The curvature modeling for the double layered clad plate by asymmetric rolling with different diameters

The plate curvature model plays an important role in the prediction and control of the double layered clad plate. However, there is currently no such a fast, precise and stable plate curvature model, and the actual shear stress on the cross section is uneven distributed actually which is conflicted with the uniform assumption of the traditional model. Based on the non-uniform distribution, this paper innovatively presents a theoretical plate curvature model using the flow function method and the upper bound method together without the complex stress analysis. The inlet boundary conditions of the model are more accurately modified and optimized as nonlinear functions. The velocity field and strain rate field were built depending on the flow function field. The plastic deformation, shear and friction power were developed by the five-node Gauss–Legendre quadrature method. The post-rolling strain model was obtained by integrating the positive strain rate and shear strain rate with time. The curvature model was constructed by calculating the curvature due to linear and shear strain differences. To demonstrate the validity of the theoretical model, the experiments and the simulation were conducted. The results showed that the relative deviation of the numerical values v_a and v_b is less than 10.0%, accounting for 95.1% and 95.4%, compared with theoretical values. The shear power difference between layer a and b is the main reason for bending. The bending phenomenon appeared at the outlet section of the plate, and the velocity difference provided the shear stress required for bending. The increase of the diameter ratios leads to the increase of the shear strain difference and shear power, and it leads to an increase in the total curvature. To certify the precision of the curvature model, the deviation of the theoretical peak curvature values is 12.05%, and the average deviation is 5.92%, compared with the simulation and experiments. The model can quickly grasp the affecting law of key rolling process parameters on curvature, which will provide theoretical and technical basis for rolling process.