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Guided Wave Inspection of Supported Pipe Locations Using Electromagnetic Acoustic Transducers
by
Nicholas Andruschak
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Mechanical and Industrial Engineering University of Toronto
© Copyright by Nicholas Andruschak 2014
ii
Guided Wave Inspection of Supported Pipe Locations Using
Electromagnetic Acoustic Transducers
Nicholas Andruschak
Master of Applied Science
Mechanical and Industrial Engineering
University of Toronto
2014
Abstract
The goal of the work in this thesis is to develop a rapid and reliable NDT system to detect hidden
corrosion at pipe-support interfaces using Electromagnetic Acoustic Transducers (EMATs).
Since there are often many support interfaces over a piping run, information is needed on the
support interface conditions to optimize subsequent detailed inspections.
In this work it is important to be able to isolate the effects produced from the support interface
and the incident guided wave. To do this an optimum EMAT operating point is first selected,
then the support interfaces and wall loss type defects are independently analyzed through
experimentally validated finite element models. It is found that operating the SH1 plate wave
mode near the ‘knee’ of its dispersion curve gives a high sensitivity to wall loss type defects
while experiencing a minimal effect from the support contact region.
iii
Acknowledgments
I would like to thank my supervisors, Dr. Anthony Sinclair and Dr. Tobin Filleter, for their
patience and guidance over the past two years. Their attention to detail and ongoing assistance in
moving the project forward was essential in getting me to where I am today. I would also like to
thank Gabriel Turcan and Mequaltech Inc., Montreal for their support and encouragement over
the past two years. Finally, to my mom and dad in Vancouver for always being there and
providing me with their love, advice and support.
iv
Table of Contents
Acknowledgments .......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ............................................................................................................................... viii
List of Figures ................................................................................................................................ ix
Chapter 1 Introduction .................................................................................................................... 1
1 Introduction ................................................................................................................................ 1
1.1 Introduction ......................................................................................................................... 1
1.2 Objectives ........................................................................................................................... 1
1.3 Thesis Outline ..................................................................................................................... 2
Chapter 2 Background and Literature Review ................................................................................ 4
2 Background and Literature Review ........................................................................................... 4
2.1 Overview of Corrosion in Industrial Piping ........................................................................ 4
2.1.1 Corrosion Cell ......................................................................................................... 4
2.1.2 Operational Trouble at Pipeline Supports ............................................................... 4
2.2 Electromagnetic Acoustic Transducers ............................................................................... 5
2.2.1 Lorentz Force Mechanism ...................................................................................... 6
2.3 Guided Wave Theory .......................................................................................................... 8
2.3.1 Introduction ............................................................................................................. 8
2.3.2 Guided Waves in Plates .......................................................................................... 9
2.3.3 Dispersion ............................................................................................................. 11
2.3.4 Guided Waves in Pipes ......................................................................................... 14
2.3.5 Specific NDT Configurations ............................................................................... 15
2.4 Periodic Permanent Magnet (PPM) EMAT’s ................................................................... 16
2.4.1 Spatial Bandwidth ................................................................................................. 17
v
2.5 Non-Destructive Testing Basics ....................................................................................... 18
2.5.1 Configurations ....................................................................................................... 18
2.5.2 Measurement Techniques ..................................................................................... 19
2.6 Pipe Support Rough Surface Contact Interfaces ............................................................... 20
2.6.1 Introduction ........................................................................................................... 20
2.6.2 Contact Stiffness ................................................................................................... 20
2.6.3 Contact Damping .................................................................................................. 21
2.7 Finite Element Modelling ................................................................................................. 22
2.7.1 Introduction ........................................................................................................... 22
2.7.2 FE Techniques For Modelling Wave Propagation ................................................ 23
2.8 Guided Wave Inspection at Supported Pipe Locations ..................................................... 24
2.8.1 Axial Wave Propagation ....................................................................................... 25
2.8.2 Circumferential Wave Propagation ....................................................................... 26
Chapter 3 EMAT Construction ..................................................................................................... 27
3 EMAT Design & Construction ................................................................................................ 27
3.1 Introduction ....................................................................................................................... 27
3.2 Proposed System Configuration ....................................................................................... 27
3.3 Equipment Details ............................................................................................................. 28
3.4 Operating Point Details ..................................................................................................... 30
3.5 EMAT Construction .......................................................................................................... 31
3.5.1 PPM Array Construction ....................................................................................... 31
3.5.2 Enclosure Construction ......................................................................................... 34
Chapter 4 Wave Propagation FE Modelling ................................................................................. 35
4 Wave Propagation FE Modelling ............................................................................................. 35
4.1 Introduction ....................................................................................................................... 35
4.2 Brief Evaluation on Wave Propagation FE Techniques ................................................... 35
vi
4.3 Infinite Domains ............................................................................................................... 36
4.4 Generation and Reception of Waveforms ......................................................................... 38
4.4.1 Generation ............................................................................................................. 38
4.4.2 Reception .............................................................................................................. 39
4.4.3 Discussion ............................................................................................................. 40
4.5 COMSOL 4.3b Implementation ........................................................................................ 40
Chapter 5 Support Investigation ................................................................................................... 43
5 Support Investigation ............................................................................................................... 43
5.1 Introduction ....................................................................................................................... 43
5.2 FE Modelling of Contact Interfaces .................................................................................. 43
5.3 Experimental Verification ................................................................................................. 46
5.3.1 Introduction ........................................................................................................... 46
5.3.2 Experimental Set-up .............................................................................................. 46
5.3.3 Load Application .................................................................................................. 48
5.3.4 Results ................................................................................................................... 48
5.3.5 Contact Damping .................................................................................................. 53
Chapter 6 Defect Investigation ..................................................................................................... 57
6 Defect Investigation ................................................................................................................. 57
6.1 The Introduction ................................................................................................................ 57
6.2 FE Modelling of Wall Loss Defects ................................................................................. 57
6.3 Experimental Validation ................................................................................................... 61
6.4 Analysis ............................................................................................................................. 62
6.4.1 Verification of Model ........................................................................................... 62
6.4.2 Sources of Error .................................................................................................... 66
7 Conclusions .............................................................................................................................. 68
7.1 Review of Thesis ............................................................................................................... 68
vii
7.2 Summary of Findings ........................................................................................................ 68
7.3 Future Work ...................................................................................................................... 69
References ..................................................................................................................................... 71
viii
List of Tables
Table 6-1 - Measured Defect Dimensions .................................................................................... 62
Table 6-2 – Relative Amplitude and Delay Data for Experimental Test Specimens ................... 62
Table 6-3 - FE Results of Test Cases ............................................................................................ 64
ix
List of Figures
Figure 2-1 - Racetrack Coil (a) and Cross Section [4] (b) .............................................................. 6
Figure 2-2 – Free Plate Problem Geometry [8] ............................................................................ 10
Figure 2-3 - Group Velocity vs. Frequency-Thickness Product for Mild Steel ............................ 12
Figure 2-4 – Phase Velocity vs. Frequency-Thickness Product for Mild Steel ............................ 13
Figure 2-5 – Reference Coordinates For a Hollow Cylinder [9] .................................................. 14
Figure 2-6 – PPM EMAT with Racetrack Coil ............................................................................ 16
Figure 2-7 – PPM EMAT Top View [15] ..................................................................................... 17
Figure 2-8 – a) Pulse Echo, and b) Pitch-Catch [17] .................................................................... 19
Figure 3-1 – Side View of Inspection System Orientation ........................................................... 28
Figure 3-2 - Innerspec PBH Instrument ........................................................................................ 29
Figure 3-3 - Signal Conditioning Module (L) and Enclosed Tuning Module (R) ........................ 29
Figure 3-4 - Dispersion Curve with Ideal Wavelength Excitation Line ....................................... 31
Figure 3-5 – Dual Racetrack Coil Configuration with Active Coil Area Indication .................... 32
Figure 3-6 - PPM EMAT Bandwidth ............................................................................................ 34
Figure 3-7 - Magnet Array (left) and Wrapped Flex Coil (right) ................................................. 34
Figure 4-1 - Schematic of PML Domain Layout .......................................................................... 36
Figure 4-2 - FFT of Hanning Windowed Input ............................................................................ 39
Figure 4-3 – Normalized SH1 Voltage Waveform at Receiver Location ..................................... 42
Figure 5-1 - Schematic of FE Contact Interface Model ................................................................ 44
Figure 5-2 - FE Model Received Signal Relative Amplitude vs. Interfacial Stiffness ................. 45
Figure 5-3 - FE Model Received Signal Delay Time vs. Interfacial Stiffness ............................. 45
Figure 5-4 - Schematic of Setup ................................................................................................... 47
Figure 5-5 - Picture of the Steel Bar Supported Clamp Region ................................................... 47
Figure 5-6 - Support ‘Load Region’ Configuration ...................................................................... 48
x
Figure 5-7 - Experimental Received Signal Relative Amplitude vs. Applied Load ..................... 49
Figure 5-8 - Experimental Received Signal Time Delay vs. Applied Load ................................. 50
Figure 5-9 - FE and Experimental Received Signal Relative Amplitude vs. Stiffness/Area ....... 52
Figure 5-10 - FE and Experimental Received Signal Delay vs. Stiffness/Area ........................... 52
Figure 5-11 - FE Model Relative Amplitude vs. Imaginary Stiffness per unit area for 3” Support
....................................................................................................................................................... 54
Figure 5-12 - FE Model Arrival Delay vs. Imaginary Stiffness per unit area for 3” Support ...... 55
Figure 6-1 - Schematic of defect cross section ............................................................................. 58
Figure 6-2 - Received Signal Amplitude vs. Defect Feature Length ............................................ 59
Figure 6-3 - Received Signal Arrival Time vs. Defect Feature Length ........................................ 59
Figure 6-4 – Specimen #1 - FE results Verification ..................................................................... 63
Figure 6-5 - Specimen #2 - FE results Verification ...................................................................... 64
Figure 6-6 - Specimen #3 - FE results Verification ...................................................................... 64
Figure 6-7 –Displacement Magnitude for Specimen #1 and #3 at a single receiver node ........... 66
1
Chapter 1 Introduction
1 Introduction
1.1 Introduction
Corrosion is a significant issue in the petrochemical industry. Because piping and pipelines
often run long distances to move products, they must be supported at regular intervals. This
leads to a large number of pipe-support interfaces over a piping run. These interfaces between
the supports and pipe are prime locations for corrosion to occur, as they can trap water and other
contaminants and are inherently difficult to inspect as the corrosion is hidden underneath the
support interface.
Due to the large number of these supports, this gives rise to the need for a rapid and reliable
nondestructive testing (NDT) technique to quickly identify severe corrosion at these interfaces.
One such NDT technique features ultrasonic guided waves which have been shown to be
effective in locating various types of corrosion defects in both plates and tubes. To generate
these guided waves, Electromagnetic Acoustic Transducers (EMAT’s) are increasingly used as
they exhibit several advantages over conventional piezoelectric transducers, most importantly
that limited surface preparation is required and specific wave modes of interest can be generated.
Since a rapid inspection technique is being developed in this thesis, preparing surfaces at each
support interface is not acceptable and extremely time consuming, so only EMAT’s are
considered.
1.2 Objectives
The general objective of this thesis is to develop a medium range guided wave NDT system in
order to rapidly and reliably detect hidden corrosion at pipe support interfaces. This objective
inherently implies two things. The first is that the guided wave EMAT system should be
sensitive to corrosion defects, so that a clear recognizable change in the signal occurs when
corrosion is present. Secondly, the effects of the support on the received signal must be
minimized so that the response of the received signal to the defect can be isolated, enabling the
defect to be identified.
2
These objectives can further be broken down into smaller fundamental objectives needed to
achieve a working EMAT inspection system. First a guided wave mode must be selected as well
as a frequency and wavelength in order to determine the characteristics of the transducers. These
parameters need to be selected in order to be sensitive to corrosion wall loss and be reasonably
insensitive to support related effects. Once these parameters are determined the EMAT’s can be
designed and built.
In NDT studies, it is important to be able to analytically model the wave propagation and
interaction with specific geometrical features. This allows prediction of the effects of these
features on wave propagation; it also enables optimization of the NDT system. Constructing
models of both the effects of the support as well as a representative corrosion defect should
enable an understanding of system performance as well as facilitate future iterations of this
design. Furthermore, as with any engineering project, it is important to provide validation for
any analytical model proposed. In this work the analytical models of the defect and support
produce different effects on the waveform and thus these effects are validated independently.
1.3 Thesis Outline
This thesis begins with background discussion in Chapter 2 on corrosion in industrial piping
networks, EMAT’s, guided wave theory for both plates and pipes, NDT inspection techniques
and some existing pipe-support inspection methods. More general background on engineering
topics such as Finite Element Modelling (FEM) and rough surface contact is covered as well.
In Chapter 3 the considerations in constructing an EMAT such as selecting an operating point
and other key parameters such as wavelength, frequency and specimen thickness are discussed.
Also covered is how the selected operating point translates to the physical characteristics of a
periodic permanent magnet (PPM) EMAT, such as the number of magnets in the PPM array as
well as their thickness.
In Chapter 4 a fundamental guided wave finite element model is developed for a uniform
isotropic plate. Important aspects of this model are discussed such as simulating infinite
domains using perfectly matched layers (PML’s), techniques for implementation into the FE
program COMSOL Multiphysics 4.3b, and techniques to approximate the generation and
3
reception of guided waves by a PPM EMAT. This model is developed with the intent that other
geometrical features can be added later such as support interfaces and corrosion defects.
