This paper deals with the springback analysis in sheet metal forming using modified Ludwik stress-strain relation. Using the deformation theory of plasticity, formulation of the problem and spring back ratio is derived using modified Ludwik stress strain relationship with Tresca and von Mises yielding criteraia. The results have been representing the effect of different value of or ratio, different values of Strain hardening index ( ), Poisson’s ratio ( ), and thickness on spring back ratio ( ). The main aim of this paper is to study the effects of the thickness, ratio, and Poisson’s ratio in spring back ratio. 1. Introduction In sheet metal working, sheets are deformed to cylindrical and helical shapes by plastic bending with the help of a punch and die set. When such bending is properly done, the inside contour of the section matches the surface contour of the die during the forming operation. However, after the release of the applied loads, the contour assumes a different shape than that of the die because of the release of elastic stresses in the metal. This elastic distortion is commonly called springback. Springback complicates tool design in that the die must be designed to compensate for it. Consequently, it is desirable to have a method of quantitatively predicting the magnitude of springback as a function of the properties of the material and geometry involved in the forming operation. In bending, the springback is a measure of elastic recovery of radius on removal of the applied bending moment or load after the bending section is beyond elastic limit. While designing the die set, the springback factor should be taken into account to avoid mismatch while assembling formed different sections. Initially, springback studies are with sheet bending operations. Sachs [1], Schroeder [2], Gardiner [3], Singh and Johnson [4], and others studied the springback considered bending of sheets of different shapes and depicted springback as a function of material thickness, length, and width of the sheets taken. Their studies were limited to V- and U-shaped dies for applying bending loads and they predicted the springback as a measure of change in the curvature distribution. Huth [5], Nadai [6], and Upadhyay [7] have all done a number of excellent work on the elasto-plastic torsion of bars with rectangular sections, but their work has been limited to monotonically increasing loads only. Dwivedi et al. [8, 9] analytically predicted the residual angle of twist and torque relation, and so forth, for bars of elastic strain-hardening materials with narrow
References
[1]
G. Sachs, Principles and Methods of Sheet Metal Fabricating, Reinhold, New York, NY, USA, 1951.
[2]
W. Schroeder, “Mechanics of sheet metal bending,” Transactions of the ASME, vol. 36, pp. 138–145, 1943.
[3]
F. J. Gardiner, “The springback of metals,” Transactions of the ASEME, vol. 49, pp. 1–9, 1958.
[4]
A. N. Singh and W. Johnson, “Springback after cylindrically bending metal strips,” in Proceedings of the Dr Karunesh Memorial International Conference, New Delhi, India, December 1979.
[5]
J. H. Huth, “A note on plastic torsion,” Journal of Applied Mechanics, vol. 22, pp. 432–434, 1955.
[6]
A. Nadai, Theory of Flow and Fracture of Solids, vol. 1, McGraw-Hill, 1950.
[7]
P. C. Upadhyay, Elasto-plastic torsion [M.Tech. thesis], Mechanical Engineering Department, I.I.T. Kanpur, 1970.
[8]
J. P. Dwivedi, A. N. Singh, S. Ram, and N. K. Das Talukder, “Springback analysis in torsion of rectangular strips,” International Journal of Mechanical Sciences, vol. 28, no. 8, pp. 505–515, 1986.
[9]
J. P. Dwivedi, P. K. Sarkar, R. S. Ram. S., N. K. D. Talukder, and A. N. Singh, “Experimental aspects of torsional springback in rectangular strips,” Journal of the Institution of Engineers, vol. 67, no. 4, pp. 70–73, 1987.
[10]
J. P. Dwivedi, A. K. Shukla, and P. C. Upadhyay, “Torsional springback of square section bars of linear wor hardening materials,” Computers and Structures, vol. 45, no. 3, pp. 421–429, 1972.
[11]
J. P. Dwivedi, P. C. Upadhyay, and N. K. Das Talukder, “Torsional springback in square section bars of nonlinear work-hardening materials,” International Journal of Mechanical Sciences, vol. 32, no. 10, pp. 863–876, 1990.
[12]
J. P. Dwivedi, P. C. Upadhyay, and N. K. D. Talukder, “Springback analysis of torsion of L-sectioned bars of work-hardening materials,” Computers and Structures, vol. 43, no. 5, pp. 815–822, 1992.
[13]
Z. T. Zhang and S. J. Hu, “Stress and residual stress distributions in plane strain bending,” International Journal of Mechanical Sciences, vol. 40, no. 6, pp. 533–543, 1998.
[14]
T. Kuwabara, “Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations,” International Journal of Plasticity, vol. 23, no. 3, pp. 385–419, 2007.
[15]
H. K. Yi, D. W. Kim, C. J. van Tyne, and Y. H. Moon, “Analytical prediction of springback based on residual differential strain during sheet metal bending,” Journal of Mechanical Engineering Science, vol. 222, no. 2, pp. 117–129, 2008.
[16]
A. El Megharbel, G. A. El Nasser, and A. El Domiaty, “Bending of tube and section made of strain-hardening materials,” Journal of Materials Processing Technology, vol. 203, no. 1–3, pp. 372–380, 2008.
[17]
E. Da-xin, H. Hau-hui, L. Xiao-yi, and N. Ru-xin, “Spring-back deformation in tube bending,” International Journal of Minerals, Metallurgy and Materials, vol. 16, no. 2, pp. 177–183, 2009.
[18]
D. E. Daxin E and Y. Liu, “Springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes under bending,” Materials and Design, vol. 31, no. 3, pp. 1256–1261, 2010.
[19]
V. K. Choubey, M. Gangwar, and J. P. Dwivedi, “Torsional springback analysis in thin tubes with non-linear work hardening,” Journal of Mechanical Engineering, vol. 7, no. 1, pp. 15–34, 2011.
[20]
V. K. Choubey, M. Gangwar, and J. P. Dwivedi, “Springback analysis of thin tubes,” Journal of Mechanical Engineering, vol. 7, no. 2, 2011.
[21]
V. K. Choubey, M. Gangwar, J. P. Dwivedi, and N. K. das Talukder, “Springback analysis of thin tubes with arbitrary stress-strain curves,” Journal of Mechanical Engineering, vol. 8, no. 1, 2011.
