On the modelling of instability and flatness defects of sheets: application to rolling process

International audienceRolling of thin sheets generally induces flatness defects due to the small thickness of the sheet and to the thermo-elastic deformation of rolls, whose profile in the roll-bite does not generally match perfectly the strip thickness profile. This leads to heterogeneous plastic deformations throughout the strip width and then to out of mid-plane displacements that relax compressive residual stresses [1]. The most important flatness defects are “edge-waves” and “center-waves” buckles. During the rolling process, the buckling waves are usually suppressed by global traction. Thus, in some cases, the sheet may appear more or less flat, or even perfectly flat on the rolling line. Nevertheless we can still talk about flatness defects, insofar as there may be residual stresses in the sheet. This is why the post-bite stress profile is called “latent flatness defects”. Few works are available in the literature dealing with instability phenomena observed in rolling process. Among them we can cite [2-4].In the present work, we develop a numerical technique to compute flatness defects of thin sheet during the rolling process. To this end, we propose a coupling technique based on Arlequin method [6] which allows us to couple a three dimensional finite element model with a shell element well adapted to large displacements, large rotations and to instability phenomena [5]. To solve the resulting non linear problem, asymptotic numerical method is used. It is a numerical tool based on high order predictor algorithm which allows to compute instability responses with high accuracy [7]. Results of this algorithm are compared successfully with experimental data.REFERENCES[1] A. Hacquin, P. Montmitonnet, P. Guillerault, A steady state thermo-elastoviscoplastic finite element model of rolling with coupled thermo-elastic roll deformation, Journal of materials processing technology. 60 (1996) 109–116. [2] F. D. Fischer, F. G. Rammerstorfer, N. Friedl, W. Wieser, Buckling phenomena related to rolling and levelling of sheet metal, International journal of mechanical sciences 42 (10) (2000) 1887–1910.[3] S. Abdelkhalek, H. Zahrouni, M. Potier-Ferry, N. Legrand, P. Monmitonnet, P. Buessler, Coupled and uncoupled approaches for thin cold strip buckling prediction, International journal of material forming. 2 (2009) 833-836. [4] R. Nakhoul, P. Montmitonnet, M. Potier-Ferry, Multi-scale method for modeling thin sheet buckling under residual stresses in the context of strip rolling, International journal of solids and structures 66 (2015) 62–76.[5] H. Zahrouni, B. Cochelin, M. Potier-Ferry, Computing finite rotations of shells by an asymptotic-numerical method, Computer methods in applied mechanics and engineering. 175 (1999) 71–85. [6] H. Ben Dhia, Multiscale mechanical problems: the Arlequin method, Comptes Rendus de l’Académie des Sciences,Serie IIb,Paris, (1998) 899-904 [7] K. Kpogan, H. Zahrouni, M. Potier-Ferry, H. Ben Dhia. Buckling of rolled thin sheets under residual stresses by ANM and Arlequin method. International Journal of Material Forming. Vol. 10 (3), pages: 389-404, 201