In Chapter 5, the effects of the support interface are analyzed. First an analytical model is
constructed by modifying the fundamental FE model developed in Chapter 4; then this model is
verified through experiments approximating conditions at a pipe-support interface. The
parameters used in the FE model and experiments are discussed as well. Also, the results and
comparison between the analytic FE model and experiments are explored in this chapter.
In Chapter 6, the effects of a representative wall thinning defect are considered. An FE model of
a gradual wall-thinning type defect is developed as an addition to the model discussed in Chapter
4. The experimental verification procedure is then discussed including the manufacture of test
specimens as well as the comparison of model results with measurements.
In Chapter 7, a summary is provided on the findings of this thesis. Also additional topics that
will be the subject of future work are detailed.
4
Chapter 2 Background and Literature Review
2 Background and Literature Review
2.1 Overview of Corrosion in Industrial Piping
Corrosion occurs due to the reaction of metals with their surroundings. It causes costly and
untimely failures of structures such as piping and pipelines. Support locations are difficult to
inspect and often the only solution is a visual inspection. This usually involves lifting the pipe
off the support to inspect the interface; this is time consuming and costly [1], particularly if the
pipe is wrapped with insulation. It has been found by plant maintenance professionals that 80-
85% of all corrosion on pipes takes place at pipe supports, with the remaining 15-20% occurring
primarily at elbows [2].
2.1.1 Corrosion Cell
For corrosion to occur, a corrosion cell is required. A corrosion cell consists of an anode,
cathode, electrolyte and a metallic pathway. At the anode, material is lost through oxidation and
the valence state increases. The opposite is true at the cathode, which undergoes a reduction
reaction and a decrease in valance state. The electrolyte is an electrically conductive solution
that must be present to transmit positive ions from cathode to anode, while in the metallic
pathway electrons flow from negative to positive, or from anode to cathode [3]. Further details
on the types of corrosion cells and the corrosion process may be found in [3].
2.1.2 Operational Trouble at Pipeline Supports
At pipe supports, corrosion develops because the geometry of the support allows for water to be
trapped and held in contact with the surface of the pipe. This causes the initial failure of the
paint system, as often coatings are not designed for submersion service. The small amount of
steel now exposed due to this initial failure begins to corrode. Once the general corrosion has
spread and compromised most of the paint in the support region, crevice corrosion initiates.
Crevice corrosion is driven by a differential aeration cell, caused by the different concentrations
of oxygen at the cathode and anode or inside and outside the support [1]. For further details on
crevice corrosion see [3].
5
2.2 Electromagnetic Acoustic Transducers
Electromagnetic Acoustic Transducers (EMAT’s) are devices that can generate and detect
ultrasound in metals. Fundamentally EMAT’s consist of a permanent or electro-magnet and a
current-carrying coil. The permanent magnet is used to provide a static bias field while the coil
is used to introduce dynamic magnetic fields in the skin depth of the inspection piece. Through
the coupling of the electromagnetic and elastic fields in the surface skin, ultrasound is generated
and received. Inherent in EMAT’s and as summarized in [4], there are three primary coupling
mechanisms: Lorentz forces, magnetostrictive forces and magnetization forces. Optimally
designing an EMAT for a specific task requires an understanding of these coupling mechanisms.
Additionally, by changing EMAT geometry such as orientations of the coil and magnets, many
different guided wave modes can be excited [4]. Guided wave fundamentals will be discussed in
Chapter 2.3.
EMAT’s have long been investigated for their potential in non-destructive testing as they have
many benefits over conventional piezoelectric transducers. Some benefits are: they do not
require contact with the test piece; they can direct ultrasonic waves at any direction into the test
piece, and they can easily generate horizontally-polarized (SH) waves in plates or torsional
waves in pipes. These SH waves are difficult to produce utilizing conventional piezoelectric
transducers and are desired in certain non-destructive testing applications due to their unique
characteristics [4] [5].
The main drawback of EMAT’s is a relatively poor signal-to-noise ratio due to the inefficiency
of the transduction mechanism. To compensate, techniques such as electrical impedance
matching of system components, high amplification, band-pass filtering of the received signal,
and excitation with a narrow tone burst are utilized [6].
In regards to this present work, only the Lorentz force transduction mechanism is considered.
The magnetization coupling is not considered as it is much smaller in magnitude than both the
Lorentz and magnetostrictive couplings, so it is often neglected in both Lorentz force and
magnetostrictive based EMAT`s. Magnetostrictive based EMAT`s are not considered for this
application as magnetostriction is highly non-linear and the magnetostriction curve (strain vs.
magnetic field) is highly material dependant. Specifically, the curve shows hysteresis,
dependence on the current stress state of the material, the exact history of magneto-mechanical
6
loading, the excitation frequency and the surface conditions. In comparison, the Lorentz force is
linear and its magnitude is dependant primarily on the static bias field and coil excitation current,
which are two parameters that can be controlled in practice [5]. The Lorentz force-based EMAT
is described further in the next section.
2.2.1 Lorentz Force Mechanism
Lorentz force EMAT’s typically use a ‘racetrack’ coil (Figure 2-1a) in order to provide
unidirectional current in a localized area under a bias magnet. This is better visualized in Figure
2-1b where a cross sectional view of the highlighted area in Figure 2-1a is shown.
Figure 2-1 - Racetrack Coil (a) and Cross Section [4] (b)
In Figure 2-1b the x-direction is perpendicular to the current-carrying wire and parallel to the
surface of the specimen. The z-direction is perpendicular to both the current carrying wire and
the surface of the test specimen. A good summary of the previous research into the Lorentz force
coupling mechanism in EMAT’s is outlined in [4].
The Lorentz force is the cross product between magnetic flux density and eddy current within the
skin depth of the specimen:
� = �� × �� (1)
The details for this derivation can be found in [4]. As the eddy current density decreases
exponentially from the surface of the specimen, the skin depth δ is defined as the depth from the
a. b.
7
surface to where the eddy current density has decreased to 1/e of its peak value. It can be
approximated as:
� = 2� μ�μ� (2)
Where ρ is the resistivity of the conductor, µ r is the relative permeability, µ0 is the permeability
of free space and ω is the angular frequency.
The Lorentz force shown in (1) can be expressed as a function of the input current to the coil.
This is explained in some depth in [4] and again summarized below. First the eddy current
density from (1) is expressed as a function of the magnetic field H:
�� = ∂���∂� − ∂���∂� (3)
Next, realizing that changes along the z-axis are typically much larger than changes along the x-
axis the following approximate relation holds in our EMAT’s:
�∂���∂� � ≫ �∂���∂� � ≈ �∂���∂� � ≫ �∂���∂� � (4)
Applying the right hand side of (3), the second term of (4) can be seen to be much smaller than
the first, and is neglected in most situations. This means (1) can be written as:
�� = ��� ∂���∂�
�� = ��� ∂���∂�
(5)
8
The alternating magnetic field generated from the coil HxM
, is approximately linearly
proportional to the input current I. For the specific arrangement shown in Figure 2-1 containing
n wires of unidirectional current, this relation is:
��� = ��2 � �!� "#�!$ (6)
Where δ is the skin depth and z is the position on the z-axis. Therefore if (5) and (6) are
combined, the Lorentz force can be seen to be a product of the static magnetic field and the input
current.
2.3 Guided Wave Theory
2.3.1 Introduction
Guided mechanical waves are stress waves that propagate within the boundaries of a structure.
They are composed of a variety of different waves that reflect, mode convert and super-impose
to produce guided wave packets that travel within structural boundaries [7]. In comparison, a
bulk wave travels inside a material away from the boundaries, hence they travel in the ‘bulk’ of
the material.
Both guided and bulk waves are governed by the same set of partial differential equations. The
difference is that guided waves must satisfy some additional physical boundary conditions.
These additional boundary conditions typically make an analytical solution difficult to find [8].
The Navier governing equation of motion for a linear elastic isotropic material is derived in
many publications such as [8] [9] or [10] and shown below:
%& + μ()*,"* + μ)",** + ��" = �), " %-, . = 1,2,3( (7)
Where λ and µ are Lame’s constants, ρ is the material density, ) is the displacement vector and�
is the force vector. Next using the Helmholtz decomposition as shown in [8] and [11], the vector
u can be expressed as the gradient of a scalar potential (ϕ) plus the curl of a vector potential (H):
9
1 = ∇3 + ∇× 4,∇⦁4 = 0
(8)
Substituting (8) into (7) yields the following:
∇ 7%& + 28(∇93 − � ∂93∂:9 ; + ∇ ×78∇94− � ∂94∂:9 ; = 0 (9)
Looking at the above equation, it is only satisfied when both terms in square brackets disappear.
Therefore equating each term in brackets to zero, and re-arranging each expression yields the
following:
∇93 = 1<=9 ∂93∂:9 and∇94 = 1<A9 ∂
94∂:9 (10)
With cL and cT defined as:
<=9 = & + 28� and<A9 = 8� (11)
The above equations shown in (10) are known as the wave equations.
2.3.2 Guided Waves in Plates
The free plate is an approximation and not fully physically realizable, however it provides a good
approximation to a number of practical configurations of engineering components, and is often
used to illustrate important guided wave principles [10]. The free plate is considered
homogenous and elastically isotropic with traction free surfaces. Therefore, it is governed by the
equation of motion shown in (7), with traction free boundary conditions at ±d/2 (Figure 2-2).
10
Figure 2-2 – Free Plate Problem Geometry [8]
Exact solutions to this problem can be obtained in different ways, but the displacement potential
method using the Helmholtz decomposition shown in (8) is popular. Assuming the only
rotations are about the x-axis (Hy = Hz =0) and assuming zero particle displacement in the x-
direction (ux= 0), equation (10) reduces to:
B∂93∂C9 + ∂93∂�9D = 1<=9 ∂93∂:9
(12)
B∂94∂C9 + ∂94∂�9D = 1<A9 ∂94∂:9
(13)
The solutions to the above equations (12) and (13) are referred to as Lamb waves. Lamb wave
modes contain wave vector components both normal and parallel to the vertical particle motion.
For particle motion in the z-direction (uz), the solutions can be seen to be either symmetric (S) or
anti-symmetric (A) about the z-axis (mid-plane of the plate) due to the presence of cosine and
sine functions in their solutions respectively. The full derivation for these solutions can be found
in [8].
Additionally, as summarized in [11] and adapted from [10], there is another family of guided
waves present in the traction free plate medium, they are referred to as horizontally polarized
shear (SH) wave modes. SH wave modes are the solutions to (12) and (13) when the scalar
potential vanishes, meaning essentially only (13) is considered. Also the only particle motion is
z d/2
-d/2
y
11
assumed to occur in the x-direction (uy = uz = 0). Applying these considerations to (12) and (13)
yields:
B∂94∂C9D = 1<A9 ∂94∂:9
(14)
Additionally Hx = 0 since uy = uz = 0. The solutions to (14) give the shear horizontal (SH) family
of plate wave modes that will be the focus of this study. Further details on the solution
procedure can be found in [10] or [12]. In [8] the final SH wave equation is expressed as:
B∂9)�∂�9 +∂9)�∂C9 D = 1<A9 ∂9)�∂:9
(15)
2.3.3 Dispersion
Guided waves are dispersive as their phase velocities vary with frequency, meaning that they
spread out over time and space when excited by a finite duration signal. This is observed as an
increase in signal duration as a function of propagation distance, which reduces the time
resolution of the pulse. There is also an accompanying decrease in signal amplitude since energy
must be conserved. This reduces the sensitivity of the inspection system [13] [14].
For the case of shear horizontal waves in a traction free isotropic plate, a dispersion relation can
be derived by considering the solutions to (15). The procedure is shown in [8], and the final
dispersion relation is given below:
B <ED9 = F <AG9 − #�HI $9 %� = 0,1,2,3… ( (16)
Where cp is the phase velocity defined in (17), cT is the shear speed defined in (11), d is the
specimen thickness in Figure 2-2 and ω is the angular frequency. Dispersion relationships are
usually visualized on a dispersion curve, where the group velocity or phase velocity relationships
shown in (17) are plotted as a function of the frequency-thickness product [10]. This is shown in
Figure 2-3 and Figure 2-4.
12
KELMN� = &� = O
KP�QRE = S SO
(17)
In (17), λ is the wavelength, f is the frequency, ω is the angular frequency and k is the
wavenumber. One very important point on dispersion curves is that for non-zero n in (16), a cut-
off frequency-thickness product exists which must be exceeded for a given wave mode to
propagate. The cut-off frequency thickness product is obtained by solving (16) for the phase
velocity and then setting the denominator to zero. This is demonstrated in [8], and the final result
is shown below:
%�I(T =�<A2 (18)
Figure 2-3 - Group Velocity vs. Frequency-Thickness Product for Mild Steel
0 2 4 6 8 100
500
1000
1500
2000
2500
3000
3500
4000
Frequency-Thickness (MHz-mm)
Gro
up v
elo
city
(m/s
)
Group Velocity Dispersion Curves - SH Waves
SH0
SH1
SH2
SH3
SH4
SH5
13
Figure 2-4 – Phase Velocity vs. Frequency-Thickness Product for Mild Steel
Similarly for Lamb waves, dispersion relations can be derived using the solutions to (10). Again
the details can be found in [8], but the end result is shown below:
tan%Vℎ(tan%Xℎ( = B 4O9XV%V9 − O9(9DT
(19)
With p and q defined as:
X = % 9<=9 − O9(Z�IV = % 9<A9 − O9(
(20)
Where k is the wave number, h is half the plate thickness and n = 1 for symmetric modes and -1
for anti-symmetric modes. Similarly to SH waves, Lamb waves are often depicted on a
dispersion curve showing the group or phase velocity plotted as a function of the product of
frequency and thickness [8].
