The central strain analytical modeling and analysis for the plate rolling process

The strain after rolling plays an important role in the prediction of the microstructure and properties and plate deformation permeability. So, it is necessary to establish a more accurate theoretical strain model for the rolling process. This paper studies the modeling method of the equivalent strain based on the upper bound principle and the stream function method. The rolling deformation region is divided into three zones (inlet rigid zone, plastic zone, and outlet rigid zone) according to the kinematics. The boundary conditions of adjacent deformation zones are modified according to the characteristics of each deformation zone. A near-real kinematics admissible velocity field is established by the stream function method on this basis. The geometric boundary conditions of the deformation region are obtained. The deformation power, friction power, and velocity discontinuous power are calculated according to the redefined geometric boundary conditions. On this basis, the generalized shear strain rate intensity is calculated according to the minimum energy principle. Finally, the equivalent strain model after rolling is obtained by integrating the generalized shear strain rate in time. The plate rolling experiments of AA1060 and the numerical simulations are carried out with different rolling reductions to verify the analytic model precision of the equivalent strain. The results show that the minimum and the maximum relative equivalent strain deviation between the analytic model and the experiment is 0.52% and 9.96%, respectively. The numerical calculation and experimental results show that the model can accurately calculate the strain along the plate thickness. This model can provide an important reference for the rolling process setup and the microstructure and properties prediction.