6016-T4 aluminium alloy; Benchmark; Deep drawing modelling; Earing profile prediction; Force prediction; Model comparisons; Thickness prediction; 6016-t4 aluminum alloy; Constitutive law; Deep drawing modeling; Finite elements simulation; Force predictions; Models comparisons; Profile prediction; Materials Science (all); General Materials Science
Abstract :
[en] This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.
Disciplines :
Materials science & engineering
Author, co-author :
Habraken, Anne ; Université de Liège - ULiège > Département ArGEnCo > Département Argenco : Secteur MS2F
Aksen, Toros Arda; Mechanical Engineering Department, University of Sakarya, Esentepe Campus, M7, 54050 Serdivan, Sakarya Turkey
Alves, José L; CMEMS, Microelectromechanical Systems Research Unit, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
Amaral, Rui L; Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465 Porto, Portugal
Betaieb, Ehssen ; Université de Liège - ULiège > Urban and Environmental Engineering
Chandola, Nitin; Department of Mechanical and Aerospace Engineering, University of Florida, REEF, 1350N. Poquito Rd, Shalimar, FL 32579 USA
Corallo, Luca; Department of Electromechanical, Systems and Metal Engineering, MST-DyMaLab Research Group, Ghent University, Technologiepark 46, 9052 Zwijnaarde, Belgium
Cruz, Daniel J; Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465 Porto, Portugal
Duchene, Laurent ; Université de Liège - ULiège > Département ArGEnCo > Analyse multi-échelles dans le domaine des matériaux et structures du génie civil
Engel, Bernd; Forming Technology (UTS), Institute of Production Technologies, University of Siegen, Breite Strasse, 11, 57076 Siegen, Germany
Firat, Mehmet; Mechanical Engineering Department, University of Sakarya, Esentepe Campus, M7, 54050 Serdivan, Sakarya Turkey
Frohn-Sörensen, Peter; Forming Technology (UTS), Institute of Production Technologies, University of Siegen, Breite Strasse, 11, 57076 Siegen, Germany
Galán-López, Jesús; MSE, Faculty 3mE, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
Ghiabakloo, Hadi; Department of Materials Engineering, KU Leuven, Leuven, Belgium
Kestens, Leo A I; Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium
Lian, Junhe; Advanced Manufacturing and Materials, Department of Mechanical Engineering, Aalto University, Puumiehenkuja 3, 02150 Espoo, Finland
Lingam, Rakesh; Graduate Institute of Ferrous and Energy Materials Technology, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673 Republic of Korea ; Indian Institute of Technology Dharwad, P.B. Road, Dharwad, Karnataka 580011 India
Liu, Wencheng; School of Civil Aviation, Northwestern Polytechnical University, Taicang, 215400 China
Ma, Jun; Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Menezes, Luís F; CEMMPRE, Department of Mechanical Engineering, University of Coimbra, Polo II, Pinhal de Marrocos, 3030-788 Coimbra, Portugal
Nguyen-Minh, Tuan; Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium
Miranda, Sara S; Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465 Porto, Portugal
Neto, Diogo M; CEMMPRE, Department of Mechanical Engineering, University of Coimbra, Polo II, Pinhal de Marrocos, 3030-788 Coimbra, Portugal
Pereira, André F G; CEMMPRE, Department of Mechanical Engineering, University of Coimbra, Polo II, Pinhal de Marrocos, 3030-788 Coimbra, Portugal
Prates, Pedro A; CEMMPRE, Department of Mechanical Engineering, University of Coimbra, Polo II, Pinhal de Marrocos, 3030-788 Coimbra, Portugal ; Center for Mechanical Technology and Automation (TEMA), Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal
Reuter, Jonas; Forming Technology (UTS), Institute of Production Technologies, University of Siegen, Breite Strasse, 11, 57076 Siegen, Germany
Revil-Baudard, Benoit; Department of Mechanical and Aerospace Engineering, University of Florida, REEF, 1350N. Poquito Rd, Shalimar, FL 32579 USA
Rojas Ulloa, Carlos ; Université de Liège - ULiège > Département ArGEnCo > Département Argenco : Secteur MS2F
Shen, Fuhui; Advanced Manufacturing and Materials, Department of Mechanical Engineering, Aalto University, Puumiehenkuja 3, 02150 Espoo, Finland ; Steel Insititute, RWTH Aachen University, Intzestr. 1, 52072, Aachen, Germany
