The decay of stresses induced by flat rolling of metal strip

Current simulation models for the prediction of residual stresses in flat metal rolling utilize heuristic assumptions about the roll-gap entrance and exit velocity distributions. The nature of the velocity distributions which occur in the strip adjoining the roll-gap is investigated. The problem is formulated in terms of velocity perturbations and the resulting nonlinear equations are approximated by a linear set of equations. The method of solution uses either the stress function or its integral to allow mixed boundary conditions of velocities and/or stresses at the elastic boundaries. The resulting semi-infinite problem is solved using a Laplace transform technique. Two examples are provided to illustrate the velocity and stress distribution behaviour in a moving elastic strip.