Influence of the sheet thickness variability on the deep drawing of a cylindrical cup

Influence of the sheet thickness variability on the deep drawing of a cylindrical cup

PEREIRA André, PRATES Pedro, PARREIRA Tomás, OLIVEIRA Marta

download PDF

Abstract. Sheet metal forming processes are widely used in industry. The quality of formed parts can be significantly affected by various sources of uncertainty inevitably associated with the forming process. The objective of this work is to quantify the influence of thickness variability on the forming process of a cylindrical cup. Using numerical simulation, the influence of the sheet thickness variance on the evolution of the punch force versus displacement, the equivalent plastic strain distribution, the earing profile and the thickness around the cup is studied for a given cup height. Four thickness distributions with different variance values and the same average thickness value were studied. It was concluded that an increase in variance leads to an increase in thickness dispersion (at the base and curvature of the cup) and an increase in equivalent strain dispersion along the cup. The earing profile of the cup is also affected by the thickness variability, but to a lesser extent. On the other hand, the development of the punch force is not affected by the thickness variability.

Keywords
Thickness Variability, Cylindrical Cup, Uncertainty

Published online 4/24/2024, 9 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: PEREIRA André, PRATES Pedro, PARREIRA Tomás, OLIVEIRA Marta, Influence of the sheet thickness variability on the deep drawing of a cylindrical cup, Materials Research Proceedings, Vol. 41, pp 1827-1835, 2024

DOI: https://doi.org/10.21741/9781644903131-202

The article was published as article 202 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.

References
[1] A. E. Marques, P. A. Prates, A. F. G. Pereira, M. C. Oliveira, J. V. Fernandes, and B. M. Ribeiro, “Performance comparison of parametric and non-parametric regression models for uncertainty analysis of sheet metal forming processes,” Metals, vol. 10, no. 4, p. 457, 2020. https://doi.org/10.3390/met10040457
[2] A. F. G. Pereira, M. F. Ruivo, M. C. Oliveira, J. V. Fernandes, and P. A. Prates, “Numerical study of the square cup stamping process: a stochastic analysis,” ESAFORM 2021, 2021. https://doi.org/10.25518/esaform21.2158
[3] P. A. Prates, A. S. Adaixo, M. C. Oliveira, and J. V. Fernandes, “Numerical study on the effect of mechanical properties variability in sheet metal forming processes,” The International Journal of Advanced Manufacturing Technology, vol. 96, no. 1–4, pp. 561–580, 2018. https://doi.org/10.1007/s00170-018-1604-y
[4] A. Col, “Investigation on press forming scatter origin,” in Proceedings of the 6th international conference on material forming, 2003, pp. 183–6.
[5] W. Hancock, and M. Zayko, M. Autio, and D. Ponagajba, “Analysis of components of variation in automotive stamping processes,” Qual Eng, vol. 10, no. 1, pp. 115–124, 1997. https://doi.org/10.1080/08982119708919114
[6] K. D. Majeske and P. C. Hammett, “Identifying sources of variation in sheet metal stamping,” International Journal of Flexible Manufacturing Systems, vol. 15, no. 1, pp. 5–18, 2003. https://doi.org/10.1023/A:1023993806025
[7] H. Müllerschön, W. Roux, D. Lorenz, and K. Roll, “Stochastic analysis of uncertainties for metal forming processes with LS-OPT,” Proceedings NUMISHEET, Interlaken, Switzerland, 2008.
[8] V. Panjkovic, “Steel Rolling: Chatter,” in Encyclopedia of Iron, Steel, and Their Alloys, CRC Press, 2016, pp. 3333–3345. doi: 10.1081/E-EISA-120050422
[9] H. Li, H. Sun, H. Liu, and N. Liu, “Loading conditions constrained wrinkling behaviors of thin-walled sheet/tube parts during metal forming,” J Mater Process Technol, vol. 296, p. 117199, 2021. https://doi.org/10.1016/j.jmatprotec.2021.117199
[10] V. Papadopoulos and M. Papadrakakis, “The effect of material and thickness variability on the buckling load of shells with random initial imperfections,” Comput Methods Appl Mech Eng, vol. 194, no. 12–16, pp. 1405–1426, 2005. https://doi.org/10.1016/j.cma.2004.01.043
[11] Y. Luo, J. Zhan, and P. Liu, “Buckling assessment of thin-walled plates with uncertain geometrical imperfections based on non-probabilistic field model,” Thin-Walled Structures, vol. 145, p. 106435, 2019. https://doi.org/10.1016/j.tws.2019.106435
[12] A. M. Habraken et al., “Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations,” International Journal of Material Forming, vol. 15, no. 5, p. 61, 2022. https://doi.org/10.1007/s12289-022-01672-w
[13] L. F. Menezes and C. Teodosiu, “Three-dimensional numerical simulation of the deep-drawing process using solid finite elements,” J Mater Process Technol, vol. 97, no. 1–3, pp. 100–106, 2000. https://doi.org/10.1016/S0924-0136(99)00345-3
[14] B. Engel and R. Steinheimer, “Obtaining more precise flow curves from uniaxial tensile tests for FE-Simulations,” 2008.
[15] F. Heße, V. Prykhodko, S. Schlüter, and S. Attinger, “Generating random fields with a truncated power-law variogram: A comparison of several numerical methods,” Environmental Modelling & Software, vol. 55, pp. 32–48, 2014. https://doi.org/10.1016/j.envsoft.2014.01.013