ultrasonic classification of defects in thin-walled structures · 2016. 11. 17. · 3.5.1 real-time...
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Ultrasonic Classification of Defects in Thin-Walled Structures
by
Rishikesh Benegal
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by Rishikesh Benegal 2016
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Ultrasonic Classification of Defects in Thin-Walled Structures
Rishikesh Benegal
Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
2016
Abstract
This thesis focused on the development of techniques to detect and estimate the size of circular
corrosion defects in thin-walled structures using ultrasonic guided waves. A 3D Finite
Element (FE) model was developed to simulate the propagation of waves in thin-walled plates.
The model was validated with experimental analysis using an Electro-Magnetic Acoustic
Transducer (EMAT).
Using a combination of fundamental and higher order horizontally polarized shear waves, the
loss in amplitude of the received waves could be correlated to the minimum diameter of a defect.
The transmitted pulse was delayed by an amount correlated to minimum defect diameter at the
bottom of the defect. The 3D FE model predicted the received signals in plates with defects with
an average error of 5%±2% for amplitude changes and 19%±17% for pulse delays. These
results suggest that a 3D model can be used to predict the effects of defects on shear wave
propagation.
iii
Acknowledgements
I would like to thank Prof. Anthony Sinclair and Prof. Tobin Filleter for giving me the
opportunity to work on this project. Their guidance with my research and the development of this
thesis has been invaluable. I would also like to thank Fatemeh, Chi-Hang, Hossein, Ben, and
Chris at UNDEL (Ultrasonic Non Destructive Evaluation Laboratory) for their assistance and
friendship. Nicholas Andruschak and Gabriel Turcan from Groupe Mequaltech have also been of
great help. Finally, I am extremely grateful to my parents for their unconditional love and
support.
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Table of Contents
Introduction .................................................................................................................................1 1
1.1 Objectives ............................................................................................................................1
1.2 Summary of Chapters ..........................................................................................................2
Background and Literature Review ............................................................................................3 2
2.1 Background ..........................................................................................................................3
2.1.1 Motivation ................................................................................................................3
2.1.2 Causes and Types of Corrosion in Pipe Supports and Tank Floors .........................4
2.1.3 Regulatory Requirements.........................................................................................4
2.1.4 Current Techniques for Detecting Corrosion ...........................................................5
2.1.5 Limitations of Current Ultrasonic Techniques ........................................................7
2.1.6 Requirements for a Better Corrosion Detection Technique .....................................8
2.2 Background on Wave Propagation ......................................................................................8
2.2.1 Phase Velocity and Group Velocity .........................................................................8
2.2.2 Bulk Waves versus Guided Waves ..........................................................................9
2.2.3 Types of Guided Waves .........................................................................................10
2.2.4 Shear Horizontal Waves ........................................................................................11
2.2.5 Dispersion and Frequency Cut-off Phenomena .....................................................12
2.3 Guided Waves in Plates and Pipes .....................................................................................15
2.4 Techniques for Detecting Step and Lake-Type Defects ....................................................16
2.5 Electro Magnetic Acoustic Transducers (EMATs)............................................................17
2.5.1 Lorentz Force EMATs ...........................................................................................19
2.6 Numerical Analysis of Wave Propagation .........................................................................26
2.6.1 Finite Element Analysis .........................................................................................26
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2.7 Absorbing Layers ...............................................................................................................30
2.7.1 Stiffness Reduction Method ...................................................................................31
2.8 Previous Work on Defect Detection using EMATs ...........................................................33
Experimental Analysis of SH Wave Propagation in the Presence of Defects ..........................35 3
3.1 Experimental Setup ............................................................................................................36
3.2 Defect Profiles ...................................................................................................................37
3.2.1 Stage 1 – Step Defects ...........................................................................................38
3.2.2 Stage 2 – Minor Lake-Type Defects ......................................................................39
3.2.3 Stage 3 – Lake-type Defects ..................................................................................40
3.3 Selection of Wave Parameters ...........................................................................................41
3.4 EMAT Design ....................................................................................................................43
3.5 Signal Processing ...............................................................................................................45
3.5.1 Real-time Signal Processing ..................................................................................47
Finite Element Model of SH Guided Wave Propagation in the Presence of Defects ...............48 4
4.1 Overview ............................................................................................................................48
4.2 Material Parameters ...........................................................................................................48
4.2.1 Time Domain vs. Frequency Domain Modeling ...................................................49
4.3 3D Finite Element Model...................................................................................................49
4.3.1 Generation of SH Waves .......................................................................................50
4.3.2 SRM Regions .........................................................................................................51
4.3.3 Mesh .......................................................................................................................52
4.3.4 Solver Configurations ............................................................................................53
Results and Discussion ..............................................................................................................54 5
5.1 Results from Experimental and FE Analysis .....................................................................54
5.1.1 Amplitude Changes Due to Defects .......................................................................54
5.1.2 Time Delay Changes Due to Defects .....................................................................58
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5.2 Discussion ..........................................................................................................................60
5.2.1 Effects of Beamwidth ............................................................................................60
5.2.2 Pulse Amplitude .....................................................................................................61
5.2.3 Time Delay Changes due to Defects ......................................................................67
5.2.4 Frequency Spectrum Changes Due to Defects .......................................................69
5.3 Summary of Defect Classification .....................................................................................72
Summary & Conclusions ..........................................................................................................73 6
6.1 Detection and Sizing of Corrosion Defects .......................................................................73
6.2 Development of 3D Finite Element Model ........................................................................73
6.2.1 Summary of Algorithm for Defect Detection and Sizing using SH1 and SH0
signals ....................................................................................................................74
6.3 Future Work .......................................................................................................................75
References ......................................................................................................................................76
Appendix A – Numerical Results ..................................................................................................81
Appendix B – Sources of Error ......................................................................................................84
Experimental Analysis .......................................................................................................84
FE Analysis ........................................................................................................................84
Appendix C - Accuracy of Detecting and Sizing Defects .............................................................86
Appendix D – Real Time Signal Processing Application ..............................................................87
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List of Tables
Table 2.1: Summary of current techniques to inspect pipes/plates [9] ........................................... 6
Table 2.2: Comparison of Guided Wave and Bulk Wave Characteristics in a Non-dispersive
Medium [14] ................................................................................................................................. 10
Table 2.3: Typical EMAT coil and magnet configurations .......................................................... 20
Table 3.1: Parameters for step defects .......................................................................................... 39
Table 3.2: Parameters used for minor gradual thinning defects in Stage 2 .................................. 40
Table 3.3: Parameters used for gradual thinning defect in Stage 3 .............................................. 41
Table 3.4: Settings used in PowerBox H during data collection .................................................. 44
Table 4.1: Material Properties Used for a Carbon Steel plate in the FE Analysis ........................ 49
Table 4.2: Stiffness Reduction Method Parameters ...................................................................... 52
Table A.1: Average received SH1/SH0 amplitude for defect diameters relative to the no-defect
case. ............................................................................................................................................... 81
Table A.2: Average received SH1/SH0 amplitudes for average defect diameters relative to the no
defect case. .................................................................................................................................... 82
Table A.3: Average time delay for defect diameters relative to the no defect case. .................... 83
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List of Figures
Figure 2.1: Cross-sectional views of step and lake-type corrosion defects in a plate with
minimum remaining wall thickness indicated ................................................................................ 4
Figure 2.2: Schematic of particle motion in a shear horizontal (SH) wave [17] .......................... 11
Figure 2.3: Mode shapes for the first three SH guided wave modes [18] .................................... 12
Figure 2.4: Group velocity vs. frequency-thickness product for mild steel [20] .......................... 13
Figure 2.5: Phase velocity vs. frequency-thickness product for a mild steel plate [20] ............... 14
Figure 2.6: Phase velocity dispersion curve for circumferential SH waves in plates and pipes [22]
....................................................................................................................................................... 16
Figure 2.7: Schematic of SH wave generation using a PPM array configuration [25] ................. 21
Figure 2.8: Dispersion curve showing the dominant wavelength generated by using magnets with
a width of 3.175 mm and 3.175 mm plate thickness [20]. ............................................................ 22
Figure 2.9: Transducer configurations in axial examinations: a) Pulse echo; (b) Pitch-catch [31]
....................................................................................................................................................... 24
Figure 2.10: a) Complete model of physical phenomenon; b) Truncated model with absorbing
layer............................................................................................................................................... 31
Figure 3.1: Configuration of the plates used for experimental analysis ....................................... 36
Figure 3.2: Top-view schematic of experimental setup ................................................................ 37
Figure 3.3: Cross-section of initial circular defect ........................................................................ 38
Figure 3.4: Cross-section of gradual slope added to defect cross section .................................... 39
Figure 3.5: Cross-section of gradual thinning defect .................................................................... 40
Figure 3.6: Dispersion curve of SH modes in 6.53 mm carbon steel plate................................... 42
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Figure 3.7: Schematic of (a) racetrack coil and PPM array; (b) Individual bar magnet ............... 43
Figure 3.8: (a) EMAT coil and PPM array; (b) Innerspec PowerBox H pulser ........................... 44
Figure 3.9: EMAT assembly on plate. The settings shown in Table 3.4 were used on the
PowerBox H for data collection. ................................................................................................... 45
Figure 3.10: Received SH0 and SH1 signals and corresponding filtered signals ......................... 46
Figure 3.11: SH1 Envelope of cases with/without defect and the corresponding cross-correlation
between the no-defect case and the defect case ............................................................................ 47
Figure 4.1: Schematic of 3D FE Model ........................................................................................ 50
Figure 4.2: Schematic of surface traction loading applied to FE model ....................................... 50
Figure 4.3: Input force applied in FE model to generate surface traction loading ....................... 51
Figure 4.4: Schematic of mesh used for 3D model. Element sizes have been scaled up 3.5x for
better visibility. ............................................................................................................................. 53
Figure 5.1: SH1/SH0 amplitude ratios, normalized by the no-defect case for 𝛼 (slope) of (a) 90°
(b) 45°, and (c) 7° for different defect diameters 𝜙 with corresponding schematics of the defect
cross-section. Error bars indicate +/- one standard deviation. ...................................................... 55
Figure 5.2: Schematic of the average defect diameter showing the cross section a 3.5 mm lake
defect with a slope of 7°. ............................................................................................................... 56
Figure 5.3: SH1/SH0 amplitude ratio normalized with the no-defect case for average defect
diameters for experimental data .................................................................................................... 57
Figure 5.4: SH1 pulse time delay at the receiver location for 𝛼 (slope) of (a) 90° (b) 45°, and (c)
7° for different defect diameters 𝜙 with corresponding schematics of the defect cross-section.
Error bars of 2 standard deviations are shown. ............................................................................. 59
Figure 5.5: Comparison between SH1 beamwidth (y-direction displacement field) and diameter
of 28.74 mm lake defect................................................................................................................ 61
x
Figure 5.6: Cross sectional view of SH0 pulse (normalized y-direction displacement field) as it
passes through a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 7°
slope at times (a) 60 μs, (b) 70 μs and (c) 90 μs after transmitter excitation ............................... 62
Figure 5.7: Top half view of SH0 pulse (y-direction displacement field) as it passes through a
6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 7° slope at times (a)
60 μs, (b) 70 μs and (c) 90 μs after transmitter excitation ........................................................... 63
Figure 5.8: Cross sectional view of SH1 pulse (normalized y-direction displacement field) as it
passes through a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 7°
slope at times (a) 70 μs, (b) 100 μs and (c) 115 μs after transmitter excitation ........................... 64
Figure 5.9: Top half view of SH1 pulse (y-direction displacement field) as it passes through a
6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 7° slope at times (a)
70 μs, (b) 100 μs and (c) 165 μs after transmitter excitation ....................................................... 65
Figure 5.10: Cross sectional view of SH0 pulse (normalized y-direction displacement field) as it
passes through a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 90°
slope at time of 80 μs after transmitter excitation ........................................................................ 66
Figure 5.11: (a) Top view of SH1 propagation for 28.74 mm lake defect indicating locations
where frequencies will be analyzed. (b) Frequency spectrum at locations around and at defect
locations ........................................................................................................................................ 68
Figure 5.12: Frequency response measured at the receiver location for the (a) Experimental
measurement and (b) FE simulations, where 𝜙 is the diameter at the bottom of the defect and 𝛼
is the defect slope .......................................................................................................................... 70
Figure 5.13: Mean SH1 Frequency Spectrum Skewness for different defect sizes and slopes for
five trials of each defect case. ....................................................................................................... 71
Figure D.1: A sample signal processing application using Python that can perform real-time
calculations ................................................................................................................................... 87
1
Introduction 1
The mechanical integrity of thin walled structures such as pipes and storage tank floors in an
industrial site can be severely undermined by the presence of defects caused by corrosion. If such
compromised structures are left unattended, the corrosion can initiate loss of material that could
eventually lead to leaks or even structural failure. The need to detect such defects accurately and
quickly is a challenging engineering problem given the extensive lengths of pipes and large sizes
of storage tanks at industrial sites.
1.1 Objectives
The two main objectives in this project are to:
1. Develop an ultrasonic testing technique that can detect and size corrosion defects in thin-
walled carbon steel industrial structures. A technician using technique should be able to
approximate the minimum defect diameter. If a defect is found during scanning, it can be
flagged and other more precise and accurate techniques can be used to size the defect.
2. Develop a 3D finite element model that can be used to simulate the propagation of
ultrasound waves through thin-walled structures that contain defects. The model should
be able to predict the results of the ultrasonic testing technique for a variety of different
defect geometries. As such, a 3D model will eliminate the need for expensive and time
consuming experiments in the future.
Both the ultrasonic testing technique and the 3D finite element model will be validated through
experimental analysis. For the purposes of this project, the defect will be constrained to a circular
shape, and the defect’s depth (wall thickness loss) will be constrained to approximately 20% of
the structure’s original wall thickness. Further details regarding the selection of defect
parameters are provided in the experimental analysis section.
2
1.2 Summary of Chapters
Chapter 2 provides background information regarding the processes and nature of corrosion
experienced in industrial structures. An introduction to current technologies for corrosion
detection, in particular ultrasonic technologies, and their limitations is provided. As well, a
background on wave propagation and the merits of shear horizontal (SH) waves are covered.
Finally, an overview of new techniques that have been developed or are under development to
detect corrosion are provided.
In Chapter 3, details regarding the experimental setup in order to investigate the effects of
defects on SH waves are given.
