Hysteresis Theory |
 
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Hysteresis Theory |
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The bending stiffness of a flexible riser differs largely for non-operating (depressurised) and operating (pressurised) conditions. The riser has a comparatively small bending stiffness when depressurised, for example during reeling before shipment and during subsequent installation at the field. The bending stiffness in this case is mainly dependent on the external sheath and, to a smaller extent, the internal sheath(s). The tensile armour layers in a depressurised riser provide little resistance to pipe bending due to free slip of each armour strip. A linear bending stiffness of between 10 kNm2 to 100 kNm2 is representative of depressurised flexible pipes.
The bending stiffness of the depressurised riser is normally used in design for computing the pipe bending radius in extreme and fatigue wave loadings. The comparatively small bending stiffness produces conservative over-estimates of the pipe bending curvature, which is normally acceptable, provided the extreme and fatigue design criteria are not exceeded. In recent years, this simplified design approach has been shown to exceed the design criteria at the touchdown of deepwater catenary risers and in fatigue analysis involving wet armour wires.
The bending stiffness of a pressurised flexible riser is characterised by a complex non-linear bending stiffness relationship known as hysteresis. Pressurising a flexible riser produces large contact pressures between the various layers in the pipe construction. The resulting frictional resistance that develops during bending prevents free slip of the tensile armour strips. The friction increases the bending stiffness by two to three orders of magnitude for small changes of pipe bending curvature. Larger changes in the bending curvature overcome the initial frictional resistance and the pipe stiffness reduces (softens) towards the depressurised condition as the tensile armour begins to slip. The riser bending stiffness is generally divided between pre-slip and post-slip conditions. A bending reversal of the riser (as induced by the dynamic wave loading) causes the stiffness to return to the pre-slip condition.
The two below figures compare the conventional depressurised (linear) and pressurised (hysteresis) moment curvature relationships of a flexible riser.
Linear Moment Curvature Relationship
Hysteresis Moment Curvature Relationship
Hysteresis has two important effects that reduce the bending motion of a riser. Firstly, the comparatively large pre-slip bending stiffness is supported for small changes of curvature at each loading reversal (and at the commencement of bending motion). Secondly, the area within a closed (or almost closed) loop represents a loss of bending energy due to friction. This is a structural damping effect that is modelled directly by Flexcom without converting it to an equivalent form of viscous damping. These two effects significantly reduce the bending motions in a pressurised riser and can greatly assist in satisfying the design criteria for the extreme bending radius and fatigue life.