determination of hydrogen zr-2.5 nb pressure high ... · pdf file2.3 hydrogen in zirconium ......
TRANSCRIPT
Determination of Hydrogen Concentration in Zr-2.5 % Nb Pressure Tube Material by High Frequency Nonlinear Ultrasonics
Cszar Georgescu
A thesis submitted in conformity with the requirements for the degree of Master's of Applied Science
Graduate Department of Mechanical and Industrial Engineering University of Toronto
@Copyright by Cezar Georgescu . June 1997
National Library 1*1 of Canada Bibliothèque nationale du Canada
Acquisitions and Acquisitions et Bibliographie Services services bibliographiques
395 Weilington Street 395, me Wellington Ottawa ON K 1 A ON4 OttawaON K1AON4 Canada Canada
The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, loan, distribute or sell copies of this thesis in microfom, paper or electronic formats.
The author retains ownership of the copyright in this thesis. Neither the thesis nor substanbal extracts fiom it may be printed or othewise reproduced without the author's permission.
L'auteur a accordé une licence non exclusive permettant a la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/nlm, de reproduction sur papier ou sur format électronique.
L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.
Determination of Hydrogen Concentration in Zr-2.59bNb Pressure Tube Material by High Frequency Noniinear Ul trasonics
Master's of Applied Science, June 1997
by Cezar Georgescu
Graduate Department of Mechanical and Industrial Engineering University of Toronto
Abstract
To a first-order approximation, ul trasound behaves in a Iinear manner when travel i ing through a solid material. However. if we consider the lattice anhmnonicity, different types of nonlinear phenomena appear. In certain cases, these non-linear effects can be valuable indicators of material properties. The goal of this study is to determine whether non-linear second order harmonic generation cm be used to indicate the concentration of hydrogen (deuterium) in CANDU nuclear reactor pressure tubes. Two high-power ultrasonic waves, at frequencies up to 200 MHz. are r~quired for this purpose; the two sound beams combine in a non-linear wave-wave interaction that is measured by piezoelectric crystals mounted ont0 test specimens. The magnitude of this nonlinear second order harmonic is measured in five pieces of Zr-2.5% Nb pressure tube which contain different levels of zirconium hydrides. Unfortunately, no consistent trend was found in the amplitude of the observed nonlinear effect versus hydrogen concentrations.
Acknowledgments
1 would like to express my gratitude to Professor Dr. A. Sinclair for his invaluable
guidance and assistance during the cntire course of my work on this project.
1 am grateful to Dr. Douglas Mair of Ontario Hydro Resecirch Division for his valuable
discussion and advice.
Finally, I wish to express my apprcciûtion to rny wife for her support and encouragement
at al1 times.
List of Symbols
- amplitude of the fundamental wave in time domain [ml.
- second order elastic constants [Pa].
- third order elastic constants [Pa].
- force [NI.
- combinations of the second and third order elastic constants;
given in Table 1 [Pa].
- wave numbers lm-' 1.
- phonon numbers.
- probability of interaction betwern phonons per unit time.
- time [s].
- displacement dong x-mis [ml.
- distance measured dong the propagation direction [ml.
- amplitudes of the input tone burst pulses in the frequency doiii:iin
[arbitrary units].
- amplitude of the nonlinear second harmonic in the frequency domain
[arbitrary units].
- nonlinear parameter [dimensionless 1.
- strain tensor.
- phase constant.
- lattice potential.
- density [kg/m3].
- circular frequency [s"].
-parameter characterizing the phonon interaction.
- interaction time Es].
List of Tables
Table 1.1 - K, . K, as combinations of the second and third order elastic
constants.
Table 4.1.1 - Normalized magnitude of nonlinear effect for interaction:
Longitudinal ( 1 O3 MHz) + Shear (59.5 MHz)- Longitudinal( 1 62.5 MHz).
Table 4.1.2 - Normalized magnitude of nonlinear effect for interaction:
Longitudinal (97 MHz) + Longitudinal (60 MHz) - Longitudinal( 157 MHz).
Table 4.1.3 - Normalized magnitude of nonlinear effect for interaction:
Longitudinal ( 15 1 .S MHz) + Longitudinal (29.5 MHz)-- Longitudinal( 18 1 MHz).
List of Figures
Figure 2.1
Figure 2.2
Figure 2.3.1
Figure 2.3.2
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5.1
Figure 3-52
Figure 3.5 J
Fipre 3.6
Figure 3.7
Figure 4.1.1
- Zirconium - Hydrogen phase diagram.
- Solubility of hydrogen in Zircaloy.
- Hydrogen platelets oriented in bands in Zr-2.5% Nb material.
- Platelets with highly preferential orientation in Zr-2.5% Nb material.
- Expenmental setup.
- Crystal ont0 delay line bonding jig.
- Delay line ont0 specimen bonding jig.
- Zr-2.5% Nb pressure tube specimen.
- Received signal. corresponding to input:
f, = 103.5 MHz from high frequency pulse generator.
- Received signal, corresponding to input:
f2 = 65.9 MHz from low frequency pulse generator.
-Received signal, corresponding to input:
f+fi = 103.5 + 65.9 MHz.
- Amplitude of nonlinear effect versus delay time.
- Received signal with no delay lines.
- Normalized magnitude of nonlinear effect for interaction:
Longitudinal ( 1 O3 MHz) + Shear(59.5 MHz) + Longitudinal( 162.5 MHz).
Figure 4.1.2 - Nomalized magnitude of nonlinear effect for interaction:
Longitudinal(97 MHz) + LongitudinaI(60 MHz) - Longitudinal( l57MHz).
Figure 4.1.3 - Nomalized magnitude of nonlinear effect for interaction:
Longitudinal ( 15 1.5 MHz) + Longitudinal(29.5 MHz- Longitudinal( 18 1 MHz).
Table of Contents
................................................................................ . Chapter 1 Introduction 3
........................................................................ . Chapter 2 Background m........5
............. 2.1 Nonlinear Theory venus Linear Theory: The Nonlinear Wave Equation 5 2.2 Noniinear Effects .................................................................................................. 7
2.2.1 Second H m o n i c Generation .................................. .... .......................... 7 2.2.2 Nonlinear Wave Interactions: General Study ............................... ,.., . . . . 7 2.2.3 Parallel Waves: Nonlinear Interaction ................................................... 9
...................................... 2.3 Experimental Evidence of Nonlinear Wave Generation 10 2.3 Hydrogen in Zirconium ........................................................................................ I I
Chapter 3 . Experimental Setup .........e......ee...ee..e.............................ea......... 16
3.0 Overview of Interaction Process ...................... .... ........................................ 17 3.1 Experimental Setup; Main Components ............................................................ 17 3.2 Piezoelectnc Crystals and Delay Lines ................................................................ 19
.............................................................................................. 3.3 Bonding Technique 19 3.3.1 Crystal-To-Delay Line Bonding Procedure .............................................. 20 3.3.2 Delay Line-to-Specimen Bonding Procedure ............................................ 21
3.4 Pressure Tube Specimens ..................................................................................... 21 ....................... 3.5 Assessrnent of Experimental Setup: Verification of Nonlinearity 22
Phenomenon 3.5.1 Frequency Combination Test ................. ... ............................................. 22 3.5.2 Delay Time Test ......................................................................................... 24 3.5.3 Direct Bonding Test ................................................................................... 25
3.6 Data Collection .................................................................................................... 26 3.7 Data Analysis ....................................................................................................... 27
Chapter 4 . Results and Discussion m........ea.......e....e..e.ee..............e..a..m..e.. eemem38
4.1 Results .................................................................................................................. 38 4.2 Discussion ..................................................................................................... 4 5
5 . 1 Conclusions .................................................................................................... 48 ............................ .....-*.....-.................... 5.2 Recommendations for further work .. 50
................................... References .......t....8...t.. ....................................................... 52
Chapter 1. Introduction
CANDU (CANada Deuterium Uranium) nuclear reactors are used in al1 nuclear
generating stations in Canada today. Two special features of this particda- reactor are the
use of naniral uranium as fuel. and heavy water (deuterium oxide) as a neutron moderator.
