Skip to main content
Log in

Numerical investigation and experimental validation of Lemaitre ductile damage model for DC04 steel and application to deep drawing process

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

During the metal forming process, the avoidance of ductile fracture has been of great interest to the scientific and engineering communities over the past decades. Hence, ductile damage prediction remains a key issue for achieving defect-free products. In this paper, the elastoplastic damage behaviour of DC04 steel has been studied and simulated to predict the fracture during the deep drawing process and reduce the industrial trial cost. In this context, a fully coupled elastoplastic damage model has been developed and implemented in the Abaqus explicit code using the VUMAT subroutine, knowing that the used elastoplastic and the damage parameters were identified by experimental tests. Numerical simulations have been performed to validate this model, followed by comparisons with the experimental results. These comparisons show a good correlation between the experimental and simulation results and good agreement with the empirical observations. Thus, the initiation of damage and its evolution leading to ductile fracture can be predicted using this model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Ahmetoglu M, Broek TR, Kinzel G, Altan T (1995) Control of blank holder force to eliminate wrinkling and fracture in deep-drawing rectangular parts. CIRP Annals 44(1):247–250. https://doi.org/10.1016/S0007-8506(07)62318-X

    Article  Google Scholar 

  2. Manabe K, Koyama H, Yoshihara S, Yagami T (2002) Development of a combination punch speed and blank-holder fuzzy control system for the deep-drawing process. J Mater Process Technol 125:440–445. https://doi.org/10.1016/S0924-0136(02)00363-1

    Article  Google Scholar 

  3. Yi S, Bohlen J, Heinemann F, Letzig D (2010) Mechanical anisotropy and deep drawing behaviour of AZ31 and ZE10 magnesium alloy sheets. Acta Mater 58(2):592–605. https://doi.org/10.1016/j.actamat.2009.09.038

    Article  Google Scholar 

  4. Modi B, Kumar DR (2013) Development of a hydroforming setup for deep drawing of square cups with variable blank holding force technique. The Int J Adv Manuf Technol 66(5):1159–1169. https://doi.org/10.1007/s00170-012-4397-4

    Article  Google Scholar 

  5. Ma W, Wang BY, Lei Fu, Jing Zhou, Huang MD. Effect of friction coefficient in deep drawing of AA6111 sheet at elevated temperatures. Transactions of Nonferrous Metals Society of China. 2015; 25(7): 2342–2351. https://doi.org/10.1016/S1003-6326(15)63849-3

  6. Modi B, Kumar DR (2019) Optimization of process parameters to enhance formability of AA 5182 alloy in deep drawing of square cups by hydroforming. J Mech Sci Technol 33(11):5337–5346. https://doi.org/10.1007/s12206-019-1026-2

    Article  Google Scholar 

  7. Preedawiphat P, Koowattanasuchat P, Mahayotsanun N, Mahabunphachai S (2020) Sheet thinning prediction method based on localized friction effect in deep-drawing. Adv Mech Eng 12(9):1–10. https://doi.org/10.1177/1687814020953941

    Article  Google Scholar 

  8. Lemaitre J (2012) A course on damage mechanics. Springer Science & Business Media

  9. İpekoğlu G, Çam G (2019) Formation of weld defects in cold metal transfer arc welded 7075–T6 plates and its effect on joint performance. IOP Conf Ser Mater Sci Eng 629(1):012007. https://doi.org/10.1088/1757-899X/629/1/012007

    Article  Google Scholar 

  10. Çam G, Koçak M (2007) Microstructural and mechanical characterization of electron beam welded Al-alloy 7020. J Mater Sci 42:7154–7161. https://doi.org/10.1007/s10853-007-1604-z

    Article  Google Scholar 

  11. Çam G, Koçak M, Dobi D, Heikinheimo L, Siren M (1997) Fracture behaviour of diffusion bonded bimaterial Ti–Al joints. Sci Technol Weld Joining 2(3):95–101. https://doi.org/10.1179/stw.1997.2.3.95

    Article  Google Scholar 

  12. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99(1):2–15. https://doi.org/10.1115/1.3443401

    Article  Google Scholar 

  13. Tvergaard V (1982) On localization in ductile materials containing spherical voids. Int J Fract 18(4):237–252. https://doi.org/10.1007/BF00015686

    Article  Google Scholar 

  14. Tvergaard V (1982) Ductile fracture by cavity nucleation between larger voids. J Mech Phys Solids 30(4):265–286. https://doi.org/10.1016/0022-5096(82)90033-3

    Article  MATH  Google Scholar 

  15. Needleman A, Tvergaard VF (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32(6):461–490. https://doi.org/10.1016/0022-5096(84)90031-0

    Article  Google Scholar 

  16. Kachanov LM (1958) Time of the rupture process under creep conditions. Izvestiia Akademii Nauk SSR (Otdelenii Techniceskih Nauk) 8:26–31

    Google Scholar 

  17. Chaboche JL (1984) Anisotropic creep damage in the framework of continuum damage mechanics. Nucl Eng Des 79(3):309–319. https://doi.org/10.1016/0029-5493(84)90046-3

