Theoretical Determination of Forming Limit Stress Diagram for Steel 1021 Sheet
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Abstract
Forming limit stress diagram represent the maximum acceptable limits of principal stresses in sheet metal forming. This diagram show the limits of major and minor true stresses for different strain paths (uniaxial tension, plane strain and equibiaxial stretching path) in sheet metal forming. It is confirmed that the Forming limit stress diagram and the Forming Limit Strain Diagram are two mathematically equivalent representations of forming limits in stress space and strain space respectively. The Forming limit stress diagram of the sheet metal is gained by the transformation relations between the strain state and stress state in deformation of sheet metal. In this paper, the Forming limit stress diagram is theoretically determined using Marciniak-Kuczynski analysis and Hosford yield criterion for steel 1021 sheet ,and compared with the experimental Forming limit stress diagram based on the experimental Forming limit strain diagram of steel 1021 sheet & theory of plasticity. The influence of normal anisotropic ratio, index of yield criterion, inhomogeneous factor and strength coefficient on the theoretical FLSD is also presented. It is shown that the limit stresses in theoretical Forming limit stress diagram is raised by increased values of the normal anisotropic ratio, the inhomogeneous factor and the strength coefficient. The limit stresses are lowered when the index of Hosford yield criterion increased.
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References
Marciniak, Z., Duncan, J.L., “Mechanics of Sheet Metal Forming”, 2nd edition, Butter worth-Heinemann, (2002).
Arrieux R, Bedrin C, Boivin M., ”Determination of an Intrinsic Forming Limit Stress Diagram for Isotropic Sheets”, In Proceedings of the 12th IDDRG congress, Santa Margherita, Ligure, Vol.2, pp. 61–71, (1982).
Gronostajski, I., “Sheet Metal Forming Limits for Complex Strain Paths”, J. Mech. Work. Tech., Vol.10 (3), pp. 349–362 (1984). DOI: https://doi.org/10.1016/0378-3804(84)90048-2
Arrieux et al, ”Determination of the Forming Limit Stress Curve for Anisotropic Sheets”, Annals of the CIRP, Vol.36, pp.235, (1990). DOI: https://doi.org/10.1016/S0007-8506(07)62584-0
Hill, R., “A Theory of the Yielding and Plastic Flow of Anisotropic Metals” ,Proceedings of the Royal Society of London Series A-Mathematical, Physical and Engineering Science A193, 281–297, (1984). DOI: https://doi.org/10.1098/rspa.1948.0045
Hosford, W.A., “On Yield Loci of Anisotropic Cubic Metals”, In Proceedings of the 7th North American Metalworking Conference, SME, Dearborn, MI, pp. 191–197, (1979).
Arrieux, R., “Determination and Use of the Forming Limit Stress Diagrams in Sheet Metal Forming”, Journal of Materials Processing Technology ,Vol.53, pp. 47–56, (1995). DOI: https://doi.org/10.1016/0924-0136(95)01960-M
Zhao, L.R., Sowerby, R., Sklad, M.P., ”A Theoretical and Experimental Investigation of Limit Strains in Sheet Metal Forming”, Int. J. Mech. Sci.,Vol.38 (12), pp. 1307–1317, (1996). DOI: https://doi.org/10.1016/0020-7403(96)00014-8
Haddad, A., Arrieux, R., Vacher, P., ”Use of Two Behavior Laws for the Determination of the Forming Limit Stress Diagram of a Thin Steel Sheet: Results and Comparisons”, Journal of Materials Processing Technology ,Vol. 106, pp. 49–53, (2000). DOI: https://doi.org/10.1016/S0924-0136(00)00637-3
Stoughton, T.B., ”A General Forming Limit Criterion for Sheet Metal Forming”, Int. J. Mech. Sci., Vol. 42 (1), pp. 1–27, (2000). DOI: https://doi.org/10.1016/S0020-7403(98)00113-1
Zimniak, Z., ”Application of a System for Sheet Metal Forming Design”, J. Mater. Process, Vol. 106, pp. 159–162, (2000). DOI: https://doi.org/10.1016/S0924-0136(00)00608-7
Stoughton, T.B., Zhu, X., “Review of Theoretical Models of the Strain-based FLD and their Relevance to the Stress-Based FLD”, International Journal of Plasticity, Vol. 20, pp. 1463–1486,(2004). DOI: https://doi.org/10.1016/j.ijplas.2003.11.004
Wu, P.D., Graf, A., Jain, M., MacEwen, S.R., “On Alternative Representation of Forming Limits”, Key Engineering Materials, Vol. 177–180, pp. 517–522, (2000). DOI: https://doi.org/10.4028/www.scientific.net/KEM.177-180.517
Wu, P.D., Graf, A., Jain, M., MacEwen, S.R., ” On Forming Limit Stress Diagram Analysis”, Vol. 42, pp. 2225-2241, (2005). DOI: https://doi.org/10.1016/j.ijsolstr.2004.09.010
Marciniak Z, Kuckzinsky K., “ Limit Strains in the Processes of Stretch Forming Sheet Metal” , International Journal of Mechanical Sciences, Vol.9, pp. 609–620 (1967). DOI: https://doi.org/10.1016/0020-7403(67)90066-5
Butuc MC, Barata da Rocha A, Gracio JJ. “An Experimental and Theoretical Analysis on the Application of Stress-based Forming Limit Criterion”, International Journal of Mechanical Sciences, vol. 48, pp. 414-429, (2006). DOI: https://doi.org/10.1016/j.ijmecsci.2005.11.007
Yoshida, K., Kuwabara, T., Narihara, K., Takahashi, S., “Experimental Verification of the Path-dependence of Forming Limit Stresses”, Int. J. Forming Processes, vol.8 (SI),pp. 283–298,(2005).
Yoshida, K., Kuwabara, T., ”Effect of Strain Hardening Behavior on Forming Limit Stresses of Steel Tube Subjected to non Proportional Loading Paths”, Int. J. Plasticity, vol. 23 (7), pp. 1260–1284, (2007). DOI: https://doi.org/10.1016/j.ijplas.2006.11.008
Graf, A. and Hosford, W.F., “Calculations of Forming Limit Diagrams”, Metall. Trans., vol. 21A, pp. 87-96, (1990). DOI: https://doi.org/10.1007/BF02656427
Grootenboer. H. J., Huetink. H. J, “Thermally Enhanced Forming of Aluminium Sheet Modelling and Experiments”, A. H. Van den Boogaard ,Hengelo, the Nether Lands, pp. 83-87, (2002).