Skip to main content
SpringerLink
Log in

A numerical-experimental coupled method for the identification of model parameters from µ-SPIF test using a finite element updating method

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

Abstract

Single-point incremental forming (SPIF) is a technology that allows obtaining complex parts using a hemispherical end tool by applying a local deformation process in sheet metal. This dieless process presents the advantage of high formability limits and low cost. The increasing need for micro-components, namely, in the medical industry (implants and medical tools and accessories), has contributed to the development of the micro-single-point incremental forming (µ-SPIF) technique. However, this technique requires meeting certain challenges related to tool wear, resistance and precision of the manufactured parts, and increased formability. So, understanding the deformation and failure mechanisms in µ-SPIF is important to achieve improved formability. This paper is aimed at improving the predictions of the shear-modified GTN damage model by proposing an identification procedure for its numerous material parameters based on an inverse method coupling the numerical predictions with experimental results. The extended GTN model is first implemented into the finite element code Abaqus. The numerical approach is assessed through numerical simulations under shear and uniaxial tension loading. Then, a complete methodology is proposed to identify the set of material parameters using tensile and micro-single-point incremental forming (µ-SPIF) experimental results. The identification approach is based on the comparison of the numerical and experimental forces used to carry out the micro-incremental forming test with a pyramidal shape tool. To show the pertinence of the identification procedure, the numerical predictions of the modified GTN model with these material parameters are compared to the experimental results of µ-SPIF tests with different tool paths and geometrical forms. Finally, it is shown that the shear modification of the GTN model can predict the failure of sheets during metal forming.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Duflou JR, Habraken A-M, Cao J, Malhotra R, Bambach M, Adams D, Jeswiet J (2018) Single point incremental forming: state-of-the-art and prospects. Int J Mater Form 11(6):743–773. https://doi.org/10.1007/s12289-017-1387-y

    Article  Google Scholar 

  2. McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 35(2):363–371. https://doi.org/10.1115/1.3601204

    Article  Google Scholar 

  3. Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields∗. J Mech Phys Solids 17(3):201–217. https://doi.org/10.1016/0022-5096(69)90033-7

    Article  Google Scholar 

  4. 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 

  5. Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17(4):389–407. https://doi.org/10.1007/BF00036191

    Article  Google Scholar 

  6. Tvergaard V (1982) Influence of void nucleation on ductile shear fracture at a free surface. J Mech Phys Solids 30(6):399–425. https://doi.org/10.1016/0022-5096(82)90025-4

    Article  MATH  Google Scholar 

  7. Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169. https://doi.org/10.1016/0001-6160(84)90213-X

    Article  Google Scholar 

  8. Besson J, Devillers-Guerville L, Pineau A (2000) Modeling of scatter and size effect in ductile fracture: application to thermal embrittlement of duplex stainless steels. Eng Fract Mech 67(2):169–190. https://doi.org/10.1016/S0013-7944(00)00056-4

    Article  Google Scholar 

  9. Chen Z, Dong X (2009) The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming. Comput Mater Sci 44(3):1013–1021. https://doi.org/10.1016/j.commatsci.2008.07.020

    Article  Google Scholar 

  10. Kiran R, Khandelwal K (2014) Gurson model parameters for ductile fracture simulation in ASTM A992 steels: Gurson model parameters for ductile fracture simulation in ASTM A992 steels. Fatigue Fract Eng Mater Struct 37(2):171–183. https://doi.org/10.1111/ffe.12097

    Article  Google Scholar 

  11. Benzerga AA, Leblond J-B, Needleman A, Tvergaard V (2016) Ductile failure modeling. Int J Fract 201(1):29–80. https://doi.org/10.1007/s10704-016-0142-6

    Article  Google Scholar 

  12. Aldakheel F, Wriggers P, Miehe C (2018) A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling. Comput Mech 62(4):815–833. https://doi.org/10.1007/s00466-017-1530-0

    Article  MathSciNet  MATH  Google Scholar 

  13. Ould Ouali M (2018) Relevance of incorporating cavity shape change in modelling the ductile failure of metals. Math Probl Eng 2018:1–9. https://doi.org/10.1155/2018/6454790