The heat resulting from fission is transferred to a steam generator by a separate heavy
water cooling system which is operated at about 10 MPa pressure and up to 300°C
temperature. This heavy water picks up the fission heat as it passes over the hot fuel
bundles. The heavy water coolant is then pumped to a steam generator where the heat is
transferred to light water which turns into steam. The resulting stearn is fed to the turbine
which drives an electric generator.
Pressurized fuel channels are central to the CANDU's unique features. The
pressure tubes in CANDU nuclear reactors contain the bundles of natural uranium fuel
and act as a pressure boundary. There are several hundred Zr-2.5%Nb pressure tubes per
reactor which are designed on the basis of one third of the minimum specified ultimate
tensile strength according to the nuclear pressure vesse1 standards of the ASME Boiler
and Pressure Vessel Code.
There have been several well publicized problems with fuel channels. and these
have resulted in shutdowns amounting up to almost 6% of the total reactor years of
commercial CANDU operation. A very significant problem is caused by free hydrogen
(deuterium) produced by corrosion of pressure tubes themselves. The hydrogen migrates
to the cool areas of the pressure tube where it may fom hydnde platelets. As a result, the
fracture resistance of the pressure tubes is significantly reduced if the hydride platelets are
onented perpendicular to the hoop stress. Under certain conditions, crack could f o m and
propagate through the pressure tube wall by fracture of the hydnde platelets.
Awareness of this problem led to questioning whether there is a way to measure
the hydrogen concentration in Zr-2.5% Nb material without undertaking the cost of
removing the pressure tubes from the reactor. Specifically, there is a strong need for a
method of in-situ assessrnent of the deuteriurn concentration in the pressure tube material
on a reguiar basis.
Suggestions have been previously made that the magnitude of nonlinear wave
interaction could be an indicator of the hydrogen concentration in the pressure tube
material (D. Mair, 1995). The goal of this work is to study the nonlinear interaction of
various combinations of ultrasonic waves in the high frequency range, and to search for
any correlation between the magnitude of the produced nonlinear effect and the hydrogen
concentration. A significant portion of this work is to develop a suitable experimental
system, procedure, and data analysis routine to study nonlinear ultrasonic effects at very
high frequencies.
Chapter 2. Background
Al1 physicai systems experience, to some degree, nonlinearities; the ongin of
these nonlinearities is in the interatomic forces and their nonlinear potential. According to
the classical harmonic approximation, the different vibration modes of the atomic lattice
are independent and they cannot exchange energy. But if we consider the lattice
anharmonicity, energy exchange takes place between the modes and new frequency
components appear.
Details on the origins of nonlinear behavior of a medium are given in Section 2.1.
Section 2.2 deals with different types of nonlinear phenornena and Section 2.3 introduces
some practical evidence supporting the theory.
2.1 Nonlinear Theory versus Linear Theory: The Nonlinear Wave
Equation
To correctly wnte and derive the nonlinear equation descnbing the propagation of
an ultrasonic wave in a crystalline lattice, one should begin with the definition of the
elastic potential energy in terms of strain by means of the second and third order elastic
constants (M. A. Breazeale 1992):
1 1 WE) = - x CC~,~E, ,E~ +- & , m ~ , ~ , ~ m n ......
2! ,, 3! ij,, Equation 2.1
where @ is the lattice potential, eij are the elements of the strain tensor E, cij, are the
elastic constants that appear in the linear approximation of stress-strain theory, and
C ï j m are the third order elastic constants which are introduced by the nonlinear theory.
If attenuation is negligible, and if the higher order terms are small. one cm write
for the propagation of a longitudinal wave almg one principal direction, x. of a cubic
crystalline lattice (M. A. Breazeale 1992)
aZu aZu - KZ 7 + ( 3 K , + K,) -- P O ~ - a~ (a; 2) Equation 2.2.
Here, u is the displacernent dong the x-axis and K2 , KJ (combinations of the
second and third order elastic constants) are given in Table I .
Table 1.1
K2 , K3 as combinations of the second and third order elastic constants
2.2 Nonlinear Effects
2.2.1 Second Harrnonic Generation
One of the nonlinear effects which has been investigated intensively in recent years is the
second harmonic generation. One could write the solution of Equation 2.2 in the
following form:
u = A, sin(kx-ot)-P~:k'xcos2(kx-oi) Equation 2.3
which shows that an initially sinusoidal longitudinal ultrasonic wave in a solid produces a
second harmonic whose amplitude is proportional to the nonlinear parameter P (M. A.
Breazeale 1992). Here A, is the amplitude of the original wave; k, O are the wave
number and the frequency of the wave.
2.2.2 Nonlinear Wave Interactions: General Study
One cm get a physical understanding of how a nonlinear interaction occurs by
studying the response of a one dimensional resonating system to a harmonic driving force
(Main, 1984). For any slightly nonlinear system. the displacement u can be expressed as a
geometric series in ternis of a general excitation force, F,
u = â ~ + b ~ ' +cF~+... Equation 2.4
where a, b, c , are constants (b, c, ... small in agreement with the srnaIl nonlinexity
assumption). If F is a single harmonic force. we can put F = F, cos(ot), where o is the
frequency of the oscillation. If we consider the effect of two coherent driving forces with
different frequencies, w > w2 , the total driving force can be written
F = FI cos(o, t ) + E cos(ol t )e iot Equation 25 .
The relative phase constant cp rnakes no difference to the following development and finai
result, and is therefore taken as zero. Funhermore, for simplicity. we assume that only the
linear and quadratic terms in Equation 2.4 are significant. Substituting Equation 2.5 in
Equation 2.4 then gives
u = a ( ~ , coso, t + F2 cosoz t ) + b ( ~ , coso, t + F2 cosw,t)'+.. . Equation 2.6.
The first half of this expression is already familiar from the linear case: to investigate the
squared term, it is expanded to give:
Equation 2.7.
Two new components appear in Equation 2.7: one based on the sum of o +a 1 2
and one based on the difference a l - O2 . An energy transfer between the vibration
modes has taken place due to the inclusion of the quadratic terms in the calculations.
