Buckling of rolled thin sheets under residual stresses by ANM and Arlequin method

K Kpogan,H Ben Dhia,M Potier-Ferry,H Zahrouni

doi:10.1007/s12289-016-1288-5

Abstract

We present a numerical technique to model the buckling of a rolled thin sheet. It consists in coupling, within the Arlequin framework, a three dimensional model based on 8-nodes tri-linear hexahedron, used in the sheet part located upstream the roll bite, and a well-suited finite element shell model, in the roll bite downstream sheet part, in order to cope with buckling phenomena. The resulting nonlinear problem is solved by the Asymptotic Numerical Method (ANM) that is efficient to capture buckling instabilities. The originalities of the paper ly, first in an Arlequin procedure with moving meshes, second in an efficient application to a thin sheet rolling process. The suggested algorithm is applied to very thin sheet rolling scenarios involving “edges-waves” and “center-waves” defects. The obtained results show the effectiveness of our global approach.

Highlights

Rolling of thin sheets generally induces flatness defects due to the thin aspect of the sheet and to thermo-elastic deformation of rolls whose profile in the roll-bite generally does not match perfectly the strip thickness profile
If we consider that residual stresses are given for our model, the only nonlinear terms come from Eq 34. This nonlinear system can be solved by classical iterative technique but in this work we propose to solve it by using the asymptotic numerical method (ANM) which is a useful tool for nonlinear problems involving structural instability [21,22,23,24]
We have proposed in this study a numerical model which consists in coupling Arlequin and Asymptotic Numerical Methods to simulate flatness defects observed in rolling process

Summary

Introduction

Rolling of thin sheets generally induces flatness defects due to the thin aspect of the sheet and to thermo-elastic deformation of rolls whose profile in the roll-bite generally does not match perfectly the strip thickness profile. This leads to heterogeneous plastic deformations throughout the strip width and to out of mid-plane displacements that relax compressive residual stresses (see Fig. 1). It is unable to model manifested flatness defects, as shown in Fig. 2: the code overestimates the stress field beyond the roll bite This is mainly due to the buckling phenomenon in thin sheets that is disregarded by LAM3 [2]. Often the width to thickness ratio is of the order of 104

Objectives

Results

Conclusion