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Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials

Yıl 2024, Cilt: 30 Sayı: 1, 1 - 9, 29.02.2024

Öz

In the cup drawing process, the tensile stress in the radial direction is dominant during the drawing. However, the sheet bends around the punch and die radiuses, and the fibers touching the punch and die are exposed to compression, while the outer surfaces are exposed to tension. Therefore, the stress state at the radius regions of punch and die becomes complicated to overcome due to the bending and may influence the final earing form. The present study investigates the influence of a plasticity model involving an advanced yield criterion coupled with a combined hardening model on the earing prediction in the cup drawing process of AA6016-T4 aluminum alloy. Therefore, isotropic hardening and combined hardening models are implemented, respectively so as to show the kinematic hardening effect on the earing prediction performance. The combined hardening model comprises Armstrong-Frederic kinematic hardening and isotropic hardening rules together to characterize the hardening behavior of the sheet, and the parameters of the hardening model were obtained by considering a reversal shear test. A sixth-order polynomial-based yield criterion was implemented to represent the anisotropic response of the sheet successfully. The Hill48 yield criterion was also considered in the present study for comparison purposes. The analyses were conducted based on the additive plasticity approach and using the implicit stress update scheme in Marc commercial software. The punch force-displacement responses and earing profile predictions were obtained numerically and compared with the experimental outcomes. It was seen that introducing the combined hardening model enhances the earing prediction capability for both yield criteria. With the incorporation of the combined hardening rule, the improvement in the prediction of the earing profile was more apparent in HomPol6 results compared to Hill48. The HomPol6 yield criterion coupled with the combined hardening rule led to a better agreement in the prediction of ear formation.

