Mixed analytic/energetic approach for a sliding orthotropic hollow cylinder. Application to coil sagging

This paper deals with the numerical simulation of coil sagging. This problem arises within the framework of the steel making industry where strips are wound on themselves for storage. Coil sagging is a major defect that can occur for recent grades undergoing phase transitions during the coiling process. The detailed mechanisms leading to coil sagging are still not well understood, making this phenomenon very difficult to prevent. The coil is a multilayer hollow cylinder where sliding takes place at each interface and significantly contributes to the overall deformation. However, a detailed numerical simulation addressing the contact problem, considering both pressure and sliding is difficult to perform under non-axisymmetric conditions. This paper presents a simplified approach considering an orthotropic hollow cylinder instead of a multilayer coil. The anisotropy is due to contact roughness that tends to decrease the radial stiffness. The hollow cylinder is subjected to gravity and an eigenstrain representing thermal expansion, phase transitions and transformation induced plasticity. Sliding at each interface is taken into account through a continuous plastic-like shear strain that is determined through an energetic principle. The proposed solution relies on analytical developments so that computation time is compatible with parametric studies. Results are addressed in order to give a better understanding of mechanisms and conditions under which coil sagging occur.