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Theses and Dissertations
2014
A study of guided ultrasonic wave propatation
characteristics in thin aluminum plate for damage
detection
Mustofa Nurhussien Ahmed
University of Toledo
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Recommended Citation
Ahmed, Mustofa Nurhussien, "A study of guided ultrasonic wave propatation characteristics in thin aluminum plate for damage
detection" (2014). Theses and Dissertations. 1688.
http://utdr.utoledo.edu/theses-dissertations/1688
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A Thesis
entitled
A Study of Guided Ultrasonic Wave Propagation Characteristics in Thin Aluminum Plate
for Damage Detection
by
Mustofa Nurhussien Ahmed
Submitted to the Graduate Faculty as partial fulfillment of the requirements for the
Master of Science Degree in Civil Engineering
_________________________________________
Dr. Douglas K Nims , Committee Chair
_________________________________________
Dr. Brian W. Randolph, Committee Member
_________________________________________
Dr. Daniel Georgiev, Committee Member
_________________________________________
Dr. Patricia Komuniecki, Dean
College of Graduate Studies
The University of Toledo
May 2014
Copyright 2014, Mustofa N Ahmed
This document is copyrighted material. Under copyright law, no parts of this document
may be reproduced without the expressed permission of the author.
An Abstract of
A Study of Guided Ultrasonic Wave Propagation Characteristics in Thin Aluminum Plate
for Damage Detection
by
Mustofa N Ahmed
Submitted to the Graduate Faculty as partial fulfillment of the requirements for the
Master of Science Degree in Civil Engineering
The University of Toledo
May 2014
The use of Lamb waves to investigate damage in thin metal plates is investigated.
This study is necessary to have a thorough understanding of Lamb wave propagation
characteristics, its dispersion phenomena, its behavior when scattered from minor flaws,
and its ability to detect damages. Nowadays, there is a growing interest to use Lamb
waves for damage detection techniques.
A literature review of Lamb waves and other types of waves pertinent to their use
in damage detection mechanisms is presented. Dispersion curves for aluminum plates are
studied for symmetric and anti-symmetric modes. Detailed comparison between the
different modes, and the merits and demerits of these wave modes which help to select an
appropriate mode for use in damage detection is also explained. Different types of
damage have been detected experimentally using a pitch-catch method and are verified
by using Waveform Revealer and finite element software, Pzflex. Based on selected
fundamental Lamb wave modes, damage inflicted by drilling a through-thickness hole in
an aluminum plate has been detected experimentally using a pitch-catch method by
applying mode conversion phenomena and is verified by using Waveform Revealer.
iii
Moreover, different sizes of through-thickness holes and cracks in an aluminum plate
have been detected by running simulations in Pzflex and using changes in time of flight
and amplitude of the wave as parameters.
Based on the experimental and simulation results, it is concluded in this paper that
Lamb waves are sensitive to cracks and holes in thin aluminum plates, and that these
types of defects can be detected by techniques using Lamb waves.
iv
Acknowledgements
I would like to express my appreciation and gratefulness to my advisor, Dr.
Douglas K Nims, for his endless support and guidance since the first day of my Masters
journey at the University of Toledo. I have learned a lot from his knowledge and
experience, and he has inspired me through every stage of this research. Thank you Dr.
Nims for everything you have done for me.
I would also like to thank Dr. Ashok Kumar, Chair of Civil Engineering
Department, and the members in the FSAT investigation team, Dr. Vijay Devabhaktuni,
Dr. Daniel Georgiev, Dr. Hong Wang, and Mr. Craig Near for their collaboration during
my stay with the team.
Thanks are given to my friends and colleagues in the research, Nischal Rimal and
Rohan Repale, for their cooperation and support especially in Matlab and Pzflex. They
are wonderful individuals to work with.
Finally, I extend my special regards and gratitude to my parents and to my family
as a whole for their tireless support, motivation, and encouragement throughout my
studies. I am indebted to them all.
v
Table of Contents
Abstract .............................................................................................................................. iii
Acknowledgements ..............................................................................................................v
Table of Contents ............................................................................................................... vi
List of Tables .....................................................................................................................x
List of Figures .................................................................................................................... xi
List of Abbreviations ....................................................................................................... xiv
List of Symbols ..................................................................................................................xv
1
Introduction
.........................................................................................................1
1.1 Problem Statement .............................................................................................1
1.2 Research Objectives ...........................................................................................1
1.3 Research Contribution .......................................................................................2
1.4 Organization of the Thesis .................................................................................2
2
Background on Elastic Waves
............................................................................5
2.1 Types of Elastic Waves – Speed and Particle Motion .......................................5
2.1.1 Pressure Waves .........................................................................................6
2.1.2 Axial Waves ..............................................................................................7
2.1.3 Shear Waves..............................................................................................7
vi
2.1.4 Flexural Waves .........................................................................................8
2.1.5 Rayleigh Waves ........................................................................................8
2.1.6 Lamb Waves .............................................................................................9
2.2 Comparison of Other Wave Types with Lamb Waves ....................................14
3
Mathematical Background …. ...............................................................................16
3.1 Undistorted Wave Propagation in Taut String .................................................17
3.2 Dispersion Principles of Waves in Taut String ................................................19
3.3 Lamb Wave Dispersion Curves of Thin Aluminum Plates .............................22
3.3.1 Importance and Use of Lamb Wave Dispersion Curves ........................22
3.3.2 Generating Lamb Wave Dispersion Curves ...........................................23
3.3.3 Phase Velocity Dispersion Curves for 1.02mm thick Al Plate ...............24
3.3.4 Phase Velocity Dispersion Curves for 5mm thick Al Plate ....................27
3.3.5 Group Velocity Dispersion Curves for Al Plate .....................................27
3.3.6 Phase Velocity Dispersion Curves using Waveform Revealer ...............28
3.4 Summary ........................................................................................................30
4
Lamb Waves in Damage Detection Techniques ..................................................31
4.1 Ultrasonic Waves in NDE Techniques ............................................................32
4.2 Advantages and Disadvantages over Traditional NDE Techniques ................33
4.3 Modes of Lamb Waves ....................................................................................35
4.4 Selection of Lamb Wave Modes for Damage Detection .................................36
4.5 Basic Lamb Wave Based Damage Detection Mechanism ...............................37
5
Pitch-Catch Experiments on Pristine Aluminum Plate and Simulation ................42
5.1 Experimental Setup ..........................................................................................42
vii
5.2 Experimental Results ......................................................................................44
5.2.1 Test - 1 Receiver Location at 10cm ........................................................45
5.2.2 Test - 2 Receiver Location at 20cm ........................................................47
5.2.3 Test - 3 Receiver Location at 30cm ........................................................48
5.3 Simulation Using Waveform Revealer…….. ..................................................50
5.3.1 Test - 1 Receiver Location at 10cm ........................................................50
5.3.2 Test - 2 Receiver Location at 20cm ........................................................52
5.3.3 Test - 3 Receiver Location at 30cm ........................................................53
5.4 Observations ....................................................................................................54
6
Damage Detection Using Mode Conversion Phenomena ......................................56
6.1 Detecting 4mm Diameter Hole in Aluminum Plate Experimentally …….. ....56
6.1.1 Experimental Setup ................................................................................58
6.1.2 Results (Receiver Location at 15cm, 20cm and 25cm) ..........................59
6.2 Verification Using Waveform Revealer…….. ................................................61
6.2.1 Simulation Results ..................................................................................61
6.3 Conclusion…….. .............................................................................................62
7
Damage Detection Using Pzflex Simulations .......................................................63
7.1 Setup and Frequency-Disc Size Tuning …….. ................................................63
7.2 Simulation Results for Undamaged Plate …….. .............................................66
7.3 Plate with Through-Thickness Hole (2, 4 and 6mm dia. Holes)…….. ...........67
7.3.1 Simulation Results and Comparison with Pristine Plate.........................68
7.4 Plate with Through-Thickness Crack (1, 2, and 3mm wide cracks)…….. .......72
7.4.1 Simulation Results and Comparison with Pristine Plate ........................73
viii
7.5 Conclusion …….. .............................................................................................76
8
Conclusions …….. .................................................................................................88
References ..........................................................................................................................82
ix
List of Tables
3.1
Material properties, and longitudinal and transverse wave speeds of Al plate ......25
5.1
Comparison between theoretical and actual distance (receiver at 10cm) ..............46
5.2
Comparison between theoretical and actual distance (receiver at 20cm) ..............48
5.3
Comparison between theoretical and actual distance (receiver at 30cm) ..............49
5.4
Comparison of distance travelled (receiver at 10cm - Waveform Revealer).........51
5.5
Comparison of distance travelled (receiver at 20cm - Waveform Revealer).........52
5.6
Comparison of distance travelled (receiver at 30cm - Waveform Revealer).........53
x
List of Figures
2-1
Rayleigh waves in solid objects ...............................................................................9
2-2
A schematic showing Lamb wave propagation in thin plates................................10
2-3
Propagation characteristics of pressure, shear and Rayleigh waves ......................11
2-4
Propagation of waves by Victor Giurgiutiu (LAMSS) ..........................................13
2-5
Frequency dependent wave speed curves for Lamb, axial, flexural, and Rayleigh
waves in 1.02mm thick aluminum plate ................................................................15
3-1
Undistorted propagation of a pulse wave in a taut sting .......................................18
3-2
Wave propagation of an initial condition displacement in a string .......................18
3-3
Distorted propagation of a pulse wave in a taut string...........................................19
3-4
String on an elastic foundation ..............................................................................20
3-5
Frequency spectrum profile for a string on elastic foundation ..............................21
3-6
Dispersion curve of a string on an elastic foundation ............................................21
3-7
Phase velocity dispersion curves of aluminum plate .............................................26
3-8
Group velocity dispersion curves of aluminum plate ............................................28
3-9
Phase velocity dispersion curves for 1.02mm thick Al plate by Waveform
Revealer .................................................................................................................29
xi
3-10
Phase velocity dispersion curves for 5mm thick Al plate by Waveform Revealer
…………………………………………………………………………………………... 29
4-1
Schematics of particle motion: A and S modes ....................................................35
4-2
Pitch-catch configuration ......................................................................................39
4-3
Pulse-echo configuration ......................................................................................39
5-1
Receiver transducer, function/arbitrary waveform generator and mixed signal
oscilloscope models ..............................................................................................43
5-2
Pitch-catch experimental setup on 1.02mm thick Aluminum plate ......................44
5-3
Waveforms achieved by oscilloscope (receiver at 10cm) .....................................46
5-4
Waveforms achieved by oscilloscope (receiver at 20cm)......................................47
5-5
Waveforms achieved by oscilloscope (receiver at 30cm)......................................49
5-6
5-cycle 500 kHz sine wave excitation signal in Waveform Revealer ..................50
5-7
Input data and received signal at 10cm receiver position ......................................51
5-8
Input data and received signal at 20cm receiver position ......................................52
5-9
Input data and received signal at 30cm receiver position ......................................53
6-1
Stages of Lamb wave interaction with damage and mode conversion ..................57
6-2
Experimental plate with 4mm diameter hole as defect ..........................................59
6-3
Received wave showing
mode conversion due to 4mm diameter hole in the
hole when receiver is a) 15cm, b) 20cm, and c) 25cm away from actuator ..........60
6-4
Waveform Revealer results showing
mode conversion ...................................61
7-1
Aluminum plate and transducers assembly in Pzflex ............................................64
7-2
Frequency tuning using Waveform Revealer showing different signal strengths
for 1.02mm thick Al plate and 20mm diameter PWAS .........................................65
xii
7-3
Screen shot of Pzflex showing wave propagation in undamaged plate and Matlab
plot of the received wave in Pzfelx ........................................................................66
7-4
A Solidworks model of Al plate and sensors with 2mm, 4mm, and 6mm dia.
