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Prediction of coupled 2D and 3D effects in springback of copper alloys after deep drawing

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Abstract

The aim of this study is to investigate the balance between 2D and 3D (or twist) springback of copper-based thin sheets after a deep drawing process. Such materials are widely used in the manufacturing of electric and electronic components, but getting an accurate final geometry is usually difficult due to springback. Three copper-based materials are considered in this study, and in a first step, the mechanical behavior is investigated with uniaxial loading-unloading tension, monotonic and cyclic simple shear and hydraulic bulge tests. In a second step, thin blanks made of these copper alloys are deformed in a U-bending process, in which they are intentionally misaligned by 2° from the tool symmetry axis; then, the deformed geometry is measured with a laser scanner and the 2D springback and twisting parameters are calculated. It is shown that pure copper and the copper-iron alloy exhibit a rather limited 2D springback but a significant twisting whereas the opposite trend is observed for the copper-beryllium alloy. Finite element simulations are carried out with isotropic and mixed hardening models, calibrated from the experimental database. The comparison of experimental and predicted punch forces, 2D springback data and twisting parameters shows the accuracy of the numerical simulations. Moreover, the distinct springback characteristics of the three copper-based materials are correctly predicted and the influence of the mechanical properties on the relative 2D and 3D contributions to springback is analyzed.

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References

  1. Choi K-S, Kang T-G, Park I-S, Lee J-H, Cha K-B (2000) Copper lead frame: an ultimate solution to the reliability of BLP package. IEEE Trans Electron Packag Manuf 23(1):32–38

    Article  Google Scholar 

  2. Khoury SL, Burkhard DJ, Galloway DP, Scharr TA (Dec. 1990) A comparison of copper and gold wire bonding on integrated circuit devices. IEEE Trans Compon Hybrids Manuf Technol 13(4):673–681. https://doi.org/10.1109/33.62578

    Article  Google Scholar 

  3. Dong Q, Shen L, Cao F, Jia Y, Liao K, Wang M (Apr. 2015) Effect of thermomechanical processing on the microstructure and properties of a cu-Fe-P alloy. J Mater Eng Perform 24(4):1531–1539. https://doi.org/10.1007/s11665-014-1352-6

    Article  Google Scholar 

  4. Pham CH, Thuillier S, Manach PY (Apr. 2014) Twisting analysis of ultra-thin metallic sheets. J Mater Process Technol 214(4):844–855. https://doi.org/10.1016/j.jmatprotec.2013.12.006

    Article  Google Scholar 

  5. Pham CH, Thuillier S, Manach PY (Dec. 2013) Twisting of sheet metals. AIP Conf. Proc. 1567(1):422–427. https://doi.org/10.1063/1.4850005

    Article  Google Scholar 

  6. Pham CH, Thuillier S, Manach PY (Sep. 2017) Experimental and numerical investigation of the formability of an ultra-thin copper sheet. J Phys Conf Ser 896:012109. https://doi.org/10.1088/1742-6596/896/1/012109

    Article  Google Scholar 

  7. Li KP, Carden WP, Wagoner RH (Jan. 2002) Simulation of springback. Int J Mech Sci 44(1):103–122. https://doi.org/10.1016/S0020-7403(01)00083-2

    Article  MATH  Google Scholar 

  8. Papeleux L, Ponthot J-P (Sep. 2002) Finite element simulation of springback in sheet metal forming. J Mater Process Technol 125–126:785–791. https://doi.org/10.1016/S0924-0136(02)00393-X

    Article  Google Scholar 

  9. Makinouchi A, Nakamachi E, Onate E, Wagoner RH (1993) NUMISHEET’93

  10. Tang B, Zhao G, Wang Z (Aug. 2008) A mixed hardening rule coupled with Hill48’ yielding function to predict the springback of sheet U-bending. Int J Mater Form 1(3):169. https://doi.org/10.1007/s12289-008-0381-9

    Article  Google Scholar 

  11. Bernert W et al (2010) Advanced high-strength steel applications, design and stamping process guidelines. AutoSteel Partnersh Southf Mich