0 2 4 6 8 10
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
Pha
se v
elo
city
(m/s
)
Frequency-Thickness (MHz-mm)
SH0
SH1 SH2 SH3 SH4 SH5
Phase Velocity Dispersion Curves - SH Waves
14
2.3.4 Guided Waves in Pipes
Guided wave inspection of cylindrical shells such as piping or steel tubes is also prominent in
industry. Techniques similar to the ones used to analyze guided wave propagation in the free
plate can be used. To start, consider guided wave propagation in an infinitely long hollow
cylinder, such as shown in Figure 2-5.
Figure 2-5 – Reference Coordinates For a Hollow Cylinder [9]
The inner and outer surfaces of the infinitely long cylinder are considered traction free, and the
equation of motion for an isotropic elastic medium shown in (7) can be applied. The solutions to
this boundary value problem were first solved in [9]. Following the terminology employed in
[8], the assumed particle displacements to satisfy the boundary value problem are of the form:
)� = [�%\( cos%�`( cos% : + O�( )a = [a%\( sin%�`( cos% : + O�( )� = [�%\( cos%�`( sin% : + O�(
(21)
In these equations, Ur, Uθ and Uz represent displacement amplitudes corresponding to Bessel or
modified Bessel Functions. Selection criteria for the Bessel or modified Bessel functions are
shown in [9] and [8] as well as other sources. Additionally n is the circumferential order and ur,
uθ and uz represent displacements in the radial, circumferential and axial directions respectively.
15
Looking at (21), it can be seen that if n = 0, the resulting wave modes will be axisymmetric, as
the θ dependence is removed. These resulting wave modes are referred to as the longitudinal and
torsional modes respectively. For nonzero n, displacement is dependent on circumferential
position. This gives rise to the flexural wave modes. To denote this, following the notation in
[8], the longitudinal modes are numbered L(0,m), the torsional modes are numbered T(0,m), and
the flexural modes are numbered F(n,m). In this notation n is still the circumferential order
while m is the mode number.
The frequency equation for n = 0 takes the form of a 6x6 matrix and is shown in [8]. This result
is adapted from Demos Gazis [9], who completed much of the initial work in hollow cylindrical
wave propagation. It is shown that if the modes are axisymmetric (n = 0), the frequency
equation can be written as a product of sub-determinants:
c = cd ∗ c9 = 0 (22)
Where the solutions of D1 = 0 correspond to the longitudinal modes, and the solutions to D2 = 0
correspond to the solutions of the torsional modes [9]. In terms of polarization, the longitudinal
modes are polarized in the (r,z) plane, with no circumferential component. Conversely, torsional
modes are polarized in the circumferential plane [8].
Relating these modes back to the plate wave modes, the longitudinal modes are analogous to the
Lamb plate wave modes and the torsional wave modes are analogous to the SH wave modes.
This is because for both torsional and SH plate waves, particles move perpendicularly to both the
direction of wave propagation and the surface normal. Similarly, both Lamb and longitudinal
waves contain particle motion perpendicular to SH and torsional modes. Flexural modes have
displacement in both the radial and circumferential directions and are often avoided in
applications due to complexity of the wave structure and non-symmetric characteristics as the
displacements in all three dimensions are coupled [8].
2.3.5 Specific NDT Configurations
In comparison to conventional ultrasonic testing where probes must be scanned over the entire
structure, guided wave testing allows an entire structure to be inspected from a single location
16
[13]. Dispersion curves are very important as they contain a large amount of information
necessary to design a guided wave non-destructive test. For example, they show the phase and
group velocities of the possible wave modes that exist at each frequency-thickness product. This
aids in selecting an operating point to ensure that the possible wave mode group velocities
adequately differ so there is separation in time between received pulses over the propagation
distance [7].
Another fundamental concern when designing a guided wave non-destructive test is the structure
of the selected wave. This includes the in-plane and out of plane particle displacements, as well
as the variance of the stress distribution throughout the material thickness. This is important
when trying to increase sensitivity to a specific defect or for increasing penetration power when
inspecting under coatings [7]. For example, for the detection of a surface defect, a wave mode
with maximum power and particle displacement on the outer surfaces would be desired [8]. To
optimize for sensitivity or penetration power, often an iterative, experimental tuning process is
used [7].
2.4 Periodic Permanent Magnet (PPM) EMAT’s
To produce horizontally polarized shear waves utilizing the Lorentz force, a periodic permanent
magnet (PPM) arrangement is used. A PPM EMAT consists of two rows of magnets of
alternating polarity atop unidirectional current-carrying conductors. This configuration is shown
in Figure 2-6, where the pattern using the front four magnets repeats to include all magnets in
each row.
Figure 2-6 – PPM EMAT with Racetrack Coil
x y
z
N
N S
S
S N
Coil Symmetry Line
17
As can be seen in Figure 2-7, using a racetrack coil causes each row of magnets to be atop
unidirectional current flow. The alternating permanent magnet configuration in each row creates
a periodic flux density in the surface of the test specimen equal to the acoustic wavelength of the
wave. This causes a periodic Lorentz force with the same period as the magnet arrangement [4].
Also, since the current flow is in opposite directions on each side of the coil centerline, the
polarity of each magnet across the centerline must also alternate for an additive Lorentz force.
This can be seen in Figure 2-6 with an eight magnet per column PPM array and Figure 2-7 with a
six magnet per column PPM array.
Figure 2-7 – PPM EMAT Top View [15]
Also the curved section of the racetrack coil will have a minimal effect on the generated wave
since there are no magnets located on top of this section of the coil.
2.4.1 Spatial Bandwidth
The finite size of the PPM arrangement gives rise to a spatial bandwidth with the dominant
wavelength corresponding to the period of the magnet arrangement. This term is defined as
follows:
Assume two columns of eight magnets as seen in Figure 2-6. The resulting Lorentz force
projected onto a y-z plane (as orientated in Figure 2-6) is approximately sinusoidal over space.
This has been shown multiple times in literature [6] [16]. This can also be inferred by looking at
the Lorentz force relation and noting the alternating polarity of the magnets and the alternating
current flow direction across the coil centerline (Figure 2-7) which cause alternating eddy current
18
polarizations. If a spatial Fast Fourier Transform (FFT) of this result is computed, a spatial
bandwidth can be defined by looking at the magnitude function of the FFT. The peak of this
magnitude function is the dominant wavelength. This process is shown in [16]. The spatial
bandwidth can then be defined as the range between some fixed amplitude drop from the peak of
the amplitude function, such as -6dB or -3dB.
Alternatively, to define the spatial bandwidth, a spatial FFT of the magnetic field from one
column of the PPM arrangement can be taken as an approximation in 2D. If a transmitter and
receiver are both used then the spatial bandwidth ‘narrows’, as it is now the product of both the
receiver and transmitter transfer functions [16].
2.5 Non-Destructive Testing Basics
2.5.1 Configurations
2.5.1.1 Pulse-Echo
Pulse-echo is an ultrasonic NDT configuration where one sensor is used as both the transmitter
and receiver. An ultrasonic pulse is generated, and any reflections from a defect return to the
probe. The location of the defects can be determined based on the time a pulse takes to return to
the probe [17]. This is shown in Figure 2-8a.
2.5.1.2 Pitch-Catch
In a pitch-catch configuration, both a transmitter and receiver probe is used. The receiver probe
can either be located on the same side of the defect as the transmitter, or on the opposite side. In
this thesis, only the orientation where the transmitter and receiver are on opposite sides of the
defect is considered so that the through transmission effects can be studied. Therefore a wave is
generated and it propagates through the corroded area and then is received on the opposite side.
This is shown in Figure 2-8b. The corrosion geometry will cause different features to appear in
the received waveform. Measurements of changes in group and phase velocity, mode conversion
and transmission coefficients can be used to characterize the corrosion damage [17]. This will be
further discussed in Section 2.5.2.
19
Figure 2-8 – a) Pulse Echo, and b) Pitch-Catch [17]
2.5.2 Measurement Techniques
There are three different guided wave characteristics that may typically be used in ultrasonic
guided wave testing: wave cut-off mode phenomena, changes in group or phase velocity, and
changes in transmission/reflection amplitudes. Each has their own advantages and
disadvantages. Additionally, aside from time-of-flight velocity measurements which can only be
used in locating a defect, each method offers unique information about a defect’s geometry and
size [18].
2.5.2.1 Cut-Off Phenomena
Many different ultrasonic guided wave modes may be present in a specimen at a single instant.
For a specified specimen thickness, there exists a frequency below which each wave mode will
not propagate. This is referred to as the mode’s cut-off frequency; the one exception is the
fundamental mode (which has no cut-off frequency). Therefore, by conducting a wide-band
frequency sweep, it is possible to locate corrosion defects by examining received wave modes to
determine which modes have propagated to the receiver, and which have not [18].
©2000 IEEE
20
2.5.2.2 Group or Phase Velocity Changes
Since guided wave modes are generally dispersive, a comparison between the group or phase
velocities of the pulse in a corroded section of pipe and the group or phase velocity in a non-
corroded zone can be made. Any differences may be correlated to the decrease in material
thickness through the dispersion relation. This effect can be studied on a dispersion curve [18].
2.5.2.3 Amplitude Changes
The amplitudes of the reflected and transmitted wave modes can be used to determine corrosion
depths assuming either calibration or reference data is available. The transmitted and reflected
pulse amplitudes are dependent on defect geometry, as this determines the angle at which the
incident wave contacts the defect. For example, a crack will typically have a steeper incident
angle than a gradual thinning-type defect due to the sharpness of the transition between the
damaged and undamaged portions of the test piece [18].
2.6 Pipe Support Rough Surface Contact Interfaces
2.6.1 Introduction
When two surfaces are brought into contact (usually by some applied load) contact does not
occur over the entire surface area of the interface unless the surfaces are perfectly smooth. As
practical engineering surfaces are not perfectly smooth, contact is visualized as being between
only a few asperities. These asperities that are in contact define the real contact area of the
interface, which is often much less than the total ‘apparent’ contact area. This is an extremely
important topic in tribology, as the estimation of real contact area is necessary in predicting
wear, contact stiffness, adhesion and electrical and thermal contact resistances [19].
2.6.2 Contact Stiffness
When two surfaces are pressed together by a normal force, both tangential and normal contact
stiffness can be defined. In literature many different models have been proposed to estimate
these contact stiffness parameters such as statistical methods or fractal geometries. A good
summary of the different techniques is contained in [19], and is out of the scope of this thesis.
One prominent model pursued in this study is the Greenwood-Williamson (G-W) model [20].
This model considers the contact between two rough surfaces as the contact between a rigid
21
plane surface and a second surface that is the combination of all the deformable features of the
two rough surfaces. The asperities of the deformable surface are considered spherical, and a
distribution of asperity heights is assumed. The asperity height distribution is usually taken as
Gaussian or exponential [21]. Further details on the G-W theory can be found in [20] [22] [23].
A convenient expression [21] based on the G-W theorem for analyzing the contact interfaces of
machined steel plate specimens is:
fT ≈ 3ghN (23)
Where Kn is the normal contact stiffness, P is the pressure and σs is the standard deviation of
asperity summit heights. This is shown in [21] and is derived by assuming an exponential
distribution of asperity heights in the G-W theorem to guarantee a closed form solution [24], then
fitting a Gaussian distribution to this exponential distribution [25]. The linear expression for the
contact stiffness based on the exponential distribution assumption is also shown in [26] and [27].
It should also be noted that these contact stiffness expressions are derived assuming no-slip.
What is useful about the above relation is that the only statistical roughness parameter required is
the standard deviation of summit heights (σs). As indicated in [21], σs can approximately be taken
to equal the average roughness (Ra), for which some tabulated values are given in literature for a
variety of surfaces. Then to obtain the tangential contact stiffness the following relation is used
[28]:
fifT = H%1 − K(2%2 − K( (24)
2.6.3 Contact Damping
Contact damping occurs due to micro-slip at the asperity level, which occurs prior to the static
friction condition being exceeded. Once the static friction condition is exceeded, relative motion
between two surfaces occurs. Fundamentally this micro-slip may be viewed as a fretting loop
where the input energy at one surface is not equal to the energy transferred to the second surface
22
as some energy is dissipated. Thus an ‘energy lost per cycle’ value is often calculated and used
to quantify this fretting effect.
To estimate contact damping, a convenient formulation is proposed in [29] and displayed below:
j =klllmF5H12G
kllm
35 + 25 #1 − o8p$qr − #1 − o8p$
9r1 − #1 − oμp$
qr − 5o6μp t1 + #1 − o8p$9ruvwwx− 1
vwwwx d
(25)
Where η is the loss factor, F is the total normal load, T is the total tangential load and µ is the
coefficient of friction between surfaces. This method is derived by considering the contact
interface to have a fractal geometry. Fractals have been used in many studies to better
understand different parameters of rough surface contact interfaces such as shown in [30] [31]
[29] and [32]. Fractals are particularly useful as they are scale invariant, as expressions are
formulated in terms of fractal dimension (D), fractal roughness (G) and scaling parameter (γ) and
not the statistical parameters used in the G-W theorem that depend on sampling length and
resolution. Although (25) is derived using fractals, it is not explicitly dependant on these fractal
parameters as they cancel out.