2.2.3 Parallel Waves: Nonlinear Interaction
To explain the interaction of two parallel longitudinal waves of frequencies a,
and oz, quantum physics theory must be applied. According to this theory, a
macroscopic plane elastic wave consists of the presence of a very large number of
phonons of a particular wavelength in the atomic lattice.
In the following development, only the generation of a second order harmonic of
frequency o, = o, + o, (corresponding to wave number k = k + k7 ) is described. It is - 3 1 -
assumed rhat the dispersion of the medium is of a normal type (Le. o is a simple function
of k ). Let r represent the time period over which wave 1 interacts with wave 2. The
probability P per unit time that a phonon from wave 1 interacts with a phonon from wave
2 to produce a phonon of wave number k is given by (S. Simons 1963. Zirnan 1960) 3
P = Y k l k l ( k I + k. )N,N.r Equation 2.8.
The numbers N , . N. are the numbers of phonons corresponding to the frequencies o I
and o, , respectively. Y is a parameter dependin; on the velocities and directions of iI
phonons, together with the density and anhannonic behavior of the medium.
If the interaction has occurred for time r. the intensity of the created acoustic wave k,
r
will be proportional to JPdt ; that is. proportional to O ($1.
2.3 Experimental Evidence of Nonlinear Wave Generation
Gedroits and Krasilnikov (1962) were the first researchers to report experimental
evidence that nonlinear effects were observable in solids using conventional ultrasonic
equipment. Their experiment involved the detection of the wave fom distortion when an
initially sinusoidal wave propagated through several different specimens. Independently,
F. R. Rollins (1965) reported nonlinear interactions in a variety of cases involving both
transverse and longitudinal angled beams.
S . Simons (1963) showed theoretically that, under suitable conditions, nonlinear
interactions may be expected between acoustic phonons travelling in the same direction.
Such interaction was experimentally studied by Mahler ( 1963) using nuclear resonance
techniques. The same type of interaction but between parallel photons was also observed
with high intensity waves in a non-linear medium by Franken and Ward (1963).
Some work has been done in studying 2 ~ 2 . 5 % Nb material propenies using
nonlinear phenornena. Alers G. and Molers M. (1991) investigated the variation of the
speed of shear ultrasonic waves in two Zr-2.5% Nb pressure tube specimens having
different hydrogen contents, as a function of temperature and extemal pressure. It was
found that the dependence of ultrasonic velocity on pressure was dependent on the
presence of hydrogen, but the limited number of specimens investigated prevented a
thorough anaiysis of the results.
Moreau A. et al. (1995) studied the second harmonic generation in the same
material. The nonlinear parameter P was measured for a number of pressure tube samples
having different concentrations of hydrogen using a Michelson interferorneter to detect
the fundamental and second harmonic acoustic fields. However, the sarnple-to-sample
variations were only slightly larger than the experimental uncertainties; therefore, no
significant correlation between the hydrogen content and the values of the nonlinear
parameter could be found.
In general, nonlinear acoustic measurernents are challenging because the nonlinear
effects are srnail. However, in many cases, it was observed that the nonlinear properties
are correlated to variations in the mechanical behavior. Therefore, an NDE technique for
detecting and evaluating the hydride content of Zr-2.58 Nb pressure tube material could
be based on measuring iis nonlinear characteristics .
2.3 Hydrogen in Zirconium
In general, the fabrication of Zr alloy components is strictly controlled so that the
hydrogen content in finished products has the acceptably low lirnit of less than 10 ppm
for CANDU pressure tubes. in power reactors, however, the zirconium alloys are used in
contact with water and, due to the reaction
Zr +2H20 + ZrOz +Xi2,
large quantities of hydrogen are produced. The Zr-hydrogen phase diagrarn in Figure 2.1
shows that zirconium alloys can significantly absorb this hydrogen, up to even 5000 ppm
in the p phase at temperatures > 500°C (C.E. Ells, 1974).
The solubility of hydrogen in the alloys decreases rapidly with decreasing
temperature (Figure 2.2, B. Cox and al.. 1983): at operation temperatures (approx. 3ûû°C)
any amount of hydrogen up to 100 ppm is in solid solution, but as the temperature falls,
the excess hydrogen precipitates as a hydride phase (hydrogen platelets). Virtually ail
zirconium alloys contain precipitates when cooled to room temperature, and at this
temperature there are three phases of Zr alloys, y (face centered tetragonal, c/a> l), 6 (face
centered cubic) and E (face centered tetragonal, c/at 1).
The hydnde phase has fundarnentally different properties than ail three phases of
the Zr-Nb alloys. The hydride phase generally exhibits low ductility at low temperatures,
and hence under some conditions has a deleterious effect on the mechanical behavior of
Zr alloy materials. These negative effects are particulad y evident at normal temperatures
of reactor operation (approx. 300aC), where the hydrogen concentrations usually present
in the Zr alloys (up to 200 ppm) can have a significant embnttling effect on pressure
tube material.
Once hydrogen enters the Zr material it diffuses up a stress gradient or down a
temperature gradient. Whenever the concentration reaches the solubility limi t, hydndes
platelets form at the grain boundaries or intragranulariy. Factors such as the texture of the
Zr alloy or the presence of any residual stress can significantly influence the general
orientation of the platelets. A case of platelets oriented in bands by through-wall
variations in the texture is shown in Figure 2.3.1 while Figure 2.3.2 illustrates platelets
having a highly preferential orientation in the Zr alloy matenal as a result of a uniform
texture. For most reactor applications, the orientation of the platelets in the material is a
cntical parameter, due to the fact that platelets largely aligned perpendicular to the tensile
axis can induce cracks during the heating up - cooling d o m thermal cycles of the reactor
core. In particular, the principal stress direction in pressure tubes is circumferential,
hence, hydndes in the radial-axial planes are highly detnmental to the mechanical
properties of the material.
The present work is aimed at detecting the influence which the hydrogen content
might have on the lattice potential and, according to the theory, on the efficiency of
generating nonlinear effects. Parameters such as the size and the orientation of the
hydride platelets are not expected to influence the nonlinear generation process and, as a
result, are not of concem in this experiment.
.J .O rn m a Y ) 6 0 ? 0
AI- hrcoai *n
Figure 2.1 Zirconium - Hydrogen phase diagram
8 0 L _ - _ _ BAND INCCUDES ALL DETERMINATIONS
/
Temperature (OC)
Figure 2.2 Solubility of hydrogen in Zircaloy
Figure 2.3.1 Bands of randornly oriented hydrogen platelets in
Zr-2.5% Nb
Figure 2.3.2 Platelets with highly preferential orientation in
Zr-2.5% Nb
Chapter 3. Experimental Setup
The objective of this experimental work was to evaiuate the nonlinear interaction
of two ultrasonic waves, with reference to the theory outlined in Chapter 2. The basic
technique consisted of measuring the amplitude of the second order harmonic
corresponding to a frequency equal to the sum of the frequencies of two interacting
waves. In particular, the purpose was to investigate whether there is any correlation
between the amplitude of this harmonic and the hydrogen concentration in the pressure
tube material Zr-2.5%Nb.
This chapter is divided into the following sections:
Section 3.0 gives an overview of the experimental system and its operation.