  12. Da-xin E, He H, Liu X, Ning R (Apr. 2009) Spring-back deformation in tube bending. Int J Miner Metall Mater 16(2):177–183. https://doi.org/10.1016/S1674-4799(09)60030-3

    Article  Google Scholar 

  13. Andersson A (Dec. 2005) Numerical and experimental evaluation of springback in a front side member. J Mater Process Technol 169(3):352–356. https://doi.org/10.1016/j.jmatprotec.2005.04.095

    Article  Google Scholar 

  14. Takamura M, Sakata M, Fukui A, Hama T, Miyoshi Y, Sunaga H, Makinouchi A, Asakawa M (Apr. 2010) Investigation of twist in curved hat channel products by elastic-plastic finite element analysis. Int J Mater Form 3(1):131–134. https://doi.org/10.1007/s12289-010-0724-1

    Article  Google Scholar 

  15. Carden WD, Geng LM, Matlock DK, Wagoner RH (Jan. 2002) Measurement of springback. Int J Mech Sci 44(1):79–101. https://doi.org/10.1016/S0020-7403(01)00082-0

    Article  MATH  Google Scholar 

  16. Wagoner RH, Lim H, Lee M-G (Jun. 2013) Advanced issues in springback. Int J Plast 45:3–20. https://doi.org/10.1016/j.ijplas.2012.08.006

    Article  Google Scholar 

  17. Fu MH, Chan KC, Lee WB, Chan LK (Apr. 1997) Springback in the roller forming of integrated circuit leadframes. J Mater Process Technol 66(1):107–111. https://doi.org/10.1016/S0924-0136(96)02503-4

    Article  Google Scholar 

  18. Panthi SK, Ramakrishnan N (Oct. 2011) Semi analytical modeling of springback in arc bending and effect of forming load. Trans Nonferrous Met Soc China 21(10):2276–2284. https://doi.org/10.1016/S1003-6326(11)61008-X

    Article  Google Scholar 

  19. Biradar A, Deshpande MD (2014) Finite element analysis of springback of a sheet metal in wipe bending process. Int J Sci Res 3(7):852–858

    Google Scholar 

  20. Zhu YX, Liu YL, Yang H, Li HP (Dec. 2012) Development and application of the material constitutive model in springback prediction of cold-bending. Mater Des 42:245–258. https://doi.org/10.1016/j.matdes.2012.05.043

    Article  Google Scholar 

  21. Yoshida F, Uemori T (Oct. 2003) A model of large-strain cyclic plasticity and its application to springback simulation. Int J Mech Sci 45(10):1687–1702. https://doi.org/10.1016/j.ijmecsci.2003.10.013

    Article  MATH  Google Scholar 

  22. Hamasaki H, Hattori Y, Furukawa K, Yoshida F (Jan. 2014) Bauschinger effect during unloading of cold-rolled copper alloy sheet and its influence on Springback deformation after U-bending. Procedia Eng 81:969–974. https://doi.org/10.1016/j.proeng.2014.10.126

    Article  Google Scholar 

  23. Adzima F, Balan T, Manach PY (2019) Springback prediction for a mechanical micro connector using CPFEM based numerical simulations. Int J Mater Form:1–11

  24. Takamura M et al (Aug. 2011) Investigation on twisting and Side Wall opening occurring in curved Hat Channel products made of high strength steel sheets. AIP Conf Proc 1383(1):887–894. https://doi.org/10.1063/1.3623699

    Article  Google Scholar 

  25. Li H, Sun G, Li G, Gong Z, Liu D, Li Q (Jun. 2011) On twist springback in advanced high-strength steels. Mater Des 32(6):3272–3279. https://doi.org/10.1016/j.matdes.2011.02.035

    Article  Google Scholar 

  26. Xue X, Liao J, Vincze G, Sousa J, Barlat F, Gracio J (Jan. 2016) Modelling and sensitivity analysis of twist springback in deep drawing of dual-phase steel. Mater Des 90:204–217. https://doi.org/10.1016/j.matdes.2015.10.127