holes located at 95mm from the actuator ...............................................................67
7-5
Comparison of waves attained when the plate is with and without 2mm diameter
hole.........................................................................................................................68
7-6
Comparison of waves attained when the plate is with and without 4mm diameter
hole.........................................................................................................................69
7-7
Comparison of waves attained when the plate is with and without 6mm diameter
hole.........................................................................................................................70
7-8
Comparison of waves attained when the plate is with 2mm, 4mm, & 6mm
diameter holes ........................................................................................................71
7-9
A Pzflex model of aluminum plate and sensors with 30mm long and 1mm, 2mm,
and 3mm wide cracks located at 95mm from the actuator ....................................72
7-10
Screen shot of wave interaction with 1mm wide crack and comparison of waves
attained when the plate is with and without the crack ............................................73
7-11
Screen shot of wave interaction with 2mm wide crack and comparison of waves
attained when the plate is with and without the crack ............................................74
7-12
Screen shot of wave interaction with 3mm wide crack and comparison of waves
attained when the plate is with and without the crack ............................................75
xiii
List of Abbreviations
Al................................Aluminum
...............................Antisymmetric Lamb wave mode
CLoVER ....................Composite long-range variable-direction emitting radar
dia...............................Diameter
FSAT ..........................Frequency Steerable Acoustic Transducer
LAMSS ......................Laboratory for Active Materials and Smart Structures
NDE ...........................Non-destructive evaluation
NDT ...........................Non-destructive testing
PWAS ........................Piezoelectric wafer active sensor
PZT ............................Piezoelectric transducer
SHM ...........................Structural health monitoring
................................Symmetric Lamb wave mode
xiv
List of Symbols
ϕ .................................Wave function
ω .................................Angular frequency, rad/sec
λ’ ................................Wavelength, m
ρ..................................Mass density of material, kg/m3
ν ..................................Poison’s ratio
µ……………………. Lame constant, given as µ =
ü..................................Wave acceleration,
λ …….……….…….. Lame constant, given as
C .................................Wave speed, mm/ µsec
..............................Axial wave speed, m/sec
..............................Flexural wave speed, m/sec
................................Pressure or longitudinal wave speed, m/sec
..............................Constant wave speed in string, m/sec
...............................Phase velocity, mm/ µsec
...............................Rayleigh wave speed, m/sec
..............................Shear or transverse wave speed, m/sec
d..................................Half-thickness of plate, mm
E .................................Modulus of Elasticity, GPa
F .................................Tension in a string, KN
f ..................................frequency of particular waves, cycles/sec
GPa.............................Giga Pascal
h..................................Thickness of plate, mm
K .................................Spring constant of a string, KN/m
k ..................................Wave number, 1/m
,
......................Antisymmetric eigenvalues
kHz .............................kilohertz (Kilo cycles per second)
,
.......................Symmetric eigenvalues
m.................................Mass per unit length, kg
mm .............................millimeter
T .................................Period of revolution, sec
t ..................................Time of wave travel, sec
xv
x ..................................Wave particle position x - axis
y ..................................Wave particle position y – axis
xvi
Chapter 1
Introduction
1.1. Problem Statement
The intent of this research is to establish the feasibility of damage detection in thin
plates using Lamb waves at the University of Toledo. This requires developing the capability
to run experiments and use wave analysis software for the first time at UT.
1.2. Research Objectives
The basic objective of this research is to establish a laboratory at the University of
Toledo that can productively study NDE of plate structures using guided ultrasonic waves.
This can be achieved through (a) development of a basic understanding of guided waves; (b)
investigating the mathematical background; (c) performing basic Lamb wave experiments;
and (d) running relevant finite element simulations.
(a) Basic understanding of guided waves is achieved by presenting an extensive literature
review of the propagation characteristics of the different types of waves commonly used
1
for non-destructive testing techniques. This helps to make proper selection of the type of
wave relevant for a particular type of damage analysis.
(b) Mathematical background of these waves involves determining and comparing wave
speeds of ultrasonic waves, describing dispersion principles in waves, and developing
dispersion curves for Lamb waves. These are all explained in detail in this paper.
(c) Lamb wave experiments are performed initially in order to determine the working
frequency for the particular test setup so that damage detection experiments can be done
successfully. In this paper the pitch-catch method is selected for this purpose, and further
damage detection experiments are performed.
(d) Finally, finite element simulations have been run to repeat the experimental analysis
under similar circumstance thereby simulating the outcomes of the experiment. This
research uses Pzflex [24] and Waveform Revealer [25] for different types of damage
analysis.
1.3. Research Contribution
The contribution of the work done in this paper to the FSAT investigation research
project is to test the workability of an experimental setup on which FSAT is to be tested.
This has been accomplished by determining the frequency at which the experimental set up
works best and only two Lamb wave modes are generated making analysis less complicated.
1.4. Organization of the Thesis
This thesis is organized in eight chapters which are arranged in a sequential manner
2
to make it easy to read and understand its content. It starts by giving brief introduction of the
research work done in Chapter 1 which explains what the problem statement of the research
is, what the research objectives are, and how it is organized. Chapter 2 deals with
background of elastic waves focusing on their important propagation parameter, speed..
Chapter 3 also deals with another yet important aspect of waves called the dispersion
principle. Dispersion principles of a taut string are introduced, and the rest of the chapter
shows effort made to mathematically develop dispersion curves of Lamb waves in thin
aluminum plates using Rayleigh-Lamb equation. Solutions of the Rayleigh-Lamb equation
represent different modes of Lamb waves, symmetric and anti-symmetric, which are
discussed in detail in Chapter 4. Chapter 4 emphasizes mainly on Lamb waves. A literature
review of the characteristics of Lamb waves explains why these waves are becoming more
popular to use them for non-destructive examination than traditional methods like ultrasonic
scanning. Merits and demerits of the lower level symmetric and anti-symmetric modes of
Lamb waves are also described in detail in this chapter. Consequently, once the specific
Lamb wave modes necessary for particular damage analysis are identified, this chapter
explains how to select these modes for damage analysis. The commonly used methods by
which damage is detected are also explained in this chapter including the methods of
transmitting and receiving signals, pitch-catch and pulse echo methods. Chapter 5 presents
pitch-catch experiment on undamaged (pristine) aluminum plate and verification by
Waveform Revealer. In chapter 6, an experiment is performed to detect a through-thickness
hole on the plate by mode conversion phenomena, and the experiment is simulated by
Waveform Revealer. Chapter 7 starts by explaining the results obtained from frequency-disc
size tuning in Waveform Revealer to select working frequency value for a particular
3
transducer size for simulation in Pzflex. Then, simulation done in Pzflex to detect throughthickness holes and cracks of different sizes in aluminum plate is presented. Finally, chapter
8 concludes the outcomes of the research, and proposes future work and equipment required
to more fully develop a guided wave laboratory at UT.
4
Chapter 2
Background on Elastic Waves
This chapter aims at introducing elastic waves defined by a general harmonic
wave equation from which speed equations are derived for different types of elastic
waves. Lamb wave speed is obtained from dispersion curves. In an attempt to show
similarities of some elastic waves with Lamb waves, wave speeds of axial, flexural and
Rayleigh waves in 1.02mm aluminum plate are calculated and plotted against frequency
in the same graph along with
and
Lamb wave dispersion curves. These speed
curves are similar to Rose’s [6].
2.1. Types of Elastic Waves – Speed and Particle Motion
Waves in elastic solids are called elastic waves. According to Giurgiutiu [23], a
harmonic wave, ϕ, propagating in the spatial direction, , in elastic medium, has the
general form
(2.1)
5
where k is the wave number,
is the wave shape at t = 0, and ω is the angular
frequency. The wave number, k, can be written in terms the wave speed, c, the angular
frequency, ω, the wave length, , and period, T, as
(2.2)
=
where ω is given by ω = 2πf, and frequency, f, is related to period, T, by f = 1/T. The
different types of elastic waves used for nondestructive evaluation (NDE) and structural
health monitoring (SHM) are pressure waves, axial waves, shear waves, flexural waves,
Rayleigh waves, and Lamb waves.
2.1.1. Pressure Waves
Pressure waves (P-waves) are also known as longitudinal, compressional, or
dilatational waves. Their particles move parallel to the direction of wave propagation, and
they exist in unbounded solid medium. According to Giurgiutiu [23], for a plane-front Pwave propagating in the -direction, its particle motion is expressed as
(2.3)
and the P-wave speed, cL, is given by
cL =
(2.4)
where λ and µ are Lame constants given by
, and
µ=
6
(2.5)
respectively, and ρ is the mass density. The Lame constants are functions of Young’s
modulus of elasticity, E, and Poisson’s ratio, ν.
