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Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria

Year 2025, Volume: 13 Issue: 2, 735 - 751, 30.04.2025
https://doi.org/10.29130/dubited.1610838

Abstract

The demand for low-cost production in vehicle manufacturing while complying with the safety and environmental regulations is an enormous challenge. To comply with these challenges, sheet metal forming industries now extensively use advanced high-strength steels (AHSSs) in their products. However, due to excellent strength levels of AHSSs, problems arising in their forming stage, such as large spring-back and fracture, hinder the manufacturing process. At this stage, implementing finite element analysis (FEA) in the design processes greatly improves manufacturing processes since it allows determining possible forming errors before the actual forming process. In this study, the formability of DP800 steel has been investigated by carrying out deep drawing experiments. For that, a series of circular sheet metals, whose diameters were incrementally increased, have been deep drawn to a cup shape to determine the limiting drawing ratio (LDR). Additionally, Modified Mohr-Coulomb damage model has been utilised to predict the LDR in FEA. It has been found that the LDR of DP800 is 2.13 and the implemented damage model can successfully predict the LDR within only 2.35% error.

References

  • [1] S. Mahabunphachai and M. Koç, “Investigations on forming of aluminum 5052 and 6061 sheet alloys at warm temperatures,” Mater. Des., vol. 31, no. 5, pp. 2422–2434, 2010, doi: https://doi.org/10.1016/j.matdes.2009.11.053.
  • [2] H. Lim, M. G. Lee, J. H. Sung, J. H. Kim, and R. H. Wagoner, “Time-dependent springback of advanced high strength steels,” Int. J. Plast., vol. 29, no. 1, pp. 42–59, 2012, doi: 10.1016/j.ijplas.2011.07.008.
  • [3] P. Chen and M. Koç, “Simulation of springback variation in forming of advanced high strength steels,” J. Mater. Process. Technol., vol. 190, no. 1–3, pp. 189–198, 2007, doi: 10.1016/j.jmatprotec.2007.02.046.
  • [4] W. Gan, S. S. Babu, N. Kapustka, and R. H. Wagoner, “Microstructural effects on the springback of advanced high-strength steel,” Metall. Mater. Trans. A, vol. 37, pp. 3221–3231, 2006.
  • [5] S. Panich, F. Barlat, V. Uthaisangsuk, S. Suranuntchai, and S. Jirathearanat, “Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels,” Mater. Des., vol. 51, pp. 756–766, 2013, doi: https://doi.org/10.1016/j.matdes.2013.04.080.
  • [6] Ö. N. Cora and M. Koç, “Promises and Problems of Ultra/Advanced High Strength Steel (U/AHSS) Utilization in Automotive Industry,” 7th Automot. Technol. Congr. (OTEKON 2014), no. November, pp. 1–8, 2014, doi: 10.13140/2.1.4725.0883.
  • [7] N. Baluch, Z. M. Udin, and C. S. Abdullah, “Advanced high strength steel in auto industry: an overview,” Eng. Technol. Appl. Sci. Res., vol. 4, no. 4, pp. 686–689, 2014.
  • [8] C. P. Singh and G. Agnihotri, “Study of deep drawing process parameters: a review,” Int. J. Sci. Res. Publ., vol. 5, no. 2, pp. 1–15, 2015.
  • [9] N. Şen and Y. Baykal, “Development of car wishbone using sheet metal tearing process via the theory of inventive problem-solving (TRIZ) method,” J. Brazilian Soc. Mech. Sci. Eng., vol. 41, no. 10, pp. 1–10, 2019, doi: 10.1007/s40430-019-1884-7.
  • [10] Ö. Şenol, V. Esat, and H. Darendeliler, “Springback analysis in air bending process through experiment based artificial neural networks,” Procedia Eng., vol. 81, no. October, pp. 999–1004, 2014, doi: 10.1016/j.proeng.2014.10.131.
  • [11] M. Aghaei and S. Ziaei-Rad, “A micro mechanical study on DP600 steel under tensile loading using Lemaitre damage model coupled with combined hardening,” Mater. Sci. Eng. A, vol. 772, no. September 2019, p. 138774, 2020, doi: 10.1016/j.msea.2019.138774.
  • [12] S. Abbasnejad Dizaji, H. Darendeliler, and B. Kaftanoğlu, “Effect of hardening models on different ductile fracture criteria in sheet metal forming,” Int. J. Mater. Form., vol. 9, no. 3, pp. 261–267, 2016, doi: 10.1007/s12289-014-1188-5.
  • [13] K. Ahn and M. H. Seo, “Effect of anisotropy and differential work hardening on the failure prediction of AZ31B magnesium sheet at room temperature,” Int. J. Solids Struct., vol. 138, pp. 181–192, 2018, doi: 10.1016/j.ijsolstr.2018.01.011.