Details regarding 3D Finite Element (FE) model developed to analyze SH wave propagation are
provided in Chapter 4. Specifics regarding the model such as material properties, geometry,
surface traction forces and boundary conditions are provided.
Chapter 5 contains the comparison of experimental and FE results. Here, it is shown that FE
analysis of wave propagation can be used to estimate the behavior in the experimental case.
Furthermore, techniques to characterize the size and type of defect based on amplitude and time
delay changes are provided.
A summary of the findings in thesis is provided in Chapter 6 along with suggestions for future
work.
3
Background and Literature Review 2
2.1 Background
In order to determine the existence, extent and location of corrosion in thin-walled structures,
background information regarding the nature of corrosion and current inspection techniques is
presented in this section.
2.1.1 Motivation
Metal corrosion is a significant issue causing an estimated yearly damage of over $276 billion in
the United States alone according to a 2002 study by NACE International1 [1]. An important
subset is that of corrosion in piping systems and tank floors. It is estimated that 80-85% of
corrosion in pipes often occurs near support locations [2]. These regions are more susceptible to
corrosion because water can stagnate in the crevices between the support and the pipe and it is
often difficult to access these areas for routine maintenance. Underground and aboveground
storage tanks are also susceptible to corrosion due to the presence of water in soil, as well as
other factors including saltwater content and microbial structures present inside and outside the
tank [3]. Such structures can be found in a variety of different industries such as utilities,
transportation, manufacturing and infrastructure [1]. In particular, oil and gas industry structures
that carry crude oil with high concentrations of sulfur and CO2 are prone to corrosion [4], [5].
In pipes, traditional NDE (Non Destructive Evaluation) inspection techniques often involve
lifting the pipe and visually checking for defects. However, such procedures are time consuming
and expensive as it may require cutting or uninstalling the support, removing insulation and plant
downtime. Lifting a pipe off a support may also undermine the structural integrity of a pipe that
may already be weakened due to corrosion. In the case of storage tanks, the area that is to be
inspected is often very large. As such, a corrosion detection technique that is fast and does not
require direct access to the corrosion location would be highly beneficial.
1 Formerly known as National Association of Corrosion Engineers
4
2.1.2 Causes and Types of Corrosion in Pipe Supports and Tank Floors
Since the purpose of this project is to develop a technique to assess the presence of corrosion, it
will focus on defects due to localized corrosion in pipes and in plates. The basic elements in a
corrosion “cell” are a cathode, anode, electrolyte and a metallic pathway [6]. The cathode
undergoes a reduction reaction gaining electrons, whereas the anode (pipe or plate) undergoes an
oxidation reaction where it loses electrons. These reactions are facilitated by the presence of
water that forms the basis of an electrolyte, providing a metallic pathway for electron flow.
Corrosion in pipes and plates can often take the form of pitting which consists of pit-type “step”
defects or develop into uniform corrosion, often referred to as gradual thinning or “lake-type”
corrosion. The difference between the two types of corrosion are is shown in Figure 2.1. For the
purposes of this thesis, the pitting defect will be referred to as a “step” defect, since there is an
abrupt change in wall thickness. The gradual thinning defect will be referred to as a lake-type
defect as this is the term often used in industry to describe such defects. In reality, it is difficult
to categorize the defect type exactly as they may often range between step or lake-type
defects [7]. However, we will consider these two general defect types separately for the purposes
of this thesis.
Figure 2.1: Cross-sectional views of step and lake-type corrosion defects in a plate with
minimum remaining wall thickness indicated
2.1.3 Regulatory Requirements
Codes such as ASME (American Society of Mechanical Engineers) B31.3 for process piping
standards specify allowable limits of defect size, geometry and wall-thickness loss for safe
operability of industrial structures [8]. Along with information regarding the defect, other factors
such as the operating environment, stress concentrations and desired life expectancy of the
structure are also used to assess whether the structure is to be repaired or replaced. Therefore, it
a) Step defect b) Lake-type defect
5
is important for a technician who is inspecting a structure to know the approximate depth, size
and geometry of a defect before a recommendation for repairing/replacing the structure is made.
2.1.4 Current Techniques for Detecting Corrosion
Currently employed NDE methods for detecting a wide range of defects in engineering structures
include visual testing (VT), penetrant testing (PT), magnetic testing (MT), radiographic testing
(RT), ultrasonic testing (UT), eddy current testing (ET), thermal infrared testing (TIR) and
acoustic emission testing (AE) [9]. As mentioned in Table 2.1 only some of these techniques are
suitable for corrosion detection and characterization.
Most testing methods applicable for corrosion detection require “direct access” to the defect
location. That is, the technique can only be applied in a small region directly underneath or
above the defect. This prevents such techniques from being used as fast scanning tools to
determine corrosion over a wide area, particularly under regions that are not readily accessible
such as under pipe supports. Attempting to access regions under support locations may result in
increased stresses on pipes that may already be damaged by corrosion. As well, scanning only
small regions of storage tank floors and walls is also very time consuming, resulting in increased
plant downtime.
6
Table 2.1: Summary of current techniques to inspect pipes/plates [9]
Technique Procedure Access
defect area
Cost per
region
Visual Visually checking for possible corrosion Yes Low*
Penetrant (mainly
for cracks)
Applying either fluorescent or visible
penetrant and a “developer” to defect
location. If a crack exists penetrant will
seep out of cracks after “development
time” has elapsed.
Yes Low*
Radiographic
X-ray radiation is projected onto
specimen. The rays penetrate the
specimen, and are captured on a film to
analyze defects.
No High**
Thermal/infrared
(mainly for
cracks)
Test specimen has to be heated up to a
high degree before inspection with an
infrared camera. Defects regions have a
different temperature.
Yes Low*
Magnetic particle
(mainly for
cracks)
Magnetic particles (iron filings) are
applied to defect area. Inducing magnetic
flux causes particle alignment to change
based on presence of defect
Yes Low*
Magnetic flux
leakage
Magnetic flux is induced in specimen.
The flux will leak out if a defect present. Yes Low*
Eddy-current
Eddy-current field generated in specimen
using a coil with pulsed current excitation.
Defects cause a change in coil impedance.
Yes Low*
Ultrasound
Generating ultrasonic waves in specimen
to determine presence of defects. Need
couplants.***
Some
techniques Low*
*Without considering any plant downtime, the cost will primarily be labour cost
**a new film is required for each scan location
***couplants are fluids with high viscosity that must be applied to a specimen’s surface to induce ultrasound waves,
and this process is very time consuming
7
2.1.5 Limitations of Current Ultrasonic Techniques
An important subset of the techniques mentioned in Table 2.1 is ultrasound based inspection.
Key advantages of such techniques include the ability to accurately detect/size defects and the
inexpensiveness of carrying out the technique (only labour costs are involved) once the
equipment is purchased. However, presently available ultrasound techniques are an unideal
solution for our corrosion detection purposes because of the time required to use such solutions
and the inability of the solutions to detect lake defects.
Most traditional ultrasound techniques require a high viscosity fluid known as a couplant to be
applied to the surface of the test specimen [9]. For instance, Dacon2 uses transducers to generate
waves that travel between a transmitter and receiver and do not require direct access to the defect
area [10]. The wave propagation time between the transmitter and receiver is used to determine
the amount of corrosion. However, a couplant is required for this technique, which results in an
increased setup time. There are products available on the market, such as the dry-coupled wheel
probe sensors by Sonatest3, that do not require a couplant [11]. Such products still require direct
contact with the test specimen in order to generate an ultrasound wave in the material. This
makes it difficult to inspect a surface that is uneven or is coated with a thin layer of paint.
Innerspec4 uses MRUT (Medium Range Ultrasonic Testing) technology which was also
designed for corrosion detection. It utilizes a special type of transducer that does not require a
couplant, but is unable to detect lake-type defects due to the type of wave used [12].
Attenuation of commonly used ultrasound waves by the medium that surrounds the test specimen
is also an issue. For example, if the specimen, such as a pipe, is surrounded by soil or if it is
filled with a fluid such as water, the ultrasound waves will be attenuated considerably [13].
Polymer coatings on pipes have also been known to attenuate the signals for particular wave
types [13]. This limits the situations where traditional ultrasound techniques that can be used.
2 Dacon Inspection Services, Ban Chang, Rayong, Thiland
3 Sonatest Ltd, Milton Keynes, UK
4 Innerspec Technologies Inc., Forest, Virginia, USA
8
2.1.6 Requirements for a Better Corrosion Detection Technique
Given the current NDE techniques available in the market and their shortcomings, it is clear that
there is a need for a new ultrasound based technique that is:
Able to quickly identify the presence of corrosion without direct access to the defect
location. In particular, the inspection technique should be able to identify lake-type type
defects which current industry standard scanning techniques are often unable to detect
Able to accommodate different surface conditions such as roughness and thin coatings as
well as presence of fluid inside a pipe
Low cost with short setup time and reduction/avoidance of plant downtime
This thesis will focus on developing a technique that meets these needs.
2.2 Background on Wave Propagation
Since many of the techniques mentioned in this report make use of ultrasonic wave propagation
concepts, a brief review of this topic will be provided in this section. Further information
regarding ultrasonic waves can be found in [14].
2.2.1 Phase Velocity and Group Velocity
“The phase velocity is the velocity of a wave front of constant phase” [15]. The phase velocity
𝑐𝑝 can be defined using Equation (1) where 𝜆 is the wavelength, f is the frequency, k is the wave
number and 𝜔 is the angular frequency.
𝑐𝑝 = 𝑓𝜆 = 𝜔/𝑘 (1)
The group velocity, 𝑐𝑔 is defined as, “the velocity of propagation of a wave packet” [15]. The
group velocity is given by:
𝑐𝑔 =𝑑𝜔
𝑑𝑘
(2)
9
2.2.1.1 Dispersion of Waves
If the wave type is dispersive, then the phase velocity of the wave is a function of frequency [14].
Waves are often launched as a short pulse that contain a range of frequencies. As the pulse
travels, lower frequency components travel at a different speed than the higher frequency
components. As a result, the pulse shape (envelope) will change with propagation distance. Pulse
duration will also increase as the wave travels further away from the source. As well, signal
amplitude will be reduced due to conservation of energy as the pulse duration increases. This
phenomenon reduces the sensitivity of a diagnostic technique that relies on measurement of the
received amplitude or arrival time of pulses.
2.2.2 Bulk Waves versus Guided Waves
Bulk ultrasound waves travel only in localized regions within the interior of a structure [14]. By
contrast, guided ultrasound waves propagate through the total thickness or at the boundaries of
the structure over large distances. This means that with a guided wave method, large areas can be
inspected by launching a guided wave from a single location. Consequently, guided waves are
ideal for inspection in cases where rapid inspection or large areas is necessary as well as cases
where it is required to inspect areas that are not easily accessible.
One of the key parameters that determines whether a guided or bulk wave is generated within a
medium by a given ultrasonic equipment setup is the system excitation frequency. The relatively
low frequencies of the guided waves make them less sensitive to defects compared to bulk waves
which are typically generated at higher frequencies [14]. A brief comparison between guided
waves and bulk waves is shown in Table 2.2.
10
Table 2.2: Comparison of Guided Wave and Bulk Wave Characteristics in a Non-
dispersive Medium [14]
Characteristic Bulk Wave (non-dispersive) Guided Wave (dispersive)
Phase Velocity Constant Function of frequency
Group Velocity Same as phase velocity Not equal to phase velocity
Pulse Shape Little change with propagation
distance
Significant change with
propagation distance
Even though guided waves tend to be dispersive and have a relatively low frequency, there are
several distinct advantages of using a guided wave for inspection. These advantages include:
Ability to inspect over longer distances instead of scanning only localized regions, and
ability to inspect regions that are not directly under the ultrasonic probe
Ability to detect defects via analysis of defect “signatures” related to dispersion, wave
scattering, attenuation, excitability, and mode selectivity characteristics [16]
2.2.3 Types of Guided Waves
There are several types of guided waves that can be generated in structures. The most common
wave types are briefly reviewed here and further information can be found in [14]:
Rayleigh Waves: Travel along a free surface of a specimen, and have an elliptical motion.
These waves are not well suited for applications such as corrosion detection in pipes and
plates, as they are overly sensitive to the pressure applied by support structures.
Lamb Waves: Flexural waves that occur in plane strain in a free plate (or pipes with a
large radius-to-thickness ratio) and travel through the thickness of the material. In
general, these waves are considered to be “leaky” as they are susceptible to attenuation
caused by any items in contact with the structure such as soil and supports. Consequently,
they are not a good fit for corrosion detection in most industrial situations.
11
Torsional Waves: These waves exist only in cylindrical structures and have dominant
motion in the circumferential direction of the structure. Since they can exist only in
cylindrical structures, and corrosion detection techniques developed based on torsional
waves may not be applicable for plates.
Shear Horizontal (SH) Waves: These waves can exist in both plate and cylindrical
structures. Unlike Rayleigh and Lamb waves, SH waves do not have displacements in
directions perpendicular to the surface and are less susceptible to attenuation. Since SH
waves will be used in this thesis, a more thorough explanation is presented in the
following section.
2.2.4 Shear Horizontal Waves
The motion of particles for this type of wave is perpendicular to the direction of wave
propagation as in the case of shear or transverse waves. However, in the shear horizontal case the
polarization of the wave is in the horizontal direction. As well, the waves travel through the
entire thickness of the material. A schematic of how the wave propagates is shown in Figure 2.2.
Figure 2.2: Schematic of particle motion in a shear horizontal (SH) wave [17]
Shear horizontal (SH) waves are of particular interest for the application of corrosion detection
since they are not overly sensitive to surface conditions (such as pipe supports, soil and coatings)
12
because the particle displacement is parallel to the test sample surface [14]. As such, this thesis
will focus on the use of SH modes since these waves are applicable for industrial structures that
often have support structures and may be in contact with soil or fluids. As well, a technique
developed with SH waves can be used to detect defects in both pipes and plates
The fundamental mode of shear horizontal waves, known as the SH0 mode, has a mode shape
(particle displacement) that is independent of depth within the test piece as shown in Figure 2.3.
It is also generally non dispersive, except in cylindrical structures where it is slightly dispersive
[14]. It is also possible to generate higher harmonics of the wave, labeled SH1, SH2, etc. The
higher order modes alternate between anti-symmetric and symmetric particle displacements in
the thickness of the material as shown in Figure 2.3. Higher order modes of the SH wave also
exhibit dispersion.
