Comparison And Verification of The Results of The GTN Damage Model and The Porous Metal Plasticity Model in The Square Deep Drawing Process

Subject Areas : Mechanical Engineering

Navid Givianpour ¹ , Hamed Deilami Azodi ^{2 *} , Shahrouz Yousefzadeh ³ , Siamak Mazdak ⁴

1 - Department of Mechanical Engineering, Aligoudarz Branch, Islamic Azad University, Aligoudarz, Iran
2 - Department of Mechanical Engineering, Arak University of Technology, Arak, Iran
3 - Department of Mechanical Engineering, Aligoudarz Branch, Islamic Azad University, Aligoudarz, Iran
4 - Engineering faculty, Tafresh University, Tafresh, Iran

Received: 2024-08-19 Accepted : 2025-02-18 Published : 2025-06-22

Keywords: ABAQUS, Deep Drawing, Drawing Depth, GTN Damage Model, Porous Metal Plasticity,

Abstract :

One of the main goals in the deep drawing process is to achieve a greater drawing depth without causing damage to the sheet; therefore, the drawing ratio is critical in this process. Maximizing the drawing depth has always been the goal of many studies. In this paper, the square deep drawing process is modeled in ABAQUS/Standard finite element software, and then the process is analyzed using the GTN damage model that is implemented by writing a UMAT subroutine. The process is also analyzed based on the porous metal plasticity model available in ABAQUS. The results obtained from these two analyses are compared, providing a comprehensive understanding of the different approaches in deep drawing process analysis. By examining the results, it was found that the results obtained using the GTN damage model are more consistent with the results obtained using the experimental method than the porous metal plasticity model.

References:

[1] Hosford, W. F., Caddell, R. M., Metal Forming: Mechanics and Metallurgy, Cambridge University Press, 2011.
[2] Lange, K., Handbook of Metal Forming, McGraw-Hill Book Company, 1985, pp. 1216.
[3] Johnson, W., Mellor, P. B., Engineering Plasticity, John Willey & Sons: New York, 1983.
[4] Kami, A., Dariani, B. M., Vanini, A. S., Comsa, D. S., and Banabic, D., Application of a GTN Damage Model to Predict the Fracture of Metallic Sheets Subjected to Deep-Drawing, Proceedings of the Romanian Academy, Series A, Vol. 15, 2014, pp. 300–309.
[5] Chen, F. K., Lin, S. Y., A Formability Index for The Deep Drawing of Stainless-Steel Rectangular Cups, The International Journal of Advanced Manufacturing Technology, Vol. 34, No. 9, 2007, pp. 878-888.
[6] Padmanabhan, R., Oliveira, M. C., Alves, J. L., and Menezes, L. F., Influence of Process Parameters on the Deep Drawing of Stainless Steel, Finite Elements in Analysis and Design, Vol. 43, No. 14, 2007, pp. 1062-1067.
[7] Gurson, A. L., 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, 1977, pp. 2–15.
[8] Tvergaard, V., Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions, International Journal of fracture, Vol. 17, No. 4, 1981, pp. 389-407.
[9] Tvergaard, V., On Localization in Ductile Materials Containing Spherical Voids, International Journal of fracture, Vol. 18, No. 4, 1982, pp. 237-252.
[10] Tvergaard, V., Needleman, A., Analysis of the Cup-Cone Fracture in A Round Tensile Bar, Acta Metallurgica, Vol. 32, No. 1, 1984, pp. 157-169.
[11] Chen, Z., Dong, X., The GTN Damage Model Based on Hill’48 Anisotropic Yield Criterion and Its Application in Sheet Metal Forming, Computational Materials Science, Vol. 44, No. 3, 2009, pp. 1013-1021.
[12] Brunet, M., Sabourin, F., and Mguil-Touchal, S., The Prediction of Necking and Failure in 3 D, Sheet Forming Analysis Using Damage Variable. Le Journal de Physique IV, Vol. 6, No. C6, 1996, pp. C6-473.
[13] Brunet, M., Mguil, S., and Morestin, F., Analytical and experimental studies of necking in sheet metal forming processes. Journal of Materials Processing Technology, 80, 1998, pp. 40-46.
[14] Khademi, M., Mirnia, M. J., and Naeini, H. M., Numerical Analysis of Ductile Fracture in Stretch Bending of AA6061-T6 Aluminum Alloy Sheet Using GTN Damage Model, International Journal of Solids and Structures, Vol. 301, 2024, pp. 112947.
[15] Sun, X., Mo, X., Liu, Y., Shen, W., Li, C., Li, Y., and Xue, F., GTN Poroplastic Damage Model Construction and Forming Limit Prediction of Magnesium Alloy Based on BP-GA Neural Network, Materials Today Communications, Vol. 41, 2024, pp. 110295.
[16] Banabic, D., and Kami, A., Applications of the Gurson’s Model in Sheet Metal Forming, In MATEC Web of Conferences, EDP Sciences, Vol. 190, 2018, pp. 01002.
[17] Aravas, N., Papadioti, I., A Non-Local Plasticity Model for Porous Metals with Deformation-Induced Anisotropy: Mathematical and Computational Issues, Journal of the Mechanics and Physics of Solids, Vol. 146, 2021, pp. 104190.
[18] Santos, R. O., Moreira, L. P., Butuc, M. C., Vincze, G., and Pereira, A. B., Damage Analysis of Third-Generation Advanced High-Strength Steel Based on the Gurson–Tvergaard–Needleman (GTN) Model, Metals, Vol. 12, No. 2, 2022, pp. 214. https://doi.org/10.3390/met12020214.
[19] Miloud, M. H., Zidane, I., and Mendas, M., Coupled Identification of The Hardening Behavior Laws and Gurson–Tvergaard–Needleman Damage Parameters-Validation on Tear Test of 12NiCr6 CT Specimen, Frattura ed Integrità Strutturale, Vol. 13, No. 49, 2019, pp. 630-642.
[20] Tvergaard, V., Needleman, A., Analysis of the Cup-Cone Fracture in A Round Tensile Bar, Acta metallurgica, Vol. 32, No. 1, 1984, pp. 157-169.
[21] Tvergaard, V., Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions, International Journal of fracture, Vol. 17, No. 4, 1981, pp. 389-407.
[22] Tvergaard, V., On Localization in Ductile Materials Containing Spherical Voids, International Journal of Fracture, Vol. 18, No. 4, 1982, pp. 237-252.
[23] Chu, C., Needleman, A., Void Nucleation Effects in Biaxially Stretched Sheets, Journal of Engineering Materials and Technology, Vol. 102, 1980, pp. 249–56.
[24] Miloud, M. H., Imad, A., Benseddiq, N., Bachir Bouiadjra, B., Bounif, A., and Serier, B., A Numerical Analysis of Relationship Between Ductility and Nucleation and Critical Void Volume Fraction Parameters of Gurson–Tvergaard–Needleman Model. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 227, No. 11, 2013, pp. 2634-2646.
[25] Cox, T., Low, J. J., An Investigation of The Plastic Fracture of AISI4340 and 18Nickel-200 Grade Maraging Steels, Metall Trans A, Vol. 5, 1974, pp. 1457–1470.
[26] Sun, D. Z., Siegele, D., Voss, B., and Schmitt, W., Application of Local Damage Models to The Numerical Analysis of Ductile Rupture, Fatigue & Fracture of Engineering Materials & Structures, Vol. 12, No. 3, 1989, pp. 201-212.
[27] Sun, D. Z., Voss, B., and Schmitt, W., Numerical Prediction of Ductile Fracture Resistance Behaviour Based on Micromechanical Models, Defect Assessment in Components-Fundamentals and Applications, 1989, pp. 447-458.
[28] Sun, D. Z., Kienzler, R., Voss, B., and Schmitt, W., Application of Micromechanical Models to The Prediction of Ductile Fracture, Astm Special Technical Publication, Vol. 1131, 1992, pp. 368-378.
[29] Guillemer-Neel, C., Feaugas, X., and Clavel, M., Mechanical Behavior and Damage Kinetics in Nodular Cast Iron: Part I. Damage Mechanisms. Metallurgical and Materials Transactions A, Vol. 31, No. 12, 2000, pp. 3063-3074.
[30] Zhang, Z. L., Thaulow, C., and Ødegård, J., A Complete Gurson Model Approach for Ductile Fracture, Engineering Fracture Mechanics, Vol. 67, No. 2, 2000, pp. 155-168.
[31] Kuna, M., Springmann, M., Determination of Ductile Damage Parameters by Local Deformation Fields, In Fracture of Nano and Engineering Materials and Structures, Springer, Dordrecht, 2006, pp. 535-536.
[32] Djouabi, M., Ati, A., and Manach, P. Y., Identification Strategy Influence of Elastoplastic Behavior Law Parameters on Gurson–Tvergaard–Needleman Damage Parameters: Application to DP980 Steel, International Journal of Damage Mechanics, Vol. 28, No. 3, 2019, pp. 427-454.
[33] Hadj Miloud, M., Modélisation De La Rupture Ductile De L’acier 12 NiCr6 Par Le Modèle Micromecanique De Gurson (Doctoral dissertation, Université Mohamed Boudiaf des Sciences et de la Technologie-Mohamed Boudiaf d'Oran), 2017.
[34] Li, Z. H., Bilby, B. A., and Howard, I. C., A study of the Internal Parameters of Ductile Damage Theory, Fatigue & Fracture of Engineering Materials & Structures, Vol. 17, No. 9, 1994, pp. 1075-1087.
[35] Zhang, Z. L., A Sensitivity Analysis of Material Parameters for the Gurson Constitutive Model, Fatigue & Fracture of Engineering Materials & Structures, Vol. 19, No. 5, 1996, pp. 561-570.
[36] Guzmán, C. F., Experimental and Numerical Characterization of Damage and Application to Incremental Forming, (A Thesis submitted to the University of Liège in Partial Ful_Llment of the Requirements for The Degree of Docteur en Sciences de l'Ingénieur), 2015.
[37] Parsa, M. H., Ettehad, M., and Matin, P. H., Forming Limit Diagram Determination of Al 3105 Sheets and Al 3105/Polypropylene/Al 3105 Sandwich Sheets Using Numerical Calculations and Experimental Investigations. Journal of Engineering Materials and Technology, Vol. 135, No. 3, 2013.
[38] Li, J., Li, S., Xie, Z., & Wang, W., Numerical Simulation of Incremental Sheet Forming Based on GTN Damage Model, The International Journal of Advanced Manufacturing Technology, Vol. 81, 2015, pp. 2053-2065.