Torsional Springback Analysis in Thin Tubes with Non-linear Work Hardening
Vikas Kumar Choubey, Institute of Engineering & Rural Technology, Engineering Degree Division), Allahabad - 211002, India
Mayank Gangwar, Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad - 211004, India. (*Corresponding Author),
J. P. Dwivedi, Department of Mechanical Engineering, Institute of Technology, Banaras Hindu University, Varanasi - 221005, India
Abstract:
A theoretical analysis of the springback of thin tubular sections of non linear work-hardening materials under torsional loading has been carried out. The non-linear behavior of the material is approximated by using Modified Ludwik type stress-strain relation. The theoretical analysis is supported by experimental results for different tubular section viz. square, triangular and rectangular sections of different thicknesses. Finally analytical generalized expressions relating angle of twist to twisting moment and residual/ springback angle of twist per unit length for thin tubular bars under plastic torsion are obtained in non-dimensionalized form. A comparison between the results obtained for thin tubes on non-linear and linear work-hardening material loaded under torsion is also made.
Keyword: Metal forming, Springback, Torsional springback, Thin tubes, Non- linear work hardening materials
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,
Vol. 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,
Vol. 61, 757-768.
[4] Johnson, W. and Singh, A. N. (1980). Springback in circular blanks ,
Metallurgia, Vol. 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, Vol. 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, vol. 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, Vol. 24, 191-200.
[8] Chu, C. (1991). The effect of restraining force on springback , International
Journal of Solids Structures, Vol. 27 (8), 1035-1046.
[9] Schmoeckel, D. and Bath, M. (1993). Springback reduction in draw-bending
process of sheet metals , Annals of CIRP, Vol. 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, Vol. 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.
29 Journal of Mechanical Engineering
[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, Vol. 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, Vol. 23, 385-419.
[15] Yi, H. K., Kim , D. W., Va n 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, Vol. 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, Vol. 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,
Vol. 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, Vol. 15(1), 33-42.
[20] Tekkaya, A. E. (2000). State-of-the-art of simulation of sheet metal forming ,
Journal of Materials Processing Technology, Vol. 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, Vol.
23, 223-229.
[22] Li, K . P., Carden, W. P. and Wagoner, R. H. (2002). Simulation of
springback , International Journal of Mechanical Sciences, Vol. 44 (1),
103-122.30 Torsional Springback Analysis
[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, Vol. 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, Vol. 187-188, 227-231.
[25] Al-Q ureshi, H. A. ( 1999). Elastic plastic analysis of tube bending ,
International Journal of Machine Tools and Manufacturing , Vol. 39, 87-104.
[26] Yang, H. and Lin, Y. (2004). Wrinkling analysis for forming limit of tube
bending processes , Journal of Materials Processing Technology, Vol. 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, Vol. 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, Vol. 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), (doi: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, Vol. 28 (8), 505-515.
[31] Dw ivedi, 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, Vol. 32 (10),
863-876.31 Journal of Mechanical Engineering
[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, Vol. 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, Vol. 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 work-hardening
materials , International Journal of Mechanical Sciences, Vol. 44, 1505- 519.
[36] Chakrabarty, J. (2006). Theory of plasticity , 3 Edition, Elsevier rd Butterworth-Heinemann, MA, USA.
[37] Timoshenko, S. and Goodier, J. N. (1987). Theory of Elasticity , 3
Edition, r d McGraw-Hill, NY, USA.
[38] Johnson, W. and MelIor, P. B. (1962). Plasticity for Mechanical Engineers ,D. Van Nostrand, London, UK.
[39] 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.
[40] Nadai, A. (1950). Theory of Flow and Fracture of Solids , 2Edition, Vol. n d 1, McGraw-Hill, NY, USA.




