A reliability study of springback on the sheet metal forming process under probabilistic variation of prestrain and blank holder force
Tóm tắt
This work deals with a reliability assessment of springback problem during the sheet metal forming process. The effects of operative parameters and material properties, blank holder force and plastic prestrain, on springback are investigated. A generic reliability approach was developed to control springback. Subsequently, the Monte Carlo simulation technique in conjunction with the Latin hypercube sampling method was adopted to study the probabilistic springback. Finite element method based on implicit/explicit algorithms was used to model the springback problem. The proposed constitutive law for sheet metal takes into account the adaptation of plastic parameters of the hardening law for each prestrain level considered. Rackwitz-Fiessler algorithm is used to find reliability properties from response surfaces of chosen springback geometrical parameters. The obtained results were analyzed using a multi-state limit reliability functions based on geometry compensations.
Tài liệu tham khảo
Lemaire, M.: Fiabilité des Structures, Couplage Méano-fiabiliste Statique. Hermès Science Publishing LTD (2005) (in French)
Ghanem, R., Spanos, P.D.: Stochastic Finite Elements: A Spectral Approach. Springer-Verlag New York Inc. New York (1991)
Ben Elechi, S., Naceur, H., Batoz, J.L.: Simulation de l’emboutissage par approche inverse améiorée pour l’estimation du retour éastique. Revue Européenne des Éléments Finis. 14, 957–984 (2005) (in French)
Gati, W.: Approche pseudo inverse pour simulations rapides du procédé d’emboutissage et de retour élastique des pièces en tóles minces. [Ph.D. Thesis], UTC, France (2002) (in French)
Souza, T., Rolfe, B.F.: Characterising material and process variation effects on springback robustness for a semicylindrical sheet metal forming process. Int. J. Mech. Sci. 52, 1756–1766 (2010)
Liu, W., Yang, Y., Xing, Z., et al.: Springback control of sheet metal forming based on the response-surface method and multiobjective genetic algorithm. Mater. Sci. Eng. A 499, 325–328 (2009)
Liu, G., Lin, Z., Xu, W., et al.: Variable blankholder force in ushaped part forming for eliminating springback error. J. Mater. Process. Technol. 120, 259–264 (2002)
Jiang, C., Hana, X., Liu, G.R., et al.: The optimization of the variable binder force in U-shaped forming with uncertain friction coefficient. J. Mater. Process. Technol. 182, 262–267 (2007)
Verma, R.K., Chung, K., Kuwabara, T.: Effect of pre-strain on anisotropic hardening and springback behavior of an ultra low carbon automotive steel. I.S.I.J. International 51, 482–490 (2011)
Makinouchi, A., Nakamachi, E., Onate Wagoner, R.H.: Numerical simulation of 3D sheet forming processes. Verification of simulation with experiment. In: Proceedings of 2nd International Numisheet’93, Isehara Japan (1993)
Mohamed, M.I.A., Terence, G.L.: The influence of prestrain on ductility in the superplastic Pb-Sn eutectic alloy. J. Mater. Sci. 18, 3535–3542 (1983)
Enami, K.: The effects of compressive and tensile prestrain on ductile fracture initiation in steels. Eng. Fract. Mech. 72, 1089–1105 (2005)
Tang, B., Zhao, G., Wang, Z.: A mixed hardening rule coupled with Hill48’ yielding function to predict the springback of sheet U-bending. Int. J. Mater. Form. 1, 169–175 (2008)
Geng, L., Wagoner, R.H.: Springback analysis with a modified hardening model. S.A.E. Tech. Pap. Ser. No. 2000-01-0768 (2000)
Aryanpour, G., Farzaneh, M.: Analysis of axial strain in onedimensional loading by different models. Acta Mech. Sin. 26, 745–753 (2010)
Aryanpour, G., Farzaneh, M., Mrad, H.: Finite element analysis of elastoplastic modeling: Application to one-dimensional loading of as-received and pre-strained materials. Acta Mech. 223, 911–922 (2012)
Jansson, T., Nilssona, L., Moshfegh, R.: Reliability analysis of a sheet metal forming process using Monte Carlo analysis and metamodels. J. Mater. Process. Technol. 202, 255–268 (2008)
Janssen, H.: Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence. J. Reliab. Eng. Syst. Safety. 109, 123–132 (2013)
Meinders, T., Konter, A.W.A., Meijers, S.E., et al.: A sensitivity analysis on the springback behaviour of the unconstrained bending problem. Int. J. Form. Process. 9, 365–402 (2006)
Mrad, H., Rachik, M., Marceau, D.: The probabilistic numerical investigation of the frictional contact problem. In: Proc. of 4th International Conference on Advances in Mechanical Engineering and Mechanics, Boussaa Publishing Co. Sousse, Tunisia (2008)
Bjerager, R.: Methods for structural reliability computation, In: Casciati F, ed. Reliability Problems: General Principles and Applications in Mechanics of Solid and Structures. Springer Verlag, New York, 89–136 (1991)