Conference PaperPDF Available

Correct sizing of reflectors smaller than one wavelength

Authors:
  • Vrana GmbH - NDE Consulting and Solutions

Abstract

In the field of ultrasonic testing there are two key questions: Which defects can be found and-in the case indications are found-do they restrict the use of the part? Regarding both questions, the prerequisite is a method for defect sizing. Over the last decades sizing methods were established like DGS (Distance Gain Size) or DAC (Distance Amplitude Correction) for defects smaller than the beam profile. Those methods utilize the echo amplitude and provide results which are proportional to the defect area. However, those approximations are only accurate for defects larger than one wavelength even that experience shows it can be applied for slightly smaller defects. With the progress of material technology and ultrasonic inspection the need to detect and size smaller defects is growing. Therefore, both for flat bottom holes and disc shaped reflectors the usability for small defects needs to be checked. In this publication, it is investigated how to correctly size small defects below one wavelength. Utilizing a grid-based simulation method the echo signals of cylinder and disc shaped reflectors of various sizes are calculated. By properly choosing the simulation method and grid it is ensured that all physical wave modes are included in the simulation and that the discretization error is negligible. A good correspondence between the simulation and classical defect sizing for defects larger than one wavelength is found. In the region between one quarter of a wavelength and one wavelength resonance effects are found, which result in classical defect sizing methods giving conservative results. In the region below one quarter of a wavelength classical DGS and DAC sizing leads to undersizing. This is discussed in detail and a formula for defect sizing is derived, which is applicable to small as well as large defects.
Creative Commons CC-BY-NC licence https://creativecommons.org/licenses/by-nc/4.0/
Correct sizing of reflectors smaller than one wavelength
Alexander Seeber1,3, Johannes Vrana2 & Hubert Mooshofer1, and Matthias Goldammer1
1 Siemens AG, Germany; hubert.mooshofer@siemens.com
2 VRANA GmbH, Germany, johannes@vrana.net
3 Ludwig-Maximilians-Universität Munich, Germany
Abstract
In the field of ultrasonic testing there are two key questions: Which defects can be
found and in the case indications are found do they restrict the use of the part?
Regarding both questions, the prerequisite is a method for defect sizing.
Over the last decades sizing methods were established like DGS (Distance Gain Size) or
DAC (Distance Amplitude Correction) for defects smaller than the beam profile. Those
methods utilize the echo amplitude and provide results which are proportional to the
defect area. However, those approximations are only accurate for defects larger than one
wavelength even that experience shows it can be applied for slightly smaller defects.
With the progress of material technology and ultrasonic inspection the need to detect
and size smaller defects is growing. Therefore, both for flat bottom holes and disc
shaped reflectors the usability for small defects needs to be checked.
In this publication, it is investigated how to correctly size small defects below one
wavelength. Utilizing a grid-based simulation method the echo signals of cylinder and
disc shaped reflectors of various sizes are calculated. By properly choosing the
simulation method and grid it is ensured that all physical wave modes are included in
the simulation and that the discretization error is negligible.
A good correspondence between the simulation and classical defect sizing for defects
larger than one wavelength is found. In the region between one quarter of a wavelength
and one wavelength resonance effects are found, which result in classical defect sizing
methods giving conservative results. In the region below one quarter of a wavelength
classical DGS and DAC sizing leads to undersizing. This is discussed in detail and a
formula for defect sizing is derived, which is applicable to small as well as large
defects.
1. Introduction
Indication sizing using ultrasonics is usually performed by echo dynamic or area
amplitude based sizing. For indications larger than the beam spread, echo dynamic
sizing (sizing by probe travel, e.g. -6 dB drop method) is used and for indications
smaller than the beam spread area amplitude based sizing methods are used (like DAC
or DGS).
Area amplitude based sizing methods compare the reflection amplitude of an indication
to the reflection amplitude of reflectors with known size, e.g. artificial reflectors like flat
bottom holes (FBH) or side drilled holes (SDH). After a correction for different sound
path lengths to the indication, the size of the indication is denoted in form of the
equivalent reflector size. Different area amplitude based sizing methods are used
depending on qualification of techniques on a location-by-location basis.
2
The most traditional methods used from the early days of ultrasonic testing employed
Distance Amplitude Correction (DAC) based on calibration using multiple flat bottom
holes machined into calibration blocks and some extrapolation based on the inverse
square law.
Already in 1950, five years after the start of ultrasonic testing (1), Kinsler and Frey
published their book about the fundamentals in acoustics (2) with a theoretical
calculation of the sound field of a piston source in the far field. Seki et al (3) took this
work a few steps further. Their work is the basis for all theory-based sizing methods.
In 1959 J. Krautkrämer published the Distance Gain Size (DGS or AVG) Method (4)
which is a method widely used in Europe. The DGS diagram (see figure 1) gives the
amplitude loss (gain) of the backwall and of different disc shaped reflector sizes (KSR
German: Kreisscheibenreflektor) and is plotted against the soundpath (logarithmic
scale). This is the gain necessary to bring reflector echoes to the same screen height.
The different curves within this coordinate system start with the backwall curve on the
top (low gain values) and the different KSR sizes in decreasing order. In the farfield the
backwall curve has a slope of 6 dB for doubling the sound path (1/s dependency) and
the KSR curves have a slope of 12 dB for doubling the sound path (1/s2 dependency).
The individual KSR curves are spaced by 12 dB for dividing the KSR size in half
(Df2 dependency). With this diagram it is not only very easy to calibrate the equipment
but also to size indications and to determine the sensitivity.
Figure 1. Conventional DGS diagram
with the backwall (BW) curve on top and different sizes of KSRs [mm] below
(In this case for a probe with round transducer with D = 23,1 mm, λ = 2,95 mm).
Equation 1 is the theoretical basis for the farfield information in the DGS diagrams, for
the inverse square law, and for indication sizing using DAC with FBHs. For a
monochromatic situation the gain V can be derived analytically by integrating over the
surface of a piston transducer (5, 6):
2
22
2
22
10 10
22 2
20log 20log 4
ff
DD
N
VD
Ds s
π
πλ