Van Bael, Albert; Department of Materials Engineering, KU Leuven, Leuven, Belgium
Verleysen, Patricia; Department of Electromechanical, Systems and Metal Engineering, MST-DyMaLab Research Group, Ghent University, Technologiepark 46, 9052 Zwijnaarde, Belgium
Barlat, Frederic; Graduate Institute of Ferrous and Energy Materials Technology, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673 Republic of Korea
Cazacu, Oana; Department of Mechanical and Aerospace Engineering, University of Florida, REEF, 1350N. Poquito Rd, Shalimar, FL 32579 USA
Kuwabara, Toshihiko; Division of Advanced Mechanical Systems Engineering, Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei-shi, Tokyo, 184-8588 Japan
Lopes, Augusto; Department of Materials and Ceramic Engineering, CICECO, Universidade de Aveiro, 3810-193 Aveiro, Portugal
Oliveira, Marta C; CEMMPRE, Department of Mechanical Engineering, University of Coimbra, Polo II, Pinhal de Marrocos, 3030-788 Coimbra, Portugal
Santos, Abel D; Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465 Porto, Portugal ; Faculty of Engineering, University of Porto, R. Dr. Roberto Frias 400, 4200-465 Porto, Portugal
Vincze, Gabriela; Center for Mechanical Technology and Automation (TEMA), Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal
ESAFORM - European Scientific Association for material FORMing
Funding number :
Grant 2021
Funding text :
The Benchmark organizers thank ESAFORM for the 10 000€ Benchmark Grant as well as the opportunity to perform and diffuse such a state-of-the-art about deep drawing simulations. As director of the Fund for Scientific Research (F.R.S.–FNRS) Anne Marie Habraken thanks this institution of Wallonia-Brussels Federation for its support. UA and UCoimbra acknowledge the support of the projects POCI-01-0145-FEDER-032362 (PTDC/EME-ESP/32362/2017), POCI-01-0145-FEDER-030592 (PTDC/EME‐EME/30592/2017), UIDB/00285/2020 and PTDC/EME‐EME/31216/2017 (POCI‐01‐0145‐FEDER‐031216). André Pereira (UC) was funded under this later project. All projects were financed by the Operational Program for Competitiveness and Internationalization, in its FEDER/FNR component, and the Portuguese Foundation of Science and Technology (FCT), in its State Budget component (OE). Sara S. Miranda is grateful to FCT for the Doctoral grant SFRH/BD/146083/2019. Carlos Rojas-Ulloa now PhD student of ULiege thanks Dommaco project for his mobility grant of the cooperation agreement WBI/AGCID SUB2019/419031 (DIE19-0005). Albert Van Bael acknowledges financial support from the FWO (K801421N). All the organizers did a marvellous job but, as responsible of this article, Anne Marie Habraken specifically thanks Marta C. Oliveira who organized so well the data collection, the results analysis and the interactions with all the participants, who are acknowledge for their positive reactions to our numerus requests. Special thanks to Oana Cazacu for her valuable input.The Benchmark organizers thank ESAFORM for the 10 000€ Benchmark Grant as well as the opportunity to perform and diffuse such a state-of-the-art about deep drawing simulations. As director of the Fund for Scientific Research (F.R.S.–FNRS) Anne Marie Habraken thanks this institution of Wallonia-Brussels Federation for its support. UA and UCoimbra acknowledge the support of the projects POCI-01-0145-FEDER-032362 (PTDC/EME-ESP/32362/2017), POCI-01-0145-FEDER-030592 (PTDC/EME‐EME/30592/2017), UIDB/00285/2020 and PTDC/EME‐EME/31216/2017 (POCI‐01‐0145‐FEDER‐031216). André Pereira (UC) was funded under this later project. All projects were financed by the Operational Program for Competitiveness and Internationalization, in its FEDER/FNR component, and the Portuguese Foundation of Science and Technology (FCT), in its State Budget component (OE). Sara S. Miranda is grateful to FCT for the Doctoral grant SFRH/BD/146083/2019. Carlos Rojas-Ulloa now PhD student of ULiege thanks Dommaco project for his mobility grant of the cooperation agreement WBI/AGCID SUB2019/419031 (DIE19-0005). Albert Van Bael acknowledges financial support from the FWO (K801421N).
