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Evaluation of non-linear strain paths using Generalized Forming Limit Concept and a modification of the Time Dependent Evaluation Method

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The prediction of formability is one of the most important tasks in sheet metal forming process simulation. The common criterion for ductile fracture in industrial applications is the Forming Limit Diagram (FLD). This is only applicable for linear strain paths. However, in most industrial simulation cases non-linear strain paths occur. To resolve this problem, a phenomenological approach is introduced, the so-called Generalized Forming Limit Concept (GFLC). The GFLC enables prediction of localized necking on arbitrary non-linear strain paths. Another possibility is the use of the Time Dependent Evaluation Method (TDEM) within the simulation as a failure criteria. During the Numisheet Benchmark 1 (2014) a two-stage forming process was performed with three typical sheet materials (AA5182, DP600 and TRIP 780) and three different blank shapes. The task was to determinate the point in time and space of local instability. Therefore the strain path for the point of maximum local thinning is evaluated. To predict the start of local necking the Generalized Forming Limit Concept (GFLC), the Time Dependent Evaluation Method (TDEM) and the modified TDEM were applied. The results of the simulation are compared with the results of the Benchmark experiment.

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  1. ISO copyright office (2006) Metallic materials-sheet and strip-determination of forming limit curves-part 2: determination of forming limit curves in laboratory. ISO/DIS 12004-2

  2. Marciniak Z, Kuczynski K (1967) Limit strains in the processes of stretch-forming sheet metal. Int J Mech. Sci., 9/9:609–62.

  3. Nakajima K, Kikuma T, Asaku K (1968) Study on the formability of steel sheet. Yawata Tech Rep 264

  4. Müschenborn W, Sonne HM (1975) Effects of the strain path on the limits of deformation of sheet metal (in German). Archiv Eisenhüttenwesen 46(9):597–602

    Article  Google Scholar 

  5. Kleemola HJ, Pelkkikangas MT (1977) Effect of predeformation and strain path on the forming limits of steel, copper and brass. Sheet Metal Ind 63:591–599

    Google Scholar 

  6. Bergström Y, Ölund S (1982) The forming limit diagram of sheet metals and effects of strain path changes on formability: a dislocation treatmen. Mater Sci Eng 56:47–61

    Article  Google Scholar 

  7. Graf A, Hosford WF (1993) Calculations of forming limit diagrams for changing strain paths. Metall Trans A 24:2497–2501

    Article  Google Scholar 

  8. Barata Da Rocha A, Jalinier JM (1984) Plastic instability of sheet metals under simple and complex strain paths. Trans Iron Steel Inst Japan 24:132–140

    Article  Google Scholar 

  9. Marciniak Z (1965) Stability of plastic shells under tension with kinematic boundary condition. Archiwum Mechaniki Stosorwanej 17:577–592

    Google Scholar 

  10. Marciniak Z, Kuchzynski K, Pokora T (1973) Influence of the plastic properties of a material on the FLD for sheet metal in tension. Int J Mech Sci 15:789–805

    Article  Google Scholar 

  11. Yao H, Cao J (2002) Prediction of forming limit curves using an anisotropic yield function with prestrain induced backstress. Int. J. Plasticity 18(8):1013–1038

    Article  MATH  Google Scholar 

  12. Stoughton TB, 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  MATH  Google Scholar 

  13. Hora P, Tong L (2006) Numerical prediction of FLC using the enhanced modified maximum force criterion. Proc FLC Zurich 2006:31–36

    Google Scholar 

  14. Ofenheimer A, Kitting D, Koplenig M, Grass H, Volk W, Lipp A, Illig R, Kupfer H (2008) Cost Effective Strategy to Predict Formability in Two-Step Sheet Forming Operations. Proceedings of Numisheet 2008, Part A:265–269

  15. Volk W, Hoffmann H, Suh J, Kim J (2012) Failure prediction for non-linear strain paths in sheet metal forming. CIRP Ann Manuf Technol 61(1):259–262

    Article  Google Scholar 

  16. Volk W, Weiss H, Jocham D, Suh J (2013) Phenomenological and numerical description of localized necking using generalized forming limit concept. In: Proceedings of IDDRG 2013, edited by P. Hora, Zurich: 16–21

    Google Scholar 

  17. Volk W (2006) New experimental and numerical approach in the evaluation of the FLD with the FE-method. Proc FLC-Zurich 2006:26–30

    Google Scholar 

  18. Feldmann P, Schatz M (2006) Effective evaluation of FLC-tests with the optical in-process strain analysis system AUTOGRID. Proc FLC-Zurich 2006:69–73

    Google Scholar 

  19. Volk W, Illig R, Kupfer H, Wahlen A, Hora P, Kessler L, Hotz W (2008) Benachmark 1 – virtual forming limit curves. Part A, Physical Tryout Report: 3–9

    Google Scholar 

  20. Li H, Cisneros J, Wu X, Chen X, Xie X, Xu N, Yang L (2013) Benchmark 1 – nonlinear strain path forming limit of a reverse draw, part B: physical tryout report. AIP Conf Proc 1567(1):27–38. doi:10.1063/1.4849978

    Article  Google Scholar 

  21. Wu X (2013) Benchmark 1 – nonlinear strain path forming limit of a reverse draw, part A: benchmark description. AIP Conf Proc 1567(1):15–26. doi:10.1063/1.4849977

    Google Scholar 

  22. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society, A193:281–297

  23. Johnson G R, Cook W H (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, Proceedings of the 7th International Symposium on Ballistics:541–547

  24. Voce E (1948) The relationship between stress and strain for homogeneous deformations. J Inst Met 74:537–562

    Google Scholar 

  25. Volk W, Hora P (2010) New algorithm for a robust user-independent evaluation of beginning instability for the experimental FLC determination. Int J Mater Form. doi:10.1007/s12289-010-1012-9

    Google Scholar 

  26. Merklein M, Kuppert A, Geiger M (2010) Time dependent determination of forming limit diagrams. Annals CIRP 59(1):295–298

    Article  Google Scholar 

  27. Volk W, Suh J (2013) Prediction of formability for Non-linear deformation history using generalized forming limit concept (GFLC), AIP conf. Proc 1567:556–561

    Google Scholar 

  28. Wu X (2013) Benchmark 1 – nonlinear strain path forming limit of a reverse draw, part C: benchmark analysis. AIP Conf Proc 1567(1):39–176. doi:10.1063/1.4849979

    Article  Google Scholar 

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The authors appreciate the Numisheet 2014 committee for organizing Benchmark 1 “Nonlinear Strain Path Forming Limit of Reverse draw”, for execution of the experimental tests and material data.

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Correspondence to Christian Gaber.

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Gaber, C., Jocham, D., Weiss, H.A. et al. Evaluation of non-linear strain paths using Generalized Forming Limit Concept and a modification of the Time Dependent Evaluation Method. Int J Mater Form 10, 345–351 (2017).

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