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Hard coatings are more and more used to improve the mechanical and tribological behavior of surfaces. Thermomechanical cracking can occur in these coatings when they slide under heavy loads. We present a two-dimensional model of a finite thickness layered medium submitted to a moving heat source. The analytical solution of the temperature and thermoelastic stress fields is obtained using Fourier transforms. The behavior of each layer is described by transfer-matrices and a relation between the displacement- and stress-vectors is given. The originality of the study is the use of a Fast Fourier Transform algorithm. With this method, calculation time is reduced, no singularity problems are met in the inverse transform and each parameter (especially the thickness of the layers) can be studied over a wide range.

Résumé -Détermination des contraintes et déplacements des couches hélicoïdales des conduites flexibles soumises à des flexions dynamiques -Cet article présente une méthode de détermination des contraintes et des déplacements dans les couches hélicoïdales des pipelines flexibles lors de flexions dynamiques. Les déplacements de chacune des couches ne peuvent être déterminés indépendamment des autres couches à cause de la présence de frottement. Un couplage de la cinématique des couches est donc nécessaire. Une comparaison avec des mesures de déformations montre que les développements théoriques sont correctement validés.Mots-clés : pipeline, flexible, flexion, déplacement, contrainte. Abstract -Calculation of Stresses and Slips in Helical Layers of Dynamically Bent Flexible PipesThis paper deals with stress and displacement calculation in dynamically bent unbounded flexible pipes.The presented method is original in that movements and stresses of all helical layers are coupled. Good correlation between strain measurements and the theory has been found, and is shown in the paper.

The accurate modeling of offshore flexible risers behaviour remains a great challenge because of (i) their complex internal structure, (ii) the variable nature of the loads along the pipe (tension, curvature, internal and external pressures), (iii) and the interactions with structures used to limit the pipe curvature. Technip and IFP have been codeveloping for many years models dedicated to stresses calculation in the armour wires, to assess the flexible lifetime. These models must account for a large number of potential inner contacts (contacts between upper and lower layers, lateral contacts between adjacent armour wires in the same layer) as well as external contacts (bend stiffener, arch, bellmouth or other curvature limitation setup). The paper presents a comparison between 3 models with different level of complexity and realism. The first one is a in house model, whereas the two others were developed on the basis of the commercial FE code Abaqus. The first model, Life6, is based on some simplified assumptions in particular the fact that periodic solutions are assumed (given constant curvature in the pipe) and uses analytical solutions of equilibrium of wires on a torus (the bend pipe). The effect of non uniform curvature (in particular end-fitting proximity) is not considered in this model. The second model, namely 3D/Periodic model, is still based on a periodic assumption, but can cope with severe loadings (such as large curvature of the pipe or compression) leading to specific wires contact interactions. Abaqus Standard (Implicit scheme) is used. The third model, called 3D/Explicit model, is a full length model, as it includes end fittings effects, outer structure (like stiffener) interactions and any curvatures variations along the pipe. All contacts interactions are considered. The number of DOFs involved in the analysis requires the use of an explicit integration scheme (Abaqus Explicit) running on a parallel platform. These models are cross validated on a dedicated case study that consisted of a pressurized pipe cyclically bent with constant curvature. The validation of the model results is very satisfying even when lateral contacts between wires occur. Finally, a comparison of the 3D/Explicit model results with experimental data is presented. This model provides a very good estimation of the flexible behavior and of the end fitting effects.