Abed-Meraim F, Trinh V-D, Combescure A (2013) New quadratic solid-shell elements and their evaluation on linear benchmark problems. Computing 95(5):373–394. 10.1007/s00607-012-0265-1 DOI: 10.1007/s00607-012-0265-1
Asaro RJ, Needleman A (1985) Overview no. 42 texture development and strain hardening in rate dependent polycrystals. Acta Metall 33(6):923–953. 10.1016/0001-6160(85)90188-9 DOI: 10.1016/0001-6160(85)90188-9
Bachmann F, Hielscher R, Jupp PE, Pantleon W, Schaeben H, Wegert E (2010) Inferential statistics of electron backscatter diffraction data from within individual crystalline grains. J Appl Crystallogr 43:1338e1355. 10.1107/S002188981003027X
Barlat F, Lian K (1989) Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int J Plast 5(1):51–66. 10.1016/0749-6419(89)90019-3 DOI: 10.1016/0749-6419(89)90019-3
Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi SH, Chu E (2003) Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast 19:1297–1319. 10.1016/S0749-6419(02)00019-0 DOI: 10.1016/S0749-6419(02)00019-0
Barlat F, Cazacu O, Zyczkowski M, Banabic D, Yoon J-W (2004) Yield surface plasticity and anisotropy. In: Raabe D, Chen L-Q, Barlat F, Roters F (eds) Continuum scale simulation of engineering materials fundamentals-microstructures-process applications. Wiley-VCH, Berlin, pp 145–185
Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transformation - based anisotropic yield functions. Int J Plast 21:1009–1039. 10.1016/j.ijplas.2004.06.004 DOI: 10.1016/j.ijplas.2004.06.004
Barros PD, Neto DM, Alves JL, Oliveira MC, Menezes LF (2015) DD3IMP, 3D fully implicit finite element solver: implementation of CB2001 yield criterion. Rom J Tech Sci - Appl Mech 60:105–136
Brown SB, Kim KH, Anand L (1989) An internal variable constitutive model for hot working of metals. Int J Plast 5:95–130. 10.1016/0749-6419(89)90025-9 DOI: 10.1016/0749-6419(89)90025-9
Bunge HJ (1982) Texture analysis in material science. Butterworths, London
Cazacu O (2018) New yield criteria for isotropic and textured metallic materials. Int J Solids Struct 139(140):200–210. 10.1016/j.ijsolstr.2018.01.036 DOI: 10.1016/j.ijsolstr.2018.01.036
Cazacu O, Barlat F (2001) Generalization of Drucker’s yield criterion to orthotropy. Math Mech Solids 6:613–630. 10.1177/108128650100600603 DOI: 10.1177/108128650100600603
Cazacu O, Revil-Baudard B, (2021) Plasticity of Metallic Materials: Modelling and Applications to Metal Forming, Elsevier, 500 pages, ISBN 978–0–12-817984-0. Nov 2020
Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal close packed metals. Int J Plast 22:1171–1194. 10.1016/j.ijplas.2005.06.001 DOI: 10.1016/j.ijplas.2005.06.001
Cazacu O, Revil-Baudard B, Chandola N (2018) A yield criterion for cubic single crystals. Int J Solids Struct 151:9–19. 10.1016/j.ijsolstr.2017.04.006 DOI: 10.1016/j.ijsolstr.2017.04.006
Cazacu O, Revil-Baudard B, Chandola N (2019) Plasticity damage couplings: from single crystal to polycrystalline materials. Springer, Berlin Heidelberg DOI: 10.1007/978-3-319-92922-4
Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149–188. 10.1016/0749-6419(86)90010-0 DOI: 10.1016/0749-6419(86)90010-0
Chaker A, Koubaa S, Mars J, Vivet A, Dammak F (2021) An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates. Eng Comput 37:2145–2157. 10.1007/s00366-020-00954-8 DOI: 10.1007/s00366-020-00954-8
Chen L, Zhang H, Song M (2020) Extension of Barlat’s yield criterion to tension–compression asymmetry: modeling and verification. Metals 10:713. 10.3390/met10060713 DOI: 10.3390/met10060713
Chun BK, Jinn JT, Lee JK (2002) Modeling the Bauschinger effect for sheet metals, part I: theory. Int J Plast 18:571–595. 10.1016/s0749-6419(01)00046-8 DOI: 10.1016/s0749-6419(01)00046-8
