Careful finite element simulations of cold rolling with accurate through-thickness resolution and prediction of residual stress

TL;DR

This paper demonstrates that high-resolution finite element simulations with at least 60 through-thickness elements are essential to accurately capture stress variations and residual stress formation in cold rolling, revealing oscillatory patterns validated by analytical work.

Contribution

It provides a detailed assessment of FE simulation resolution requirements and uncovers deterministic oscillatory stress patterns affecting residual stress and curvature prediction.

Findings

At least 60 elements through-thickness are needed for accurate stress resolution.

Oscillatory stress patterns are validated by analytical comparison.

Accurate stress modeling impacts microstructure, damage, and surface finish predictions.

Abstract

Metal rolling is a widespread and well-studied process, and many finite-element (FE) rolling simulations can be found in the scientific literature. However, these FE simulations are typically limited in their resolution of through-thickness variations. In this paper, we carefully assess the accuracy of a number of FE approaches, and find that at least 60 elements through-thickness are needed to properly resolve through-thickness variation; this is significantly more than is used elsewhere in the metal rolling literature. In doing so, we reveal an oscillatory stress pattern, which is not usually observed in simulations but which we can validate by comparison with recent analytical work, and which is completely deterministic, not arising from numerical noise or error. We show that these oscillations contribute to the formation of residual stress and may help predict curvature in asymmetric rolled sheets, a phenomenon which is currently not well understood. Accurate through-thickness variation of stress and strain would also have implications for modelling microstructure evolution, damage, and surface finish.