Kaynakça

  • [1] Köksal NS, Uzkut M. “Determination of formability parameters of Erdemir 6114 sheets tempered at dual phase regions”. Pamukkale University Journal of Engineering Sciences, 7(3), 337-341, 2001.
  • [2] Chung K, Shah K. “Finite element simulation of sheet metal forming for planar anisotropic metals”. International Journal of Plasticity, 8, 453-476, 1992.
  • [3] Yoon JW, Barlat F, Chung K, Pourboghrat F, Yang DY. “Influence of initial back stress on the earing prediction of drawn cups for planar anisotropic aluminum sheets”. Journal of Materials Processing Technology, 80-81, 433-437, 1998.
  • [4] Yoon JW, Barlat F, Chung K, Pourboghrat F, Yang DY. “Earing predictions based on asymmetric nonquadratic yield function”. International Journal of Plasticity, 16, 1075-1104, 2000.
  • [5] Yoon JW, Barlat F, Dick RE, Karabin ME. “Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function”. International Journal of Plasticity, 22, 174-193, 2006.
  • [6] Yoon JH, Cazacu O, Yoon JW, Dick RE. “Earing predictions for strongly textured aluminum sheets”. International Journal of Mechanical Science, 52, 1563-1578, 2010.
  • [7] Vladimirov IN, Schwarze M, Reese S. “Earing prediction by a finite strain multiplicative formulation for anisotropic elastoplastic materials”. GAMM Mitteilungen, 33, 116-129, 2010.
  • [8] Chatti S, Chtioui N. “Sheet metal forming simulation using finite elastoplasticity with mixed isotropic/kinematic hardening”. European Journal of Computational Mechanics, 20, 427-453, 2011.
  • [9] Vrh M, Halilovic M, Starman B, Stok B, Comsa DS, Banabic D. “Capability of the BBC2008 yield criterion in predicting the earing profile in cup deep drawing simulations”. European Journal of Mechanics A/Solids, 45, 59-74, 2014.
  • [10] Park T, Chung K. “Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing”. International Journal of Mechanical Sciences, 115-116, 553-563, 2016.
  • [11] Othmen KB, Sai K, Manach PY, Elleuch K. “Reverse deep drawing process: Material anisotropy and work-hardening effects”. Journal of Materials: Design and Application, 233, 699-713, 2019.
  • [12] Grillo TJ, Valente RAF, Alves de Souza RJ. “Modelling non-quadratic anisotropic yield criteria and mixed isotropic-nonlinear kinematic hardening: analysis of forward and backward-Euler formulations”. International Journal of Material Forming, 8, 533-547, 2015.
  • [13] Izadpanah S, Ghaderi SH, Gerdooei M. “Material parameters identification procedure for BBC2003 yield criterion and earing prediction in deep drawing”. International Journal of Solids and Structures, 49, 3582-3593, 2012.
  • [14] Singh A, Basak S, Prakash L, Roy GG, Jha MN, Mascarenhas M, Panda SK. “Prediction of earing defect and deep drawing behavior of commercially pure titanium sheets using CPB06 anisotropy yield theory”. Journal of Manufacturing Processes, 33, 256-267, 2018.
  • [15] Feng Z. Yoon SY “Prediction of earing defect and deep drawing behavior of commercially pure titanium sheets using CPB06 anisotropy yield theory”. Journal of Manufacturing Processes, 33, 256-267, 2018.
  • [16] Habraken AM, Aksen TA, Alves JL, et al. “Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations”. International Journal of Material Forming, 15, 1-96, 2022.
  • [17] Kim J, Pham QT, Ha J, Kim YS. “Constitutive modeling of commercial pure titanium sheet based on non-associated flow rule and differential hardening”. International Journal of Mechanical Sciences, 230, 1-17, 2022.
  • [18] Taherizadeh A, Green DE, Ghaei A, Yoon JW. “A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming”. International Journal of Plasticity, 26, 288-309, 2010.
  • [19] Mendiguren J, Rolfe B, Weiss M. “On the definition of an kinematic hardening effect graph for sheet metal forming process simulations”. International Journal of Mechanical Sciences, 92, 109-120, 2015.
  • [20] Prager W. “A new method of analyzing stresses and strains in work hardening plastic solids”. ASME Journal of Applied Mechanics, 23, 493-496, 1956.
  • [21] Ziegler HA. “A modification of Prager’s hardening rule”. Quarterly of Applied Mechanics, 17, 55-65, 1959.
  • [22] Besseling JF. “A theory of plastic and creep deformations of an initially isotropic material”. ASME Journal of Applied Mechanics, 25, 529-536, 1958.
  • [23] Mroz Z. “On the description of anisotropic work hardening”. Journal of Mechanics and Physics of Solids, 15, 163-175, 1967.
  • [24] Dafalias YF, Popov EF. “Plastic internal variables formalism of cyclic plasticity”. ASME Journal of Applied Mechanics, 98, 645-651, 1976.
  • [25] Armstrong PJ, Frederic CO. “A Mathematical Representation of the Multiaxial Bauschinger Effect”. Scientific Report, G.E.G.B. Report RD/B/N, Scientific Report, 731, 1966.
  • [26] Ohno N, Wang JD. “Kinematic hardening rules with critical state of dynamic recovery. Part 1: Formulations and basic features for ratcheting behavior”. International Journal of Plasticity, 9, 375-390, 1993.
  • [27] Yıldız H, Kırlı O. “Non-linear finite element modeling of deep drawing process”. Pamukkale University Journal of Engineering Sciences, 10(3), 317-326, 2004.
  • [28] Hill R. “A theory of the yielding and plastic flow of anisotropic metals”. Proceeding of the Royal Society London A, 193A, 291-297,1948.
  • [29] Gotoh M. “A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)“. International Journal of Mechanical Sciences, 19, 505-512, 1977.
  • [30] Soare S, Yoon JW, Cazacu O. “On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming”. International Journal of Plasticity, 24, 915-944, 2008.
  • [31] Soare SC. On the Use of Homogeneous Polynomials to Develop Anisotropic Yield Functions with Applications to Sheet Forming. PhD Thesis, University of Florida, Florida, USA, 2007.
  • [32] Firat M. (2008) “A numerical analysis of sheet metal formability for automotive stamping applications”. Computational Materials Science, 43, 802-811, 2008.
  • [33] Paul SK, Sivaprasad S, Dhar S, Tarafder M, Tarafder S. “Simulation of cyclic plastic deformation response in SA333 C-Mn steel by a kinematic hardening model”. Computational Materials Science, 48, 662-671, 2010.
  • [34] Zang SL, Guo C, Thuillier S, Lee MG. “A model of one surface cyclic plasticity and its application to springback prediction”. International Journal of Mechanical Sciences, 53, 425-435, 2011.
  • [35] MSC. Software Corporation. “Volume A: Theory and User Information”. https://simcompanion.hexagon.com/customers/s/article/msc-marc-volume-a--theory-and-user-information-doc9245 (27.10.2023).
  • [36] MSC. Software Corporation. “Volume B: Element Library”. https://simcompanion.hexagon.com/customers/s/article/volume-b--element-library-doc9246 (27.10.2023).

