Navi: Journal Volume 7 Volume 7 No 1 Torsional Springback Analysis in Thin Tubes with Non-linear Work Hardening

Torsional Springback Analysis in Thin Tubes with Non-linear Work Hardening

E-mail Print PDF

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.