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Identification of Post-necking Tensile Stress–Strain Behavior of Steel Sheet: An Experimental Investigation Using Digital Image Correlation Technique

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Abstract

The stress–strain behavior of sheet metal is commonly evaluated by tensile test. However, the true stress–strain curve is restricted up to uniform elongation of the material. Usually, after the uniform elongation of the material the true stress–strain is obtained by extrapolation. The present work demonstrates a procedure to find out the true tensile stress–strain curve of the steel sheet after necking using digital image correlation (DIC) technique. Hill’s normal anisotropic yield criteria and local strains measured by DIC technique are used to correct the local stress and strain states at the diffuse necked area. The proposed procedure is shown to successfully determine the true tensile stress–strain curve of ferritic and dual-phase steel sheets after necking/uniform elongation.

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References

  1. J. Davis, Tensile Testing, 2nd ed., ASM International, Materials Park, OH, 2004

    Google Scholar 

  2. A. Nasser, A. Yadav, P. Pathak, and T. Altan, Determination of the Flow Stress of Five AHSS Sheet Materials (DP 600, DP 780, DP780-CR, DP 780-HY and TRIP 780) Using the Uniaxial Tensile and the Biaxial Viscous Pressure Bulge (VPB) Tests, J. Mater. Process. Technol., 2010, 210, p 429–436

    Article  CAS  Google Scholar 

  3. V. Tvergaard, Necking in Tensile Bars with Rectangular Cross-section, Comput. Methods Appl. Mech. Eng., 1993, 103(1), p 273–290

    Article  Google Scholar 

  4. I. Scheider, W. Brocks, and A. Corneck, Procedure for the Determination of True Stress–Strain Curves from Tensile Tests with Rectangular Cross-section Specimens, ASME J. Eng. Mater. Technol., 2004, 126, p 70–76

    Article  Google Scholar 

  5. S. Coppieters, S. Cooreman, H. Sol, P. Van Houtte, and D. Debruyne, Identification of the Post-necking Hardening Behaviour of Sheet Metal by Comparison of the Internal and External Work in the Necking Zone, J. Mater. Process. Technol., 2011, 211, p 545–552

    Article  CAS  Google Scholar 

  6. N. Tardif and S. Kyriakides, Determination of Anisotropy and Material Hardening for Aluminum Sheet Metal, Int. J. Solids Struct., 2012, 49(25), p 3496–3506

    Article  CAS  Google Scholar 

  7. L. Wang and W. Tong, Identification of Post-necking Strain Hardening Behavior of Thin Sheet Metals from Image-Based Surface Strain Data in Uniaxial Tension Tests, Int. J. Solids Struct., 2015, 75–76, p 12–31

    Article  Google Scholar 

  8. K. Zhao, L. Wang, Y. Chang, and J. Yan, Identification of Post-necking Stress–Strain Curve for Sheet Metals by Inverse Method, Mech. Mater., 2016, 92, p 107–118

    Article  Google Scholar 

  9. D. Gerbig, A. Bower, V. Savic, and L.G. Hector, Jr., Coupling Digital Image Correlation and Finite Element Analysis to Determine Constitutive Parameters in Necking Tensile Specimens, Int. J. Solids Struct., 2016, 15, p 496–509

    Article  Google Scholar 

  10. S. Marth, H.-A. Haggblad, M. Oldenburg, and R. Ostlund, Post Necking Characterisation for Sheet Metal Materials Using Full Field Measurement, J. Mater. Process. Technol., 2016, 238, p 315–324

    Article  Google Scholar 

  11. P.W. Bridgman, Studies in Large Plastic Flow and Fracture, McGraw Hill, New York, 1952

    Google Scholar 

  12. Z.L. Zhang, M. Hauge, J. Odegard, and C. Thaulow, Determining True Stress–Strain Curve from Tensile Specimens with Rectangular Cross-section, Int. J. Solids Struct., 1999, 36, p 3497–3516

    Article  Google Scholar 

  13. P. Koc and B. Štok, Computer-Aided Identification of the Yield Curve of a Sheet Metal After Onset of Necking, Comput. Mater. Sci., 2004, 31, p 155–168

    Article  CAS  Google Scholar 

  14. J. Kajberg and G. Lindkvist, Characterisation of Materials Subjected to Large Strains by Inverse Modeling Based on In-Plane Displacement Fields, Int. J. Solids Struct., 2004, 41, p 3439–3459

