Upper bound analysis of plane strain rolling using a flow function and theweighted residuals method

This paper presents an innovative approach for analysing plane strain rolli ng. The approach is based on a solution resulting from the combination of t he upper-bound method with the weighted residuals method. The upper bound m ethod is applied to estimate the rolling torque and to model the material f low within the region of deformation between the rolls. The weighted residu als method is utilized for obtaining the distribution of stress, the roll s eparating force and the normal contact pressure along the surface of the ro lls. Coupling between the two methods is made by using the upper bound dist ribution of the strain-rate in conjunction with the rate form of the Levy-M ises constitutive equations to determine an approximate distribution of the stress field by means of the weighted residuals method. The main advantage of this approach over classical upper bound solutions, is the possibility of solving stress equilibrium everywhere throughout the plastically deformi ng workpiece and on its surface. Such an analysis ensures a complete descri ption of all the variables with interest to the rolling process. The validi ty of the proposed approach is discussed by comparing the theoretical predi ctions with experimental data found in the literature. Copyright (C) 1999 J ohn Wiley & Sons, Ltd.