Measurement and Analysis of the Differential Hardening of Ultralow Carbon Steel Sheets

Abstract:

Multiaxial tube expansion tests were performed to precisely measure the work hardening behavior of mild steel sheets with different r-values for a range of strain from initial yield to fracture. The testing machine is capable of applying an arbitrary linear stress path to a tubular specimen using an electrical, closed-loop servo-control system for the axial force and internal pressure applied to the tubular specimen. Tubular specimens with an inner diameter of 44.6 mm were fabricated from the as-received sheet sample by roller bending and laser welding. Nine linear stress paths, σ_x(rolling direction) :σ_y (transverse direction) =1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1, in the first quadrant of the principal stress space were applied to the tubular specimens to measure the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work, or equivalently with increasing the reference plastic strain ; the test materials exhibited differential hardening (DH). The general trend of the DH appeared to be affected by the average r-value, or equivalently by the texture, of the materials.

• Periodical: Key Engineering Materials (Volumes 651-653)
• Pages: 552-557
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.651-653.552
• Online since: July 2015
• Authors: Chiharu Sekiguchi*, Masazumi Saito, Toshihiko Kuwabara
• Keywords: Biaxial Tensile Test, Multiaxial Tube Expansion Test, Sheet Metal Forming

References

[1] M. Kuroda, V. Tvergaard, V., Effect of strain path change on limits to ductility of anisotropic metal sheets, International Journal of Mechanical Sciences 42 (2000) 867–887.

DOI: 10.1016/s0020-7403(99)00029-6

[2] D. Banabic, F. Barlat, O. Cazacu, T. Kuwabara, Advances in anisotropy and formability, International Journal of Material Forming 3 (2010) 165–189.

DOI: 10.1007/s12289-010-0992-9

[3] T. Kuwabara, Biaxial stress testing methods for sheet metals. In Comprehensive Materials Processing; Van Tyne, C. J., Ed.; Elsevier Ltd., (2014) Vol. 1, p.95–111.

DOI: 10.1016/b978-0-08-096532-1.00106-0

[4] T. Kuwabara, Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations, Int. J. Plasticity 23 (2007) 385–419.

DOI: 10.1016/j.ijplas.2006.06.003

[5] S. Bruschi, T. Altan, D. Banabic, P.F. Bariani, A. Brosius, J. Cao, A. Ghiotti, M. Khraisheh, M. Merklein, A.E. Tekkaya, Testing and modelling of material behavior and formability in sheet metal forming, CIRP Annals - Manufacturing Technology 63 (2014).

DOI: 10.1016/j.cirp.2014.05.005

[6] T. Kuwabara, A. Van Bael and E. Iizuka, Measurement and analysis of yield locus and work hardening characteristics of steel sheets with different r-values, Acta Materialia 50 (2002) 3717–3729.

DOI: 10.1016/s1359-6454(02)00184-2

[7] ISO 16842: 2014 – Metallic materials – Sheet and strip – Biaxial tensile testing method using a cruciform test piece.

DOI: 10.3403/30430367

[8] T. Kuwabara, F. Sugawara, Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range, International Journal of Plasticity 45 (2013) 103–118.

DOI: 10.1016/j.ijplas.2012.12.003

[9] T. Hakoyama, T. Kuwabara, Measurement of the forming limit stress curve using a multi-axial tube expansion test with a digital image correlation system, Proceedings NUMISHEET 2014, AIP Conference Proceedings 1567 (2014) 636-641.

DOI: 10.1063/1.4850053

[10] T. Kuwabara, M. Ishiki, M. Kuroda, S. Takahashi, Yield locus and work-hardening behavior of a thin-walled steel tube subjected to combined tension-internal pressure, Journal de Physique IV 105 (2003) 347–354.

DOI: 10.1051/jp4:20030206

[11] T. Kuwabara, K. Yoshida, K. Narihara, S. Takahashi, Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure, International Journal of Plasticity 21 (2005) 101–117.

DOI: 10.1016/j.ijplas.2004.04.006

[12] Z. Marciniak, K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences 9 (1967) 609–620.

DOI: 10.1016/0020-7403(67)90066-5

[13] K. Ichikawa, T. Kuwabara, S. Coppieters, Forming simulation considering the differential work hardening behavior of a cold rolled interstitial-free steel sheet, Key Engineering Materials 611-612 (2014) 56–61.

DOI: 10.4028/www.scientific.net/kem.611-612.56

[14] 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, International Journal of Solids and Structures 31 (1994) 2999–3021.

DOI: 10.1016/0020-7683(94)90065-5

[15] 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, International Journal of Plasticity 19 (2003) 1297–1319.

DOI: 10.1016/s0749-6419(02)00019-0

[16] D. Yanaga, H. Takizawa, T. Kuwabara, Formulation of Differential Work Hardening of 6000 Series Aluminum Alloy Sheet and Application to Finite Element Analysis, Journal of Japan Society for Technology of Plasticity 55 (2014) 55–61. (in Japanese).

DOI: 10.9773/sosei.55.55

[17] A. Van Bael, P. Eyckens, J. Gawad, S. Coppieters, T. Kuwabara, D. Roose and P. Van Houtte, Multi-scale virtual experiments for the calibration of differential hardening models and applications for metal forming FE simulations, Proc. Plasticity 2015 (CD-ROM).

DOI: 10.1016/j.ijplas.2014.12.004