Application of Case I and Case II of Hill’s 1979 Yield Criterion to Predict FLD
محورهای موضوعی : EngineeringM Aghaie-Khafri 1 , M Torabi-Noori 2
1 - Faculty of Mechanical Engineering, K.N. Toosi University of Technology
2 - Faculty of Mechanical Engineering, K.N. Toosi University of Technology
کلید واژه: Localization, Yield function, Forming limit diagrams,
چکیده مقاله :
Forming limit diagrams (FLDs) are calculated based on both the Marciniak and Kuczynski (M-K) model and the analysis proposed by Jones and Gillis (J-G). J-G analysis consisted of plastic deformation approximation by three deformation phases. These phases consisted of homogeneous deformation up to the maximum load (Phase I), deformation localization under constant load (phase II) and local necking with a precipitous drop in load (phase III). In the present study, case I and case II of Hill’s non-quadratic yield function were used for the first time. It is assumed that sheets obey the power-law flow rule and in-plane isotropy is satisfied. Calculated FLDs from this analysis are compared with the experimental data of aluminum alloys 3003-O, 2036-T4 and AK steel reported by other references. Calculated FLDs showed that limit strain predictions based on case I and case II of the Hill’s non-quadratic yield function are fairly well correlated to experiments when J-G model is used.
[1] Keeler S.P., 1969, Circular grid system: a valuable aid for evaluation sheet forming, Sheet Metal Industrial 45: 633-640.
[2] Goodwin G.M., 1969, Application of strain analysis to sheet metal forming problems, Metall Ital 60: 767-771.
[3] Liu J., Liu W., Xue W., 2013, Forming limit diagram prediction of 5052/polyethylene/AA5052 sandwich sheets, Materials and Design 46: 112-120.
[4] Aghaie-Khafri M., Mahmudi R., 2005, The effect of preheating on the formability of an Al–Fe–Si alloy sheet, Journal of Materials Processing Technology 169: 38-43.
[5] Friedman P.A., Pan J., 2000, Effects of plastic anisotropy and yield criteria on prediction of forming limit curves, International Journal of Mechanical Sciences 42: 29-48.
[6] Zhang L., Wang J., 2012, Modeling the localized necking in anisotropic sheet metals, International Journal of Plasticity 39: 103-118.
[7] Velmanirajan K., Syed Abu Thaheer A., Narayanasamy R., Ahamed Basha C., 2012, Numerical modelling of aluminium sheets formability using response surface methodology, Materials and Design 41: 239-254.
[8] Hart E.W., 1967, Theory of the tensile test, Acta Metallurgica 15: 351-355.
[9] Hill R., 1952, On discontinuous plastic states with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 1: 19-30.
[10] Gillis P.P., Jones S.E., 1979, Tensile deformation of a flat sheet, International Journal of Mechanical Sciences 21: 109-117.
[11] Marciniak Z., Kuczynski K., 1967, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences 9: 609-620.
[12] Mohebbi M.S., Akbarzadeh A., 2012, Prediction of formability of tailor welded blanks by modification of MK model, International Journal of Mechanical Sciences 61: 44-51.
[13] Jones S.E., Gillis P.P., 1984, An analysis of biaxial stretching of a flat sheet, Metallurgical Transactions A 15: 133-138.
[14] Choi W., Gillis P.P., Jones S.E ., 1989, Calculation of the forming limit diagram, Metallurgical Transactions A 20:1975-1987.
[15] Choi W., Gillis P.P., Jones S.E., 1989, Forming Limit Diagrams: Concepts, Methods and Applications, edited by Wagoner R.H., Chan K.S., Keeler S.P., Published, TMS Warendale.
[16] Jones S.E., Gillis P.P., 1984, Analysis of biaxial stretching of a flat sheet, Metallurgical Transactions A 15: 133-138.
[17] Jones S.E., Gillis P.P., 1984, Generalized quadratic flow law for sheet metals, Metallurgical Transactions A 15: 129-132.
[18] Pishbin H., Gillis P.P., 1992, Forming limit diagrams calculated using Hill’s nonquadratic yield criterion, Metallurgical Transactions A 23: 2817-2831.
[19] Aghaie-Khafri M., Mahmudi R., 2004, Predicting of plastic instability and forming limit diagrams, International Journal of Mechanical Sciences 46: 1289-1306.
[20] Aghaie-Khafri M., Mahmudi R., Pishbin H., 2002, Role of yield criteria and hardening laws in the prediction of forming limit diagrams, Metallurgical Transactions A 33: 1363-1371.
[21] Noori H., Mahmudi R., 2007, Prediction of forming limit diagrams in sheet metals using different yield criteria, Metallurgical Transactions A 38: 2040-2052.
[22] Rezaee-Bazzaz A., Noori H., Mahmudi R., 2011, Calculation of forming limit diagrams using Hill’s 1993 yield criterion, International Journal of Mechanical Sciences 53: 262-270.
[23] Chung K., Kim H., Lee C., 2014, Forming limit criterion for ductile anisotropic sheets as a material property and its deformation path insensitivity. Part I: Deformation path insensitive formula based on theoretical models, International Journal of Plasticity 58: 3-34.
[24] Avila A.F., Vieira E.L.S., 2003, Proposing a better forming limit diagram prediction: a comparative study, Journal of Materials Processing Technology 141: 101-108.
[25] Chiba R., Takeuchi H., Kuroda M., Kuwabara T., 2013, Theoretical and experimental study of forming-limit strain of half-hard AA1100 aluminium alloy, Computational Materials Science 77: 61-71.
[26] Panich S., Barlat F., Uthaisangsuk V., Suranuntchai S., Jirathearanat S., 2013, Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels, Materials & Design 51 : 756-766.
[27] 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, Computational Materials Science 45: 195-204.
[28] Kuroda M., Tvergaard V., 2000, Forming limit diagrams for anisotropic metal sheets with different yield criteria, International Journal of Solids and Structures 37: 5037-5059.
[29] Hill R., 1979, Theoretical plasticity of textured aggregates, Mathematical Proceedings of the Cambridge Philosophical Society 75: 179-191.
[30] Lian J., Zhou D., Baudelet B., 1989, Application of Hill’s new yield theory to sheet metal forming part I. Hill’s 1979 criterion and its application to predicting sheet forming limit, International Journal of Mechanical Sciences 31: 237-247.
[31] Considére A., 1885, Annales des Ponts et Chaussées 9: 574-775.
[32] Bridgeman P.W., 1952, Studies in Large Plastic Flow and Fracture, McGraw-Hill, New York.
[33] Ghosh A.K., 1977, The Influence of Strain Hardening and Strain-Rate Sensitivity on Sheet Metal Forming, Trans ASME: Journal of Engineering Materials and Technology 99: 264-274.
[34] Hecker S.S., 1975, Formability of aluminum alloy sheets, Trans ASME: Journal of Engineering Materials and Technology 97: 66-73.
[35] Hill R., 1993, A user-friendly theory of orthotropic plasticity in sheet metals, International Journal of Mechanical Sciences 35:19-25.
