Abstract
In order to predict the initiation of necking in metal bellows forming process, a methodology for determination of the forming limit diagram and the forming limit stress diagram is represented in this paper. The methodology is based on the Marciniak and Kuczynski (M–K) model. Comparison between the experimental and theoretical results for hydroforming stress and strain-limit diagrams as predicted by different methods indicates that the present approach is suitable for prediction of necking in tube hydroforming processes. Afterwards, the implementation of the hydroforming strain- and stress-limit diagrams into finite element numerical simulations for the forming of the metal bellows is established. A satisfactory agreement between the finite element method (FEM) and test results is achieved.
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Satoshi I, Hiroshi K, Masanori K (2000) Evaluation of mechanical behavior of new type bellows with two directional convolutions. Nucl Eng Des 197(1, 2):107–114
Lee SW (2002) Study on the forming parameters of the metal bellows. J Mater Proc Tech 130–131:47–53. doi:10.1016/S0924-0136(02)00787-2
Hyun KB, Yong LM, Man SS, Hoon MY (2007) Forming various shapes of tubular bellows using a single-step hydroforming process. J Mater Proc Tech 194(1–3):1–6. doi:10.1016/j.jmatprotec.2007.02.029
Gh F Mosavi Mashhadi M., Norouzifard V. (2008). Evaluation of effective parameters in metal bellows forming process. J Mater Process Technol (in press). doi:10.1016/j.jmatprotec.2008.07.057
Arrieux R, Bedrin C, Bovin M (1982) Determination of an intrinsic forming limit stress diagram for isotropic sheets. In: Proceedings of the 12th IDDRG congress, Santa Margherita, Ligure. 2, pp. 61-71
Stoughton TB (2000) A general forming limit criterion for sheet metal forming. Int J Mech Sci 42(1):1–27. doi:10.1016/S0020-7403(98)00113-1
Stoughton TB, Zhu X (2004) Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD. Int J Plast 20(8–9):1463–1486. doi:10.1016/j.ijplas.2003.11.004
Hashemi R (2007) Consideration of path effects on prediction of forming limit diagrams, M.S. Thesis, Department of Mechanical Engineering, Sharif University of Technology
Assempour A, Hashemi R, Abrinia K, Ganjiani M, Masoumi E (2009) A methodology for prediction of forming limit stress diagrams considering the strain path effect. Comput Mater Sci 45(2):195–204. doi:10.1016/j.commatsci.2008.09.025
Wu PD, Graf A, MacEwen SR, Lloyd DJ, Jain M, Neale KW (2005) On forming limit stress diagram analysis. Int J Solids Struct 42(8):2225–2241. doi:10.1016/j.ijsolstr.2004.09.010
Butuc MC, Gracio JJ, Barata da Rocha A (2006) An experimental and theoretical analysis on the application of stress-based forming limit criterion. Int J Mech Sci 48(4):414–429. doi:10.1016/j.ijmecsci.2005.11.007
Zimniak Z (2000) Implementation of the forming limit stress diagram in FEM simulations. J Mater Process Technol 106(1–3):261–266. doi:10.1016/S0924-0136(00)00627-0
Chen MH, Gao L, Zuo DW, Wang M (2007) Application of the forming limit stress diagram to forming limit prediction for multi-step forming of auto panels. J Mater Process Technol 187–188:173–177. doi:10.1016/j.jmatprotec.2006.11.178
Kim J, Kim YW, Kang BS, Hwan SM (2004) Finite element analysis for bursting failure prediction in bulge forming of a seamed tube. Finite Elem Anal Des 40:953–966. doi:10.1016/j.finel.2003.05.003
Xing HL, Makinouchi A (2001) Numerical analysis and design for tubular hydroforming. Int J Mech Sci 43(4):1009–1026. doi:10.1016/S0020-7403(00)00046-1