Figure 2.3: Mode shapes for the first three SH guided wave modes [18]
2.2.5 Dispersion and Frequency Cut-off Phenomena
For higher harmonics of SH waves, the phase velocities are dependent on frequency. The phase
velocity 𝑐𝑝 is governed by Equation (3):
(2𝜋𝑓
𝑐𝑝)
2
= (2𝜋𝑓
𝑐𝑠)
2
− (𝑛𝜋
𝑑)
2
(𝑛 = 0,1,2,3 … ) (3)
13
where 𝑓 is the frequency, 𝑐𝑠 is the shear speed of the material and 𝑑 is the specimen wall
thickness and n the harmonic (wave mode) of the wave. The theoretical derivations are described
by Auld in [19].
A convenient way of visualizing the phase and group velocities corresponding to a particular
type of wave mode, geometry and material is a dispersion curve. The group or phase velocity is
plotted as a function of the frequency-thickness of a plate as shown in Figure 2.4 and Figure 2.5.
The frequency in the frequency-thickness refers to the center frequency of the SH wave and the
thickness is the wall thickness of the plate. These graphs allow one to conveniently select the
frequency required to generate a particular type of wave corresponding to any specified
specimen thickness and material.
Figure 2.4: Group velocity vs. frequency-thickness product for mild steel [20]
14
Figure 2.5: Phase velocity vs. frequency-thickness product for a mild steel plate [20]
If there is no dispersion, as in the case of the SH0 mode in a plate, the group velocity of the
waveform will be the same as the phase velocity.
2.2.5.1 Frequency-Thickness Cut-off Phenomena
From Figure 2.4 and Figure 2.5 it is possible to see that the higher order SH wave modes (SH1,
SH2, SH3, etc.) cannot propagate below a particular frequency-thickness product. This is a key
concept that will be exploited in this project.
Equation (4) provides a convenient way to calculate the cut-off frequency-thickness product for
any given wave frequency 𝑓, thickness 𝑑 and wave mode 𝑛 based on a material’s shear speed 𝑐𝑠
[14].
(𝑓𝑑)𝑛 =𝑛𝑐𝑠
2 (𝑛 = 0,1,2,3 … )
(4)
Using Equation (4), we can see that the frequency-thickness cut-off for SH1 waves (where n = 1)
in a mild carbon steel plate with a 𝑐𝑠 of 3230 m/s, is approximately 1.6 MHz-mm. This means
that if a plate has a wall thickness of 6.35 mm, for example, it would not be possible for a SH1
wave to exist below a frequency of approximately 252 kHz since any frequency below this value
15
would give a frequency-thickness product that is less than 1.6 MHz-mm. Alternatively, if we
generate a SH1 wave of 365 kHz, for example, it is not possible for a SH1 wave of this
frequency to exist below a wall-thickness of 4.38 mm.
We can use this cut-off effect to our advantage in order to detect wall thickness changes in
materials. Since we know that a particular frequency cannot exist below a particular wall
thickness threshold, we can transmit a pulse of higher order SH wave that contains these
frequencies that are prone to get reflected or scattered below the selected thickness. If the
received wave no longer contains all the frequencies that were transmitted, it is likely that there
is some location between the transmitter and receiver where wall thickness loss is present.
It has been shown that transmitting pulses of higher order SH waves at frequency-thickness
products that are on the “knee” region of the SH curve, work well for detecting wall thickness
losses at defect locations [21]. For example, a SH1 pulse of 2.3 Mhz-mm for mild steel is on the
knee of the curve. In cases where there is wall thickness loss of approximately 25%, the lower
frequencies in the pulse can no longer propagate through the material and are reflected from the
defect location. Therefore, the received wave at a receiver location will be considerably different
from what was transmitted. We will use a similar approach for this project of selecting points on
the “knee” of the curve.
2.3 Guided Waves in Plates and Pipes
The dispersion characteristics that have been calculated for a plate are not exactly applicable to a
pipe unless the wall thickness to outer radius ratio is less than approximately 10% [22]. This is
illustrated in Figure 2.6, where it is seen that in general, shear horizontal waves are more
dispersive in pipes than plates. The parameter n is the wave mode, d is the wall thickness and R
is the outer radius of the cylinder.
16
Figure 2.6: Phase velocity dispersion curve for circumferential SH waves in plates and
pipes [22]
Consequently, it is possible to conduct experiments or numerical simulations with a plate and
extend its results to several standard sizes of thin-walled pipe.
2.4 Techniques for Detecting Step and Lake-Type Defects
Corrosion defects in pipes and plates usually display characteristics of either step or lake-type
defects as mentioned Section 2.1.2. Previous researchers have focused on using bulk wave
methods for sizing step-type defects as they often have smaller diameters, and guided SH wave
methods for sizing the larger lake-type defects.
Detecting and resolving very small step defects requires an ultrasonic wave of relatively high
frequency, such that its wavelength is less than the diameter of the defect. As such, bulk wave
ultrasonic NDE techniques using traditional piezo-electric transducers have been developed for
such purposes. For instance, Shivraj et al have developed a technique that uses 1 MHz
circumferentially-polarized guided waves that can detect pitting type defects using a traditional
piezo-wedge transducer [23]. Similarly, a Higher Order Modes Cluster (HOMC) transducer that
Note: n is the wave
mode, d is the wall
thickness, and R is
the outer radius
17
generates frequencies up-to 2.25 MHz was used for providing greater sensitivity and sizing
capability for corrosion pits [24].
The use of SH waves for characterizing lake-type defects has been investigated by several
authors. A key consideration is the relatively small reflection coefficient for the fundamental
SH0 mode from lake-type defects. It has been found by Nurmalia et al that if the defect is such
that the slope of the defect wall is less than 5 degrees, then no significant reflection of the
fundamental mode will be observed [25]. In such a case, there will be close to 100% wave
transmission of the SH0 mode underneath the defect. It is therefore very difficult to detect the
presence of lake-type defects with traditional SH0 methods that are prevalent in industry. Similar
results have been found for torsional waves in the case of pipes where it is not possible to detect
lake-type defects with the fundamental torsional mode [26]. One possible technique to increase
the sensitivity to lake defects is to utilize a higher order mode. Higher order SH modes have been
studied both experimentally and by simulation for such a purpose, with positive results [25],
[21].
In this thesis the possibility of using SH waves for both step and lake type defects will be
investigated with the use of higher order SH modes.
2.5 Electro Magnetic Acoustic Transducers (EMATs)
Given the attractiveness of using SH guided waves in ultrasonic NDE, it is useful to consider the
use of electromagnetic acoustic transducers (EMATs) to generate and receive the ultrasonic
signals. In particular, EMATs have several advantages that can be used to develop a fast
scanning tool for corrosion detection in plates or pipes. Advantages of EMATs include:
Generation of ultrasonic waves in a metallic test piece via electromagnetic induction [27].
EMATs are dry non-contact transducers. Consequently, no couplant is necessary for
transduction of the wave. The wave can be generated with the transducer being as far as a
millimeter away from the specimen. This allows for inspection of parts that may be hot or
have thin coatings on them.
18
Ability to easily generate and detect guided waves, and in particular SH waves. Unlike
traditional piezoelectric-based transducers, the wave generation mechanism of an EMAT
is not affected by the angle the transducer makes with the surface of the specimen [9]. As
well, SH waves cannot be generated easily using piezoelectric-based transducers as the
low density couplants used to cover plates or cylinders impede the generation of these
waves [12].
While it has distinct advantages, there are also some disadvantages that the technology has [27]:
The transduction mechanism is generally weak, which results in noisy signals and a low
signal to noise ratio (SNR).
Although EMATs can tolerate some degree of separation from the test specimen, known
as lift-off, the performance of an EMAT is very sensitive to this lift-off.
There are three key force-generation mechanisms that are possible in EMATs that can be used to
generate ultrasound waves: magnetization, magnetostrictive forces and Lorentz forces.
Magnetization forces are usually of little consequence during analysis due to their relatively
small magnitude [28] and will not be considered further.
Magnetostriction is a phenomenon that occurs in certain ferromagnetic materials where the
metals undergo dimensional changes when a magnetic field is applied. EMATs that are designed
to exploit the magnetostriction force-generation mechanism can generate substantial signal
magnitudes in certain materials such as nickel [28]; however, the phenomenon is highly non-
linear and overly sensitive to variation in the specimen’s magnetic permeability. Furthermore,
magnetostriction-based EMATs are generally restricted to testing on some ferromagnetic
materials that exhibit significant magnetostriction [29]. In cases where a test specimen, such as
carbon steel, does not have considerable magnetostriction a technique to enhance transduction is
bonding a magnetostrictive material to the test specimen. In the case of carbon steel structures,
Ribicini et al. have shown that carbon steel specimens with bonded nickel can generate the
highest magnitude of SH waves when compared to Lorentz force EMATs and non-bonded
magnetostrictive EMATs [28]. However, the bonding processes prohibits the development of a
fast diagnostic method and negates the advantages of a non-contact NDE method.
19
Lorentz force EMATs are applicable for all conductive materials such as metals. As well,
Lorentz force EMATs can generate higher magnitudes than a non-bonded magnetostrive EMAT
on materials such as carbon steel [28]. Consequently, this project will focus on EMATs based on
the Lorentz force mechanism due to its wider applicability for industrial structures, plates and
pipes in particular, which are often constructed out of carbon steel.
2.5.1 Lorentz Force EMATs
A typical Lorentz force EMAT consists of a current carrying coil and a permanent magnet (or
sometimes an electromagnet). A large-amplitude alternating current is fed into a transmitter
EMAT coil; this generates an alternating magnetic field that penetrates into a metallic test
specimen, which in turn generates eddy currents Je in the surface skin of the specimen. These
eddy currents then interact with the static magnetic field B generated in the specimen by the
permanent magnet. The Lorentz force F generated within the skin depth of the test specimen is
the cross product of the two fields. It can be summarized by [27]:
𝑭 = 𝑱𝒆 × 𝑩 (5)
From Equation (5), the Lorentz forces and the resultant ultrasonic wave amplitude are linearly
proportional to both the applied magnetic field magnitude and eddy current density and are
therefore relatively easy to analyze. One key consideration with the generation of the static
magnetic field B, however, is that the magnetic field generated in a material depends on
magnetic permeability of the material. This magnetic permeability can be strongly
inhomogeneous in a metal test specimen. Consequently, the magnitude of force generated is also
a function of the material properties of the test specimen. Any testing technique that depends on
analyzing the changes in the amplitude of Lorentz force in the presence of defects must take this
effect into account.
There are two key parameters that a designer can control when designing an EMAT: the
magnetic field profile & amplitude and the coil. A combination of different coils and magnets
can be used to generate a variety of different wave modes as shown in Table 2.3.
20
Table 2.3: Typical EMAT coil and magnet configurations
Magnet Type (side
view)
Coil Configuration (top view) Typical Wave
Generated
Typical Uses
Periodic Permanent
Magnet (PPM) Array
Racetrack
Shear
Horizontal
Guided wave flaw
detection
Bar
Meander
Lamb Guided wave
thickness
measurement/flaw
detection
Bar
Pancake
Shear
Horizontal
(radially
polarized)
Bulk wave
thickness
measurement
Of particular interest for this report is the Periodic Permanent Magnet (PPM) array magnet
configuration with a racetrack coil as it can be used to generate SH waves. A schematic of the
wave generation mechanism is provided in Figure 2.7. Note that the PPM EMAT launches SH
waves in two directions simultaneously, as indicated in the figure.
N
S
N
S
21
Figure 2.7: Schematic of SH wave generation using a PPM array configuration [25]
The wavelength 𝜆 of the SH wave generated with the PPM array depends on the width of two
magnets. In Figure 2.7, the width of one magnet is 3.175 mm and so the only wavelength that the
EMAT will generate SH waves at is 6.35 mm.
The wavelength constraint can be visualized on a dispersion curve by drawing lines of constant
wavelength as shown in Figure 2.8. In this figure, the x-axis has been re-scaled to show only the
frequency for a plate that is 3.175 mm, instead of the frequency-thickness product (i.e. the
frequency-thickness axis was divided by the thickness). To create the dispersion curves Equation
(3) was used with cs of 3230 m/s, n = 0 for the SH0 dispersion curve, and n = 1 for SH1
dispersion curve. Then, a line where the ratio of the phase velocity to the frequency, that is cp/f,
was 6.35 mm was plotted to show the dominant wavelength that will be selected by using a
magnet width of 3.175 mm.
22
Figure 2.8: Dispersion curve showing the dominant wavelength generated by using
magnets with a width of 3.175 mm and 3.175 mm plate thickness [20].
The central frequency of the SH wave generated is related to the central frequency of the current
pulse provided to the racetrack coils. From Figure 2.8 we can see that if we were to provide a
pulse with central frequency of 500 kHz to the EMAT with a magnet width of 3.175 mm, a pulse
that primarily contains a SH0 wave will be generated as the dominant wavelength line intersects
the SH0 curve at 500 kHz. Similarly, providing a pulse with a central frequency of 730 kHz will
allow the EMAT to generate a pulse that primarily contains a SH1 wave.
It must be noted that while attempting to generate a particular mode, some frequencies of other
modes may also exist depending on range of frequencies present in the current pulse and the
number of magnets. A greater number of magnets allows for generating a narrower range of
wavelengths near the dominant wavelength. Similarly, a greater number of cycles in a current
pulse enables generation of a narrower range of frequencies around the central frequency.
Since the frequency of the wave generated is specified by the magnets and the frequency of
current provided to the racetrack coils, EMATs can generate a narrow band signal. As such, it is
Dominant wavelength line of 𝜆 = 6.35 mm
23
possible to detect defects based on a SH pulse sent from an EMAT transmitter to a receiver by
analyzing the:
(a) Signal amplitude/frequency changes, and/or
(b) Pulse propagation time
(c) Cut-off frequency characteristics of higher order signal modes.
2.5.1.1 Skin Depth
The skin depth 𝛿 in a material is defined as the depth at which the externally-induced eddy
current density has decreased to 1
𝑒 of its surface value. It is a function of the conductor’s
resistivity 𝜌, relative permeability 𝜇𝑟, permeability of free space 𝜇0 and the angular frequency of
the coil current 𝜔 [30]:
𝛿 = √2𝜌
𝜔𝜇𝑟𝜇0
(6)
Consequently, as the frequency used to excite the EMAT transmitter is increased, the depth of
the eddy current penetration decreases, resulting in a decrease of the Lorentz force generated.
