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Development of Ultrasound Phased Array System for Weld Inspections at Elevated Temperatures
by
Mohammad Hassan Marvasti
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy (PhD)
Department of Mechanical and Industrial Engineering University of Toronto
© Copyright by Mohammad Hassan Marvasti 2014
ii
Development of Ultrasound Phased Array System for Weld
Inspections at Elevated Temperatures
Mohammad Hassan Marvasti
Doctor of Philosophy (PhD)
Mechanical and Industrial Engineering
University of Toronto
2014
Abstract
Interruption of plant operation can be avoided if non destructive testing inspections are
performed on-line at operating temperatures, which may be up to several hundred degrees
Celsius in a petrochemical or electric power generating plant. However, there are operational
temperature limits of the phased array transducers and associated plastic wedges used for
ultrasonic inspections. In addition, there is a major gap in terms of professionally-approved high-
temperature inspection techniques. In this project, the design and operation of an ultrasonic
phased array system are described for inspections of engineering components such as pipe welds
at elevated temperatures of up to 350oC. Wedges are built from plastics resistant to high
temperature degradation, and equipped with a cooling jacket around the array. A model of the
ultrasonic beam skew pattern due to thermal gradients inside a wedge is developed. The model is
used in a separate algorithm to calculate transmission and reception time delays on individual
array elements for generation of plane waves or focused beams in a hot test piece, while
compensating for thermal gradient effects inside the wedge.
The algorithm is also used to investigate the magnitude of thermal gradient effect on the
calculated time delays of the phased array elements. The algorithm results for inspections of test
iii
pieces at 150oC demonstrate that application of conventional element time delays can lead to
serious phase errors. This results in major distortion of the desired beam profile, and very poor
imaging resolution. However, experimental trials indicate that plane waves and focused beams
can be generated in a hot test piece using the new focal law algorithm with appropriate timing
delays applied to all active array elements.
iv
Acknowledgments
I would like to express my sincere gratitude to my supervisor, Professor Anthony Sinclair, for his
guidance and support without which this research work thesis would not have been possible to be
completed.
I am grateful to National Science and Engineering Research Council of Canada (NSERC), and
Eclipse Scientific for sponsoring my research and more importantly, for giving me a
distinguished opportunity to work on a rewarding academic/industrial collaborative research
project.
I wish to thank my colleagues Jonathan Lesage, Hossein Amini, Babak Shakibi and Jill Bond at
Ultrasonic Nondestructive Evaluation Laboratory at the University of Toronto for their help and
assistance in this project.
I would also like to express my gratitude to Robert Ginzel, Edward Ginzel, Jeff van Heumen and
the team at Eclipse Scientific for their kind helps in this project. Working with them was an
invaluable experience for me.
Finally, I am particularly thankful to my wonderful wife, my parents and my family for their
support and encouragement throughout the course of my thesis.
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Table of Contents
Abstract……………………………………………………………………………………………ii
Acknowledgments .......................................................................................................................... iv
Table of Contents ............................................................................................................................ v
List of Tables ................................................................................................................................ vii
List of Figures .............................................................................................................................. viii
1 Introduction .............................................................................................................................. 1
2 Background Theory and Literature Review.......................................................................... 4
2.1 Ultrasonic Non-Destructive Testing ................................................................................... 4
2.2 Fundamentals of Ultrasonic Wave Propagation in Solid Media ......................................... 4
2.2.1 Wave Propagation Modes ....................................................................................... 4
2.2.2 Speed of Propagation .............................................................................................. 5
2.2.3 Reflection, Refraction and Mode Conversion ........................................................ 6
2.2.4 Ultrasonic NDE System .......................................................................................... 6
2.2.5 Display Modes ........................................................................................................ 7
2.3 Principles of Phased Array Ultrasound ............................................................................... 9
2.3.1 Beam Steering and Focusing Using Phased Arrays .............................................. 10
2.3.2 Phased Array ultrasonic Inspection System .......................................................... 11
2.3.3 Phased Array Scanning Configuration .................................................................. 13
2.3.4 Phased Array Display Modes ................................................................................ 15
2.4 Weld Inspections with Phased Arrays .............................................................................. 16
2.5 Phased Array Inspection at Elevated Temperatures ......................................................... 17
3 High Temperature Wedges ................................................................................................... 20
4 Temperature Distribution Model ......................................................................................... 23
5 Velocity Measurements at Elevated Temperatures ............................................................ 26
vi
6 Focal Law Algorithm – Planar Waves ................................................................................. 31
6.1 Room Temperature Inspection .......................................................................................... 31
6.2 Elevated Temperature Inspection ..................................................................................... 35
7 Experimental Validation – Planar Waves............................................................................ 44
7.1 Concept for Experimental Validation ............................................................................... 44
7.2 Experimental Details ......................................................................................................... 46
7.3 Experimental Results and Analysis - Room Temperature ................................................ 47
7.3.1 Systematic Errors .................................................................................................. 49
7.3.2 Random Errors ...................................................................................................... 51
7.4 Experimental Results and Analysis - Elevated Temperature ............................................ 53
8 Focal Law Algorithm – Focused Beam ................................................................................ 64
8.1 Algorithm Details .............................................................................................................. 65
8.2 Magnitude of Thermal Gradient Effect ............................................................................. 68
8.3 Experimental Evaluation ................................................................................................... 73
9 Summary, Conclusions and Future Work ........................................................................... 82
References ..................................................................................................................................... 84
vii
List of Tables
Table 7-1 Inputs to the focal law calculating algorithm at room temperature: the levels of
uncertainty in the measured values of inputs are listed and the magnitude of their resulting effect
on the bias error on the first element of the aperture is presented. ............................................... 50
Table 7-2 Magnitude of the experimental results associated with generation of a 45o shear plane
wave at 150oC as depicted in Figure 7.5. The results of 15 repeated time delay measurements of
echo signals of the first and central elements of the active aperture are presented for two cases:
active aperture = elements 1-16; and active aperture = elements 49-64. ..................................... 59
Table 7-3 Experimental results associated with generation of a 60o shear plane wave at 150
oC as
depicted in Figure 6. The results of 15 repeated time delay measurements of echo signals of
selected elements of the active aperture are listed in separate columns. ...................................... 62
viii
List of Figures
Figure 2.1 Ultrasonic wave propagation modes: (a) Longitudinal (Compression) mode and (b)
Shear (Transverse) mode [5]. .......................................................................................................... 5
Figure 2.2 Refraction and mode conversion of a longitudinal wave at the boundary of two media
[6]. ................................................................................................................................................... 6
Figure 2.3 Major components of a typical ultrasonic inspection set up in pulse/echo configuration
mode where one transducer is used for both transmission and reception of the ultrasonic waves
[8]. ................................................................................................................................................... 7
Figure 2.4 Representation of A-scan display: (a) transducer position, (b) signal display [9]. ....... 8
Figure 2.5 Representation of B-scan: (a) test configuration, (b) scan display [9]. ......................... 8
Figure 2.6 Representation of C-scan display: (a) transducer movement pattern (b) C-scan display
[9]. ................................................................................................................................................... 9
Figure 2.7 Phased array probe cross-sectional view [13]. ............................................................ 10
Figure 2.8 Beam steering with phased arrays, (a) unfocused beam (plane wave) and (b) focused
beam [14]. ..................................................................................................................................... 11
Figure 2.9 Typical components of a phased array inspection system. .......................................... 12
Figure 2.10 Electronic (linear) scan performed by focused beam normal to array elements [17].14
Figure 2.11 Sectorial scanning with phased arrays: the sound beam sweeps through a series of
angles [17]. .................................................................................................................................... 14
Figure 2.12 S-scan of 3 side drilled holes in a steel block through phased array sectorial scanning
[18]. ............................................................................................................................................... 15
ix
Figure 2.13 Scan plan of a phased array ultrasonic inspection of a weld in a steel block, as
generated by a ray-tracing algorithm. The scan plan covers a range of inspection angles (46o-72
o)
inside the steel piece. The blue lines represent the direction normal to the plane wave fronts
generated by the active phased array elements. ............................................................................ 17
Figure 3.1 PEI high temperature wedge schematic with sloped front and dampening material at
the top of the wedge: ray 1 (solid line) and ray 2 (dashed line) illustrate reflection pattern of steep
and shallow beam incidence at the wedge bottom. As a result of wedge elongation and angled
front, the internally reflected beams reflect to the top of the wedge where they are absorbed by
the dampener. ................................................................................................................................ 22
Figure 3.2 High temperature phased array inspection system including: Eclipse WA10-HT55S-
IH-B PBI wedge prototype based on the geometry of the Olympus linear phased array model
5L16-A10 with 16 elements and center frequency of 5MHz, water cooling jacket, coolant tubing
system and mounting arms. ........................................................................................................... 22
Figure 4.1 PEI wedge temperature distribution modeling result, the color palate represents the
temperature distribution inside the wedge between 25oC and 150
oC. Surface temperature
measurements located on the dashed lines were used to validate the model results. ................... 25
Figure 4.2 Comparison of COMSOL and experimental results for the temperature distribution on
the surface of the PEI wedge mounted on a 150oC steel pipe. Solid lines on the graph and the
error bars represent average temperature values of 5 experiments and standard deviations of the
measurements: the red circles represent COMSOL model results at the specified locations on the
wedge surface. ............................................................................................................................... 25
Figure 5.1 Phase velocity measurement from two successive backwall echoes. The phase of
each pulse is determined relative to left side of the pulse acquisition window. ........................... 27
Figure 5.2 Experimental set up for measuring phase velocity at high temperatures. The sample
and the delay line were wrapped in high temperature insulation to lessen the temperature gradient
inside the plastic block. The mean block temperature was estimated from thermocouples placed
on top and bottom of the plastic block. ......................................................................................... 28
x
Figure 5.3 Phase velocity data of PEI (a) and PBI (b) plastic blocks at selected elevated
temperatures. Solid lines and the error bars represent the mean and standard deviation of 5
repeated experimental measurements. .......................................................................................... 29
Figure 5.4 Phase velocity of PEI (a) and PBI (b) as a function of temperature at 5 MHz
frequency. The empirical relations shown on the graphs indicate the functional change of phase
velocity results with temperature T expressed in degrees Centigrade. ......................................... 30
Figure 6.1 Wave propagation pattern for a shear plane wave at angle Фs in a steel block at a
uniform temperature of 25oC. The ray traces are applicable for a wave transmitted from the array
into the test piece, or equivalently for a wave travelling from the test piece back to the array. In
the latter case, the waves associated with sample points along an arbitrary plane wave front
propagate in a direction perpendicular to the wave front and reach the piece-wedge interface at
locations labeled as interface points. Then they refract into the wedge based on Snell’s law and
propagate through the wedge to the array-wedge interface at points labeled as array-line points.
....................................................................................................................................................... 33
Figure 6.2 Wave propagation pattern for a shear plane wave at angle Фs in a steel block at a
uniform temperature of 150oC. The ray traces are applicable for a wave transmitted from the
array into the test piece, or equivalently for a wave traveling from the test piece back to the array.
In the latter case, the waves associated with sample points along an arbitrary plane wave front
propagate in a direction perpendicular to the wave front and reach the piece-wedge interface at
locations labeled as interface points. Then they refract into the wedge based on Snell’s law and
propagate through the wedge to the array-wedge interface at points labeled as array-line points.
The waves propagate along arced paths (red lines) in the wedge due to thermal gradient induced
velocity variation. ......................................................................................................................... 37
Figure 6.3 Calculated relative element time delays for the generation of a 60o shear plane wave
for Eclipse WA12-HT55S-IH-G PEI wedge and the Olympus linear phased array model 5L64-
A12 one a) the first 16 elements of the array (elements 1-16) were used and b) the last 16
elements of the array (elements 49-64) were used. The blue and red data points represent the
results for room (25oC) and elevated temperature (150
oC) inspection condition respectively and
the delays are expressed relative to the first element of the used active aperture......................... 39
xi
Figure 6.4 Temperature profile inside an Eclipse WA12-HT55S-IH-G PEI wedge for inspection
of test piece at 150oC, the color palate represents the temperature distribution inside the wedge
between 25oC and 150
oC as obtained by our COMSOL finite element model. Waves emitted
from elements 1-16 propagate along the shortest path length in the wedge with a relatively steep
temperature gradient, compared to the waves emitted from elements 49-64. .............................. 40
Figure 6.5 Calculated element time delays for the generation of a 45o shear plane wave for an
Eclipse WA12-HT55S-IH-G PEI wedge and the Olympus linear phased array model 5L64-A12
one a) the first 16 elements of the array (elements 1-16) were used and b) the last 16 elements of
the array (elements 49-64) were used. The blue and red data points represent the results for room
(25oC) and elevated temperature (150
oC) inspection condition respectively and the delays are
expressed relative to the last element of the used active aperture. ............................................... 43
Figure 7.1 propagation of a wavefornt corresponding to a shear plane wave at an angle Фs in a
steel test block at elevated temperature: the wavefront is not straight inside the wedge due to
non-uniformity of the medium. However, it turns into a planar surface when the wave refracts
into the steel test piece at the wedge-piece interface. ................................................................... 45
Figure 7.2 Experimental results for the case of generating a 45o shear plane wave in the 45
o-
angled steel test block at a uniform temperature of 25oC using the first 16 elements of the array
(elements 1-16): the blue data points represent transmitting time delays applied to the elements in
transmission mode as calculated by our model. The solid red line represents the mean of 10
measurements of receiving delays at the same individual array elements. The error bars indicate
the standard deviation of the measurements at each individual element. ..................................... 48
Figure 7.3 Deviation times between the measured received echo time delays on each individual
elements and their associated theoretical value as calculated by our model for the case of
generating a 45o shear plane wave in the 45
o-angled steel test block at a uniform temperature of
25oC using the first 16 elements (data illustrated in Figure 7.2). The solid line and error bars are
associated with the mean and standard deviation of the measurements on each individual array
element. Note the very fine time scale on the vertical axis. ......................................................... 49
Figure 7.4 Experimental set up for evaluation of model results for generation of shear plane
waves in an angled steel test block at 150oC. An Eclipse WA12-HT55S-IH-G PEI wedge was
xii
used along with an Olympus 5L64-A12 array for plane wave generation with a cooling jacket
around the array. The steel test block was located on a temperature-controlled hot plate and
wrapped in high temperature insulation which led to temperature variation over the entire volume
of the test piece of less than 10oC. ................................................................................................ 54
Figure 7.5 Experimental results for generation of a 45o shear plane wave in a 45
o-angled steel test
block at 150oC using an Olympus 5L64-A12 array and Eclipse WA12-HT55S-IH-G PEI wedge
when the first 16 elements (a) and last 16 elements (b) of the array were used. The red and green
data points represent the relative time delays calculated by our algorithm, and the mean of the
measured echo time delays, respectively. The green points are each the average of 15 repeated
experiments and error bars indicate the uncertainty level in the value of the green points. Blue
data points represent the calculated time delays for room temperature inspection. ..................... 56
Figure 7.6 Experimental results for generation of a 60o shear plane wave at 150
oC when the first
16 elements (a) and last 16 elements (b) of the array were used. The red and green data points
represent the relative time delays calculated by our algorithm, and mean of the experimentally
measured received echo time delays, respectively. The green points are each the average of 15
repeated experiments; the associated error bars indicate the uncertainty level in the value of the
green points. Blue data points represent the calculated time delays for room temperature
inspection, presented for sake of comparison. .............................................................................. 61
Figure 8.1 Wave propagation pattern for focusing an ultrasonic beam at an arbitrary focal point
in a steel block at a uniform temperature of 25oC. Wave propagation paths are shown from
various array-line points along the phased array to the selected focal point. The propagation paths
are straight lines in both the wedge and the steel block, each with a single wave propagation
velocity at 25oC. The refraction angle at each interface point is determined by Snell’s Law. ..... 66
Figure 8.2 Wave propagation pattern for focusing an ultrasonic beam at an arbitrary focal point
in a steel block at a uniform temperature of 150oC. Wave propagation paths are shown from
various array-line points along the phased array to the selected focal point. The propagation paths
are straight lines in the steel block based on the assumption of uniform temperature inside the
block (blue lines). After the waves refract into the wedge, they propagate along arced paths (red
lines) due to velocity variations across the heated wedge that are induced by thermal gradients. 68
xiii
Figure 8.3 Location of the selected focal points and calculated near field points in a steel block
on the sound paths representing the waves with refraction angles of 40o, 55
o and 70
o using an
Eclipse WA12-HT55S-IH-G PEI wedge-5L64-A12 Olympus array system. The first 16 elements
of the aperture are used for beam formation and the each sound path is represented by a straight
line emitted from the point located at the center of the active aperture. ....................................... 69
Figure 8.4 The calculated time delays of individual elements for focusing an ultrasonic beam at
the selected focal points located on the wave sound paths representing (a) 45o, (b) 55
o and (c) 70
o
refraction angles inside a steel test block using an Eclipse WA12-HT55S-IH-G PEI wedge-5L64-
A12 Olympus array system (as depicted in Figure 8.3). The first 16 elements of the aperture are
used for beam formation. The blue and red data points represent the results for room (25oC) and
elevated temperature (150oC) inspection condition respectively. In each case, delays are
expressed relative to the element associated with the longest travel time from array to the focal
point. This element is fired first with delay time defined as time zero; all other elements are then
fired at their relative delay times. ................................................................................................. 71
Figure 8.5 Calibration block for steering assessment of phased array probe based on the
amplitudes of the echo signals received from a series of 2-mm diameter side drilled holes. The
holes are located at 5o interval on an arc 50 mm from the surface location where the midpoint of
the array’s active aperture is located. A focused beam is electronically swept along the arc with
1o angular steps. Amplitudes of the received echo signals are analyzed. High amplitudes are
expected to correspond to the locations of the holes. The clarity of the amplitude peaks as a
function of steering angles indicates the angular range of the array. ............................................ 74
Figure 8.6 Design specifications of a steel block for performance assessment of a wedge-array
system. The block was specifically designed for use with Eclipse WA12-HT55S-IH-G PEI
wedge and first 16 elements of the 5L16-A12 linear phased array probe. The blue straight lines
represent the wave paths associated with refraction angles ranging from 40o up to 70
o in 1
o
increments. The red arc represents the boundary of the near field on the specified sound paths.