  • [14] R. Li, Z. Zheng, M. Zhan, H. Zhang, and Y. Lei, “A comparative study of three forms of an uncoupled damage model as fracture judgment for thin-walled metal sheets,” Thin-Walled Struct., vol. 169, no. August, p. 108321, 2021, doi: 10.1016/j.tws.2021.108321.
  • [15] R. Billardon and L. Moret-Bailly, “Fully coupled strain and damage finite element analysis of ductile fracture,” Nucl. Eng. Des., vol. 105, no. 1, pp. 43–49, 1987.
  • [16] C. Soyarslan and A. E. Tekkaya, “A damage coupled orthotropic finite plasticity model for sheet metal forming: CDM approach,” Comput. Mater. Sci., vol. 48, no. 1, pp. 150–165, 2010.
  • [17] C. Y. Tang, J. P. Fan, and T. C. Lee, “Simulation of necking using a damage coupled finite element method,” J. Mater. Process. Technol., vol. 139, no. 1–3, pp. 510–513, 2003.
  • [18] P.-O. Bouchard, L. Bourgeon, S. Fayolle, and K. Mocellin, “An enhanced Lemaitre model formulation for materials processing damage computation,” Int. J. Mater. Form., vol. 4, pp. 299–315, 2011.
  • [19] M. E. Korkmaz, “Verification of Johnson-Cook parameters of ferritic stainless steel by drilling process: experimental and finite element simulations,” J. Mater. Res. Technol., vol. 9, no. 3, pp. 6322–6330, 2020.
  • [20] H. Talebi-Ghadikolaee, H. Moslemi Naeini, M. J. Mirnia, M. A. Mirzai, S. Alexandrov, and H. Gorji, “Experimental and numerical investigation of failure during bending of AA6061 aluminum alloy sheet using the modified Mohr-Coulomb fracture criterion,” Int. J. Adv. Manuf. Technol., vol. 105, pp. 5217–5237, 2019.
  • [21] M. B. Gorji and D. Mohr, “Predicting shear fracture of aluminum 6016-T4 during deep drawing: Combining Yld-2000 plasticity with Hosford–Coulomb fracture model,” Int. J. Mech. Sci., vol. 137, pp. 105–120, 2018.
  • [22] Y. Bao, “Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios,” Eng. Fract. Mech., vol. 72, no. 4, pp. 505–522, 2005.
  • [23] T. Güzelderen and H. Darendeliler, “Effects of triaxiality and lode parameter on deep drawing process,” Mater. Res. Proc., vol. 41, 2024.
  • [24] J. Mulder, H. Vegter, H. Aretz, S. Keller, and A. H. Van Den Boogaard, “Accurate determination of flow curves using the bulge test with optical measuring systems,” J. Mater. Process. Technol., vol. 226, pp. 169–187, 2015.
  • [25] A. F. Ávila and E. L. S. Vieira, “Proposing a better forming limit diagram prediction: a comparative study,” J. Mater. Process. Technol., vol. 141, no. 1, pp. 101–108, 2003, doi: https://doi.org/10.1016/S0924-0136(03)00162-6.
  • [26] S. P. S. S. Sivam, N. Harshavardhana, and R. Rajendran, “Artificial Neural Network prediction of forming limit diagram for directionally-rolled, size scaled copper strips,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 238, no. 8, pp. 3299–3307, 2024, doi: 10.1177/09544062231184396.
  • [27] A. J. Martínez-Donaire, M. Borrego, D. Morales-Palma, G. Centeno, and C. Vallellano, “Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF,” Int. J. Mech. Sci., vol. 151, pp. 76–84, 2019.
  • [28] T. Sjöberg, S. Marth, J. Kajberg, and H.-Å. Häggblad, “Experimental characterisation of the evolution of triaxiality stress state for sheet metal materials,” Eur. J. Mech., vol. 66, pp. 279–286, 2017.
  • [29] D.-K. Leu, “Prediction of the limiting drawing ratio and the maximum drawing load in cup-drawing,” Int. J. Mach. Tools Manuf., vol. 37, no. 2, pp. 201–213, 1997.
  • [30] D. Van Dinh, S. Van Nguyen, A. N. Pham, L. Van Nguyen, and V. D. Do, “Investigation and establishment of rational geometric factors of die in the deep drawing without a blank holder,” EUREKA Phys. Eng., no. 1, pp. 105–115, 2024.
  • [31] M. Colgan and J. Monaghan, “Deep drawing process: analysis and experiment,” J. Mater. Process. Technol., vol. 132, no. 1–3, pp. 35–41, 2003.
  • [32] W. Sun, W. Liu, and S. Yuan, “Suppressing wrinkles in thin-walled dome parts: A novel deep drawing method with active stress control,” J. Mater. Process. Technol., vol. 324, p. 118249, 2024.
  • [33] A. Taşkın and C. G. Dengiz, “Experimental and numerical optimization of deep drawing process parameters for square medical container design with the Taguchi method,” Int. J. Adv. Manuf. Technol., vol. 132, no. 5, pp. 2643–2659, 2024.