2.1.2. Axial Waves
Similar to P-waves, axial waves have particle motion parallel to wave
propagation. Nevertheless, they are low frequency approximations of more complicated
symmetric waves in bars and plates where the displacement field is uniform across the
cross section. For a 1-D slender bar, axial speed has the expression as given by [23]
(2.6)
For a 2-D plate, the axial wave speed, also called the longitudinal wave speed, is given by
(2.7)
(2.8)
2.1.3. Shear Waves
Shear waves (S-waves), also known as transverse waves or distortional waves,
have particle displacement perpendicular to the direction of propagation. The transverse
particle motion for a plane-front S-wave propagating in the -direction is given by [23] as
(2.9)
where k = ω / cS ,
is initial displacement, and cS is the S-wave speed given by
cS
(2.10)
7
2.1.4. Flexural Waves
Giurgiutiu [23] described flexural waves as waves resulting from the bending
deformation of beams and plates in response to a transverse motion
deformation causes a secondary in-plane motion,
. The bending
, which varies linearly across
the beam or plate thickness. The in-plane displacement field across the beam or plate
thickness is expressed as
=
(2.11)
For a beam of flexural stiffness EI and mass per unit length m, the flexural wave speed is
given by
cF
(2.12)
If the beam is rectangular with thickness h and width b, then cF takes the form
cF
(2.13)
For a plate of thickness h, the flexural wave speed is given by
cF
(2.14)
2.1.5. Rayleigh Waves
Rayleigh waves, also called surface acoustic waves (SAW), are free waves that
propagate on a traction free surface of a semi-infinite solid, with amplitude decreasing
rapidly with depth as schematically shown in Figure 2-1. The effective depth of
penetration is less than one wavelength. The real root solution of a cubic equation with up
8
to three possible roots gives Rayleigh wave velocity, which is most useful for practical
purposes [23].
cR (ν) = cS
(2.15)
where cS is shear wave speed given in Equation (2.10)
Figure 2-1: Rayleigh waves in solid objects (From [6])
2.1.6. Lamb Waves
Lamb waves, also known as guided elastic waves, plate waves, or acoustoultrasonic waves, are a type of ultrasonic wave that propagates between two parallel
stress free surfaces such as the upper and lower surfaces of a plate. They are two
dimensional stress waves guided by the geometry of the plate-like structure. A schematic
representation of Lamb wave propagation is given in Figure 2-2. Lamb waves are
generated by the interference of multiple reflections and mode conversion of longitudinal
(P-waves) and transverse (S-waves) between the upper and lower boundaries of the plate
under investigation. Their propagation properties depend on density, elastic properties,
and geometric structure.
9
Figure 2-2: Showing Lamb wave propagation in thin plates (From [6])
Both Rayleigh and Lamb developed solutions to guided wave problems and the waves
are named after them. Solutions to guided wave problems are explained in detail in
chapter 3.
10
Figure 2-3: Propagation characteristics of (a) Pressure Waves (b) Shear Waves (c)
Rayleigh Waves by Lawrence W. Braile [19]
11
(a) Symmetric Lamb wave
(b) Antisymmetric Lamb wave
(c) Rayleigh wave
12
(d) Flexural wave
(e) Pressure wave
(f) Shear waves
Figure 2-4: Propagation of waves by Vicotor Giurgiutiu (LAMSS)
13
2.2. Comparison of other Wave Types with Lamb Waves
In order to make the comparison, wave speeds of various elastic wave types are
determined. The speed values are then plotted against frequency together with dispersion
curves of Lamb waves in Figure 2-5 which is similar to Rose’s [6]. At different
frequencies, some waves tend to show coinciding speed curves, and [6] developed
similarities between the waves based on this.
For 1.02mm thick Aluminum plate, the axial, shear, flexural, and Rayleigh wave
speeds are determined using Equations (2.7), (2.10), (2.12), and (2.15). Aluminum has
modulus of elasticity (E = 69 GPa), poison’s ratio (ν = 0.33), and density (ρ = 2700
Kg/m3). The axial wave speed ( ) is 5355 m/s, shear wave speed (cS) is 3100 m/s and
accordingly Rayleigh speed (cR) is calculated as 2889 m/s. The flexural wave speed (cF)
varies with frequency. Wave speed is plotted against source frequency to give wave
speed curves of different waves as shown in Figure 2-5. Lamb wave speed-frequency
relationship for
and
modes, also called dispersion curves which will be discussed
in detail in the upcoming chapters, is also incorporated in the figure for comparison.
At lower frequency values, the symmetric Lamb waves resemble the axial waves
while the anti-symmetric Lamb waves behave like flexural waves. Referring to the wavespeed dispersion curves of
and
Lamb wave modes, axial waves, flexural waves,
and Rayleigh waves as shown in Figure 2-5, at low frequency, the
Lamb wave mode
curve is similar to the axial wave curve with wave speed values closer to each other. As
frequency increases, their wave speed values differ substantially. Therefore, axial waves
are low frequency approximations of
modes. Similarly, at low frequency, flexural
14
waves and
Lamb wave modes have similar wave speed curves. Hence, flexural waves
are low frequency approximations of
Lamb wave modes.
At higher frequency, however, the speed of
and
Lamb wave modes
converge to Rayleigh wave speed. Their wave speed curves become identical to Rayleigh
speed curves. Thus, Rayleigh waves are high frequency approximations of
and
Lamb wave modes.
Axial wave (
)
Lamb wave
mode
Figure 1.1icAluminum plate.
Rayleigh wave (cR)
Flexural wave (cF )
Lamb wave
mode
Figure 2-5: Frequency dependent wave speed curves for Lamb (
flexural, and Rayleigh waves in 1.02mm thick aluminum plate
15
and
modes), axial,
Chapter 3
Mathematical Background
The mathematical aspect of waves that is of interest to this paper is the dispersion
phenomena, and hence dispersion curves of Lamb waves. This chapter begins by
explaining basic distortion characteristics of waves in a taut string. Rose in his book [6]
explains distortion as one which occurs when the wave in the string travels with varying
speed; and he referred it as dispersion when the speed varies with frequency. This chapter
compares undistorted waves with distorted waves on an elastic foundation based on
variety of propagation speed.
Dispersion curves of Lamb waves are similarly explained as curves showing
speed variation with frequency. There are two types of dispersion curves namely phase
and group velocity dispersion curves. This chapter explains in greater detail what phase
and group velocity dispersion curves of Lamb waves are, what their importance is in
damage analysis, and how they are developed and used for damage analysis. Phase and
group velocity dispersion curves are developed for 1.02mm and 5mm thick aluminum
plates, 1.02mm plate is one on which damage detection was performed, and Waveform
16
Revealer results of these curves are also presented for comparison. Modes of Lamb
waves will be dealt with in the following chapter 4.
3.1. Undistorted Wave Propagation in Taut String
Equation (3.1) shows one-dimensional, homogeneous, governing equation for
wave propagation in a string as given by Rose [6].
uy =
uy is the displacement,
=
where
is wave speed (
,
(3.1)
, where F is the tension in the string
=
and ρ is mass density per unit length of material), and t is time of propagation. This
equation represents free (without external force) transverse motion of a string. A solution
to the wave equation by Separation of Variables results in undistorted constant speed
wave propagation as shown in Figure 3-1. Considering initial displacement conditions
based on D’Alembert’s solution (given in Equation 3.2), wave propagation at different
times is developed with constant speed.
u(x, t) = U(x -
t) + U(x +
t)
(3.2)
Assume 40 units long string fixed at both ends, and remember the boundary condition of
a string between intervals –a and a at time t is as follows:
= U(x) =
,
x=
t, position on string
(3.3)
Using Matlab, the wave propagation at different times along the string is developed based
on the initial condition displacement
= +1. See Figure 3-2.
17
Figure 3-1: Undistorted propagation of a pulse wave in a taut string
Figure 3-2: Wave propagation of an initial condition displacement in a string
18
3.2. Dispersion Principles of Waves in Taut String
An original pulse wave which is Fourier superposition of harmonic waves gets
distorted when each component propagates with its own velocity. Unlike simple wave
equation without distortion, the velocity varies with frequency for each wave component.
Damped waves are observed when displacement diminishes with time along the media of
propagation as in Figure 3-3.
Figure 3-3: Distorted propagation of a pulse wave in a taut string
A good example of waves subjected to distortions is waves in a string on an elastic base
schematically presented in Figure 3.4. We have a dispersive equation derived for a string
on an elastic base as
,
is the wave number, ω is angular frequency, and K is elastic spring constant.
19
(3.4)
Figure 3-4: String on an elastic foundation
Results for the string are graphically represented in Figures 3-5 and 3-6, and these graphs
display the dispersive character of the waves. Frequency spectrum and dispersive curve
are some of the representations. To obtain a frequency spectrum, plot ω versus k in
Equation 3.4 using Matlab. A graphical form of frequency spectrum for aluminum string
is illustrated in Figure 3-5. Phase velocity
is extracted from the frequency spectrum in
Figure 3-5 as a slope of the curve in the k real region,
=
. Then, dispersion curve
is produced by plotting the phase velocity versus the real wave number in Figure 3-6.
Both these curves explain the dependency of wave velocity on the parameters of wave
characteristics, the wave number and its frequency. This phenomenon is called
Dispersion. Hence, contrary to undistorted waves where the wave speed (
distorted waves travel with a unique speed which is a function of frequency.
20
) is constant,
Figure 3-5: Frequency spectrum profile for a string on elastic foundation
Figure 3-6: Dispersion curve of a string on an elastic foundation
21
3.3. Lamb Wave Dispersion Curves of Thin Aluminum Plates
3.3.1. Importance and Use of Lamb Wave Dispersion Curves
Lamb wave dispersion curves, commonly presented as a plot of phase velocity or
group velocity versus the frequency-thickness product, describe the propagation
characteristics of Lamb waves and the natural resonance of a material. They constitute
the constructive interference of the waves that reflect inside a structure, and show the
kinds of waves that could actually propagate. They predict the relationship between phase
or group velocity, frequency, thickness and wave mode. They are essential for
quantitative application of guided waves mainly for signal interpretation and
identification.