The black arc links the locations of the focal points on the presented sound paths. These are
located at the same travel time distance from the center of the active aperture, and are all within
the near field. ................................................................................................................................ 76
xiv
Figure 8.7 Configuration of the designed steel block for angular resolution and steering
assessment of an Eclipse WA12-HT55S-IH-G PEI Wedge-5L64-A12 Olympus array system: a
set of four side drilled holes are selected as reflectors. The holes are centered on the focal points
which lie along the sound paths representing the refraction angles s of 44o, 49
o, 56
o and 66
o.
The straight lines represent the wave paths associated with refraction angles ranging from 40o up
to 70o in 1
o increments. The black and red points represent the location of focal points (steering
samples) and the near field points on the specified sound paths. ................................................. 77
Figure 8.8 Experimental set up for evaluation of model results for focusing the ultrasonic beam
in a steel test block at 25oC. An Eclipse WA12-HT55S-IH-G PEI wedge was used with a 5L64-
A12 Olympus array for generation of focused beams. The steel test block contains four side
drilled holes at locations specified in Figure 8.7. ......................................................................... 77
Figure 8.9 Assessment results of an Eclipse WA12-HT55S-IH-G PEI wedge-5L64-A12 Olympus
array system at ambient temperature of 25oC. The focused beam was swept electronically along
the focal points as depicted in Figure 8.7 and Figure 8.8. The maximum amplitude of the
analytical form of the echo signals was plotted versus the refraction angles (blue points). The
local amplitude peaks correspond to refraction angles of 44o, 49
o, 56
o and 66
o inside the steel test
block (dashed lines). These represent the location of the side drilled holes. ................................ 78
Figure 8.10 Assessment results of an Eclipse WA12-HT55S-IH-G PEI wedge-5L64-A12
Olympus array system at 150oC. The focused beam was swept electronically along the focal
points as depicted in Figure 8.7 and Figure 8.8 and the maximum amplitude of the analytical
form of the echo signals was plotted versus the refraction angles. Two sets of focal laws were
used for beam formation: First, the focal laws calculated for ambient temperature condition
(25oC) and then the focal laws calculated by our new model for the actual experimental condition
(150oC test block). The results corresponding to these cases are presented by the blue and red
points, respectively. The dashed lines represent refraction angles which correspond to location of
the side drilled holes in the steel test block. .................................................................................. 80
1
1 Introduction
Many industrial sectors such as power generation, petrochemical production, and metal
processing have systems that operate at elevated temperatures for extended time periods, during
which some failure mechanisms can be significantly accelerated. Regular Non-Destructive
Testing (NDT) of high-temperature systems is therefore required. In particular, ultrasonic NDT
with phased array transducers has been found to be an accurate and convenient method for
inspection of many industrial piping systems and welds.
Phased array ultrasonic transducers create a user-specified beam profile by a controlled pulse
sequencing of the array elements determined by software known as a focal law calculator. A
phased array’s beam forming capability introduces unique benefits for weld inspection:
electronic beam steering provides rapid and accurate scanning of the weld sections, and
inspection angles can be tailored based on weld geometry to increase scanning efficiency
specifically for complex-shaped welds.
For a weld inspection, the beam travels from the array through a plastic wedge, which has the
primary function of coupling sound energy from the array transducer to the test piece at a
prescribed angle. An ultrasonic beam refracts from the wedge into the test piece where it
interacts with flaws; echoes are then returned to the same wedge and transducer, or a separate
receiver for analysis to determine flaw locations and sizes.
Interruption of plant operation can be avoided if NDT inspections can be performed on-line at
operating temperatures; this may be up to several hundred degrees Celsius. This capability
avoids costly downtime and reduces the risk of damage from thermal cycling associated with
periodic shutdowns. However, high temperature phased array inspections cannot be routinely
performed: there are operational temperature limits of the phased array transducers and plastic
wedges; in addition, there is a gap in terms of approved and appropriate high temperature
inspection techniques.
Wedges for high temperature inspections can be built from materials that have low ultrasonic
attenuation, appropriate values of acoustic impedance, and resistance to high temperature
degradation. A cooling jacket can be placed on the wedge to protect the array. However, this
2
introduces new problems: inside the wedge, thermal gradients lead to variations in temperature-
dependent wave velocity and skewing of the waves; the focal law calculator, which is based on
the assumption of wave propagation in homogeneous propagation media, would become
inaccurate. Refraction angles of ultrasound into the test piece become altered by elevated wedge
temperature and skewed ultrasound propagation paths. To date, the significance of these factors
has not been thoroughly evaluated.
The objectives of this research are to:
1) Model the beam skew induced by thermal gradients inside the heated wedge,
2) Develop an algorithm to calculate appropriate time delays for individual array elements for
generation of a shear plane wave or a focused beam in a hot test piece,
3) Investigate the amount of distortion to the focal law calculator at elevated temperature, as a
function of key scanning parameters; these parameters include the selection of the active array
aperture, plus the magnitude and orientation of the thermal gradient inside the high temperature
wedges, and
4) Validate the new focal law calculator experimentally.
In Chapter 2, we present a brief overview of the fundamentals of ultrasonic wave propagation in
solid media, basics of non-destructive testing, a description of a typical phased array weld
inspection system and its limitations at elevated temperature.
In Chapters 3 to 8 of this thesis, we progress through 6 major steps of this project. First, the
design specifications of high-temperature wedges with a cooling jacket around the array are
described in Chapter 3. The temperature distribution inside the wedges is modeled using
COMSOL Multiphysics1 finite element software package and validated experimentally (Chapter
4). Next, the dependence of compression wave velocity on temperature in wedge materials is
measured experimentally, and the results are presented in Chapter 5.
1 1 New England Executive Park, Burlington, USA.
3
The material from Chapters 3-5 is then combined with a numerical ray-tracing technique to
model the skewed path of waves propagating across thermal gradients in the heated wedge. This
is followed by development of an original algorithm to calculate appropriate time delays for
individual array elements for generation (or reception) of a shear plane wave in a hot test piece
based on the beam skew model results. The newly developed algorithm is described in Chapter 6
and its results for generation of planar shear waves at refraction angles of 45o and 60
o inside a
steel test piece at elevated temperature are presented.
In chapter 7, a set of experiments are conducted to evaluate the quality of the shear plane wave
generated in a hot steel test piece using the new focal law calculator described in Chapter 6.
Finally, in Chapter 8, a second set of experiments is conducted to evaluate the performance of
the new focal law calculator. This time, the goal is to focus the array at a single user-specified
point inside the hot test piece. The experimental results are presented and analyzed.
Conclusions are presented in Chapter 9. This includes a summary of results and suggestions for
future work.
4
2 Background Theory and Literature Review
2.1 Ultrasonic Non-Destructive Testing
Many industrial sectors have systems that operate under severe conditions such as elevated
temperatures and corrosive environments. Failure mechanisms can be significantly accelerated
under these conditions [1]. Regular non-destructive testing (NDT) is therefore required to avoid
costly failures [2]. In particular, ultrasonic NDT has been found to be an accurate and convenient
method for inspection of many industrial piping systems and welds [3] [4].
In ultrasonic inspections, high-frequency mechanical waves travel through materials and
partially reflect from discontinuities. The reflected or transmitted signal is detected and displayed
as an electric signal. Analysis of the obtained signals provides information on the location and
size of the discontinuities [5].
A brief review of the fundamentals of ultrasonic wave propagation in solid media and the basics
of ultrasonic non-destructive testing will be presented in the following sections.
2.2 Fundamentals of Ultrasonic Wave Propagation in Solid Media
2.2.1 Wave Propagation Modes
An ultrasonic wave can be generated by applying a time-varying mechanical stress to a medium.
This leads to vibrational motion of particles (atoms) in the medium about their equilibrium
positions. The sound waves propagate through the medium in different modes based on the way
the particles oscillate. Longitudinal and shear modes are the two modes of propagation in bulk
media that are widely used in ultrasonic testing [5].
A longitudinal (compression) wave or L-wave is generated by applying a normal stress to the
material surface. In this mode, particle vibrations occur in the direction of wave propagation and
cause compression and refraction regions along the propagation path (Figure 2.1.a).
Shear (transverse) wave or S-wave is excited by applying a shear force at the surface of a
medium; this causes wave propagation through the medium by shear stresses. This mode results
in atomic oscillations perpendicular to the direction of wave propagation (Figure 2.1.b).
5
Figure 2.1 Ultrasonic wave propagation modes: (a) Longitudinal (Compression) mode and (b) Shear (Transverse)
mode [5].
2.2.2 Speed of Propagation
The speed at which the wave propagates depends on the properties of the medium. In an elastic,
isotropic, solid medium the speed of ultrasound is determined by the elastic constants (Young’s
and Shear modulus) and density of the medium. Variations of these parameters result in changes
to wave speed as it propagates through the medium [5] [6].
Temperature variation is frequently a cause of non-homogeneity in a wave propagation medium.
A material’s elastic moduli and its density are both temperature dependent properties. Therefore,
the presence of a thermal gradient in a medium results in regions with different local mechanical
properties. As a wave propagates in such media, its velocity varies due to a dependency on local
temperature-dependent mechanical properties [7].
6
2.2.3 Reflection, Refraction and Mode Conversion
When an ultrasonic wave reaches an interface between two media with different mechanical
properties (Figure 2.2), part of the sound is reflected back into the first medium and the rest is
refracted and transmitted into the second medium according to Snell’s Law. Ultrasonic waves
can also undergo mode conversion between shear and longitudinal modes upon oblique
incidence at an interface. In the case of spatially continuous variation of material properties (e.g.,
due to temperature gradients), there can be a continuous change in the propagation amplitude and
direction (skewing) of the wave [6].
Figure 2.2 Refraction and mode conversion of a longitudinal wave at the boundary of two media [6].
2.2.4 Ultrasonic NDE System
Major components of a typical ultrasonic NDE system are shown in Figure 2.3. An ultrasonic
pulser generates short high-voltage pulses at regular intervals. The pulses excite an ultrasonic
transducer which contains a piezoelectric element that converts electrical pulses into mechanical
pulses and vice versa. Mechanical pulses propagate through the engineering component as
ultrasound waves and reflect back to the transducer after interaction with flaws. The transducer
now acts as a receiver and the piezoelectric element converts the received ultrasonic waves to
electric signals. The signals are then amplified, digitized and displayed on an oscilloscope or a
computer screen for further analysis [8].
7
Figure 2.3 Major components of a typical ultrasonic inspection set up in pulse/echo configuration mode where one
transducer is used for both transmission and reception of the ultrasonic waves [8].
2.2.5 Display Modes
Ultrasonic signals generated by single-element transducers are commonly collected and
displayed in one of the three following formats [6] [7]:
A-Scan: in this type of display, the amplitude of the received signal is plotted versus time as
shown in Figure 2.4. Information on the location of the flaws can be provided by analysis of
time-of-arrival of ultrasonic reflector echoes.
B-Scan: to form a B-scan display, a sequence of A-scans is generated by moving the transducer
along the top surface of the specimen (x-axis). The A-scans are each converted to an intensity
graph (gray-scale pattern) and placed side-by-side. A cross sectional view of the specimen can be
obtained using a B-scan (Figure 2.5).
8
Figure 2.4 Representation of A-scan display: (a) transducer position, (b) signal display [9].
Figure 2.5 Representation of B-scan: (a) test configuration, (b) scan display [9].
9
C-Scan: The C-scan provides a two dimensional view of specimen flaw echoes within a specified
depth range z. The transducer is moved in a raster-like manner on the top x-y surface plane of
the specimen and captures A-scans at each step. The magnitude of the largest echo within the
specified z depth range for each A-scan is then converted to a gray-scale pattern for display. An
example of the transducer movement pattern and a C-scan display are shown in Figure 2.6.
Figure 2.6 Representation of C-scan display: (a) transducer movement pattern (b) C-scan display [9].
2.3 Principles of Phased Array Ultrasound
Ultrasonic phased arrays were initially introduced in the field of medical imaging. More recently,
numerous advantages of utilizing phased array ultrasound technology over conventional
ultrasonic transducers have led to their increasing use for many industrial settings such as weld
inspections [10] [11] [12].
Conventional ultrasonic transducers commonly consist of a single piezoelectric element which
can function as transmitter, receiver or both. A phased array transducer, however, contains
10
multiple individual piezoelectric elements. The elements are connected to separate electric
channels and can be pulsed individually. Figure 2.7 illustrates a linear array with rectangular
footprint which is a common configuration of a phased array probe.
Figure 2.7 Phased array probe cross-sectional view [13].
The piezoelectric elements in a phased array transducer can be fired at different times. After
being pulsed, the waves generated by different elements undergo constructive and destructive
interference with each other to create a new composite wave. The element firing times can be
adjusted to steer the composite beam at different angles, or to create a focused beam at a point
located at a depth specified by the user.
2.3.1 Beam Steering and Focusing Using Phased Arrays
To generate a planar wave which propagates at a certain angle in a homogenous and isotropic
medium, the piezoelectric elements should be fired with specific relative time delays. In this case
the acoustic fields generated by all the individual array elements should interfere constructively
to produce uniform acoustic pressure along each plane that is normal to the desired direction of
propagation. The appropriate delay pattern and its magnitude depend on factors such as speed of
ultrasonic waves in the medium, spacing between the array elements and desired propagation
angle of the beam with respect to the array line [7] [10] [14].
11
A set of delay times to be applied to the elements for composition of a desired beam is known as
the focal law. By changing the focal law applied to array elements, the angle of the generated
beam can be controlled electronically. A sequence of incremental changes in the focal law results
in steering the composite beam generated by the array, i.e., sweeping out a fan-shaped sector.
The array can also be used to generate a composite beam focused at a specified point in the
medium. To achieve this, an appropriate focal law must be applied to the elements such that
waves generated by individual elements all interfere constructively at the desired location. Travel
times of the waves from each element to the focal point are evaluated to obtain the appropriate
focal law. Figure 2.8 illustrates beam steering and focusing with phased arrays.