Homojen polinom tabanlı akma fonksiyonunun birleşik pekleşme modeli ile kullanımının anizotropik metalik malzemeler üzerindeki kulaklanma tahmin performansı

Yıl 2024, Cilt: 30 Sayı: 1, 1 - 9, 29.02.2024

Öz

Kap çekme işlemi esnasında, radyal yön boyunca çekme gerilmesi mevcuttur. Bununla birlikte şekillendirilecek sac, zımba ve kalıp köşelerinin etrafında bükülmektedir ve köşelere temas eden iç yüzeyler basma gerilmesi etkisi altındayken, dış yüzeyler ise çekme etkisi altındır. Bu durum sacın zımba ve kalıp köşelerinde bükülen bölümlerindeki gerilme durumunu karmaşık bir hale getirmektedir ve nihai kulak formunu etkileyebilmektedir. Bu çalışma, gelişmiş bir akma fonksiyonu ve bir birleşik pekleşme modeli içeren bir plastisite modelinin kulaklanma tahmin performansını incelemektedir. Bu kapsamda AA6016-T4 alüminyum alaşımının derin çekme işlemi incelenmiştir. Birleşik pekleşme modelinin kulaklanma tahmin performansına etkisini daha net ortaya koymak amacıyla, izotropik ve birleşik pekleşme kuralları ayrı ayrı analizlere entegre edilmiştir. Malzemenin pekleşme davranışını tanımlamak amacıyla kullanılan birleşik pekleşme modeli, Armstrong-Frederic kinematik pekleşme ve izotropik pekleşme modellerinin birleşimidir ve birleşik pekleşme modelinin parametreleri bir tersinir kayma testinin verileri kullanılarak elde edilmiştir. Sacın anizotropik davranışını isabetli bir şekilde tanımlamak amacıyla altıncı dereceden homojen polinom tabanlı bir akma fonksiyonu kullanılmıştır. HomPol6 kriterinin tahmin performansını göstermek için simülasyonlar Hill48 akma kriteri kullanılarak da yürütülmüştür. Simülasyonlar Marc ticari yazılımında eklemeli plastisite yaklaşımı ve kapalı zaman adımlı gerilme güncelleme şeması kullanılarak yürütülmüştür. Zımba kuvvet-deplasman davranışları ve kulak profil tahminleri sayısal olarak elde edilmiş ve deneysel sonuçlarla kıyaslanmıştır. Birleşik pekleşme modelinin kulaklanma tahmin yeteneğini iki akma kriteri için de iyileştirdiği görülmüştür. Bu iyileşmenin HomPol6 sonuçları için daha belirgin olduğu da kaydedilmiştir. En iyi kulak oluşum tahmininin, HomPol6 akma kriteri ile birleşik pekleşme kuralı kullanıldığında gerçekleştiği görülmüştür.