In Lamb waves, there are two types of such curves namely, Phase velocity and
Group velocity dispersion curves. Phase velocity is the velocity of individual waves;
whereas, Group velocity is the propagation speed of wave energy or group of waves of
similar frequency. According to Lord Rayleigh (Rose’s book [6]), group velocity of
waves in still water is less than that of individual waves. Heisenberg used the term
“velocity of wave packets”. It is this group velocity that we measure in a laboratory in
order to carry out location analysis for a particular discontinuity. The waves formed by
throwing a stone into water can help explain the difference between phase and group
velocity. The velocity of a particular wave in the packet of waves that are propagating is
the phase velocity and the group velocity is the packet velocity.
Each Lamb wave mode has a value of frequency-thickness product, fd, below
which the wave mode doesn’t exist. This value is termed as Cut-off frequency of the
22
given mode. Normally, when the frequency is low and the plate is thin, which means
lower cut-off frequency, then the dispersion curves will only have the lower modes, for
example, the
and
modes (meaning only few of these modes are able to be
produced). Since most damage identification techniques recommend using
mode, the need to distinctly generate
and/or
or
modes becomes vital. In order to
accomplish this however, phase velocity dispersion curves have to be developed from
which cut-off frequencies of the different modes is obtained and an appropriate frequency
can then be selected to excite the required modes. Frequency selection allows us to
decide the mode types that would actually propagate in the structure. For instance, to
generate
and
modes only, use fd values lower than the cut-off frequency of
mode in the phase velocity dispersion curves. In both the curves and at lower frequency,
it is observed that
Lamb Wave mode has higher phase velocity than
, and can be
distinguished easily.
3.3.2. Generating Lamb Wave Dispersion Curves
Lamb derived the dispersion relation for different waves traveling across the
plane of a traction free plate [6]. He indicated that only some frequency-velocity pairs
can propagate through it. These pairs can be obtained from the dispersion relations that
are developed at the end of the nineteenth century. In general, the solution to a guided
wave problem must satisfy the governing wave equations and the boundary conditions.
The governing equations are partial differential equations for displacement, or equations
of motion. Different approaches have been in use to determine the exact solution of this
problem. In this case, solutions from the method of Displacement Potentials are used,
23
which is the most popular. The boundary conditions needed to be satisfied are the stresses
at the top and bottom faces of the plate which must be equal to zero. Each solution of the
Rayleigh-Lamb equation corresponds to a single Lamb wave mode. The Rayleigh-Lamb
equation (dispersion equations) for a traction-free homogeneous and isotropic plate is
expressed as
=
=
where
,
Symmetric mode
(3.5)
Anti-symmetric mode
(3.6)
, ω = 2πf, k is wavenumber, and cL and cS are the
longitudinal and transverse waves given by Equations (2.5) and (2.10) respectively. The
numerical solution of Equation (3.5) yields symmetric eigenvalues,
from Equation (3.6) the anti-symmetric eigenvalues,
,
,
The Lamb wave speed, also called the phase velocity given by cp
wave speed which is a function of the product
thickness,
. A plot of cp versus
. . . and
, . . . are produced.
, is dispersive
between frequency, , and half the plate
is the phase velocity dispersion curve.
3.3.3. Phase Velocity Dispersion Curves for 1.02mm Al Plate
For any given frequency, infinite number of wave numbers will satisfy equations
(3.5) and (3.6). This will result in a finite number of real solutions and infinite complex
solutions. For an unloaded plate, only the real values of the wave number are necessary
for characterizing the wave propagation properties [6]. These real solutions represent the
24
undamped propagating modes. Equations (3.5) and (3.6) are re-arranged to produce only
the real solutions as shown below:
Symmetric mode
(3.7)
Anti-symmetric mode
(3.8)
For T6061 Aluminum plate, the material properties are given in table 3.1, and
Lame constants, λ and µ, are determined using equation (2.6). Finally, longitudinal (cL)
and transverse (cS) wave speeds are calculated using equations (2.5) and (2.10)
respectively to be used as constant inputs for the numerical solution of equations (3.7) and
(3.8).
Table 3.1: Material properties, and longitudinal (cL) and transverse (cS) wave speeds of
aluminum plate
Material
T6061
Aluminum Plate
cL
cS
E
(GPa)
ν
ρ
(Kg/m3)
λ
(GPa)
µ
(GPa)
(m/s)
(m/s)
69
0.33
2700
50.35
25.94
6153.3
3099.6
The plate chosen for investigation is 1.02mm thick. Numerical solution of
equations 3.5 and 3.6 yields both symmetric and anti-symmetric modes by varying input
frequency for each mode characterized by its wave number ( ), and simultaneously
evaluating respective wave speeds (cp). The graphical outcome is a plot of phase velocity
(cp) versus frequency-thickness product (fd) for all possible modes, which is called phase
25
velocity dispersion curves. The phase velocity dispersion curve for an aluminum plate is
illustrated in Figure 3-7 below.
Cut-off frequency
MHz-mm)
Figure 3-7: Phase velocity dispersion curves of aluminum plate
As said earlier, Lamb waves exist in different modes. At any given frequency of
excitation, at least two modes (one symmetric and one anti-symmetric) are generated. As
frequency increases, Lamb wave excitation generates many more modes which exist
simultaneously. In Figure 3-7, eight different lamb wave modes are generated. The cutoff fd value of
mode is 1.88 MHz-mm which corresponds to a frequency of 1.88 MHz,
if the plate thickness is 1.02mm. This means for any exciting frequency less than 1.88
MHz, only
and
modes exist in the 1.02mm thick plate.
26
3.3.4. Phase Velocity Dispersion Curves for 5mm Al Plate
If the plate thickness is 5mm, which is the plate on which FSAT is mounted for
testing in the laboratory, the cut-off frequency of
mode is equivalent to 376 KHz,
which is much lower than that of 1.02mm plate. This indicates that at a frequency greater
than 376 KHz, more than two modes propagate in the plate, making signal processing and
interpretation more complex. Therefore, to simplify signal processing for the current
FSAT testing setup, the function generator shall transmit source wave to the plate with a
frequency less than 376 KHz. In general, the thinner the plate is, the larger the plate’s
mode cut-off frequency and the wider the range of frequency necessary to excite fewer
modes. Thus, thinner plates make damage detection easier.
3.3.5. Group Velocity Dispersion Curves of Al Plate
Once the phase velocity is known, the group velocity of Lamb waves can then be
obtained using Equation (3.8) given below.
where
is the group velocity and
(3.9)
is the phase velocity. Similarly, numerical solution
of equations 3.5, 3.6 and 3.9 produce group velocity dispersion curves (Figure 3-8),
which is a plot of group velocity ( ) versus fd.
27
Figure 3-8: Group velocity dispersion curves of aluminum plate
3.3.6 Phase Velocity Dispersion Curves using Waveform
Revealer
Waveform Revealer outputs phase velocity dispersion curves for plates with
varying thickness. To verify the accuracy of phase velocity dispersion curves obtained
using Matlab in previous topic, a largely scaled dispersion curves acquired from
Waveform Revealer are presented here for 1.02mm and 5mm thick plates.
28
Figure 3-9: Phase velocity dispersion curves for 1.02mm thick Al plate by Waveform
Revealer
Figure 3-10: Phase velocity dispersion curves for 5mm thick Al plate by Waveform
Revealer
It can be observed from Figure 3-9 that the cut-off frequency for
mode is less
than 2000 kHz, which matches the exact value of 1.88MHz in Figure 3-7. For 5mm thick
plate, both Figure 3-10 and Figure 3-8 have same cut-off frequency of
mode with a
value of 376 kHz. Therefore, dispersion curves obtained theoretically using Matlab in
Chapter 3 are verified by Waveform Revealer.
29
3.4. Summary
At this point, dispersion principle is explained. Rayleigh-Lamb equations are
numerically solved to generate phase velocity and group velocity dispersion curves of
aluminum plate. The importance of these curves in damage detection experiments is
discussed. By looking at the cut-off frequency value of modes in the phase velocity
dispersion curves, we are now able to determine the type of modes that need to be excited
in a given thickness of plate. At a given frequency of excitation and known plate
thickness, the propagation velocity of different wave modes can be extracted from group
velocity dispersion curves for damage detection analysis. Moreover, dispersion curves of
aluminum plate using Waveform Revealer are also presented for comparison.
30
Chapter 4
Lamb Waves in Damage Detection Techniques
Now that the mathematical background which defines Lamb waves is established
in previous chapters, this chapter will be dealing with the nature of Lamb waves as to
their use in damage identification processes. First, introduction of ultrasonic waves and
their application in non-destructive examination techniques is discussed. Some studies
made by different people on NDE techniques are also cited. Next, the reason behind
preferring Lamb waves for NDE techniques over other ultrasonic waves is mainly
because Lamb waves have superior advantages which will be discussed in this chapter.
As introduced in the previous chapter, Lamb waves have infinite modes that can exist in a
particular excitation, classified as symmetric and ant-symmetric waves. The lower order
modes are more suitable for damage detection. This chapter discusses the propagation
characteristics of these modes; identifies the most effective modes for particular damage
type; and provides techniques used by some researchers on this study to selectively excite
those required modes alone to make analysis simple. Different methods by which Lamb
waves are transmitted and received in a plate such as pitch-catch and pulse echo methods
31
are also described. At the end of the chapter, various techniques commonly used for basic
damage detection analysis in plates have been highlighted, and the experiments in the
following chapters are based on one of these techniques.
4.1. Ultrasonic Waves in NDE Techniques
Unlike bulk waves, Lamb and Rayleigh waves are guided waves in which a
boundary is required for their propagation. As a result of a boundary in a plate or
interface, waves are subjected to reflection and mode conversion inside a structure, and
the superimposing of the constructive and destructive interference of the waves finally
leads to the well behaved guided wave packets.
The most commonly used technique to generate ultrasonic waves is the use of an
angle beam transducer [11]. A pulse is applied to a piezoelectric element on a Plexiglas
wedge mounted on a test surface. Refraction at the interface between the wedge and the
test specimen creates different waves that undergo mode conversion and reflection from
the surfaces, and this leads to interference patterns which produce guided waves. Another
technique is by using a comb transducer. In this technique, transducers placed on the
structure pump energy into the structure causing ultrasonic guided wave energy to
propagate in both directions along the structure.