Figure 2.8 Beam steering with phased arrays, (a) unfocused beam (plane wave) and (b) focused beam [14].
2.3.2 Phased Array Ultrasonic Inspection System
The major components of a typical industrial phased ultrasonic inspection system can be seen in
Figure 2.9. The phased array probe is connected to a pulser/receiver instrument, and mounted on
a plastic wedge in direct contact with the test piece. The ultrasonic beam propagates through the
wedge and refracts into the test piece where it interacts with flaws; echoes are then returned to
the same wedge and transducer (or a second wedge and transducer) and received by the phased
array instrument for further analysis to determine flaw locations and sizes.
12
Figure 2.9 Typical components of a phased array inspection system.
The phased array instrument contains software known as a focal law calculator, which
determines the relative pulse delay time for each array element based on the desired beam angle,
focal distance, probe and wedge characteristics as well as acoustical properties of the test piece
material. The focal law calculator software is connected to electrical channels that apply the
appropriate excitation sequence to the individual array elements [10] [14].
Phased array probes can be found in a wide range of sizes, shapes, frequencies and number of
elements. However, the linear array with a rectangular footprint is the most common
configuration for industrial use. The resonant frequency of the probe, number of elements,
element spacing and element dimensions are the main factors to be considered in probe selection.
These parameters influence a probe’s capability in focusing and steering and it’s functionality in
generating desirable beam profiles. Therefore, probe selection should be driven by the
application [15].
13
A phased array probe assembly usually includes a plastic wedge. The ultrasonic wedge is a key
component of the inspection system and has the primary function of coupling sound energy from
the phased array transducer to the test piece at a specified contact angle. At the wedge-test piece
interface, the wave refracts according to Snell’s law, and may also convert between shear and
compression modes according to the wedge design [16]. The wedge typically has an added
component called a dampener (Figure 2.9), which absorbs any incident ultrasonic pulses so that
they do not bounce back into the wedge and generate spurious “ghost echo” signals. The wedges
come in many different sizes and styles to be compatible with different probe arrays.
2.3.3 Phased Array Scanning Configurations
Focal laws applied to individual elements in a multi-element phased array probe can be
controlled by computer. The ability of applying fast-changing automated computer–controlled
excitation to the array elements and the capability to generate beams with defined parameters
such as angle and focal distance, enable unique scanning configurations such as electronic
(linear) scanning and sectorial scanning.
In electronic (linear) scanning configuration, the same focal law is multiplexed across a group of
array elements and fixed beam angles are produced and scanned electronically along the array.
This is equivalent to mechanically scanning a conventional ultrasonic transducer along a distance
equal to the length of the phased-array probe. Using phased arrays, both focused and unfocused
beams can be generated for scanning electronically along a desired length in the medium. Figure
2.10 shows a linear scan performed by a focused beam with constant angle along the probe
length [10] [14].
14
Figure 2.10 Electronic (linear) scan performed by focused beam normal to array elements [17].
In the sectorial scanning configuration however, ultrasonic pulses are launched sequentially at a
sequence of angles into the test specimen by automated application of multiple focal laws. Focal
laws are produced to generate beams which sweep through an angular range with a specific
increment. Figure 2.11 illustrates the principle of sectorial scan.
Figure 2.11 Sectorial scanning with phased arrays: the sound beam sweeps through a series of angles [17].
15
With these scanning configurations, a large area can be covered for inspection in a very short
time.
2.3.4 Phased Array Display Modes
A-scan, B-scan and C-scan modes obtained with conventional single-element transducers can
also be generated by phased array equipment. In addition to these conventional display modes,
another mode known as a sectorial scan (S-scan) can be generated by the application of phased
arrays. The A-scan echo signal corresponding to each angle (focal law) is recorded and
transformed to a colour intensity graph of signal intensity vs. travel distance. The A-scans are
then assembled together sequentially to form a cross sectional view of a pre-shaped sector of the
specimen [10] [14]. Figure 2.12 illustrates an S-scan representation of three side-drilled holes in
a steel block.
Figure 2.12 S-scan of 3 side drilled holes in a steel block through phased array sectorial scanning [18].
16
2.4 Weld Inspections with Phased Arrays
Defects are often generated through the welding process. These defects may propagate under
operational service conditions and cause mechanical failures leading to severe consequences.
Regular non-destructive testing is therefore required.
Ultrasonic NDT with phased arrays has been found to be an accurate and convenient method for
inspection of many industrial weld systems. A phased array’s beam forming capability
introduces unique benefits for weld inspection: 1) weld sections are scanned rapidly and
accurately by electronic beam steering, 2) sectorial scanning provides a large field of coverage
from a single probe location, using beams with a sequence of refraction angles, 3) inspection
angles can be tailored based on weld geometry to increase scanning efficiency specifically for
complex-shaped welds, and 4) defect detection probability can be maximized by optimizing
beam shape and size through electronic focusing [19] [20].
Application of phased array ultrasound for weld inspection has increased in recent years due to
the above mentioned advantages. Therefore, many codes and standards have been developed
describing requirements and criteria for weld inspections using phased arrays. A key point
emphasized in these codes is that appropriate settings and scanning parameters must be selected
that ensure full inspection coverage of the weld area [21].
A document known as a “scan plan” is normally prepared before an inspection to lay out the
inspection methodology. Potential scanning configurations and beam angles are developed
through the scan plan and beam directions are identified to check that full coverage of the weld
section is achieved.
Ray tracing software is commonly used for scan plan generation. These computer programs
provide a simplified pictorial view of the projected path of the selected ultrasonic beams inside
the wedge and the test piece, along with a graphical representation of the weld overlay. An
example of use of such a ray tracing program is illustrated in Figure 2.13.
In this Figure, each beam is approximated by a straight line emitted from a point located at the
center of the active array elements to show its propagation direction. For the example of Figure
17
2.13, it is demonstrated that full volume coverage of the weld section is obtained using a set of
beams with refraction angles ranging from 46o to 72
o in a sectorial scan configuration. It is seen
that visualization of beam path helps the inspector to optimize the scanning parameters for
efficient inspection of a specific weld geometry.
Once the scanning parameters have been finalized through the scan plan, an appropriate time
delay for excitation of each active array element is obtained by the focal law calculator. Plane
waves with desired propagation directions are then generated. Ultrasonic waves refract from the
wedge into the test piece where then interact with flaws; echoes may then be returned to the
same wedge and transducer for analysis to determine flaw locations. When the weld
discontinuity has been detected and located, electronic focusing can be used to optimize beam
shape and size at the expected defect location for accurate sizing and flaw characterization [14].
Figure 2.13 Scan plan of a phased array ultrasonic inspection of a weld in a steel block, as generated by a ray-tracing
algorithm. The scan plan covers a range of inspection angles (46o-72
o) inside the steel piece. The blue lines represent
the direction normal to the plane wave fronts generated by the active phased array elements.
2.5 Phased Array Inspection at Elevated Temperatures
Interruption of plant operation can be avoided if NDT inspections can be performed on-line at
operating temperatures; this may be up to several hundred degrees Celsius. This capability
18
avoids costly downtime and reduces the risk of damage from thermal cycling associated with
periodic shutdowns [22]. However, high temperature phased array inspections cannot be
routinely performed. There are operational temperature limits of the phased array transducers
and plastic wedges; in addition, there is a gap in terms of approved, appropriate high temperature
inspection techniques. These limitations are explained briefly in the following paragraphs.
High temperature application of phased array transducers is limited due to two important factors:
the piezoelectric element and internal bonding of the multi-layered structure. PZT is the most
common piezoelectric material used in phased array transducers and its maximum operational
temperature is approximately 270oC [22]. However, the upper operational temperature limit for
phased array transducers is about 50oC [15]. At higher temperatures, the transducer’s internal
bonds and plastic-based materials can undergo permanent damages due to thermal expansion and
distortion.
Efforts have been made to develop single-element ultrasonic transducers to operate at elevated
temperatures, up to several hundred degrees Celsius. Many different candidate piezoelectric
materials have been tested to check their functionality at these temperatures. Also, efforts have
been made to optimize techniques used for bonding transducer’s internal layers in a manner such
that they can withstand high temperatures. These efforts have led to custom manufacturing of
high temperature conventional ultrasound probes. However, manufacturing processes have
generally been reported to be challenging and costly [22].
Only a few attempts were reported on manufacturing high temperature ultrasonic arrays. Kirk et
al. designed a piezoelectric linear array structure to operate at up to 400oC. They replaced
conventional piezoelectric materials with lithium niobate and used a single plate of piezoelectric
element to avoid the costs and challenges of manufacturing multiple elements. A series of
discrete narrow electrodes were defined and precisely clamped on the lithium niobate plate by a
patterning technique. Array operation was then achieved by activating the electrodes in
sequence. Once an electrode was activated, an electric field was applied to the small part of the
piezoelectric plate in contact with the electrode leading to generation of an ultrasound pulse. The
array was attached to a steel block with simulated defects and its capability was demonstrated by
scanning for defects at elevated temperatures [23].
19
A similar approach was used by Shih et al. They reported the development of an ultrasonic array
transducer for non-destructive testing at 150oC. The array was made by spraying a newly
developed piezoelectric composite film on a titanium foil by the sol-gel method followed by
colloidal silver spraying to deposit electrodes. The manufactured array was attached to a steel
pipe and used for thickness measurements through post-processing of the signals stored in pulse-
echo mode using each single element as a transmitter and multi elements as receivers [24].
The arrays described above are intended to be fixed permanently to the test subjects at a single
location. Their use is generally confined to sites where defects have already been found, to
monitor their growth behavior over a period of time. This application is further limited by piping
and pressure vessel codes which prohibit attachment of inspection instruments to some
engineering components to avoid the possible promotion of flaw generation.
The limited potential application of high temperature arrays precludes their high development
and manufacturing costs. Therefore there is a great interest in developing systems which use
conventional phased arrays probes and wedges for inspection at elevated temperatures.
This project describes the design of a phased array system for inspection of test pieces at
elevated temperatures of up to 350oC using conventional phased array probes and specially
designed wedges. Wedges are built from plastics resistant to high temperature attack and
equipped with a cooling jacket around the array. However, inside the wedge, thermal gradients
lead to variations in temperature-dependent wave velocity and skewing of the ultrasonic waves.
Therefore, a conventional focal law calculator, which is based on the assumption of wave
propagation in straight lines at a single velocity, would yield inaccurate results.
A model of the beam skew pattern in the presence of thermal gradients inside the wedge is
developed to predict the magnitude of this effect. The model is then used to redesign the focal
law calculator to accommodate the non-homogeneity of wave speeds in the heated wedge. Beam
forming accuracy of the redesigned focal law calculator is evaluated experimentally to
demonstrate the applicability of the system for performing phased array inspections at elevated
temperatures. Details are provided in Chapters 3 to 8 of this thesis.
20
3 High Temperature Wedges
The ultrasonic wedge is a key component of the inspection system and has the primary function
of coupling sound energy from the phased array to the test piece. At the wedge-test piece
interface, the wave refracts according to Snell’s law, and may also convert between shear and
compression modes according to the wedge design.
Rexolite2 is a commonly used wedge material for phased array inspection of pipelines and
pressure vessels. It is an isotropic, inexpensive, polystyrene plastic with a moderately low level
of attenuation. However, use of Rexolite is limited to temperatures well below 100oC, which is
close to its glass transition temperature [25].
For elevated temperature inspection purposes, ultrasonic wedges must be manufactured using
plastics with a high glass temperature and suitable acoustic properties. Polyetherimide (PEI) and
polybenzimidazole (PBI) plastics are two such candidate materials. PEI is a polyetherimide
thermoplastic high heat resistant polymer, and PBI is a polybenzimidazole engineering plastic,
with glass temperatures of 210oC and 413
oC, respectively [26] [27].
A prototype wedge with water cooling jacket was designed out of PEI based on the geometry of
the Olympus3 linear phased array model 5L64-A12 with 64 elements and center frequency of
5MHz. The wedge was designed to generate shear waves with a nominal 55o angle inside the test
piece (steel) using Snell’s law and an initial assumption of a uniform temperature of 20oC inside
the wedge.
The path of propagating waves can be monitored using ray-tracing software such as the
BeamTool4 package that is based on the assumption of linear wave propagation in each
homogeneous, isotropic material, with Snell’s law to determine the refraction angles at each
material interface.
2 C-LEC Plastics Inc., 6800 State Rd, Philadelphia, PA 19135, United States.
3 Olympus NDT Canada, 505, boul du parc-Technologique Quebec City, QC, Canada.
4 Eclipse Scientific Inc., Waterloo, ON, Canada.
21
Conventional wedges have a dampening material embedded at the front of the wedge to diffuse
any internally reflected signals. Because of the low heat tolerance of the dampening material, this
traditional approach is not practical in a high temperature environment as the dampening
material could melt off the wedge or, even combust during inspection.
In order to be able to provide adequate damping within high temperature wedges three major
design elements were implemented by engineers at Eclipse Scientific Inc. First, the dampening
material was installed at top of the wedge rather than on the front of the wedge. This provides
adequate isolation from the high-temperature test piece to protect the dampening material.
Second, the wedge itself was elongated. Elongation of the wedge provides a beam path for
reflected signals generated from steep incident angles to be reflected to the top of the wedge and
diffused by the dampener and third, the front of the wedge was angled to cause signals generated
at a shallow incident angle to be reflected up to the top of the wedge and diffused by the
dampener. These three innovations allow the high temperature wedge to eliminate internally
reflected signals as effectively as a traditional wedge. These design concepts are illustrated in a
PEI wedge schematic picture shown in Figure 3.1.
A similar procedure was followed for designing PBI high temperature wedges with a water
cooling jacket to protect the arrays. Room temperature water circulates through the jacket to
maintain the probe-wedge interface well below the critical temperature (<40oC) [15].
The final assembled system for high temperature inspection with a PBI wedge is seen in Figure
3.2.
22
Figure 3.1 PEI high temperature wedge schematic with sloped front and dampening material at the top of the wedge:
ray 1 (solid line) and ray 2 (dashed line) illustrate reflection pattern of steep and shallow beam incidence at the
wedge bottom. As a result of wedge elongation and angled front, the internally reflected beams reflect to the top of
the wedge where they are absorbed by the dampener.
Figure 3.2 High temperature phased array inspection system including: Eclipse WA10-HT55S-IH-B PBI wedge
prototype based on the geometry of the Olympus linear phased array model 5L16-A10 with 16 elements and center
frequency of 5MHz, water cooling jacket, coolant tubing system and mounting arms.
23
4 Temperature Distribution Model
The compression wave speed in an isotropic material is determined by its elastic modulus and its
density, all of which are temperature dependent [6]. Therefore, the temperature distribution must
be determined in order to characterize ultrasonic wave propagation in a wedge. The procedure
for obtaining this temperature distribution is described in this Chapter, followed by temperature-
dependent sound velocity measurements in the next Chapter.
The temperature distribution inside the wedge was modeled using the COMSOL finite element
package. A critical part of the model was to specify appropriate boundary conditions to represent
the various surfaces of the wedge.
The bottom of the wedge is heated when placed on the hot surface of a test piece, such as a
heated pipe. Therefore, a temperature-based boundary condition can be used to describe the
bottom of the wedge.
The array-wedge contact boundary is cooled by a circulating water jacket. Room temperature
water circulates through the channel with a minimum flow rate of 100 mL/min absorbing heat
from the boundary area. Laboratory measurements showed that the water maintained a
temperature of 25oC +/- 0.5
oC. Therefore, a temperature-based boundary condition was also
specified on this boundary of the wedge.
The remaining wedge surfaces are cooled by the surrounding air through natural convection.
Natural convection boundary conditions can be very challenging to model accurately due to the
complex nature of the cooling process and sensitivity to minor changes in the environmental
conditions. This involves the combination of heat transfer and laminar flow in a fluid (air) with
coupled temperature-velocity fields, accompanied by heat transfer within the solid. This leads to
density gradients in the air that cause buoyancy forces, which then lead to air flow [28].