Section 3.1 describes the main experimental setup hardware, and Section 3.2 discusses
the main characteristics of the piezoelectnc crystals, delay lines and the problems
associated with their implementation. Section 3.3 describes the bonding technique and the
mechanical devices used for bonding the crysrals, while Section 3.4 describes briefly the
Zr-2.5%Nb pressure tube material and the geometric characteristics of the specimens.
Section 3.5 outlines the details of the data colIection and Section 3.6 describes
supplementary tests performed to better understand the nonlinear interaction. Section 3.7
shows how the data was analyzed to determine the magnitude of the nonlinear effect
under investigation.
3.0 Overview of Interaction Process
Two tone burst ultrasonic pulses are introduced into a specimen with opposing
directions of propagation, as shown in Figure 3.1. The first wave (of a relatively high
frequency, o ) is introduced from the top face into the specimen; when it starts reflecting 1
from the bottom face of the specimen, the second wave, having a lower frequency
( O < O ), is introduced at the bottom face. The two waves are then traveling in paraIlel 2 1
directions and interacting with each other. The result is received at the high frequency
piezoelectric crystal at the top face and sent on to the electronics for analysis. According
to theory, this signal should have frequency components centered at o, , 04, and
C03=01 f CO2.
3.1 Experirnental Setup; Main Components
Two key components in the experimental setup shown in Figure 3.1 were two
pulse generators and receivers, mode1 Matec 7700. The lower frequency instrument had a
Model 760V R.F. plug-in pulse generator. tunable in the 10-95 MHz range; the other
generator heceiver had a Model 765V R.F plug-in pulse generator, adjustable in the 90-
300 MHz range). These pulse generators were capable of producing tone burst waves of
high voltage (600-80 V, depending on the external load) and adjustable pulse duration
(up to 100 ps) to excite piezoelectric crystals mounted on the Zr-2.5% Nb specirnens. In
this project, the high frequency pulse generator acted both as generator of the high
frequency sound wave. and as receiver for the expected second order harmonic wave. Due
to the fact that the voltage levels produced by the pulse generators were very high, fixed
attenuators of various values were mounted in series with the pulse generators in order to
control the amplitude of the tone burst signals and avoid saturating components of the
experimental system. These attenuators could operate at frequencies up to 2 GHz and
their values varied between 2 and 20 dB.
The delay generator controlled the timing sequence of the entire experirnent. It
had 4 adjustable time delay outputs with values between 0-10 p, and a resolution of O. 1
P-
To link the various electronic components. regular 50 R cables (50 cm) with BNC
connectors were used. The 50 cm cable length was chosen to prevent the cables from
becoming active circuit components at high frequencies. A "TV connector connected the
high frequency pulse generator to both the high frequency piezoelectnc crystal and the
receiving module of the Pulse Generator 1 (refer to Figure 3.1). The 'T' connector
introduced an impedance mismatch between the pulse output and the cabling; therefore a
50 R impedance adapter (or power splitter) was built to balance the circuit.
An adjustable narrow band pass filter having a 90-300 MHz range was used to
isolate the second harmonic component of the received signal. and allow measurement of
its amplitude. The filter output was fed to a digital oscilloscope, where key components
of the signal were digitized and sent to a personal cornputer for analysis.
3.2 Piezoelectric Crystals and Delay Lines
Lithium-Niobate piezoelectric crystals were used for generating longitudinal (36
degree rotated Y cut) and shear (41 degree X cut) ultrasonic pulses. The nominal resonant
frequency values were 20 MHz and 30 MHz for the longitudinal crystals, and 20 MHz for
the shear crystals. Each crystal was driven at either its third or fifth harmonic frequency
by one of the two Matec pulse generaton. The crystals were 0.635 mm in diameter, gold
plated and overtone polished, having two chrome electrodes in order to connect thern to
the electronics.
To aid in the temporal resolution of the ultrasonic echoes from the transmitted
pulses, and also for producing consistent repeatable acoustic coupling between
piezoelectric crystals and specimens, the crystals were bonded ont0 delay lines which in
tum were bonded to the Zr-2.5% Nb specimens. These delay lines were quartz cylinders
having a length of 25 mm and a diameter of 15 mm.
3.3 Bonding Technique
The bonding agent chosen for linking the crystals to the delay lines, and the delay
lines to the specimens, was Salol (Phenyl Salicylate). The physical properties of Salol
rnake it very suitable for fabricating bonds of repeatable quality (i.e. it is solid at room
temperature, melts/solidifies at 47OC. has a high viscosity and has a very good acoustic
transmission properties in the solid state).
During prelirninary expenments, it was found that the repeatability of a Salol
bond was significantly influenced by factors such as the quantity of Salol used and the
pressure applied during solidification. In order to control these two parameters, the m a s
of Salol was carefully controlled and two speciai bonding jigs were designed and
manufactured, as shown in Figure 3.2 and Figure 3.3. The first jig was used for bonding
the ultrasonic crystals to the delay lines. whereas the second one was used for bonding the
delay lines to the specimens. For ultrasonic measurements on a series of specimens it was
expedient to pennanently bond crystals onto delay lines, and to evaluate the 2 ~ 2 . 5 % Nb
specimens by only destroying and remaking the relatively simple delay line/specimen
bonds.
3.3.1 Crystal-To-Delay Line Bonding Procedure
Due to the fragility of the piezoelectric crystals and their small diameter (0.635
mm), the crystal to delay line bond was found to be the most critical. The following
procedure was therefore developed.
A srna11 crystal of Salol (approxirnately 0.01 mg) was placed on one face of the
delay line, which was then heated to 60°C for 15 minutes in an oven. The delay line. with
melted Salol covering about 3 mm2 on one end. was then put into the bonding frame (Fig.
3.2). The piezoelectric crystai was placed on top of the liquefied Salol and pressure was
applied by rotation of the mbber/screw rnechanism until the mbber tip was compressed
by 3 mm. The assembly was left to cool for a period of 10 minutes, sufficient time for the
specimen to reach room temperature. Solidification of the liquefied Salol was then
initiated by touching it with a piece of crystalline Salol. Another waiting period of 5
minutes was then taken for the solidification front to propagate through the mass of Salol.
The crystai-delay line assembly was taken away from the jig. and was then ready to be
bonded to a Zr-2.5%Nb specimen.
The procedure was repeated for one crystal of each type (20 MHz longitudinal, 20
MHz shear, 30 MHz longitudinal), yielding 3 delay line/crystal assemblies.
3.3.2 Delay Line-to-Specimen Bonding Procedure
Once a single piezoelectric crystal of each type was bonded ont0 a delay line, the
next step was to bond combinations of two crystal/deiay line assemblies onto a Zr-
2.5%Nb specimen. A mass of 0.5 mg of Salol was placed on the specimen of interest,
which was then placed in the oven for 15 minutes at 60°C. Then the specimen was
inverted (the mass of Salol previously applied was prevented from dripping by surface
tension), and a second 0.5 mg of Salol was placed ont0 the opposite face. After 15 more
minutes the specimen was removed from the oven and a delay line was placed over each
pool of Salol. The specimen waç then ready for the final bonding step.