    Article  Google Scholar 

  18. Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107(1):83–89. https://doi.org/10.1115/1.3225775

    Article  Google Scholar 

  19. Lemaitre J (1985) Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng 51(1–3):31–49. https://doi.org/10.1016/0045-7825(85)90026-X

    Article  MATH  Google Scholar 

  20. Cao TS (2017) Models for ductile damage and fracture prediction in cold bulk metal forming processes: a review. IntJ Mater Form 10(2):139–171. https://doi.org/10.1007/s12289-015-1262-7

    Article  Google Scholar 

  21. Cai S, Chen L (2021) Parameter identification and blanking simulations of DP1000 and Al6082-T6 using Lemaitre damage model. Adv Manuf 9(3):457–472. https://doi.org/10.1007/s40436-021-00350-5

    Article  Google Scholar 

  22. Kumar P, Tandon P (2022) Investigating the capability of the Lemaitre damage model to establish the incremental sheet forming process. Arch Civil Mech Eng 22(2):1–18. https://doi.org/10.1007/s43452-022-00391-y

    Article  Google Scholar 

  23. Wang C, Daniel WJT, Lu H, Liu S, Meehan PA (2021) A comparative investigation of damage models for fracture prediction in two-point incremental forming. Int J Adv Manuf Technol 112(11):3069–3081. https://doi.org/10.1007/s00170-020-06587-x

    Article  Google Scholar 

  24. Fan JP, Tang CY, Tsui CP, Chan LC, Lee TC (2006) 3D finite element simulation of deep drawing with damage development. Int J Machine Tools Manuf 46(9):1035–1044. https://doi.org/10.1016/j.ijmachtools.2005.07.044

    Article  Google Scholar 

  25. Khelifa M, Oudjene M, Khennane A (2007) Fracture in sheet metal forming: effect of ductile damage evolution. Comput Struct 85(3–4):205–212. https://doi.org/10.1016/j.jmatprotec.2007.08.041

    Article  Google Scholar 

  26. Saxena RK, Gautam SS, Dixit PM (2010) Numerical simulation of fracture in cup drawing. IntJ Mater Form 3(1):117–120. https://doi.org/10.1016/j.finel.2011.04.003

    Article  Google Scholar 

  27. Amaral R, Teixeira P, Santos AD, de Sá JC (2018) Assessment of different ductile damage models and experimental validation. IntJ Mater Form 11(3):435–444. https://doi.org/10.1007/s12289-017-1381-4

    Article  Google Scholar 

  28. Chalal H, Abed-Meraim F (2017) Numerical predictions of the occurrence of necking in deep drawing processes. Metals 7(11):455. https://doi.org/10.3390/met7110455

    Article  Google Scholar 

  29. Boussaid O, Bourgeois N, Martiny M, Ferron G, Chaoui K (2008) Experimental characterization of mild steel in deep drawing. Int Rev Mech Eng 2(4):632–637

    Google Scholar 

  30. Ghennai W, Boussaid O, Bendjama H, Haddag B, Nouari M (2019) Experimental and numerical study of DC04 sheet metal behaviour—plastic anisotropy identification and application to deep drawing. Int J Adv Manuf Technol 100(1):361–371. https://doi.org/10.1007/s00170-018-2700-8

    Article  Google Scholar 

  31. Ghennai W, Boussaid O, Bendjama H, Guersi N (2019) Pressure and friction effects on the mechanical behaviour of a ductile material during deep drawing. In Int J Eng Res Africa Trans Tech Publications Ltd 41:8–19.https://doi.org/10.4028/www.scientific.net/JERA.41.8

    Article  Google Scholar 

  32. Von-Mises R (1913) Mechanik der festen Körper im plastischdeformablen Zustand. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. 582–592

  33. Lee SW, Pourboghrat F (2005) A simulation for the punchless piercing process using lemaitre damage model. In AIP Conf Proc Am Inst Physics 778(1):505–510. https://doi.org/10.1016/j.ijmecsci.2005.06.009

    Article  MATH  Google Scholar 

  34. Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1(1):1–18. https://doi.org/10.1016/0022-5096(52)90002-1

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Industrial Vehicles Company (SNVI VIR) in Rouiba, Algiers, Algeria, for giving us the opportunity to do an internship there and providing us with the used material for the study.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study’s conception and design. Material preparation, data collection, and analysis were performed by [Salah LABOUBI], [Ouzine BOUSSAID], [Mohamed ZAAF], and [Walid GHENNAI].

Corresponding author

Correspondence to Salah Laboubi.

Ethics declarations

Consent for publication

The present work is a numerical investigation and experimental validation of the Lemaitre ductile damage model for DC04 steel and application to the deep drawing process. I certify that the submission is original. The manuscript has not been previously published, is not currently submitted for review to any other journal, and will not be submitted elsewhere before a decision is made by this journal.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Laboubi, S., Boussaid, O., Zaaf, M. et al. Numerical investigation and experimental validation of Lemaitre ductile damage model for DC04 steel and application to deep drawing process. Int J Adv Manuf Technol 126, 2283–2294 (2023). https://doi.org/10.1007/s00170-023-11244-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-11244-0

Keywords

Navigation