Modeling the Forming Limit Curve of Steel Sheets Using GTN Model Parameters and Swift Hardening Equation Variables

Document Type : Original Articles

Authors

Mahdi Chelovian

Abdolvahed Kami

Faculty of Mechanical Engineering, Semnan University, Semnan, Iran.

10.22067/jmme.2024.87801.1147

Abstract

The precise prediction of forming limit curves (FLCs) is vital for improving the formability of steel sheets, significantly impacting industries like automotive and aerospace manufacturing. Despite its significance, current approaches for determining FLCs are complex and necessitate more reliable prediction models. This paper aims to introduce theoretical relationships for accurately predicting limit strains and constructing the FLC of steel sheets. By selecting four specific points on the FLC, the corresponding maximum and minimum limit strains were determined using analytical models based on finite element simulations of the M-K model. Two sets of parameters were considered: GTN damage model parameters (micro-scale) and Swift's equation variables (macro-scale). The seven studied parameters, including void volume fractions, adjustment parameter (q2), critical void volume fraction, nucleation void volume fraction, coefficient of strength, initial strain, and hardening exponent, were used as inputs for a central composite design of experiments. Each experiment represented a combination of the parameters and was simulated in four forming paths, providing coordinates for the FLC points. Interpolation of data from the finite element simulations led to the development of practical analytical functions for predicting the FLC of steel sheets. The functions' validity was demonstrated by computing multiple FLCs with randomly chosen parameter values and comparing them to FLCs obtained from the M-K model's simulations. The findings indicated that the formulated equations precisely determine the FLC of steel sheets. The predicted limit strain in the AISI304’s plane strain zone was 0.3647, exhibiting an error of 0.44% relative to the experimental value of 0.370.

Keywords

GTN model

Forming limit curve

M-K model

Steel sheet

AISI304

Subjects

• Metal Forming

---

References

[1]    A. L. Gurson, "Continuum theory of ductile rupture by void nucleation and growth Part I-Yield criteria and flow rules for porous ductile media," Journal of Engineering Materials and Technology, vol. 99, no. 1, pp. 2-15, 1977.

[2]    Z. Marciniak and K. Kuczyński, "Limit strains in the processes of stretch-forming sheet metal," International Journal of Mechanical Sciences, vol. 9, no. 9, pp. 609-620, 1967.

[3]    D. Banabic, D.-S. Comsa, P. Eyckens, A. Kami, and M. Gologanu, "Advanced models for the prediction of forming limit curves," Multiscale Modelling in Sheet Metal Forming, D. Banabic, Ed.: Springer,  pp. 205-300. 2016.

[4]    C. Zhao, T. Wang, Z. Li, J. Liu, Z. Huang, and Q. Huang, "Prediction of magnesium alloy edge crack in edge-constraint rolling process by using a modified GTN model," International Journal of Mechanical Sciences, vol. 241, p. 107961, 2023.

[5]    V. Tvergaard, "On localization in ductile materials containing spherical voids," International Journal of Fracture, vol. 18, no. 4, pp. 237-252, 1982.

[6]    V. Tvergaard and A. Needleman, "Analysis of the cup-cone fracture in a round tensile bar," Acta Metallurgica, vol. 32, no. 1, pp. 157-169, 1984.

[7]    D. Banabic, A. Kami, D.-S. Comsa, and P. Eyckens, "Developments of the Marciniak-Kuczynski model for sheet metal formability: A review," Journal of Materials Processing Technology, vol. 287, p. 116446, 2021.

[8]    M. Gologanu, D. S. Comsa, and D. Banabic, "Theoretical model for forming limit diagram predictions without initial inhomogeneity," AIP Conference Proceedings, vol. 1532, no. 1, pp. 245-253, 2013.

[9] A. Kami and D.-S. Comsa, "A Simplified Description of the Uniaxial Tensile Test Used for Calibrating Constitutive Models of Orthotropic Porous Sheet Metals," AUT Journal of Mechanical Engineering, vol. 2, no. 2, pp. 127-136, 2018.

[10] X. Chen, "Numerical simulation of effects of cladding and superimposed hydrostatic pressure on fracture in metals under tension," Master Thesis, McMaster University, 2009.

[11] A. Melander, “A new model of the forming limit diagram applied to experiments on four copper-base alloys,” Materials Science and Engineering, vol. 58, no. 1, pp. 63-88, 1983.

[12]M. Chelovian and A. Kami, " Study on formability of AISI 304 steel sheet using MK model and GTN damage criterion," Journal of Mechanical Engineering, vol. 50, no. 1, pp. 71-79, 2020.

[13] M. E. Hosseini, S. J. Hosseinipour, and M. Bakhshi-Jooybari, “Theoretical FLD Prediction Based on M-K Model using Gurson's Plastic Potential Function for Steel Sheets,” Procedia Engineering, Conference Paper, vol. 183, pp. 119-124, 2017.

[14] Y.-b. Wang, C.-s. Zhang, Z.-j. Meng, L. Chen, and G.-q. Zhao, “A novel three-dimensional M-K model by integrating GTN model for accurately identifying limit strains of sheet metal,” Transactions of Nonferrous Metals Society of China, vol. 33, no. 7, pp. 1953-1962, 2023.

[15] A. Barfeh, R. Hashemi, R. Safdarian, D. Rahmatabadi, A. Aminzadeh, and S. Sattarpanah Karganroudi, “Predicting the forming limit diagram of the fine-grained AA 1050 sheet using GTN damage model with experimental verifications,” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 237, no. 14, pp. 2325-2335, 2022.