The assembly consisting of two delay lines. piezoelectnc crystals, and specimen
was quickly placed in the bonding jig s h o w in Fig. 3.3. A pressure of 27 N was applied
to the assembly by rotating the screw into the spnng mechanism. After a cooling time of
10 minutes. the solidification of the two layers of Salol was initiated using a small crystal
of Salol. In 5 more minutes. the assembly was ready to be used in experiments.
3.4 Pressure Tube Specimens
The analyzed specirnens were 5 flattened and machined sarnples of Zr-2.5%Nb
pressure tube, which had been infused with the following nominal levels of hydrogen
(measured by weight): O ppm, 60 ppm, 100 ppm. 150 ppm and 200 ppm. The dimensions
of the specimens are given in Figure 3.4. The specimens were provided by Ontario
Hydro; the accuracy and unifomity of the quoted hydrogen concentrations in each
specimen were not specified in the reports accompanying them.
The specimens were minor polished using diamond paste. The final roughness of
the surfaces was less then 1 Pm, as measured by a profilorneter.
3.5 Assessrnent of Experimental Setup: Verification of Nonlinearity
Phenornenon
Three tests were performed in order to prove that the predicted second harmonic
generation was indeed taking place as expected. In al1 these three (3.5.1-3.5.2) tests two
longitudinal ultrasonic waves were sent into the material and the result of the nonlinear
interaction between them was a longitudinal wave as well. The first test was used to
venfy that received signal components with frequency w, = a, +oz were due to
nonlinear interaction, and not artifacts of the experiment equipment and setup. The
second and third tests were used to confirm that this non-linear interaction took place
within the Zr-2.5% Nb specimen. and not in the delay lines.
These tests are described in the following three subsections.
3.5.1 Ftequency Combination Test
As described in the previous Sections. when two parallel ultrasonic waves of
frequencies o, and o, travel in the same space and tirne. they are expected to interact
with each other to generate a second harmonic having the frequency a, = w, +a2.
The basic idea behind this test was to compare the spectral composition of the
received signal when only one narrow band wave was sent into the specimen. against the
received signal when two waves of frequencies CO, and 0: were sent into the specimen.
First, the low frequency pulse generator was switched off. The high frequency
generator and upper piezoelectric crystal (Figure 3.1) were used to send tone burst signals
with f, = m,/27t = 103.5 MHz into the Zr-2.5% Nb specimen with hydrogen concentration
of 100 ppm. The signal reflected by the bottom surface of specimen was received back at
the upper crystd, band pass filtered, and sent to the oscilloscope and cornputer. The
signal spectrum is displayed in Figure 3.5.1, and shows that the equipment is operating as
expected. A prominent peak is seen at 103.5 MHz; apart from very low level noise, no
other signai components are visible.
This procedure was then repeated with the low frequency system switched on, and
the high frequency system switched off. No adjustments were made to any of the settings
on equipment such as pulse generators or filter. The received signal spectrum, plotted in
Figure 3.5.2, again shows the equipment operating as expected: a strong peak with small
side lobes is seen at fi = = 65.9 MHz. Linear upper harmonic of the fundamental of
the piezoelectric crystal are faintly visible in the spectmm.
The important feature to note about Figures 3.5.1 and 3.5.2 is that no significant
signal energy is received at f3 = W/2a = 169.4 MHz. where Q = + a.
The spectrum for the case when both waves at frequencies oi and are sent into
the specimen is plotted in Figure 3.5.3. Equipment settings such as the filter range, pulse
voltages, pulse duration, and damping controls were not changed from the values used to
generate Figures 3.5.1 and 3.5.2. It can be noted that the f, and f2 components are still
present. However, a third significant spectral component, having a frequency f3 = f, + B =
169.4 MHz, is now present as well. The logical explanation is that this spectral
cornponent is generated by the interaction between the high and low frequency signals
since it was not present in any of the individual spectra shown in Figure 3.5.1 or Figure
3.5.2. This third peak is not an artifact generated by imperfect signal processing
equipmen t.
3.5.2 Delay Time Test
The second test consisted of varying the tngger time of one of the input waves
relative to the other. The test was mn in order to ensure that the nonlinear interaction
occun only when the two waves are propagating in the same space and time in the Zr-
2.5% Nb specimen.
The lengths of both high frequency and low frequency pulses were adjusted to the
minimum duration allowed by the pulse genentors, i.e.. approximately 0.6 p. Given that
the thickness of the sample is approximately 3.1 mm. and the speed of sound for a
longitudinal wave in Zr-2.5% Nb is about 4.7 mm@, the high frequency longitudinal
pulse took 1.32 p to propagate through the sample. Let to = O be the reference tirne when
the high frequency wave was first launched into the specimen.
The Ieading edge of the low frequency wave was launched into the specimen at a
delay time t,. Initially, t1 was set to equal the exact moment when the leading edge of the
high frequency wave started reflecting against the back wall, which is half the round trip
time, tr= 0.66 p. Two perfectly overlapping longitudinal pulses, both of 0.4 ps duration,
are then propagating through the sample and interacting with each other.
To study what happens when one wave is delayed with respect to the other such
that the two waves do not overlap entirely, the delay time t1 was increased in steps of O. 1
p with respect to the high frequency pulse. The result is illustrated in Figure 3.6. and
shows that the amplitude of the nonlinear harmonic decreased when the pulse interaction
time decreased. When t, reached approximately 1.26 p, there was no overlap in space
and time of the two input waves. At this point. the second order harrnonic was no longer
visible in the received signal.
3.5.3 Direct Bonding Test
The third test aimed to provide additional evidence that the nonlinear interaction
occurred predominantly in the Zr-2.5% Nb specimen and not in the delay lines. The test
consisted of bonding the piezoelectric crystals directly ont0 the specimen, without any
deIay lines. Due to the fact that in this case the nonlinear interaction occurred in the near
acoustic field of the transducer, even small imperfections in the bond produced a very
large deviation from the circular symmetry of the propagation pattern. However. after
repeating the bonding procedure several times, an adequate bond was obtained and the
100 ppm sample was analyzed for the following nonlinear harmonic combination:
Longitudinal (104 MHz) + Longitudinal (59.5 MHz) - Longitudinal( 163.5 MHz).
The result is plotted in Figure 3.7 and provides clear evidence of the generation
of a significant nonlinear peak in the absence of the delay lines. This shows that the
observed nonlinear effect occurs even when no delay Iines are present. i.e., it occurs
inside the Zr-2.5% Nb specimen. It is noted, however. that it is preferable to use the delay
lines when characterizing the 2 ~ 2 . 5 % Nb specimens. as the delay lines help with
temporal resolution and pulse shaping.
3.6 Data Collection
For a given specimen and combination of piezoelectric crystals (e-g. longitudind-
longitudinal or longitudinal-transverse). the following data collection procedure was
adopted. Each crystal was independently driven at its third or fifth harmonic by
appropriately tuiiing the output frequency of the corresponding pulse generator. By setting
the central frequency of the narrow high p a s band filter to the sum of the low frequency
plus high frequency value, other undesired frequencies were partial1 y fil tered out. The
first ultrasound echo signal received by the upper piezoelectric crystal in Figure 3.1. was
digitized at a sampling rate of 700 MHz and stored for further anaiysis.
