Two-dimensional plane strain rolling: An asymptotic approach to the estimation of inhomogeneous effects
In sheet rolling, a long strip of a perfectly plastic material flows between two rigid cylinders. The width of the sheet generally exceeds the length of the roll gap by a factor of one hundred times. This implies that it is perfectly plausible to regard the state of strain flow inside the strip as ``plane'', in the sense that it is independent of the position in the transversal direction. However, at the edges of the strip this assumption breaks down. In order to analyze the plastic flow in the regions close to the edges still applying the equations of two-dimensional plasticity, it is convenient to consider the vertical and horizontal equilibrium of a volume element, and the geometric relationships between the velocity components along the roll surface, which is no longer plane but cylindrical. The authors consequently obtain two equations which play the role of boundary conditions along the roll surface. The field equations and the boundary conditions are nonlinear, and an effective procedure to construct the solution is that of expanding the unknowns in a double power series in \(x\), the longitudinal coordinate, and \(\eta\), a parameter denoting the roll gap. The solution is then obtained by perturbation method.
scientific article; zbMATH DE number 755012