 
= = 
 





.
(1)
Hereby Df denotes the diameter of the FBH or KSR, s the soundpath, D the effective
diameter of the transducer, N the nearfield, and λ the wavelength.
0
20
40
60
80
100
120
140
10 100 1000
Gain V [dB]
Soundpath s [mm]
BW
16
12
8
6
4
3
2
1,5
1,0
0,7
3
This derivation uses a simplified analytic point source approach which assumes that the
Kirchhoff approximation holds. The Kirchhoff approximation basically assumes that the
scattered field of a reflector is generated by sources on the “illuminated” side with the
inverse amplitude of the incident field, and no sources on the shadow side. Because of
the Kirchhoff approximation, the echo amplitude of a reflector is proportional to its
illuminated area. However, it is a good approximation only if the reflector curvature is
small compared to the wave length. Obviously, this is the case for the inner area of a
disc or FBH but not for its edge. This means that the approximation can be used only for
larger reflectors, where the inside dominates over its edge. Consequently, the use is
possible only for defects not significantly smaller than the wave length (6, 7, 8).
Both KSRs and FBHs are models for indications and are alike, except that FBHs extend
in one direction all the way to the surface. This means that FBHs can also be seen as a
model for KSRs with the benefit that they can be machined. Meaning the abstraction
chain goes from real indications over KSRs to FBHs. Usually this difference between
KSRs and FBHs is insignificant. However, for the indication sizes discussed in this
paper they get important as section 3.2 shows.
With the enhancements in ultrasonic testing (9) and metallurgy the sizing of small
defects becomes increasingly important. Therefore, the questions arise:
How far can DGS, DAC and equation 1 be used?
How to extend sizing for small reflectors?
Standard ultrasonic simulation tools use a point source approach and are restricted, like
equation 1, by the Kirchhoff approximation. Experiments with small flat bottom holes
are challenging and it needs to be questioned whether small FBHs are a good model for
small KSRs.
2. Methodology
Goal of this work is to determine the reflection amplitude of defects (including defects
smaller than a wave length) by means of a physically accurate simulation. By physically
accurate it is meant that the simulation covers all physically allowed phenomena (and is
not restricted by the Kirchhoff approximation). 3D-EFIT was chosen, as it simulates all
physical wave modes possible in linear elastodynamics and allows to quantitatively
assess numerical dispersion (10). Hence the only constraint is linearity, which is
generally well satisfied in NDT.
2.1 Elastodynamic Finite Integration Technique (EFIT)
The basic equations of linear elastodynamics are the conservation of momentum
(Newton-Cauchy equation), the strain rate equation, and the material equations. Putting
these together the wave equations in their integral form specialized for isotropic,
homogenous media can be written as follows (10, 11):
: ( ,) { ( ,)} ( ,)
VS V
s T R t dV sym nv R t dS h R t dV= +
∫∫∫ ∫∫ ∫∫∫
(2)
ρ( ,) ( ,) ( ,)
V SV
v R t dV T R t dS f R t dV= ⋅+
∫∫∫ ∫∫ ∫∫∫
.
(3)
Hereby T(R,t) denotes the symmetrical stress tensor, v(R,t) the particle velocity vector,
h(R,t) the induced deformation rate tensor, f(R,t) the induced force density vector, s the
compliance tensor, and ρ the mass density at rest.
4
Figure 2. The dual orthogonal grid system used by EFIT (11). The elements of the velocity vector
and of the stress tensor are bound to different positions within an elementary cell.
