Un exemple de flambage sous contraintes internes : étude des défauts de planéité en laminage à froid des tôles minces (étude numérique et comparaison avec l'expérience)

摘要

Lam3/Tec3 is a 3D steady-state FEM rolling model using a hexahedral mesh, proved in the past to be poorly adapted to modelling flatness defects in strip rolling. Shell elements are indeed much more suitable for this purpose, i.e. to predict buckling of plates under residual stresses. Thus, the purpose of this work is to improve Lam3/Tec3 by coupling it iteratively with a shell FEM of plate buckling under residual stresses. This model, called “MAN”, is based on the Asymptotic Numerical Method for the resolution of non linear problems. Compared to existing models in the literature, it shows sufficient accuracy to compute the critical buckling loads and the corresponding buckling modes, it can solve more complex cases (complex residual stress fields and buckling modes), and has a post-buckling capability, which distinguishes it from the other models. We have compared results of Lam3/Tec3-MAN in the decoupled as well as the iteratively coupled modes, and also with a version of Lam3/Tec3 including a simplified buckling model proposed by Counhaye (simple and fast, but unable to study post-buckling). The analysis of the results is focussed on the one hand on the comparison with experimental transverse profiles of the longitudinal stress, obtained by "flatness rolls", on the other hand on the interactions between the mechanical fields in the roll bite and post bite. Profiles obtained at the position of the flatness rolls are in good agreement with the measurements. The results prove the importance of a coupled rolling / buckling model, be it coupled strongly or iteratively, to capture the details of the stress profiles. It is also shown that it is essential to reproduce the latter with a precision of a few MPa in order to predict correctly buckling and post-buckling.