    Article  MathSciNet  MATH  Google Scholar 

  14. He Z, Zhu H, Hu Y (2021) An improved shear modified GTN model for ductile fracture of aluminium alloys under different stress states and its parameters identification. Int J Mech Sci 192:106081. https://doi.org/10.1016/j.ijmecsci.2020.106081

    Article  Google Scholar 

  15. Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46(1):81–98. https://doi.org/10.1016/j.ijmecsci.2004.02.006

    Article  Google Scholar 

  16. Lou Y, Huh H (2013) Evaluation of ductile fracture criteria in a general three-dimensional stress state considering the stress triaxiality and the lode parameter. Acta Mech Solida Sin 26(6):642–658. https://doi.org/10.1016/S0894-9166(14)60008-2

    Article  Google Scholar 

  17. Xue L (2008) Constitutive modeling of void shearing effect in ductile fracture of porous materials. Eng Fract Mech 75(11):3343–3366. https://doi.org/10.1016/j.engfracmech.2007.07.022

    Article  Google Scholar 

  18. Nahshon K, Hutchinson JW (2008) Modification of the Gurson model for shear failure. Eur J Mech A Solids 27(1):1–17. https://doi.org/10.1016/j.euromechsol.2007.08.002

    Article  MATH  Google Scholar 

  19. Malcher L, Reis FJP, Andrade Pires FM, César de Sá JMA (2013) Evaluation of shear mechanisms and influence of the calibration point on the numerical results of the GTN model. Int J Mech Sci 75:407–422. https://doi.org/10.1016/j.ijmecsci.2013.08.008

    Article  Google Scholar 

  20. Malcher L, Andrade Pires FM, César de Sá JMA (2014) An extended GTN model for ductile fracture under high and low stress triaxiality. Int J Plast 54:193–228. https://doi.org/10.1016/j.ijplas.2013.08.015

    Article  Google Scholar 

  21. Kami A, Dariani B, Sadough VS, Comsa D-S, Banabic D (2014) Application of a GTN damage model to predict the fracture of metallic sheets subjected to deep-drawing. In: Proceedings of the Romanian Academy - Series A: mathematics, physics, technical sciences, information science 15:300–309

  22. Kami A, Dariani BM, Sadough Vanini A, Comsa DS, Banabic D (2015) Numerical determination of the forming limit curves of anisotropic sheet metals using GTN damage model. J Mater Process Technol 216:472–483. https://doi.org/10.1016/j.jmatprotec.2014.10.017

    Article  Google Scholar 

  23. Gatea S, Ou H, Lu B, McCartney G (2017) Modelling of ductile fracture in single point incremental forming using a modified GTN model. Eng Fract Mech 186:59–79. https://doi.org/10.1016/j.engfracmech.2017.09.021

    Article  Google Scholar 

  24. Belouettar K, Mohand OO, Nasereddine Z, Sébastien T (2021) Investigation of the influence of incremental sheet forming process parameters using response surface methodology. Metall Res Technol 118(4):401. https://doi.org/10.1051/metal/2021039

    Article  Google Scholar 

  25. Ying L, Wang D, Liu W, Wu Y, Hu P (2018) On the numerical implementation of a shear modified GTN damage model and its application to small punch test. IntJ Mater Form 11(4):527–539. https://doi.org/10.1007/s12289-017-1362-7

    Article  Google Scholar 

  26. Achouri M, Germain G, Dal Santo P, Saidane D (2013) Numerical integration of an advanced Gurson model for shear loading: application to the blanking process. Comput Mater Sci 72:62–67. https://doi.org/10.1016/j.commatsci.2013.01.035

    Article  Google Scholar 

  27. Achouri M, Germain G, Dal Santo P, Saidane D (2013) Experimental characterization and numerical modeling of micromechanical damage under different stress states. Mater Des 50:207–222. https://doi.org/10.1016/j.matdes.2013.02.075

    Article  Google Scholar 

  28. Aguir H, Marouani H (2010) Gurson-Tvergaard-Needleman parameters identification using artificial neural networks in sheet metal blanking. IntJ Mater Form 3(S1):113–116. https://doi.org/10.1007/s12289-010-0720-5

    Article  Google Scholar 

  29. Marouani H, Aguir H (2012) Identification of material parameters of the Gurson–Tvergaard–Needleman damage law by combined experimental, numerical sheet metal blanking techniques and artificial neural networks approach. IntJ Mater Form 5(2):147–155. https://doi.org/10.1007/s12289-011-1035-x

