Abstract
The recent trend to reduce the thickness of metallic sheets used in forming processes strongly increases the likelihood of the occurrence of wrinkling. Thus, in order to obtain defect-free components, the prediction of this kind of defect becomes extremely important in the tool design and selection of process parameters. In this study, the sheet metal forming process proposed as a benchmark in the Numisheet 2014 conference is selected to analyse the influence of the tool geometry on wrinkling behaviour, as well as the reliability of the developed numerical model. The side-wall wrinkling during the deep drawing process of a cylindrical cup in AA5042 aluminium alloy is investigated through finite element simulation and experimental measurements. The material plastic anisotropy is modelled with an advanced yield criterion beyond the isotropic (von Mises) material behaviour. The results show that the shape of the wrinkles predicted by the numerical model is strongly affected by the finite element mesh used in the blank discretization. The accurate modelling of the plastic anisotropy of the aluminium alloy yields numerical results that are in good agreement with the experiments, particularly the shape and location of the wrinkles. The predicted punch force evolution is strongly influenced by the friction coefficient used in the model. Moreover, the two punch geometries provide drawn cups with different wrinkle waves, mainly differing in amplitude.
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References
Banabic D (2010) Sheet metal forming processes: constitutive modelling and numerical simulation. Springer, Berlin. doi:10.1007/978-3-540-88113-1
Pham CH, Thuillier S, Manach PY (2014) Twisting analysis of ultra-thin metallic sheets. J Mater Process Technol 214:844–855. doi:10.1016/j.jmatprotec.2013.12.006
Kim S-H (2007) Improvement of the surface quality of an automotive member by a modification of the stamping tool. J Mater Process Technol 187-188:387–391. doi:10.1016/j.jmatprotec.2006.11.210
Anarestani SS, Morovvati MR, Vaghasloo YA (2015) Influence of anisotropy and lubrication on wrinkling of circular plates using bifurcation theory. Int J Mater Form 8:439–454. doi:10.1007/s12289-014-1187-6
Schwindt CD, Bertinetti MA, Iurman L, et al. (2015) Numerical study of the effect of martensite plasticity on the forming limits of a dual-phase steel sheet. Int J Mater Form. doi:10.1007/s12289-015-1236-9
Dick RE, Yoon JW (2015) Wrinkling during cup drawing with NUMISHEET2014 benchmark test. Steel Res Int. doi:10.1002/srin.201500018
Shafaat MA, Abbasi M, Ketabchi M (2011) Investigation into wall wrinkling in deep drawing process of conical cups. J Mater Process Technol 211:1783–1795. doi:10.1016/j.jmatprotec.2011.05.026
Wang C-T, Kinzel G, Altan T (1994) Wrinkling criterion for an anisotropic shell with compound curvatures in sheet forming. Int J Mech Sci 36:945–960. doi:10.1016/0020-7403(94)90056-6
Wang X, Cao J (2000) On the prediction of side-wall wrinkling in sheet metal forming processes. Int J Mech Sci 42:2369–2394. doi:10.1016/S0020-7403(99)00078-8
Agrawal A, Reddy NV, Dixit PM (2007) Determination of optimum process parameters for wrinkle free products in deep drawing process. J Mater Process Technol 191:51–54. doi:10.1016/j.jmatprotec.2007.03.050
Kim JB, Yang DY (2003) Prediction of wrinkling initiation in sheet metal forming processes. Eng Comput 20:6–39. doi:10.1108/02644400310458810
Kim JB, Yoon JW, Yang DY (2003) Investigation into the wrinkling behaviour of thin sheets in the cylindrical cup deep drawing process using bifurcation theory. Int J Numer Methods Eng 56:1673–1705. doi:10.1002/nme.629
Yu TX, Johnson W (1982) The buckling of annular plates in relation to the deep-drawing process. Int J Mech Sci 24:175–188. doi:10.1016/0020-7403(82)90036-4
Riks E (1979) An incremental approach to the solution of snapping and buckling problems. Int J Solids Struct 15:529–551. doi:10.1016/0020-7683(79)90081-7
Cao J, Boyce MC (1997) Wrinkling behavior of rectangular plates under lateral constraint. Int J Solids Struct 34:153–176. doi:10.1016/S0020-7683(96)00008-X
Kawka M, Olejnik L, Rosochowski A, et al. (2001) Simulation of wrinkling in sheet metal forming. J Mater Process Technol 109:283–289. doi:10.1016/S0924-0136(00)00813-X
Henriques MP, de Sousa RJA, Valente RAF (2010) Numerical implicit strategies for wrinkling prediction in free and flange forming of anisotropic sheets. Int J Mater Form 3:907–910. doi:10.1007/s12289-010-0915-9
Kim J, Kang S-J, Kang B-S (2003) A comparative study of implicit and explicit FEM for the wrinkling prediction in the hydroforming process. Int J Adv Manuf Technol 22:547–552. doi:10.1007/s00170-003-1540-2
Isik K, Silva MB, Tekkaya AE, Martins PAF (2014) Formability limits by fracture in sheet metal forming. J Mater Process Technol 214:1557–1565. doi:10.1016/j.jmatprotec.2014.02.026