To avoid the challenges described above, an alternative procedure is commonly used for
modeling natural convection in which an “average” heat transfer coefficient is specified on the
boundaries that interface with the surrounding fluid [29]. This heat transfer coefficient can be
difficult to specify; its value depends on several factors such as geometry and orientation of a
surface. In addition, the temperature of the surrounding fluid may not drop off uniformly to an
24
ambient level far from the wedge. For example, a large heated pipe under inspection can greatly
distort the temperature distribution in the surrounding air and hence its flow pattern and cooling
capacity.
Empirical and theoretical correlations have been provided in the literature to estimate the heat
transfer coefficient for common geometries such as a vertical wall, inclined wall and horizontal
plate. Using such correlations, COMSOL provides built-in functions for estimating the average
convective heat transfer coefficient of a surface based on its geometry and the ambient
temperature [29].
These correlations were used to solve for the temperature distribution inside a wedge made of
PEI on a hot steel pipe at a steady state condition, where the steel pipe surface temperature, the
surrounding air temperature and cooling water temperature were 150oC (PEI’s maximum
operating temperature), 23oC and 25
oC respectively.
Model results can be seen in Figure 4.1. Only half the wedge was modeled due to symmetry.
Temperature values calculated on the wedge surface lines specified in Figure 4 were compared to
experimental data obtained with thermocouple measurements averaged over five trials. Results
of the comparison are shown in Figure 4.2. According to this figure, the maximum difference
between the model and experiment results is not larger than 5oC. This discrepancy will have a
negligible effect on estimates of compression wave velocity (see Chapter 5).
25
Figure 4.1 PEI wedge temperature distribution modeling result, the color palate represents the temperature
distribution inside the wedge between 25oC and 150
oC. Surface temperature measurements located on the dashed
lines were used to validate the model results.
Figure 4.2 Comparison of COMSOL and experimental results for the temperature distribution on the surface of the
PEI wedge mounted on a 150oC steel pipe. Solid lines on the graph and the error bars represent average temperature
values of 5 experiments and standard deviations of the measurements: the red circles represent COMSOL model
results at the specified locations on the wedge surface.
26
5 Velocity Measurements at Elevated Temperatures
The compression wave velocities of both PEI and PBI were measured experimentally from room
temperature up to their maximum operating temperature. The experimental procedure and results
are described in this Chapter. These data will then be combined with the calculated temperature
distribution inside a wedge to allow determination of beam paths and refraction angles.
In attenuative materials, ultrasonic waves are dispersive in nature, meaning that the phase
velocity and group velocity are frequency dependent [6] [30]. This has the effect of distorting the
wavefront, such that highly localized pulses become increasingly spread out as the pulse
propagates. Plastics are well-known to be dispersive media due to their viscoelastic nature [31]
[32].
Phase velocities can be obtained from two successive backwall echoes in a sample with two
parallel faces. The roundtrip travel time as a function of frequency is obtained from a comparison
of the phase spectra (f) of the two successive backwall echoes [33] [34] [35]. An example of
these calculations is illustrated in Figure 5.1 for two successive backwall signals (labeled first
backwall and second backwall) of a sample of thickness The governing equations are shown
below where and represent the time difference of the two backwall echoes and
the associated phase velocity respectively.
represents the time difference between two signal acquisition windows, as illustrated in Figure
5.1.
27
Figure 5.1 Phase velocity measurement from two successive backwall echoes. The phase of each pulse is
determined relative to left side of the pulse acquisition window.
The phase velocities of PEI and PBI plastics were measured at room temperature using 10 mm
thick sample blocks with smooth parallel surfaces. A 10 MHz Panametrics5 highly-damped
ultrasonic contact probe was used with a useful frequency band of 3-11 MHz. Two successive
backwall echoes of the plastic blocks were obtained in the contact pulse-echo mode.
After the room temperature measurements, the procedure was modified to accommodate
measurements at elevated temperatures. The plastic test blocks were located on a temperature-
controlled hot plate. A glass delay line was placed between the ultrasound probe and the block
surface to avoid direct exposure of the piezoelectric elements to temperatures higher than 50oC,
the recommended operational temperature limit of the transducer [36]. The sample and the delay
line were then wrapped in high temperature insulation to minimize the temperature gradient
inside the plastic block. Two 0.001’’ diameter thermocouples were placed on either side of the
plastic block to measure the surface temperatures. The mean of these two temperature values was
used for the calculations, assuming an approximately linear dependence of phase velocity on
temperature within a narrow temperature range. The experimental set up can be seen in Figure
5.2.
5 Olympus, Waltham, Massachusetts, USA.
28
Measurements were performed at 10oC increments at mean temperatures ranging from 30
oC up
to 120oC for the block made of PEI, and up to 300
oC for the PBI block. Each test was repeated 5
times; results are shown in Figure 5.3 for selected temperatures.
Figure 5.4 shows the temperature dependence of the phase velocity at 5 MHz which is the center
frequency of the phased array probe used with the high-temperature wedge prototypes. It can be
seen that the phase velocity decreases in both high-temperature wedge materials as temperature
increases. The data were fit to a linear function shown in Figure 5.4-a and Figure 5.4-b for PEI
and PBI, respectively. According to these Figures, the maximum difference of 5oC between the
COMSOL temperature distribution model and experiment results presented in the previous
Chapter can lead to less than 0.4% error in estimation of compression wave velocity.
Figure 5.2 Experimental set up for measuring phase velocity at high temperatures. The sample and the delay line
were wrapped in high temperature insulation to lessen the temperature gradient inside the plastic block. The mean
block temperature was estimated from thermocouples placed on top and bottom of the plastic block.
29
Figure 5.3 Phase velocity data of PEI (a) and PBI (b) plastic blocks at selected elevated temperatures. Solid lines and
the error bars represent the mean and standard deviation of 5 repeated experimental measurements.
30
Figure 5.4 Phase velocity of PEI (a) and PBI (b) as a function of temperature at 5 MHz frequency. The empirical
relations shown on the graphs indicate the functional change of phase velocity results with temperature T expressed
in degrees Centigrade.
31
6 Focal Law Algorithm – Planar Waves
Thermal gradients inside a high temperature wedge lead to variations in the temperature-
dependent wave velocity and skewing of the direction of ultrasonic wave propagation; such
conditions invalidate conventional calculation of relative delay times on individual elements of a
phased array that are based on a homogenous propagation medium.
In this project we use a numerical ray-tracing technique to approximate the arced path of waves
propagating across thermal gradients in an isotropic wedge. The results are then used in a
separate algorithm to modify the phased array focal law; this will yield the required delays for
individual array elements to generate a plane wave or a focused beam, while compensating for
thermal gradient effects inside the wedge.
The numerical ray-tracing technique and modified focal law algorithm are described in this
chapter.
6.1 Room Temperature Inspection
Ray tracing is an established technique to estimate the wave path as it propagates in a medium
based on tracking a point on the wavefront rather than the complete wave field. This is achieved
based on the mechanical properties of each region and interface through which the wave passes.
Application of ray tracing techniques for calculations of wave paths through a medium with non-
uniform propagation velocity has been reported by several researchers. In seismology, for
example, a ray tracing technique is used to record ground motion caused by the passage of
seismic waves [37] [38].
Application of ray-tracing techniques to the field of NDT has also been reported by several
researchers [39] [40], e.g., Nowers et al who introduced ray-tracing algorithms for the inspection
of anisotropic weld sections using ultrasonic arrays [41].
As described in Chapter 2, a scan plan is normally prepared before any industrial phased array
inspection is initiated. The scan plan ensures total inspection coverage of the region of interest in
a test piece, such as a weld section. This is achieved by an optimized selection of scanning
parameters such as wedge geometry and range of scanning angles. Planar waves are typically
used to locate any flaws and determine their approximate size quickly; plane wave generation is
32
therefore a very common use of phased arrays. Once discontinuities have been located using the
plane waves, a focused beam may be used at the defect locations for more accurate sizing and
flaw characterization.
For a planar wave, the particles lying on any plane that is perpendicular to the wave vector are all
vibrating in phase with each other and along parallel paths. For a plane wave to be generated by
a phased array, the acoustic fields generated by all the individual array elements should interfere
constructively to produce uniform acoustic pressure along each plane that is normal to the
direction of propagation. (This is mathematically possible only for a single two-dimensional
transducer of infinite area. However, the effect can be approximated over a small wavefront
using a linear array with a finite number of elements). To generate this pseudo plane wave with a
specified direction of propagation, the array elements must be excited with appropriate relative
time delays.
Consider first the case of generating a shear plane wave in a steel test block in contact with an
array-wedge system at a uniform room temperature of 25oC (Figure 6.1). This Figure illustrates
an Eclipse WA12-HT55S-IH-G PEI wedge designed to mate with a linear phased array with 64
elements and center frequency of 5 MHz (Olympus model 5L64-A12); this system is configured
to generate planar shear waves with nominal angle Фs=55o inside a steel test piece at 20
oC if all
phased array elements are fired simultaneously. Also shown in Figure 6.1 is an arbitrary
wavefront in the steel, on which all sample points are vibrating in phase with each other.
33
Figure 6.1 Wave propagation pattern for a shear plane wave at angle Фs in a steel block at a uniform temperature of
25oC. The ray traces are applicable for a wave transmitted from the array into the test piece, or equivalently for a
wave travelling from the test piece back to the array. In the latter case, the waves associated with sample points
along an arbitrary plane wave front propagate in a direction perpendicular to the wave front and reach the piece-
wedge interface at locations labeled as interface points. Then they refract into the wedge based on Snell’s law and
propagate through the wedge to the array-wedge interface at points labeled as array-line points.
To calculate the appropriate element time delays for generation of such plane waves, the travel
time of the wave emitted from each element to the specified wave front must be obtained. To
achieve this, wave propagation paths from various “array-line points” spaced at intervals along
the phased array to the plane wave front are first selected, as shown schematically by ray traces
in Figure 6.1.
It will be convenient to conduct the calculation of the focal law in the reverse direction, i.e.,
model the waves originating from a few “sample points” on the selected plane wave front in the
test piece, and traveling back along the ray traces to their respective “interface points”, and then
to the “array line points”. This is shown schematically by the arrow directions on the ray traces
of Figure 6.1.
34
The propagation paths are straight lines inside each homogenous isotropic medium, i.e., the
wedge and the test piece, each with a single wave propagation velocity corresponding to 25oC.
The waves propagate in a direction perpendicular to the wave front and reach the piece-wedge
interface (at locations labeled interface points in Figure 6.1). At the interface they refract into the
wedge according to Snell’s law and then propagate through the wedge to the array-wedge
interface (array-line points). Note that the same propagation paths are applicable in both
directions, i.e., from array to plane wave front, and from the plane wave front back to the array.
The lengths of each shown wave propagation path can be calculated geometrically in both the
test piece and the wedge sections. Given the ultrasonic shear wave velocity in the steel and
compression wave speed of the wedge, the travel times along each propagation path in the two
materials can be calculated. Finally, the travel time inside the piece and the wedge are added
together to find the total travel time along each propagation path. Note that these travel times and
propagation paths also apply in the opposite direction as well, for waves originating from the
array and traveling into the steel test piece.
The total travel time will vary linearly along the array-line points and can be interpolated to yield
travel times as a continuous function of position along the array-wedge boundary. The function
can be used to find the travel time associated with each element on the array. These yield the
required relative time delays for excitation of each element to ensure that all points on the
wavefront in the steel are in phase with each other. The same time delays are also applicable to
the summing of received signals at the array elements, originating from a planar wave traveling
through the test piece and impinging on the transducer assembly.
This simple procedure can be quickly applied to construct a conventional focal law calculator for
room temperature inspections. However, for inspections of test pieces at elevated temperatures
with high-temperature wedges and cooling jacket around the array, this simple focal law
calculator will no longer work. The presence of thermal gradients inside the wedge leads to
variations in temperature-dependent wave velocity and skewing of the wave directions inside the
wedge; this invalidates the conventional calculation procedure. Account must also be taken of
the change in wave velocity associated with elevated temperature in the test piece. These issues
are explored in the next Section.
35
6.2 Elevated Temperature Inspection
The beam skew pattern caused by thermal gradients inside wedges mounted on test pieces at
elevated temperature can be approximated utilizing ray-tracing techniques. However, the
problem is now more complex. We use a discretized analytical ray-tracing technique utilizing
temperature distribution model data and phase velocity measurements of the wedge materials at
elevated temperatures.
Ultrasonic waves traveling in a two-dimensional isotropic medium with smoothly varying
mechanical properties are described by a system of first-order ordinary differential equations. To
simplify the mathematics, we track the progression of a single point on the wave front, with
propagation vector in the x-y plane. The wave front moves at the local compression wave speed
V(x,y) at an angle with respect to the x-axis [42] [43].
Combining equations (6.1) and (6.2) yields:
The above equations can be integrated numerically over fine time steps using Matlab [44], from
any starting point {xo,yo} and initial wave trajectory inside an ultrasonic wedge. This then yields
the propagation path and travel time. The velocity profile V(x,y) is based on the temperature
profile as calculated by the finite element program COMSOL. Note that the parameter
represents the amount of skew in the beam per unit time.
The results of these wave propagation simulations, performed for a specific series of wave
starting points and trajectories, are then fed into a separate algorithm to develop a new phased
array focal law – analogous to the simulation described in Section 6.1 for an inspection
performed at room temperature. This in turn will yield the required time delays for individual
36
array elements to generate any desired beam profile inside a high temperature wedge and test
piece, even in the presence of strong thermal gradients in the wedge.
Figure 6.2 illustrates the wave paths for generation of the same shear plane wave depicted in
Figure 6.1 when the steel block is at a uniform temperature of 150oC and the wedge is cooled by
ambient air at 25oC plus the array’s water jacket. This arrangement will cause the wedge
temperature to range from close to 150oC where it contacts the test piece, down to approximately
30oC adjacent to the cooling jacket. The same sample points on the plane wave front in the test
piece shown in Figure 6.1 are again selected here to demonstrate the focal law calculation, using
the same ray tracing procedure used in Section 6.1. The following differences between Figure
6.1 and Figure 6.2 should be noted:
1) Wave path lengths in the steel test piece are the same in both Figure 6.1 and Figure 6.2,
given that the test piece is at a uniform temperature in both Figures; however, the
associated wave velocities and travel times in the test piece are now changed due to its
elevated temperature of 150oC.
2) The angle Фs of the waves at the wedge-piece interface is the same in both Figures.
However, the associated angles of the waves inside the wedge will be different; this is a
result of Snell’s Law and variations in the temperature-dependent sound velocities in both
the test piece and bottom of the wedge.
3) Once the waves refract into the wedge, their paths will no longer be straight lines, as the
thermal gradients inside the wedge lead to skewing of the waves. The wave paths and
their travel times inside the wedge are simulated with the ray-tracing algorithm of
Equations 6.1 to 6.3, utilizing temperature distribution data from our COMSOL finite
element model, and phase velocity data of the wedge material at elevated temperatures.
The solid red lines in Figure 6.2 represent the skewed paths followed by rays originating
from the sample points.
It is noted that the amount of skew is not equal for all the waves. The reason is that the
amount of skew depends on the amount of misalignment between the propagation vector
(at angle in equation 6.3) and the gradient of the temperature or velocity field (gradient
=
.
37
4) Once the new travel times of the waves have been obtained in both the wedge and test
piece, the total travel time and the appropriate delay times are calculated as described
before in Section 6.1.
Figure 6.2 Wave propagation pattern for a shear plane wave at angle Фs in a steel block at a uniform temperature of
150oC. The ray traces are applicable for a wave transmitted from the array into the test piece, or equivalently for a
wave traveling from the test piece back to the array. In the latter case, the waves associated with sample points along
an arbitrary plane wave front propagate in a direction perpendicular to the wave front and reach the piece-wedge
interface at locations labeled as interface points. Then they refract into the wedge based on Snell’s law and
propagate through the wedge to the array-wedge interface at points labeled as array-line points. The waves
propagate along arced paths (red lines) in the wedge due to thermal gradient induced velocity variation.
The model results for the generation of the 60o shear plane wave are illustrated in Figure 6.3 for
the Olympus linear phased array model 5L64-A12 with 64 elements and center frequency of 5
MHz. Typically, only a subset of 16 elements on the array are selected to be used at one time.