The tangential contact stiffness can also be derived using fractals, but due to a lack of sufficient
tabulated data to calculate fractal parameters for a range of contact interfaces, this is not pursued
in this thesis.
2.7 Finite Element Modelling
2.7.1 Introduction
Finite element analysis (FEA) is a numerical technique for finding approximate solutions to
boundary value problems for differential equations. In this section discussion will be restricted
to finite element techniques utilized in the modelling of guided waves. In this thesis the finite
element software utilized is COMSOL 4.3b.
23
2.7.2 FE Techniques For Modelling Wave Propagation
When configuring a wave propagation finite element (FE) simulation there are a few ‘guidelines’
that should be followed to obtain an accurate solution. As discussed in [12], for wave
propagation problems at least 7 elements are required per wavelength for acceptable accuracy.
y� ≤ &{"T7 (26)
Where ∆x is the element size and λmin is the minimum wavelength within the signal bandwidth.
This quickly leads to large memory requirements and simulation times if the ratio between any
structural dimension and wavelength is large. Often this makes 3D simulations impractical
especially if the wave is to travel a distance of many wavelengths. In published literature, the
two prominent solution methods to model guided wave propagation are time domain simulation
and frequency domain simulation.
2.7.2.1 Time Domain Solution Procedures
When setting up an FEA study in the time domain, it is important to note the difference between
explicit and implicit time marching schemes. Implicit schemes are inherently stable, and
dynamic equilibrium is satisfied at the end of the time step or at t+∆t. Displacements are
obtained by solving the equation of motion, meaning that at each time step the stiffness matrix
must be inverted. This is what makes implicit schemes unconditionally stable and thus larger
time steps may be used.
Conversely, explicit schemes are conditionally stable and the time step must be smaller than
some calculated critical time step. Dynamic equilibrium is enforced at the beginning of the time
step (time t). As a consequence, this means that the stiffness matrix does not need to be inverted
for the solution of displacements at t+∆t, see [33], [34] and [11].
The advantage of an implicit scheme is that the time step can be chosen without respect to the
critical time step requirement as required in an explicit scheme. This can be advantageous as
acceptable accuracy may still be achieved in the solution while utilizing less resources. However
in wave propagation problems, explicit schemes are preferred as the time step required for
acceptable accuracy is often less than the critical time step, thus the explicit scheme is
24
advantageous as the stiffness matrix does not need to be inverted at each step. This makes
explicit schemes much more efficient for these types of problems and thus implicit time schemes
for wave propagation will no longer be discussed in this thesis [11].
2.7.2.2 Frequency Domain Solution Procedures
Another finite element method is modelling the wave propagation in the frequency domain. In
this technique the waveguide is subjected to a continuous harmonic excitation and the steady
state response at a single frequency is calculated. If this is done for all frequencies in the signal
bandwidth then the time domain signal can be recovered by calculating the Inverse Fast Fourier
Transform (IFFT). In the FE software used in this thesis (COMSOL 4.3b) solutions for the
frequency domain equations are computed implicitly.
To obtain an equivalent simulation time to an explicit time marching scheme, the frequency step
should be calculated as:
∆� = 1~∆: (27)
Where N is the number of time steps in the time simulation and ∆t is the time step. The
frequency step must also satisfy Nyquist criteria. It is also important to note, that prior to
performing the IFFT on the resulting complex nodal displacements to obtain the time dependant
signal, appropriate zero padding should be performed. This is important because as shown in
[35] it is essential to reproduce the correct shape of the time dependant waveform.
2.8 Guided Wave Inspection at Supported Pipe Locations
Guided wave testing has made it possible to inspect a large section of a pipe from a single
location by propagating waves axially down the pipe. This serves as a rapid inspection technique
but suffers from difficulties due to signal attenuation over large propagation distances. Thus the
T(0,1) mode is often used to try and mitigate signal losses as this mode exists at low frequencies
where attenuation tends to be relatively low, features shearing action, and is easier to interpret as
it is non-dispersive.
25
Another option is to propagate guided waves circumferentially around a pipe. Theoretically,
since the circumferential distance is shorter than the axial propagation distance, higher
frequencies and more dispersive wave modes can be used. This allows for smaller defects to be
resolved. Additionally, the wave structure can be optimized to be sensitive to specific types of
defects. However, the disadvantage is that the sensor configuration must be moved down the
pipe axis for multiple measurements as the wave is not guided in the axial direction. This can
cause inspections to take longer.
The following two sections summarize previous literature in the areas of ultrasonic defect
detection and characterization at supported sections of pipe.
2.8.1 Axial Wave Propagation
Pulse-echo configurations have often been investigated for guided wave testing since only one
access point is needed on the pipe; this is advantageous as often pipes are buried or otherwise
difficult to access [36]. Since the T(0,1) guided wave mode is axisymmetric, it is only able to
provide information on the axial position of a defect.
An array of active elements such as piezoelectric transducers encircling a pipe may be used to
generate the T(0,1) mode. A low frequency (8-25 kHz) commercial system based on this
principle is used in [37] to investigate the T(0,1) mode interaction with simple pipe supports to
develop an inspection procedure. It is observed that when the support contact area becomes a
significant fraction of the wavelength, the fundamental torsional mode exhibits a non-zero cut-
off frequency [37].
Other investigations into support interactions with the T(0,1) mode include clamped supports
[38] and welded supports [39]. In [38] an experimental investigation measured reflection
amplitudes as a function of torque applied from the clamped support. It is concluded that higher
torques lead to higher reflection amplitudes [38]. In [39] the reflection peak from a welded
support is found to be delayed from its actual physical location. At low frequencies, this could
lead to confusion, as the echo from the pipe support might overlap with reflections from defects
located past the support.
26
2.8.2 Circumferential Wave Propagation
Performing an inspection using waves that propagate circumferentially around a pipe is a slower
inspection method as it requires some form of axial translation to inspect an entire length of pipe.
Often the translation is accomplished either manually or by mounting the transducers on a ‘rig’
that can travel down the pipe axis autonomously.
For example, horizontally polarized waves, such as the SH0 and SH1 plate wave modes are
investigated for the detection of just external [40] and both internal and external [41] corrosion
of pipes. Both of these studies take advantage of the different properties of the SH0 and SH1
wave modes in order to locate and identify different types of defects. Although these studies are
not specifically directed to the detection of corrosion around pipe supports, often the rigs the
transducers are mounted on must pass over supported pipe sections.
Deviating slightly from horizontally polarized guided wave inspection, propagating higher
frequency Lamb waves circumferentially has been used to detect pinhole type defects at
supports. As the wave propagation distance is shorter, higher frequencies and more dispersive
wave modes may be used. This is important as pinhole defects are small, and the wave pulse
must have a wavelength on the order of the dimension of the defect (or less) to get a well-
resolved image of the damage. In [42] a piezo-crystal transducer in pulse echo mode is used to
detect and size pitting type corrosion at the pipe-support interfaces.
Recently, Higher Order Mode Cluster’s (HOMC’s) have been used to inspect pipe support
interfaces. HOMC’s are composed of many individual wave modes and occur at high frequency-
thickness products (15-35 MHz-mm) at which the group velocities of all observed modes are
similar [43]. Thus all these modes form a ‘cluster’ and may be seen to approximately propagate
as a single non-dispersive envelope. Due to the relatively high frequencies and thus small
wavelengths of the HOMC, this inspection method has been applied to detection of small pitting
type defects in pipe support regions using circumferential propagation in [44], and axial wave
propagation in [43].
27
Chapter 3 EMAT Construction
3 EMAT Design & Construction
3.1 Introduction
In the design of an EMAT, the first step is determining an appropriate operating point based on
knowledge of the probe configuration and desired operating characteristics. Coils and magnets
are then purchased and combined to achieve this operating point using well known EMAT
design steps to select parameters such as operating frequency and the number and width of the
magnets.
In this chapter, an outline of the chosen EMAT inspection arrangement is first discussed,
followed by the selection of a suitable operating point. Finally a description of the EMAT
design and construction procedure is given.
3.2 Proposed System Configuration
As the goal of this thesis is the detection of corrosion at pipe-support interfaces using a medium
range guided wave system, an orientation using a pitch-catch EMAT probe configuration
orientated axially on a pipe is investigated (Figure 3-1). In this orientation the probes are
translated circumferentially. Since waves are generated in both +/- y-directions in Figure 2-6 by
an EMAT probe, the axial probe orientation simplifies the signal processing as the second wave
generated by the EMAT will not interfere with the results since it propagates away from the
inspection area. Additionally there is more flexibility with this arrangement as the two
transducers are not restricted to being in-line along the pipe circumference. This allows the
separation distance to be adjusted, as well as support geometries such as clamps or hangers to be
evaluated without changing the system geometry.
28
Figure 3-1 – Side View of Inspection System Orientation
To simplify this situation with reasonable accuracy it is assumed that the effect of a guided wave
propagating in a pipe axially over a short distance approximates that of a guided wave in a plate
[45]. This approximation can be made if the ratio between wall thickness and the radius is small.
This implies that the pipe curvature is neglected.
The SH family of modes were pursued as they only contain particle motion in the surface plane
of the specimen, normal to the direction of wave propagation. This means the particle motion
will be normal to the direction of load application from the support, likely minimizing the effect
on the received wave. All of our transducer development work is conducted for the inspection of
a 3mm mild carbon steel plate, but the basic steps are also applicable to other specimen
thicknesses.
3.3 Equipment Details
The Temate® PowerBox H (PBH)1, handheld pulser and receiver is used due to its small
footprint and ease of use in the field (Figure 3-2).
1 Innerspec Technologies, Lynchburg Virginia
Receiver Transmitter
Wave Propagation
Support
Probe Translation
Pipe
29
Figure 3-2 - Innerspec PBH Instrument
A convenient aspect of this instrument is that it is accompanied by a catalogue of stock coils that
easily interface to the instrument through a signal conditioning module (Figure 3-3) that is
mounted on the top.
Figure 3-3 - Signal Conditioning Module (L) and Enclosed Tuning Module (R)
The PBH generates high voltage tone-bursts with an adjustable frequency, repetition rate and
cycles per tone-burst to power a transmitter EMAT. The pulser is capable of generating 1200V
or 8kW peak power at a pulse repetition rate of up to 300 pulses per second. It also contains a
low noise amplifier with a high gain that connects to a receiver EMAT. A pulse-echo
configuration is also possible for cases where the same EMAT transmits and receives the
ultrasonic signal (Chapter 2.5.1.1).
30
The EMAT coils connect to the PBH through a signal conditioning module shown in Figure 3-3.
This signal conditioning module interfaces with a tuning module designed to interface with a
specific coil (Figure 3-3-right). It also contains the appropriate impedance matching network for
the coil. Therefore all that is required when changing coils/transducers is swapping this
detachable tuning module to the one that accompanies the new coil/transducer.
3.4 Operating Point Details
The SH1 mode is selected for use in this inspection system since it is dispersive. As discussed in
Chapter 2.3.3, dispersion causes changes in signal duration and amplitude due to geometrical
changes in a waveguide. Thus in comparison to the non-dispersive SH0 mode, additional
information through arrival time and phase changes can be obtained. From this logic, it follows
then that operating in a more dispersive region of the dispersion curve (steeper slope) will yield
larger group delay and phase delay changes due to any asymmetry (defect, contact interface, etc.)
in the plate. For the gradual thinning type defect considered in this thesis, these dispersive
characteristics are desired as they will indicate a change in specimen thickness. There is also a
concern that any reflected energy due to the gradual nature of this thickness change may be small
if using a non-dispersive mode such as SH0 [46], making SH0 mode ineffective in detecting the
corrosion.
For this study an operating point is selected at the ‘knee’ of the SH1 dispersion curve (730 kHz)
for a 3 mm mild steel plate. This point is chosen to yield sufficient group delay changes for any
geometrical change in the plate, as well as to be sufficiently far from the cut-off frequency. This
will allow the SH1 mode to continue to propagate for a reasonable range of wall losses, allowing
a range of measurements to be made prior to the frequency-thickness product decreasing to
below the cut-off (Figure 2-3). Once an operating point is selected, a line is then drawn through
this point intersecting the plot origin on a phase velocity dispersion curve. The slope of this line
is equal to the dominant or peak wavelength referred to in Chapter 2.4.1. This is shown in
Figure 3-4 where the slope of the line is 6.6 mm. Also it is important to note that the dominant
wavelength line intersects the SH0 wave mode line as well. This means it can also be generated
with this wavelength at an excitation frequency equal to the frequency of the intersection point.
This implies the need for a narrowband excitation so that only the desired mode is excited.