This is an important consideration when generating higher order modes because the frequencies
required to generate such modes are higher than the fundamental mode. Therefore, a SH1 mode
will be used in this thesis as it has the lowest operating frequency when compared to other higher
order modes.
2.5.1.2 Pitch Catch versus Pulse Echo
There are two typical configurations used for EMATs: pitch-catch (also called through
transmission) and pulse echo. In pulse-echo mode a single transducer acts as both the transmitter
and receiver, and in pitch-catch mode there are two transducers (one transmitter and one
receiver). Schematics of the two configurations are shown in Figure 2.9.
24
Figure 2.9: Transducer configurations in axial examinations: a) Pulse echo; (b) Pitch-catch
[31]
In a pulse echo configuration, the detection of a defect is done by checking for reflected
ultrasound waves from the defect. However, in some cases it is possible that the defect only
causes ultrasound waves to scatter, without having any significant reflection. Consequently, a
“back-wall” echo is often used to gauge the amount of scattering. This back-wall echo is
reflection from an edge of the structure, where the edge could be the edge of the material or
some other feature that causes reflections such as a weld. If the amplitude of the back-wall echo
is reduced, the transmitted wave has likely scattered due to a defect. Therefore, if a back-wall
reflection is present, it is often convenient to use a pulse echo configuration because only one
transducer is required.
In the case of examining pipes or large plates, however, there may be no edge or weld near the
corroded area that can provide a clear back-wall echo. Especially in the case of long pipes where
the edge of the pipe may be a far away from the area being inspected. This creates an issue when
the defect causes the transmitted ultrasound wave to scatter since only a small component of the
ultrasound wave will be reflected back to the transducer. Consequently, for our purposes of
detecting and sizing corrosion defects in pipes and plates, a pulse-echo mode is not ideal.
25
For a pitch-catch configuration the detection of a defect is based on the changes in received
signals caused by the wave passing through the defect. Since two transducers are used, one
receiver and one transmitter, both scattering and reflection of the wave from the defect will cause
a change in the received ultrasound wave signals. As well, no back-wall echo is required to
interpret the signal. Therefore, it is more convenient to use a pitch-catch configuration for our
purposes.
26
2.6 Numerical Analysis of Wave Propagation
There are three main types of modeling that can be performed to study EMAT transduction
mechanisms and wave propagation: analytical methods, finite element (FE) methods and
boundary element (BE) methods. While analytical methods such as those presented in [14]
provide an exact solution, they are only applicable to a limited number of very simple
geometries. For more elaborate geometries, FE methods and BE methods are required. Much
work has been done to model and optimize the electromagnetic induction component of EMATs
by Mirkhani [30] and Shapoorabadi [32]. However, in this project the focus is to better
understand the interaction of the propagating SH wave with lake-type defects when using the
ultrasonic testing technique developed. Consequently, this report will focus on ultrasonic wave
propagation, and not on the generation or reception of the waves by transducers. A FE method
will be used for this report since several commercial FE software packages appropriate for this
task are readily available.
For the case of simulating SH waves in a plate, a two-dimensional (2D) plane strain FEM model
is not appropriate because the dominant particle vibration occurs in the plane that is normal to
the direction of wave propagation [14]. The geometry of a finite plate or pipe can only be
properly described using a three-dimensional model. As such, a FEM model should ideally be
three-dimensional (3D). This is challenging because large amounts of memory and processing
power are required to compute the solution. However, recent advances in computer hardware
have allowed FE software such as COMSOL Multiphysics5 to perform 3D analysis.
2.6.1 Finite Element Analysis
To perform FE analysis, a numerical model of the specimen is divided into discrete elements
using a process called meshing. Differential equations are then mapped to the elements, and the
solution for parameters of interest (such as displacement) of an element is computed using
numerical methods.
5 COMSOL Inc., Stockholm, Sweden
27
When performing FE analysis of ultrasound propagation, it is required that a minimum of 7
elements per ultrasonic wavelength are used to minimize the error for wave propagation
problems [33]:
Δ𝑥 ≤𝜆𝑚𝑖𝑛
7
(7)
where Δ𝑥 is the element size, and 𝜆𝑚𝑖𝑛 is the smallest wavelength simulated. This constraint in
particular has prevented researchers in the past from creating elaborate 3D models, as such
models can require very large amounts of memory and processing power.
There are two common types of analysis that can be performed using FE software package such
as COMSOL: time domain analysis and frequency domain analysis. For reasons stated later on in
Section 2.6.1.1, a time domain analysis will be used in this project. As such, a more detailed
background on time domain analysis is provided here.
2.6.1.1 Time Domain Analysis
In the time domain, a linear viscoelastic material is modeled by the following equation [34]:
𝑚𝜕2𝒖
𝜕𝑡2+ 𝑐
𝜕𝒖
𝜕𝑡+ 𝑘𝒖 = 𝑓(𝑡)
(8)
In this equation, u is the displacement, m is the mass, c is the damping parameter, k is the
stiffness of the system and f(t) is the time dependent forcing term.
In the one-dimensional case, the displacement u is:
𝑢(𝑥, 𝑡) = 𝑒𝑖(𝑘𝑥𝑥−𝜔𝑡) (9)
where kx is the wave number in the x-direction and 𝜔 is the angular frequency of the wave [35].
The damping parameter c can be defined in terms of the mass and stiffness [34]:
𝑐 = 𝑐𝑚𝑚 + 𝑐𝑘𝑘 (10)
where the parameter 𝑐𝑚 is the mass damping constant, with units of 1/s and 𝑐𝑘 is the stiffness
damping constant with units of s.
28
Explicit and Implicit Methods
In order to solve Equation (8) numerically by a finite element scheme, there are two general
classes of methods that can be used: explicit methods and implicit methods. In explicit methods,
the displacement u at all mesh nodes is determined through an iterative formulation in which the
updated estimate of the displacement 𝑢𝑛+1 determined at each iteration n is given as [36]:
𝑢𝑛+1 = 𝑢𝑛 + 𝑓(𝑡𝑛, 𝑢𝑛)Δ𝑡 (11)
From Equation (11) it is seen that 𝑢𝑛+1 is a function of the previous displacement estimate 𝑢𝑛. It
is also dependent on a function f whose value depends on previous time input 𝑡𝑛 and
displacement 𝑢𝑛, multiplied by the time step Δ𝑡. Consequently, the explicit method is a straight
forward time marching method.
The primary difference between an explicit and implicit solver is that in the latter case the
function f is dependent on 𝑡𝑛+1 and 𝑢𝑛+1 [36]:
𝑢𝑛+1 = 𝑢𝑛 + 𝑓(𝑡𝑛+1, 𝑢𝑛+1)Δ𝑡 (12)
While implicit methods are more stable compared to the explicit methods, and even
unconditionally stable in some situations, they are also less efficient computationally as they
require inversions of large matrices and a greater number of iterations.
Numerical Damping
Implicit methods also lead to numerical damping or diffusion where high frequency effects are
filtered out by the numerical integration procedure. In particular, implementing a Backward
Differentiation Formula (BDF) similar to Equation (12) results in significant damping of higher
frequencies [37]. To counter this effect, methods such as the Generalized-𝛼 method have been
developed [38]. In this method, each iteration depends on parameter values from both the
previous and next iterations. A simplified version of the relationship is as follows:
29
𝑢𝑛+1−𝛼 = 𝛼𝑢𝑛 + (1 − 𝛼)𝑓(𝑡𝑛+1, 𝑢𝑛+1)Δ𝑡 (13)
Here 𝛼 is a factor that ranges between 0 and 0.5. By specifying a value for 𝛼 one can control the
amount of high frequency dissipation/damping as well as the amount of iterations required for
the solution to converge. The algorithm is unconditionally stable provided 𝛼 is set to a value
between 0 and 0.5. Setting 𝛼 closer to 0 results in increased efficiency as less iterations are
required for convergence. However, doing so also damps out high frequency vibrations, which in
the case of solving wave propagation problems, leads to erroneous results. Conversely, setting an
𝛼 value close to 0.5 reduces the amount of high frequency damping, but results in decreased
computational efficiency as more iterations are required for convergence. The ideal value of 𝛼
that leads to accurate results needs to be determined through experimentation [39].
Time Step Requirements
As a rule of thumb, it is often recommended that at least five to ten time steps are used for one
period of the central frequency for the wave we wish to simulate [14]. However, in order for the
FE simulation to converge a necessary, but not sufficient, condition that must be met is the
Courant–Friedrichs–Lewy (CFL) condition [40]. This condition for the 3D case is given by
Equation (14) where 𝑢 is the maximum magnitude of the velocity in the x, y or z direction
direction, 𝛥t is the Courant time step and 𝛥𝑥, Δ𝑦 and Δ𝑧, are the element lengths in the x, y and
z directions.
𝐶 = Δ𝑡 (𝑢𝑥
Δ𝑥+
𝑢𝑦
Δ𝑦+
𝑢𝑧
Δ𝑧) ≤ 𝐶𝑚𝑎𝑥
(14)
As a consequence of the condition, decreasing the element size to obtain better spatial resolution
also results in a decrease in the maximum time step allowed in order to maintain stability. The
value of 𝐶𝑚𝑎𝑥 depends on the type of numerical solver used but is typically set to unity in the
case of an explicit solver. Implicit methods are less sensitive to the value of 𝐶𝑚𝑎𝑥.
2.6.1.2 Frequency Domain Analysis
For frequency domain analysis an excitation force is applied to model at a series of different
frequencies. Then, the resultant displacement at each of these individual frequencies is calculated
for all nodes. In this manner, one can calculate the response of the system for any desired range
30
of frequencies by performing a frequency sweep. The finite element results can then be
converted into the time domain signal by performing an Inverse Fast Fourier Transform (IFFT).
Frequency domain analysis is often faster than time domain analysis in the case of modeling
EMAT based systems because EMATs generate signals in only a narrow frequency band. This
limits the number of individual frequencies that need to be modeled. The frequency step Δ𝑓
required for performing an IFFT for a desired number of steps N and time step Δ𝑡 is given as
follows:
Δ𝑓 =1
𝑁Δ𝑡
(15)
2.7 Absorbing Layers
One key issue when performing FE analysis for wave propagation problems is that such
simulations are very computationally intensive due to constraints posed by element size and
time/frequency step requirements. If the experimental case is modeled in its entirety, the model
will result in millions of degrees of freedom. This leads to very large memory and processing
power requirements. Consequently, absorbing layers can be used to truncate the model to the
area of interest, such as the areas around defect. This reduces the number of elements in the mesh
and reduces the memory and processing power requirements to perform the FE analysis.
The absorbing layers are placed at the boundaries of the truncated region such that waves hit
these truncation limits and are not reflected back into the area of study. This is effectively the
same as the wave propagating away from the area of study in an experimental case since such
waves do not affect the results significantly. This concept is illustrated in Figure 2.10.
31
Figure 2.10: a) Complete model of physical phenomenon; b) Truncated model with absorbing
layer
Three techniques for implementing the absorbing layer concept have been used in the literature:
(1) Absorbing Layers by Increasing Damping (ALID), (2) Stiffness Reduction Method (SRM) in
the time-domain, and (3) Perfectly Matched Layers (PMLs) in the frequency domain [35]. As
well, a technique known as Infinite Element Layers exists, but is rarely used for wave
propagation problems as it often causes reflections that lead to erroneous results [41]. ALID,
SRM and PML all gradually dampen any waveform entering the absorbing layer so as to
minimize reflection.
In most cases the SRM technique requires a smaller absorbing layer length than ALID [41].
This makes SRM the preferred choice for time domain simulations because a smaller absorbing
layer length results in a smaller mesh size and increases the efficiency of the model. In frequency
domain analysis, the PML technique accomplishes a task similar to that of SRM but may require
a slightly larger absorbing layer length to prevent erroneous results [41], [33].
2.7.1 Stiffness Reduction Method
Stiffness Reduction Method (SRM) is a technique where the damping is gradually increased over
the length of the absorbing layer while simultaneously decreasing the stiffness of the material
[41]. If we consider the equation of dynamic equilibrium shown in Equation (8), we can
formulate an equivalent matrix form where [M], [C] and [K] are the mass, damping and stiffness
matrices and [F] represents the external force. SRM controls the [C] portion of the equation in
the absorbing layer.
[𝑀]�̈� + [𝐶]�̇� + [𝐾]𝑢 = [𝐹] (16)
a) b)
32
In commercial FE software a wave can be damped by changing the damping [C] matrix in
Equation (16). Analogous to Equation (10) the damping matrix [C], depends on a combination of
mass proportional damping constant CM and stiffness proportional damping CK constant and can
be expressed as:
[𝐶] = 𝐶𝑀[𝑀] + 𝐶𝐾[𝐾] (17)
In general, a non-zero CK value may lead to convergence issues and adversely affects the
computational time [41]. Consequently, the CK value is always set to zero in the SRM technique,
and only a CM value is specified. An optimal value for the CM term can be computed using [41]:
𝐶𝑀(𝑥) = 𝐶𝑀𝑀𝑎𝑥𝑋(𝑥)𝑝 (18)
Here 𝐶𝑀𝑀𝑎𝑥 is a positive real value with the units of rad/s (since CM has a unit of rad/s) and is the
maximum damping at the outer extremity of the absorbing layer. 𝑋(𝑥) is a function that ranges
from 0 at the inner boundary of the absorbing layer to 1 at the outer extremity. The power 𝑝 is a
positive number greater than unity and using a value of 3 was found to be sufficient by the
authors [35], [41].
In order to be able to efficiently apply damping without causing wave reflections back into the
plate’s area of interest, the stiffness 𝐸(𝑥) is also decreased simultaneously along with the
increase in CM according to:
𝐸(𝑥) = 𝐸0𝑒−𝛼(𝑥)𝑘𝑖𝑛𝑐𝑥 (19)
In Equation (19) 𝐸0 is the initial value of the Young’s modulus in the area of study, 𝛼(𝑥) is the
attenuation factor for the absorbing region and 𝑘𝑖𝑛𝑐 is the wavenumber for the incident wave
entering the absorbing region. The value for 𝛼(𝑥) is given by:
𝛼(𝑥) = 𝛼𝑚𝑎𝑥𝑋(𝑥)𝑝 (20)
Where 𝛼𝑚𝑎𝑥 is to be set such that the stiffness E(x) at the outer extremity of the absorbing layer
has a value equal to 1% of 𝐸0 [41]. Using Equation (19) we can calculate the value to be
−ln (0.01)/𝑘𝑖𝑛𝑐𝑥 where x is to be replaced with the length corresponding to the outer extremity
of the absorbing layer.