Figure 6.3-a and Figure 6.3-b illustrate the calculated delays vs. their corresponding element
numbers when the first 16 elements (elements 1 to 16) and last 16 elements (elements 49 to 64)
of the array are used. The blue and red data points represent the results for room (25oC) and
elevated temperature (150oC) inspection conditions respectively. Delay times are expressed
relative to the first element of the 16 elements used to form the plane wave. The reason is that
delay times are usually expressed relative to the element associated with the longest travel time
38
from array to the plane wave front inside the test piece. This element is the first element of the
aperture for the case of generation of a 60o shear plane wave in a test piece. This element should
be fired first at a time defined as t=0; all other elements are then fired at their respective relative
delay times.
For the simulation results shown in Figure 6.3-a, application of conventional room-temperature
focal laws for inspections of steel test pieces at 150oC lead to incorrect time delays on array
elements of up to 100 ns; this is approximately one half a period of the pulse central frequency of
5 MHz (period of 200 ns) in the test piece. The associated phase delay difference of up to 50% of
the wave period would lead to destructive interference, major distortion of the desired beam
profile, and consequently poor imaging resolution. The corresponding timing errors are much
lower for the pulse generated by firing array elements 49-64; Figure 6.3-b model results show a
minor difference of up to 10 ns (5% of the wave period) between the delay times generated by
the conventional focal law (designed for room temperature) and our new algorithm for elevated
temperature.
Figure 6.3 results illustrate how the effects of thermal gradients on the optimal element delay
times have a complicated dependence on several test parameters, such as test temperature, wedge
geometry & thermal gradients, locations of array elements, etc. This dependence is explored in
the following paragraphs.
For the example results depicted in Figure 6.3 (inspection of the test piece at 150oC), the wedge
temperature varies from close to 150oC where it contacts the test piece, down to approximately
30oC on the wedge-array interface adjacent to the cooling jacket. Therefore, the emitted waves
from all elements propagate through a similar temperature drop of about 120oC when
propagating through the wedge to the test piece. However, the path length and steepness of the
gradient varies based on the location of each transmitting array element. This variation is
considerably larger if the first 16 elements of the array are used, as opposed to the last 16
(elements 49-64). That variation over the 16 elements contributes to a non-linear delay pattern in
the timing of array element excitation, compared to the linear pattern obtained by room
temperature delays (Figure 6.3-a). The temperature profile inside the wedge associated with the
described inspection condition and the locations of elements 1-16 and 49-64 are depicted in
39
Figure 6.4. The color palate shows the temperature distribution inside the wedge according to the
COMSOL finite element results.
Figure 6.3 Calculated relative element time delays for the generation of a 60o shear plane wave for Eclipse WA12-
HT55S-IH-G PEI wedge and the Olympus linear phased array model 5L64-A12 one a) the first 16 elements of the
array (elements 1-16) were used and b) the last 16 elements of the array (elements 49-64) were used. The blue and
red data points represent the results for room (25oC) and elevated temperature (150
oC) inspection condition
respectively and the delays are expressed relative to the first element of the used active aperture.
40
Figure 6.4 Temperature profile inside an Eclipse WA12-HT55S-IH-G PEI wedge for inspection of test piece at
150oC, the color palate represents the temperature distribution inside the wedge between 25
oC and 150
oC as
obtained by our COMSOL finite element model. Waves emitted from elements 1-16 propagate along the shortest
path length in the wedge with a relatively steep temperature gradient, compared to the waves emitted from elements
49-64.
Beam skewing is caused by ultrasonic wave propagation across a thermal gradient. The angle
between the thermal gradient and the ultrasound propagation vector varies strongly with the
choice of array elements used (Figure 6.4). This angle (and resultant beam skew) is generally
much larger if the upper array elements are used (e.g., 49-64) as opposed to the lower array
elements. This angle also tends to be larger if the system is set to generate a plane wave in the
test piece with a large refracted angle s (e.g., 65 degrees) as opposed to a small refracted angle.
These various effects combine in a non-linear manner to determine the total correction to the
optimal array element delay sequence for a high temperature inspection. In some cases, as shown
in Figure 6.3-b, the various effects may largely cancel out such that the optimal delay pattern is
similar to that for a room temperature inspection. However, it would be expected that
41
modifications to the focal law would become increasingly important if inspections were carried
out at even higher temperatures than those shown in Figure 6.3, e.g., 350oC.
To confirm these observations, the model results for the generation of a 45o shear plane wave are
illustrated in Figure 6.5 for the same array-wedge configuration used in Figure 6.2, and using the
same interface points on the piece-wedge interface as shown in Figure 6.2. Sample points are
selected on an arbitrary 45o plane wavefront in the test piece based on straight line propagation
paths inside the piece at a uniform temperature.
Figure 6.5-a and Figure 6.5-b illustrate the relative element delay times calculated by our new
algorithm when the first 16 elements (elements 1 to 16) and last 16 elements (elements 49 to 64)
of the array are used. The blue and red data points represent the results for room (25oC) and
elevated temperature (150oC) of the test piece respectively. Note that in the case of generation of
a 45o shear plane wave, delay times are expressed relative to the last element of the 16 elements
used to form the plane wave. In this case, it takes the longest time for the wave emitted from the
last element of the aperture to travel from the array to the plane wave front selected for
calculation. Therefore, this element should be fired first at a time defined as t=0; all other
elements are then fired at their respective relative delay times with respect to this reference
element.
Model results depicted in Figure 6.5 demonstrate similar trends to those seen in Figure 6.3, and
show the necessity of our new high-temperature array focal law. For the case of using elements
1-16 of the array (Figure 6.5-a) the required correction is up to 120 ns – over half a cycle period
in the 5 MHz burst. However, once again the magnitude of the correction is far smaller if the last
16 elements of the array are used (Figure 6.5-b) – a maximum of 25 ns.
Comparison of the results illustrated in Figure 6.3-a and Figure 6.5-a demonstrates how the
distortional effect of the temperature gradient depends on the selected shear plane wave angle Фs
in the test piece. This dependency on Фs is complicated as the following effects must be
considered:
1) Path lengths vary linearly across the width of the plane wave front in the steel test piece;
this variation, and the associated travel times along each ray depend on Фs.
2) A change to Фs leads to an associated change in the trajectories of the waves inside the
wedge through Snell’s Law. This leads to a complete change of the path of each ray
42
through the wedge, as determined by our ray tracing algorithm of Equations 6.1 to 6.3.
This leads to a change in the misalignment between each propagation vector and the
gradient of the temperature field (and associated velocity field). This in turn causes a
change in the amount of beam skew.
All of these changes, precipitated by a decision to perform an inspection at a different beam
angle Фs, lead to changes in beam travel times in both the wedge and test piece. Combining all
these effects, our wave propagation algorithm determines the appropriate delay time for each
array element to yield a pseudo-plane wave in the test piece at the desired Фs.
An experiment has been designed to validate our algorithm for determining appropriate element
time delays on a heated wedge. The results obtained from our algorithm for generation of shear
plane waves with 45o and 60
o refraction angles inside a steel test piece at 150
oC were used to
experimentally evaluate the generation of a plane wave in the test piece. The details of the
experiments and results are described in the following chapter.
43
Figure 6.5 Calculated element time delays for the generation of a 45o shear plane wave for an Eclipse WA12-
HT55S-IH-G PEI wedge and the Olympus linear phased array model 5L64-A12 one a) the first 16 elements of the
array (elements 1-16) were used and b) the last 16 elements of the array (elements 49-64) were used. The blue and
red data points represent the results for room (25oC) and elevated temperature (150
oC) inspection condition
respectively and the delays are expressed relative to the last element of the used active aperture.
44
7 Experimental Validation – Planar Waves
In the previous chapter, we described an algorithm to calculate a new array focal law for plane
wave inspections of test pieces at elevated temperatures using high temperature wedges. The
algorithm was based on a numerical technique to determine the arced path of ultrasonic waves
propagating across thermal gradients in an isotropic wedge; this yielded the required delays for
individual array elements to generate a plane wave in a hot test piece.
In order to validate the algorithm, we will now use the results for element time delays in the
examples described in chapter 6 to experimentally evaluate the quality of shear plane wave
generation in a test piece at 150oC. First, we describe the overall concept of how experimental
validation will be accomplished. This is then followed by a detailed description of the
experiment itself. These are followed by results and analysis.
7.1 Concept for Experimental Validation
Consider the generation of a shear plane wave at an angle Фs in a steel test block, as shown in
Figure 7.1. Note that the right side of the block is also cut at the same angle Фs as the desired
angle of wave propagation. The array element delay times calculated in Chapter 6 are now
applied to the individual array elements, using a phased array instrument to provide the
excitation pulses.
Once the array elements are fired with these calculated relative time delays, their individual
acoustic fields interfere with each other to create an acoustic field which propagates through the
wedge. The exact shape of the field depends on both the individual element delay times and the
thermal gradients. However, at each instant of time, a surface can be found along which all the
particles are vibrating in-phase with each other; such a surface is called a wave front (Figure
7.1).
It should be noted that this wavefront is not straight inside the wedge, due to the non-uniformity
of the medium; the wavefront shape undergoes continuous change as it propagates through the
wedge due to the temperature dependence of the wave speed. However, if the array element
times have been correctly implemented, the wave front should turn into a planar surface when
the wave refracts into the steel test piece at the wedge-piece interface. The particles which are
45
vibrating in phase with each other along any selected wavefront in the steel will then lie on
planes perpendicular to the propagation vector (arrows shown in Figure 7.1).
Figure 7.1 propagation of a wavefornt corresponding to a shear plane wave at an angle Фs in a steel test block at
elevated temperature: the wavefront is not straight inside the wedge due to non-uniformity of the medium. However,
it turns into a planar surface when the wave refracts into the steel test piece at the wedge-piece interface.
From the geometry shown in Figure 7.1, the shear plane wave will strike the slanted right hand
surface of the test block perpendicularly (wave vector perpendicular to this block boundary).
Therefore, the plane wave reflects straight back towards the wedge-piece interface on the same
propagation path, with an 180o change in phase caused by reflection at a free surface. The
reflected wave should then refract into the wedge with the same incident-refraction angle system
as the original transmitted wave. i.e., the reflected wave should retrace its exact path back into
the wedge and back to the individual elements of the array. This implies that the echo signals
should be received back at the individual elements with the same relative time delays as those
applied in transmission mode, provided that an appropriate focal law calculator was used to
generate the original wave. Measurement of the relative echo delays at the array elements can
therefore be used as one criterion to evaluate our algorithm as a focal law calculator. Details are
given in the following Section.
46
7.2 Experimental Details
Two angled steel test blocks of the general shape shown in Figure 7.1 were prepared with slanted
face angles Фs of 45o and 60
o, to be used in two separate algorithm validation experiments. An
Eclipse WA12-HT55S-IH-G PEI wedge was used along with a 5L64-A12 Olympus linear array
for wave generation, matching the simulation parameters described in the two cases presented in
Chapter 6. The array was connected to a Focus LT6 phased array instrument which can apply
user-specified relative element time delays to the selected active elements of the array using
Tomoview6 software. The wedge-array system was placed sequentially on the two test blocks for
generation of the desired plane waves. The following experiment was performed individually for
each block.
The relative element time delays determined in Chapter 6 were applied to the selected active
array elements (transmitting delays). Tests were performed using the first 16 elements (element
numbers 1 to 16), and then the last 16 elements (element numbers 49 to 64) of the array; the
orientation of the array element numbering system is shown in Figure 7.1. After transmitting
pulses from the selected 16 elements, the system was then switched to receiving mode, and the
echo signals were captured at the same 16 elements as used in transmission. The relative time
delays among the received echo signals at the 16 array elements are measured and compared to
the time delays applied to their associated elements in the transmitting mode.
Theoretically, if the plane wave has been generated properly in the test piece using the element
time delays calculated by our new focal law calculator, then the measured receiving delays
should be equal to the applied transmitting delays. For example, the array element that was fired
first should be the last one to receive an echo pulse. However, this experimental result may not
exactly match the model predictions due to possible inaccuracies in the new theoretical model
and/or the experiments. In order to investigate the validity of our model, it is important to
identify the sources of experimental and modeling errors, and quantify their effect on this series
of tests.
6 Olympus, Quebec City, Canada
47
To this end, we first perform all of the experiments with the test piece and wedge at room
temperature, using the conventional focal laws described in Section 6.1. The associated sources
of errors for this relatively simple case are identified, and their magnitudes estimated as
accurately as possible in Section 7.3. The experiments are then repeated with the wedge on a hot
steel test piece at 150oC; the wedge is allowed to reach an equilibrium temperature distribution
(as estimated by the COMSOL finite element model) before any measurements are taken.
Estimates are made of the additional sources of error introduced to the experiments by the
elevated temperature of the test piece. The experimental results are then used to evaluate the
validity of our algorithm as a focal law calculator; deviations in our experimental results from
those predicted by our new algorithm are compared to the various sources of error. This analysis
provides one measure of the validity of our new model, and the possible consequences of
ignoring the effects of elevated temperatures when using phased arrays for inspections at
elevated temperatures. Details are given in the following sections.
7.3 Experimental Results and Analysis - Room Temperature
Figure 7.2 shows the results of a set of experiments performed for the case of generating a 45o
shear plane wave in the 45o-angled steel test block at a uniform temperature of 25
oC, using the
first 16 elements of the linear array. The blue data points represent the relative time delays for
excitation of each element in transmission mode, as determined in Chapter 6 using our
conventional focal law calculating algorithm (Section 6.1). The delays are specified relative to
the excitation time of element #16. By convention, a positive delay time for an individual
element indicates that it is pulsed after the excitation of reference element #16. Elements #1-15
all have positive delay times in Figure 7.2; this implies that element #16 was pulsed first.
The solid red line in Figure 7.2 represents the relative time delays of the echo pulses received at
the same 16 individual array elements (receiving delays). Each point on this line is the average of
10 repeated experiments. The error bars indicate the random fluctuations associated with
measured data of each individual element as described by the standard deviation of the
measurements.
48
If the desired plane wave has been properly generated in the angled block, the measured echo
pulse delays corresponding to each array element should be equal to the applied transmitting
delays as calculated in Chapter 6. However, slight deviations are seen between the experimental
results and their associated theoretical expected values in Figure 7.2. These deviation times are
depicted on a more detailed scale in Figure 7.3. Note that because element #16 is used as the
reference for timing purposes, its delay times in both transmission of the outgoing pulse, and
reception of the echo pulse, are zero by definition. Therefore its deviation between theory and
experiment is always zero.
It is important to understand the sources of the deviations shown in Figure 7.3, and quantify the
overall impact of these sources of error on the objective of generating a planar shear wave in a
hot test specimen. We find it convenient to categorize the deviations illustrated in Figure 7.3 into
two independent groups: systematic errors and random errors. Such a categorization represents a
slight simplification of the true situation, but makes the analysis more tractable.
Figure 7.2 Experimental results for the case of generating a 45o shear plane wave in the 45
o-angled steel test block at
a uniform temperature of 25oC using the first 16 elements of the array (elements 1-16): the blue data points represent
transmitting time delays applied to the elements in transmission mode as calculated by our model. The solid red line
represents the mean of 10 measurements of receiving delays at the same individual array elements. The error bars
indicate the standard deviation of the measurements at each individual element.
49
Figure 7.3 Deviation times between the measured received echo time delays on each individual element and their
associated theoretical value as calculated by our model for the case of generating a 45o shear plane wave in the 45
o-
angled steel test block at a uniform temperature of 25oC using the first 16 elements (data illustrated in Figure 7.2).
The solid line and error bars are associated with the mean and standard deviation of the measurements on each
individual array element. Note the very fine time scale on the vertical axis.
