Pipes for deepwater applications possess a diametertothickness ratio in a region where failure is dominated by both instability and plastic collapse. This implies that prior to failure the compressive yield strength of the material must be exceeded, followed by ovalisation and further local yielding. This paper presents an investigation into the mechanics of this specific problem and develops an analytical approach that accounts for the effects of geometrical and material data on the collapse pressure of inhomogeneous rings under external hydrostatic pressure. The analytical expressions have been correlated to numerical and experimental test data, proving their accuracy.
In deep and ultradeep waters the diameter of trunk lines coupled with the hydrostatic pressure tends to lead to failure of the pipeline by external collapse. This failure mode is an instability phenomenon that is governed by the geometry of the pipeline and its material properties. Failure of a pipeline section takes place according to a subtle combination of its properties and to various factors [
In the present paper an analytical treatment is developed that can provide adequate prediction of collapse pressure of a pipe section with varying material properties. The proposed approach has its route in the fundamental mechanics of the problem and is capable of blending transitions between elastic collapse for thinwalled structures and plastic collapse for thicker sections.
Through this understanding of the actual mechanisms involved in the buckling of the pipe it is hoped that further improvements in performance could be gained through optimisation of the pipe manufacturing process, the pipe form, or its mechanical properties.
The majority of the pipes used in offshore applications are commonly manufactured by coldforming plates through the UOE process. This means that a steel plate is folded along its edges, formed into a Ushape and then pressed into an Oshape between two semicircular casts. The pipe is successively welded closed and circumferentially expanded to obtain a highly circular shape, see Figure
Schematic UOE forming steps.
A large number of experiments have demonstrated that these steps, especially the final expansion, tend to degrade the mechanical properties of the pipe and may occasionally result in a significant variation of the material strength along the circumference of the crosssection. To further enlighten this point, a number of accurate tests on UOE pipes have been recently performed by Tata Steel in accordance with ASTM E989a [
Average strength variation with pipe angular position (Tata Steel, 2010).
From the graph, in a few cases the difference in compressive strength between the
Such variability in material properties may significantly affect the carrying capacity of the pipe and, to the best of authors’ knowledge, differently from variations in thickness [
In order to account for the variability of the material properties around the ring circumference, an analytical treatment that extends the applicability of an already proposed and assessed formulation for uniform rings [
It is worth pointing out that the development focuses on the carrying capacity of a pipe section and that the extension to the case of a long cylindrical shell can be obtained in the Timoshenko fashion [
With reference to Figure
A ring under external pressure.
For the sake of simplicity but without loss of generality, four different material regions, symmetric with respect to the
Nonhomogeneous material regions.
Three nonhomogeneous secondorder linear differential equations, based on the EulerBernoulli theory of the elastica, can be written for each of the three sectors with different material properties in which half of the circumference results in being partitioned,
On the basis of experimental evidence it is commonly accepted that the most suitable representation of the stressstrain curves for carbon steels is represented by the RambergOsgood (RO) power law [
Thus, in such a case the Tangent modulus,
According to the results from material testing on UOE pipes discussed in the previous section, with respect to the reference material of region
The stressstrain curves for regions
Stressstrain curves for the material regions (1) through (3).
The general solution for each of the differential Equations (
The values of the unknown constants
The nonzero entries
Provided that
Once the expression of the radial displacement,
With reference to the sections of the ring wall where the maximum bending moment,
However, when instability and plasticity phenomena coexist, the response of a crosssection of the ring is more realistically governed by an elasticplastic behaviour. For this reason, reference is made to the following axial forcebending moment relationship:
Elastic, elasticplastic, and plastic loci in the
In fact, in the case
Therefore, with reference to the sections of the ring wall where the maximum bending moment,
In fact, since the regions into which the circumference is divided are characterised by different material properties, it is
However, the value of the external pressure corresponding to the first occurrence of at least one plastic hinge in the inhomogeneous ring can be directly obtained from (
In the next Section it will be shown that this approach can provide a very accurate bound to the collapsing pressure of inhomogeneous rings.
Needless to say, in case all the regions share the same material properties, the presented development straightforwardly reduces to the result pertaining to a homogeneous ring, see [
The proposed analytical treatment has been assessed against a few case studies.
For all the examples the Ramberg Osgood material data for the region
Some experimental stressstrain curves from samples taken along the pipe section (Tata, 2010).
The yield strengths for the regions
The amplitude of the initial imperfection,
The case studies made reference to a ring characterised by a diameter of 457.2 mm and three different wall thicknesses,
Figure
Contour plot of the yield function values,
It is evident that in the case of the homogeneous ring a fully plastic status is achieved at the same time at four sections, located at
In order to validate the results, the case studies taken into consideration have been analysed by means of the commercial finite element (FE) package ANSYS [
The model was carefully calibrated against carefully conducted experimental results [
FE modelling of a inhomogeneous ring.
Table
Collapse pressures [MPa] for homogeneous rings (H) and lower bound pressures [MPa] for inhomogeneous rings (I)


 

H  I  H  I  H  I  
Theory  FEM  Theory  FEM  Theory  FEM  Theory  FEM  Theory  FEM  Theory  FEM 
 
35.27  34.59  27.88  28.07  51.20  50.83  42.83  42.34  68.44  68.43  58.56  57.60 
It is immediate to notice that the analytical and the FE results agree very well for all the case studies. Moreover, it can be pointed out that the lower bounds from the proposed treatment essentially coincide with the collapse pressures from the FE analyses. In fact, with reference to Figure
Evolution of the hoop strains at impending collapse (
Overall, it can be stated that the attainment of a fully plastic state takes place in the inhomogeneous ring at a value of the external pressure which ranges from about 81 to 85% of the value of the critical pressure for the homogeneous case. Therefore, the reduction in the lower bound to the collapsing pressure results in being higher in percentage than the variation in the material properties. Also, the decrease in the carrying capacity with respect to the homogeneous case results in being directly proportional to the
A preliminary confirmation of the results for the case
In the present work an analytical approach that can provide an adequate prediction of the collapse pressure of a pipe section in the case of UOE formed deepwater pipelines and that accounts for the effects of geometrical data and varying material properties has been presented and discussed. The proposed approach has its route in the fundamental mechanics of the problem and is capable of blending transitions between elastic collapse and plastic collapse.
With respect to the recourse to numerical methods, such as finite element analyses, it is felt that the proposed approach can provide a thorough understanding of the actual mechanisms involved in the buckling of the pipe and, by focusing on the few parameters which govern the phenomenon, may open the way to improvements in performance through optimisation of the pipe manufacturing process.
The present study has been motivated and financially supported by Tata Steel, UK. In particular, the authors are grateful to Dr. Richard Freeman for all his assistance.