33
A key step in implementing SRM is the selection of the maximum damping value of the CMMax.
A value that is too large may result in reflections as the wave enters the non-linear region, where
as a value that is too small will result in reflections due to insufficient damping. It was found that
the ideal value of CMMax was on order of the angular frequency 𝜔 of the incident wave [41]. As
well the width of the SRM layer can initially be set to 1.5𝜆 where 𝜆 is the wavelength of the
incident wave [41].
2.8 Previous Work on Defect Detection using EMATs
Much work has been done previously on estimating the presence and magnitude of corrosion
defects on pipes and plates. In general, the techniques can be differentiated by the type of
ultrasound mode used, and whether pulse-echo or pitch-catch configurations were employed.
In the case of pulse-echo analysis, Carandente et al describes how the reflection of the
fundamental torsional mode can be used to determine the defect size and type (step and lake-type
defects) in pipes [42], [43]. Cobb et al used a combination of SH0, SH1 and SH2 waves in order
to be able to estimate the relative size of step-type defects using a reflection approach [18]. Since
the analysis was done for 2D cases, both researchers concluded that the reflections from defects
were primarily correlated to the amount of wall loss (i.e. depth of defect) that had occurred.
Andruschak et al [21] and Clough et al [44] have presented pitch-catch guided wave inspection
systems that use the SH1 wave mode to determine the presence of corrosion in pipe lines. Both
systems are based on detecting amplitude loss and time delays that are present in signals that
pass through defects. However, the analysis was again confined to defects that could be easily
modeled with 2D analysis. As such, the results were only applicable for detecting the presence of
large defects and estimating the amount of wall loss.
This thesis will focus on a technique that uses both SH0 and SH1 waves for determining the
presence as well as estimating the size and type (step or lake-type defects) through experimental
analysis. As well, instead of the 2D FE models presented by others, a 3D finite element model
will be developed that can predict the propagation of SH0 and SH1 waves through thin-walled
plates containing any defect geometry. This model will be validated by experimental analysis.
34
Therefore, with the development of a validated 3D model, new testing systems and signal
analysis strategies can also be developed in the future.
35
Experimental Analysis of SH Wave Propagation in the 3
Presence of Defects
In order to establish a technique for detection, sizing and classification of corrosion defects,
several experiments using SH wave modes were conducted to assist in the validation of the finite
element model.
There are several experimental parameters that can potentially affect the amplitude, frequency
content, or phase shift of the received waveform in a pitch-catch configuration, where a defect is
located somewhere between the transmitter and receiver. These include:
1. Defect type/geometry
2. Material type
3. Material processing history (cold rolled, hot rolled, annealed)
4. Temperature
5. Specimen geometry and specimen size relative to the defect size
6. Measurement/surface condition parameters:
a. Lift-off (gap between transducers and specimen)
b. Presence of welds
c. Specimen coatings, with the possibility of coating disbonding
This project will be confined to the influence of defect geometry on transmission of SH0 and
SH1 wave modes. This chapter will describe the experimental component of that study, used to
validate the complementary numerical study presented in Chapter 4. Once it is established that
relatively slow and expensive experimental work can be accurately simulated by finite element
analysis, the experimental component for this type of study can be greatly reduced in future
work.
36
3.1 Experimental Setup
In order to investigate the applicability of SH modes for characterizing defects, circular defects
were machined on plates. A plate was used for these experiments to simplify the analysis, given
the similarities between SH mode propagation in a plate and a thin-walled pipe. Each plate had a
general configuration as shown in Figure 3.1.
Figure 3.1: Configuration of the plates used for experimental analysis
A carbon steel plate was used as carbon steel alloys currently represent the single largest class of
industrial alloys in use [7]. Furthermore, 6.35 mm thick plates were selected as they are
commonly found on storage tank floors. To machine defects of different sizes, four different
plates were used. As well, a pitch-catch configuration with two EMATs (one transmitter and one
receiver) was used to launch and receive SH waves as shown in Figure 3.2.
37
Figure 3.2: Top-view schematic of experimental setup
The dimensions of the plate were selected such that any waves reflected from the plate
boundaries would arrive sufficiently late at the receiver EMAT location [45]. This ensured that
any reflections would not interfere significantly with the primary pitch-catch waves travelling
through the defect area.
3.2 Defect Profiles
This thesis will focus on detecting a wall loss of 20% in circular step and lake-type defects of
various diameters. There are three reasons for focusing on a wall loss of 20%:
1. Codes, such as ASME B31.3, permit a 12.5% tolerance in the wall thickness for
pressurized piping [8]. So, there is a possibility that the wall thickness is slightly less than
the nominal thickness even without the presence of any corrosion. Therefore, it is
unnecessary to flag any areas where the wall thickness loss is less than 12.5% of the
nominal thickness.
2. EMATs cannot be used to precisely detect the wall loss due to the use of low frequency
ultrasound waves and a low signal to noise ratio. Previous studies have found that shear
horizontal EMATs can detect depth close to 10% accuracy for step defects [18].
Furthermore, the technique being developed in this thesis is meant as an initial screening
tool and as such will only be used to flag a potential defect and determine its approximate
size and defect-type. It is intended that a more precise defect finding technique will be
38
used after the initial screening to size the defect and its characteristics. Consequently, a
value of 20% was selected to provide some margin over the value of 12.5% so as not to
trigger false positives.
3. The amount of material loss will be greater in a defect with depth greater than 20%. As
such, the effects experienced by an ultrasound wave passing through the defect area (such
as reflection and scattering) should be amplified. Therefore, if it is possible to detect a
defect with a depth of 20% then it is expected that deeper defects can also be detected
using a similar technique.
The experiments were divided into three stages and the defect geometry on each of the four
plates was progressively altered after each stage. While the depth of each circular defect was
maintained at 20% wall loss (1.27 mm) for all plates, each plate had a defect of different
diameter and type. The slope at the edge of each defect was sequentially set at 90°, 45° and 7° for
each of the three stages. Specifics regarding the selection of defect shapes are given in the
following sections. Each plate was assigned a number (such as Plate #1) and this plate number
corresponds to the same plate in each stage of the experiment.
3.2.1 Stage 1 – Step Defects
One circular defect was initially machined into each plate with a standard end mill using a
plunge move. The main purpose of collecting data for these defects was to establish a
baseline for the smallest defect that can be reliably detected using ultrasonic amplitude and
time delay measurements. A schematic of the defect and the parameters used for each plate
are given in Figure 3.3 and
Table 3.1.
Figure 3.3: Cross-section of initial circular defect
39
Table 3.1: Parameters for step defects
Plate # ∅ (diameter) [mm] 𝛼 (angle) B (depth) [mm]
1 3.52 90 1.27
2 6.38 90 1.27
3 13.86 90 1.27
4 28.74 90 1.27
3.2.2 Stage 2 – Minor Lake-Type Defects
The experimental configuration of Figure 3.4 was used to collect ultrasonic data corresponding
to the four defects described in Table 3.2. To do so, the step defects created in the plates as
described in Section 3.2.1 were modified using a chamfer end mill to “soften” the defect edges as
illustrated in Figure 3.4. The new defect shape, now with an angle of 45o, was used to simulate
plate degradation part-way between a sharp cylinder (pitting defect) and gradual thinning (lake-
type defect).
Figure 3.4: Cross-section of gradual slope added to defect cross section
40
Table 3.2: Parameters used for minor gradual thinning defects in Stage 2
Plate # ∅ (diameter) [mm] 𝛼 (angle) A [mm] B (depth) [mm]
1 3.52 45 1.27 1.27
2 6.38 45 1.27 1.27
3 13.86 45 1.27 1.27
4 28.74 45 1.27 1.27
3.2.3 Stage 3 – Lake-type Defects
The final step, labeled Stage 3, involved enlarging the defect (decreasing the angle to 7° ± 2°)
to resemble a state of lake-type corrosion as shown in Figure 3.5, using a grinder to machine the
plate to the nominal dimensions provided in Table 3.3.
Figure 3.5: Cross-section of gradual thinning defect
41
Table 3.3: Parameters used for gradual thinning defect in Stage 3
Plate # ∅ (diameter) [mm] 𝛼 (angle) A [mm] B (depth)[mm]
1 3.52 7±2 11 1.27
2 6.38 7±2 11 1.27
3 13.86 7±2 11 1.27
4 28.74 7±2 11 1.27
3.3 Selection of Wave Parameters
In order to select the optimal operating frequency for the EMAT transmitter, Equation (4) was
used (𝑓𝑑𝑛 =𝑛𝑐𝑠
2) to find the cut-off frequency of a SH1 wave. If a 6.35 mm plate has
experienced 20% wall loss, its wall thickness at that point will be 4.76 mm. Therefore, using a
parameter d of 4.76 mm, n of 1 (for a SH1 wave) and 𝑐𝑠 of 3230 m/s (for a carbon steel plate),
we get a cut-off frequency f of approximately 335 kHz.
As well, the magnet width in the PPM array needs to be selected as it controls the wavelengths of
the SH modes that can be generated (see Section 2.5.1, Figure 2.7). Therefore, a magnet width of
6.35 mm, which generates SH modes with a wavelength of 12.7 mm, was selected to get
operating points near the ideal frequency of 335 kHz for the SH1 wave. This selection was based
on two considerations:
1. The availability of off-the-shelf magnets is limited to a number of standard sizes. One
such standard size is 6.35 mm.
2. Our requirement to generate both SH0 and SH1 modes in the test plates with a single
EMAT transmitter. If we choose a smaller wavelength such as 6.35 mm, for example,
attempting to generate a SH1 mode also results in generating a significant SH0
component at the same time. To avoid signal analysis problems, a magnet size was
selected such that the SH0 and SH1 modes do not overlap in the received signal.
42
The dispersion chart of Figure 3.6 shows SH wave modes for a 6.35 mm carbon steel plate, with
a dominant wavelength of 12.7 mm.
Figure 3.6: Dispersion curve of SH modes in 6.53 mm carbon steel plate
It is possible to generate a SH1 mode with an excitation current that has a central frequency of
365 kHz and a SH0 mode at 250 kHz. Note that the SH1 frequency operating point is on the
“knee” of the curve, and it has been shown that waves in such regions are very sensitive to wall
loss [21]. As well, the actual wave that propagates will contain a range of frequencies around the
central frequency.
Both the SH0 and SH1 wave modes are analyzed to investigate the possibility of using the SH0
signal to normalize the SH1 signal. The main purpose for this normalization is to negate the
effects of variations in lift-off and magnetic permeability that could lead to erroneous signs of
corrosion in the received ultrasonic signals.
43
3.4 EMAT Design
Both the transmitting and receiving EMATs consisted of an Innerspec Inc.6 racetrack coil and a
4x2 PPM array consisting of 25.4 x 12.7 x 6.35 mm thick magnets in the configuration shown in
Figure 3.7 (schematic) and Figure 3.8 (a).
It has been found that EMATs are very sensitive to the gap between the transducer and specimen
surface, known as lift-off. The amplitude of the wave generated drops exponentially as lift-off
increases; wave amplitudes generated by a PPM EMATs are most sensitive between a lift-off of
0 mm and 0.5 mm [46]. During inspection, a thick layer of paint, for example, could induce lift-
off between the transducer and the steel substrate of the pipe or plate specimen. For this reason, a
0.7 mm thick layer of gorilla tape7 was applied to the bottom of each transmitter and receiver
coil to reduce the sensitivity of the system and prevent spurious amplitude changes due to lift-off
during inspection.
Figure 3.7: Schematic of (a) racetrack coil and PPM array; (b) Individual bar magnet
An Innerspec PowerBox H pulser (Figure 3.8 b) was used to provide the coil excitation current
with the appropriate impedance matching circuitry between pulser and both EMATs. The
impedance matching was centered at a frequency of 350 kHz to accommodate both SH0 (250
kHz) and SH1 (at 365 kHz) wave generation. The specific settings used on the PowerBox are
6 Innerspec Inc., Forest, VA, USA
7 Gorilla Glue Inc., Cincinnati, OH, USA
a) b)
44
shown in Table 3.4. A sampling frequency of 50 MHz was used as it was much higher than twice
the highest frequency found in the generated and received waves. The signal fed from the
receiver EMAT to the receiver portion of the PowerBox H was captured by the onboard DAQ
(data acquisition) module and then transferred to a computer for further analysis. The signal
averaging and coincidence filtering mentioned in Table 3.4 were applied to the data after the data
was captured by the DAQ, whereas the gain specified was applied before the DAQ module.
Figure 3.8: (a) EMAT coil and PPM array; (b) Innerspec PowerBox H pulser
Table 3.4: Settings used in PowerBox H during data collection
Pulse Repetition
Frequency (PRF)
Gain Sampling
Frequency
Signal Averaging Coincidence
Filter
25 Hz 20 dB 50 MHz 16 signals 5
Figure 3.9 shows the actual setup used for experiments. An aluminum EMAT enclosure built by
Groupe Mequaltech8 was used to ensure constant separation distance and alignment between the
8 Groupe Mequaltech, Montreal, QC, Canada
a) b)
45
EMAT transmitter and receiver. Aluminum was used for the enclosure to block interference from
magnetic fields.
Figure 3.9: EMAT assembly on plate. The settings shown in Table 3.4 were used on the
PowerBox H for data collection.
3.5 Signal Processing
The signals obtained from EMATs are often noisy due to their weak transduction mechanism. In
order to reduce the noise, the signal was first filtered using a 6th
order zero-phase change
butterworth bandpass filter set to permit passage of frequency content within ±200 kHz of the
wave’s center frequency. Then, to calculate the signal amplitude and time delays corresponding
to each wave mode, a Hilbert transform of the signal was taken to generate the signal envelope.
To obtain the normalized SH1/SH0 amplitude the maximum amplitude of the SH1 pulse
envelope was divided by the maximum amplitude of the SH0 pulse envelope.
Figure 3.10 shows the unfiltered received SH0 and SH1 pulses on Plate #1 before defects were
machined. The corresponding filtered pulses, and their Hilbert envelopes are also shown.
