component analysis. Springer, New York

    Book  Google Scholar 

  24. Buljak V, Maier G (2011) Proper orthogonal decomposition and radial basis functions in material characterization based on instrumented indentation. Eng Struct 33:492–501

    Article  Google Scholar 

  25. Kleiber M, Antunez H, Hien TD, Kowalczyk P (1997) Parameter sensitivity in non-linear mechanics. Willey, Chichester

    Google Scholar 

  26. Bui HD (1994) Inverse problems in the mechanics of materials: an introduction. CRC Press, Boca Raton

    Google Scholar 

  27. Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. Society for industrial and Applied Mathematics, Philadelphia

    Book  MATH  Google Scholar 

  28. Buhmann MD (2003) Radial basis functions. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

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Acknowledgments

Thanks are expressed by the authors to Tetrapak Company, Modena Factory, for support to Dr. V. Buljak during his research activity in Milan.

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Correspondence to M. Bocciarelli.

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This paper is dedicated to Professor Piotr Perzyna, outstanding scientist in solid mechanics, who passed away last year.

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Buljak, V., Bocciarelli, M. & Maier, G. Mechanical characterization of anisotropic elasto-plastic materials by indentation curves only. Meccanica 49, 1587–1599 (2014). https://doi.org/10.1007/s11012-014-9940-y

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  • DOI: https://doi.org/10.1007/s11012-014-9940-y

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