EFIT discretizes the integral form of the wave equations in space and time so that they
can be calculated numerically (The differential form of the equations could be solved
with methods like the FDTD (Finite Difference Time Domain)). For the spatial
discretization a dual orthogonal grid system is used as shown in figure 2. The time
discretization of the velocity vector and the stress tensor are shifted by half a time step
against each other. To model reflectors boundary conditions are introduced. For a KSR
or FBH reflector stress free boundaries are placed on the surface of the reflector.
2.2 Accuracy and computability
Not only the physics of the wave propagation has to be simulated, but high amplitude
accuracy has to be reached at the same time. And the simulation effort in terms of
number of operations and memory usage – must be manageable. First, the discretization
must be fine enough to account for the smallest possible wave length (shear waves) at
the highest relevant frequency (center frequency plus upper part of bandwidth).
Secondly, the reflector discretization must be fine enough to accurately model its area as
the interest lies in the relation between defect area and echo amplitude. And thirdly, the
numeric dispersion must be small enough to ensure that the simulated signal shapes are
not distorted by numerical effects.
Considering a typical inspection scenario (steel, 2 MHz, band width 100%, sound path
100 mm), the 3D-EFIT requirements on the grid are:
( )
( )
min min min max
min max
//
/3
x x G c Gf
tt x c
λ
∆ ≤∆ = =
∆ ≤∆ =∆
(4
)
where x and t define the grid in space and time.
With an accuracy factor G of 10, a maximum frequency of 3 MHz (taking into the
bandwidth), and the shear and long wave sound speed of standard steel, the grid must be
100 µm spatially and 9 ns temporal or finer. The required relative accuracy p of the
reflector discretization is calculated from the ratio of defect area A over circumference
U:
()
()
/ /4
f
x p AU p D∆≤ ⋅ = ⋅
. (5
)
For a KSR with Df = 1 mm and a relative accuracy p of 2% the maximum grid size
calculates to 5 µm / 0.45 ns, which is quite an ambitious requirement. And finally, the
maximum simulated time is limited by the condition for avoiding numerical dispersion
(10).
5
2.3 Utilization of reciprocity
For a sound path length of 100 mm and a limitation of the simulated volume to a small
tube with 10 mm width the simulated volume would comprise 20k 2k 2k = 80G cells.
With at least 9 float values per grid cell this would impose a memory requirement of
2,9 TByte of RAM. Without even considering the number of computations it is obvious,
that a more economical way of calculation is needed.
As the interest lies in the far-field reflection coefficient of the defect only, the
simulation of the sound propagation over the long distance can be omitted. Instead a
plane wave is coupled into the EFIT simulation. This not only simplifies the simulation,
it automatically normalizes the result to the incident wave amplitude.
In analogy to the method presented in (12, 13) Auld’s reciprocity theorem (ART) is
used instead of simulating the propagation back to the probe. The ART allows
calculating the reflection coefficient change between two scenarios based on the fields
on a surface S enclosing the defect. The reflection coefficient refers to the electrical
signal of the transducer. Hence, if (1) a scenario with defect and (2) another one without
defect is considered, the echo signal E(t) of the defect can be calculated as (11, 12, 13):
(1) ( 2) (2) (1)
11
() .
4()
tS
E t FFT v T v T ndS
f
ω
ω


