Nonlinear stress path experiment using mild steel sheet for validation of material model

Nonlinear stress path experiment using mild steel sheet for validation of material model

TAKADA Yusuke, KUWABARA Toshihiko

download PDF

Abstract. A linear stress path (LSP) experiment was performed using uniaxial and biaxial tensile tests with a cold-rolled mild steel sheet (SPCD; nominal thickness: 0.8 mm) as the test material. In the LSP experiment, nine LSPs were applied to the specimens to measure the contours of plastic work and the directions of the plastic strain rates, β, for a plastic strain range of 0.002 ≤〖 ε〗_0^p ≤ 0.234. Then, the Yld2000-2d yield function (Barlat et al., 2003) was used to identify a material model that accurately reproduces the experimental data observed in the LSP experiment. Furthermore, a nonlinear stress path (NLSP) experiment was performed. The NLSP consists of two linear stress paths with σ_x:σ_y = 4:1 and 1:1, and a curved stress path connecting the LSPs. The measured work hardening behavior and β values were compared with those calculated using the Yld2000-2d yield function identified from the LSP experiment. It was found that the deformation behavior of the test sample predicted by the material model determined from the LSP experiment clearly shows some deviation from that observed for the NLSP experiment.

Mechanical Test, Biaxial Stress, Mild Steel Sheet, Yield Function, Linear Stress Path, Nonlinear Stress Path, Contour Of Plastic Work, Biaxial Tube Expansion Test

Published online 4/19/2023, 8 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: TAKADA Yusuke, KUWABARA Toshihiko, Nonlinear stress path experiment using mild steel sheet for validation of material model, Materials Research Proceedings, Vol. 28, pp 779-786, 2023


The article was published as article 85 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] T. Kuwabara, S. Ikeda, K. Kuroda, Measurement and analysis of differential work-hardening in cold-rolled steel sheet under biaxial tension, J. Mater. Process. Technol. 80-81 (1998) 517-523.
[2] T. Kuwabara, A. Van Bael, E. Iizuka, Measurement and analysis of yield locus and work-hardening characteristics of steel sheets with different R-values, Acta Mater. 50 (2002) 3717-3729.
[3] T. Kuwabara, F. Sugawara, Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range. Int. J. Plast. 45 (2013) 103-118.
[4] S.S. Hecker, Yield surfaces in prestrained aluminum and copper, Metal. Trans. 2 (1971) 2077-2086.
[5] K. Ikegami, A historical perspective of experimental study on subsequent yield surfaces for metals (part 1), J. Soc. Mat. Sci., Jpn. 24 (1975) 491-504 (in Japanese)
[6] K. Ikegami, A historical perspective of experimental study on subsequent yield surfaces for metals (part 2), J. Soc. Mat. Sci., Jpn., 24 (1975) 709-719 (in Japanese).
[7] Y. Ohashi, K. Kawashima, T. Yokochi, Anisotropy due to plastic deformation of initially isotropic mild steel and its analytical formulation, J. Mech. Phys. Solid. 23 (1975) 277-294.
[8] E. Shiratori, K. Ikegami, K. Kaneko, The influence of the Bauschinger effect on the subsequent yield condition, Bull. JSME 16 (1973) 1482-1493.
[9] F. Barlat, S.Y. Yoon, S.Y. Lee, M.S. Wi, J.H. Kim, Distortional plasticity framework with application to advanced high strength steel, Int. J. Solids Struct. 202 (2020) 947-962.
[10] J.J. Ha, M.-G. Lee, F. Barlat, Strain hardening response and modeling of EDDQ and DP780 steel sheet under non-linear strain path, Mech. Mater. 64 (2013) 11-26.
[11] H. Kim, F. Barlat, Y. Lee, S.B. Zaman, C.S. Lee, Y. Jeong, A crystal plasticity model for describing the anisotropic hardening behavior of steel sheets during strain-path changes, Int. J. Plast. 111 (2018) 85-106.
[12] J. Qin, B. Holmedal, O.S. Hopperstad, A combined isotropic, kinematic and distortional hardening model for aluminum and steels under complex strain-path changes, Int. J. Plast. 101 (2018) 156-169.
[13] M.S. Wi, S.Y. Lee, J.H. Kim, J.M. Kim, F. Barlat, Experimental and theoretical plasticity analyses of steel materials deformed under a nonlinear strain path, Int. J. Mech. Sci. 182 (2020) 105770.
[14] S.S. Hecker, Experimental Investigation of Corners in the Yield Surface, Acta Mech. 13 (1972) 69-86.
[15] T. Kuwabara, M. Kuroda, V. Tvergaard, K. Nomura, Use of abrupt strain path change for determining subsequent yield surface: experimental study with metal sheets, Acta Mater. 48 (2000) 2071-2079.
[16] K. Yoshida, T. Tsuchimoto, Plastic flow of thin-walled tubes under nonlinear tension-torsion loading paths and an improved pseudo-corner model, Int. J. Plast. 104 (2018) 214-229.
[17] T. Hama, S. Yagi, K. Tatsukawa, Y. Maeda, Y. Maeda, H. Takuda, Evolution of plastic deformation behavior upon strain-path changes in an A6022-T4 Al alloy sheet, Int. J. Plast. 137 (2021) 102913.
[18] Y. Takada, T. Kuwabara, Nonlinear biaxial tensile stress path experiment without intermediate elastic unloading for validation of material model, Int. J. Solid. Struct. 257 (2022) 111777.
[19] ISO 16842: 2014 Metallic materials −Sheet and strip −Biaxial tensile testing method using a cruciform test piece.
[20] T. Hakoyama, T. Kuwabara, Effect of biaxial work hardening modeling for sheet metals on the accuracy of forming limit analyses using the Marciniak-Kuczynski approach, in: H. Altenbach, T. Matsuda, D. Okumura (Eds.), From Creep Damage Mechanics to Homogenization Methods, Springer, 2015, pp. 67-95.
[21] F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, D.J. Lege, F. Pourboghrat, S.H. Choi, E. Chu, Plane stress yield function for aluminum alloy sheets-part 1: theory, Int. J. Plast. 19 (2003) 1297-1319.
[22] R. Hill, J.W. Hutchinson, Differential hardening in sheet metal under biaxial loading: a theoretical framework, J. Appl. Mech. 59 (1992) S1-S9.
[23] R. Hill, S.S. Hecker, M.G. Stout, An investigation of plastic flow and differential work hardening in orthotropic brass tubes under fluid pressure and axial load, Int. J. Solid. Struct. 31 (1994) 2999-3021.