Ultrasonic wave inspection techniques are proposed to inspect large areas of a
structure [14], and have wide applications in NDE. A work reported in [12] makes use of
train-generated ultrasound travelling down a rail track, whereby sensors placed on the rail
determine reflections from damaged rail. Another use of this technique is in boiler tube
inspection with access only from one side [11]. Ultrasonic energy from transducers
32
placed over the surface travels over a pipeline to determine corrosion or defects close to
the surface of the pipe. Many aircraft investigations have also made use of guided wave
inspection, where ultrasonic energy is made to travel across a test joint or crack. The
possible difficulty in this technique, though, is the need to select the right mode and
frequency that allows the energy to leak from layer one to layer two. If the wrong mode
and frequency is used, energy reflects back to the transducer before reaching the receiver.
Steel plates embedded in concrete can also be investigated by guided wave
application [11]. To investigate the steel, previous scanning methods have required the
removal of concrete, which is tremendously expensive. Now guided wave inspection can
send ultrasonic energy along the steel plate with minimal leakage into the concrete, and
locate corrosion and cracking in the steel plate. Likewise, the technique can be used to
inspect structures under tar coating, commonly used in the power generating industry and
underground gas pipe inspection. Ultrasonic energy penetrates the coating and allows the
inspection to be done without removing the tar coating, which otherwise is very
expensive.
4.2. Advantages and Disadvantages over Traditional NDE
Techniques
Nowadays, Lamb waves are more popularly used in damage identification
techniques. In conventional methods using ultrasonic waves, since transducers cover a
small area, the process becomes tedious for large structures. At the same time, the
transducers cannot effectively access non-uniform regions and buried structures. Acoustic
emission techniques, although effective in detecting damage, are unable to further
33
evaluate damage severity. On the other hand, Lamb waves can propagate for large
distances with little attenuation, making it possible for a single transducer to detect flaws
over a wider area of the plate [5]. Lamb waves can be used to detect, localize and
quantify damage. Lamb waves are also considered to be highly sensitive to very small
damages which cause discontinuity in the plate. Lamb waves can inspect inaccessible
regions of complex structures.
The type of damage that can influence Lamb wave propagation includes cracks,
through-thickness holes, notch, corrosion, variation in thickness of the plate, void,
porosity, fiber breakage, debonding, delamination, resin variation, matrix cracking, fiber
misalignment and cure variations [5]. These damages are capable of scattering the
propagation of Lamb waves in plates.
Damage identification techniques using Lamb waves have the following
advantages over the traditional NDE testing techniques [5]:
a. ability to inspect a large area with few transducers and in a short time;
b. capability to detect both internal and surface damages;
c. high sensitivity to even smaller defects and therefore high identification precision
d. cost effective and low energy consumption;
e. fast and can be repeated easily;
f. the possibility of diagnosing coated or insulated structures; and
g. the possibility of associating the types of damage to the different wave modes;
surface defects to
mode and internal damages to
34
mode.
Nonetheless, Lamb waves are highly dispersive in nature, multiple wave modes
exist, making signal processing and interpretation techniques more complex. Lamb wave
based diagnostic techniques also strongly depend on prior models or benchmark signals.
4.3. Modes of Lamb Waves
Waves in isotropic plates are classified according to polarization of the plate, that
is, direction of displacement vectors of the particles, in to X-Z plane and Y plane waves.
Y plane waves are the anti-plane shear waves. The waves in the X-Z plane are classified
as extensional or compressional waves, and flexural waves. The compressional waves,
are symmetric waves denoted by S, displace the particles in an in-plane mode causing the
plate thickness to bulge and contract. The flexural, anti-symmetric waves denoted as A
mode, are characterized by the out of plane particle displacement which causes constant
plate-thickness bending. Both S and A modes are shown schematically in Figure 4-1.
Lamb waves excited in plates can occur in different modes. In general, these wave modes
are either symmetric, S mode, or anti-symmetric, A mode.
Direction of wave propagation
Figure 4-1: Schematics of particle motion: A and S modes respectively ([5])
35
4.4. Selection of Lamb Wave Modes for Damage Detection
Experimental and analytical studies reported in [5] indicate that only the lowest
wave modes, the
(symmetrical) and
(anti-symmetrical), are the most damage
sensitive guided wave modes commonly used for lamb wave inspection to detect
damages. These modes exist at lower frequencies depending on the nature of the
propagation media. Although both the
and
modes can be employed in the damage
identification techniques, selecting the proper mode for the experimental purpose is
crucial. In general, a wave that is suitable for damage identification should have low
dispersion, low attenuation, high sensitivity, good detectability, and should be easy to
excite. Both
and
modes are sensitive to damage.
mode has higher sensitivity to
internal damages in the plate thickness such as holes, whereas the
detecting surface damages such as cracks.
mode is superior in
mode has the following merits over the
mode [5]:
1) it travels faster and is captured by the receiving sensor before the arrival of complex
wave reflections; and this allows the
mode to be identified easily and
unnecessary waves can be disregarded;
2) it has lower attenuation, due to its in-plane particle displacement, than the
mode,
which leaks some energy to the surrounding environment while propagating as a
result of out-of-plane movement of particles.
The
mode, on the other hand, can more easily be activated. It has stronger
wave signal than the
mode; and its shorter wave length helps it to interact with small
damages.
36
Therefore, an appropriate single mode needs to be selected to ease damage
detection analysis because at any given frequency at least two wave modes occur.. Recent
studies suggested selective excitation techniques of either the
has suggested that it is possible to excite either
or
or
mode. Giurgiutiu
mode by tuning the excitation
frequency [2]. Mode selection can also be achieved by two-dimensional tuning, that is
frequency and phase velocity (incident angle between the transmitting transducer and the
plate surface) [7]. Incidence angle is a function of phase velocity of the mode at a given
frequency as given by Snell’s law in Equation 4.1.
(4.1)
Where
is the phase velocity,
is the longitudinal or pressure wave velocity
(Equation 2.5), and α is incident angle (angle between transducer and the plate). Also, by
using piezoelectric transducer parameter selection, a single mode can be excited [8]. The
use of CLoVER transducers, which are capable of selectively exciting individual Lamb
modes, as actuators has also been suggested [3]. Many other methods have been proposed
for this purpose. Actual damage detection experiments in this paper are done by exciting
both modes, and none of these mode selection methods is utilized. In all the pitch-catch
experiments, both
or
modes are generated simultaneously and are identified by
their velocity and time of arrival.
4.5. Basic Lamb Wave Based Damage Detection Mechanism
During Lamb wave propagation in a plate, an interaction of the wave with damage
triggers scattering of the wave in the form of reflection, transmission, or mode
37
conversion. Different types of damages, different location and severity, cause unique
wave scattering phenomena. Lamb wave velocities vary with frequency-thickness
product. Thus, any material change in the plate as a result of the many types of damages
mentioned above influences the propagation characteristics of the wave such as its
velocity of propagation, its signal amplitude, and the time of its flight. According to the
basic damage detection technique, these parameters of the wave signal from the damaged
plate are compared to the wave parameters of the signal transmitted when the plate is
without any defects or pristine plate. Any difference in the parameters of the wave signals
between the damaged and pristine plate exposes reflections from any existing damage
sites, and is considered a good indication of the presence of a defect in the plate. Many
researchers in this field have followed different procedures to detect damage [1, 7]. Some
researchers have gone further to locate and measure the severity of the damage [15]. For
detection purposes only, techniques based on the comparison of Lamb wave signals
resulted from defected media with the ones obtained from pristine condition (baseline
data) of the structure are widely used and will be adopted for experiments in the
upcoming chapters. However, varying operational and environmental conditions, like
temperature and noise, can cause a variation in the wave signal and hence, this method
can lead to a false comparison if those conditions are not stable. Usually the lower modes
and
modes are mostly used for damage detection considering their merits, and
hence the investigation can be done on either mode (
or
).
There are two most widely used means by which signals are transmitted and
received in the process. Two setups are discussed, pitch-catch and pulse-echo methods.
38
1) Pitch-catch: The transmitter or actuator is placed at the center of the plate, and the
receiver at some distance from the actuator. The signal from the transmitter travels
across the plate, and is captured by the receiving sensor at the other end.
Figure 4-2: Pitch-catch configuration
2) Pulse-echo: A single transducer placed on the plate serves as transmitter and
receiver. In this case, a narrow band tone burst is applied as an input signal. A
receiver placed on top center of the actuator is also a pulse-echo set-up. In this
configuration, the transmitted signal reaches the boundary of the plate or a flaw, and
the echoed wave signal is captured by the receiver.
Figure 4-3: Pulse-echo configuration
39
Pitch-catch method of transmitting and receiving signals is adopted, as signals
captured by Pulse-echo may not be sufficiently sensitive to defects because waves echoed
from remote damage (back scattering waves) travel longer distance and lose important
information regarding the defect. However, many studies suggested a pulse-echo method
for localizing defects because the pitch-catch method requires more than one sensor.
In the upcoming chapters of this paper, damage is going to be simulated by
through-thickness holes and cracks because studies [7] indicate that both
and
modes could detect almost all sizes of hole diameters from 0.8 to 4.0mm. To inspect the
presence of a defect, a receiver transducer is placed at a distance from the source and
signals are recorded with the pristine plate. Then, known size damage is inflicted on the
plate and record the signal generated under similar circumstances. When the original
wave interacts with the hole (obstacle), some waves are transmitted through the hole and
continue propagation, some are reflected back from the hole edges to the source, some
undergo multiple reflections between the entering and exiting edges before they get
transmitted toward the receiver while others remain to form standing waves, and some
undergo mode conversion [15, 25]. Due to this phenomena, defected signals are expected
to have a delay in their time of flight and less amplitude than signals in an undamaged
plate. Therefore, amplitude or time of flight changes between the two signals indicates
the presence of a defect. Nevertheless, change in amplitude and time of flight of a signal
can also be caused by temperature variation [3], and enough care should be taken to
account for this effect.
The use of an effective damage interrogation approach and the efficient excitation
of Lamb waves are two important aspects of damage detection techniques. Two
40
approaches have been used to record Lamb wave field generated experimentally. The
first consists of bonding piezoelectric sensors on the surface of the plate under
investigation to record the strain field produced by the actuator. Some important
disadvantages of this approach are the fact that the sensor’s performance is susceptible to
environmental conditions, such as electromagnetic interference, and that information is
only recorded at the point where the sensor is placed. The second approach is based on a
non-contact technique using laser vibrometry, where a laser beam is used to record the
velocities induced by the piezoelectric actuator using the Doppler shifting phenomenon.