= ⋅ −⋅



∫∫
(7
)
The layout of the simulated volume is illustrated in figure 3. The defect is in the center
which imposes the stress-free boundary conditions. The defect is enclosed by the ART
box, which serves to capture the input data for equation (7). Outside the ART box there
is more simulated volume surrounded by a convolutional perfectly matched layer
(CPML), which is optimized to absorb incoming energy with almost no reflections. The
coupling plane, where the incident wave is introduced is just left of the CPML on the
right side.
Figure 3. Layout of the simulation volume (left) and example for a simulated reflection (right).
The incident P-wave travels from right to left.
3. Results
For the investigation how far DGS, DAC with FBHs, and equation 1 can be used
different sizes of FBHs and KSRs were simulated for an ultrasonic longitudinal wave
with a wavelength of 2,95 mm (2 MHz wavelength in steel). The largest KSRs and
FBHs had a diameter of 9 mm, the smallest 0,1 mm. Meaning the largest artificial
Dummy grid
CPML
Coupling plane
Reflector
ART-Box
Restriction free vol ume
6
reflectors are clearly bigger than the wavelength. The smallest on the other hand are
clearly smaller and should be a good indicator how to extend the theory.
3.1 KSRs
Figure 4 shows the simulation results for KSRs as red points together with the quadratic
dependency on the diameter Df as a black dashed line (the expected dependency
according to equation 1). In addition, figure 4 shows a cubic dependency on the
diameter Df as a red dashed line.
Figure 4. Quadratic (red dashed line) and cubic dependency on the diameter Df (black dashed line)
computed gain values for KSRs (red dots);
theoretical description according to equation (9) (thick line)
and equation (8) with Q = 1,5 (thin line slightly above the thick line and mainly visible around λ/4)
In the results three regions can be identified:
Between 1,5 (λ/2) and 9 mm the simulation results follow the known DGS
theory. This is the region of geometrical scattering, where the Kirchhoff
approximation holds.
Around 0,7 mm (λ/4) the simulation results are higher. Those results are created
by resonance effects and depend on the shape of the reflector.
For defects smaller than 0,5 mm (λ/6) the simulation results follow the cubic
dependency. The cubic dependency results of Rayleigh scattering (14) (not to
be confused with the well-known fourth-power dependency of the frequency for
Rayleigh scattering processes).
The following formula was found to match the complete simulation results well and is
shown in Figure 4 besides the simulation results (the basis for this equation is a heuristic
approach based on Bode diagrams):
3
2
2
10 2
41
20log 16 4
1
144
f
ff
D
i
VD
s
DD
ii
Q
λπ
λλ







=




++





. (8
)
0
20
40
60
80
100
120
140
0,1 110
Gain V [dB]
Df[mm KSR]
Df²
Df³
KSR
Theory (Q=1)
Theory (Q=1,5)
7
Hereby Q denotes the quality factor of the resonance effect. As the shape of a real
reflector is unknown a conservative solution needs to be chosen by ignoring any
resonance effects (Q = 1):
2
2
2
10 222
4
20log 4
16 4
ff
ff
DD
VD
s
D iD
π
λλλ



