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

This paper presents an innovative approach for analysing plane strain rolling. The approach is based on a solution resulting from the combination of the upper-bound method with the weighted residuals method. The upper bound method is applied to estimate the rolling torque and to model the material ßow within the region of deformation between the rolls. The weighted residuals method is utilized for obtaining the distribution of stress, the roll separating force and the normal contact pressure along the surface of the rolls. Coupling between the two methods is made by using the upper bound distribution of the strain-rate in conjunction with the rate form of the LevyÐMises constitutive equations to determine an approximate distribution of the stress Þeld 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 deforming workpiece and on its surface. Such an analysis ensures a complete description of all the variables with interest to the rolling process. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature. Copyright