Although this approach allows excellent visualization of the wave field which is valuable
in studying its interaction with different damage types, it is impractical for online based
inspection and post-processing of the data recorded. In this paper, experiments use the
first approach, whereas the second approach is recommended for future work.
41
Chapter 5
Pitch-Catch Experiment on Pristine Aluminum Plate
and Simulation
5.1. Experimental Setup
The experiment was performed on a 1.02mm thick aluminum plate, which had
dispersion curves made available in the previous chapters for mode and frequency
selection. The signal actuator of type PZT-SA3 disc is partially welded to the plate at the
center, and the receiver transducer (Figure 5-1 (a)) is arbitrarily mounted at varying
distances from the actuator. The receiver is attached to the plate by means of petroleum
jelly.
The signal is generated by 20MHz capacity function/arbitrary waveform
generator (model 33220A – Agilent technologies), and mixed signal oscilloscope (model
MSO70148B – Agilent) which receives and displays the received waveform.
42
(a)
(b)
(c)
Figure 5-1: (a) receiver transducer, (b) function/arbitrary waveform generator (Agilent
model: 33220A), (c) mixed signal oscilloscope (Agilent model: MSO70148B)
The input signal for the experiment is a 5-cycle sine wave burst signal with 10V
peak to peak amplitude. Frequency of excitation is picked from phase velocity dispersion
curves based on the number of wave modes desired. For this experiment 500 kHz is used,
and two modes
and
are expected to exist. It is important to remember that these
modes can also exist at any frequency less than 1.88 MHz (
mode cut-off frequency).
Nevertheless, the transducer – receiver combination works best at around 500 kHz. For
instance, at frequencies less than 100 kHz, no signal was received. At frequencies greater
43
than 575 kHz, peak frequencies matching the initial signal frequency were not recorded.
Beyond 750 kHz, no signal was measurable. The reason for this could be due to the
limited working frequency range of both the disc and the receiver transducer. However,
at 500 kHz, the set up gave strong wave signal output with two identifiable modes. Figure
5-2 shows the entire setup of the experiment.
Figure 5-2: Pitch-catch experimental setup on 1.02mm thick Aluminum plate
5.2. Experimental Results
Three receiver locations have been tested and the results are presented below.
Referring to group velocity dispersion curves in Figure 3-8, for 500 kHz input frequency
and 1.02mm thick plate,
mode has group wave velocity value of 5293 mm/µsec and
mode has a value of 2887 mm/µsec. In addition, only these two modes are produced
in the plate. The two modes are identified by calculating the theoretical distance they
44
travelled to reach the sensor (receiver) by using their group velocities and the time of
flight obtained from the oscilloscope, and comparing the results with the actual actuatorreceiver distance on the plate.
5.2.1 Test 1- Receiver Location at 10cm
The receiver transducer is placed 10 cm center to center (8.85 cm edge to edge)
away from the source. The wave acquired is shown in Figure 5-3 and the theoretical
distance travelled is calculated in Table 5.1 for comparison with the actual distance on
the plate.
45
ΔX
(a)
ΔX
(b)
Figure 5-3: (a) & (b) Waveforms achieved by oscilloscope (receiver at 10cm)
Table 5.1: Comparison between theoretical and actual distance (receiver at 10cm)
Modes
Group
velocity
(m/sec)
5293
Time (ΔX)
(µsec)
Actual
distance
(cm)
8.85
Comparison
(Difference, %)
17.16
Theoretical
Distance
travelled (cm)
9.08
2887
31.044
8.96
8.85
1.23
46
2.53
5.2.2 Test 2- Receiver Location at 20cm
The receiver transducer is placed 20 cm center to center (18.85 cm edge to edge)
away from the source. The wave acquired is shown in Figure 5-4 and the theoretical
distance travelled is calculated in Table 5.2 for comparison with the actual distance on
the plate.
ΔX
(a)
ΔX
(b)
Figure 5-4: (a) & (b) Waveforms achieved by oscilloscope (receiver at 20cm)
47
Table 5.2: Comparison between theoretical and actual distance (receiver at 20cm)
Modes
Group
velocity
(m/sec)
5293
Time (ΔX)
(µsec)
Actual
distance
(cm)
18.85
Comparison
(Difference, %)
35.568
Theoretical
Distance
travelled (cm)
18.83
2887
63.648
18.38
18.85
2.49
0
5.2.3 Test 3- Receiver Location at 30cm
The receiver transducer is placed 30 cm center to center (28.85 cm edge to edge)
away from the source. The wave acquired is shown in Figure 5-5 and the theoretical
distance travelled is calculated in Table 5.3 for comparison with the actual distance on
the plate.
48
ΔX
(a)
ΔX
(b)
Figure 5-5: (a) & (b) Waveforms achieved by oscilloscope (receiver at 30cm)
Table 5.3: Comparison between theoretical and actual distance (receiver at 30cm)
Modes
Group
velocity
(m/sec)
5293
Time (ΔX)
(µsec)
Actual
distance
(cm)
28.85
Comparison
(Difference, %)
54.60
Theoretical
Distance
travelled (cm)
28.90
2887
98.28
28.37
28.85
1.66
49
0
5.3. Simulation Using Waveform Revealer
Waveform Revealer is a predictive tool to simulate multimode guided waves in
thin plates. It is developed by Laboratory for Active Materials and Smart Structures
(LAMSS) at the University of South Carolina. The simulation is carried out under similar
conditions as the pitch-catch experiment. Piezoelectric wafer active sensors (PWAS) are
used as signal receivers. To validate both modes, similar to the pitch-catch experiment,
the distance travelled by the modes is determined using their group velocity and
compared to the actual distance of the receiver. The comparison is shown in Tables 5.4 to
5.6.
Figure 5-6: 5-cycle 500 kHz sine wave excitation signal in Waveform Revealer
5.3.1 Receiver Location at 10cm
The receiver transducer is placed at 10cm from the actuator, and the wave signal
acquired is shown in Figure 5-7.
50
Figure 5-7: Input data and received signal waveform at 10cm receiver position
Table 5.4: Comparison of distance travelled (receiver at 10cm – Waveform Revealer)
Modes
Group
velocity
(m/sec)
5293
Time (ΔX)
(µsec)
Distance
travelled (cm)
19
2887
34
51
Comparison
(Difference, %)
10.06
Actual
distance
(cm)
10
9.82
10
1.8
0
5.3.2 Receiver Location at 20cm
The receiver transducer is placed at 20cm from the actuator, and the wave signal
acquired is shown in Figure 5-8.
Figure -5.8: Input data and received signal waveform at 20cm receiver position
Table 5.5: Comparison of distance travelled (receiver at 20cm – Waveform Revealer)
Modes
Group
velocity
(m/sec)
5293
Time (ΔX)
(µsec)
Distance
travelled (cm)
38
2887
68
52
Comparison
(Difference, %)
20.11
Actual
distance
(cm)
20
19.63
20
1.85
0.55
5.3.3 Receiver Location at 30cm
The receiver transducer is placed at 30cm from the actuator, and the wave signal
acquired is shown in Figure 5-9.
Figure 5-9: Input data and received signal waveform at 30cm receiver position
Table 5.6: Comparison of distance travelled (receiver at 30cm – Waveform Revealer)
Modes
Group
velocity
(m/sec)
5293
Time (ΔX)
(µsec)
Distance
travelled (cm)
57
2887
103
53
Comparison
(Difference, %)
30.17
Actual
distance
(cm)
30
29.74
30
0.87
0.57
5.4. Observations
For all the three test locations in the experiment, the comparison between the
actual and theoretical sensor distance gave matching results with acceptable differences.
The maximum difference occurred for Test 1 (receiver 10cm) with a percentage of 2.53
which is still acceptable considering the factors that cause the variation. The small
variations were indeed expected to occur due to some irregularities in the test. The actual
group velocity value should be used in place of theoretical group velocity obtained from
the dispersion curves in Figure 3-8. Moreover, the time readings from the oscilloscope
denoted by ΔX are approximate because it is difficult to accurately read the arrival times
of both the modes on the waveforms displayed by the oscilloscope. Finally, lack of
accuracy in measuring the sensor distance on the plate might have also contributed to
some variations. However, for Test 2 (receiver 20cm) and Test 3 (receiver 30cm), the
distances calculated using
mode are equal to the actual distance measured on the plate.
Lamb waves were generated and received successfully through the pitch-catch
method using the setup shown in Figure 5-2. It is proved that only two Lamb wave modes
exist at 500 kHz frequency as expected, and they are identified as
and
modes
through their velocity of propagation and travel distance.
Lamb waves produced by the Waveform Revealer resemble those waves in the
pitch-catch experiment in their type, modes, and propagation characteristics. From
Figures 5-7, 5-8, and 5-9, it is concluded that the two modes appearing in the plate at 500
kHz are
and
modes based on the comparison of their theoretical distance travelled
to the receiver and the actual receiver distance, which fulfills the expectation. The slight
discrepancy in the distances is due to lack of extracting exact time readings from the
54
Waveform Revealer. Consequently, Lamb wave experiments using pitch-catch method
are simulated by Waveform Revealer under similar circumstances, and the results agree
with the experiment’s outcome.
55
Chapter 6
Damage Detection Using Mode Conversion
6.1. Detecting 4mm Diameter Hole in Aluminum Plate
Experimentally
As discussed in Chapter 4 (4.5), when Lamb waves interact with a defect or
obstacle, mode conversion phenomena take place. As a result, a low amplitude wave is
formed and propagates in the plate trailing the original transmitted wave. Thus, a defect
can be detected when new waves appear due to mode conversion. Figure 6-1 shows the
stages of Lamb wave interaction with damage and mode conversion simulated using
Waveform Revealer with a 350 kHz 5-cycle sine burst signal. It is also important to
remember that while the transmitted waves propagate in the original direction, the
reflected waves travel in the opposite direction.
56
a)
b)
c)
d)
Mode conversion
Figure 6-1: Stages of Lamb wave interaction with damage and mode conversion (a)
before interaction, (b) during
conversion and
interaction, (c)
interaction.