46
Figure 3.10: Received SH0 and SH1 signals and corresponding filtered signals
For estimating the SH0 or SH1 pulse time delay caused by a defect, a cross-correlation technique
was used. A cross-correlation technique was found to be less sensitive to noise than techniques
such as tracking peak amplitudes, centroids and threshold crossings [47].
The cross-correlation 𝑅𝑥𝑦 between the signals of a plate without a defect, 𝑥 and a plate with a
defect, 𝑦 for one signal of length N is:
𝑅𝑥𝑦 =1
𝑁∑ 𝑥(𝑛)𝑦(𝑛 − 𝑙)
𝑁−1
𝑛=0
(21)
The time-lag l between x and y is then the maximum amplitude of 𝑅𝑥𝑦 .
47
As an example, Figure 3.11 shows the filtered SH1 signal envelopes of a wave pulse from a plate
without any defects and a case with a 20% wall loss defect of 28.74 mm and a slope angle of
90° (i.e step defect). The cross-correlation function between the no-defect case and the defect
case is also shown.
Figure 3.11: SH1 Envelope of cases with/without defect and the corresponding cross-
correlation between the no-defect case and the defect case
To compute the time delay, the lag with the maximum amplitude was divided by the sampling
frequency. In this case, a lag of 270 was divided by the sampling frequency of 50 MHz to obtain
a time delay of 5.4 μs.
3.5.1 Real-time Signal Processing
Since it is required to determine the amplitude and time delay information in real-time (or close
to real-time) for a fast scanning technique, the time that is required to process the signal is also
important.
To assess the speed of the algorithms a sample computer application that processes signals was
developed using the Python programming language. Details regarding the application are
presented in Appendix D.
48
Finite Element Model of SH Guided Wave Propagation 4
in the Presence of Defects
This chapter provides an overview of the steps taken to model the propagation of shear
horizontal guided waves in carbon steel plates with defects by Finite Element (FE) analysis. The
parameters, techniques and rationale for the FE model are covered.
4.1 Overview
The main purpose of the FE model was to develop a tool that could be used to predict the
received waveform signals for SH waves that pass through carbon steel plates with step and lake-
type defects. Such a model can later be modified to develop models for various defect geometries
and material types, eliminating the need for expensive experiments. The 3D model that
replicated experimental conditions was created in COMSOL9 FE software using the Structural
Mechanics Module. Once the FE model was constructed, its results were compared and validated
with experimental results as described in Chapter 5. Since the transduction mechanism between
EMATs and the test specimen has been studied by other researchers in detail (see Section 2.6),
that topic was not pursued here. Instead, our model focused on the propagation of SH0 and SH1
waves in plates.
4.2 Material Parameters
Material properties used to model the carbon steel plates used in the experiments of Chapter 3
are shown in Table 4.1.
9 COMSOL Inc., Stockholm, Sweden
49
Table 4.1: Material Properties Used for a Carbon Steel plate in the FE Analysis
Property Parameter
Material type Linear Elastic
Density 7850 kg/m3
Poisson’s Ratio 0.33
Modulus of Elasticity 200 GPa
Shear Speed 3230 m/s
Note: Material values were obtained from COMSOL Multiphysics’s material database
4.2.1 Time Domain vs. Frequency Domain Modeling
As described in Section 2.6, wave propagation can be numerically simulated in either the time or
frequency domain. In general, frequency domain simulations are preferred because of the ability
to use parallel processing to compute the response at several different frequencies
simultaneously. In time domain analysis, the response of the system must be calculated for each
time step sequentially and generally results in a longer simulation time. However, in this thesis
time domain models were used to create intuitive graphical representations of the wave at each
time step to better understand how it propagates with and without defects.
4.3 3D Finite Element Model
A schematic of the general 3D model developed in COMSOL version 5.1 using the Structural
Mechanics Module is shown in Figure 4.1. Using an anti-symmetry boundary condition, only
half of the 3D model was simulated in order to minimize the model size and computational
requirements. Stiffness Reduction Method (SRM) regions (see Section 2.7.1 for theory) were
used on sides of the model to reduce the mesh size.
50
Figure 4.1: Schematic of 3D FE Model
A model similar to that of Figure 4.1 was constructed for each of the 12 defect cases in the
experimental condition. Furthermore, a model without any defects at the center of the plate was
used to model the “no-defect” case. The SH0 and SH1 pulses were simulated separately on each
of the models, and the received waves were captured at the received signal location.
4.3.1 Generation of SH Waves
In order to model the generation of the SH wave, surface traction loading was applied. A
schematic of the surface loading scheme is shown in Figure 4.2. Each region represents the
forces that are present under the magnets in the experiments.
Figure 4.2: Schematic of surface traction loading applied to FE model
The input force pulse applied at each of the loading regions in the FE studies had the same
profile as the current provided by the pulser to the transmitter EMAT in the experiments of
Chapter 3; this profile is shown in Figure 4.3. The loading profile was created in the FE
51
simulations by modulating 5.5 cycles of a sin wave of the required frequency (250 kHz for SH0
and 365 kHz for SH1) with a Tukey window [48] using an 𝛼 parameter of 0.4.
Figure 4.3: Input force applied in FE model to generate surface traction loading
4.3.2 SRM Regions
While simulating SH waves, the waves generated in the model from the “surface traction
applied” region in Figure 4.1 will have one pulse traveling in the positive x-direction and another
in the negative x-direction. This is analogous to the waves generated in EMATs, as shown in
Figure 2.7. The SH waves that travel in the negative x-direction will reflect from the edge of the
plate and may interfere with the waves that pass through the defect.
One way to avoid this problem is to increase the length of the plate in the x-direction to ensure
that the waves reflected from the edges arrive at a much later time at the defect and receiver
locations. A more efficient way, where the size of the model can be smaller, is to use SRM
regions to absorb reflections in the x-direction. Furthermore, it is also easier to visually interpret
the results due to absence of reflections from the plate edges. As such SRM regions will be used
for the 3D model in this thesis.
52
As suggested in Section 2.7.1 the width of the SRM region was selected to be 1.5𝜆 (19.4 mm) in
order to absorb any incoming SH waves. Similarly, based on suggestions in Section 2.7.1, the
values of CMMax, and 𝑘𝑖𝑛𝑐 for using Equations 18 - 19 were selected as shown in Table 4.2.
Table 4.2: Stiffness Reduction Method Parameters
Parameter SH0 (f = 250 kHz) SH1 (f = 365 kHz)
CMMax 1.5x106 2.3x10
6
𝑘𝑖𝑛𝑐 494
4.3.3 Mesh
In order to meet the element size requirements mentioned in Equation (7) and provide acceptable
computational performance at the same time, a maximum element size that was 1/7th
of the
wavelength or 0.91 mm was used near the defect, and gradually increase to as big as 1/3rd
of the
wavelength (2.12 mm) at the outer extremities of the model. To mesh the defect geometry,
triangular elements were used in the vicinity of the defect, whereas square elements were used
everywhere else. Large quadrilateral elements were used at the outer extremities of the model
since accurate results for wave propagation were not necessary in this region. A schematic of the
mesh used is shown in Figure 4.4 with the element sizes scaled up for better visibility.
53
Figure 4.4: Schematic of mesh used for 3D model. Element sizes have been scaled up 3.5x
for better visibility.
4.3.4 Solver Configurations
It was found that in order for the model to converge when using the explicit time solver provided
in COMSOL, a time step that ranged from 1/2 to 1/8th
of the Courant time step (see Section
2.6.1.1) was required, resulting in very large computational time. This is likely due to the actual
solver used and smaller element sizes in the mesh near defect areas than the nominal mesh size.
Therefore, an implicit solver was used as it was able to tolerate a larger time-step and thereby
yield a lower computation time.
4.3.4.1 Selection of 𝜶 Parameter
Since the implicit solver can distort the FE results due to numerical damping, the
Generalized-𝛼 technique mentioned in Section 2.6.1.1 was selected in order to minimize loss of
higher frequencies in the received signal. A 𝛼 value of 0.4 was used for the 3D models.
54
Results and Discussion 5
5.1 Results from Experimental and FE Analysis
Results from the experiments and finite element analysis conducted in the previous chapters are
presented in the following sections.
To measure amplitude and pulse travel time changes due to defects, the SH0 and SH1 signals at
the receiver location were collected for each of the twelve defect cases as well as the “no-defect”
case for all four plates. Five trials were conducted for each case in the experimental case to
assess signal variability, whereas only one FE simulation was required for each defect geometry.
As well, both the experimental and FE signals were filtered using a sixth order Butterworth
bandpass filter with the passband being ±200 kHz of the pulse’s center frequency, in order to
remove noise. Signal envelopes were then calculated for all signals using a Hilbert transform.
Details regarding the computations and sample signal waveforms can be found in Section 3.5.
5.1.1 Amplitude Changes Due to Defects
In this section, we examine the changes in received signal amplitude for both the SH0 and SH1
modes due to the presence of defects; finite element and experimental results are compared. The
peak value in the SH1 Hilbert envelope value for a particular case was divided by the peak SH0
envelope value; it was hypothesized that this procedure would reduce the effects of lift-off and
the variability in magnetic permeability between the plates. This relative value for each plate
with a defect was further normalized by dividing it by the average value of the “no-defect” case
for all four plates. Therefore, the no-defect case had a normalized amplitude of unity, and all
cases featuring a plate with a defect had an amplitude less than unity.
Figure 5.1 shows a comparison between the normalized maximum envelope values for
experimental measurements and 3D finite element simulations. The plotted data points are the
mean value of the five trials along with error bars showing ± one standard deviation. Cross
sections of the defect type are shown beside the corresponding graphs. Details of the data used to
construct Figure 5.1 are provided in Appendix A.
55
Figure 5.1: SH1/SH0 amplitude ratios, normalized by the no-defect case for 𝜶 (slope) of (a)
90° (b) 45°, and (c) 7° for different defect diameters 𝝓 with corresponding schematics of the
defect cross-section. Error bars indicate +/- one standard deviation.
(a)
(b)
(c)
56
As can be seen from Figure 5.1, an increase in defect diameter causes a decrease in amplitude of
the received SH1/SH0 wave ratio. The average difference between the experimental and FE
cases is 4.76% (standard deviation = 1.95%). This difference is well within the generally
accepted uncertainty of finite element modelling of this type. As such, we can say that the FE
model can be used to approximate the SH0/SH1 amplitude results that can be expected in
experiments similar to the one presented in this thesis. Appendix B lists several sources of error
that may have caused discrepancies between experimental results and FE simulations. Appendix
C discusses the accuracy of detecting and sizing defects.
From Figure 5.1 (c) it can be seen that for a defect diameter at the bottom of the defect 𝜙 of
3.5 mm, an amplitude decrease of approximately 40% was observed. However, in Figure 5.1 (a)
and (b), a similar 40% amplitude drop corresponds to a diameter 𝜙 of approximately 15 mm.
Therefore, the amplitude ratio cannot directly provide an indication of the diameter at the bottom
of the defect.
This is likely because the diameter at the top of lake-type defects was much larger than the
diameter at the bottom. For instance, a defect with a slope of 7° and a bottom diameter of 3.5 mm
actually had a diameter at the top of the defect of 24.3 mm. As such, another parameter that can
be used is the average defect diameter: the sum of the largest and smallest diameter divided by
two. The difference between the average defect diameter and defect diameter at the bottom of the
defect is illustrated in Figure 5.2.
Figure 5.2: Schematic of the average defect diameter showing the cross section a 3.5 mm
lake defect with a slope of 7°.
57
In Figure 5.3, the SH1/SH0 amplitude ratios from Figure 5.1 are plotted with respect to the
average defect diameter for the three different defect slopes. From this figure it is clear that the
amplitude ratio is a better indicator of the average diameter of a defect. The average difference of
4.76% between the FE and experimental cases is still applicable for Figure 5.3.
Figure 5.3: SH1/SH0 amplitude ratio normalized with the no-defect case for average defect
diameters for experimental data
There is still some ambiguity in determining the exact defect size. For instance, an amplitude
decrease of 50% could signify the presence of either a step defect with an average defect
diameter of 22 mm, or alternatively, there could be a lake defect with an average defect diameter
30 mm. Therefore, a limitation of using the SH1/SH0 amplitudes is that we can only estimate the
average minimum defect diameter for a given defect. Furthermore, the amplitude ratio does not
provide an indication of whether a defect is step-type or lake-type.
58
5.1.2 Time Delay Changes Due to Defects
To obtain the time delay the cross-correlation function between the received no-defect SH1
signal and the SH1 defect signal was computed. The time-lag corresponding to the maximum
cross-correlation value was taken as the pulse time delay caused by the defect.
The SH1 pulse time delays for all plates as determined by both experiment and 3D finite element
(FE) analysis are shown in Figure 5.4. The graphs plot the mean value of the five trials along
with error bars of ± one standard deviation. Cross sections of each defect type are shown beside
the corresponding graphs. The time delay average difference between the experimental and FE
cases is 0.74 μs (standard deviation = 0.53 μs), or alternatively 19%±17%. While this error is
significant considering that the largest time delay observed was approximately 6 μs, the FE
simulations still provide a rough estimate of the time delay. There are several sources of error,
documented in Appendix B, that may have resulted in discrepancies between experimental
results and FE simulations. A discussion on the accuracy of detecting and sizing defects is
presented in Appendix C.
Based on experimental data all three defect slopes in Figure 5.4 exhibit similar time delays,
despite the fact that the average defect diameters between the step-type and lake-type defects are
quite different. Therefore, the data suggests that the pulse delay depends more so on the diameter
at the bottom of the defect.
The type of defect can be determined by comparing the minimum average diameter data from the
SH1/SH0 data obtained from Figure 5.3 to the defect diameter at the bottom of the defect
obtained from the time delay in Figure 5.4. If the diameter at the bottom is much smaller than the
average diameter, lake-type corrosion is likely present. Otherwise, if both Figure 5.3 and Figure
5.4 provide the same diameter, the defect may be step-type.
It must be noted that Figure 5.4 provides an estimate of only the minimum defect diameter at the
bottom of the defect. For example, if a time delay of 6 μs is observed, the bottom defect diameter
may be either 28 mm in the case of a step defect, or any diameter greater than 14 mm in the case
of a lake defect. Therefore, if the defect is very large, then it may not be possible to determine
the defect type exactly as there will be some ambiguity in the data.
59
Figure 5.4: SH1 pulse time delay at the receiver location for 𝜶 (slope) of (a) 90° (b) 45°, and
(c) 7° for different defect diameters 𝝓 with corresponding schematics of the defect cross-
section. Error bars of 2 standard deviations are shown.