31
Figure 3-4 - Dispersion Curve with Ideal Wavelength Excitation Line
3.5 EMAT Construction
3.5.1 PPM Array Construction
To construct the PPM EMAT’s for the selected wavelength of 6.6mm and frequency of 730 kHz,
the first step is to select a magnet thickness. Referring to Chapter 2.4, for a PPM EMAT, the
wavelength is equal to double the magnet thickness. Standard magnet sizes are less expensive,
so magnets 3.175 mm (1/8 in) thick were selected as this is close to half the desired wavelength
of 6.6 mm. Additionally the Innerspec LP-R-0.250-600kHz tuning module is selected as its
recommended frequency range is 500-800 kHz which contains the optimum SH1 excitation
frequency of 730 kHz (Figure 3-4). The accompanying coil is the Innerspec PC-LA-R-1.000-
2.000, which is dual wound in order to increase the amount of current under the static magnetic
field. As mentioned in Chapter 3.3, it is also matched in terms of impedance to the selected
tuning module. It also has approximately a one inch active area [47].
100 200 300 400 500 600 700 800 900 1000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
Frequency (kHz)
Pha
se v
elo
city
(m/s
)
SH1
SH0
Dominant WavelengthLine
Phase Velocity Curves with Possible Wavelengths
32
Figure 3-5 – Dual Racetrack Coil Configuration with Active Coil Area Indication
Eight magnets per column were used for the PPM array, based on the active area of the coil.
Thus the magnet array is epoxied together as two columns of eight magnets (Figure 2-6), with a
spacing between magnet rows of approximately 0.125 mm to give an effective wavelength of 6.6
mm.
It is noted that the final epoxied magnet array exceeds the active area of the coil slightly and
encroaches onto the curved area of the racetrack shape coil (Figure 3-5). This encroachment is
small, and any additional waves generated from the direction change of the induced eddy current
and the encroached bias field will be orders of magnitude less than what is generated from the
active portion, so the effect is ignored.
The eight magnets used in one of the PPM array columns are used in defining the spatial
bandwidth of this EMAT. As discussed in Chapter 2.4.1, the spatial bandwidth can roughly be
calculated by taking the magnitude of the spatial FFT of the magnetic field distribution from a
column of the PPM array. The field roughly takes the form of a windowed sinusoid, where the
number of periods is equal to half the number of magnets in one column of the array and a period
is equal to twice the magnet thickness. As discussed in Chapter 2.4.1, the -6dB amplitude drop
1in Active Area
PPM Array Width
Current In From Pulser
Current Out to Pulser
Coil #1 – Upper Layer
Coil #2 – Lower Layer
Current Out to Coil #2
Current In From Coil #1
33
of the FFT magnitude profile is then used to define the spatial bandwidth. The -6dB spatial
bandwidth is shown plotted on the dispersion curve in Figure 3-6 as red dashed lines. The spatial
bandwidth shows all the wavelengths that can be generated at sufficient amplitude due to a
specific PPM configuration. Therefore in Figure 3-6 all the lines that can be drawn that intersect
the origin and any point on the SH1 dispersion curve between the red dashed lines falls within
the spatial bandwidth of the transmitter-receiver pair.
The frequencies encapsulated by the -6dB dashed red lines and the desired wave mode (in this
case SH1) should be well separated in frequency from the intersection of the -6dB red dashed
lines and other wave modes (in this case SH0). This is because if a sufficiently narrowband
excitation is used (long time duration), it is possible to excite only the desired wave mode.
Alternatively, if a sufficiently narrowband excitation is not possible, having sufficient frequency
separation between the intersection of the -6dB lines and each mode allows for the undesirable
wave modes (in this case SH0) to be filtered out after being generated since they will be
contained in much different frequency bands.
In Figure 3-6, the -6dB spatial bandwidth of the transmitter-receiver pair intersects the SH0
mode at approximately 410 kHz to 560 KHz and the SH1 mode at 680 kHz to 780 kHz, with the
majority of the energy occurring at the dominant wavelength (twice the magnet thickness).
Therefore the intersection of the -6dB lines and each mode are well separated in frequency,
meaning any SH0 component that is generated can be filtered out using a simple digital filtering
algorithm in the received signal. It is important to note that often iteration is required between
selecting a desired operating point and wavelength (Chapter 3.4) and the number of magnets
(which controls the width of the spatial bandwidth) to achieve a final design.
34
Figure 3-6 - PPM EMAT Bandwidth
3.5.2 Enclosure Construction
Aluminum enclosures are designed to hold the magnet array and coil in place. These enclosures
are solid aluminum blocks with a section milled out of the bottom to allow the magnet array to
be inserted (Figure 3-7 – Left). The magnet array is then epoxied in place. The flexible coil is
then ‘wrapped’ around the base of the enclosure and bolted in place (Figure 3-7 – Right).
Figure 3-7 - Magnet Array (left) and Wrapped Flex Coil (right)
100 200 300 400 500 600 700 800 900 1000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
Frequency (kHz)
Pha
se v
elo
city
(m/s
)
SH1
SH0
Phase Velocity Curves with Spacial Bandwidth
-6dB Spacial Bandwidth
Dominant Wavelength
35
Chapter 4 Wave Propagation FE Modelling
4 Wave Propagation FE Modelling
4.1 Introduction
Analytical wave models are effective in modelling guided wave propagation in uniform
structures. However with the introduction of structural features such as defects or contact
interfaces, discrete methods are needed. Finite element modelling (FEM) is an effective tool for
modelling the interaction of guided waves with asymmetrical structural features [34].
The purpose of this section is to develop a fundamental model for guided wave propagation in a
uniform plate. This is so that structural features such as a supported section or a thinned section
can subsequently be added to determine their effect on the SH1 wave. It is also important that
the FE model be efficient so parameter iteration studies can be carried out quickly and
efficiently. Additionally the guided wave propagation modelling is done in two dimensions,
meaning that the geometry is unchanging over the plate width. This is done to reduce the
computational intensity of the model and for simplicity as the effects of the wave ‘spreading’
around any geometrical features will be neglected.
4.2 Brief Evaluation on Wave Propagation FE Techniques
As seen in Chapter 2.8, guided wave finite element modelling can be done either in the
frequency domain or the time domain (explicit). In this thesis, frequency domain simulations
are pursued as they are more efficient and align more closely with the stated objectives of the
model. This is because ‘time marching’ through the large number of time steps (thus solving for
the large number of nodal displacements at each time step) is computationally intensive, and can
be avoided with a frequency domain model. In the frequency domain model all that is required
is a frequency sweep over the signal band of interest. Since EMAT’s are narrowband, this
amounts to a much shorter simulation time.
36
4.3 Infinite Domains
One other significant advantage of frequency domain simulations is that there are a variety of
well-understood ways to simulate an infinite domain. Simulating an infinite domain removes
unwanted reflections that occur from the boundaries of a finite domain. Often in time domain
simulations, the simulation domain must be enlarged so that any reflections are well separated
from the signal of interest (Alternating Layers with Increasing Damping (ALID) may also be
used, see [37] or [34] but will not be discussed further in this thesis). Lengthening the simulation
domain is undesirable as it increases the number of elements and the time of simulation.
One computationally efficient technique to simulate an infinite domain that is readily
implementable in the frequency domain is using ‘Perfectly Matched Layers’ or PML’s. PML’s
are absorbing domains that may be added to the extremities of the simulation domain (Figure
4-1).
Figure 4-1 - Schematic of PML Domain Layout
At the boundary between the PML layer and the simulation domain, the impedance is perfectly
matched, thus there should be no reflection of the incident wave. The damping in the PML
domain then increases exponentially until the wave reaches the end of the PML domain where it
reflects. By the time the wave re-enters the simulation domain it should be almost totally
attenuated [34].
One of the challenges in implementing a PML is proper selection of the layer parameters.
Parameters such as the absorption rate and length of the PML domain should be optimized to
successfully damp out the wave, while minimally contributing to the computational intensity of
the model. This is addressed by Mikael Drozdz in [34], where analytical relations for the various
PML Domain PML Domain Simulation
Domain (Plate)
Generate Wave Receive Wave
37
layer parameters were devised. These relations are used in defining the PML parameters in this
thesis.
In keeping with the notation and technique in [34] but adapting for the form of the SH wave
equation shown in (14), the change of axis variable z would be:
Where the z-direction is as shown in Figure 2-2 and αz is a variable that controls the level of
dissipation in the PML. Alternatively (and also much simpler), this can be viewed as replacing
all the partial derivatives with respect to the direction of propagation (z-direction) with the
following expression.
Where αz is defined as:
��%�( = ���E (30)
Here p is the attenuation parameter and is taken to be at least 2 for continuity (details in [34]).
The parameter Az used in defining αz is defined as:
�� = −0.5B X + 1O{M��Q�E�dD �� F10����9� G (31)
Where kmax is the maximum wavenumber, Lor is the shortest wavelength and RCdB is the
acceptance criterion for the reflected wave. In [34] the acceptance criterion is taken to be a
99.99% reduction of the incident wave or -60dB. The length of the PML region is then defined
as:
� → �%1 + -��( (28)
SS� → % 11 + -��( SS� (29)
38
���= = �Q� FO{M�O{"TGdE�d
(32)
With kmin being the minimum wavenumber. One word of caution on PML’s is that evanescent
waves are not correctly dealt with, so it is necessary that the PML be located a sufficient distance
away from any feature that can produce evanescent waves, such as defects or excitation sources.
This is because since evanescent waves decay on their own as a function of distance from the
feature that produced them, so locating the PML sufficiently far away allows these waves to
decay naturally prior to entering the PML. This distance is given as:
�N = −F 12O��{"TG �� F10����9� G (33)
Where k’’
min is the smallest evanescent wavenumber in the signal bandwidth.
4.4 Generation and Reception of Waveforms
In order to simulate the generation and reception of waves by the transmitter and receiver PPM
EMAT’s in a 2D wave propagation model, the following procedure is implemented.
4.4.1 Generation
To simulate the generation of the SH wave, first the FFT of a Hanning windowed 5-cycle 730
kHz excitation pulse is computed (Figure 4-2). This is analogous to the excitation current. The
resulting frequency transform is then multiplied with a spatially dependent windowed sinusoidal
function. This function is analogous to the PPM magnetic field. For the eight-magnets-per-
column PPM EMAT’s described in Chapter 3.5.1, the magnetic field profile must have four
complete cycles.
As can be seen in Figure 4-2, the majority of the signal energy is between approximately 500
kHz and 900 kHz, so the frequency sweep in the FE model will be conducted in this frequency
range.
39
Figure 4-2 - FFT of Hanning Windowed Input
4.4.2 Reception
The reception process essentially works in the reverse of transmission. In the frequency domain
the FE simulation yields a series of frequency-dependant nodal displacements. To convert this to
a time dependant amplitude, the IFFT of the frequency dependant results must be computed to
obtain time dependant nodal displacements. Then as shown in [48], the induced electric field
can be calculated as:
� = S1S: �� (34)
Where u is the particle velocity and B is the magnetic field density. Thus to simulate the
reception process for an EMAT in this 2D model, the time dependent nodal displacements at a
specified receiver location are now differentiated with respect to time. The resulting particle
velocities are then multiplied with the same spatially dependent windowed sinusoidal waveform
representing the magnetic field as used for the transmitter. The resulting signal is then integrated
over the length of the receiving EMAT’s active area. This is because all nodes that compose the
representative spatially dependent windowed sinusoid contribute to the induced electric field. If
2 4 6 8 10 12
x 105
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
Norm
alized A
mplitu
de
FFT of 5-cycle Sinusoid
40
the voltage signal is required, multiplication by the appropriate constants will yield the time
dependant voltage signal.
4.4.3 Discussion
It is noted that as seen in [6], the PPM field is largest at the ends of the two columns of magnets
and therefore not exactly in the shape of a rectangular windowed sinusoid. However since the
results will always be taken relative to a simulation on a homogenous, unsupported and
undamaged plate, this effect will be negligible. Specifically results will be computed as a
relative amplitude and time delay relative to a homogenous plate simulation with the same
reception and generation procedures. This should cancel any amplitude effects and any effects
on the computation of the spatial bandwidth (Chapter 2.4.1) will be small.
4.5 COMSOL 4.3b Implementation
Since the structural mechanics module in COMSOL 4.3b does not allow for boundary conditions
on out-of-plane displacements, the “Wave-equation Physics” of the “Mathematics PDE module”
is used and is governed by the following equation:
�M S9)S:9 + �⦁%−<�)( = � (35)
Where ea is labelled as the mass coefficient, c labelled as the diffusion coefficient and f is the
source term. The techniques mentioned in Chapter 4.3 to implement the PML domains were
adapted for implementation into the COMSOL PDE interface. The implementation is described
below.
First to formulate (35) as the standard SH wave equation shown in (15) but in the frequency
domain, the ea coefficient is set to zero, f is set to ρω2u and c is set to isotropic and equal to
ρcs2,where ρ is the plate density and cs is the shear speed in steel. Next, to aid in the following
discussions a parameter Sz is defined as the coefficient on the right side of (29) and shown below
[34]:
41
To implement the PML’s using the allowable inputs (ea, c and f) to (35), the c parameter is now
changed to anisotropic to implement the change of variable in the direction of wave propagation
shown in (29), and the original value of the f parameter (ρω2u) is divided by Sz. The final result
is shown below:
�⦁%−<�)( = � 9)��
< = ��<N9�� 00 �<N9�� �
(37)
Thus as shown in Figure 4-1 the FE model consists of a propagation domain with a PML domain
attached on each end. It is important that Sz be equal to 1 in the propagation domain, so the
governing equation in (37) will simplify to (35), as the PML should have no effect in this
domain. Then in the PML domains Sz varies according to the relationships given in Chapter 4.3.
