Springback Analysis of Thin Tubes with Arbitrary Stress-Strain Curves

Springback Analysis of Thin Tubes with Arbitrary Stress-Strain Curves

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Mayank Gangwar*
Department of Mechanical Engineering
Motilal Nehru National Institute of Technology
Allahabad-211004, India
Vikas Kumar Choubey
Institute of Engineering & Rural Technology
(Engineering Degree Division)
Allahabad-211002, India
J. P. Dwivedi
Department of Mechanical Engineering
Institute of Technology
Banaras Hindu University
Varanasi-221005, India
N. K. Das Talukder
Institute of Technology
Banaras Hindu University
Varanasi-221005, India
*Corresponding Author / Email: This email address is being protected from spambots. You need JavaScript enabled to view it.

ABSTRACT
A general theoretical method for determining springback of arbitrary shaped thin tubular section of materials having arbitrary stress-strain relationship under torsional loading is presented. The theoretical analysis has been compared with earlier analysis of tubular sections of particular materials and has been shown that the expressions obtained in the, work presented. The theoretical results also have been found to quit in agreement with the results obtained experimentally. It has been shown that when applied torque is kinetic loading or angle of twist given is kinetic loading, springback angle and residual angle of twist can directly be calculated from the shear stress-strain curve, avoiding any idealization/approximation for the same.

 

Keywords: Metal forming, Springback, Torsional springback, Thin tubes, Arbitrary stress-strain curves

 