57
transmitted after interaction, (d) mode
6.1.1. Experimental Setup
The experiment used the same pitch-catch setup already established in the
previous pristine plate experiments in chapter 5 (Figure 5-2). The input signal for the
experiment is sine wave 5-cycle burst signal triggered with 10V peak to peak. The plate
is drilled to make a 4mm diameter through-thickness hole at 95mm from the actuator as
shown in Figure 6-2. The frequency of excitation selected is 350 kHz, which is different
from the frequency (500 kHz) used in previous experiments when the plate is free of
defects. The reason behind this selection is that mode conversion occurs due to the
constructive interference of the waves reflected from the front and back edges of the hole
or obstacle, and this constructive interference develops when the ratio of the hole
diameter to the wavelength is equal to 0.25 according to [16,17]. The damage detection
analysis is to be based on
before
mode because the waves due to mode conversion arrive
mode and can easily be identified, unlike
mode where complex reflections
from plate edges make it more difficult to identify the converted modes. At 350 kHz,
has a velocity of 5293 m/s, a wavelength of 15mm, and the ratio of 4mm hole diameter
to the wavelength is approximately equal to 0.25. Therefore, a frequency of 350 kHz
satisfies the condition above for
mode and
mode conversion is expected to occur at
this frequency in a plate with 4mm diameter hole.
58
1.02mm thick Al Plate
4mm diameter hole
Receiver
Actuator
Figure 6-2: Experimental plate with 4mm diameter hole as a defect
6.1.2. Results (Receiver Location at 15cm, 20cm and 25cm)
The receiver is placed 15cm, 20cm and 25cm away from the actuator in the
direction of the hole. The waves acquired by the oscilloscope include
modes as a result of mode conversion. See Figure 6-3 below.
59
,
, and new
Mode conversion
a)
Time, µsec
Mode conversion
b)
Time, µsec
Mode conversion
c)
Time, µsec
Figure 6-3: Received wave showing
mode conversion due to 4mm diameter hole in
the plate when receiver is a) 15cm, b) 20cm, and c) 25 cm away from the actuator
60
6.2. Verification Using Waveform Revealer
Simulation was carried out under similar circumstances as the experiment. The
signal source is a 5-cycle sine wave burst signal with a frequency of 350 kHz. The
damage is located at 95mm away from the source. The plate is 1.02mm thick made of
aluminum T6061. Waveform results are given in Figure 6-4. The downward arrow
indicates the mode conversion as a result of interaction of the wave with the damage.
6.2.1. Simulation Results
Figure 6-4: Waveform revealer results showing
mode conversion when receiver is
15cm, 20cm, and 25 cm away from the actuators respectively
61
6.3. Conclusion
Three trials with different receiver locations were conducted. They all show
modes resulting from mode conversion phenomena (Figures 6-3 and 6-4). From the
experiment, it has been observed that the frequency selection based on the hole diameter
to wavelength ratio was successful in generating the required modes and allowing mode
conversion to take place. The simulation results from Waveform Revealer (Figure 6-4)
agree with the experimental results as well. Although hole diameters less than 4mm were
tried in the experiment, the best result was obtained with 4mm diameter hole. Therefore,
a 4mm diameter hole defect in the plate was detected by the presence of modes due to
mode conversion, and the
mode is less sensitive to smaller diameter holes.
Nonetheless, this type of detection method requires beforehand knowledge of the
defect size in order to select frequency. Otherwise, frequency will be selected by trial and
error, which is tedious.
62
Chapter 7
Damage Detection Using Pzflex Simulations
7.1. Setup and Frequency – Disc Size Tuning
The simulation setup is similar to the experiment. Two 20mm diameter and 5mm
thick PZTs, one an actuator and the other a receiver, are mounted on 1.02mm thick
aluminum in Solidworks and the assembly is imported into Pzflex. The assembly is
shown in Figure 7-1. Four edges of the plate are set as absorbing edges to avoid
reflections, and top and bottom faces of the plate are free surfaces to allow reflections so
that Lamb waves can propagate. The simulation was run with 150 KHz – 500V peak to
peak sine burst signals.
63
1.02mm thick
60x 60cm Al plate
Sensor PZT
Actuator PZT
Figure 7-1: Aluminum plate and transducers assembly in Pzflex
The selection of frequency is based on the actual PZT disc size. Using a 20mm
diameter disc, trials with varying frequencies displayed waveforms of different natures,
some with or without the required fundamental modes and others with poor signal
strength. The required modes can be obtained when there is optimized actuation and
sensing, and that is achieved when the transducer dimension is equal to half of the signal
wavelength [21]. At 130 kHz,
has a velocity of 5.3 km/s and a wavelength
approximately equal to 40mm which is twice the disc diameter. Therefore, the
mode
meets this condition at 130 kHz, however the signal looks much stronger at 150 kHz in
Pzflex. Frequency tuning results in Waveform Revealer (receiver at 15cm) in Figure 7.2
also indicate the presence of a strong signal when frequency is between 110 kHz and 150
kHz. Therefore, 150 kHz is selected for simulation as it yields a strong
and
mode as well.
64
mode signal
20 kHz
70 kHz
110 kHz
150 kHz
200 kHz
Figure 7-2:
Frequency tuning using Waveform Revealer showing different signal
strengths for 1.02mm thick aluminum plate and 20mm diameter PWAS
65
7.2. Simulation Results for Undamaged Plate
The plate is free of any defects. A simulated wave signal received by a receiver
placed at 20cm from the source is presented in Figure 7-3.
Receiver
Actuator
a)
(b)
Figure 7-3: (a) Screen shot of Pzflex showing wave propagation in undamaged plate, and
(b) a Matlab plot of the received wave in Pzflex consisting of
66
and
mode
7.3. Plate with Through - Thickness Hole (2mm, 4mm and
6mm dia. holes)
Through – thickness holes with 2mm, 4mm, and 6mm diameters are modeled
separately in the plate to serve as known defects (Figure 7-4). The objective is to
determine the sensitivity of
and
modes to the discontinuity created by the defects,
consequently detecting their presence by comparing time of flight and amplitude of the
disrupted wave with the wave obtained in Figure 7-3 when the plate is free of defects.
Figure 7-4: A Solidworks model of aluminum plate and sensors with 2mm, 4mm, and
6mm diameter holes located at 95mm from the actuator
67
7.3.1. Simulation Results and Comparison with Pristine Plate
Figure 7-5: Comparison of waves attained when the plate is with and without 2mm
diameter hole
68
Figure 7-6: Comparison of waves attained when the plate is with and without 4mm
diameter hole
69
Figure 7-7: Comparison of waves attained when the plate is with and without 6mm
diameter hole
70
Figure 7.8: Comparison of waves attained when the plate is with 2mm, 4mm, and 6mm
diameter holes
Referring to figure 7-8, results from the three different hole diameter plates were
compared to show the effect of hole size on amplitude and time of flight of the wave.
Although a difference in amplitude between the waves can be observed, it is not
significant enough to make a conclusion.
71
7.4. Plate with Through – Thickness Crack (1mm, 2mm, 3mm
and 4mm wide cracks)
Likewise, 30mm long through – thickness cracks have been modeled in the plate
to test sensitivity of both
and
modes to such type of defects. The setup is shown in
Figure 7-9 and tests are done for 1mm, 2mm, and 3mm wide cracks. A comparison
between the resulting waves from these cracks and the undamaged waves at 15cm from
the source is plotted in Matlab.
Figure 7-9: A Pzflex model of Aluminum plate and sensors with 30mm long and 1mm,
2mm, and 3mm wide cracks located at 95mm from the actuator
72
7.4.1. Simulation Results and Comparison with Pristine Plate
(a)
(b)
Figure 7-10:
(a) Screenshot of wave interaction with 1mm wide crack and (b)
Comparison of waves attained when the plate is with and without the crack
73
(a)
(b)
Figure 7-11:
(a) Screenshot of wave interaction with 2mm wide crack and (b)
Comparison of waves attained when the plate is with and without the crack
74
(a)
(b)
Figure 7-12:
(a) Screenshot of wave interaction with 3mm wide crack and (b)
Comparison of waves attained when the plate is with and without the crack
75
7.5. Conclusion
Figures 7-5, 7-6 and 7-7 show a difference between the pure wave (pristine plate)
labeled by red color and the disturbed wave (when the plate is with holes) labeled by blue
dotted line. There is a change in time of flight (a delay in arrival) and amplitude of the
wave for both
and
modes. This confirms that both these modes interacted with the
holes (2mm, 4mm and 6mm), and their propagation has been influenced as a result of
scattering of the waves from the hole edges. Therefore, it can be concluded that both
and
modes are sensitive to through-thickness holes, which agrees with previous
studies [7], and can detect the presence of these holes (defects) when an appropriate
frequency is used. Also, an increase in size of the hole from 2mm to 6mm caused a
decrease in amplitude of the wave (Figure 7-8). Hence, larger size holes apparently have
more scattering effect on the propagating wave. However, the difference doesn’t seem to
be significant enough to make that conclusion.
Likewise, a delay in arrival time and decrease in amplitude is observed for both
and
modes in Figures 7-10, 7-11, and 7-12 due to 1mm, 2mm, and 3mm cracks in
the plate. Consequently, both
and
and
mode in these cracks.
is more sensitive than
modes are sensitive to through-thickness cracks,
The frequency of excitation depends on the size of the PZT disc used. According
to previous study [21] and frequency tuning results in Waveform Revealer, it is found
that the best working frequency for the setup with 20mm diameter PZT discs is between
110 kHz and 150 kHz.
76
A mode conversion phenomenon was not observed in Pzflex at 150 kHz. The
frequency has to be tuned for disc size and hole diameter simultaneously in order to
observe a strong
signal and mode conversion.
Finally, it is concluded that damage in aluminum plate, through-thickness hole
and crack, is detected successfully in Pzflex by comparing the fundamental
and
modes of the undamaged plate wave with the wave obtained when the plate is damaged.
77
Chapter 8
Conclusions
The objective of this research is to establish a NDE laboratory setup by studying
basic guided wave phenomena, investigating the mathematical background, performing
Lamb wave experiments, running relevant finite element simulations, and finally
identifying equipment necessary to complete the laboratory setup for advanced tests. The
results and achievements are presented below.