Lee MG, Kim D, Kim C, Wenner ML, Chung K (2005) Spring-back evaluation of automotive sheets based on isotropic – kinematic hardening laws and non-quadratic anisotropic yield functions, part I: theory and formulation. Int J Plast 21:861–882. 10.1016/j.ijplas.2004.05.014 DOI: 10.1016/j.ijplas.2004.05.014
Coër J, Laurent H, Oliveira MC, Manach P-Y, Menezes LF (2018) Detailed experimental and numerical analysis of a cylindrical cup deep drawing: pros and cons of using solid-shell elements. Int J Mater Form 11:357–373. 10.48550/arXiv.1703.10126 DOI: 10.48550/arXiv.1703.10126
Coppieters S, Hakoyama T, Eyckens P, Nakano H, Van Bael A, Debruyne D, Kuwabara T (2019) On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based plasticity model. Int J Mater Form 12:741–759. 10.1007/s12289-018-1444-1 DOI: 10.1007/s12289-018-1444-1
Coulomb CA (1821). Théorie des machines simples en ayant égard au frottement de leurs parties et à la roideur des cordages. Bachelier
Danckert J, K. B. Nielsen, P. Højbjerg. (1999) Experimental investigation of NUMISHEET’99 benchmark test C: (The Aalborg Benchmark test). Proceedings of the NUMISHEET’99, 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes. In: Gelin JC, Picart P (eds) University of France-Comté and E.N.S.M.M., BURS 1:637–642
Dick RE, Yoon J-W, Huh H, Bae G. (2011) BM1 − Earing Evolution during Drawing and Ironing Processes. Part C: Benchmark Problems and Results. Proceedings of the 8th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Huh H, Chung K, Han SS, Chung WJ. (Eds.), Kaist Press, 11–48
Dick R, Cardoso R, Paulino M, Yoon JW. (2013) Benchmark 4 - Wrinkling during cup drawing. AIP Conference Proceedings 1567, NUMISHEET 2014, The 9th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, 262–327. 10.1063/1.4849984
Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. J Appl Mech 16:349–357. 10.1115/1.4010009 DOI: 10.1115/1.4010009
Duchêne L (2003) FEM study of metal sheets with a texture based, local description of the yield locus. Ph. D. Thesis, Uliege, Liège, Belgium, available from http://hdl.handle.net/2268/135058
Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the royal society of London. Series A Math Physical Sci 241(1226):376–396. 10.1098/rspa.1957.0133 DOI: 10.1098/rspa.1957.0133
Frohn-Sörensen P, Cislo C, Paschke H, Stockinger M, Engel B (2021) Dry friction under pressure variation of PACVD TiN surfaces on selected automotive sheet metals for the application in unlubricated metal forming. Wear 476:203750. 10.1016/j.wear.2021.203750
Galán J, Verleysen P, Lebensohn RA (2014) An improved algorithm for the polycrystal viscoplastic self-consistent model and its integration with implicit finite element schemes. Model Simul Mater Sci Eng 22(5):055023. 10.1088/0965-0393/22/5/055023
Galán-López J, Hidalgo J (2020) Use of the correlation between grain size and crystallographic orientation in crystal plasticity simulations: application to AISI 420 stainless steel. Crystals 10(9):819. 10.3390/cryst10090819 DOI: 10.3390/cryst10090819
Galdos L, Otegi N, Mendiguren J, Trinidad J, Saenz de Argandoña E (2021) Contact pressure, sliding velocity and viscosity dependent friction behavior of lubricants used in tube hydroforming processes. Paper presented at ESAFORM 2021. 24th International Conference on Material Forming, Liège, Belgique. https://popups.uliege.be/esaform21/index.php?id=2081
Gawad J, Van Bael A, Eyckens P, Samaey G, Van Houtte P, Roose D (2013) Hierarchical multi-scale modeling of texture induced plastic anisotropy in sheet forming. Comput Mater Sci 66:65–83. 10.1016/j.commatsci.2012.05.056 DOI: 10.1016/j.commatsci.2012.05.056
Gelin JC, Picart P. (1999) Benchmark problems and results. Proceedings of the NUMISHEET’99, 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Gelin JC, Picart P (Eds.), University of France-Comté and E.N.S.M.M., BURS (Eds.), 2:751–928, ISBN: 2–84449–001-8
