Calculation of Deformation-Related Quantities in a Hot-Rolling Process

The hot deformation of metal as a nonlinear system is mathematically described by a local linear model associated with the working conditions using a transfer function (TF) in the Laplace domain. Experimental data (true stress vs. true strain curves) are obtained using the established compressive uniaxial deformation test, where experimental conditions (strain rate and temperature) define the working conditions of the local linear TF model, which is intrinsically a function of strain. Based on the TF model, three important physical quantities of the tested metal are determined exactly: the work done per unit deformation, the average flow stress, and the flow-stress derivative with respect to the strain based on a particular TF. The exactly determined quantities, determined as a function of strain, can replace the previously used approximations in some rolling force and torque calculations.