Kaynakça

  • [1] Köksal NS, Uzkut M. “Determination of formability parameters of Erdemir 6114 sheets tempered at dual phase regions”. Pamukkale University Journal of Engineering Sciences, 7(3), 337-341, 2001.
  • [2] Chung K, Shah K. “Finite element simulation of sheet metal forming for planar anisotropic metals”. International Journal of Plasticity, 8, 453-476, 1992.
  • [3] Yoon JW, Barlat F, Chung K, Pourboghrat F, Yang DY. “Influence of initial back stress on the earing prediction of drawn cups for planar anisotropic aluminum sheets”. Journal of Materials Processing Technology, 80-81, 433-437, 1998.
  • [4] Yoon JW, Barlat F, Chung K, Pourboghrat F, Yang DY. “Earing predictions based on asymmetric nonquadratic yield function”. International Journal of Plasticity, 16, 1075-1104, 2000.
  • [5] Yoon JW, Barlat F, Dick RE, Karabin ME. “Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function”. International Journal of Plasticity, 22, 174-193, 2006.
  • [6] Yoon JH, Cazacu O, Yoon JW, Dick RE. “Earing predictions for strongly textured aluminum sheets”. International Journal of Mechanical Science, 52, 1563-1578, 2010.
  • [7] Vladimirov IN, Schwarze M, Reese S. “Earing prediction by a finite strain multiplicative formulation for anisotropic elastoplastic materials”. GAMM Mitteilungen, 33, 116-129, 2010.
  • [8] Chatti S, Chtioui N. “Sheet metal forming simulation using finite elastoplasticity with mixed isotropic/kinematic hardening”. European Journal of Computational Mechanics, 20, 427-453, 2011.
  • [9] Vrh M, Halilovic M, Starman B, Stok B, Comsa DS, Banabic D. “Capability of the BBC2008 yield criterion in predicting the earing profile in cup deep drawing simulations”. European Journal of Mechanics A/Solids, 45, 59-74, 2014.
  • [10] Park T, Chung K. “Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing”. International Journal of Mechanical Sciences, 115-116, 553-563, 2016.
  • [11] Othmen KB, Sai K, Manach PY, Elleuch K. “Reverse deep drawing process: Material anisotropy and work-hardening effects”. Journal of Materials: Design and Application, 233, 699-713, 2019.
  • [12] Grillo TJ, Valente RAF, Alves de Souza RJ. “Modelling non-quadratic anisotropic yield criteria and mixed isotropic-nonlinear kinematic hardening: analysis of forward and backward-Euler formulations”. International Journal of Material Forming, 8, 533-547, 2015.
  • [13] Izadpanah S, Ghaderi SH, Gerdooei M. “Material parameters identification procedure for BBC2003 yield criterion and earing prediction in deep drawing”. International Journal of Solids and Structures, 49, 3582-3593, 2012.
  • [14] Singh A, Basak S, Prakash L, Roy GG, Jha MN, Mascarenhas M, Panda SK. “Prediction of earing defect and deep drawing behavior of commercially pure titanium sheets using CPB06 anisotropy yield theory”. Journal of Manufacturing Processes, 33, 256-267, 2018.
  • [15] Feng Z. Yoon SY “Prediction of earing defect and deep drawing behavior of commercially pure titanium sheets using CPB06 anisotropy yield theory”. Journal of Manufacturing Processes, 33, 256-267, 2018.
  • [16] Habraken AM, Aksen TA, Alves JL, et al. “Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations”. International Journal of Material Forming, 15, 1-96, 2022.
  • [17] Kim J, Pham QT, Ha J, Kim YS. “Constitutive modeling of commercial pure titanium sheet based on non-associated flow rule and differential hardening”. International Journal of Mechanical Sciences, 230, 1-17, 2022.
  • [18] Taherizadeh A, Green DE, Ghaei A, Yoon JW. “A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming”. International Journal of Plasticity, 26, 288-309, 2010.
  • [19] Mendiguren J, Rolfe B, Weiss M. “On the definition of an kinematic hardening effect graph for sheet metal forming process simulations”. International Journal of Mechanical Sciences, 92, 109-120, 2015.
  • [20] Prager W. “A new method of analyzing stresses and strains in work hardening plastic solids”. ASME Journal of Applied Mechanics, 23, 493-496, 1956.
  • [21] Ziegler HA. “A modification of Prager’s hardening rule”. Quarterly of Applied Mechanics, 17, 55-65, 1959.
  • [22] Besseling JF. “A theory of plastic and creep deformations of an initially isotropic material”. ASME Journal of Applied Mechanics, 25, 529-536, 1958.
  • [23] Mroz Z. “On the description of anisotropic work hardening”. Journal of Mechanics and Physics of Solids, 15, 163-175, 1967.
  • [24] Dafalias YF, Popov EF. “Plastic internal variables formalism of cyclic plasticity”. ASME Journal of Applied Mechanics, 98, 645-651, 1976.
  • [25] Armstrong PJ, Frederic CO. “A Mathematical Representation of the Multiaxial Bauschinger Effect”. Scientific Report, G.E.G.B. Report RD/B/N, Scientific Report, 731, 1966.
  • [26] Ohno N, Wang JD. “Kinematic hardening rules with critical state of dynamic recovery. Part 1: Formulations and basic features for ratcheting behavior”. International Journal of Plasticity, 9, 375-390, 1993.
  • [27] Yıldız H, Kırlı O. “Non-linear finite element modeling of deep drawing process”. Pamukkale University Journal of Engineering Sciences, 10(3), 317-326, 2004.
  • [28] Hill R. “A theory of the yielding and plastic flow of anisotropic metals”. Proceeding of the Royal Society London A, 193A, 291-297,1948.
  • [29] Gotoh M. “A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)“. International Journal of Mechanical Sciences, 19, 505-512, 1977.
  • [30] Soare S, Yoon JW, Cazacu O. “On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming”. International Journal of Plasticity, 24, 915-944, 2008.
  • [31] Soare SC. On the Use of Homogeneous Polynomials to Develop Anisotropic Yield Functions with Applications to Sheet Forming. PhD Thesis, University of Florida, Florida, USA, 2007.
  • [32] Firat M. (2008) “A numerical analysis of sheet metal formability for automotive stamping applications”. Computational Materials Science, 43, 802-811, 2008.
  • [33] Paul SK, Sivaprasad S, Dhar S, Tarafder M, Tarafder S. “Simulation of cyclic plastic deformation response in SA333 C-Mn steel by a kinematic hardening model”. Computational Materials Science, 48, 662-671, 2010.
  • [34] Zang SL, Guo C, Thuillier S, Lee MG. “A model of one surface cyclic plasticity and its application to springback prediction”. International Journal of Mechanical Sciences, 53, 425-435, 2011.
  • [35] MSC. Software Corporation. “Volume A: Theory and User Information”. https://simcompanion.hexagon.com/customers/s/article/msc-marc-volume-a--theory-and-user-information-doc9245 (27.10.2023).
  • [36] MSC. Software Corporation. “Volume B: Element Library”. https://simcompanion.hexagon.com/customers/s/article/volume-b--element-library-doc9246 (27.10.2023).
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliği (Diğer)
Bölüm Makale
Yazarlar