60
5.2 Discussion
This section further discusses the reasons for the results and provides an overview of the
implications for the corrosion detection technique based on the SH1 and SH0 modes.
5.2.1 Effects of Beamwidth
In previous studies that focused on analyzing SH1 and SH0 propagation through 2D cross-
sections of defects, the amount of amplitude/pulse time delay change of a wave was found to be
an indicator of the amount of wall loss [18], [21], [44]. However, all defects in this thesis had the
same approximate wall loss but the amplitude/pulse delay results were quite different for each
diameter. Consequently, for the 3D case of defects considered in this thesis, the amplitude/pulse
time delay changes can also be used for defect diameter sizing.
Figure 5.5 shows a top view of the beam width of the SH1 wave as it approaches a 28.74 mm
lake-type defect, which is the largest defect considered in this thesis. Here, the propagation of the
wave is represented by the y-direction displacement field. A positive/negative y-direction
displacement indicates displacements (in meters) at node locations in the positive/negative y-
directions. It is possible to see that the -12 dB beamwidth, or region in which around 75% of the
energy of the pulse is concentrated, is almost twice as wide as the defect in this particular
situation.
61
Figure 5.5: Comparison between SH1 beamwidth (y-direction displacement field) and
diameter of 28.74 mm lake defect
So, when considering a 3D case where the defect has a finite width, it is also necessary to
consider the possibility the SH wave scattering around a defect. This is true for all defect cases in
this thesis because the beamwidth of both the SH1 and SH0 case are wider than the defect.
5.2.2 Pulse Amplitude
As mentioned in Section 5.1.1 a reduction in the SH1/SH0 amplitude ratio can be correlated to
the average defect diameter, but not necessarily the defect type (step or lake-type). There are two
main reasons a defect causes a loss of transmitted pulse amplitude: reflection and/or scattering
(the primary cause), and mode-conversion energy loss. The amount of scattering and reflection
that occurs for each wave mode depends considerably on the defect slope and is explored in the
following sections.
In the case of lake-type defects, the majority of the amplitude loss in the received SH1/SH0
signal can be attributed to scattering. For step-type defects, both scattering and reflection occur.
This discussion will focus on lake defects as it is considerably difficult to detect lake type defects
using industry standard techniques.
5.2.2.1 Lake-type Defects (7° Defect Slopes)
Lake-type defects do not have a significant effect on the amplitude of SH0 waves. This is
demonstrated in the 3D model of SH0 wave propagation in Figure 5.6. The cross-sectional view
of the plate shows the intensity of the normalized displacement field in the y-direction of the 3D
model, which represents the shear component of the SH0 pulse.
62
Figure 5.6: Cross sectional view of SH0 pulse (normalized y-direction displacement field) as
it passes through a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss
with 7° slope at times (a) 60 𝛍𝐬, (b) 70 𝛍𝐬 and (c) 90 𝛍𝐬 after transmitter excitation
In Figure 5.6, and other cross sectional views of FE simulations presented in this thesis, areas of
positive/negative y-direction displacement represent node displacement into/out of the plane of
the cross section.
It can be seen that no significant reflection of the SH0 pulse occurs due to the lake-type defect.
This is consistent with previous 2D studies conducted by Nurmalia et al [25]. Any decrease in
the pulse’s transmitted amplitude is primarily due to beam spread as the wave propagates; the
decrease due to beam spread occurs regardless of whether a defect is present. Figure 5.7 shows
the propagation of a SH0 pulse past a defect from a top view of the plate. It further confirms that
no significant reflection or scattering has taken place as the SH0 wave travels through the defect.
63
Figure 5.7: Top half view of SH0 pulse (y-direction displacement field) as it passes through
a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 7° slope at
times (a) 60 𝛍𝐬, (b) 70 𝛍𝐬 and (c) 90 𝛍𝐬 after transmitter excitation
As the SH1 pulse passes through a gradual thinning defect, however, its spectrum of wave
numbers shifts downwards as the wavelength increases. This is illustrated Figure 5.8 in where a
SH1 pulse propagates along a plate that contains a 28.74 mm diameter defect with 7° slope.
64
Figure 5.8: Cross sectional view of SH1 pulse (normalized y-direction displacement field) as
it passes through a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss
with 7° slope at times (a) 70 𝛍𝐬, (b) 100 𝛍𝐬 and (c) 115 𝛍𝐬 after transmitter excitation
The results of the change in wave as the SH1 pulse travels down the slope of the defect in the 3D
case was consistent with the results for a 2D cross-sectional model [25]. As the wave travels
down the 7° slope, the frequency-thickness product of the wave decreases because the thickness
is gradually decreasing. If the frequency-thickness product decreases, the 365 kHz operating
point will shift to the left of the SH1 dispersion curve until it approaches the cut-off frequency-
thickness (see Figure 3.6). As a result, the group velocity of the pulse decreases and the phase
velocities increase. As well, the wave number spectrum decreases as the wavelength increases.
However, in the 2D case the pulse experiences considerable reflection after it encounters the
bottom of the defect.
In the 3D case, the wave is able to scatter around the defect instead of reflecting. Figure 5.9
shows the top view a SH1 pulse propagating along a plate that contains a 28.74 mm diameter
defect with 7° slope. This amount of wall loss at the defect location is sufficient to disrupt the
propagation of the wave and result in scattering of the SH1 pulse. By the time the pulse reaches
the receiver location, its amplitude has decreased significantly due to scattering.
65
Figure 5.9: Top half view of SH1 pulse (y-direction displacement field) as it passes through
a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall loss with 7° slope at
times (a) 70 𝛍𝐬, (b) 100 𝛍𝐬 and (c) 165 𝛍𝐬 after transmitter excitation
It is also possible to analyze the frequency content at the defect region and around the defect
region to better understand how the wave behaves. This will be discussed in Section 5.2.3 as the
time delay of the pulse and frequency content are related.
66
5.2.2.2 Step-Defects (90° and 𝟒𝟓° Defect Slopes)
Although SH0 pulses are not sensitive to lake-type defects, there is sensitivity to step defects.
Since defects with 90° and 45° slopes have relatively abrupt changes in wall loss, a SH0 pulse
experiences both reflection and scattering from the defect walls. Figure 5.10 shows a cross-
sectional view of the y-direction displacement field determined by finite element analysis, that
illustrates how the SH0 wave experiences reflection at such a defect.
Figure 5.10: Cross sectional view of SH0 pulse (normalized y-direction displacement field)
as it passes through a 6.32 mm thick plate with a 28.74 mm diameter defect of 20% wall
loss with 90° slope at time of 80 𝛍𝐬 after transmitter excitation
As well, SH1 pulses are also more sensitive to step-defects due to additional reflection from the
step-defect. The scattering shown in Figure 5.9 is also present in the case of a step-defect. In
cases where the remaining wall thickness is below the cut-off thickness, it has been shown that
the SH1 pulse completely mode converts into the symmetric SH0 wave since the SH1 wave
cannot exist at this thickness [25]. For defects considered in this thesis, the remaining wall
thickness was always greater than the cut-off thickness; so, only a downward shift in the
spectrum of wave numbers, as in the lake-type defect, is observed.
5.2.2.3 Benefits of Using the SH0/SH1 Ratio
Although we now know that SH1 is more sensitive to both step and lake defects, there are three
potential benefits of using the SH1/SH0 amplitude ratio to determine the average defect diameter
of a step or lake defect:
67
1. The effects of lift-off and magnetization are reduced: Since generation and detection of
both SH1 and SH0 pulses are almost equally affected by any changes in a material’s
magnetic permeability and transducer lift-off, evaluation of the SH1/SH0 amplitude ratio
should cancel out such effects on individual pulse amplitudes.
2. The SH1/SH0 amplitude ratio can be used to check for false positives: A complete loss of
the SH1 signal component by itself may indicate that there is a defect present or it may
also mean that the SH1 wave was not properly generated. Improper transduction can
occur due to a variety of reasons such as an extremely rough surface, excessive probe lift-
off, or thick coatings of paint/insulation. The SH0 mode, however, is not as sensitive to
partial wall loss defects and will not likely experience total scattering/reflection in the
situations we are considering. Therefore, if there is also no SH0 component is present in
the received signal, it is likely that there was an issue with the EMAT’s transduction
mechanism.
3. The SH1/SH0 amplitude ratio is more sensitive to lake-type defects than step defects:
The amplitude of the SH0 component in a received signal will not decrease due to the
presence of lake-type defects. Consequently, a benefit is that the magnitude of the
SH1/SH0 ratio will decrease when a lake-type defect is present.
In the case of step defects, the SH0 amplitude will also decrease slightly as SH0 waves
will experience reflection. However, SH1 waves also experience additional reflection in
the case of step defects, preventing any significant loss of sensitivity.
While it may be possible to analyze the changes in SH0 and SH1 to determine if a defect is step-
type or lake-type, it will not be considered in this thesis. Instead, the approach based on
analyzing the change in the time delay of the SH1 pulse will be used.
5.2.3 Time Delay Changes due to Defects
A benefit of using the pulse’s time delay as an indicator is that it is independent of the amplitude
of the pulse as it depends on the frequency spectrum of the pulse. So, the time delay of the pulse
can be used to verify whether the amplitude loss in a received signal is due to the presence of a
defect, or due to other factors related to the transduction of the wave such as a defective
transducer, transducer lift-off, and magnetic permeability changes.
68
To understand how the time delay occurs, it is possible to analyze the frequencies of the wave as
it travels around the wave. Two locations around/at the defect will be considered and are shown
in Figure 5.11 (a). The corresponding normalized frequency responses at those locations are
shown in Figure 5.11 (b).
Figure 5.11: (a) Top view of SH1 propagation for 28.74 mm lake defect indicating locations
where frequencies will be analyzed. (b) Frequency spectrum at locations around and at
defect locations
From Figure 5.11 it is possible to see that the wave travelling around the defect contains more
low-frequency content than the wave that passes through the defect. The frequencies components
in the 250 – 300 kHz range correspond to the faster travelling SH0 waves that increase the SH1
pulse’s group velocity. This observation is consistent with the observations made in 2D cross-
a)
b)
69
section studies [21]. This suggests that the decrease in thickness in the defect region affects the
propagation of the wave.
One important observation in the 3D case was that the lower frequency components of the wave
had merely scattered around the defect instead of experiencing reflection as noted in the 2D case
[21]. As such, it may be possible for a portion of the scattered frequency components to merge
with the received signal depending on defect shape and size. This would make it difficult to use a
time delay based approach to detect the defect.
From the time delay graphs presented in Section 5.1.2, we can see that the SH1 pulse
experiences a time delay that can be related primarily to the defect diameter at the bottom of the
defect, regardless of whether the defect is step or lake-type. This is expected since region at the
bottom of the defect is close to cut-off thickness (of has the lowest frequency-thickness) and the
pulse experiences the changes in group velocity only for this region of decreased wall thickness.
5.2.4 Frequency Spectrum Changes Due to Defects
Since the time delay caused by plate defects can be related to the frequency content in the
received signal, it is also possible to observe a change in the frequency spectrum of the received
SH1 pulses.
Figure 5.12, shows the frequency spectrum of received signals from a “no-defect” case and two
7° slope cases (with defect diameter at bottom of the defect being 3.52 mm and 28.74 mm) after
transmitting a SH1 pulse. These particular defect sizes were chosen to show the variability of the
frequency spectrum between different defect diameters. The frequency spectrum amplitudes,
computed by taking the Fast Fourier Transform (FFT) of the filtered signals, have been
normalized such that all signals have a maximum amplitude of unity.
70
(a) (b)
Figure 5.12: Frequency response measured at the receiver location for the (a) Experimental
measurement and (b) FE simulations, where 𝝓 is the diameter at the bottom of the defect
and 𝜶 is the defect slope
From Figure 5.12 we can see that the experimental and FE simulations do not have similar
frequency responses. This is likely because the experimental frequency results are affected by the
narrow bandwidth of the EMAT whereas the FE results do not have this “filtering” effect.
A statistical parameter that can be used to quantify the amount of frequency spectrum shift that
has occurred is the skewness of the frequency spectrum. The skewness is a measure of the
asymmetry in a distribution, and is given for a data set X1, X2, …, XN by [49]:
Skewness =Σ𝑖=1
𝑁 [(𝑋𝑖 − �̅�)]3/𝑁
𝑠3
Here N is the number of data points, and s is the standard deviation of the data set.
If the skewness of a distribution is negative, it signifies that the “mass” of the distribution lies to
the right of the mean. In the cases where the lower frequencies of the spectrum have been
reflected or scattered by the defect, such they are lost to the main pulse, one expects the
71
skewness of the frequency spectrum to be negative. The remaining pulse spectrum delivered to
the receiver when defects are present skews towards higher frequencies, i.e., to the right of the
spectrum. Figure 5.13 shows the frequency spectrum skewness in the received SH1 signal for
various defect sizes.
Figure 5.13: Mean SH1 Frequency Spectrum Skewness for different defect sizes and slopes
for five trials of each defect case.
Evidently, as the defect diameter at the bottom of the defect increases, the skewness decreases.
As such, negative skewness seems to be a strong indicator that some of the lower frequencies of
the pulse are no longer present in the received signal while the higher frequencies pass through
uninterrupted. This also suggests that the amount partial frequency loss that occurs depends
primarily on the diameter at the bottom of the defect as the wall thickness changes affect the
operating point of the wave on the dispersion curve.
72
5.3 Summary of Defect Classification
It is possible to use a combination of pulse time delay and amplitude to provide an indication of
the presence of a defect. The following steps describe how one can estimate the defect diameter
and type based on the analysis presented in Sections 5.1 and 5.2:
Step 1: Establish the presence of a defect
Based on information presented in Appendix C, if the amplitude decrease of the SH1/SH0 ratio
is greater than 14% then it is likely that there is a defect is present.
Step 2: Assess SH1/SH0 amplitude ratio drop to estimate average defect diameter
The minimum average defect diameter can be determined using a set of FE results similar to
those shown in Figure 5.3. To calibrate and automate a system similar to the one used in this
report, data as shown in Table A.2 in Appendix A can be used with an
interpolation/extrapolation procedure.