Kim Y, Son Y (2000) Study on wrinkling limit diagram of anisotropic sheet metals. J Mater Process Technol 97:88–94. doi:10.1016/S0924-0136(99)00346-5
Dick RE, Cardoso R, Paulino M, Yoon JW (2013) Benchmark 4 - wrinkling during cup drawing. AIP Conf Proc 1567:262–327. doi:10.1063/1.4849984
ASTM-A681 (2008) Standard Specification for Tool Steels Alloy. doi:10.1520/a0681-08
Menezes LF, Teodosiu C (2000) Three-dimensional numerical simulation of the deep-drawing process using solid finite elements. J Mater Process Technol 97:100–106. doi:10.1016/S0924-0136(99)00345-3
Oliveira MC, Alves JL, Menezes LF (2008) Algorithms and strategies for treatment of large deformation frictional contact in the numerical simulation of deep drawing process. Arch Comput Methods Eng 15:113–162. doi:10.1007/s11831-008-9018-x
Neto DM, Oliveira MC, Menezes LF, Alves JL (2014) Applying Nagata Patches to smooth discretized surfaces used in 3D frictional contact problems. Comput Methods Appl Mech Eng 271:296–320. doi:10.1016/j.cma.2013.12.008
Neto DM, Oliveira MC, Menezes LF, Alves JL (2013) Nagata patch interpolation using surface normal vectors evaluated from the IGES file. Finite Elem Anal Des 72:35–46. doi:10.1016/j.finel.2013.03.004
Alart P, Curnier A (1991) A mixed formulation for frictional contact problems prone to newton like solution methods. Comput Methods Appl Mech Eng 92:353–375. doi:10.1016/0045-7825(91)90022-X
Yamada Y, Yoshimura N, Sakurai T (1968) Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method. Int J Mech Sci 10:343–354. doi:10.1016/0020-7403(68)90001-5
Menezes LF, Neto DM, Oliveira MC, Alves JL (2011) Improving computational performance through HPC techniques: case study using DD3IMP in-house code. AIP Conf Proc 1353:1220–1225. doi:10.1063/1.3589683
Hughes TJR (1980) Generalization of selective integration procedures to anisotropic and nonlinear media. Int J Numer Methods Eng 15:1413–1418. doi:10.1002/nme.1620150914
Teodosiu C, Daniel D, Cao H-L, Duval J-L (1995) Modelling and simulation of the can-making process using solid finite elements. J Mater Process Technol 50:133–143. doi:10.1016/0924-0136(94)01375-B
Moreira L, Ferron G, Ferran G (2000) Experimental and numerical analysis of the cup drawing test for orthotropic metal sheets. J Mater Process Technol 108:78–86. doi:10.1016/S0924-0136(00)00660-9
Barlat F, Maeda Y, Chung K, et al. (1997) Yield function development for aluminum alloy sheets. J Mech Phys Solids 45:1727–1763. doi:10.1016/S0022-5096(97)00034-3
Cazacu O, Barlat F (2001) Generalization of Drucker’s yield criterion to orthotropy. Math Mech Solids 6:613–630. doi:10.1177/108128650100600603
Flores P, Tuninetti V, Gilles G, et al. (2010) Accurate stress computation in plane strain tensile tests for sheet metal using experimental data. J Mater Process Technol 210:1772–1779. doi:10.1016/j.jmatprotec.2010.06.008
Chaparro BM, Thuillier S, Menezes LF, et al. (2008) Material parameters identification: gradient-based, genetic and hybrid optimization algorithms. Comput Mater Sci 44:339–346. doi:10.1016/j.commatsci.2008.03.028
Soare S, Yoon JW, Cazacu O (2008) On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming. Int J Plast 24:915–944. doi:10.1016/j.ijplas.2007.07.016
Barros PD, Simões VM, Neto DM, et al. (2013) On the influence of the yield parameters identification procedure in cylindrical cups earing prediction. AIP Conf Proc. 1567:512–515. doi:10.1063/1.4850024
Neto DM, Oliveira MC, Alves JL, Menezes LF (2014) Comparing faceted and smoothed tool surface descriptions in sheet metal forming simulation. Int J Mater Form. doi:10.1007/s12289-014-1177-8
Oliveira MC, Alves JL, Chaparro B, Menezes LF (2007) Study on the influence of work-hardening modeling in springback prediction. Int J Plast 23:516–543. doi:10.1016/j.ijplas.2006.07.003
Neto DM, Oliveira MC, Alves JL, Menezes LF (2014) Influence of the plastic anisotropy modelling in the reverse deep drawing process simulation. Mater Des 60:368–379. doi:10.1016/j.matdes.2014.04.008
Yoon JW, Dick RE, Barlat F (2011) A new analytical theory for earing generated from anisotropic plasticity. Int J Plast 27:1165–1184. doi:10.1016/j.ijplas.2011.01.002
Chung K, Kim D, Park T (2011) Analytical derivation of earing in circular cup drawing based on simple tension properties. Eur J Mech - A/Solids 30:275–280. doi:10.1016/j.euromechsol.2011.01.006
Acknowledgments
The authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) under project PTDC/EMS-TEC/1805/2012. The first author is also grateful to the FCT for the Postdoctoral grant SFRH/BPD/101334/2014 and P.D. Barros is grateful to the FCT for the PhD Grant SFRH/BD/98545/2013.
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Neto, D.M., Oliveira, M.C., Dick, R.E. et al. Numerical and experimental analysis of wrinkling during the cup drawing of an AA5042 aluminium alloy. Int J Mater Form 10, 125–138 (2017). https://doi.org/10.1007/s12289-015-1265-4
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DOI: https://doi.org/10.1007/s12289-015-1265-4