Modified- Mohr Coulomb Hasar Kriteri Kullanılarak DP800 Çeliğinin Derin Çekme Oranının Tahmini

Year 2025, Volume: 13 Issue: 2, 735 - 751, 30.04.2025
https://doi.org/10.29130/dubited.1610838

Abstract

Araç imalatında güvenlik ve çevre düzenlemelerine uyum sağlarken düşük maliyetli üretim talebi muazzam bir zorluktur. Bu zorluklara uyum sağlamak için, sac metal şekillendirme endüstrileri artık ürünlerinde yaygın olarak gelişmiş yüksek dayanımlı çelikler (AHSS'ler) kullanmaktadır. Ancak, AHSS'lerin mükemmel dayanım seviyeleri nedeniyle, büyük geri yaylanma ve kırılma gibi şekillendirme aşamalarında ortaya çıkan sorunlar üretim sürecini engellemektedir. Bu aşamada, tasarım süreçlerinde sonlu elemanlar analizinin (FEA) uygulanması, gerçek şekillendirme sürecinden önce olası şekillendirme hatalarının belirlenmesine olanak tanıdığı için üretim süreçlerini büyük ölçüde iyileştirmektedir. Bu çalışmada, derin çekme deneyleri gerçekleştirilerek DP800 çeliğinin şekillendirilebilirliği araştırılmıştır. Bunun için, çapları kademeli olarak artırılan bir dizi dairesel sac metal, derin çekme oranını (LDR) belirlemek için bardak formunda derin çekilmiştir. Ek olarak, Değiştirilmiş Mohr-Coulomb hasar modeli, FEA'daki LDR'yi tahmin etmek için kullanılmıştır. DP800'ün LDR'sinin 2.13 olduğu ve uygulanan hasar modelinin LDR'yi sadece %2.35 hata payıyla başarılı bir şekilde tahmin edebildiği bulunmuştur.

