An Asymptotic Analysis of Cold Sheet Rolling

We examine the plane strain cold rolling problem of thin strip implementing a perturbation scheme upon the governing equations. The analysis accounts for transverse variations in the flow and inhomogeneous work hardening. We establish deformation regimes based upon the parameters μ, the friction coefficient, τ, the ratio of the initial yield stress and the maximum roll pressure, and δ, a measure of the small gap reduction. We see that the inclusion of these inhomogeneous effects gives mildly different results for values of μ/τ > 0(1) or τ δ/μ = 0(1). We gauge these effects by examining the roll pressure, shear stress, longitudinal stress, yield stress, front and back tensions and torque to see how they are affected by the inclusion of inhomogeneous flow effects.