A Fatigue-Life Prediction Model for Metallic Tube Umbilicals
Authors: Hoffman Joe , Dupont Wayne , Reynolds Brandon 
Published: October 2008

Abstract
With the ever-increasing need to use metallic tube umbilicals in dynamic applications, the need for a fatigue life prediction model developed. Consequently, this paper presents a method for predicting the fatigue life of the metallic tubes taking into account static, dynamic, as well as frictional stresses within the umbilical. While the static and primary dynamic stresses such as bending are easily quantifiable, the frictional stress is not easily determined. Therefore, full scale dynamic testing of umbilicals commenced not only to qualify the particular umbilical design for the given application but also to quantify the friction aspect of metallic tubes within umbilicals in general. Based upon the results of the full scale testing, an equivalent friction factor has been determined. With the proposed model and given the equivalent friction factor, the designer will be able to assess the fatigue life of an umbilical for a given dynamic application.

Introduction
Metallic tube umbilicals consist of metallic tubes, electric and fiber optic cables helically assembled into a bundle. For dynamic applications the bundle typically has a thermoplastic sheath extruded around it for mechanical protection of the underlying components as well as for abrasion resistance at the touch down point of the riser. A typical cross section of a metallic tube umbilical is shown in Figure 1 for reference.
A key design aspect of the umbilical is that the individual components that make up the bundle slip relative to one another and bend around their own neutral axis. An additional design aspect of umbilicals is that the ends of the umbilical are not sealed and the annular region around the tubes is allowed to free flood. This is important in that the external hydrostatic pressure does not increase the contact forces of the tubes, which would increase the frictional stress thus decreasing the fatigue performance of the umbilical.
The model combines the average tensile, bending, end cap, hoop and radial stresses using the von Mises criterion to calculate the mean stress component. Cyclic stress due to variations in axial tension, change in curvature and internal frictional are then derived to give the mean stress and cyclic stress components for each sea state. Use of the Goodman line then enables a corresponding cyclic stress at zero mean stress to be derived, which can then be used with an S-N curve for the tube material to predict the allowable number of cycles. Finally, the life of each tube is determined for each sea state and the damage is summed using Palmgren-Miner rule for fatigue. The model proposed herein should only be used for high cycle fatigue and umbilical components laid at shallow lay angles.
Validation of the model and determination of the friction factor has been determined through full scale testing of prototype umbilicals including a Joint Industry Project (JIP) and other project specific tests. The umbilicals are subjected to a flex fatigue test which simulates the loading at the top connection of an umbilical riser connected to a floating production vessel