References

  • [1] S. Mahabunphachai and M. Koç, “Investigations on forming of aluminum 5052 and 6061 sheet alloys at warm temperatures,” Mater. Des., vol. 31, no. 5, pp. 2422–2434, 2010, doi: https://doi.org/10.1016/j.matdes.2009.11.053.
  • [2] H. Lim, M. G. Lee, J. H. Sung, J. H. Kim, and R. H. Wagoner, “Time-dependent springback of advanced high strength steels,” Int. J. Plast., vol. 29, no. 1, pp. 42–59, 2012, doi: 10.1016/j.ijplas.2011.07.008.
  • [3] P. Chen and M. Koç, “Simulation of springback variation in forming of advanced high strength steels,” J. Mater. Process. Technol., vol. 190, no. 1–3, pp. 189–198, 2007, doi: 10.1016/j.jmatprotec.2007.02.046.
  • [4] W. Gan, S. S. Babu, N. Kapustka, and R. H. Wagoner, “Microstructural effects on the springback of advanced high-strength steel,” Metall. Mater. Trans. A, vol. 37, pp. 3221–3231, 2006.
  • [5] S. Panich, F. Barlat, V. Uthaisangsuk, S. Suranuntchai, and S. Jirathearanat, “Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels,” Mater. Des., vol. 51, pp. 756–766, 2013, doi: https://doi.org/10.1016/j.matdes.2013.04.080.
  • [6] Ö. N. Cora and M. Koç, “Promises and Problems of Ultra/Advanced High Strength Steel (U/AHSS) Utilization in Automotive Industry,” 7th Automot. Technol. Congr. (OTEKON 2014), no. November, pp. 1–8, 2014, doi: 10.13140/2.1.4725.0883.
  • [7] N. Baluch, Z. M. Udin, and C. S. Abdullah, “Advanced high strength steel in auto industry: an overview,” Eng. Technol. Appl. Sci. Res., vol. 4, no. 4, pp. 686–689, 2014.
  • [8] C. P. Singh and G. Agnihotri, “Study of deep drawing process parameters: a review,” Int. J. Sci. Res. Publ., vol. 5, no. 2, pp. 1–15, 2015.
  • [9] N. Şen and Y. Baykal, “Development of car wishbone using sheet metal tearing process via the theory of inventive problem-solving (TRIZ) method,” J. Brazilian Soc. Mech. Sci. Eng., vol. 41, no. 10, pp. 1–10, 2019, doi: 10.1007/s40430-019-1884-7.
  • [10] Ö. Şenol, V. Esat, and H. Darendeliler, “Springback analysis in air bending process through experiment based artificial neural networks,” Procedia Eng., vol. 81, no. October, pp. 999–1004, 2014, doi: 10.1016/j.proeng.2014.10.131.
  • [11] M. Aghaei and S. Ziaei-Rad, “A micro mechanical study on DP600 steel under tensile loading using Lemaitre damage model coupled with combined hardening,” Mater. Sci. Eng. A, vol. 772, no. September 2019, p. 138774, 2020, doi: 10.1016/j.msea.2019.138774.
  • [12] S. Abbasnejad Dizaji, H. Darendeliler, and B. Kaftanoğlu, “Effect of hardening models on different ductile fracture criteria in sheet metal forming,” Int. J. Mater. Form., vol. 9, no. 3, pp. 261–267, 2016, doi: 10.1007/s12289-014-1188-5.
  • [13] K. Ahn and M. H. Seo, “Effect of anisotropy and differential work hardening on the failure prediction of AZ31B magnesium sheet at room temperature,” Int. J. Solids Struct., vol. 138, pp. 181–192, 2018, doi: 10.1016/j.ijsolstr.2018.01.011.
  • [14] R. Li, Z. Zheng, M. Zhan, H. Zhang, and Y. Lei, “A comparative study of three forms of an uncoupled damage model as fracture judgment for thin-walled metal sheets,” Thin-Walled Struct., vol. 169, no. August, p. 108321, 2021, doi: 10.1016/j.tws.2021.108321.
  • [15] R. Billardon and L. Moret-Bailly, “Fully coupled strain and damage finite element analysis of ductile fracture,” Nucl. Eng. Des., vol. 105, no. 1, pp. 43–49, 1987.
  • [16] C. Soyarslan and A. E. Tekkaya, “A damage coupled orthotropic finite plasticity model for sheet metal forming: CDM approach,” Comput. Mater. Sci., vol. 48, no. 1, pp. 150–165, 2010.
  • [17] C. Y. Tang, J. P. Fan, and T. C. Lee, “Simulation of necking using a damage coupled finite element method,” J. Mater. Process. Technol., vol. 139, no. 1–3, pp. 510–513, 2003.
  • [18] P.-O. Bouchard, L. Bourgeon, S. Fayolle, and K. Mocellin, “An enhanced Lemaitre model formulation for materials processing damage computation,” Int. J. Mater. Form., vol. 4, pp. 299–315, 2011.
  • [19] M. E. Korkmaz, “Verification of Johnson-Cook parameters of ferritic stainless steel by drilling process: experimental and finite element simulations,” J. Mater. Res. Technol., vol. 9, no. 3, pp. 6322–6330, 2020.
  • [20] H. Talebi-Ghadikolaee, H. Moslemi Naeini, M. J. Mirnia, M. A. Mirzai, S. Alexandrov, and H. Gorji, “Experimental and numerical investigation of failure during bending of AA6061 aluminum alloy sheet using the modified Mohr-Coulomb fracture criterion,” Int. J. Adv. Manuf. Technol., vol. 105, pp. 5217–5237, 2019.
  • [21] M. B. Gorji and D. Mohr, “Predicting shear fracture of aluminum 6016-T4 during deep drawing: Combining Yld-2000 plasticity with Hosford–Coulomb fracture model,” Int. J. Mech. Sci., vol. 137, pp. 105–120, 2018.
  • [22] Y. Bao, “Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios,” Eng. Fract. Mech., vol. 72, no. 4, pp. 505–522, 2005.
  • [23] T. Güzelderen and H. Darendeliler, “Effects of triaxiality and lode parameter on deep drawing process,” Mater. Res. Proc., vol. 41, 2024.
  • [24] J. Mulder, H. Vegter, H. Aretz, S. Keller, and A. H. Van Den Boogaard, “Accurate determination of flow curves using the bulge test with optical measuring systems,” J. Mater. Process. Technol., vol. 226, pp. 169–187, 2015.
  • [25] A. F. Ávila and E. L. S. Vieira, “Proposing a better forming limit diagram prediction: a comparative study,” J. Mater. Process. Technol., vol. 141, no. 1, pp. 101–108, 2003, doi: https://doi.org/10.1016/S0924-0136(03)00162-6.
  • [26] S. P. S. S. Sivam, N. Harshavardhana, and R. Rajendran, “Artificial Neural Network prediction of forming limit diagram for directionally-rolled, size scaled copper strips,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 238, no. 8, pp. 3299–3307, 2024, doi: 10.1177/09544062231184396.
  • [27] A. J. Martínez-Donaire, M. Borrego, D. Morales-Palma, G. Centeno, and C. Vallellano, “Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF,” Int. J. Mech. Sci., vol. 151, pp. 76–84, 2019.
  • [28] T. Sjöberg, S. Marth, J. Kajberg, and H.-Å. Häggblad, “Experimental characterisation of the evolution of triaxiality stress state for sheet metal materials,” Eur. J. Mech., vol. 66, pp. 279–286, 2017.
  • [29] D.-K. Leu, “Prediction of the limiting drawing ratio and the maximum drawing load in cup-drawing,” Int. J. Mach. Tools Manuf., vol. 37, no. 2, pp. 201–213, 1997.
  • [30] D. Van Dinh, S. Van Nguyen, A. N. Pham, L. Van Nguyen, and V. D. Do, “Investigation and establishment of rational geometric factors of die in the deep drawing without a blank holder,” EUREKA Phys. Eng., no. 1, pp. 105–115, 2024.
  • [31] M. Colgan and J. Monaghan, “Deep drawing process: analysis and experiment,” J. Mater. Process. Technol., vol. 132, no. 1–3, pp. 35–41, 2003.
  • [32] W. Sun, W. Liu, and S. Yuan, “Suppressing wrinkles in thin-walled dome parts: A novel deep drawing method with active stress control,” J. Mater. Process. Technol., vol. 324, p. 118249, 2024.
  • [33] A. Taşkın and C. G. Dengiz, “Experimental and numerical optimization of deep drawing process parameters for square medical container design with the Taguchi method,” Int. J. Adv. Manuf. Technol., vol. 132, no. 5, pp. 2643–2659, 2024.
There are 33 citations in total.