7.3.1 Systematic Errors
Systematic errors are biases in measurements, which are seen each time the same experimental
measurement is repeated. Therefore, their magnitude cannot be reduced by repeating a
measurement or the entire experiment and using the average result. Such errors result in a
deviation between the mean of very many separate repeated measurements of a parameter and its
theoretically expected value. Therefore, the solid line in Figure 7.3 can be used to provide a
rough estimate for the magnitude of the systematic errors in the above described experiment. The
magnitude of the systematic errors varies for results associated with different elements, and
reaches a maximum of approximately 18 ns at element #1 (Figure 7.3). These systematic errors
could arise from repeatable imperfections in the performance of the equipment (e.g., calibration
issues), geometrical errors in the shape of the block, and uncertainties in the value of the inputs
used for focal law model calculations, etc. As expected, there is a general trend for the
magnitude of the bias error to increase as one moves away from the reference element #16,
where the bias error is zero by definition.
50
Inputs to the algorithm for the focal law calculation at room temperature include sound velocity
in both the wedge and the steel test piece, plus the wedge and block angles. The wedge and steel
blocks angles were measured by a digital angle gauge and the wave velocities were measured by
the procedure described in Chapter 4. The levels of uncertainty in these measured values are
listed in Table 7-1. In order to verify whether the uncertainties in these data values are consistent
with the magnitudes of bias errors seen in Figure 7.3, these data input values were individually
varied in our model by an amount equal to their estimated level of uncertainty. The resulting
effects on array element delay times are shown in Table 7-1.
Table 7-1 Inputs to the new focal law algorithm at room temperature: the levels of uncertainty in the measured
values of inputs are listed and the magnitude of their resulting effect on the bias error on the first element of the
aperture is presented.
Model Input Measured Value Measurement
Uncertainty
Associated Bias Error
on Element #1
Steel Block Angle 45o ± 0.1
o 8 ns
Wedge Angle 38o ± 0.1
o 12 ns
Sound Velocity in the Wedge 2460 m/s ± 10 m/s 15 ns
Sound Velocity in the Steel Block 3230 m/s ± 10 m/s 14 ns
The total interactive effect of these systematic errors on the bias errors seen in Figure 7.3 will
depend on each experimental set-up, such that it can’t be uniquely quantified. However,
experiments were conducted on several systems such as those shown in Figure 7.2 using a 64-
element 5-MHz linear array at room temperature, using various selections of 16 active elements
and two frequently-employed refraction angles Фs: 45o and 60
o. The results all had bias
deviations in the element time delays that were of the same order as those shown in Figure 7.3,
i.e., bias error ranging from zero for the reference element, up to a maximum value of the order
51
of 20 ns for elements most distant from the reference element. These bias deviations are of the
same order of magnitude as the combined measurement uncertainties shown in Table 7-1.
Although these experiments were conducted at room temperature, the results can be used to help
estimate the magnitudes of bias error sources in experiments conducted at elevated temperature.
It is noted that the observed bias deviation of up to 20 ns represents only 10% of the wave period
for a 5 MHz transducer. That is, the phase difference variation among the wave vectors
associated with the 16 active array elements is of the order of +/- 18 degrees. This is consistent
with the requirement of a phased array that echoes received at the active elements should be
approximately in phase with each other, once the appropriate time delay is applied to each
element echo pulse. This then allows the 16 echoes to be added together constructively, to
achieve an enhanced signal-to-noise ratio compared to that seen individually at each element.
Last, we note the jagged nature of the solid line in Figure 7.3. This would not be due to any of
the bias error sources noted in Table 7-1, which would affect the deviations for all elements in a
smoothly varying manner. The jagged nature might be reduced somewhat by increasing the
number of measurements – this would further reduce any contribution of random errors, such as
noise that is affecting our estimate of the mean deviation at each element, as represented by the
solid line in Figure 7.3. However, the jagged nature of the line may also indicate that there are
additional systematic errors (beyond those listed in Table 7-1) that are individually dependent on
each element, e.g., imperfections in the individual array element alignments. In particular, it is
noted that the limited timing resolution of 10 ns of the Focus LT system for applying individual
delay times to each element, is of the same order of magnitude as the jagged oscillations in the
solid line of Figure 7.3.
7.3.2 Random Errors
Random errors are caused by unpredictable variations in the experiment, measuring system or
surrounding environment. The statistical distribution of random errors may be known
theoretically, or approximated through repeated measurement. In our case, the effects of these
random errors on the measured arrival times of echo pulses at each array element are indicated
by the error bars in Figure 7.2 and Figure 7.3. It is noted that in many cases, these “random”
52
errors may not be completely random – there may actually be some pattern, bias, or deterministic
component to the fluctuations in experimental results that we label as “random”. In the case of
our experiments, three factors can be identified as the main sources of the random errors in the
results:
1) Instrument resolution; all instruments have finite precision that limits their measurement
resolution. For example, the Focus LT instrument applies a maximum sampling frequency of 100
MHz for digitizing the ultrasonic echo signals; this leads to a timing resolution of 10 ns in the
digitized echo signal of each array element, yielding a random temporal rounding error of the
order of ± 5 ns.
2) Instrument noise errors; noise is an unwanted disturbance caused by inherently unpredictable
electric fluctuations in the circuit of an electrical instrument, e.g., the effects of stray electrical
fields in the air or from the electrical power source.
3) Couplant effect; a couplant layer is required between the wedge and the test block to transmit
the ultrasonic energy efficiently through the interface. Ultrasonic waves generated by the
elements travel through the thickness of such a layer before entering the test piece. However, the
couplant thickness distribution between the wedge and the test piece varies from one experiment
to the next, and among various locations on the wedge/piece interface. These seemingly random
fluctuations are due to pressure-induced flow. These transients in couplant thickness lead to
changes in wave travel times through the interfacial layer, and random variation in the delay time
of echo arrival at each array element.
The magnitude of the combined effects of all these random errors can be estimated by repeating
the experiments and calculating the standard deviation of the obtained results. Note that the
magnitude of random error is zero on element #16 by definition as it is used as the reference for
calculations.
The random component in the timing deviations in the results of Figure 7.3 was also assessed for
all of the room temperature experiments, with different combinations of block angles and active
array elements. The standard deviation of the random fluctuations in our echo arrival times was
of the order of 15 ns (or less) for all test cases. This can be used as a benchmark for evaluating
the magnitude of random errors in the experiments performed at elevated temperatures.
53
However, it is noted that some sources of random fluctuations, particularly those related to
couplant flow may be larger at elevated temperature. For laboratory experiments, the influence
of random errors can be minimized by performing each measurement many times and calculating
the mean result of many measurements, as done in Figure 7.3. However, this may not be
practical for field NDT inspections where time is precious, such that both random errors and
systematic errors will play a role.
7.4 Experimental Results and Analysis - Elevated Temperature
In the previous section, we evaluated our model results experimentally for the case of generating
shear plane waves in a steel test piece at room temperature (25oC). The possible sources of error
on delay times for individual array elements were described briefly and their maximum
magnitudes were estimated to be of the order of 20 ns (systematic errors) and 15 ns (random
errors).
These same experiments are now repeated at elevated temperatures for the much more
challenging case of the steel blocks at 150oC, using the new focal law algorithm to calculate the
optimal time delay for each array element. Experimental details are described in the following
paragraphs, followed by presentation and analysis of the results. It is noted that limitations in
experimental equipment prevented us from conducting these experiments at higher temperatures.
The same wedge-array system was used for the elevated temperature experiments as used for the
room temperature experiments. The two angled steel blocks were placed on a temperature-
controlled hot plate, and the block-wedge surface was kept at 150oC. The steel test pieces were
wrapped in high temperature insulation to minimize heat loss (Figure 7.4). This led to
temperature variations over the entire volume of each test piece of less than 10oC, as indicated by
experimental measurement at selected locations.
54
Figure 7.4 Experimental set up for evaluation of model results for generation of shear plane waves in an angled steel
test block at 150oC. An Eclipse WA12-HT55S-IH-G PEI wedge was used along with an Olympus 5L64-A12 array
for plane wave generation with a cooling jacket around the array. The steel test block was located on a temperature-
controlled hot plate and wrapped in high temperature insulation which led to temperature variation over the entire
volume of the test piece of less than 10oC.
Once the temperature was stabilized in the test piece and wedge system, the relative element time
delays determined in Chapter 6 were applied to the selected active array elements (transmitting
delays). Tests were again performed using the first 16 element (element numbers 1 to 16) and
last 16 elements (element numbers 49 to 64) of the 5 MHz array. After transmitting pulses from
the selected 16 elements, the system immediately switched to receiving mode.
The received echo signals were then analyzed. Only a limited number of detailed analyses of
echo signals are presented here; equipment limitations forced an extensive amount of time and
data processing to be undertaken for echo analysis at each element. A particular emphasis was
therefore placed on only three elements of the active aperture: elements 1, 8 and 16 when the
first 16 elements of the array were used for beam generation, and elements 49, 54 and 64 when
55
the last 16 elements of the array were active. However, the presented results and analysis are
sufficient to assess the overall performance of the system for all array elements.
The relative time delays of the received three echo signals were measured and compared to the
time delays applied to their associated elements in the transmitting mode. The experimental
results for the generation of the 45o shear plane wave at 150
oC are illustrated in Figure 7.5-a and
Figure 7.5-b when the first 16 elements and last 16 elements of the array were used, respectively.
The red data points represent the relative time delays of the elements calculated by our algorithm
for this elevated temperature inspection condition (Chapter 6). As for the case of the room
temperature experiments of Section 7.3, these delay times are expressed relative to the last
element of the selected aperture and were applied to the aperture elements in the transmitting
mode to form a plane wave with propagation angle Фs in the steel test piece.
The green data points on the graphs represent the experimentally measured time delays of the
received echo signals at the array elements that are being analyzed in detail. These points are
each the average of 15 repeated experiments and the error bars indicate the level of uncertainty in
calculated averages (green data points) due to the presence of random errors.
The dark green data point represents the average of the measured data corresponding to the first
element of the aperture and the light green data point represents the same for the middle element
of the aperture. These time delays were calculated relative to the last element of the active
aperture, which served as a reference as done for the room temperature measurements.
To illustrate the effects of temperature changes on phased array timing considerations, the
calculated time delays for room temperature (25oC) inspection used in Section 7.3 are also
shown in blue for comparison.
56
Figure 7.5 Experimental results for generation of a 45o shear plane wave in a 45
o-angled steel test block at 150
oC
using an Olympus 5L64-A12 array and Eclipse WA12-HT55S-IH-G PEI wedge when the first 16 elements (a) and
last 16 elements (b) of the array were used. The red and green data points represent the relative time delays
calculated by our algorithm, and the mean of the measured echo time delays, respectively. The green points are each
the average of 15 repeated experiments and error bars indicate the uncertainty level in the value of the green points.
Blue data points represent the calculated time delays for room temperature inspection.
If our new algorithm for calculating time delays of individual array elements worked perfectly,
the two green dots in each of Figure 7.5-a and Figure 7.5-b would fall directly on top of the red
line. That is, the experimentally measured time delays of the echo signals would exactly match
the calculated time delays. Instead, we see some deviation, which can be analyzed in terms of
57
systematic and random errors. Several possible sources of systematic and random sources were
described in Section 7.3 for the case of room temperature experiments. These, plus additional
error sources are present for the experiments conducted at elevated temperatures. These
additional error sources include:
Uncertainties in the temperature distribution in the wedges as estimated by the finite
element model (systematic error)
Uncertainties in the temperature dependence of compression wave velocity in the wedge
material, and the temperature dependence of shear waves in the steel test specimen
(systematic error)
Time-dependent fluctuations in the temperature distribution in the wedge, test piece, and
couplant (random error)
Our strategy is first to quantify the magnitude of the systematic and random errors. Then we can
analyze whether there is any significant deviation between our experimental results (e.g., green
data points shown in Figure 7.5) and the theoretical delay times predicted by our new algorithm
(red line).
Raw data values corresponding to results presented in Figure 7.5 are presented in Table 7-2, in
four separate columns. Each column represents the experimentally measured time delays of the
received echo signals at an individual element. The first two columns represent data
corresponding to the first and middle elements of the aperture, when the first 16 elements of the
array (elements 1-16) were used; these data are depicted by the dark and light green points,
respectively, in Figure 7.5-a. The third and fourth column of Table 7-2 represent the data
corresponding to the first and middle elements of the active aperture when the last 16 elements of
the array (elements 49-64) were used, as depicted by the dark and light green points,
respectively, in Figure 7.5-b. It is noted again that these delay times are all expressed relative to
the last element of the selected aperture, which is the first element fired in transmission mode
(Figure 7.5).
Each measurement was performed 15 times. The mean values of the 15 repeated experiments are
presented in the first row of Table 7-2. The associated standard deviations are shown in the
second row, and represent the magnitude of random fluctuation associated with each individual
test. From these data, the maximum magnitude of random errors in high temperature experiments
58
is of the order of 24 ns. Note that this value is slightly larger than the 15 ns reported for room
temperature experiments. This increase is believed to be due to the influence of temperature
fluctuations in the wedge, couplant, or test piece, and thickness variations in the couplant.
The magnitudes of the uncertainty in the measured mean values are presented in the third row of
Table 7-2, as illustrated by the error bars in Figure 7.5. These are estimated from the standard
deviations (second row) and the number of measurements (N=15), based on statistical
distribution associated with the T-test with a 95% confidence interval [45].
The fourth row of the Table shows the time delays calculated by our model (red dots in Figure
7.5) for specific array elements. Finally, the deviations between the mean of the 15 repeated
measurements (row 1) and their associated theoretical values (row 4) are presented in the last
(fifth) row of the Table.
It is seen that in three of the presented cases, the deviation between the mean of the
measurements and its associated theoretical value is within the range of the uncertainty in the
experimental measurement’s mean value (comparison of data in the third and fifth row of the
Table). This means that in these cases there is no significant deviation between our experimental
results (e.g., green data points shown in Figure 7.5) and the theoretical delay times predicted by
our new algorithm (red data points in Figure 7.5).
For the case presented in the second column of Table 7-2, the magnitude of the deviation
between the mean and its associated theoretical value exceeds the range of the uncertainty in the
measurement’s mean (12 ns > ± 7 ns). This is the case associated with echo time delays of the
middle element of the aperture when the first 16 elements of the array were used. However, the
magnitude of deviation is within the systematic error range of up to +/-20 ns in the focal law
calculator, noted to be present in the room temperature tests due to uncertainties in input data.
59
Table 7-2 Magnitude of the experimental results associated with generation of a 45o shear plane wave at 150
oC as
depicted in Figure 7.5. The results of 15 repeated time delay measurements of echo signals of the first and central
elements of the active aperture are presented for two cases: active aperture = elements 1-16; and active aperture =
elements 49-64.
Фs=45o
N=15
Tests Using Elements 1-16
(Figure 7.5-a)
Tests Using Elements 49-64
(Figure 7.5-b)
Element No. 1
(dark-green)
Element No. 8
(light-green)
Element No. 49
(dark-green)
Element No. 56
(light-green)
1 Experimental Mean
(green dots in Fig. 7.5)
475 ns 258 ns 395 ns 203 ns
2 Standard Deviation of
Individual
Measurements
20 ns 13 ns 24 ns 20 ns
3 Uncertainty in the
Mean (error bars)
± 11 ns ± 7 ns ± 13 ns ± 11 ns
4 Model Prediction
(Transmitting Delay)
479 ns 246 ns 383 ns 205 ns
5 Deviation of the Mean
from the Model
prediction
-4 ns +12 ns +12 ns -2 ns
The above results indicate that the experimentally measured echo delay times agree with our
calculated element time delays, within the range of experimental systematic and random errors
for generation of a 45o shear plane wave in a steel test piece at a uniform temperature of 150
oC.
Figure 7.6 is similar to Figure 7.5, but for the case of generation of a 60o shear plane wave in a
steel test piece at 150oC. Figure 7.6-a and Figure 7.6-b illustrate the results when the first 16 and
last 16 elements of the array were used, respectively. The red data points represent the relative
time delays of the elements calculated by our algorithm for this elevated temperature (150oC)
inspection condition, as described in Chapter 6. These delay times are expressed relative to the
first element of the selected aperture and were applied to the aperture elements in the
transmitting mode to form a plane wave with propagation angle Фs in the steel test piece.
60
Continuing to follow the format of Figure 7.5, the green data points in Figure 7.6 represent the
experimentally measured time delays of the received echo signals at the array elements that are
being analyzed in detail. These points are each the average of 15 repeated experiments and the
error bars indicate the level of uncertainty in calculated averages (green data points) due to the
presence of random errors.
