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Necking Limits of Anisotropic Metal Sheets Using M-K Theory and Improved Plasticity Models

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Abstract:

Accurate prediction of the forming limit curve (FLC) is critical for evaluating sheet metal formability, yet the influence of plastic anisotropy remains controversial. In this study, the yielding behavior, hardening response, and strain-rate sensitivity of DC01 steel are experimentally characterized. Different yield criteria combined with a Swift hardening law and the Marciniak-Kuczyński (M-K) model are employed to predict the FLC. The results show that the high-order non-quadratic Yld2k-2d yield criterion captures both the yielding behavior and the forming limits. Numerical experiments using this material framework are then conducted. Variations in r-values have a limited effect on the FLC, in contrast to the common notion that high r-values mean high formability, whereas the equibiaxial tensile yield stress strongly governs the right-hand side.

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Periodical:

Solid State Phenomena (Volume 388)

Pages:

227-236

DOI:

https://doi.org/10.4028/p-zmGcu2

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Cite this paper

Online since:

April 2026

Authors:

Yong Hou*, Monica Trask, Yannis P. Korkolis

Keywords:

Formability, Marciniak-Kuczynski Theory, Necking Limit, Plastic Anisotropy

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Creative Commons CC BY 4.0

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References

[1] W. Lankford, S. Snyder, J. Bauscher, New Criteria in Predicting the Press Performance of Deep Drawing Sheets, Trans. ASM. 42 (1950) 1197-1232.

Google Scholar

[2] W. Panknin, J. Grosch, The Effect of Workpiece Material on Cracks in Deep Drawing of Unkilled Steels, Bänder Bleche Röhre. 10 (1969) 339-348.

Google Scholar

[3] L. Lilet, M. Wybo, Investigation into the Effect of Plastic Anisotropy and Rate of Work Hardening in Deep Drawing, Sheet Met. Ind. 41 (1964) 783-803.

Google Scholar

[4] S. Kohara, Forming-limit curves of aluminum and aluminum alloy sheets and effects of strain path on the curves, J. Mater. Process. Technol. 38 (1993) 723-735.

DOI: 10.1016/0924-0136(93)90046-9

Google Scholar

[5] Z. Marciniak, K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal, Int. J. Mech. Sci. 9 (1967) 609-620.

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

Google Scholar

[6] J. Hutchinson, K. W. Neale, Sheet necking-II. Time-independent behavior, Mechanics of Sheet Metal Forming: Material Behavior and Deformation Analysis. Boston, MA, Springer US (1978) 127-153.

DOI: 10.1007/978-1-4613-2880-3_6

Google Scholar

[7] R. Sowerby, J. L. Duncan, Failure in sheet metal in biaxial tension, Int. J. Mech. Sci. 13(3) (1971) 217-229.

DOI: 10.1016/0020-7403(71)90004-x

Google Scholar

[8] A. Graf, W. F. Hosford, Calculations of forming limit diagrams, Metall. Trans. A. 21(1) (1990) 87-94.

DOI: 10.1007/bf02656427

Google Scholar

[9] ISO 16808 (2014) Metallic Materials - Sheet Strip - Determination of biaxial stress-strain curve by means of a bulge test with optical measuring systems.

DOI: 10.3403/30254283u

Google Scholar

[10] N. Tardif, S. Kyriakides, Determination of anisotropy and material hardening for aluminum sheet metal, Int. J. Solids Struct. 49(25) (2012) 3496-3506.

DOI: 10.1016/j.ijsolstr.2012.01.011

Google Scholar

[11] M. Baral, J. Ha, Y. P. Korkolis, Plasticity and ductile fracture modeling of an Al–Si–Mg die-cast alloy, Int. J. Fract. 216(2) (2019) 101-121.

DOI: 10.1007/s10704-019-00345-1

Google Scholar

[12] C. P. Dick, Y. P. Korkolis, Anisotropy of thin-walled tubes by a new method of combined tension and shear loading, Int. J. Plast. 71 (2015) 87-112.

DOI: 10.1016/j.ijplas.2015.04.006

Google Scholar

[13] H. Tian, B. Brownell, M., Y. P. Korkolis, Earing in cup-drawing of anisotropic Al-6022-T4 sheets, Int. J. Mater. Form. 10(3) (2017) 329-343.

DOI: 10.1007/s12289-016-1282-y

Google Scholar

[14] ISO 12004 (2021) Metallic Materials - Determination of forming-limit curves for sheet and strip - Part 2: Determination of forming-limit curves in the laboratory.

DOI: 10.3403/30150423

Google Scholar

[15] W. Volk, P. Hora, New algorithm for a robust user-independent evaluation of beginning instability for the experimental FLC determination, Int. J. Mech. Sci. 4(3) (2011) 339–346.

DOI: 10.1007/s12289-010-1012-9

Google Scholar

[16] Q. Hu, X. Li, J. Chen, New robust algorithms for Marciniak-Kuczynski model to calculate the forming limit diagrams, Int. J. Mech. Sci. 148 (2018) 293-306.

DOI: 10.1016/j.ijmecsci.2018.09.004

Google Scholar

[17] 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(9) (2003) 1297-1319.

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

Google Scholar