Basic Lamb wave phenomena have been discussed. After studying the nature and
characteristics of different types of waves, Lamb waves have been selected for damage
detection analysis because techniques using Lamb waves are more effective and more
efficient. Since Lamb waves exist in different modes categorized as Symmetric (S) and
Anti-symmetric (A), damage detection analyses have to be based on either of the lower
modes identified as
and
. Although both modes are capable of detecting through-
thickness holes and cracks in thin plates,
can be more easily identified and is selected
for the analysis.
78
Mathematical background of Lamb waves has been investigated. Dispersion
principles of waves are discussed, and dispersion curves of Lamb waves are developed by
solving the Rayleigh-Lamb equation. Phase velocity dispersion curves have been used to
determine the cut-off frequency of a particular mode below which the required modes can
be produced. The cut-off frequency of
plate, and only
and
mode is 1.88 MHz in a 1.02mm aluminum
modes can be produced for frequencies below this value. The
frequencies used in this paper are 150, 350, and 500 kHz; thus, only
and
are
produced in all experiments and simulations. Group velocity dispersion curves have been
used to extract speed of propagation of
and
modes at given frequencies which are
used in calculating the distance travelled by the wave mode.
A simple pitch-catch experiment has been performed on a pristine plate. The
experiment was intended to determine the frequency at which the setup works best. This
has been achieved by using frequency of 500 kHz, at which the expected modes,
and
, have been generated. This has been verified by simulation results from Waveform
Revealer by comparing distance travelled by the modes with their theoretical distance
determined by using their speed from group velocity dispersion curves and time of flight.
Moreover, a defect (4mm diameter hole) has been detected experimentally on a 1.02mm
aluminum plate by using mode conversion of the
mode as a parameter. Frequency
selected is 350 kHz based on hole diameter to wavelength ratio. Results from Waveform
Revealer also showed that
has undergone mode conversion at 350 kHz when there is
damage in the plate.
Simulations in Pzflex verified the pitch-catch experiment and further detected
damage in the plate. Frequency tuning for 20mm PZT disc size in Waveform Revealer
79
showed the frequency at which
mode can be generated successfully is between 110
and 150 kHz. Also, frequency based on the disc size to wavelength relationship for
mode is around 130 kHz. Therefore, 150 kHz was selected to run simulations in Pzflex.
Through-thickness holes and cracks in 1.02mm aluminum plates have been detected in
Pzflex by comparing wave amplitude or time of flight of
with the one in a damaged plate. This concluded that
mode in an undamaged plate
and
modes are sensitive to
such type of defects.
Now that the experiments were successful in the current setup, more work is
needed to identify and add relevant equipment capable of carrying out more complex
experiments in the future. It is noted that some of the important aspects that must be
considered in the development of a Lamb wave based inspection method are: the size and
types of transducers to be used and how they are applied to the structure; and the type of
signal acquisition and processing to be applied [22]. Based on this, PZT transducers of
the same type and size are preferred to make selection of frequency easier. A variable
angle beam shoe transducer can be employed to vary the incidence angle if it is
determined that the inspection will be based on a single mode. Sufficient bonding
between transducers and the plate can be achieved through Epotek 301 bonding agent.
Most importantly, the current setup requires a sophisticated data acquisition system for
acquiring signal smoothing and de-noising signal. A scheme of Lab view with digitizer is
required to complete the setup. It is also relevant to propose a non-contact technique
using Laser Vibrometry (Polytec PSV- 400 scanning laser vibrometer), where a laser
beam is used to record the velocities induced by the PZT actuator using Doppler shifting
80
phenomenon. This technique allows excellent visualization of the wave field which is
valuable in studying its interaction with different damage types.
As a continuation to this paper, damage experiments based on time of flight and
amplitude as parameters have to be performed and compared with the Pzflex results. For
consistency, the same size through-thickness holes and cracks need to be modeled in
1.02mm thick aluminum plate at similar locations as the simulation. The objective will be
to detect the defects and to verify the outcome with the simulation results. Once damage
detection is completed successfully, the next step should involve measuring the severity
of the damage or size of the damage. To quantify (or size) damage, run experiments with
different hole diameters and measure each time of flight or amplitude. Establish a plot or
relationship between the measured damage index (DI) which is either time of flight or
amplitude and known damage parameter (hole diameter or crack width). Then, obtain the
damage index with supposedly unknown hole diameter or crack width. Interpolating or
extrapolating the damage index in the plot, the unknown hole diameter or crack width can
be estimated. Moreover, damage localization should also be performed. Note that
locating damage requires more PZT discs to offer multiple forward-scattering wave
signals upon which damage localizing analysis can be performed.
81
References
[1] Chahbaz, A., Mustafa, V., and Hay, D., Tektrend International (Canada), “Corrosion
Detection in Aircraft Structures using Guided Lamb Waves,” NDTnet, Vol.1 No.11
November 1996.
[2] Hui-Ru Shih, Wilbur L. Walters, Wei Zheng, and Jessica Everett, “ Course Modules
on Structural Health Monitoring with Smart Materials,” The Journal of Technology
studies, JOTS Volume 35, Number 2, VirginiaTech, Winter 2009.
[3] Ken, I. Salas and Carlos, E. S., “Cesnik. Guided Wave Experimentation using
CLoVER
Transducers
for
Structural
Health
Monitoring,”
49th
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference, AIAA 2008-1970, April 2008.
[4] Nieuwenhuis, J.H., Neumann, J., Geve, D.W., and Oppenheim, I.J., “Generation and
detection of guided waves using pzt wafer transducers”
[5] Zhongqing Su and Lin Ye, “Identification of Damage using Lamb Waves,” Lecture
Notes in Applied and Computational Mechanics, Vol 48, 346 p., 2009 [978-1-84882-7837].
[6] Rose, J. L., “Ultrasonic Waves in Solid Media,” Cambridge University Press, 1999.
[7] Hee Don Jeong, Hyeon Jae Shin, and Joseph L. Rose,” Detection of Defects in a Thin
Steel Plate Using Ultrasonic Guided wave,” Proceedings of 15th World Conference on
NDT, Roma, Italy, October 2000.
[8] Zhang Hai-Yan and Yu Jian-Bo, “Piezoelectric transducer parameter selection for
exciting a single mode from multiple modes of Lamb waves,” Chinese Physical Society
and IOP Publishing Ltd, Vol 20, No. 9, (2011) 094301.
82
[9] Pablo Gomez, Jose Paulino Fernandez and Pablo David Garcia, “Lamb Waves and
Dispersion Curves in Plates and its Applications in NDE Experiences Using Comsol
Multiphysics,” excerpt from proceedings of 2011 COMSOL Conference, Stuttgart, 2011.
[10] Liu Zhenqing, “Lamb Wave Analysis of Acousto-Ultrasonic Signals in Plate,”
Institute of Acoustics, Tongji University Shanghai 200092, P.R.China.
[11] Rose, J. L., “A Baseline and Vision of Ultrasonic Guided Wave Inspection
Potential,” Journal of Pressure Vessel Technology, Vol. 124/273, August 2002.
[12] Rose, J. L., and Avioli, M. J., 2000, “Elastic Wave Analysis for Broken Rail
Detection,” 15th World Conference on Non-Destructive Testing, Rome, Italy, October 1521.
[13] Yilmaz Bingol, “Development of an Ultrasonic NDE&T Tool for Yield Detection in
Steel Structures”, PhD Dissertation, Agricultural and Mechanical College, Louisiana
State University, August 2008.
[14] Michaels, T. E., and Michaels, J. E., “Application of Acoustic Wavefield Imaging to
Non-contact Ultrasonic Inspection of Bonded Components”, in review of progress in
Quantitative Nondestructive Evaluation, Vol 25, ed. by D. O. Thompson and D. E.
Chimenti, American Institute of Physics, pp. 7354-0312, 2006.
[15] Hyung Jin Lim, Hoon Sohn, Chul Min Yeum, and Ji Min Kim, “Reference-free
damage detection, localization, and quantification in composites”, Acoustical Society of
America, Vol. 133, No. 6, June 2013.
[16] Diligent, O. and Lowe, M. J. S., “Reflection of the S0 Lamb mode from a flat
bottom circular hole”, Journal of Acoustical Society of America, Vol. 118, No. 5, 2005,
pp. 2869-2879.
[17] Grahn, T., “Lamb wave scattering from a circular partly through-thickness hole in a
plate”, Wave motion, Vol. 37, No. 1, 2003, pp. 63-80.
[18] Diligent, O., Grahn, T., Bostrom, A., Cawley, P., and Lowe, M. J. S., “The lowfrequency reflection and scattering of the S0 Lamb mode from a circular throughthickness hole in a plate: Finite Element analytical and experimental studies”, Journal of
Acoustical Society of America, Vol. 112, No. 6, 2002, pp. 2589-2601.
83
[19] Lawrence, W. Braile, “Seismic Waves and the Slinky: A Guide for Teachers”,
Purdue University, 2009
http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htm... (accessed April 2013)
[20] Qiaojian Huang, Sridhar Krishnaswamy, Oluwaseyi Balogun, and Brad Regez,
“Structural Health Monitoring for Life Management of Aircraft – SHM of Adhesivelybonded Composites”, Center for Quality Engineering and Failure Prevention,
Northwestern University, Evanston, IL. date
[21] Carlos Silva, Bruno Rocha, Afzal Suleman, “Guided Lamb Waves Based Structural
Health Monitoring Through a PZT Network System”, 2nd International Symposium on
NDT in Aerospace 2010 – We.1.B.4.
[22] Hillger, W. and Pfeiffer, U., “Structural Health Monitoring Using Lamb Waves”, 9th
European Conference on Non-Destructive Testing – ECNDT, Berlin, Germany, 2006.
[23] Giurgiutiu, V., Lyshevski, S.E., “Micromechatronics: Modeling, Analysis, and
Design with MATLAB”, 2nd Edition, Taylor & Francis CRC Press, ~900 pages, ISBN
978-1420065626, 2009.
[24] PZFlex version 3.0, Virtual Prototyping, Weidlinger Associates, 2012.
[25] Waveform Revealer 3.0, LAMSS Swearingen Engineering Center, University of
South Carolina, 2013.
84