%0 Journal Article
%T Springback Analysis in Sheet Metal Forming Using Modified Ludwik Stress-Strain Relation
%A Sanjay Kumar Patel
%A Radha Krishna Lal
%A J. P. Dwivedi
%A V. P. Singh
%J ISRN Mechanical Engineering
%D 2013
%R 10.1155/2013/640958
%X 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
%U http://www.hindawi.com/journals/isrn.mechanical.engineering/2013/640958/