Theoretical Framework for Axial Thermal Gradients and Interface Slip in Pressure Sheath Layers of Flexible Pipes
Authors: Hansen Rasmus 
Published: October 2017

Axial thermal gradients in flexible pipes is a relatively novel area of research. New studies are putting focus on how the structural integrity of flexible pipes can be challenged by axial thermal gradients [1]. Significant axial thermal gradients occur, in particular, during start-up (heating) and shut-down (cooling) of the pipe in the vicinity of transition zones from pipe directly exposed to the surrounding environment, i.e. water or air, to thermally insulating parts, e.g. external anti-wear and fire protection layers, bend restrictors, bend stiffeners, and buoyancy modules. Along with differences in thermal expansion coefficients of the different pipe layers, the axial thermal gradients can cause significant shear stress in the interfaces between pipe layers. Thereby, axial thermal gradients may potentially cause relative axial displacement, or a slip displacement, between e.g. the pressure sheath and the pressure armor layers. In this way, axial loads in the pipe layers may not be properly transferred to, and thereby supported by, the tensile armor layer. A primary concern is the risk of e.g. pressure sheath pull-out of the end-fitting or carcass tearing failures.
The present paper partially builds upon, and extends, the results presented earlier [1], primarily concerned with interface shear loads and slip displacements between the inner pipe layers, i.e. carcass, pressure sheath, and pressure armor, and extends that study in several ways. 1) Reconsiderations of the thermomechanical coupling between the radial and the axial spatial direction, and a detailed scale analysis, leads to a more rigorous derivation of the shear stress in the carcass / pressure sheath and pressure sheath / pressure armor interfaces in response to axial thermal gradients. These results deviate from the earlier published result only in terms of Poisson’s ratio dependent numerical pre-factors. 2) The established theoretical framework includes a thorough coupling between the interface shear stresses, and the radial, axial, and azimuthal normal stresses. This allows for an exhaustive evaluation of the mechanical state of the pipe in both pre-slip and post-slip conditions, including residual states. 3) The results are generalized to transient thermo-viscoelastic analysis, which is critical for conservatism due to the viscoelastic stress relaxation of the polymeric pressure sheath material during heating, cooling, and thermal cycling.
Possible failure modes due to axial thermal gradients are currently not covered explicitly by design codes and conventional qualification testing. The model presented in this article can form basis for risk evaluations related to axial thermal gradients, input to formulations of design codes, and engineering design tools. The model contains the mechanisms that govern criticality in relation to axial thermal gradients, and its implications on interface shear stress, potential interface slip, and forces in the pipe, thereby also providing insights into possible mitigation actions for related failure modes.