Tirosh J, Neuberger A, Shirizly A (1996) On tube expansion by internal fluid pressure with additional compressive stress. Int J Mech Sci 38:839–851. doi:10.1016/0020-7403(95)00113-1
Xia ZC (2001) Failure analysis of tubular hydroforming. J Eng Mater Technol 123:423–429. doi:10.1115/1.1394966
Nefussi G, Combescure A (2002) Coupled buckling and plastic instability for tube hydroforming. Int J Mech Sci 44(5):899–914. doi:10.1016/S0020-7403(02)00031-0
Asnafi N (1999) Analytical modelling of tube hydroforming. Thin-Walled Struct 34:295–330. doi:10.1016/S0263-8231(99)00018-X
Kim J, Kim SW, Song WJ, Kang BS (2004) Analytical approach to bursting in tube hydroforming using diffuse plastic instability. Int J Mech Sci 46(10):1535–1547. doi:10.1016/j.ijmecsci.2004.09.001
Kim J, Kim SW, Song WJ, Kang BS (2005) Analytical approach to bursting in tube hydroforming using diffuse plastic instability. Int J Mech Sci 47(7):1023–1037. doi:10.1016/j.ijmecsci.2005.02.011
Kim SW, Song WJ, Kang BS, Kim J (2008) Bursting failure prediction in tube hydroforming using FLSD. Int J Adv Manuf Technol 41:311–322. doi:10.1007/s00170-008-1488-3
Marciniak Z, Kuczynski K (1967) Limit strains in the process of stretch-forming sheet metal. Int J Mech Sci 9:609–620. doi:10.1016/0020-7403(67)90066-5
Zhao L, Sowerby R, Sklad MP (1996) A theoretical and experimental investigation of limit strain in sheet metal forming. Int J Mech Sci 38(12):1307–1317. doi:10.1016/0020-7403(96)00014-8
Ganjiani M, Assempour A (2007) An improved analytical approach for determination of forming limit diagrams considering the effects of yield functions. J Mater Proc Tech 182(1–3):598–607. doi:10.1016/j.jmatprotec.2006.09.025
Assempour A, Safikhani AR, Hashemi R (2009) An improved strain gradient approach for determination of deformation localization and forming limit diagrams. J Mater Process Technol 209(4):1758–1769. doi:10.1016/j.jmatprotec.2008.04.030
Safikhani AR, Hashemi R, Assempour A (2009) Some numerical aspects of necking solution in prediction of sheet metal forming limits by strain gradient plasticity. J. Mater Des 30(3):727–740
Ahmadi S, Eivani AR, Akbarzadeh A (2008) An experimental and theoretical study on the prediction of forming limit diagrams using new BBC yield criteria and M–K analysis. Comput Mater Sci 4(4):1272–1280. doi:10.1016/j.commatsci.2008.08.013
Ganjiani M, Assempour A (2007) Implementation of a robust algorithm for prediction of forming limit diagrams. J Mater Eng Perform 17(1):1–6. doi:10.1007/s11665-007-9121-4
Asnafi N, Skogsga°rdh A (2000) Theoretical and experimental analysis of stroke-controlled tube Hydroforming. Mater Sci Eng A 279(1, 2):95–110. doi:10.1016/S0921-5093(99)00646-2
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran 77: The art of scientific computing, Chapter 9, 2nd edn. Cambridge University Press, Cambridge
Hill R (1948) A theory of the yielding and plastic flow of anisotropic materials. Proc R Soc Lond A Math Phys Sci 193:281–297. doi:10.1098/rspa.1948.0045
Simha CHM, Gholipour J, Bardelcik A, Worswick MJ (2007) Prediction of necking in tubular hydroforming using an extended stress-based flc. ASME J Eng Mater Technol 129(1):136–147
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Hashemi, R., Faraji, G., Abrinia, K. et al. Application of the hydroforming strain- and stress-limit diagrams to predict necking in metal bellows forming process. Int J Adv Manuf Technol 46, 551–561 (2010). https://doi.org/10.1007/s00170-009-2121-9
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DOI: https://doi.org/10.1007/s00170-009-2121-9