    Article  Google Scholar 

  15. H. Tao, N. Zhang, and W. Tong, An Iterative Procedure for Determining Effective Stress–Strain Curves of Sheet Metals, Int. J. Mech. Mater. Des., 2009, 5, p 13–27

    Article  Google Scholar 

  16. S. Holmberg, B. Enquist, and P. Thilderkvist, Evaluation of Sheet Metal Formability, J. Mater. Process. Technol., 2004, 145, p 72–83

    Article  CAS  Google Scholar 

  17. M. Merklein, J. Lechler, and M. Geigner, Characterisation of the Flow Properties of the Quenchenable Ultra High Strength Steel 22MnB5, Ann. CIRP, 2006, 1, p 229–232

    Article  Google Scholar 

  18. M. Grediac and F. Pierron, Applying the Virtual Fields Method to the Identification of Elasto-Plastic Constitutive Parameters, Int. J. Plast., 2006, 22(4), p 602–627

    Article  CAS  Google Scholar 

  19. Y. Ling, Uniaxial True Stress–Strain After Necking, AMP J. Technol., 1996, 5, p 37–48

    Google Scholar 

  20. M.S. Joun, J.G. Eom, and M.C. Lee, A New Method for Acquiring True Stress–Strain Curves over a Large Range of Strains Using a Tensile Test and Finite Element Method, Mech. Mater., 2008, 40(7), p 586–593

    Article  Google Scholar 

  21. J.-H. Kim, A. Serpantié, F. Barlat, F. Pierron, and M.-G. Lee, Characterization of the Post-necking Strain Hardening Behavior Using the Virtual Fields Method, Int. J. Solids Struct., 2013, 50, p 3829–3842

    Article  Google Scholar 

  22. M. Dunand and D. Mohr, Hybrid Experimental–Numerical Analysis of Basic Ductile Fracture Experiments for Sheet Metals, Int. J. Solids Struct., 2010, 47(9), p 1130–1143

    Article  Google Scholar 

  23. P.C. Chakraborti and M.K. Mitra, Microstructure and Tensile Properties of High Strength Duplex Ferrite-Martensite (DFM) Steels, Mater. Sci. Eng. A, 2007, 466(1–2), p 123–133

    Article  Google Scholar 

  24. LaVision, 2017, http://www.lavision.de/en/products/strainmaster/strainmaster-dic.php.

  25. C.C. Tasan, J.P.M. Hoefnagels, and M.G.D. Geers, Identification of the Continuum Damage Parameter: An Experimental Challenge in Modeling Damage Evolution, Acta Mater., 2012, 60, p 3581–3589

    Article  CAS  Google Scholar 

  26. S.K. Paul, Predicting the Flow Behavior of Metals Under Different Strain Rate and Temperature Through Phenomenological Modeling, Comput. Mater. Sci., 2012, 65, p 91–99

    Article  CAS  Google Scholar 

  27. P. Ludwik, Element der Technologischen Mechanik, Springer, Berlin, 1909

    Book  Google Scholar 

  28. E. El-Magd and M. Abouridouane, Einfluss der Umformgeschwindigkeit und temperatur auf das Fließverhalten der Magnesiumlegierung AZ80, Z. Metallk., 2001, 92-1, p 1231–1235

    Google Scholar 

  29. E. Voce, The Relationship Between Stress and Strain for Homogeneous Deformation, J. Inst. Met., 1948, 74, p 537–562

    CAS  Google Scholar 

  30. J.H. Sung, J.H. Kim, and R.H. Wagoner, A Plastic Constitutive Equation Incorporating Strain, Strain-Rate, and Temperature, Int. J. Plast., 2010, 26, p 1746–1771

    Article  CAS  Google Scholar 

  31. J.E. Hockett and O.D. Sherby, Large Strain Deformation of Polycrystalline Metals at Low Homologous Temperatures, J. Mech. Phys. Solid, 1975, 23–2, p 87–98

    Article  Google Scholar 

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Correspondence to Surajit Kumar Paul.

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Paul, S.K., Roy, S., Sivaprasad, S. et al. Identification of Post-necking Tensile Stress–Strain Behavior of Steel Sheet: An Experimental Investigation Using Digital Image Correlation Technique. J. of Materi Eng and Perform 27, 5736–5743 (2018). https://doi.org/10.1007/s11665-018-3701-3

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  • DOI: https://doi.org/10.1007/s11665-018-3701-3

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