This is implemented through a piece-wise function.
A simulation result is shown in Figure 4-3 for the case of a 30 cm distance between the
generation and reception locations for a 3mm thick steel sheet. Since this result is computed on
an isotropic homogeneous plate, the maximum amplitude of this result is used to normalize
future simulations and the arrival time is used to compute the pulse arrival delay of future
simulations. The result is displayed in Figure 4-3 normalized by its peak amplitude. In this
simulation, the input excitation is shown in Figure 4-2 and the windowed sinusoidal spatial
distribution of the magnetic field has a period of 6.6 mm. The generation and reception
processes of the SH1 waveform were as discussed in Chapter 4.4.1 and Chapter 4.4.2
respectively. Parameters used for carbon steel were a shear speed of 3230 m/s and density of
7800 kg/m3. The required wavelength and wavenumber values for determining the PML domain
�� = 11 + -�� (36)
42
parameters were calculated using the input frequency band of 500kHz to 900kHz and the
dispersion curves of Figure 2-3 and Figure 2-4.
Figure 4-3 – Normalized SH1 Voltage Waveform at Receiver Location
To verify the presence of the SH1 mode, the group velocity of this received waveform is
calculated by computing the arrival time of the waveform in Figure 4-3 (30 cm transducer
separation), then computing the arrival time of a similar simulation but with a transducer
separation of 25cm. The group velocity is then computed as the difference in separation distance
divided by the difference in arrival time. The resulting group velocity is approximately 2172 m/s
which compares well to the group velocity shown on the dispersion curve in Figure 2-3 for a 730
kHz excitation (2180 m/s). The small discrepancy is likely due to the approximations made in
the generation and reception mechanisms in the FE model.
Overall, in this chapter the generation, propagation and reception of the SH1 wave mode on a
homogeneous isotropic plate is discussed. This is done to compute a ‘baseline’ result for
comparison in subsequent chapters where geometrical effects such as support interfaces and
corrosion type defects are introduced to the FE model.
0 0.5 1 1.5 2 2.5
x 10-4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Norm
alize
d A
mp
litu
de
Time (s)
Normalized SH1 Waveform 30cm from Excitation
43
Chapter 5 Support Investigation
5 Support Investigation
5.1 Introduction
The purpose of this chapter is to determine the effect of a contact interface on the SH1 mode of
propagation. To do this a finite element model is developed. The finite element model is
implemented as a modification to the foundational model developed in Chapter 4. The FE model
is then experimentally validated within a practical load range by comparing the experimental
results to the theoretical FE results.
5.2 FE Modelling of Contact Interfaces
To construct the FE model, a similar approach is adopted to that used in [49] for Lamb waves,
but adapted for SH wave propagation. As mentioned in Chapter 2.6, the contact interface can be
represented by an interfacial stiffness parameter connecting two surfaces. The modelling of the
interfacial stiffness is implemented as shown in [49] as a displacement discontinuity between
two domains, with the boundary force per unit area on the plate and support surface equal to:
hE = fA%)N−)E( hN = fA%)E−)N(
(38)
Where σs and σp are the force per unit area on the support and plate domains respectively, KT is
the stiffness parameter (N/m3) and us and up are the displacements of the support and plate
domain nodes respectively. Thus an additional domain is introduced into the FE model
developed in Chapter 4 to represent the steel support, and is shown in Figure 5-1. The boundary
interface between the plate and support is then configured using (38) with the interfacial stiffness
parameter assumed to be real-valued (no damping/losses). This interfacial stiffness parameter is
treated as the dependant variable in the study, and a range of values is assessed using a frequency
sweep over the signal bandwidth at a given support length. The support length is defined as the
length of the contact boundary in 2D between the support and plate domains (shown in red in
Figure 5-1). All other parameters were the same as indicated in Chapter 4.
44
Figure 5-1 - Schematic of FE Contact Interface Model
The amplitude of the received signal is calculated as the peak of the Hilbert transform magnitude
function, while the arrival time is calculated as the time at which this peak value occurs. Then as
mentioned in Chapter 4, all results in this thesis are reported relative to the homogeneous plate
base case computed in Chapter 4.5. Thus the delay time is the arrival time difference between a
given support simulation case and the homogeneous plate case, and the relative amplitude is the
amplitude of the support simulation case divided by the peak amplitude of the homogeneous
case. The results of varying the contact stiffness at a given support length on the amplitude and
arrival time of the received SH1 signal are shown in Figure 5-2 and Figure 5-3 respectively. In
these figures, the data points are connected with dashed lines to better emphasize the trend
between support lengths.
Considering the formulations (23) and (24), the effect of varying the stiffness for a given support
length is equivalent to varying the applied load at this support length. Also, the effect of
changing the support length between runs is equivalent to changing the nominal area of contact.
The reason we approached the simulations with this methodology is that it allows for the effect
of increasing the stiffness and the effect of applying a given stiffness over a larger portion of the
wave propagation path to be independently analyzed.
PML
Domain
PML
Domain
Support
Domain
Simulation
Domain (Plate)
Elastic Boundary
45
Figure 5-2 - FE Model Received Signal Relative Amplitude vs. Interfacial Stiffness
Figure 5-3 - FE Model Received Signal Delay Time vs. Interfacial Stiffness
106
108
1010
1012
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Stiffness per unit area (N/m3)
Rela
tive
Am
plit
ud
e
Relative Amplitude vs. Stiffness per Unit Area
3" Support
4" Support
6" Support
106
108
1010
1012
0
1
2
3
4
5
6x 10
-6
Stiffness per unit area (N/m3)
Dela
y (
s)
Delay vs. Stiffness per Unit Area
3" Support
4" Support
6" Support
46
As can be seen from the results, increasing the stiffness per unit area has a minimal effect on the
amplitude and delay of the received wave until a critical value is reached, which we will refer to
as the ‘knee’. After this ‘knee’ is exceeded, there are large relative amplitude decreases and
delay time increases. Another observation is that the support length has a minimal effect on the
‘knee’ location, as changes in amplitude and arrival time start occurring at approximately the
same stiffness per unit area regardless of the support length. However once the stiffness per unit
area exceeds this ‘knee’ value, increasing the support length will increase both the slope of the
amplitude drop and the slope of delay increase. Based on these observations, it can be seen that
the main factor affecting the SH1 propagation is the stiffness per unit area parameter and not the
length of the support. An analogous conclusion is reached in [37] regarding the change of the
transition point of the reflection coefficient with support length.
5.3 Experimental Verification
5.3.1 Introduction
The purpose of this section is to experimentally verify the results of the FE simulation in Chapter
5.2. To do this an experimental arrangement is constructed to represent a contact interface
between a plate and a steel bar. As indicated in Chapter 1, since this situation is supposed to be a
simplified representation of a pipe in contact with a support, the experimental load range
considered is kept within a range that would be expected on a pipe support. As a starting point
for this range we used the ASME guidelines for support spacing and then calculated what the
load would be due to a section of this length. Using the guidelines for a ¼” thick empty pipe it is
found the expected load would be of the order of 1000N. For experimental purposes a range of 0
to approximately 6000N is used in order to account for extreme cases as well as obtain a better
understanding of the situation.
5.3.2 Experimental Set-up
The experiments were conducted on a 3mm thick, 0.356 m wide and 1.22 m long mild carbon
steel plate. To minimize reflections from the plate edges as well as properly support the plate, the
plate is supported at the edges by pieces of foam. The central region or ‘load region’ as seen in
Figure 5-4 consists of the plate resting on a steel bar running the width of the plate (into the
page). A photograph of this arrangement can be seen in Figure 5-5. This steel bar is then raised
47
and rests on steel blocks to allow for the clamps to fit underneath the arrangement. The location
of the clamps can be seen in the cross section of the ‘load region’ in Figure 5-6.
Since the plate is relatively thin (3mm), this support ‘structure’ must be rigid to mitigate any
effects due to plate bending when clamped on the received waveform. The ‘support’ is then
centered between the transmitter and receiver which are separated by 30cm.
Figure 5-4 - Schematic of Setup
Figure 5-5 - Picture of the Steel Bar Supported Clamp Region
Steel Bar Steel block
Receiver Transmitter
Wood
Foam
Plate
Load Region
48
5.3.3 Load Application
In this sub-section the plate loading mechanism is described. The load cells2 used for this
application have a load range of 0-1000 kg each and come with readily implementable interfaces
for a variety of software programs. Interfacing is done with a bridge controller/amplifier which
interfaces the load cells with a computer USB input. Full details can be found in [50]. To apply
the load, the configuration shown in Figure 5-6 is used. First a wooden bar is placed across the
top of the plate with a thin piece of steel on top to form a ‘sandwich’. The load cells are then
placed across this piece of steel. This is to prevent the load cells from ‘digging’ into the wood
when loaded. Finally another steel bar is placed on top of the load cells to help distribute the load
and the entire arrangement is clamped with a series of large C-clamps. Care is taken to ensure
the load cells all read the same load to ensure even load distribution before data is taken at each
load step.
Figure 5-6 - Support ‘Load Region’ Configuration
5.3.4 Results
As mentioned in Chapter 5.3.1, the force range considered in these experiments is 0N–6000N
applied through a series of C-clamps on the support area shown in Figure 5-6. To align with the
FE results, 3”, 4” and 6” support lengths were considered. Thus an experimental run consisted
of ‘stepping’ through the force range at a given support length. This is then repeated for all
support lengths considered. The results are shown in Figure 5-7 and Figure 5-8. The relative
2 Phidgets Inc, Calgary Alberta
Clamp Here
Steel Support 3mm Steel Plate
Wood
Steel Bars Load Cells
49
amplitude and delay are calculated relative to a measurement on the unloaded plate at 30cm
transducer separation.
Figure 5-7 - Experimental Received Signal Relative Amplitude vs. Applied Load
0 1000 2000 3000 4000 5000 6000
0.94
0.96
0.98
1
1.02
1.04
1.06
Normal Force (N)
Rela
tive
Am
plit
ude
Relative Amplitude vs. Applied Normal Load
3" Support Length
4" Support Length
6" Support Length
50
Figure 5-8 - Experimental Received Signal Time Delay vs. Applied Load
As can be seen in Figure 5-7 and Figure 5-8, within the load range achievable with our
experimental system, there is no significant effect of applied load on the amplitude or arrival
time of the received pulse. Also for the load range considered, there is no significant effect due
to the support length on the amplitude and pulse arrival delay. These results are consistent with
the FE results in Chapter 5.2, if it can be shown that the experimental conditions (applied force,
nominal area, etc.) lead to a stiffness per unit area (N/m3) that is less than the transition point
(‘knee’) of the curves shown in Figure 5-2 and Figure 5-3. The transition point is where sharp
changes in amplitude and arrival time begin to occur (approx. 1012
N/m3).
Our method for relating the force applied experimentally on a support, to a support “stiffness”
value in the finite element formulation is based on the theory presented in Chapter 2.6; it also
draws on the techniques from tribology studies developed for rough surface contact. Using the
simplified Greenwood-Williamson method shown in [21], the theoretical stiffness values can be
estimated from the experimental load range, but this requires the standard deviation of the
surface roughness profile as an input. However as indicated in [21], this can be approximated as
the average roughness (Ra). This average roughness parameter is usually obtained using
0 1000 2000 3000 4000 5000 6000-3
-2
-1
0
1
2
3x 10
-6
6" Support Length
4" Support Length
3" Support Length
Normal Force (N)
Dela
y (
s)
Group Arrival Delay vs. Applied Normal Load
51
measurements from a profilometer in tribological studies, but this is not done in this project.
Instead, tabulated values for common commercial steels are used as estimated values.
As mentioned in Chapter 2.6, The Greenwood-Williamson theory is based on a configuration of
an equivalent rough surface pressed into a smooth plane. Therefore, the equivalent roughness of
this surface needs to be determined in order to use (23). This is done as shown in [21] by
combining the average roughness of the plate and support bar as��ME9 + �M�9 to give the
equivalent roughness. The roughness of the steel bar is approximated as 2 µm, which according
to [51] is the measured roughness for a commonly purchased hot rolled steel grade without
excessive scaling build up. For a steel plate with a matte finish, the roughness is estimated to be
around 1.2 µm [52], which also aligns well with the data given in [21] [30]. Thus the calculated
equivalent average roughness is 2.33 µm.
Now using (23) and (24) the tangential contact stiffness per unit area can be determined by using
the experimental load values and nominal contact areas. This means that the experimental data
can now be expressed as a function of contact stiffness per unit area as opposed to load.
Therefore these results can now be superimposed onto the FE results shown in Figure 5-2 and
Figure 5-3. This is shown in Figure 5-9 and Figure 5-10, where the experimental results are
indicated with a ‘*’.
52
Figure 5-9 - FE and Experimental Received Signal Relative Amplitude vs. Stiffness/Area
Figure 5-10 - FE and Experimental Received Signal Delay vs. Stiffness/Area
106
108
1010
1012
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Stiffness per unit area (N/m3)
Rela
tive
Am
plit
ud
e
Experimental and Theoretical Amplitude Results
3" Support
4" Support
6" Support
106
108
1010
1012
-1
0
1
2
3
4
5
6x 10
-6
Stiffness per unit area (N/m3)
Dela
y (
s)
Experimental and Theoretical Arrival Delay Results
3" Support
4" Support
6" Support
53
Considering (23) and (24), it is seen that the maximum contact stiffness per unit area attained
using the experimental conditions is close to 1.85x1011
N/m3 for the case with the 3” support
length’s nominal contact area and a 5900N load. Looking at Figure 5-9 it is seen that the curve
‘knee’, does not occur until approximately 1012
N/m3, meaning that the largest experimental
stiffness per unit area considered is approximately an order of magnitude less than what is
required to cause significant measureable changes in the received signal. There is therefore no
discrepancy between experimental and FE results, although there is an insufficient range of
experimental data to properly validate the finite element model.
