In this chapter the physics of guided wave propagation along pipes have been discussed in section 2.1, while the use of guided waves for the detection of damage in pipelines has been described and reviewed in section 2.2.
Chapter 3
The Interaction of Guided Waves with
Simple Supports in Pipes
Pipeline corrosion is a major problem for the petrochemical industry. Wall thinning as well as localised pitting corrosion can occur on both the inside and the outside pipe walls. Lo- cations where pipelines rest on simple supports such as round bars and I-beams are partic- ularly problematic since it is common for moisture and dirt to accumulate near the contact interfaces, thereby creating favourable conditions for corrosion initiation. Formally, a sim- ple support is defined as a hard and non-conformable surface, such as the top surface of the I-beam exemplified in figure 3.1, on which a pipeline rests but to which it is not bonded, clamped or secured in any way.
Inspection at simple support locations presents a number of challenges. Common methods utilised to measure wall thickness, such as Ultrasonic Testing (UT) and Eddy Currents (EC), require direct access to the area to be inspected. At simple support locations this is difficult, impractical and often prohibitively expensive to obtain, and consequently such inspection methods do not represent a viable option. Furthermore, even visual inspection may be dif- ficult to perform at a simple support location since the geometrical layout tends to hide the presence of severe corrosion. Guided wave inspection represents a potential solution to this problem as it enables the remote inspection of pipelines at simple support locations without requiring direct access, thus dramatically reducing inspection costs.
The interaction of guided waves with damage in pipelines is a thoroughly studied topic [4– 19]. However, the successful detection of damage at simple support locations relies on the ability to distinguish between the echoes produced by the support itself and the echoes pro-
duced by damage. Depending on loading conditions, pipe size and support geometry, it is possible for a simple support to produce a significant echo that might mask or be mistaken for damage, especially since echoes from damage are likely to present the same degree of asymmetry as echoes from simple supports. Consequently, it is essential to understand how the echoes produced by simple supports behave. Very little work has so far been reported on this subject, primarily because the echoes from simple supports are below the typical report- ing thresholds for standard guided wave pipeline inspection. Cheng et al. [65] performed an experimental study of the effect of clamped supports on the propagation of the fundamental torsional mode T(0,1), focussing on the attenuation caused by the presence of rubber gas- kets and the implications this has on the detectability of damage located past the supports. Utilising experimentally gathered data as well as finite elements simulations, Yang et al. [66] studied the interaction between an incident T(0,1) guided wave packet and axially welded supports with an emphasis on the detection of damage located past the support.
The increase in resolution, sensitivity and signal-to-noise ratio associated with the intro- duction of permanently installed sensors and enhanced guided wave inspection equipment creates a growing need to better understand the characteristics of simple support echoes so that they can be distinguished from damage echoes. This chapter presents an attempt to develop a systematic understanding of how guided waves propagating along a pipe, and in particular the fundamental torsional mode T(0,1), interact with simple supports. First of all, in section 3.1 the general mechanical properties of a contact interface between a pipe and a simple support are derived from Hertzian theory. Guided wave propagation along a supported section of pipe is then analysed in section 3.2 utilising the Semi-Analytical Finite Element (SAFE) method in order to establish which modes can propagate and how they dif- fer from those that can propagate in a free pipe. In section 3.3, Finite Element Analysis (FEA) is utilised to study the echoes from simple supports, and the defining characteristics of these echoes are interpreted in light of the results from the guided wave propagation analysis per- formed utilising the SAFE method. Finally, in section 3.4 simple support echoes recorded experimentally are compared to those obtained from FEA simulations and utilised to vali- date them.
3.1 Contact Interface
Consider a length of pipe resting on a simple support, as exemplified in figure 3.1. A contact interface exists between the two bodies with an extent e along the axial direction of the pipe,
3.1. Contact Interface st st sn 2w e Contact Interface
Figure 3.1: Diagram of the contact interface between a pipe and a simple support.
a width 2w along the circumferential direction, a normal stiffness snthat acts in the radial di-
rection and a tangential stiffness st that acts in the circumferential and axial directions. The
two contacting bodies can be assumed to reasonable accuracy to have smooth surfaces, to be loaded within the elastic limits of their material and to be non-conformable. The contact stiffness can therefore be calculated utilising Hertzian contact theory [67].
Note that in practice there may be occasions where the previously discussed assumptions are not valid. For example, under loading a simple support may bend around the pipe, or the pipe wall may flatten around the contact zone. In such cases, the problem involves con- formable bodies and presents an increased degree of complexity since contact stiffness can vary significantly along the interface as a function of the actual contact area, the physical condition of the surfaces in contact, etc. The use of dedicated FEA models, which is beyond the scope of this study, would then be required to represent the contact interface [67]. John- son [67] thoroughly discusses the assumptions behind Hertzian contact theory.
Two variants of Hertzian contact theory describe two different types of non-conformable contact [67]: three-dimensional Hertzian theory describes point contact, i.e. elliptical con- tact, while two-dimensional Hertzian theory describes line contact. Elliptical contact occurs when two non-conforming bodies come into contact, as in the case of a pipe resting on a
round bar. Conversely, line contact occurs when infinitely long cylinders with parallel axes come into contact. Away from end effects, the line contact model adequately describes the interaction between contacting solids in commonly occurring circumstances such as a pipe resting on a I-beam, as shown in figure 3.1. In the present study the analysis is restricted to the case of line contact only because initial experiments as well as FEA simulations revealed that point contact supports typically produce negligible echoes due to their extremely short axial section.
According to Hertzian theory [67–69], in the case of line contact the contact interface is as- sumed to have constant width
2w = 2 Ç
2PR?
πE? (3.1)
over the contact length e , where P = F /e is the force per unit length normal to the contact interface, i.e. the force per unit length with which the two bodies are pressed together, and F , also referred to as contact loading, is the total force normal to the contact interface, i.e. the total force with which the two bodies are pressed together. The contact modulus E?is given
by 1 E? = 1− ν12 E1 + 1− ν22 E2 (3.2)
where ν1, E1, ν2and E2are respectively Poisson’s ratio and Young’s modulus for the material of the first and second body, while the relative radius R?equivalent to a cylinder on a plane
is given by 1 R? = 1 R1+ 1 R2 (3.3)
where R1and R2are respectively the radius of the first and second cylinder. Note that in the case of contact between a cylinder of radius R1, i.e. the pipe, and a planar surface, e.g. an I-beam, R?is equal to R
1since R2tends to infinity. On the basis of the approach of distant points, it can be shown that normal interface stiffness sn is given by [67–69]
sn= πe 1− ν12 E1 d? 1+ 1− ν22 E2 d? 2− 1 E? d? 1= 2ln 4d 1 w − 1 (3.4) d? 2= 2ln 4d 2 w − 1
where d1= 2R1and d2= 2R2. In the case of contact between a cylinder of radius R1and a planar surface then d1= d2= 2R1.