A New Analytical Approach for the Velocity Field in Rolling Processes and Its Application in Through-Thickness Texture Prediction

A new analytical model is presented that expresses kinematically admissible velocity fields in rolling processes. Opposed to conventional streamline approaches, the current model does not force the material to flow along the prescribed lines, but introduces a new coordinate that is constant over these lines, to prescribe a fixed component of the velocity in the rolling direction as a function of that coordinate and the coordinate along the rolling direction. The interaction between the rolls and the surface is incorporated in the model via two scalar parameters which depend on the friction conditions between the roll and the sheet, and the properties of rolled material. The scalar parameters can be tuned with experimental observations of deformation flow across the thickness. The modelled material flow does not reveal significant deviation from the one calculated by streamlines. The obtained analytical expressions for the velocity gradient tensor components combined with polycrystal plasticity models enables the prediction of the through-thickness texture evolution for various friction conditions.