Toros Arda Akşen

Murat Özsoy

Mehmet Fırat

Yayımlanma Tarihi 29 Şubat 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 30 Sayı: 1

Kaynak Göster

APA Akşen, T. A., Özsoy, M., & Fırat, M. (2024). Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 30(1), 1-9.
AMA Akşen TA, Özsoy M, Fırat M. Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. Şubat 2024;30(1):1-9.
Chicago Akşen, Toros Arda, Murat Özsoy, ve Mehmet Fırat. “Earing Prediction Performance of Homogeneous Polynomial-Based Yield Function Coupled With the Combined Hardening Model for Anisotropic Metallic Materials”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 30, sy. 1 (Şubat 2024): 1-9.
EndNote Akşen TA, Özsoy M, Fırat M (01 Şubat 2024) Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 30 1 1–9.
IEEE T. A. Akşen, M. Özsoy, ve M. Fırat, “Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, c. 30, sy. 1, ss. 1–9, 2024.
ISNAD Akşen, Toros Arda vd. “Earing Prediction Performance of Homogeneous Polynomial-Based Yield Function Coupled With the Combined Hardening Model for Anisotropic Metallic Materials”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 30/1 (Şubat 2024), 1-9.
JAMA Akşen TA, Özsoy M, Fırat M. Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2024;30:1–9.
MLA Akşen, Toros Arda vd. “Earing Prediction Performance of Homogeneous Polynomial-Based Yield Function Coupled With the Combined Hardening Model for Anisotropic Metallic Materials”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, c. 30, sy. 1, 2024, ss. 1-9.
Vancouver Akşen TA, Özsoy M, Fırat M. Earing prediction performance of homogeneous polynomial-based yield function coupled with the combined hardening model for anisotropic metallic materials. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2024;30(1):1-9.





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