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Application of a Graphical Method on Estimating Forming Limit Curve of Automotive Sheet Metals

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Abstract

In the automotive engineering community, the modified maximum force criterion proposed by Hora and co-workers is considered acceptable for theoretically estimating the forming limit curve (FLC) of sheet metals. Based on this criterion, a graphical method is proposed to simplify evaluation of the FLC. This paper investigates the proposed graphical method in a special case by using a power-hardening law and the Mises yield function, which leads to an explicit expression of the critical strains according the strain paths. The FLC of a DP590 sheet estimated using the proposed method is compared with that estimated using existing analytical methods. The proposed method provides the best prediction of the FLC of the tested material. For verification, the calculated FLC is then adopted into the finite-element method to predict the punch stroke at fracture of several notched specimens subjected to Nakazima tests. The good agreement between the predicted and experimentally determined values of the punch strokes verifies the ability and potential of the proposed method in industrial engineering.

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References

  • Chu, C. (1982). An investigation of the strain path dependence of the forming limit curve. Int. J. Solids and Structures 18, 3, 205–215.

    Article  Google Scholar 

  • Do, V. C., Pham, Q. T. and Kim, Y. S. (2017). Identification of forming limit curve at fracture in incremental sheet forming. Int. J. Advanced Manufacturing Technology 92, 9–12, 4445–4455.

    Article  Google Scholar 

  • Hill, R. (1950). Mathematical Theory of Plasticity. Clarendon Press. Oxford, UK.

    MATH  Google Scholar 

  • Hill, R. (1952). On discontinuous plastic states with special reference to localized necking inn thin sheets. J. Mechanics and Physics of Solids 1, 1, 19–30.

    Article  MathSciNet  Google Scholar 

  • Hora, P., Tong, L. and Berisha, B. (2013). Modified maximum force criterion, a model for the theoretical prediction of forming limit curves. Int. J. Material Forming 6, 2, 267–279.

    Article  Google Scholar 

  • Korhonen, A. S. (1978). On the theories of sheet metal necking and forming limits. J. Engineering Materials and Technology 100, 3, 303–309.

    Article  Google Scholar 

  • Marciniak, Z. and Kuczynski, K. (1967). Limit strains in the processes of stretch-forming sheet metal. Int. J. Mechanical Sciences 9, 9, 613–620.

    Article  Google Scholar 

  • Pham, Q. T., Lee, B. H., Park, K. C. and Kim, Y. S. (2018). Influence of the post-necking prediction of hardening law on the theoretical forming limit curve of aluminium sheets. Int. J. Mechanical Sciences, 140, 521–536.

    Article  Google Scholar 

  • Pham, Q. T., Nguyen, D. T., Kim, J. J. and Kim, Y. S. (2018). A graphical method to estimate forming limit curve of sheet metals. Proc. AEPA2018, Jeju, Korea.

  • Pham, Q. T., Nguyen, D. T., Kim, J. J. and Kim, Y. S. (2019). A graphical method to estimate forming limit curve of sheet metals. Key Engineering Materials, 794, 55–62.

    Article  Google Scholar 

  • Sing, W. M. and Rao, K. P. (1993). Prediction of sheet metal formability using tensile test results. J. Materials Processing Technology 37, 1–4, 37–51.

    Article  Google Scholar 

  • Storen, S. and Rice, J. R. (1975). Localized necking in thin sheets. J. Mechanics and Physics of Solids 23, 6, 421–441.

    Article  Google Scholar 

  • Stoughton, T. B. and Zhu, X. (2004). Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD. Int. J. Plasticity 20, 8–9, 1463–1486.

    Article  Google Scholar 

  • Swift, H. W. (1952). Plastic instability under plane stress. J. Mechanics and Physics of Solids 1, 1, 1–18.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgement

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019R1A2C1011224).

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Correspondence to Young Suk Kim.

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This paper was significantly extended and modified from the original paper presented in Asia-Pacific Symposium on Engineering Plasticity and its Applications 2018, and recommended by the Scientific & Technical Committee for journal publication.

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Pham, Q.T., Kim, J., Luyen, T.T. et al. Application of a Graphical Method on Estimating Forming Limit Curve of Automotive Sheet Metals. Int.J Automot. Technol. 20 (Suppl 1), 3–8 (2019). https://doi.org/10.1007/s12239-019-0122-8

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  • DOI: https://doi.org/10.1007/s12239-019-0122-8

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