The dark green data point represents the average of the measured data corresponding to the first
element of the aperture and the light green data point represents the same for the middle element
of the aperture. These time delays were calculated relative to the first element of the aperture,
which served as a reference as done for the room temperature measurements. For comparison
purposes, the calculated time delays for room temperature (25oC) inspection used in Section 7.3
are also shown in blue.
Raw data values corresponding to results presented in Figure 7.6 are presented in Table 7-3 with
the same format as used for Table 7-2. The first two columns represent data corresponding to the
middle and last elements of the aperture, when the first 16 elements of the array (elements 1-16)
were used; these data are depicted by the dark and light green points, respectively, in Figure 7.6-
a. The third and fourth column of Table 7-3 represent the data corresponding to the middle and
last elements of the active aperture when the last 16 elements of the array (elements 49-64) were
used, as depicted by the dark and light green points, respectively, in Figure 7.6-b. It is noted that
these delay times are expressed relative to the first element of the selected aperture.
61
Figure 7.6 Experimental results for generation of a 60o shear plane wave at 150
oC when the first 16 elements (a) and
last 16 elements (b) of the array were used. The red and green data points represent the relative time delays
calculated by our algorithm, and mean of the experimentally measured received echo time delays, respectively. The
green points are each the average of 15 repeated experiments; the associated error bars indicate the uncertainty level
in the value of the green points. Blue data points represent the calculated time delays for room temperature
inspection, presented for sake of comparison.
62
Table 7-3 Experimental results associated with generation of a 60o shear plane wave at 150
oC as depicted in Figure
7.6. The results of 15 repeated time delay measurements of echo signals of selected elements of the active aperture
are listed in separate columns.
Фs=60o
N=15
Tests Using Elements 1-16
(Figure 6-a)
Tests Using Elements 49-64
(Figure 6-b)
Element No. 8
(dark-green)
Element No. 16
(light-green)
Element No. 56
(dark-green)
Element No. 64
(light-green)
1
Experimental Mean
(green dots in Fig. 7.6)
55 ns
109 ns
83 ns
175 ns
2
Standard
Deviation
20 ns
23 ns
13 ns
15 ns
3
Uncertainty in the
Mean (error bars)
± 11 ns
± 13 ns
± 7 ns
± 8 ns
4
Model Prediction
(Transmitting Delay)
49 ns
119 ns
99 ns
215 ns
5
Deviation of the mean
from the Model
prediction
+6 ns
-10 ns
-16 ns
-40 ns
The results presented in the first two columns of Table 7-3 indicate that there is no significant
statistical deviation between the experimental echo time delay measurements and the theoretical
delay times calculated by our algorithm when the first 16 elements of the array were used for
plane wave generation in a piece at 150oC. The deviation between the mean of the measured time
delays and their associated theoretical values are within the range of the estimated uncertainty.
When the last 16 elements of the array are used for plane wave generation, the deviation between
the mean of measured time delays and their associated theoretical values exceed the estimated
uncertainty. These cases are presented in the third and fourth column of Table 7-3. The deviation
is within the estimated systematic error of up to 20 ns for the results associated with the middle
element of the aperture (element number 56, as presented in the third column of Table 7-3).
However the deviation magnitude is about 40 ns for the measurements associated with the last
element of the aperture (element number 64, as presented in the fourth column). This is
63
significantly larger than the maximum estimated systematic error magnitude of 20 ns observed
for room temperature experiments.
Larger systematic errors are expected for the case of high temperature experiments due to the
presence of additional bias error sources, i.e., errors in the convection cooling estimates for the
heated wedge; inaccuracies in the calculation of temperature distribution in the heated wedge;
errors in the temperature dependence of wave velocities. These additional error sources would
combine with the systematic errors of +/- 20 ns estimated for room temperature experiments, to
yield larger deviations between experimental and theoretical determinations of element timing
delays.
The experimental results indicate that the overall magnitude of the bias errors is dependent on
the shear plane wave angle and the selection of active elements. The largest deviation between
experimental and theoretical results occurs for the most challenging case of generating a shear
plane wave with a large refraction angle in a test piece. The deviation is also larger when the last
elements of the array are used for plane wave generation as compared to elements 1-16. Element
numbers 49-64 are the most distant from the wedge-piece interface, such that waves associated
with those elements undergo the longest path through the heated wedge. In addition, waves
associated with this last 16 elements traverse the thermal gradient at the widest angle, and
therefore experience far more beam skew, as described in Section 6.2.
In summary, the experimental results indicate that the new focal law calculator determines
element time delays for shear planar wave inspection of a heated test piece, that are not
inconsistent with experimental results. In the next Chapter we modify the focal law calculator to
calculate element time delays for generation of a beam focused at a single point in a hot piece.
64
8 Focal Law Algorithm – Focused Beam
As described in Chapter 2, a scan plan is prepared before any industrial phased array inspection
is initiated. This is achieved by an optimized selection of scanning parameters such as wedge
geometry and range of scanning angles. Typically, planar waves are first used for the inspection
to locate any flaws and determine their approximate size. Once discontinuities have been located
using plane waves, a focused beam may be used at the defect locations for more accurate sizing
and flaw characterization. Focusing of the ultrasound beam at a particular location has the effect
of narrowing the beam diameter and increasing the local ultrasound energy per unit area. This
results in higher sensitivity to small reflectors, improved signal-to-noise ratio, and better image
resolution.
In Chapter 6 we introduced a numerical ray-tracing technique to model the arced path of waves
propagating across thermal gradients in an isotropic wedge. The results were then used in a
separate algorithm to modify the phased array focal law for generation of desired shear plane
waves in a hot piece, while compensating for thermal gradient effects inside the wedge. The
calculated relative time delays for individual array elements were presented for generation of
shear plane waves with two different angles in a steel test piece at 150oC. These were then used
to experimentally evaluate the quality of shear plane wave generation in a hot steel test piece.
The experimental results were presented and analyzed in Chapter 7.
In this chapter we introduce a second set of validation trials for our new focal law calculator, but
this time for the generation of a beam focused at a single point in the hot test piece. To this end,
we follow parallel steps to those described in Chapters 6 and 7 for the generation of a plane wave
in a hot test piece.
In Section 8.1, we develop the overall algorithm to calculate a focal law for generation of a
focused beam in a hot test piece, while compensating for thermal gradient effects inside the
wedge. In Section 8.2, the algorithm will be applied to a number of trial focal points in a
hypothetical hot test piece; the magnitude of the thermal gradient effects on the focal law
calculation will be quantified for those focal points and analyzed. In Section 8.3, experiments
will be carried out to validate the numerical model results of Section 8.2 for generating a focused
beam at any user-specified point in a hot test piece. Chapter 8 will then conclude with an analysis
of the results.
65
8.1 Algorithm Details
Figure 8.1 illustrates the same inspection system as described in Chapter 6 (Figures 6-1 and 6-2)
with an Eclipse WA12-HT55S-IH-G PEI wedge and an Olympus linear phased array model
5L64-A12 with 64 elements and center frequency of 5 MHz. Also shown in Figure 8.1 is an
arbitrary focal point in a test piece at 25oC.
In order to calculate the appropriate element time delays for focusing the ultrasonic beam at the
specified focal point, the travel time of the wave emitted from each element to the focal point
must be obtained. To achieve this, the same steps and principles are followed as described in
Chapter 6. First, wave propagation paths from various “array-line points” along the phased array
to the focal point are determined, as shown schematically by ray traces in Figure 8.1. Also
labeled in Figure 8.1 are “interface points” on the wedge-piece interface; note that a single
interface point is applicable for each wave path between the focal point and an array-line point.
The propagation paths are straight lines inside each homogenous isotropic medium, i.e., the
wedge and the test piece, each with a single wave propagation velocity corresponding to 25oC.
The refraction angle at each Interface Point is determined by Snell’s Law. Note that the same
propagation paths are applicable in both directions, i.e., from array to focal point, and from focal
point back to the array.
66
Figure 8.1 Wave propagation pattern for focusing an ultrasonic beam at an arbitrary focal point in a steel block at a
uniform temperature of 25oC. Wave propagation paths are shown from various array-line points along the phased
array to the selected focal point. The propagation paths are straight lines in both the wedge and the steel block, each
with a single wave propagation velocity at 25oC. The refraction angle at each interface point is determined by
Snell’s Law.
It will be convenient to conduct the calculation of the focal law in the “reverse” direction, i.e.,
model a pulse originating at the selected focal point and travelling along the various propagation
paths to the Interface points, and then on the Array Line Points. This is shown schematically by
the arrow directions on the ray traces of Figure 8.1.
The travel distances in both the test piece and the wedge sections can be calculated geometrically
along each of the shown propagation paths. These are divided by the ultrasonic shear wave
velocity in the steel and compression wave speed in the wedge to calculate the pulse travel times
along each propagation path in each of the two materials. The two travel-time components are
then added together to find the total travel time along each propagation path; these travel times
are each applicable to pulses travelling in either direction along that propagation path.
Knowing the total travel time associated with each of the array line points, those data can be
interpolated to yield travel time as a continuous function of position along the array-wedge
boundary. Specifically, one can interpolate the total travel time from the focal point associated
with each element on the array. These travel times then represent the relative element time delays
67
required for excitation of the array to yield constructive interference of all waves arriving at the
specified focal point in the test piece: the same relative time delays apply to both transmitted
waves from array to focal point, and echo signals travelling from focal point to the array
elements.
This procedure for calculation of an array focal law becomes a bit more complex for inspection
of test pieces at elevated temperatures using a high temperature wedge with a cooling jacket
around the array. The presence of thermal gradients inside the wedge leads to variations in
temperature-dependent wave velocity and skewing of the wave directions inside the wedge. Our
intent is to utilize the ray-tracing technique introduced in Section 6.2 to model the beam skewing
effect in the generation of a focused beam.
Figure 8.2 illustrates schematically the wave paths for generation of a focused beam at the same
focal point as depicted in Figure 8.1, but now with the steel test block at a uniform temperature
of 150oC and the wedge cooled by ambient air at 25
oC plus the array’s water jacket. This
arrangement causes the wedge temperature to range from close to 150oC where it contacts the
test piece, down to approximately 30oC adjacent to the cooling jacket. The same interface points
on the test piece-wedge interface shown in Figure 8.1 are again selected here to illustrate the
focal law calculation, using the same ray tracing procedure as described for the ambient
temperature case moving from the focal points towards the array. The following differences
between Figure 8.1 and Figure 8.2 are noted:
1) Wave path lengths in the steel test piece are the same in Figure 8.1 and Figure 8.2, given
that the test piece is at a uniform temperature in both Figures; however, the associated
wave velocities and travel times in the test piece are now changed due to its elevated
temperature of 150oC.
2) The incident angles of the waves in the steel specimen at the wedge-piece interface are
the same in both Figures. However, the associated angles of the waves inside the wedge
will be different; this is a result of Snell’s Law and the temperature-dependent sound
velocities in both the test piece and bottom surface of the wedge.
3) Once the waves refract into the wedge, their paths will no longer be straight lines, as the
thermal gradients inside the wedge lead to skewing of the waves. The wave paths and
their travel times inside the wedge are simulated with the ray-tracing algorithm
introduced in Section 6.2, utilizing temperature distribution data from our COMSOL
68
finite element model, and phase velocity data of the wedge material at elevated
temperatures. The solid red lines in Figure 8.2 represent the skewed ray paths originating
from the interface points.
4) Once the new travel times associated with each ray path have been obtained in both the
wedge and test piece, the total travel time and the appropriate relative delay times are
calculated as described in Chapter 6.
Figure 8.2 Wave propagation pattern for focusing an ultrasonic beam at an arbitrary focal point in a steel block at a
uniform temperature of 150oC. Wave propagation paths are shown from various array-line points along the phased
array to the selected focal point. The propagation paths are straight lines in the steel block based on the assumption
of uniform temperature inside the block (blue lines). After the waves refract into the wedge, they propagate along
arced paths (red lines) due to velocity variations across the heated wedge that are induced by thermal gradients.
In the next Section, we provide examples to demonstrate the magnitude of the thermal gradient
effects on the elements delay times calculated by the above described algorithms.
8.2 Magnitude of Thermal Gradient Effect
In order to quantify the magnitude of the thermal gradient effect on the focal law calculations,
we consider a case of focusing the ultrasonic beam at a series of three specific focal points in a
steel test block using the wedge-array system described in Section 8.1. The focal points lie along
69
the sound paths representing the waves with refraction angles of 40o, 55
o, and 70
o inside the test
block when using elements #1-16 of the probe array, as shown in Figure 8.3. As is standard
practice in simplified training manuals for industrial phased array systems, the three test cases
are each represented by a straight line emitted from a point located at the center of the active
array region.
Figure 8.3 Location of the selected focal points and calculated near field points in a steel block on the sound paths
representing the waves with refraction angles of 40o, 55
o and 70
o using an Eclipse WA12-HT55S-IH-G PEI wedge-
5L64-A12 Olympus array system. The first 16 elements of the aperture are used for beam formation and each sound
path is represented by a straight line emitted from the point located at the center of the active aperture.
Theoretically, the desired focal points can be selected at any distance along the specified sound
paths. This means that focal laws can be calculated and applied to the elements for generation of
a focused beam at any distance along the sound paths. However, the focusing efficiency
decreases beyond the near field distance along each sound path. The near field distance is the
distance from the face of the transducer to the location with the last local maximum in the sound
field pressure, which then decreases monotonically due to beam spreading beyond this point. For
a wedge-array system, the near field distance depends on the size of the active aperture, the
center frequency of the probe, refraction angle (40o – 70
o), plus the ultrasonic sound velocity
inside the wedge and steel test specimen [14] [46]. The red points on Figure 8.3 represent the
location of the near field distance on each sound path.
70
The black points shown in Figure 8.3 represent the location of focal points selected along each
sound path for characterizing the new focal law calculator. They are all located at the same travel
time distance from the center of the active array aperture, and within the near field. For the case
of the ray representing a 55o refraction angle path in the test piece (the nominal refraction angle
of the wedge), the selected focal point lies at approximately 90% of the near field distance from
the center of the active array.
(a)
71
Figure 8.4 The calculated time delays of individual elements for focusing an ultrasonic beam at the selected focal
points located on the wave sound paths representing (a) 45o, (b) 55
o and (c) 70
o refraction angles inside a steel test
block using an Eclipse WA12-HT55S-IH-G PEI wedge-5L64-A12 Olympus array system (as depicted in Figure
8.3). The first 16 elements of the aperture are used for beam formation. The blue and red data points represent the
results for room (25oC) and elevated temperature (150
oC) inspection condition, respectively. In each case, delays are
expressed relative to the element associated with the longest travel time from array to the focal point. This element
is fired first with delay time defined as time zero; all other elements are then fired at their relative delay times.
(b)
(c)
72
Figure 8.4-a, Figure 8.4-b and Figure 8.4-c show the calculated relative delay times associated
with ultrasonic waves focused at the selected focal points on the 40o, 55
o, and 70
o refraction
sound paths respectively. The blue and red data points represent the results corresponding to
room (25oC) and elevated temperature (150
oC) of the steel test piece, respectively. Delay times
are expressed relative to the element associated with the longest travel time from array to focal
point. This element should be fired first at a time defined as t=0; all other elements should then
be fired at their respective relative delay times.
Application of conventional (i.e., room-temperature) array focal laws for generation of a focused
beam at 40o yielded time delay errors for array elements of up to 174 ns when applied to a test
block at 150oC, as seen in Figure 8.4-a; this timing error is approximately 87% of one period at
the pulse central frequency of 5 MHz (period of 200 ns) in the test piece. Such large percentage
errors imply that the ultrasound pulses arriving from all the array elements would not all
constructively add together at the focal point. Instead there would be appreciable destructive
interference of the beam, significant distortion of the desired profile and loss of ultrasound
amplitude at the focal point, and non-optimal imaging resolution.