    Article  Google Scholar 

  30. Abbassi F, Belhadj T, Mistou S, Zghal A (2013) Parameter identification of a mechanical ductile damage using Artificial Neural Networks in sheet metal forming. Mater Des 45:605–615. https://doi.org/10.1016/j.matdes.2012.09.032

    Article  Google Scholar 

  31. Sun Q, Lu Y, Chen J (2020) Identification of material parameters of a shear modified GTN damage model by small punch test. Int J Fract 222(1–2):25–35. https://doi.org/10.1007/s10704-020-00428-4

    Article  Google Scholar 

  32. Corigliano A, Mariani S, Orsatti B (2000) Identification of Gurson-Tvergaard material model parameters via Kalman filtering technique. I. Theory. Int J Fract 104(4):349–373. https://doi.org/10.1023/A:1007602106711

    Article  Google Scholar 

  33. Springmann M, Kuna M (2005) Identification of material parameters of the Gurson–Tvergaard–Needleman model by combined experimental and numerical techniques. Comput Mater Sci 32(3–4):544–552. https://doi.org/10.1016/j.commatsci.2004.09.010

    Article  Google Scholar 

  34. Springmann M, Kuna M (2006) Determination of ductile damage parameters by local deformation fields: measurement and simulation. Arch Appl Mech 75(10–12):775–797. https://doi.org/10.1007/s00419-006-0033-9

    Article  MATH  Google Scholar 

  35. Muñoz-Rojas PA, Cardoso EL, Vaz M (2010) Parameter identification of damage models using genetic algorithms. Exp Mech 50(5):627–634. https://doi.org/10.1007/s11340-009-9321-y

    Article  Google Scholar 

  36. Ghouati O, Gelin JC (1998) Identification of material parameters directly from metal forming processes. J Mater Process Technol 80–81:560–564. https://doi.org/10.1016/S0924-0136(98)00159-9

    Article  Google Scholar 

  37. Ben Hmida R, Richard F, Thibaud S, Malécot P (2015) Elastic-plastic damage behavior identification in micro scale length from instrumented micro-single point incremental forming. 4M/ ICOMM2015 conf. Research Publishing, Milan, Italy, pp 230–233. https://doi.org/10.3850/978-981-09-4609-8_059

  38. Hapsari G, Richard F, Ben Hmida R, Malécot P, Thibaud S (2018) Instrumented incremental sheet testing for material behavior extraction under very large strain: Information richness of continuous force measurement. Mater Des 140:317–331. https://doi.org/10.1016/j.matdes.2017.12.002

    Article  Google Scholar 

  39. Aravas N (1987) On the numerical integration of a class of pressure-dependent plasticity models. Int J Numer Meth Eng 24(7):1395–1416. https://doi.org/10.1002/nme.1620240713

    Article  MATH  Google Scholar 

  40. Zhang ZL (1995) Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models. Comput Methods Appl Mech Eng 121(1–4):29–44. https://doi.org/10.1016/0045-7825(94)00707-T

    Article  MathSciNet  MATH  Google Scholar 

  41. Ben Chabane N, Aguechari N, Ould Ouali M (2022) Study of the slant fracture in solid and hollow cylinders: experimental analysis and numerical prediction. Frattura ed Integrità Strutturale 17(63):169–189. https://doi.org/10.3221/IGF-ESIS.63.15

  42. Nahshon K, Xue Z (2009) A modified Gurson model and its application to punch-out experiments. Eng Fract Mech 76(8):997–1009. https://doi.org/10.1016/j.engfracmech.2009.01.003

    Article  Google Scholar 

  43. Ben Hmida R, Thibaud S, Gilbin A, Richard F (2013) Influence of the initial grain size in single point incremental forming process for thin sheets metal and microparts: experimental investigations. Mater Des 45:155–165. https://doi.org/10.1016/j.matdes.2012.08.077

    Article  Google Scholar 

  44. Gréban F, Monteil G, Roizard X (2007) Influence of the structure of blanked materials upon the blanking quality of copper alloys. J Mater Process Technol 186(1–3):27–32. https://doi.org/10.1016/j.jmatprotec.2006.11.226