During the data collection procedure the time length of the high frequency pulse
was adjusted to the minimum duration allowed by the corresponding pulse generator, i.e..
approxirnately 0.4 p. In order to ensure that the nonlinear interaction was produced with
high efficiency within the specimen. the time length of the low frequency pulse was made
much longer, i.e., approximately 6 p.
As shown in Section 3.1, fixed attenuators were used to damp the generated
pulses. This helped to avoid saturat ing the di fferent setup components; the values used
were a function of the frequencies of the pulses (lower frequencies needed higher
attenuation values), and they varied between 5 and 25 dB.
The specimen which had been tested was then replaced with another one having a
different concentration of hydrogen. This switch was managed by destroying and
remaking the delay linekpecimen bonds. Main taining precisel y the same tuning for the
instrumentation. the data acquisition procedure was repeated for al1 five specimens.
Three types of wave interaction were studied, each of them being attempted under
identical conditions for the entire set of five pressure tube specimens. Each test sequence
was repeated at least three times for each of the five specimens. The three types of wave
interaction are listed below:
1. Longitudinal ( 103 MHz) + S hear (59.5 MHz) - Longitudinal( 162.5 MHz);
II. Longitudinal (97 MHz) + Longitudinal (60 MHz) - Longitudinal( 157 MHz);
m. Longitudinal ( 15 1.5 MHz)+ Longitudinal (29.5 MHz) --+ Longitudinal( 18 1 MHz).
3.7 Data Analysis
To evaluate the amplitude of the nonlinear harmonic generation effect, frequency
domain analysis was used.
With respect to the frequency spectrum shown in Figure 3.5.3. let X, be the
amplitude of the high frequency peak, X2 the amplitude of the low frequency peak and Xt
the amplitude of the nonlinear second order harmonic. For the purpose of the data
analysis, XI, X2, are used as relative indicators of the total strength of the input signais,
and X3 for the strength of the nonlinear harmonic. It should be noted in Figure 3-53. that
Xl and XÎ amplitudes are highly suppressed due to fact that the central frequency of the
band pass filter is set to @=~>1+&, and strongly attenuates frequencies in the
neighborhood of a, and &.
As descnbed in Section 3.3, a bonding procedure was established in order to
produce the most repeatable bonds possible. However. the most critical factor for
obtaining significant measurements was still found to be the quality of the delay
line/specimen bonds. (The piezoelectric crystaVdelay line bonds do not influence the
relative amplitude of X3 versus hydnde levels, as those particular bonds are common to
ultrasonic rneasurements on al1 five Zr-2.5% Nb specirnens).
A supplementary source of enor in the results may be a non-uniform distribution
of hydrogen in the samples. To minimize any effect of such variations. the series of
measurements were repeated at least three times for each specimen, at slightly different
locations near the central area of the specimens.
Dunng the experimental work. it was evident that inadequate delay line-to-
specimen bonds could attenuate the amplitudes XI and X2 of the input waves. However,
due to the fact that the amplitude of the second order h m o n i c component X. is directly
linked to the amplitudes of the input waves, Iower X1 and X2 levels corresponded with a
lower X3 amplitude. In fact, the bonding jigs shown in Figure 3.3 generated delay line-to-
specimen bonds with an acoustic transmission efficiency that was repeatable to within a
few percent. However, to compensate for the small amount of variability in this bond, X3
was nomalized with respect to the high and low frequency amplitudes X1 and X2 for each
x3 of the acquired signals. The normalized ratio - was then plotted against the x,x2
hydrogen concentration for each particular sample. The results are shown in Chapter 4.
Figure 3.1 Experimental setup
Cornputer
Delay
Pulse Generator and Receiver
1 (90-300 MHz)
Sampie
Crystal
-7- Crystai
Attenuator - - - - - - - - * - - - - - - . - - - _ _ _ _
Pulse Generator
Generator b 2
(10-90 MHz)
Figure 3.2 Crystal ont0 delay line bonding jig
Piezoelectric crystd ___--------
Figure 3.3 Delay line ont0 specimen bonding jig
al01 ------ 1~2.5% - - -__ Nb Specirnen
iezoelectric Crystal -----
Figure 3.4 2 ~ 2 . 5 % Nb Pressure tube specimen
Axis of ultrasonic testing
Figure 3.5.1 Received signal. corresponding to input fi = 103.5 MHz
from high frequency pulse generator
Xi (arbitrary units)
Frequency (MHz)
Figure 3.5.2 Received signal, corresponding to input f2 = 65.9 MHz from low frequency
pulse generator
Xi (arbitrary units)
160 180 200
Frequency (MHz)
Figure 3.5.3 Received signai. corresponding to input f,+f, = 103.5 + 65.9 M H z
Amplitude of Received Signal (arbitrary units)
two peaks attenuated
Frequency (MHz)
Figure 3.6 Amplitude of nonlinear effect versus delay time
for triggenng of low frequency pulse
i
1 0.66 0.76 0.86 0.96 1 .O6 1.16 i
1.26
! Delay Tirne (microseconds)
Amplitude of Figure 3.7 Received signal with no delay lines Received Signal (arbitrary units)
Frequency (MHz)
Chapter 4. Results and Discussion
4.1 Results
As described in Chapter 3. when the interaction of two ultrasonic waves occurs
within the pressure tube material, a nonlinear harmonic is generated. The nominal
amplitude, X3 , of this signal component was measured in the frequency domain and the
result was normalized wirh respect to the amplitudes of the signal inputs X, and XI.
The electrical components of the system have a significant frequency dependence,
therefore it is not possible to compare the absolute magnitudes of the three spectral
components X,, X2 and X3. However, it is possible to measure any dependence of the
on the hydrogen content in the five Zr-2.5% Nb specimens. This parameter - X J 2
relative dependence is shown in Tables 4.1.1 - 4.1.3. and plotted in Figures 4.1.1 - 4.1.3.
Table 4.1.1 Normalized magnitude of nonlinear effect for interaction
Longitudinal ( 1 O3 MHz) + Shear (59.5 MHz) + Longitudinal(l62.5 MHz).