Details

Primary Language English
Subjects Numerical Modelling and Mechanical Characterisation
Journal Section Research Article
Authors

Nuri Şen 0000-0002-6501-5858

Tolgahan Civek 0000-0002-1487-5903

Elifnaz Baba 0009-0005-5657-1042

Submission Date December 31, 2024
Acceptance Date January 13, 2025
Publication Date April 30, 2025
Published in Issue Year 2025 Volume: 13 Issue: 2

Cite

APA Şen, N., Civek, T., & Baba, E. (2025). Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria. Duzce University Journal of Science and Technology, 13(2), 735-751. https://doi.org/10.29130/dubited.1610838
AMA Şen N, Civek T, Baba E. Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria. DUBİTED. April 2025;13(2):735-751. doi:10.29130/dubited.1610838
Chicago Şen, Nuri, Tolgahan Civek, and Elifnaz Baba. “Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria”. Duzce University Journal of Science and Technology 13, no. 2 (April 2025): 735-51. https://doi.org/10.29130/dubited.1610838.
EndNote Şen N, Civek T, Baba E (April 1, 2025) Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria. Duzce University Journal of Science and Technology 13 2 735–751.
IEEE N. Şen, T. Civek, and E. Baba, “Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria”, DUBİTED, vol. 13, no. 2, pp. 735–751, 2025, doi: 10.29130/dubited.1610838.
ISNAD Şen, Nuri et al. “Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria”. Duzce University Journal of Science and Technology 13/2 (April2025), 735-751. https://doi.org/10.29130/dubited.1610838.
JAMA Şen N, Civek T, Baba E. Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria. DUBİTED. 2025;13:735–751.
MLA Şen, Nuri et al. “Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria”. Duzce University Journal of Science and Technology, vol. 13, no. 2, 2025, pp. 735-51, doi:10.29130/dubited.1610838.
Vancouver Şen N, Civek T, Baba E. Prediction of Deep Drawing Ratio for DP800 Steel by Using Modified-Mohr-Coulomb Damage Criteria. DUBİTED. 2025;13(2):735-51.