=


−⋅ + +


. (9
)
The difference in reflectivity of large (Df 2) and small (Df 3) KSRs is caused by the
relative size of an KSR in comparison with the wavelength. Figure 5 shows three
snapshots (after 0,25, 0,5 and 1,1 µs) of the displacement at the front and at the back of
the KSR for both a 3.0 mm and a 0.1 mm . KSRs larger than λ/2 see in the
beginning mainly a displacement of the front surface. KSRs smaller than λ/6 on the
other hand see a displacement of both the front and back surface. This is caused by the
wave enclosing the small KSR and moving it completely instead of exciting only the
top surface.
This is also the reason why large KSRs cause longer return signals than small KSRs.
Small KSRs just move with the exciting wave where the excitation of large KSRs
causes waves from the rim to the middle of the KSR.
Figure 5. All images show in blue the displacement at the front of an KSR and in red at the back (the 4
or respectively 14 stationary dots left and right of the reflector show the starting point)
top row: displacement of a “big” reflector with 3.0 mm (after 0,25, 0,5 and 1,1 µs)
bottom row: displacement of a “small” reflector with 0.1 mm (after 0,25, 0,5 and 1,1 µs)
For KSRs between λ/6 and λ/2 those different wave modes can interfere on the surface,
shifting the maximum height of the echo signal.
8
3.2 FBHs
Often the DAC calibration based on FBHs is used instead of DGS or to measure DGS
diagrams. As detailed in section 1 FBHs are like KSRs however they extend in one
dimension to the surface.
Figure 6 shows the simulation results for FBHs as red points together with the quadratic
dependency on the diameter Df as a black dashed line (the expected dependency
according to equation 1). In addition, figure 6 shows the cubic dependency on the
diameter Df as a red dashed line.
Figure 6. Quadratic (black dashed line) and cubic dependency on the diameter Df (red dashed line);
simulation results for FBHs (red points)
Like KSRs, FBHs follow the known theory between 1 and 9 mm. However, no
resonance effects occur, and below λ/4 the simulation results are between the quadratic
and the cubic dependency (close to the quadratic dependency). This is caused by the
bore. Due to the bore extending in one direction the wave cannot enclose the complete
FBH. Real defects have no bore extending in one direction and real small defects will
get excited more like the small KSRs. Therefore, in the case FBHs are used for
calibration or as a source for DGS diagrams a compensation is necessary for small
reflectors.
4. Ultrasonic calibration for small defects
4.1 Conventional Methods
Figure 7 shows the undersizing of both conventional methods, DGS and DAC with
FBHs. Both methods work up to a lower limit of ~λ/4. Below that limit both methods
show serious undersizing.
0
20
40
60
80
100
120
140
0,1 110
Gain V [dB]
Df[mm FBH]
Df²
Df³
FBH
9
Figure 7. Undersizing of DAC using FBHs (blue) and conventional DGS (red)
4.2 Extended DGS
By using equation (8) or (9) DGS can be extended for any indication size. For
indications larger than λ/4 this results in the well-known 12 dB spacing, for indications
smaller than λ/4 an 18 dB spacing has to be used. Figure 8 shows such an extended DGS
diagram. It also shows the good agreement with the conventional DGS (up to λ/4) by
including the conventional DGS diagram as dashed lines.
Figure 8. Extended DGS diagram (farfield calculated by equation 9)
with the backwall (BW) curve on top and different sizes of KSRs [mm] below;
The gray dashed lines represent the conventional diagram from Fig. 1
(In this case for a probe with round transducer with D = 23,1 mm, λ = 2,95 mm).
-2
0
2
4
6
8
10
12
14
16
18
20
0,1 110
Undersizing [dB]
Df[mm KSR]
FBH
DGS
0
20
40
60
80
100
120
140
160
180
10 100 1000
Gain V [dB]
Soundpath s [mm]
BW
16
12
8
6
4
3
2
1,5
1,0
0,7
0,5
0,35
0,25
0,15
0,10
10
5. Conclusions and Outlook
The simulation results show that both conventional DGS and DAC (using FBHs) can be
used up to a lower limit of a quarter of the wavelength. Below that limit both lead to
serious undersizing. However, as shown in this paper, DGS can be extended to smaller
wavelengths by changing from a quadratic dependency from the indication diameter to a
cubic dependency. This extension is given both by an extended DGS diagram and an
extended DGS formula. For calibration using flat bottom holes smaller than a quarter of
the wavelength the reflectivity difference to disc shaped reflectors must be considered.
For shear waves and dual element pitch catch probes it is expected that those results can
be transferred.
Acknowledgements
The authors would like to thank Dr. Gregor Ballier for his support solving the issues
with the CPML implementation.