Material Hydrogen Concentration
x3
XlX2
(relative values)
100 ppm -- -
150 ppm 200 pprn
Table 4.1.2 Normalized magnitude of nonlinear effect for interaction
Longitudinal (97 MHz) + Longitudinal (60 MHz) -rtongitudinal( 157 MHz)
Waterial Hydrogen O PPm 60 PPm Soncentration
:relative values) 0.574 0.541
100 ppm 150 ppm 200 ppm
Table 4.1.3 Normalized magnitude of nonlinear effect for interaction
Longitudinal ( 15 1.5 MHz) + Longitudinal (29.5 MHz) -Longitudinal( 18 1 MHz)
Material Hydrogen Concentration
(relative values)
'0 PPm
0.755
0.714
0.889
0.867
60 ppm
0.830
0.934
0.771
0.803
150 ppm
1 .O00
0.979
0.827
0.787
100 ppm
0.899
0.91 2
0.929
0.828
200 ppm
0.882
0.845
0.969
0.909
X Figure 4.1.1 Norrnalized magnitude of nonlinear effect, for interaction
XJ,
Longinidinal ( 1 O3 MHz) + S hear(59.5 MHz)- Longitudinal( 162.5 MHz)
x3 Figure 4.1.2 Normal ized rnagni tude of nonlinear effect, - for interaction X,XI
Longitudinal (97 MHz) + Longitudinal(60 M H z ~ L o n g i t u d i n d ( 157 MHz)
X Figure 4.1.3 Nomalized magnitude of non 1 inear effec t. -t for in teraction
XJ,
Longitudinal( 15 I .5 MHz) + Longitudinal(29.5 MHz)+Longitudinal( 18 1 MHz)
O PPm 60 pprn 100 ppm 150 pprn 200 ppm
Hydrogen (PPW
4.2 Discussion
For the experimental work. it has been highlighted that the major challenge to be
overcome was the production of bonds of repeatable quality; therefore the bonding
procedure descnbed in Chapter 3 was applied. However. due to the high frequencies of
the ultrasonic pulses used in the experiment, the inherent imperfections in the quality of
the bonds were partially responsible for the scatter of the levels of the input pulses XI and
X ,; the scatter was caused by the variability in quality of the bonds between the delay
lines and specimens, since the piezoelectric crystal-to-delay line bonds were kept intact
for ail measurements. It can be noted that a first order correction for variabiiity in crystal-
to-delay line bond was achieved through norrnalization of the amplitude of the second
order harmonic X3 by the input amplitudes X, and X ,.
As explained in Chapter 3. three wave combinations were attempted, and it was
shown that the amplitude of the nonlinear harmonic was higher for the Longitudinal +
Longitudinal interactions than for Longitudinal + Shear interaction. This result is due to
the fact that the longitudinal piezoelectric crystals have a higher efficiency in generating
ultrasound pulses than the shear ones, and the magnitude of the nonlinear harmonic is
directly proportional to the power of the waves involved in the interactions. In addition,
high frequency shear waves can suffer significant attenuation even over distances of a few
mm.
As c m be noted from Figures 4.1.1 - 4.1.3. the variations of the magnitude of the
nonlinear effect for each individual specimen were larger than the variations in mean
values among the five examined specimens. There was no clear, consistent trend of the
amplitude of the generated harmonic versus hydrogen concentration in the hydrided
specimens for my of the attempted wave combinations. This contrats to preliminary
work by at least one researcher indicating that such a trend might exist.
Results from the present project indicate that the lirnited scatter in the normdized
amplitude of the second harmonic may be attributed to factors such as bond repeatability,
surface roughness variations among samples or to actual spatial variation of the hydrogen
distribution within each specimen.
One reason for not detecting any correlation between the hydrogen content and the
amplitude of the nonlinear harmonic generation may be the fact that the measurements
were performed at room temperature. As shown in Chapter 2, at this temperature the
hydrogen is precipitated in the form of hydride platelets located at the grain boundaries.
The percentage of dissolved hydrogen is the same in al1 five specimens and it is this
dissolved hydrogen which is enpected to change the lattice potential. The platelets do not
significantly change the material lattice potential, such that variations in the total
hydrogen content of the Zr alloy (as a matter of fact variations in the amount of
precipitated hydrogen) do not significantly influence the efficiency of generating a
nonlinear effec t.
Apart from the negative results of this work. the implementation of the nonlinear
harmonic characterization of pressure tubes in the field would be very difficult for
several reasons. High frequency ultrasonic measurements are subject to signifiant
experimental errors; in the high frequency range, any passive setup component can
become active, introducing an additional and often unknown impedance to the circuit
(Le., cables, connectors, and in the case of this experimental work, acoustic bonds). Also,
it is very difficult to transmit low-level high frequency elcctnc signals over significant
distances. This would be of particular concem in a nuclear generating station where the
cables are in high radiation fields which would significantly increase the noise level.
The wavelengths associated with the frequencies used in the experiment were
approximately 12 pm for the shear waves and 25 pm for the longitudinal waves. As
mentioned in Section 3, the specimens were mirror polished and the surface roughness
was less than 1 pm. As the ratio of roughness-to-wavelengh is less than 1: 10, it is
expected that the roughness would have a minimal effect on the transmission or scattering
of ultrasound. However, in a CANDU reactor. the pressure tubes have a significantly
higher surface roughness would pose a significant challenge to high frequency work.
Chapter 5. Conclusions and Recommendations
5.1 Conclusions
The purpose of this work was to investigate the feasibility of using the amplitude
of the nonlinear wave-wave interaction at frequencies above 100 MHz as an indicator of
the hydrogen content of Zr-2.58Nb pressure tube material.
The following sumrnarizes the results and conclusions:
1. An appropriate expenmental setup was built for testing the hydrided samples
using high frequency ultrasound. A nonlinear second order harmonic spectral component
was generated and was shown to occur within the Zr-2.557aNb specimens.
2. Two bonding jigs were designed and built. A reliable and repeatable novel
bonding technique was established for bonding very fragile high frequency piezoelectric
crystals onto delay lines. These delay lines were then bonded ont0 the specimens under
investigation. As a result, the amplitudes of the input ultrasonic pulses XI and X2 were
shown to be repeatable within a few percent.
3. Three different wave interaction combinations (Le. two frequency combinations for
the longitudinal-longitudinal interaction. and one for longitudinal-transverse) were
attempted. For the three combinations, the amplitude of the nonlinear harmonic was
measured in five Zr-2.510Nb pressure tube samples with levels of hydrogen ranging
up to 200 ppm.
4. No statisticall y significant correlation between the normalized magnitude of the
X 3 and the hydrogen concentrations could be found; the second order effect, XlX2
variations within each specimen were larger than the variations among the average
values for the five specimens. The sample population was not very large but was
adequate enough to indicate the absence of any trend.
5. The lack of positive results, and the practical difficulty in conducting high frequency
data collection in high radiation fields offer little incentive for pursuing this technique
for measuring hydride Ieveis in pressure tubes.
5.2 Recommendations for further work
Based on the results obtained in this project. it was concluded that the nonlinear
ultrasonic interaction investigated here is not suited for indicating hydrogen levels in Zr-
2.5% Nb material.
However, other related techniques could be attempted as well:
1. As underlined in Chapter 4. one of the reasons this detection technique failed is
that at room temperanire the hydrogen is largely not in the solid solution, but is present as
hydride platelets. Measurements at elevated temperatures are more promising due to the
fact that the dissolved hydrogen is expected to significantly change the lattice potential
and, consequently, the efficiency of generating nonlinear effects. There have been
previous reports showing measurable changes in the elastic modulus of Zr alloys with
hydrogen content at high temperature.
2. A promising method to keep the hydrogen in solid solution at room temperature
(such that hydrogen content variations change the efficiency of generating second order
effects) would be to fast quench the pressure tube specimens to room temperature.
However, it is not clear if the quench maintains the hydrogen in solid solution or the
hydrogen precipitates and produces very small hydride plaielets.
