2-DIMENSIONAL LATERAL-MATERIAL-FLOW MODEL REDUCED FROM 3-DIMENSIONAL THEORY FOR FLAT ROLLING

The present generalized 2-D theory aims at the analysis of 3-D deformation relating to shape and crown phenomena and the width broadening in flat rolling. The equation system is derived by de-coupling the lateral and longitudinal equilibrium equations in the rigorous 3-D theory. The longitudinal equilibrium equation is reduced to the plane strain rolling theory and the lateral one to a simple ordinary differential equation. The approximations employed in the derivation of these are well supported by the 3-D analysis. The resulting model not only agrees with a variety of experiments, but also helps us to have an overview on the behavior of material deformation, including the mechanism of the pressure hill in the lateral direction, and the width broadening, in relation with the thickness distribution.