Analytical Model for the Material Flow during Cold Rolling

An analytical description of conventional cold rolling, is developed with a novel mathematical algorithm, based on finite element (FEM) and flow-line (FLM) method calculations. A new function, enabling the formulation of deformation, accurately describes the possible reverse displacement near the surface of a rolled sheet. The corresponding value of deformation can be determined for various friction coefficients and roll gap geometries by employing the expressions developed. Knowing the material flow, the amount of deformation and stress distribution along the thickness of the rolled sheet can be calculated. The results obtained were compared to the counterparts computed by FEM and FLM. It was shown that the extended model ensures accurate description of the material flow for small thickness reductions and low friction coefficients, where the phenomena of reverse displacement are observed, and many numerical approaches fail to capture this type of deformation pattern. The model was tested on both experimentally measured results and data obtained from various literature sources.