Step 3: Use the SH1 pulse’s time delay to estimate diameter at bottom of the defect
If significant amplitude loss has occurred, it will be accompanied by a corresponding increase in
time delay to infer that a defect is present. An estimate of the minimum diameter at the bottom of
the defect can then be determined from Figure 5.4. Alternatively, data from Table A.3 can be
used with an interpolation/extrapolation procedure.
Note that the defect diameter at the bottom is not the same as the average defect diameter in the
case of lake defects. If defect diameter at the bottom of the defect estimated from the time delay
information is much smaller than the average defect diameter estimated from the amplitude drop,
lake-type corrosion is likely present. Otherwise, if both the average and the bottom defect
diameters are similar, a step defect is likely present.
For the purposes of this thesis, only 24 different defect cases were considered with the intention
of validating the FE model. Using the FE model, a database can now be created of SH1 and SH0
received signal amplitudes and pulse time delays, for various different defect shapes that may be
encountered in practical situations.
73
Summary & Conclusions 6
6.1 Detection and Sizing of Corrosion Defects
The first objective of this thesis was to develop an ultrasonic testing technique that can be used
to detect and size corrosion defects. This objective was met by investigating the propagation of
SH0 and SH1 waves, generated with EMATs in a pitch-catch configuration, through defects with
different geometries. In the presence of a defect, the amplitude of the received SH1/SH0 signal
ratio amplitude was correlated to the minimum average defect diameter (sum of the diameter at
the top and bottom of defect divided by two). By operating in the “knee” region of the SH1
dispersion curve, it was found that the SH1/SH0 ratio was able to detect both step-type and lake-
type defects. The time delay of the received SH1 pulse was correlated to the minimum diameter
at the bottom of the defect (diameter at 20% wall loss).
Since defects with diameters smaller than the SH wave’s beamwidth were considered in this
thesis, the main cause of reduction in the amplitude was scattering. In general, SH0 waves were
not sensitive to lake-type defects and only slightly sensitive to step-defects. However, the
transmitted SH1 pulse significant scattering for all defect types. As well, loss of lower
frequencies in the SH1 pulse that passed through defects accounted for a time delay of the
received pulse. Therefore, using EMATs in a pitch-catch configuration to transmit/receive SH
waves can be a viable method of detecting and sizing corrosion defects in thin-walled structures.
6.2 Development of 3D Finite Element Model
The second objective was to develop a 3D finite element model that can approximate the
propagation of SH0 and SH1 waves in plates with step and lake-type defects. As such, a 3D FE
model validated with experimental data was presented in this thesis.
The 3D model was able to predict the scattering and cut-off effects that were expected from
defects that had a diameter smaller than the SH wave’s beamwidth. When compared to the
experimental analysis, the amplitude data from the model had an average error of 5%±2%;
whereas the average time delay error was 19%±17%. Consequently, it would be possible to use
similar models to simulate the propagation of SH0 and SH1 waves for several different defect
sizes without the need for expensive and time consuming experiments.
74
6.2.1 Summary of Algorithm for Defect Detection and Sizing using SH1 and
SH0 signals
Based on the results from this thesis, the following procedure can be used to determine the size
and type of defect where the wall loss is 20%:
1. Using the dispersion curve for the specimen (material and thickness) to be tested, select
an operating point on the knee of the SH1 curve as mentioned in Section 3.3.
2. Collect reference SH1 and SH0 signals from a sample where there are no defects
3. Collect SH1 and SH0 signals from a specimen that is to be tested for defects.
4. Take the Hilbert envelope of all signals.
5. Obtain the peak value of the Hilbert envelope value of all signals and compute the ratio
of:
(𝑆𝐻1𝑆𝐻0
)defect
(𝑆𝐻1
𝑆𝐻0)
no−defect
This provides the normalized SH1/SH0 amplitude of the signal.
6. Compute the cross-correlation between the SH1no-defect and SH1defect envelopes, and store
the time lag (time delay) where the maximum value of the cross correlation of the two
occurs.
7. Determine the minimum average defect diameter from look-up table similar to that of
Table A.2 using the normalized SH1/SH0 amplitude computed in Step 5. Interpolation or
extrapolation would likely be required.
8. Determine the estimated minimum bottom defect diameter from a look-up table similar to
that of Table A.3 using the time delay from Step 6. In the case where the bottom defect
diameter is similar to that of the average defect diameter found in Step 7, then it is likely
that the defect is a step-defect. If the defect diameter based on the time delay is much
smaller than the diameter found in Step 7, then a lake-type defect is likely present.
75
6.3 Future Work
1. Investigate how defect depth can affect the received signals: While the case of detecting
20% wall loss defects was considered in this thesis, knowing the approximate amount of
wall loss can be useful. It is known that SH1 modes cannot propagate when the wall loss
is below cut-off thickness (approximately 20% wall-loss for the parameters used in this
thesis). However, it would be useful to determine the effects of defect wall loss between
20% and 40% on the amplitude and time delay. Being able to determine the depth of the
defect will provide more information on whether a defect warrants a detailed inspection
using a precise testing method.
2. Perform FE simulations for additional defect geometries: It has been shown in this thesis
that there was very good agreement between the finite element simulations and
experimental measurements. Additional simulations can be done for larger defect sizes,
different defect shapes, and different slopes in order to build a database of results for
several different geometries. As well, the possibility of using frequency domain
simulations can be investigated to take advantages of parallel processing techniques to
reduce simulation times.
3. Analysis of propagation when there is damping applied on the plate/pipe due to soil or
fluid present on the surface of the pipe or plate: It is known that coatings, fluids, and
other materials such as soil can dampen guided waves, attenuating the amplitude and
resulting in increased time-delays. As such, it would be necessary to investigate these
effects if there is a possibility that on-site investigations involve coatings, soil, or fluids.
4. Investigating effects of interference from multiple defects, welds and edges of structures:
Since we know that considerable scattering occurs due to defects, it is also possible that
the scattered waves interact with other defects, welds etc., causing further
scattering/reflection of the waves. If this additional scattering is such that some of the
waves arrive near the receiver location, it is possible that the amplitude and time delay
indicators mentioned in this thesis no longer apply.
76
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Appendices
Appendix A – Numerical Results
This appendix contains detailed numerical data that were summarized in Figure 5.1, Figure 5.3,
and Figure 5.4 shown in Section 5.1.
Table A.1 shows the numerical values for the data points shown in Figure 5.1. The average
difference between the experimental and FE results is 4.76%, with a standard deviation of
1.95%.
Table A.1: Average received SH1/SH0 amplitude for defect diameters relative to the
no-defect case.
Average Relative Amplitude for Defect Diameter (%)
3.52 mm 6.38 mm 13.86 mm 28.74 mm
Slope Exp FE Diff Exp FE Diff Exp FE Diff Exp FE Diff
90° 94.3 89.7 4.6 81.6 79.1 2.5 66 65.5 0.5 36.1 28.4 7.7
45° 94.7 90.6 4.1 77.9 85.1 7.2 68.4 71.9 3.5 29.3 36.2 6.9
7° 60.8 65.1 4.3 61.3 56.4 4.9 56.1 50.4 5.7 36.4 41.6 5.2
Note: Exp: Experimental case, FE: Finite element case, Diff: Difference between the experimental and
the finite element case
82
Table A.2 shows the same information presented in Figure 5.3, that is the average estimated
defect diameter based on the received amplitude of the signal, in a look-up table format.
Table A.2: Average received SH1/SH0 amplitudes for average defect diameters relative to
the no defect case.
Average defect
diameter [mm]
Slope [°] Relative Received Experimental
Amplitude [%]
Relative Received FE
Amplitude [%]
3.52 90 94.3 89.7
4.79 45 94.7 90.4
6.38 90 81.6 79.1
7.65 45 78 85.1
13.86 90 66 65.5
14.52 7 60.8 65.1
15.13 45 68.4 71.9
17.38 7 61.3 56.4
24.86 7 56.1 50.4
28.74 90 36.1 28.4
30.01 45 29.3 36.2
39.74 7 36.4 41.6
83
Table A.3 shows the average time delays shown in Figure 5.4. The average difference between
the experimental and FE results is 0.74 μs (or 19% on average), with a standard deviation of 0.53
μs (17%).
Table A.3: Average time delay for defect diameters relative to the no defect case.
Average Pulse Time Delay for Defect Diameter (𝝁s)
3.52 mm 6.38 mm 13.86 mm 28.74 mm
Slope Exp FE Diff Exp FE Diff Exp FE Diff Exp FE Diff
90° 1.77 1.6 0.17 4.62 3.21 0.41 4.69 3.6 0.39 4.84 5.2 0.38
45° 2.65 2.4 0.25 4.04 3.36 0.58 4.05 3.58 0.47 5.62 4.05 1.57
7° 2.02 0.70 1.32 4.14 2.24 1.90 6.31 7 0.69 6.09 6.86 0.77
Note: Exp: Experimental case, FE: Finite element case, Diff: Difference between the experimental and
the finite element case
84
Appendix B – Sources of Error
The sources of error in the experimental analysis and finite element model are discussed in this
appendix.
Experimental Analysis
1. Machining of defects: Since the defects were carved out using a milling machine that was
not numerically controlled, there was some amount of variability in the actual dimensions
of the defects. In particular, the tolerances for the 7° defect were slightly less because
hand tools were used to machine the defect. In the 3D models, it was found that a change
of ±0.05 mm (or 0.7% wall thickness) defect depth resulted in amplitude changes of
approximately 1.3%. Nevertheless, care was taken to measure the exact dimensions of the
defect before modeling them.
2. Noise due to transduction mechanism: As a result of the noise and fluctuations of the
signal received from the EMAT, the standard deviation of the trials in the experimental
case was up to 6% for the amplitude measurements and as much as 17% for time delay
measurements. Clearly, the time delay measurements were more sensitive to the
fluctuations in the signal and may have negatively impacted the errors between the FE
and experimental results. Attempts were made to minimize effects of noise in the
experiments by using an algorithm that calculates the signal envelope, utilizes filtering
for the amplitude data and by using a cross-correlation based approach to calculate the
pulse time delay. However, using more powerful magnets, such as Grade N52 magnets,
and a higher powered pulser could help in improving the signal to noise ratio.
FE Analysis
1. Mesh size and meshing of defect regions: A mesh of 7 elements per wavelengths was
used in the area of study as this was determined to be the minimum requirement for an
acceptable amount of error as mentioned in Section 2.6.1. However, it is likely possible
to reduce the error further by using a finer mesh.
2. Numerical damping due to algorithm used: Since an implicit time stepping algorithm was
used, some of the higher frequencies of the received signal were damped due to the
85
numerical procedures used, resulting in errors particularly when calculating the time
delay. To prevent this, an efficient frequency domain model could be developed where
the higher frequencies will not be damped
3. Difference in geometry and material properties: Although the nominal sizes of the plates
used in the experimental were fixed, manufacturing tolerances for the plates resulted in
slightly different actual plate dimensions. Care was taken to accurately model the plate in
3D simulations. As well, since the alloying proportions in the actual material likely
differed from the ideal carbon steel parameters used in the simulations, some degree of
error will be present in the simulated results. In particular, estimation of the time delays
from pulses will vary considerably if in correct material properties are used since the
phase/group speeds could differ between experimental and FE cases.
86
Appendix C - Accuracy of Detecting and Sizing Defects
This appendix discusses the accuracy of detecting and sizing defects based on Figure 5.1 and
Figure 5.4. The estimations of accuracy in this section are applicable only to the experimental
setup used in this experiment. As such, each EMAT setup should be characterized individually.
In general, the accuracy of the techniques presented in this thesis are low when compared to
bulk-wave techniques. However, is not a major issue since the objective was to develop a fast
scanning tool that does not require direct access to the defect location.
SH1/SH0 Amplitude Ratio
Based on Figure 5.1 the two standard deviation (SD) range of the SH1/SH0 amplitude data
collected for the no-defect case (5 trials on each of the four plates) was ±14% of the mean value.
This means that a drop of up-to 14% may be observed in the SH1/SH0 wave ratio during an
inspection without a defect present. Therefore, based on amplitude data, only defects that result
in an amplitude drop of greater than 14% can be detected accurately.
The ±SD amplitude range for the 3.52 mm 𝜙 step defect is approximately ±5 percent. However,
since the 3.52 mm 𝜙 step defect amplitude range intersects the no-defect amplitude range,
accurate detection of very small step defects is not possible. A step defect of at least 6.38 mm
average diameter would be required for it be considered detectable. In the case of lake defects,
the average defect diameter would have to be 6.38 mm.
Provided the amplitude drop is much greater than 14% sufficient it is possible to estimate the
minimum average defect diameter with an accuracy of approximately ±3 mm based on an
average ±SD amplitude range of ±4.6%.
SH1 Pulse Time Delays
For estimating pulse time delays, the ±2 SD range from Figure 5.4 for the no-defect case
corresponded to a time delay change of ±0.6 μs. As such, it may be possible to detect defects
with a bottom diameter as small as 3.52 mm. However, the ±SD time delay range of ±0.7% for
smaller defect diameters may result in an uncertainty of up to ±2.5 μs, preventing accurate
87
detection. If the defect diameter is very large only an estimate of the minimum defect diameter
can be found.
Appendix D – Real Time Signal Processing Application
This section shows a sample computer program, developed using the Python programming
language, that can be used to identify the presence of defects. The application receives the
received waveform signal from the pulser and can be used to perform real-time analysis on the
signal.
Figure D.1: A sample signal processing application using Python that can perform real-
time calculations
a)
b)
c)
d) e)
88
The program was written in Python version 3.410
with PyQtGraph11
as the graphing front-end. It
can compute calculations that, as indicated in Figure D.1, include: a) filtering signal, b)
calculating signal envelope, c) calculating signal frequencies d) calculating cross-correlation
based time delays between defect & no-defect cases and e) calculating the max cross correlation
values between defect & no-defect cases. The computational complexity is O (N log N) where N
is the number of points, based on the use of FFT algorithms.
In order to perform the above function, the following algorithms were used from the SciPy12
and
NumPy13
libraries:
a. Signal filtering: A third order zero-phase change Butterworth filter was used in
this program, but any other similar bandpass filter can be used
b. Determining the signal envelope using a Hilbert transform
c. Determining the frequency spectrum of a signal using a fast Fourier transform
(FFT)
d. Calculating cross-correlations between envelopes and finding the time lag of the
maximum cross-correlation value
10 https://www.python.org/download/releases/3.4.0/
11 http://www.pyqtgraph.org/
12 https://www.scipy.org/
13 http://www.numpy.org/