Continuous roll forming including in-line welding and post-cut within an ALE formalism

Cold roll forming is a rather old process for which there is a renewed interest due to its capacity to form ultra high-strength steels. For the first time ever in the literature, the manufacturing chain involving both the continuous cold roll-forming process, the in-line welding operation for closed sections and the post-cut operation is numerically modelled. The first phase of this process sequence consists in computing the hopefully steady state configuration of the strip for the total length of the roll-forming mill, including the in-line welding phase. For addressing this problem, the Arbitrary Lagrangian Eulerian (ALE) formalism is used. Once the ALE steady state is reached, the computation is pursued with a second Lagrangian phase which is aimed at simulating the post-cut operation that releases the formed section from the rolling tools of the mill, enabling to determine the final geometry of the product. In this paper, the computational modelling framework employed within the in-house finite element code METAFOR is described. In particular, the proposed techniques - which are definitely original within an ALE formalism - for modelling the in-line welding operation and the post-cut operation are extensively detailed. The welding is considered with three different methods: (1) symmetry boundary conditions coupled with a well-suited node relocation procedure, (2) a closed mesh of the closed section coupled with a well-suited node relocation procedure, and (3) sticking elements based on a spring constitutive formulation. A set of simple numerical examples demonstrates the confidence in all the proposed modelling methods. Finally, these methods are successfully applied in the cases of two complex roll-forming mills of closed tubular sections.