The average roughness estimate used for the steel bar (2 µm) is likely low, as hot-rolling is
known to produce relatively rough surfaces compared to other manufacturing processes. This is
discussed in [51] where the effects of rolling parameters are shown on the steel roughness values
and oxide build-up. If a larger roughness value is used in (23) to calculate the support stiffness,
the maximum stiffness of the experimental system would be even less than indicated in Figure
5-9 and Figure 5-10. This would have the effect of shifting the experimental data points further
to the left. This further supports our conclusion that within the considered range of experimental
load parameters, there is no significant effect on the SH1 wave propagation due to the contact
interface.
One final note is that in Figure 5-8 there are oscillations in the delay measurements between runs
at different support lengths. However a preliminary analysis indicates that these oscillations are
on the same order of magnitude as the oscillations between runs when holding the support length
constant, and thus are not likely to be an effect of the support length. Also referring to Figure
5-10, at the stiffness ranges predicted using the experimental conditions there should be no
observable effect due to support length on the SH1 mode. Therefore due to the time consuming
nature of these experiments and the very small amplitudes of these oscillations, this effect was
not investigated any further at this time. However some possible sources include oscillations in
the equipment ground or electromagnetic coupling between the EMAT’s.
5.3.5 Contact Damping
As indicated in Chapter 2.6.3, energy loss due to tangential loading at a contact interface may be
modelled as hysteretic damping. This is formulated mathematically as a loss factor (η) shown in
(25). This loss factor is implemented into the FE model by changing KT parameter shown in
54
(38), to the form of KT(1+iη). The stiffness value used in the computation of Figure 5-2, Figure
5-3, Figure 5-9 and Figure 5-10 is the real component of KT(1+iη), obtained by assuming η = 0
(no damping) as is typical in these types of contact problems.
However in this section a brief analysis is conducted on the effects of a non-zero damping factor
(η). To do this, a similar parameter sweep FE study as described in Chapter 5.2 is conducted for
the 3” support case. The real tangential stiffness component is set to 1.85 x 1011
N/m3, which is
the maximum value obtained with the experimental conditions. The imaginary component of the
contact stiffness is then treated as a parameter, simulating the effect of changing the loss factor
(η) in KT(1+iη). Thus the maximum value for the imaginary contact stiffness per unit area is the
value of KT, as the loss factor should not be greater than 1. The results for received signal
amplitude and arrival time are shown in Figure 5-11 and Figure 5-12.
Figure 5-11 - FE Model Relative Amplitude vs. Imaginary Stiffness per unit area for 3”
Support
106
107
108
109
1010
1011
0.95
0.96
0.97
0.98
0.99
1
1.01
Imaginary Stiffness per unit area (N/m3)
Rela
tive
Am
plit
ud
e
3" Support Length
Relative Amplitude vs. Imaginary Stiffness per unit area
55
Figure 5-12 - FE Model Arrival Delay vs. Imaginary Stiffness per unit area for 3” Support
As can be seen in Figure 5-11, with a fixed real stiffness component of 1.85 x 1011
N/m3, a
‘knee’ occurs at an imaginary stiffness (iηKT) value of approximately 1010
N/m3, after which
larger decreases in amplitude occur. This indicates that decreases in the SH1 signal amplitude
can be present at KT values prior to the ‘knee’ in Figure 5-2, if a sufficient imaginary stiffness is
also present (through a sufficiently large loss factor). Additionally when comparing the plots of
Figure 5-3 and Figure 5-12, there are no observable effect in terms of pulse arrival time due to
the imaginary stiffness. This indicates the primary effect of the imaginary stiffness and
hysteretic damping is an amplitude decrease at the receiver position once iηKT exceeds the ‘knee’
value.
There is a great deal of difficulty in estimating a loss factor based on our experimental set-up
without direct measurement ofη. When deriving the tangential stiffness per unit area (KT) value
in Chapter 2.6.2, a no-slip assumption is used, resulting in a linear tangential stiffness per unit
area vs. applied load relationship [27]. However, the next step of deriving a loss factor from the
tangential stiffness requires that micro-slip be present [29]. These two contradictory assumptions
106
107
108
109
1010
1011
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10
-8
Imaginary Stiffness per unit area (N/m3)
Dela
y(s
)
Arrival Delay vs. Imaginary Stiffness per unit area
3" Support Length
56
cannot be resolved to produce a convenient mechanism to compute the complex stiffness per unit
area KT(1+iη).
Non-linear contact stiffness values for micro-slip cases have been investigated ( [29] or [30]), but
not considered in this thesis as they require additional statistical roughness parameters that are
not available here. The linear stiffness that is used here is also commonly used in other sources
such as [27], [26] and [21]. This issue is deemed to be not serious, as our experiments yielded no
amplitude decrease as a function of load or stiffness (Figure 5-2 and Figure 5-9 ). This implies
that the experimental results must lie to the left of the ‘knee’ in Figure 5-11 and that damping
from the support mechanism does not impact our results. It also agrees with other studies
considering pipe supports [37] and contact interfaces [26] which have deemed damping
negligible.
57
Chapter 6 Defect Investigation
6 Defect Investigation
6.1 The Introduction
The purpose of this chapter is to develop an experimentally verified 2D finite element model of
wave propagation in a plate or pipe with a gradual wall loss type defect. This defect type is
selected so as to emphasize the dispersive attributes of the SH1 mode. The FE model is
constructed by modifying the FE model described in Chapter 4 by introducing a wall thinning
type defect to the simulation domain. The defect is constructed with parameterized dimensions
so that the effects on the SH1 mode can be evaluated as a function of these dimensions. Finally,
this model is experimentally validated through three defect ‘test cases’ machined into three mild
steel plates.
6.2 FE Modelling of Wall Loss Defects
To develop the FE model for the gradual thinning/wall loss defect, a domain containing the
defect geometry is created in COMSOL 4.3b and added to the center of the simulation domain
described in Chapter 4. Since a primary objective of this thesis is the detection of hidden
corrosion at pipe supports, the total length of the defect is kept less than the smallest support
width discussed in Chapter 5 (3 inches). No external loads to represent a pipe support are
considered in this chapter.
The schematic of the gradual thinning type geometry considered is shown in Figure 6-1. This
defect type is very similar to the one discussed in [46], but additional dimensions are
parameterized and the minimum plate wall thickness remaining after corrosion is not restricted to
being below the SH1 cut-off limit. Specifically in [46] only the slope of the defect on either side
of the flat section is evaluated as a parameter. In this work the slope is not explicitly evaluated
as a parameter, but instead more concern is placed on evaluating the effects of the length of the
defect features (A, B and C in Figure 6-1) on the received signal prior to the defect length
exceeding the support length (At that point, the defect could be detected visually and guided
wave identification is not necessary). It is noted that by changing the defect parameters A, B,
58
and C shown in Figure 6-1 the slope changes as well and thus the result reported in [46] will be
considered.
In Figure 6-1, the parameter A refers to the length of the sloped regions, B is the depth and C is
the length of the central flat portion. This defect domain is then simply added into the FE model
described in Chapter 4 at the center of the existing simulation domain. For the simulation runs,
the ultrasonic wave is generated 12.5 cm from the center of the defect and received 12.5cm from
the center of the defect on the other side. All other simulation parameters are kept the same as
discussed in Chapter 4 when no defect is present.
Figure 6-1 - Schematic of defect cross section
To verify the model’s functionality, simulations were conducted by varying the A, B or C length
parameter while keeping the other two constant at a set value. Results in Figure 6-2 and Figure
6-3 are displayed in terms of arrival time and amplitude relative to the uniform plate case result
discussed in Chapter 4, but with a 25 cm separation between the center of the wave generation
and reception regions (as opposed to the 30 cm used in that chapter). The reference dimensions
used are: A = 1.8 cm, B = 0.31 mm, and C = 1.4 cm.
Wave Propagation
A
C
B
59
Figure 6-2 - Received Signal Amplitude vs. Defect Feature Length
Figure 6-3 - Received Signal Arrival Time vs. Defect Feature Length
The lengths of the ‘flat’ and ‘sloped’ regions of the defect corresponding to Figure 6-2 and
Figure 6-3 are evaluated with a remaining wall thickness well above the value that causes the
frequency-thickness product to cut off for the SH1 mode (see Figure 2-3). For future discussions
in this section, it is seen in Figure 2-3 that once the frequency-thickness product drops below the
1.6 1.8 20.958
0.959
0.96
0.961
0.962
0.963
0.964
0.965
0.966
Sloped Section Length (cm)
Rela
tive
Am
plit
ud
e
(A) Parameter
0.1 0.2 0.3 0.4 0.50.88
0.9
0.92
0.94
0.96
0.98
1
Depth (mm)
Rela
tive
Am
plit
ud
e
(B) Parameter
1.2 1.4 1.60.957
0.958
0.959
0.96
0.961
0.962
0.963
0.964
0.965
0.966
0.967
Flat Section Length (cm)
Rela
tive
Am
plit
ud
e
(C) Parameter
1.6 1.8 22.5
2.55
2.6
2.65
2.7
2.75
2.8
2.85x 10
-6
Sloped Section Length (cm)
Dela
y(s
)
(A) Parameter
0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6
7x 10
-6
Depth (mm)
Dela
y (
s)
(B) Parameter
1.2 1.4 1.62.45
2.5
2.55
2.6
2.65
2.7
2.75
2.8
2.85x 10
-6
Flat Section Length (cm)
Dela
y (
s)
(C) Parameter
60
cut-off limit, the SH1 mode cannot propagate. Since the excitation frequency is not varied, this
leads to the existence of a cut-off specimen thickness. The thickness that causes the mode to cut-
off will now be referred to as the cut-off thickness.
From Figure 6-2 and Figure 6-3, the following can be observed:
1) The defect depth (B) has a much greater effect on the amplitude and arrival time than
either A or C.
Increasing the depth (B) of the defect significantly decreases the amplitude and increases the
measured delay of the received SH1 signal. Also the scale of the amplitude and delay time effect
from changing the depth (B) is significantly greater in magnitude than the effect due to changing
either the A or C parameters. This is expected since the operating point is selected as being in
the highly dispersive region of the SH1 dispersion curve. For example, changing the depth from
roughly 0 to 0.4mm results in approximately a 10% amplitude change, while changing the A or
C parameter by 4mm only results in a 0.6% and 0.8% amplitude decrease respectively.
2) Increasing the flat section length (C) increases the SH1 arrival time and decreases its
amplitude linearly
As the length of the flat section increases, the arrival time also increases since the ‘thinned’
section becomes a greater percentage of the propagation path (the group velocity is lower in
thinner regions). The amplitude decreases since the SH1 mode is dispersive and spreads out over
time and space (Chapter 2.3.3), leading to a corresponding amplitude decrease to maintain
energy conservation. Thus as the wave is passing through a thinned section (which significantly
increases the dispersion) different frequencies are travelling at much different speeds (or
spreading out) leading to an amplitude decrease at the receiver position. These effects on the
received waveform are linked to the percentage of the propagation path that is ‘thinned’, leading
to the linear trend.
3) Increasing the slope run (A) increases the SH1 arrival time and decreases its amplitude.
The slope run plays a significant role on the received waveform as well. Considering the
parameterization in Figure 6-1, both the A and B parameters will dictate the slope. However
since the effect of the defect depth (B) is so dominant on the dispersion characteristics, it should
61
be set first in any modelling runs. Then the A parameter can be adjusted to yield the desired
defect slope. In [46], it is shown how the SH1 mode’s instantaneous group velocity decreases as
the pulse moves down the sloped section as the specimen is getting thinner; the group velocity
reaches its minimum value once the flat section is reached. In [46], this process is referred to as
“wave number modification with slope”, as the wavenumber is a function of thickness shown
mathematically in (16).
It is also noted that there is also a small amount of energy converted to the SH0 mode, but it
contributes little to the received waveform [40]. One other very important point as shown in
[46], is that the slope plays a large role in the reflection and transmission characteristics for this
defect type, especially when the remaining thickness is below the cut-off thickness. This will be
discussed in much more depth in Chapter 6.4.1.
6.3 Experimental Validation
The defects shown schematically in Figure 6-1 were machined across the entire width of the mild
carbon steel plates to correlate with the two-dimensional FE model. Each plate had one defect
machined into it, and the dimensions of the plate were those specified in Chapter 5.3. Due to the
importance of the exact plate thickness on the ultrasonic measurements, the thickness is
measured for each plate and listed in Table 6-1.