The effects of thermal gradients on the optimal element time delays is even more severe for the
case of generating a focused beam at larger refraction angles in a test piece, such as the focal
point located on a 55o refraction sound path as depicted in Figure 8.4-b. In this case, the
calculated time delays for the case of generating a focused beam in a hot test piece show a
significantly different profile from the delays calculated for inspection at room temperature. It is
noted that the high temperature time delays are expressed relative to element number 16 and the
room temperature time delays are expressed relative to element number 1. This indicates that the
wave associated with element number 1 undergoes a longer travel time to the focal point
compared to the waves emitted from all the other elements at room temperature condition.
However, at an elevated temperature condition the wave emitted by this element reaches the
focal point more quickly compared to all other elements, due to wave skew and the temperature
profiles in the wedge and test piece.
For the case of generating a focused beam at a focal point located on a 70o refraction path line
(Figure 8.4-c), the maximum discrepancy between element delay times calculated by the
conventional room-temperature focal law calculator and the new algorithm is 147 ns; this is
73
approximately 73% of a period of the pulse central frequency of 5 MHz. A lack of proper
focusing at the desired focal point would result.
The three graphs of Figure 8.4 illustrate how the effects of thermal gradients on the optimal
element delay times have a complicated dependence on the location of the focal point in the steel
test piece. The following points are noted:
1) The general profile of the optimal time delay pattern is dependent on the refraction angle
associated with the focal point in the test piece.
2) The magnitude of thermal gradient effect on the array focal law for generation of a
focused beam in a hot test piece depends on the refraction angle associated with the focal
point in the test piece. The effect is larger when there is a significant deviation between
the direction of the thermal gradient and the direction of wave propagation: larger
deviations between these two directions lead to greater beam skewing.
The next step is to design an experiment to evaluate the accuracy of the focal laws calculated by
our model for the generation of a focused beam in a hot test piece. This is described in Section
8.3.
8.3 Experimental Evaluation
In this section, we develop an experiment to evaluate the effectiveness of the new algorithm with
respect to the focusing performance of a phased array system at elevated temperatures. Sectorial
scans are commonly used for inspection of welds in pipes, plates, and pressure vessels.
Furthermore, a focused beam can be used in a sectorial configuration, i.e., focused beams sweep
along a range of desired angles and depths in the test piece. Use of focused beams increases the
resolution of the scan image by increasing the local sound pressure and decreasing the beam spot
size.
Several methods of phased array performance assessment are described in ultrasonic inspection
guides. In particular, standardized calibration blocks are often used for checking the capabilities
of a phased array ultrasonic system. These blocks contain a series of reflectors such as side
drilled holes which are distributed within the block in a specific pattern. The echo signals
74
received from these reflectors are analyzed for calibration purposes based on established codes
[47] [48].
Figure 8.5 illustrates an example of such a block for assessment of phased array steering
capability [47]. This block is designed for phased array probe steering assessment when the
probe is used in direct contact with the block (no wedge). A series of 2 mm diameter side drilled
holes are located at 5o intervals on an arc, 50 mm from the surface location where the midpoint
of the active aperture is located. Once the probe is located at the proper position, a focused beam
is electronically swept along the 50 mm arc with 1o angular steps. Amplitudes of the received
echo signals are plotted versus their corresponding steering angle. High amplitudes would be
expected to correspond to the locations of the side drilled holes. Therefore, the clarity of these
amplitude peaks as a function of steering angle indicates the angular range of the array.
Figure 8.5 Calibration block for steering assessment of phased array probe based on the amplitudes of the echo
signals received from a series of 2-mm diameter side drilled holes. The holes are located at 5o interval on an arc 50
mm from the surface location where the midpoint of the array’s active aperture is located. A focused beam is
electronically swept along the arc with 1o angular steps. Amplitudes of the received echo signals are analyzed. High
amplitudes are expected to correspond to the locations of the holes. The clarity of the amplitude peaks as a function
of steering angles indicates the angular range of the array.
75
The block depicted in Figure 8.5 can also be used for resolution assessment of the phased array
probe in a sectorial scanning configuration. The resolution capability in a sectorial scan is
identified as “angular resolution” [48]. The angular resolution is the minimum angular separation
at which two identical targets located at the same sound path distance (same wave travel time
between the source and the targets) can be separated. By one definition, two identical targets at
the same sound path distance are considered resolved in angle when the echo amplitude from a
location midway between the two targets is at least 6 dB less than the echo from either target
[48].
This type of calibration block cannot be used for performance assessment of a wedge-array
system, in which the apparent beam exit point from the wedge varies strongly with refraction
angle. In such a case, the length of the sound path would be different for each side-drilled hole
and distort the results. In this project, we have therefore designed a modified steel block for
angular resolution and steering assessment of our wedge-array system, using a set of only four
side drilled holes as reflectors. The locations of the reflectors were selected to compensate for the
dependence of path length in the wedge and test block on refraction angle.
The block was specifically designed for use with the Eclipse WA12-HT55S-IH-G PEI wedge
and first 16 elements of the model 5L64-A12 Olympus linear phased array probe. A series of
focal points was selected along an arc in the steel block; the focal points were associated with
refraction angles ranging from 40o up to 70
o in 1
o increments (31 focal points), as shown in
Figure 8.6. Each sound path is approximated by a single straight line originating at the center of
the active array aperture. The red arc in Figure 8.6 represents the boundary of the near field, and
the black arc links the locations of the 31 focal points. Locations of both arcs were determined
using the same procedure as described in Section 8.2.
Four side drilled holes were located on the black line. The diameter of the doles was selected to
be 1.5 mm which is higher than the wavelength of the wave propagating in the steel block as
specified by the phased array performance assessment code [47]. The side drilled holes were
centered on the focal points which lie along the sound paths representing the refraction angles of
44o, 49
o, 56
o and 66
o. The block configuration, focal points and side drilled holes are depicted in
Figure 8.7. Also illustrated in this Figure are the wave sound paths in the steel corresponding to
the various refraction angles inside the block as depicted in Figure 8.6.
76
Figure 8.6 Design specifications of a steel block for performance assessment of a wedge-array system. The block
was specifically designed for use with Eclipse WA12-HT55S-IH-G PEI wedge and first 16 elements of the 5L16-
A12 linear phased array probe. The blue straight lines represent the wave paths associated with refraction angles
ranging from 40o up to 70
o in 1
o increments. The red arc represents the boundary of the near field on the specified
sound paths. The black arc links the locations of the focal points on the presented sound paths. These are located at
the same travel time distance from the center of the active aperture, and are all within the near field.
The designed block was first used for assessment of our wedge-array system at ambient
temperature of 25oC. The appropriate element time delays were calculated for focusing the
ultrasonic beam at the selected focal points based on the conventional room temperature focal
law calculation procedure as described in Section 8.1. The array was connected to a Focus LT
phased array instrument which can apply any user-specified relative element time delays to the
selected active elements of the array using TomoView software. The wedge-array system was
placed on the designed steel test block for generation of the focused beams, as shown in Figure
8.8.
77
Figure 8.7 Configuration of the designed steel block for angular resolution and steering assessment of an Eclipse
WA12-HT55S-IH-G PEI Wedge-5L64-A12 Olympus array system: a set of four side drilled holes are selected as
reflectors. The holes are centered on the focal points which lie along the sound paths representing the refraction
angles s of 44o, 49
o, 56
o and 66
o. The straight lines represent the wave paths associated with refraction angles
ranging from 40o up to 70
o in 1
o increments. The black and red points represent the location of focal points (steering
samples) and the near field points on the specified sound paths respectively.
Figure 8.8 Experimental set up for evaluation of model results for focusing the ultrasonic beam in a steel test block
at 25oC. An Eclipse WA12-HT55S-IH-G PEI wedge was used with a 5L64-A12 Olympus array for generation of
focused beams. The steel test block contains four side drilled holes at locations specified in Figure 8.7.
78
For each of the 31 focal points, the relative element time delays were calculated for the selected
active array elements (elements 1 to 16). The focused beam was then swept electronically along
the focal points, representing refraction angles of 40o to 70
o in 1
o increments. For each of the 31
focal points, the echo signals received at the 16 active array elements were summed
electronically, using the same relative time delays as applied to the transmitted signals. The
resultant total echo signals were then converted to their analytical form. The maximum
amplitudes of the obtained analytical signals were plotted versus the corresponding refraction
angles, Figure 8.9. The experiment repeated three times to ensure the results were reproducible
with negligible difference.
Figure 8.9 Assessment results of an Eclipse WA12-HT55S-IH-G PEI wedge-5L64-A12 Olympus array system at
ambient temperature of 25oC. The focused beam was swept electronically along the focal points as depicted in
Figure 8.7 and Figure 8.8. The maximum amplitude of the analytical form of the echo signals was plotted versus the
refraction angles (blue points). The local amplitude peaks correspond to refraction angles of 44o, 49
o, 56
o and 66
o
inside the steel test block (dashed lines). These represent the location of the side drilled holes.
The local amplitude peaks in Figure 8.9 correspond to refraction angles of approximately 44o,
49o, 56
o and 66
o inside the steel test block - the locations of the side drilled holes were
successfully identified through the sectorial scanning with a focused beam. The following points
are noted:
79
1) The amplitude peaks corresponding to all the side drilled holes are not identical in
magnitude. This is partly because the sound path length from the array to the focal points
varies with refraction angle. Therefore, the echo signals corresponding to the holes
undergo different level of attenuation and beam spreading as they travel through the
wedge and steel test block. In addition the transmission coefficient from the wedge to the
test block varies with the refraction angle.
2) The echo profile in Figure 8.9 does not consistently meet the resolution criterion of a 6
dB drop in signal amplitude between reflectors located with 5o angular separation. This
point is particularly evident for the target holes on sound paths corresponding to 44o and
49o refraction angles (see Figure 8.7). However, a skilled technician would have little
difficulty in resolving the adjacent target reflectors. The results indicate that the angular
resolution limit of the inspection system is close to 5o for ambient temperature (25
oC)
inspection conditions.
Once the focusing effectiveness of our system was evaluated for the case of room temperature
inspection, the same experiment was repeated at elevated temperature for the more challenging
case of the steel block at 150oC. The same wedge-array system was used for the elevated
temperature experiment as used for the room temperature experiment. The designed block was
placed on a temperature-controlled hot plate, and the block-wedge surface was kept at 150oC.
The steel block was wrapped in high-temperature insulation to minimize heat loss and
temperature gradients in the block. This led to temperature variations over the entire volume of
the test piece of less than 5oC, as indicated by experimental measurement at selected locations.
Once the temperature stabilized in the test piece and wedge system, the calculated relative
element time delays were applied to the selected active array elements (elements 1 to 16) to
generate the focused beams. The experiment was performed twice: First, with time delays
calculated for ambient temperature (25oC) conditions with no compensation for the effect of
thermal gradients inside the wedge. The experiment was then repeated using the focal laws
calculated by our new model for the actual experimental condition of elevated temperature
(150oC test block) and thermal gradient in the wedge. The motivation for running the experiment
twice in this manner was to help assess whether use of the high-temperature focal law actually
yields a significant improvement in ultrasonic inspection results.
80
For both cases the relative element time delays were applied to the selected active array elements
(elements 1 to 16) for signal transmission. The received elements echo signals were summed
using the same relative time delays. The amplitudes of the summed echo signals were plotted
versus refraction angle, in the same manner as was done for the ambient temperature results of
Figure 8.9.
The results of the elevated-temperature experiments are shown in Figure 8.10. The blue and red
data points represent the results corresponding to the application of the room temperature
(incorrect) and elevated temperature (correct) focal laws, respectively, for generation of focused
beams in the steel test piece.
Figure 8.10 Assessment results of an Eclipse WA12-HT55S-IH-G PEI wedge-5L64-A12 Olympus array system at
150oC. The focused beam was swept electronically along the focal points as depicted in Figure 8.7 and Figure 8.8
and the maximum amplitude of the analytical form of the echo signals was plotted versus the refraction angles. Two
sets of focal laws were used for beam formation: First, the focal laws calculated for ambient temperature condition
(25oC) and then the focal laws calculated by our new model for the actual experimental condition (150
oC test block).
The results corresponding to these cases are presented by the blue and red points, respectively. The dashed lines
represent refraction angles which correspond to location of the side drilled holes in the steel test block.
As seen in Figure 8.10, in both cases four peaks can be identified in the amplitude-angle curve
which represents the four side-drilled holes in the sample block. As expected, the peaks do not
81
match exactly with the actual location of the holes when the incorrect focal laws were used (blue
points). This implies that application of incorrect relative element delay times led to non-optimal
focusing of the beam at the desired location inside the piece.
When the correct (high-temperature) focal laws were used with accommodation for beam skew,
there is a slight shift of the peak amplitudes toward the expected locations. This would help in
determining the location of flaws detected in an ultrasonic inspection. The change in signal
amplitude and resolvability is negligible; a major source of error is believed to be uncertainty in
the temperature profile in the wedge and the associated velocity profile. It is noted that the test
piece temperature considered in this experiment was only 150oC. Use of the new focal law is
expected to become increasingly important as temperatures are raised further. Although the new
wedge materials can tolerate temperatures up to 350oC, limitations in the laboratory experimental
system prevented conducting our tests at this more demanding temperature.
82
9 Summary, Conclusions and Future Work
The design and operation of an ultrasonic phased array system were described for inspections of
engineering components such as pipe welds at elevated temperatures of up to 350oC. Wedges
were built from plastics resistant to high temperature degradation, and equipped with a cooling
jacket around the array. The temperature distribution inside the wedges was modeled with finite
element software and validated experimentally. Ultrasonic compression wave velocities of
wedge materials were measured as a function of temperature. These were used to model the
skewed path of waves propagating across thermal gradients in the heated wedge utilizing a
numerical ray-tracing technique.
A new algorithm was developed based on the beam skew model, to calculate transmission and
reception time delays on individual array elements for generation of plane waves or focused
beams in test pieces at elevated temperatures, while compensating for thermal gradient effects
inside the wedge. The following results and key points were noted:
1. The amount of beam skew depends on the amount of misalignment between the beam
propagation vector and the gradient of the temperature or velocity field inside the wedge.
2. Application of conventional array focal law for phased array inspections at elevated
temperatures leads to incorrect time delays on array elements, significant distortion of the
desired beam profile, and a reduction in imaging resolution.
3. The magnitude of the thermal gradient effect on the array focal law for generation of a
shear plane wave in a test piece strongly depends on the location of the active elements
on the array, the angle s of plane wave propagation in the test piece, and the magnitude
and orientation of the thermal gradient inside the high temperature wedge. These items
are all inter-related; for example, the angle between the thermal gradient and the
ultrasound propagation vector varies strongly with the choice of array elements used for
plane wave formation. That angle and resultant beam skew are generally larger if the
upper array elements are used as opposed to the lower array elements. That angle also
83
tends to be larger if the system is set to generate a plane wave in the test piece with a
large refracted angle s as opposed to a small refracted angle.
4. The magnitude of the thermal gradient effect on the array focal law for generation of a
focused beam depends on the refraction angle associated with the focal point in the hot
test piece. The effect is larger when there is a significant deviation between the direction
of the thermal gradient and the direction of wave propagation: larger deviations between
these two directions lead to greater beam skewing.
Element time delays calculated by the new algorithm were validated experimentally for
generation of shear plane waves and focused beams in a steel block at 150oC. The experimental
results indicate that the new algorithm does determine appropriate element time delays for
inspection of a heated piece using both shear planar waves and focused beams.
Several further steps can be carried out to complement this thesis:
1. The new wedge materials can tolerate temperatures up to 350oC, and laboratory
verification tests should be carried out at such temperatures. Experimental validation of
the new focal law was not possible in our case for temperatures greater than 150oC, due
to limitations of laboratory equipment. The effects of the thermal gradients should be
much larger at 350oC, and therefore the improvements enabled by the new focal law
should be more evident.
2. The new algorithm for focal law generation should be implemented in an automated
scanning system to perform scans at elevated temperatures.
3. The high temperature scanning system can be used for inspection of blocks which contain
defects with known size and location at elevated temperatures. The scan result can be
used to further evaluate the effects of temperature on signal amplitude.
4. The results in step 3 can be used for developing standards for performance of high
temperature inspections with phased array systems.
84
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