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Stress-based forming limit diagrams (SFLD) considering strain rate effect and ductile damage phenomenon

Farid Hosseini Mansoub, Ali Basti, Abolfazl Darvizeh and Asghar Zajkani

Abstract

Although drawing forming limit diagrams is a suitable tool for analyzing material formability, it can only be used when loading is proportional. In other words, when the ratio between main strains stays unaffected during the formation process. Since forming limit diagrams are strictly dependent on strain path, the significance of the limit increases. As the path of the strain changes in a formation process, the forming limit diagrams and therefore the designer's decision changes as well. In order to eliminate this issue, stress-based forming limit diagrams (SFLD) which are independent from the strain path are gaining attention. This paper gives an efficient method to determine the SFLDs and can accurately predict the location for the onset of failure, including strain rate calculations. Furthermore, introducing a damage function based on a simple continuum damage mechanics is dependent on the stress state (Triaxiality and Lode parameters). As a characterization parameter, elastic modulus is eventually chosen to measure the ductile damage in the process of plastic deformation of the material. Furthermore, a UMAT subroutine is developed in finite element simulation by ABAQUS according to original formulations, in order to analyze and link the related essential models. To examine the accuracy of the results from the present simulative study and compare with the experimental results, applicability is considered. Forming limit tests are also performed for St 13 sheets measuring the FLD and then transforming to SFLD. It should be noted that the rule of these simulative SFLDs is in good agreement with the experimental points. Results revealed that the level of the stress-based forming limit diagram for the material St 13 increases with enhancing the strain rate.


Correspondence address, Dr. Ali Basti, Department of Mechanical Engineering, University of Guilan, Rasht, Iran. Tel: +98 9112362309, E-mail:

References

[1] H. Takuda , K.Mori, N.Hatta: J. of Mater. Processing Technol.95 (1999) 116121. 10.1016/S0924-0136(99)00275-7 Search in Google Scholar

[2] X. Ma , F.Li, J.Li, Q.Wang, Z.Yuan, Y.Fang: J. materials and design.68 (2015) 134145. 10.1016/j.matdes.2014.12.029 Search in Google Scholar

[3] L. Xue : PhD thesis, Ductile Fracture Modeling-Theory, Experimental Investigation and Numerical Verification, Massachusetts Institute of Technology, Dept. of Mechanical Engineering, USA (2007). Search in Google Scholar

[4] Y. Bai , T.Wierzbicki: Int. J. Plast.24 (2008) 10711096. 10.1016/j.ijplas.2007.09.004 Search in Google Scholar

[5] C.H.M. Simha , S.Xu, W.R.Tyson: J. Eng. Fract. Mech.118 (2014) 6682. 10.1016/j.engfracmech.2014.01.009 Search in Google Scholar

[6] R. Sowerby , J.L.Duncan: Int. J. Mech. Sci.13 (1971) 217229. 10.1016/0020-7403(71)90004-X Search in Google Scholar

[7] H.B. Campos , M.C.Butuc, J.J.Grácio, J.E.Rocha, J.M.F.Duarte: J. Mater. Process. Technol.179 (2006) 5660. 10.1016/j.jmatprotec.2006.03.065 Search in Google Scholar

[8] J. Huh , H.Huh, C.S.Lee: Int. J. Plast.44 (2013) 2346. 10.1016/j.ijplas.2012.11.012 Search in Google Scholar

[9] Johnson, G.R., Cook, W.H.: 7th International Symposium on Ballistic. The Hague, Netherlands, (1983) 54154. Search in Google Scholar

[10] A.H. Clausen , T.B⊘rvik, O.S.Hopperstad, A.Benallal: J. Mater. Sci. Eng.A 364 (2004) 260272. 10.1016/j.msea.2003.08.027 Search in Google Scholar

[11] B. Erice , F.Gálvez, D.A.Cendón, V.Sánchez-Gálvez: J. Eng. Fract. Mech.79 (2012) 117. 10.1016/j.engfracmech.2011.08.023 Search in Google Scholar

[12] J.H. Kim , J.H.Sung, K.Piao, R.H.Wagoner: Int. J. Plast.27 (2011) 16581676. 10.1016/j.ijplas.2011.02.009 Search in Google Scholar

[13] Y. Lou , J.W.Yoon, H.Huh: Int. J. Plast.54 (2014) 5680. 10.1016/j.ijplas.2013.08.006 Search in Google Scholar

[14] X. Sun , K.S.Choi, W.N.Liu, M.A.Khaleel: Int. J. Plast.25 (2009) 18881909. 10.1016/j.ijplas.2008.12.012 Search in Google Scholar

[15] G. Gruben , E.Fagerholt, O.S.Hopperstad, T.B⊘rvik: Eur. J. Mech. A/solids.30 (2011) 204218. 10.1016/j.euromechsol.2011.01.004 Search in Google Scholar

[16] K. Chung , N.Ma, T.Park, D.Kim, D.Yoo, C.Kim: Int. J. Plast.27 (2011) 14851511. 10.1016/j.ijplas.2011.01.007 Search in Google Scholar

[17] S. Curtze , V.-T.Kuokkala, M.Hokka, P.Peura: Mater. Sci. Eng.A 507 (2009) 124131. 10.1016/j.msea.2008.11.050 Search in Google Scholar

[18] A. Zajkani , A.Bandizaki: Int. J. Mech. Sci.133 (2017) 794803. 10.1016/j.ijmecsci.2017.09.054 Search in Google Scholar

[19] C.C. Roth , D.Mohr: Int. J. Plast.56 (2014) 1944. 10.1016/j.ijplas.2014.01.003 Search in Google Scholar

[20] A. Zajkani , A.Bandizaki: Int. J. Adv. Manuf. Technol.95 (2018) 14. 10.1007/s00170-017-1230-0 Search in Google Scholar

[21] H.J. Kleemola , M.T.Pelkkikangas: Effect of pre-deformation and strain path on the forming limits of steel copper and brass, Sheet Met. Ind, London, UK (1977). Search in Google Scholar

[22] R. Arrioux , C.Bedrin, M.Boivin: J. CIRP Annals.36 (1987) 195198. 10.1016/S0007-8506(07)62584-0 Search in Google Scholar

[23] T.B. Stoughton : Int. J. Mech. Sci.42 (2000) 127. 10.1016/S0020-7403(98)00113-1 Search in Google Scholar

[24] M. Jie , C.H.Cheng, L.C.Chan, C.L.Chow: Int. J. Mech. Sci.51 (2009) 269275. 10.1016/j.ijmecsci.2009.01.007 Search in Google Scholar

[25] F. Hosseini Mansoub , A.Basti, A.Darvizeh, A.Zajkani: Int. J. Adv. Manuf. Technol.104 (2019) 867879. 10.1007/s00170-019-03951-4 Search in Google Scholar

Received: 2018-11-10
Accepted: 2019-08-13
Published Online: 2020-01-31
Published in Print: 2020-02-12

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