    Article  Google Scholar 

  45. Hapsari G, Thibaud S, Richard F, Malécot P, Hmida RB, Bonnardot C (2020) Thin sheet behaviour identification by µ-InDef and identifiability analysis. Proc Manuf 47:1481–1489. https://doi.org/10.1016/j.promfg.2020.04.330

    Article  Google Scholar 

  46. Voce E (1955) A practical strain-hardening function. Metallurgica 51:219–226

    Google Scholar 

  47. Oh C-K, Kim Y-J, Baek J-H, Kim Y-P, Kim W (2007) A phenomenological model of ductile fracture for API X65 steel. Int J Mech Sci 49(12):1399–1412. https://doi.org/10.1016/j.ijmecsci.2007.03.008

    Article  Google Scholar 

  48. Nielsen KL, Tvergaard V (2009) Effect of a shear modified Gurson model on damage development in a FSW tensile specimen. Int J Solids Struct 46(3–4):587–601. https://doi.org/10.1016/j.ijsolstr.2008.09.011

    Article  MATH  Google Scholar 

  49. Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Q Appl Math 2(2):164–168

    Article  MathSciNet  MATH  Google Scholar 

  50. Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2):431–441

    Article  MathSciNet  MATH  Google Scholar 

  51. Richard F (1999) MIC2M: Modélisation et identification du comportement mécanique des matériaux. Université de Franche-Comté. http://mic2m.univ-fcomte.fr. Accessed 2022

  52. Thibaud S, Ben Hmida R, Richard F, Malécot P (2012) A fully parametric toolbox for the simulation of single point incremental sheet forming process: numerical feasibility and experimental validation. Simul Model Pract Theory 29:32–43. https://doi.org/10.1016/j.simpat.2012.07.004

    Article  Google Scholar 

  53. Brun R, Reichert P, Künsch HR (2001) Practical identifiability analysis of large environmental simulation models. Water Resour Res 37(4):1015–1030. https://doi.org/10.1029/2000WR900350

    Article  Google Scholar 

  54. Richard F, Villars M, Thibaud S (2013) Viscoelastic modeling and quantitative experimental characterization of normal and osteoarthritic human articular cartilage using indentation. J Mech Behav Biomed Mater 24:41–52. https://doi.org/10.1016/j.jmbbm.2013.04.012

    Article  Google Scholar 

  55. Ould Ouali M, Aberkane M (2009) Micromechanical modeling of the rolling of a A1050P aluminum sheet. IntJ Mater Form 2(1):25–36. https://doi.org/10.1007/s12289-008-0387-3

    Article  Google Scholar 

  56. Torki ME, Tekoğlu C, Leblond J-B, Benzerga AA (2017) Theoretical and numerical analysis of void coalescence in porous ductile solids under arbitrary loadings. Int J Plast 91:160–181. https://doi.org/10.1016/j.ijplas.2017.02.011

    Article  Google Scholar 

  57. Khan IA, Srivastava A, Needleman A, Benzerga AA (2021) An analysis of deformation and failure in rectangular tensile bars accounting for void shape changes. Int J Fract 230(1–2):133–156. https://doi.org/10.1007/s10704-021-00532-z

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Advanced Manufacturing and Control Techniques Laboratory, Ecole Militaire Polytechnique (EMP), 16111, Algiers, Algeria

    Karim Belouettar

  2. FEMTO-ST Institute, Univ. Bourgogne Franche-Comté, CNRS/UFC//ENSMM/UTBM, 25000, Besançon, France

    Sébastien Thibaud

  3. Laboratory of Elaboration and Characterization of Materials and Modeling (LEC2M), University of Tizi-Ouzou, Tizi-Ouzou, 15100, Algeria

    Mohand Ould Ouali

  4. Engineering Materials Laboratory, Ecole Militaire Polytechnique (EMP), 16111, Algiers, Algeria

    Mohamed Karim Harouche

Authors
  1. Karim Belouettar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sébastien Thibaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohand Ould Ouali
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamed Karim Harouche
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karim Belouettar.

Ethics declarations

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

Belouettar, K., Thibaud, S., Ould Ouali, M. et al. A numerical-experimental coupled method for the identification of model parameters from µ-SPIF test using a finite element updating method. Int J Adv Manuf Technol 128, 5195–5208 (2023). https://doi.org/10.1007/s00170-023-12210-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-12210-6

Keywords

Search

Navigation