2. During the present work, only interactions between parallel waves were
studied; an interaction involving two angled waves may be more sensitive to the
hydrogen content. Such experiments have been atternpted and documented by several
researchers.
3. A simple technique which could be investigated would be to study the
modulation of a high frequency acoustic wave in Zr-2.5% Nb material, in which the
sound velocity varies under the influence of a strong low frequency "pump" wave. The
presence of hydrogen in rnetals such as Zr-2.5% Nb is believed to lead to increased
friction when transmitting an acoustic wave. Consequently, a pump wave could induce
intemal friction in the atomic lattice of the material and cause a perturbation in the
acoustic nonlinear properties. To study such phenornena, the experimental setup should
be similar to the one described in the present work. where the low frequency piezoelectric
crystal is bonded ont0 one side of the sarnple and the high frequency crystal ont0 the
other. The changes in the acoustic wave speed should be monitored as the purnp wave
power is increased. Since speed measurernents are fairly simple and accurate. the method
could be sufficiently sensitive to detect low hydrogen levels in 2 ~ 2 . 5 % Nb material.
References
1. A. A. Gedroits and V. A. Krasilnikov, "Finite amplitude elastic waves and deviation s
from Hooke's law", J. Exp. Theor. Phys., vol. 13, 1962, p. 1592.
2. A. Breazeale. "Nonlinear acoustics and how she grew", Review of Progress in
Quantitative Nondestructive Evaluation, vol. 1 1. edited by D. O. Thomson and D. E.
Chimenti, NY, 1993.
3. A. Moreau et al., "Linear and nonlinear acoustic characterization of Zr-Nb pressure
tube material for the CANDU nuclear reactor". CNRC-NRC Report, l995/i 0.
4. B. A. Cheadle, '"The physical metallurgy of Zirconium alloys". A.E.C.L., Chalk River
Laboratories, October, 1974.
5. B. Cox and al., "Effect of hydrogen injection on hydrogen uptake by BWR fuel
cladding", A.E.C.L. - Final Report, 1983, p. 1-3.
6. C. E. Ells, "Behavior of hydrogen in zirconium alloys", The physical metallurgy of
Zirconium alloys. A.E.C.L., 1974, p. 65.
7. C. S. Menon and R. Ramji Rao, "Lattice dynamics. third order elastic constants and
Iow temperature lattice thermal expansion of zirconium", J. Phys. Chern. Solids,
1972, vol. 33, p. 1325.
8. D. C. Hurley et al., "Experimental comparison of ultrasonic techniques to detmine
the nonlinearity panmeter", Review of Progress in Quantitative Nondestmctive
Evaluation, vol. 1 1, edited by D. O. Thomson and D. E. Chimenti, NY. 199 1.
9. Doug Mair, Private Communication, 1995.
10. F. R. Rollins, L. H. Taylor and P. H. Todd. "Ultrasonic study of three phonon
interactions. Experimental Results.", Physical Review, vol. 3A, 1964, p. 136.
11. F. R. Rollins, L. H. Taylor, "Ultrasonic study of three phonon interactions. Theory.",
Physical Review, vol. 136, 1964, p. 59 1.
12. G. L. Jones and Donald R. Kobett, "Interaction of elastic waves in an isotropic
13. G.A. Alers and M. Moles, "Measurements of the hydride content in Zr-Nb pressure
tubes by the third order elastic constants". Review of Progress in Quantitative
Nondestructive Evaluation, vol. IOB, edited by D. O. Thomson and D. E. Chimenti,
NY, 1991.
14. H. Douglas Mair, "Measurement of hydrogen in Zr-2.5% Nb using high accuracy
velocity ratio measurements", Review of Progress in Quantitative Nondestructive
Evaluation, vol. 1 1. edited by D. O. Thomson and D. E. Chimenti, NY, 1992, p. 1669.
15. 1. G. Main, "Vibrations and waves in physics". Cambridge University Press,
Cambridge, 1984.
16. J. D. Childress and C. G. Hambrick, "Interaction between elastic waves in an
isotropic solid", Physical Review, vol. 136, Number 2A, 1964, p. 4 1 1.
17.1. M. Ziman, "Electrons and phonons", Oxford. Clarendon Press, 1960.
18. John H. Cantrell and William Yost, "Nonlinear acoustic assesment of precipitation
induced coherency strains in aluminum alloy 2024". ", Review of Progress in
Quantitative Nondestructive Evaluation, vol. 15. edited by D. O. Thomson and D. E.
Chimenti, NY. 1996, p. 136 1.
19. K. Brugger, "Detemination of third order elastic coefficients in crystals", Journal of
Applied Physics, vol. 36, 1965, p. 768.
20. N. S. Shiren, "Nonlinear acoustic interaction in M g 0 at 9 Gdsec", Physical Review
Letters, vol. 1 1 , 1963, p. 3.
21. 0. V. Rudenko et al., "Problems in the theory of nonlinear acoustics", ". Sov. Physics
Acoustic, vo1.20, Nov. 1974, p. 272.
22. P. I. Kielczynski. A. Moreau and 3. F. Bussiere, "Determination of texture
coefficients in hexagonal polycrystalline aggregates with onhorhombic syrnmetry
using ultrasounds", J. Acoust. Soc. Am.. vol. 95. 1994, p. 8 13.
23. S. Simons, "On the mutual interaction of parallel phonons". Proc. Phys. Soc., vol. 82,
1963, p. 5.
24. Silvia Pangraz and W. Arnold. "Quantitative determination of nonlinear biding forces
by ultrasonic technique", Review of progress in quantitative nondestructive
evaluation, vol. 13, 1994, p. 1995.
solid ". The Journal of The Acoustical Society of Arnerica, vol. 1 , 1963. p. 35.
25. T. Bateman et al., 'Third order elastic moduli of Germanium", Journal of Applied
Physics, vol. 32, p. 928.
26. V. A. Krasilnikov, Hung Hsiu-fen and L. K. Zarembo, "Nonlinear interaction of
elastic waves in solids", Soviet Physics Acoustic, vol. 1 1. 1965, p. 89.
27. V. E. Nazarov and S . V. Zimenkov, "Modulation of sound by sound in metal
resonators", Sov. Physics Acoustic, Oct. 199 1. p. 538.
28. V. E. Nazarov, "Attenuation of sound by sound in annealed copper", Sov. Physics
Acoustic, August 199 1, p. 432.
29. V. E. Nazarov, "Interaction of elastic waves in media with a strong acoustic
nonlinearity", Sov. Physics Acoustic, Sept 1992. p. 493.
30. V. E. Nazarov, "Nonlinear damping of sound by sound in metals", Sov. Physics
Acoustic, Nov. 1991, p. 616.
3 1 . V. V. Lemanov and G . A. Smolenskii. "Nonlinear effects in the propagation of high
frequency elastic waves in crystals". Soviet Physics Acoustics. vol. 20, 1974. p. 259.
IMAGE EVALUATION TEST TARGET (QA-3)
APPLIED I M G E . Inc - = 1653 East Main Street - -. - Rochester, NY 14609 USA -- --= Phone: i l W482-0300 -- -- - - f a ~ : 71 61288-5989
0 1993. Appiied Image. Inc.. All Rqhrs Reserved