Gorji MB, Mozaffar M, Heidenreich JN, Cao J, Mohr D (2020) On the potential of recurrent neural networks for modeling path dependent plasticity. J Mech Physics Solids 143:103972. 10.1016/j.jmps.2020.103972
Groche P, Nitzsche G, Elsen A (2008) Adhesive wear in deep drawing of aluminum sheets. CIRP Ann - Manuf Technol 57:295–298. 10.1016/j.cirp.2008.03.042 DOI: 10.1016/j.cirp.2008.03.042
Groeber MA, Jackson MA (2014) DREAM. 3D: a digital representation environment for the analysis of microstructure in 3D. Integr Mater Manuf Innov 3(1):56–72. 10.1186/2193-9772-3-5 DOI: 10.1186/2193-9772-3-5
Habraken A (2004) Modelling the plastic anisotropy of metals. Arch Comp Methods Eng 11:3–96. 10.1007/BF02736210 DOI: 10.1007/BF02736210
Habraken AM, Duchêne L (2004) Anisotropic elasto-plastic finite element analysis using a stress–strain interpolation method based on a polycrystalline model. Int J Plast 20:1525–1560. 10.1016/j.ijplas.2003.11.006 DOI: 10.1016/j.ijplas.2003.11.006
Han F, Diehl M, Roters F (2020) Raabe D (2020) using spectral-based representative volume element crystal plasticity simulations to predict yield surface evolution during large scale forming simulations. J Mater Proc Tech 277:116449. 10.1016/j.jmatprotec.2019.116449 DOI: 10.1016/j.jmatprotec.2019.116449
Hanabusa Y, Takizawa H, Kuwabara T (2010) Evaluation of accuracy of stress measurements determined in biaxial stress tests with cruciform specimen using numerical method. Steel Res Int 81(9):1376–1379
Hanabusa Y, Takizawa H, Kuwabara T (2013) Numerical verification of a biaxial tensile test method using a cruciform specimen. J Mater Process Technol 213:961. 10.1016/j.jmatprotec.2012.12.007 DOI: 10.1016/j.jmatprotec.2012.12.007
Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face centred cubic crystals. J Appl Mech 21:241–249. 10.1115/1.4010900 DOI: 10.1115/1.4010900
Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond Ser A 193A(1033):281–297. 10.1098/rspa.1948.0045 DOI: 10.1098/rspa.1948.0045
Hol J (2013) Multiscale friction modeling for sheet metal forming. PhD Thesis University of Twente, Enschede
Hsu YC, Yu C-H, Buehler MJ (2020) Using Deep learning to predict fracture patterns in crystalline solids. Matter 3(1):197–211 DOI: 10.1016/j.matt.2020.04.019
Hutchinson WB, Lindh E & Bate P (1999) On the determination of textures from discrete orientation measurements. Proc. IICOTOM 12th McGill University, Montreal, Canada, August 9-13, Ed. by Jerzy A. Szpunar in NRC Research Press, 35–39
Inal K, Mishra RK, Cazacu O (2010) Forming simulation of aluminum sheets using an anisotropic yield function coupled with crystal plasticity theory. Int J Solids Struct 47(2010):2223–2233. 10.1016/j.ijsolstr.2010.04.017 DOI: 10.1016/j.ijsolstr.2010.04.017
Inoue T, Takizawa H, Kuwabara T, Nomura S. (2018) Benchmark 2 – Cup drawing of anisotropic thick steel sheet, NUMISHEET 2018, 11th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, J Phys: Conf Ser 1063, Hama T, Kuroda M, Kuwabara T, Takahashi S, Yamanaka A (Eds.), 59–127
ISO 16842 (2014) Metallic materials — Sheet and strip — Biaxial tensile testing method using a cruciform test piece
Kaiping L, Habraken A, Bruneel H (1995) Simulation of square cup deep drawing with different finite elements. J Mater Process Technol 50(1–4):81–91 10.1016/0924-0136(94)01371-7 DOI: 10.1016/0924-0136(94)01371-7
Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41:1859–1886. 10.1016/0022-5096(93)90073-O DOI: 10.1016/0022-5096(93)90073-O
Kasemer M, Falkinger G, G., Roters F. (2020) A numerical study of the influence of crystal plasticity modeling parameters on the plastic anisotropy of rolled aluminum sheet modelling Simul. Mater Sci Eng 28(2020):085005. 10.1088/1361-651X/abb8e2 DOI: 10.1088/1361-651X/abb8e2