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Turbinenscheiben unterliegen im Betrieb hohen Beanspruchungen und werden daher im Rahmen des Herstellungsprozesses mit Ultraschall geprüft. Bei besonders hoch belasteten Scheiben wird inzwischen – neben der klassischen Ultraschallprüfung - eine SAFT Analyse (Synthetic Aperture Focusing Technique) durchgeführt, durch die das Signal-Rausch-Verhältnis und die Defektlokalisierung verbessert werden. Hierzu wird ein von Siemens entwickeltes Verfahren eingesetzt, Quantitative SAFT oder auch DGS-SAFT genannt. Es beruht auf den Arbeiten von Böhm, Heinrich und Mooshofer und gestattet die Beurteilung jedes Voxels des SAFT-Ergebnisses in Einheiten eines Ersatzreflektors. Dadurch kann die Zulässigkeit auch kleiner Defektanzeigen beurteilt werden. Im Rahmen dieses Beitrages wird auf die Validierung des Verfahrens eingegangen. Es wurde eine umfassende Validierung durchgeführt, die alle Schritte von der Ultraschallphysik über Prüfgerät/Prüfanlage bis hin zur Algorithmik umfasst. Sie erfolgte mit Hilfe einer Testscheibe, in die als Reflektoren Flachbodenbohrungen unterschiedlicher Größe und Orientierung für die zur Prüfung verwendeten Einschallrichtungen präpariert wurden. In dem Beitrag wird diskutiert, wie die Genauigkeit der in die Validierung eingehenden Größen sichergestellt wird und welche Störeinflüsse bei der Validierung berücksichtigt werden müssen, wie z.B. Abweichungen von der nominellen Prüfkopffrequenz. Als Ergebnis der Validierung wird die Übereinstimmung zwischen dem Durchmesser der Flachbodenbohrungen, klassischer Ultraschallprüfung und SAFT-Rekonstruktion quantitativ ausgewertet und diskutiert.
Article
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Große Rotor-Schmiedeteile, die in der Regel eines der kritischsten Bauteile in landgestützten Turbinen und Generatoren für die Energieerzeugung darstellen, setzen für eine ausreichende Lebensdauer eine aufwändige volumetrische Prüfung voraus. Diese wird für gewöhnlich manuell oder automatisiert mit Ultraschall durchgeführt. Durch neue Anforderungen, Designs und Materialien wird eine empfindlichere Prüfung notwendig. Dies kann durch die Synthetic Aperture Focusing Technique (SAFT), auch Ultraschall Computertomographie genannt, erreicht werden. SAFT geht auf das Synthetic Aperture Radar (SAR) zurück und wurde von mehreren Universitäten weiterentwickelt. Eine Einführung von SAFT in die Serienfertigung großer Schmiedeteile wurde durch die Einführung des von Siemens entwickelten Quantitative-SAFT, auch AVG- oder DGS-SAFT genannt, möglich, das eine Beurteilung eines jeden Voxels in Einheiten eines Ersatzreflektors erlaubt, und durch eine Beschleunigung, die die Rekonstruktion des kompletten Volumens eines großen Schmiedebauteils erlaubt. In dieser Veröffentlichung wird von den Erfahrungen berichtet, die bei der Einführung der SAFT-Prüfung in die Serienfertigung gewonnen werden konnten. Dabei werden die Herausforderungen für Level 2/3-Prüfer diskutiert, wie z. B. die volumenkorrigierte Anzeige der Ergebnisse, der Umgang mit großen Datenmengen, die Fokussierung von Anzeigen, die Amplitudendarstellung in Einheiten eines Ersatzreflektors und der Umgang mit der Software. Des Weiteren wird dargestellt, wie Anzeigen durch SAFT dargestellt werden, wie bei Quantitative-SAFT die Nachweisgrenze bestimmt werden kann und welche Artefakte bei der Serienprüfung mit SAFT auftreten können.
Presentation
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In the field of ultrasonic testing there are two key questions: Which defects can be found and – in the case indications are found – do they restrict the use of the part? Regarding both questions, the prerequisite is a method for defect sizing. Over the last decades sizing methods were established like DAC (Distance Amplitude Correction) or DGS (Distance Gain Size) for defects smaller than the beam profile. Those methods utilize the echo amplitude and provide results which are proportional to the defect area. However, those approximations are only accurate for defects larger than one wavelength even that experience shows it can be applied for slightly smaller defects. With the progress of material technology and ultrasonic inspection the need to detect and size smaller defects is growing. Therefore, both for flat bottom holes and disc shaped reflectors the usability for small defects needs to be checked. In this publication, it is investigated how to correctly size small defects below one wavelength. Utilizing a grid-based simulation method the echo signals of cylinder and disc shaped reflectors of various sizes are calculated. By properly choosing the simulation method and grid it is ensured that all physical wave modes are included in the simulation and that the discretization error is negligible. A good correspondence between the simulation and classical defect sizing for defects larger than one wavelength is found. In the region between one quarter of a wavelength and one wavelength resonance effects are found, which result in classical defect sizing methods giving conservative results. In the region below one quarter of a wavelength DAC and classical DGS sizing leads to undersizing. This is discussed in detail and a formula for defect sizing is derived, which is applicable to small as well as large defects.
Conference Paper