The experiment is set up in a similar configuration to that used for the support experiments
described in Chapter 5, with foam supports under each end of the plate but no support structure
in the middle. Since the three test cases were designed to validate the 2D FE model, three
different geometries where machined by varying the A, B and C defect parameters. After
machining, the defect features were measured as shown in Table 6-1:
62
A B C Thickness
(mm)
Specimen #1 1.80 cm 0.31 mm 1.40 cm 3.00
Specimen #2 1.80 cm 0.76 mm 1.10 cm 2.95
Specimen #3 1.70 cm 0.72 mm 1.85 cm 2.90
Table 6-1 - Measured Defect Dimensions
The transmitter and receiver EMAT’s are then placed on opposite sides of the defect, which is
centered between them. The transducer and receiver are separated by 25 cm corresponding to
the separation distance in the FE model. The received signal amplitudes and arrival times are
calculated relative to measurements taken with the transducers separated by 25 cm on an
undamaged section of each plate. The relative amplitude and arrival times are calculated using
the peak of the Hilbert transform on the received waveforms and shown in Table 6-2.
Relative Amplitude (%) Delay (µs)
Specimen #1 97.87 2.14
Specimen #2 39.99 14.49
Specimen #3 36.51 22.40
Table 6-2 – Relative Amplitude and Delay Data for Experimental Test Specimens
6.4 Analysis
6.4.1 Verification of Model
To properly verify the 2D FE model of the defect, the measured dimensions (A, B and C
parameters) from the experimental test cases were input into the model. The resulting
waveforms for the three test cases are shown in Figure 6-4 to Figure 6-6. The waveforms have
had their amplitude normalized using the maximum amplitude of the uniform plate case and have
63
been time shifted by the arrival time of the uniform plate case allowing for an easier comparison
to be made between the FE and experimental results.
Figure 6-4 – Specimen #1 - FE results Verification
-1 -0.5 0 0.5 1 1.5
x 10-4
-1
-0.5
0
0.5
1
time (s)
Norm
alize
d A
mp
litu
de
Experimental Specimen #1
-1 -0.5 0 0.5 1 1.5
x 10-4
-1
-0.5
0
0.5
1
FE Specimen #1
time (s)
Norm
alized A
mp
litu
de
-1 -0.5 0 0.5 1 1.5
x 10-4
-1
-0.5
0
0.5
1
time (s)
Norm
alize
d A
mp
litu
de
Experimental Specimen #2
-1 -0.5 0 0.5 1 1.5
x 10-4
-1
-0.5
0
0.5
1
FE Specimen #2
time (s)
Norm
alized A
mp
litu
de
64
Figure 6-5 - Specimen #2 - FE results Verification
Figure 6-6 - Specimen #3 - FE results Verification
The measured arrival time and amplitudes are shown in the table below. Additionally the
difference between the experimental results and the FE case is computed and shown in the table
as well.
Relative Amplitude (%) Delay (µs) Difference
Specimen
#
FE Experimental FE Experimental Amplitude
(%)
Delay
(µs)
1 98.02 97.87 2.65 2.14 0.15 0.510
2 40.33 39.99 15.07 14.49 0.34 0.129
3 36.26 36.51 22.53 22.40 0.22 0.125
Table 6-3 - FE Results of Test Cases
-1 -0.5 0 0.5 1 1.5
x 10-4
-1
-0.5
0
0.5
1
FE Specimen #3
time (s)
Norm
alized A
mp
litu
de
-1 -0.5 0 0.5 1 1.5
x 10-4
-1
-0.5
0
0.5
1
time (s)
Norm
alize
d A
mp
litu
de
Experimental Specimen #3
65
Considering the defect measurements in Table 6-1 and the dispersion curves shown in Figure
2-3, it is seen that the remaining plate thickness in the defect area of Specimen #1 leads to a
frequency-thickness product above the cut-off for a 730 kHz excitation. The effects of the A, B
and C parameters on the resulting waveform were discussed in Chapter 6.2, and illustrated in
Figure 6-2 and Figure 6-3.
The remaining plate thickness in the defect region for Specimen #2 and #3 is below the cut-off
for a 730kHz excitation. This means the SH1 mode cannot propagate. This situation is analyzed
in [46] and it is shown that the relative amounts of energy transmission and reflection are highly
dependent on the defect slope. Specifically, if the slope is sufficiently shallow (5° is the
minimum evaluated in [46]), then the SH1 mode will be almost completely reflected with
little/no propagation through the defect region. Alternatively, if the change is abrupt (steep
slope), then most of the SH1 mode energy will convert into the SH0 mode and be transmitted
through the defect region, and back to SH1 upon leaving; a small proportion of the original
SH1energy will be reflected back from the defect as a SH1 wave due to the geometry change.
This causes the measured group velocity of the SH1 mode at the receiver to increase (or arrival
time to decrease) due to the mode conversion to relatively fast SH0 in the defect region. The
effect of the flat section length of length C is not considered in [46], but should not affect the
relative proportion of reflected and transmitted energy.
Since the slopes considered in this study were less than the 5 degree value used in [46] the SH1
wave should be reflected from the defect region, with negligible energy transmission to the far
side of the defect. However the results for Specimen #2 and #3 (Table 6-3) show that some
wave energy has propagated through the defect region, although a significant amount of
amplitude has been lost and the wave has been delayed. What is occurring is that due to the
finite length of the input excitation, the SH1 pulse contains a band of frequencies. Therefore,
although the thickness is sufficiently small for the dominant center frequency to be cut off at the
defect such that the energy is reflected, there is still significant signal energy present at higher
frequencies above the cut-off in the SH1 mode band that will propagate in the defect region.
However these propagating components are very close to the cut-off limit and thus propagate
with very slow group velocities leading to the observed time delays.
66
This point is demonstrated through examination of Figure 6-7 where the displacement
magnitude at a single node underneath the receiver is plotted as a function of frequency for both
the Specimen #1 and #3 FE cases. The amplitudes are normalized to the maximum of the
Specimen #1 displacement profile at the node. The plate defect imparts a ‘high-pass’ filter
effect, where the lower frequencies in the SH1 mode band cannot propagate and are reflected by
the defect, as the product of these frequencies with the remaining thickness in the thinned region
of the plate is below the cut-off limit.
Also in Figure 6-7, a small-amplitude low-frequency SH0 component of the original signal
passes unaffected through the gradual thinning defect region at about 550 kHz, even though the
central frequency of the excitation is at 730 kHz. This small amplitude SH0 component exists
due to the finite frequency bandwidth of the transmitter (Figure 3-6). This effect on the SH0
wave is opposite to what is observed for the SH1 waves that are incident on the defect whose
reflection is greater at gentler slopes [46].
Figure 6-7 –Displacement Magnitude for Specimen #1 and #3 at a single receiver node
For other defect types (other than gradual thinning) based on the results in [46], if the defect
geometry is more discrete, such as crack or notch, there should be an amplitude decrease due to a
reflection of signal energy, but also a transmission of energy due to mode conversion if the
remaining thickness is below the cut-off. Therefore the same observed received signal delays
5 5.5 6 6.5 7 7.5 8 8.5 9
x 105
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
Norm
alized A
mp
litu
de
- D
ispla
cem
ent
Pro
file
Re
ce
ive
r N
ode
Specimen #1
Specimen #3
67
and frequency spectrum changes discussed in this chapter for a gradual thinning type defect will
not be observed.
6.4.2 Sources of Error
Since the defect dimensions have a significant effect on the received waveform, the errors in
measuring the parameters A, B, and C depicted in Figure 6-1 is likely the leading cause of any
discrepancies between experimental and FE model results. Most importantly, due to the
operation in the highly dispersive region of the SH1 dispersion curve, the amplitude and arrival
time are extremely sensitive to the defect depth. As a result, a small uncertainty of +/- 0.01mm
on the flaw depth B has a large effect on the FE results (Figure 6-2). Therefore, extreme care is
taken in measuring the defect dimensions accurately which is done by using a height gauge on a
flat table. Since there is variance in the point to point measurements, multiple measurements
were taken in the wave propagation path and an average is computed.
To reduce the sensitivity to small variations in the defect depth, future experiments could be
performed on a thicker plate so that small uncertainties in the dimension depth are a smaller
fraction of the overall thickness. This will reduce the sensitivity of the dispersion characteristics
to a small error in B. Additionally, using a thicker plate will allow for easier machining as some
difficulty is experienced using a CNC machine to create our plate defects due to vibrations of the
thin specimen.
Experimental difficulties prevented our measurement of the actual curvature of the slope of the
defects; instead, the slope is assumed to be constant between its two end points. The effect of
asymmetry between the sloped sections on either side of the flat section is not explored in this
work either. These topics can be the subject of future work.
The FE and experimental waveforms also have slightly different shapes as seen in Figure 6-4 to
Figure 6-6. This discrepancy is likely due to the errors in curvature used in the FE model,
asymmetry of the sloped sections as well as measurement uncertainty in the defect dimensions.
Another source of error is due to the 2D model approximation, as the variance in the defect
profile across the plate width is not accounted for in any of the A, B or C dimensions. Due to the
vibration of the plate in the CNC machine, this could be significant.
68
One final point is that in practice defects will be three dimensional. This will increase the
complexity in analyzing the received signal because a portion of the received signal energy will
travel through the thinned region, but also some energy will spread around the defect region.
This is mentioned in [40], for ‘dish’ shaped defects and not considered in this thesis.
7 Conclusions
7.1 Review of Thesis
In this thesis, a method for the detection of hidden corrosion at pipe support interfaces is
proposed and investigated. The focus has been to utilize a PPM EMAT configuration to
facilitate a rapid and accurate inspection of wall loss at a rough surface contact interface. The
system consists of two PPM EMAT’s operating in a pitch-catch mode with an operating point at
the ‘knee’ of the SH1 dispersion curve. By operating in this highly dispersive region, changes to
the received signal caused by geometrical factors such as defects and supports are magnified.
7.2 Summary of Findings
Based on this study, the following conclusions were reached:
i. The SH1 mode operating near the dispersion curve ‘knee’ offers the best potential for
interfacial corrosion detection
In this work this operating point is initially selected based on its dispersion and polarization
characteristics: (a) it yields a large received signal response in cases of specimen thickness
changes, and (b) the mode is polarized normal to the support loading. It is verified through both
FE models and experiments that within the range of experimental parameters there are minimal
effects on the received SH1 mode due to the support interface, but significant amplitude and
arrival time changes from wall thinning corrosion defects.
ii. Within the experimental parameters the contact stiffness has a minimal effect on the
received SH1 mode, but for larger contact stiffness values there are significant
amplitude and arrival time effects on the SH1 waveform
Within the range of support loads encountered in our experiments or in a field situation, the FE
model agrees well with the experimental results. However the FE model also indicates
69
significant amplitude and arrival time effects on the SH1 wave after a ‘threshold’ or ‘knee’
stiffness per unit area value (KT) is exceeded. This ‘threshold’ stiffness per unit area is larger
than the maximum value investigated experimentally. It is also shown through the FE model that
the ‘threshold’ KT value is relatively unaffected by the support length, but once the threshold KT
value is exceeded, the slope magnitude of the amplitude and arrival time plots increase as the
support length increases.
iii. The 2D FE gradual thinning defect model accurately represents effects on the SH1
mode arrival time and amplitude
This is confirmed by comparing the FE model’s performance on three experimental test cases. It
is shown that when the remaining plate thickness is above the cut-off value, the amplitude and
delay of the received signal are strongly dependant on the maximum defect depth and to a lesser
extent on the fractional amount of the wave propagation path that is thinned. This extends the
conclusions in [46]
iv. Critical corrosion depths are indicated by large signal amplitude reductions and delays
Due to the relatively wideband nature of the excitation pulse, when the 2D defect FE model is
used to evaluate defects with a minimum remaining thickness less than the cut off thickness, the
dominant frequency and lower frequency components of the incident wave were reflected. The
high frequency components still propagated to the receiver however, causing large changes in
amplitude and arrival time of the received signal. Specifically it is shown that a wall loss of
approximately 20% (Specimen #2) causes the central frequency of the original signal to be cut-
off, leading to a large amplitude reduction and delay of the signal arriving at the receiver. This is
important because this amount of wall loss depth is the critical threshold that must be easily and
quickly detectable using standard field instrumentation.
7.3 Future Work
Based on the results of this work, several topics are considered for further investigation:
i. Investigation of the support contact interface at higher contact pressures
70
This is needed to verify the large decreases in amplitude and arrival time observed after the curve
‘knee’ in the 2D FE model. This requires either much greater loads which are not achievable
with our current set-up, or a reduction in nominal contact area by at least a factor of 10. To
maintain the 2D approximation, reducing the area would mean reducing the support length only.
This would likely lead to a small support length, so some combination of increasing the applied
load and reducing the support length is the most plausible scenario.
ii. Analysis of a 3D support contact interface
Analysis of a 3D contact case would be useful to account for possible wave ‘spreading’ around
the contact patch. Also, higher contact pressures can be obtained since there is a third dimension
that can be adjusted. For example, a simply supported pipe is investigated in [37] assuming
Hertzian line contact, leading to significantly less nominal contact area than what is considered
in this thesis.
iii. Further analysis of 3D gradual thinning type defects
This is needed as practical defects will have a third dimension and it will have significant effects
on the received signal. This is because the defect geometry can now change over the third
dimension, and the wave can potentially now propagate or scatter ‘around’ the defect. Some
discussion on this issue is provided in [40] for dish shaped defects.
iv. Expanded analysis of damping effects
In this study, the hysteretic loss factor is not fully investigated since there is no observable effect
of damping on the received signal within the experimental conditions. However factors such as
pipe coatings, surface conditions and different contact pressure ranges at the pipe support
interface may lead to damping being no longer negligible, and identification of a loss factor may
become necessary.
71
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