Kawka M, Makinouchi A (1996) Plastic anisotropy in FEM analysis using degenerated solid element. J Mater Process Technol 60:239–242. 10.1016/0924-0136(96)02336-9 DOI: 10.1016/0924-0136(96)02336-9
Khalfallah A, Alves JL, Oliveira MC, Menezes LF (2015) Influence of the characteristics of the experimental data set used to identify anisotropy parameters. Simul Model Pract Theory 53:15–44. 10.1016/j.simpat.2015.02.007 DOI: 10.1016/j.simpat.2015.02.007
Kuwabara T, Sugawara F (2013) Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range. Int J Plast 45:103–118. 10.1016/j.ijplas.2012.12.003 DOI: 10.1016/j.ijplas.2012.12.003
Kuwabara T, Mori T, Asano M, Hakoyama T, Barlat F (2017) Material modeling of 6016-O and 6016-T4 aluminum alloy sheets and application to hole expansion forming simulation. Int J Plast 93:164–186. 10.1016/j.ijplas.2016.10.002 DOI: 10.1016/j.ijplas.2016.10.002
Lebensohn RA, Tomé CN (1993) A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall Mater 41(9):2611–2624. 10.1016/0956-7151(93)90130-K DOI: 10.1016/0956-7151(93)90130-K
Lee JY, Barlat F, Lee MG (2015) Constitutive and friction modeling for accurate springback analysis of advanced high strength steel sheets. Int J Plast 71:113–135. 10.1016/j.ijplas.2015.04.005 DOI: 10.1016/j.ijplas.2015.04.005
Levenberg K (1944) A method for the solution of certain nonlinear problems. Q Appl Math 2:164–168. https://www.jstor.org/stable/43633451
Lian J, Shen F, Jia X, Ahn D-C, Chae D-C, Münstermann S, Bleck W (2018) An evolving non-associated Hill48 plasticity model accounting for anisotropic hardening and r-value evolution and its application to forming limit prediction. Int J Solids Struct 151:20–44. 10.1016/j.ijsolstr.2017.04.007 DOI: 10.1016/j.ijsolstr.2017.04.007
Liu W, Chen BK, Pang Y, Najafzadeh A (2020) A 3D phenomenological yield function with both in and out-of-plane mechanical anisotropy using full-field crystal plasticity spectral method for modelling sheet metal forming of strong textured aluminum alloy. Int J Solids Struct 193–194:117–133. 10.1016/j.ijsolstr.2020.02.008 DOI: 10.1016/j.ijsolstr.2020.02.008
Ma J, Li H, Wang D et al (2018) Tribological behaviors in titanium sheet and tube forming at elevated temperatures: evaluation and modeling. Int J Adv Manuf Technol 97:657–674. 10.1007/s00170-018-1985-y DOI: 10.1007/s00170-018-1985-y
Makinouchi A (1996) Sheet metal forming simulation in industry. J Mater Process Technol 60:19–26. 10.1016/0924-0136(96)02303-5 DOI: 10.1016/0924-0136(96)02303-5
Manach P-Y, Coër J, Jégat A, Laurent H, Yoon JW (2016) Benchmark 3 – Springback of an Al-mg alloy in warm forming conditions. Proceedings of NUMISHEET 2016, 10th international conference and workshop on numerical simulation of 3D sheet metal forming processes. J Physics: Conf Series, R Cardoso, OB Adetosro (Eds) 734:1–25. 10.1088/1742-6596/734/2/022003 DOI: 10.1088/1742-6596/734/2/022003
Muhammad W, Brahme AP, Kang J, Eyr E, Wilkinson DS, Inal K (2020) A method to incorporate grain boundary strength and its effects on plastic deformation in FCC Polycrystals. IOP Conf Ser: Mater Sci Eng 967:012026. 10.1088/1757-899X/967/1/012026 DOI: 10.1088/1757-899X/967/1/012026
Nielsen CV, Bay N (2018) Review of friction modeling in metal forming processes. J Mater Process Technol 255:234–241. 10.1016/j.jmatprotec.2017.12.023 DOI: 10.1016/j.jmatprotec.2017.12.023
Peirce D, Asaro RJ, Needleman A (1983) Material rate dependence and localized deformation in crystalline solids. Acta Metall 31:1951–1976. 10.1016/0001-6160(83)90014-7 DOI: 10.1016/0001-6160(83)90014-7
Plunkett B, Cazacu O, Barlat F (2008) Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals. Int J Plast 24(5):847–866. 10.1016/j.ijplas.2007.07.013 DOI: 10.1016/j.ijplas.2007.07.013