References
[1] Wang, C. (2002). “An industrial outlook for springback predictability, measurement reliability and compensation technology”, Proceedings of the 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, NUMISHEET 2002). 597-604, Jeju Island, Korea, 2002.
[2] Gardiner, F. (1957). “The springback of metals”, Transactions of the ASME, 79, 1-9.
[3] Queener, C. and De Angelis, R. J. (1968). “Elastic springback and residual stresses in sheet metal formed by bending”, Transactions of the ASME,61, 757-768.
[4] Johnson, W. and Singh, A. N. (1980). “Springback in circular blanks”,Metallurgia, 47, 275-280.
[5] El-Domiaty, A. and Shabaik, A. (1984). “Bending of working-hardening metals under the influence of axial load”, Journal of Mechanical Working Technology, 10, 57-66.
[6] Chu, C. (1986). “Elastic-plastic springback of sheet metals subjected to complex plane strain bending histories”, International Journal of Solids Structures, 22(10), 1071-1081.
[7] El-Megharbel, A., El-Domiaty, A. and Shaker, M. (1990). “Springback and residual stresses after stretch bending of working sheet metal”, Journal of Materials Processing Technology, 24, 191-200.
[8] Chu, C. (1991). “The effect of restraining force on springback”, International Journal of Solids Structures, 27(8), 1035-1046.
[9] Schmoeckel, D. and Bath, M. (1993). “Springback reduction in drawbending process of sheet metals”, Annals of CIRP, 42(1), 339-342
[10] Tan, Z., Li, W. and Persson, B. (1994). “On analysis and measurement of residual stress in the bending of sheet metals”, International Journal of Mechanical Sciences, 36(5), 483-491.
[11] Morestin, F., Boivin, M. and Silva, C. (1996). “Elasto plastic formulation using a kinematic hardening model for springback analysis in sheet metal forming”, Journal of Materials Processing Technology, Vol. 56, 619-630.
[12] Zhang, Z. and Hu, S. (1998). “Stress and residual stress distributions in plane strain bending”, International Journal of Mechanical Sciences, Vol.40(6), 543-553.
[13] Asnafi, N. (2000). “Springback and fracture in v-die air bending of thick stainless steel sheets”, Materials and Design, 21, 217-36.
[14] Kuwabara, T. (2007). “Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations”, International Journal of Plasticity, 23, 385-419.
[15] Yi, H. K., Kim, D. W., Van Tyne, C. J. and Moon, Y. H. (2008). “Analytical prediction of springback based on residual differential strain during sheet metal bending”, Proc. IMechE, Vol. 222 (part 2). Part C, J. Mechanical Engineering Science pages, 117-129.
[16] Bakhshi-Jooybari, M., Rahmani, B., Daeezadeh, V. and Gorji, A. (2009). “The study of spring-back of CK67 steel sheet in V-die and U-die bending processes”, Materials and Design, 30, 410-419.
[17] Wang, C., Kinzel, G. and Altan, T. (1993). “Process simulation and springback control in plane-strain sheet bending”, Sheet Metal and Stamping Symposium, SAE Special Publications, 944, 45-54.
[18] Hsu, T. C. and Shien, I. R. (1997). “Finite element modeling of sheet forming process with bending effects”, Journal of Materials Processing Technology, 63, 733-737.
[19] Kutt, L. M., Nardiello, J. A., Ogilvie, P. L., Pifko, A. B. and Papazian, J. M. (1999). “Nonlinear finite element analysis of springback”,Communications in Numerical Methods in Engineering, 15(1), 33-42.
[20] Tekkaya, A. E. (2000). “State-of-the-art of simulation of sheet metal forming”, Journal of Materials Processing Technology, 103(1), 4-22. 
[21] Esat, V., Darendeliler, H. and Gokler, M. I. (2002). “Finite element analysis of springback in bending of aluminium sheets”, Materials & Design, 23, 223-229.
[22] Li, K. P., Carden, W. P. and Wagoner, R. H. (2002). “Simulation of springback”, International Journal of Mechanical Sciences, 44(1), 103-122.
[23] Ling, Y. E., Lee, H. P. and Cheok, B. T. (2005). “Finite element analysis of springback in L-bending of sheet metal”, Journal of Materials Processing Technology, 168, 296-302.
[24] Liu, W., Liu, Q., Ruan, F., Liang, Z. and Qiu, H. (2007). “Springback prediction for sheet metal forming based on GA–ANN technology”, Journal of Materials Processing Technology, 187-188, 227-231.
[25] Al-Qureshi, H. A. (1999). “Elastic-plastic analysis of tube bending”, International Journal of Machine Tools and Manufacturing”, 39, 87-104.
[26] Yang, H. and Lin, Y. (2004). “Wrinkling analysis for forming limit of tube bending processes”, Journal of Materials Processing Technology, 152, 363-369.
[27] Megharbel, A., Nasser, G. A. and Domiaty, A. (2008). “Bending of tube and section made of strain-hardening materials”, Journal of Materials Processing Technology, 203, 372-80.
[28] Da-xin, E., Hua-hui, H., Xiao-yi, L. and Ru-xin, N. (2009). “Experimental study and finite element analysis of spring-back deformation in tube bending”. International Journal of Minerals, Metallurgy and Materials, 16(2) 177-183.
[29] Daxin, E. and Liu, Y. (2009). “Springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes under bending”, Materials & Design (Accepted). (oi:10.1016/j.matdes.2009.09.026).
[30] Dwivedi, J. P., Singh, A. N., Sohan, R. and Talukder, N. K. D. (1986). “Springback analysis in torsion of rectangular strips”, International Journal of Mechanical Sciences, 28(8), 505-515.
[31] Dwivedi, J. P., Sarkar, P. K., Sohan, R. and Talukder, N. K. D. (1987). “Experimental aspects of torsional springback in rectangular strips”, Journal of the Institution of Engineers (India). Vol. 67 (Part ME-4). 70-83.
[32] Dwivedi, J. P., Upadhyay, P. C. and Talukder, N. K. D. (1990). “Torsional springback in square section bars of non-linear work-hardening materials”, International Journal of Mechanical Sciences, 32(10), 863-876.
[33] Dwivedi, J. P., Upadhyay, P. C. and Talukder, N. K. D. (1992). “Springback analysis of torsion of L-sectioned bars of work-hardening materials”, Computer & Structures, 43(5), 815-822.
[34] Dwivedi, J. P., Upadhyay, P. C. and Talukder, N. K. D. (1992). “Parametric assessment of torsional springback in members of work-hardening materials”, Computers & Structures, 45(3), 421-429.
[35] Dwivedi, J. P., Shah, S. K., Upadhyay, P. C. and Talukder, N. K. D.(2002). “Springback analysis of thin rectangular bars of non-linear workhardening materials”, International Journal of Mechanical Sciences, 44,1505-1519.
[36] Choubey, V., Gangwar, M. and Dwivedi, J. P., “Springback analysis in torsion of thin tubes”, Journal of Mechanical Engineering, JMechE, UiTM (Comunicated).
[37] Chakrabarty, J. (2006). “Theory of plasticity”, 3rd Edition, Elsevier Butterworth-Heinemann, MA, USA.
[38] Timoshenko, S. and Goodier, J. N. (1987). “Theory of Elasticity”, 3rd Edition, McGraw-Hill, NY, USA.
[39] Johnson, W. and MelIor, P. B. (1962). “Plasticity for Mechanical Engineers”, D. Van Nostrand, London, UK.
[40] Talukder, N. K. D. and Chakraborti, R. K. (1965). “Torsion of bars under plastic deformations”. Journal of the Institution of Engineers (India). Part ME-2, XLV (3), 67-71.