  In this paper, we carefully develop a finite element (FE) model that gives
accurate through-thickness predictions of stress and strain distributions
during the steady-state cold rolling process. These through-thickness
predictions unveil an oscillatory pattern that is shown to have important
consequences for residual stress in the rolled sheet. We believe this is the
first time that through-thickness FE results have been accurately validated by
comparison to non-FE results, in this case by comparison to a recent analytical
model of through-thickness variation in cold rolling. While we use here the
ABAQUS commercially available FE software, our observations are relevant to all
FE simulations of cold rolling. Care is taken by considering both convergence
in number of elements through thickness, convergence to a steady state, and the
avoidance of other numerical artefacts such as shear locking and hourglassing.
We find that previous FE models of cold rolling are usually woefully
under-resolved through-thickness; e.g. using 10 elements through-thickness,
while we require 60 here for convergence. Convergence of roll force and roll
torque, used in previous studies to validate models, are shown to be poor
indicators of through-thickness convergence. We also show that the
through-thickness oscillatory pattern may have important consequences for
predicting curvature during asymmetric rolling.