Pres P, Stembalski M, Skoczynski W (2013) Determination of the friction coefficient as a function of sliding speed and normal pressure for steel C45 and steel 40 HM. Arch Civ Mech Eng 13:444–448. 10.1016/j.acme.2013.04.010 DOI: 10.1016/j.acme.2013.04.010
Recklin V, Dietrich F, Groche P (2017) In-situ-measurement of the friction coefficient in the deep drawing process. J Phys Conf Ser 896:012027. 10.1088/1742-6596/896/1/012027 DOI: 10.1088/1742-6596/896/1/012027
Roters F, Eisenlohr P, Hantcherli L et al (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater 58:1152–1211. 10.1016/j.actamat.2009.10.058 DOI: 10.1016/j.actamat.2009.10.058
Roters F, Diehl M, Shanthraj P et al (2019) DAMASK – the Düsseldorf advanced material simulation kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Comput Mater Sci 158:420–478. 10.1016/j.commatsci.2018.04.030 DOI: 10.1016/j.commatsci.2018.04.030
Rovinelli A, Sangid MD, Proudhon H et al (2018) Using machine learning and a data-driven approach to identify the small fatigue crack driving force in polycrystalline materials. Npj Comput Mater 4:35. 10.1038/s41524-018-0094-7 DOI: 10.1038/s41524-018-0094-7
Saff EB, Kuijlaars ABJ (1997) Distributing many points on a sphere. Math Intell 19:5–11. 10.1007/BF03024331 DOI: 10.1007/BF03024331
Schwarze M, Reese S (2009) A reduced integration solid-shell finite element based on the eas and the ans concept-geometrically linear problems. Isnt J Numer Meth Eng 80(10):1322–1355. 10.1002/nme.2653 DOI: 10.1002/nme.2653
Sener B, Esener E, Firat M (2021) Modeling plastic anisotropy evolution of AISI 304 steel sheets by a polynomial yield function. SN Appl Sci 3(181):1–12. 10.1007/s42452-021-04206-2 DOI: 10.1007/s42452-021-04206-2
Shanthraj P, Eisenlohr P, Diehl M, Roters F (2015) Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials. Int J Plast 66:31–45. 10.1016/J.IJPLAS.2014.02.006 DOI: 10.1016/J.IJPLAS.2014.02.006
Shen F, Münstermann S, Lian J (2021) Forming limit prediction by the Marciniak–Kuczynski model coupled with the evolving non-associated Hill48 plasticity model. J Mater Process Technol 287:116384. 10.1016/j.jmatprotec.2019.116384
Shisode M, Hazrati J, Mishra T et al (2021a) Modeling boundary friction of coated sheets in sheet metal forming. Tribol Int 153:106554. 10.1016/j.triboint.2020.106554 DOI: 10.1016/j.triboint.2020.106554
Shore D, Leo K, Jurij S, Van Houtte P, Van Bael A (2018) Process parameter influence on texture heterogeneity in asymmetric rolling of aluminum sheet alloys. Int J Mater Form 11(2):297–309. 10.1007/s12289-016-1330-7 DOI: 10.1007/s12289-016-1330-7
Sigvant, M., Hol, J., & Chezan, T. (2015). Friction modelling in sheet metal forming simulations: application and validation on an u-bend product, 8th forming technology forum 2015: advanced constitutive models in sheet metal forming, 135–142
Soare SC, (2007). On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming. University of Florida, Department of Mechanical and Aerospace Engineering. Ph.D. Thesis
Society TR (1976) Bounds and self-consistent estimates for creep of polycrystalline materials. Proc R Soc London A Math Phys Sci 348:101–127. 10.1098/rspa.1976.0027 DOI: 10.1098/rspa.1976.0027
Sou (2019) Desenvolvimento de um Sistema de Controlo e Aquisição de Dados para Máquina Universal de Ensaios de Chapas Metálicas (in portuguese), João Paulo Sousa, MSc thesis (pp.46), Faculty of Engineering, University of Porto
Stoughton TB, Yoon JW (2009) Anisotropic hardening and non-associated flow in proportional loading of sheet metals. Int J Plast 25:1777–1817. 10.1016/j.ijplas.2009.02.003 DOI: 10.1016/j.ijplas.2009.02.003
Swift HW (1952) Plastic instability under plane stress. J Mech Physics Solids 1(1):1–18. 10.1016/0022-5096(52)90002-1 DOI: 10.1016/0022-5096(52)90002-1
Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324