    Article  Google Scholar 

  27. Liao J, Chen S, Xue X, Xiang H (Aug. 2019) On twist springback of a curved channel with pre-strain effect. Int J Lightweight Mater Manuf. https://doi.org/10.1016/j.ijlmm.2019.08.006

  28. Xie Y-M, Huang R-Y, Tang W, Pan B-B, Zhang F (Apr. 2018) An experimental and numerical investigation on the twist Springback of transformation induced plasticity 780 steel based on different hardening models. Int J Precis Eng Manuf 19(4):513–520. https://doi.org/10.1007/s12541-018-0062-7

    Article  Google Scholar 

  29. Pham CH, Thuillier S, Manach P-Y (2015) 2D Springback and twisting of ultra-thin stainless steel U-shaped parts. Steel Res Int 86(8):861–868. https://doi.org/10.1002/srin.201400569

    Article  Google Scholar 

  30. Xue X, Liao J, Vincze G, Barlat F (2017) Twist springback characteristics of dual-phase steel sheet after non-axisymmetric deep drawing. Int J Mater Form 10(2):267–278. https://doi.org/10.1007/s12289-015-1275-2

    Article  Google Scholar 

  31. Kitayama S, Ishizuki R, Yokoyaka M, Kawamoto K, Natsume S, Adachi K, Noguchi T, Ohtani T (2019) Numerical optimization of variable blank holder trajectory and blank shape for twist springback reduction using sequential approximate optimization. Int J Adv Manuf Technol 103(1-4):63–75. https://doi.org/10.1007/s00170-019-03521-8

    Article  Google Scholar 

  32. Chang Z, Chen J (2020) Mechanism of the twisting in incremental sheet forming process. J Mater Process Tech 276:116396. https://doi.org/10.1016/j.jmatprotec.2019.116396

    Article  Google Scholar 

  33. Pham CH, Adzima F, Coër J, Manach PY (Apr. 2017) Anti-buckling device for ultra-thin metallic sheets under large and reversed shear strain paths. Exp Mech 57(4):593–602. https://doi.org/10.1007/s11340-017-0256-4

    Article  Google Scholar 

  34. Adzima F, Balan T, Manach P-Y, Bonnet N, Tabourot L (2017) Crystal plasticity and phenomenological approaches for the simulation of deformation behavior in thin copper alloy sheets. Int J Plast 94:171–191. https://doi.org/10.1016/j.ijplas.2016.06.003

    Article  Google Scholar 

  35. Adzima F (2016) Modélisation et simulation de procédés de mise en forme de tôles métalliques ultrafines (Modeling and simulation of shaping processes for ultra-thin metal sheets), Doctoral Thesis, Paris, ENSAM

  36. Thuillier S, Pham CH, Manach PY (Jul. 2018) 2D springback and twisting after drawing of copper alloy sheets. J Phys Conf Ser 1063:012124. https://doi.org/10.1088/1742-6596/1063/1/012124

    Article  Google Scholar 

  37. Kuwabara T, Takahashi S, Akiyama K, Miyashita Y (1995) 2D springback analysis for stretch-bending processes based on total strain theory. SAE Technical papers 950691. https://doi.org/10.4271/950691

  38. Chalal H, Racz SG, Balan T (2012) Springback of thick sheet AHSS subject to bending under tension. Int J Mech Science 59(1):104–114. https://doi.org/10.1016/j.ijmecsci.2012.03.011

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge BPIfrance for the financial support via EXPRESSo project.

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Correspondence to S. Thuillier.

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The authors acknowledge BPIfrance for the financial support via EXPRESSo project. The authors declare that they have no conflict of interest.

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Ha, G., Oliveira, M.G., Andrade-Campos, A. et al. Prediction of coupled 2D and 3D effects in springback of copper alloys after deep drawing. Int J Mater Form 14, 1171–1187 (2021). https://doi.org/10.1007/s12289-021-01631-x

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