Thiébaut C, Voltz C, Platon R. (1999) Limiting drawing height test with hydroforming. Proceedings of the NUMISHEET’99, 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Gelin JC, Picart P (Eds.), University of France-Comté and E.N.S.M.M., BURS (Eds.), 1:631–636, ISBN: 2–84449–001-8
Tome C, Canova GR, Kocks UF, Christodoulou N, Jonas JJ (1984) The relation between macroscopic and microscopic strain hardening in FCC polycrystals. Acta Metall 32(10):1637–1653. 10.1016/0001-6160(84)90222-0 DOI: 10.1016/0001-6160(84)90222-0
Toth L, Van Houtte P (1992) Discretization techniques for orientation distribution-functions. Text Microstruct 19(4):229–244. 10.1155/TSM.19.229 DOI: 10.1155/TSM.19.229
Trzepiecinski T, Lemu HG, Fejkiel R (2017) Numerical simulation of effect of friction directionality on forming of anisotropic sheets. Int J Simul Model 16:590–602. 10.2507/IJSIMM16(4)3.392 DOI: 10.2507/IJSIMM16(4)3.392
Van Houtte, P. (1995). MTM-FHM Software, Ver. 2. User Manual
Van Houtte P, Li S, Engler O (2004) Modelling deformation texture of aluminium alloys using grain interaction models. Aluminium 80(6):702–706
Van Houtte P, Li S, Seefeldt M, Delannay L (2005) Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int J Plast 21(3):589–624. 10.1016/j.ijplas.2004.04.011 DOI: 10.1016/j.ijplas.2004.04.011
Van Houtte P, Yerra SK, Van Bael A (2009) The facet method: a hierarchical multilevel modelling scheme for anisotropic convex plastic potentials. Int J Plast 25(2):332–360. 10.1016/j.ijplas.2008.02.001 DOI: 10.1016/j.ijplas.2008.02.001
Van Houtte P, Gawad J, Eyckens P, Van Bael B, Samaey G, Roose D (2011) A full-field strategy to take texture-induced anisotropy into account during FE simulations of metal forming processes. JOM 63(11):37–43. 10.1007/s11837-011-0189-9 DOI: 10.1007/s11837-011-0189-9
Vincze G, Barlat F, Rauch EF, Tome CN, Butuc MC, Grácio JJ (2013) Experiments and modeling of low carbon steel sheet subjected to double strain path changes. Metall Mater Trans A A44:4475–4479. 10.1007/s11661-013-1895-4 DOI: 10.1007/s11661-013-1895-4
Vincze G, Butuc MC, Barlat F (2016) “Mechanical behavior of TWIP steel under shear loading”, Numisheet 2016, IOP publishing. J Phys Conf Ser 734:032111 pp. 1-4 DOI: 10.1088/1742-6596/734/3/032111
Vladimirov IN, Pietryga MP, Reese S (2011) On the influence of kinematic hardening on plastic anisotropy in the context of finite strain plasticity. Int J Mater Form 4:255. 10.1007/s12289-011-1038-7 DOI: 10.1007/s12289-011-1038-7
Voce E (1948) The relationship between stress and strain for homogeneous deformation. J Inst Met 74:537–562
Watson M, Dick R, Helen Huang Y, Lockley A, Cardoso R, Santos A. (2016) Benchmark 1 – Failure Prediction after Cup Drawing, Reverse Redrawing and Expansion. Proceedings of NUMISHEET 2016, 10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Journal of Physics: Conference Series, R. Cardoso, O.B. Adetosro (Eds.), 734:1–85. 10.1088/1742-6596/734/2/022001
Wu L, Nguyen VD, Kilingar NG, Noels L (2020) A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths. Comput Methods Appl Mech Eng 369:113234. 10.1016/j.cma.2020.113234 DOI: 10.1016/j.cma.2020.113234
Yamanaka A, Kamijyo R, Koenuma K et al (2020) Deep neural network approach to estimate biaxial stress-strain curves of sheet metals. Mater Des 195:108970. 10.1016/j.matdes.2020.108970
Yang D-Y, Soo Ik O, Kim HHEYH. (2002) Benchmark Results of test A - Deep Drawing of a Cylindrical Cup, Proceedings of the NUMISHEET 2002, 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes - Verification of Simulation with Experiment, Yang DY, Soo Ik O, Kim HHEYH (Eds.) 2:677–756. October 21-25
Yoon JW, Dick RE, Barlat F (2011) A new analytical theory for earing generated from anisotropic plasticity. Int J Plast 27:1165–1184. 10.1016/j.ijplas.2011.01.002 DOI: 10.1016/j.ijplas.2011.01.002