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Sizing of indications and the determination of the inspection sensitivity are core tasks in ultrasonic testing. They ensure that critical inhomogenities can be detected and assessed. For the Synthetic Aperture Focussing Technique (SAFT) the sizing of indications is currently performed by evaluating the spatial extent in the reconstruction result, i.e. counting the number of voxels belonging to an indication. This limits sizing to the resolution of SAFT, which is in the order of one wavelength. For smaller defects sizing is not possible. Moreover, no information about the sensitivity of the inspection method is provided. Compared to classical UT inspection SAFT significantly improves the signal-to-noise ratio (SNR), regarding stochastic noise and grain noise. However, this improvement of the sensitivity cannot be utilized adequately without a method for determination of the sensitivity and for sizing small indications. Similar to classic UT there is a second option to gain information about indications: The amplitude sum, which incorporates the echo amplitude, the angle dependent scattering characteristics, the probe parameters and the specimen geometry. In this paper we show that the amplitude sum is suitable for sizing of small indications and for the determination of sensitivity. The relation between the amplitude sum and the size of indications is explained, and it is shown, that the location of indications and the shape of the object to inspect must be considered. Based on these results a method for sizing of small indications using SAFT is developed which translates the amplitude sum of each voxel in an equivalent reflector size, similar to the Distance Gain Size method (DGS) in classical UT. This sizing method completes SAFT, growing it from an imaging tool to a full-fledged quantitative measurement technique.
Conference Paper
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Heavy rotor forgings for land-based power generation turbines and generators are inspected ultrasonically. Several decades ago the first inspections were conducted using manual, straight beam, contact transducers with simple, non-descript reporting requirements. The development of ultrasonic inspection capabilities, the change in design engineer requirements, improvements of fracture mechanics calculations, experience with turbine operation, experience with the inspection technology, and probability of detection (PoD) drove the changes that have resulted in the current day inspection requirements: sizing technologies were implemented, detection limits were lowered, angle and pitch/catch (dual crystal) scans were introduced, and most recently automated equipment for the inspection was required. Due to all these changes, model based sizing techniques, like DGS, and modern ultrasonic techniques, like phased array, are being introduced globally. This paper describes the evolution of the ultrasonic inspection requirements over the last decades and presents an outlook for tomorrow.
Book
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Ultrasonic Nondestructive Testing of Materials: Theoretical Foundations explores the mathematical foundations and emerging applications of this testing process, which is based on elastic wave propagation in isotropic and anisotropic solids. In covering ultrasonic nondestructive testing methods, the book emphasizes the engineering point of view, yet it relies on the physics and mathematics aspects involved in elastic wave propagation theory. As a result, this resource becomes a missing link in the literature by combining coverage of the theoretical aspects of testing and providing intuitive assessments of numerous standard problems to illustrate fundamental assertions. Content includes a brief description of the theory of acoustic and electromagnetic fields to underline the similarities and differences as compared to elastodynamics. It also covers vector algebra and analysis, elastic plane and Rayleigh surface waves, and ultrasonic beams, as well as transducer radiation, inverse scattering, and ultrasonic nondestructive imaging. Includes numerical computations to explain wave propagation phenomena and compare results of analytical formulations Although ultrasonic nondestructive testing can often be roughly understood in terms of plane waves and beams, this book addresses the key issues of transducer radiation and defect scattering and imaging, respectively. The authors physically formulate point source synthesis, and, in mathematical terms, they use representation integrals with Green functions, always including intuitive interpretations with mathematical evaluations. Replacing cumbersome index notation with a coordinate-free version, this reference offers step-by-step documentation of relevant tensorial elastodynamic cases involving isotropic and anisotropic materials. It provides all necessary mathematical tools readers require to understand the mathematical and physical basis for ultrasonic nondestructive testing.
Article
Vorschläge zur Vereinheitlichung von Ultraschall-Prüfbefunden für die Aufstellung von Richtreihen und Vorschriften durch Zuordnung von Ersatzfehlergrößen zu kleinen Fehlstellen auf Grund ihrer Echohöhe. Durchführbarkeit des Verfahrens mit beliebigen Geräten, Prüfköpfen, Frequenzen und einer Platte aus dem Werkstoff des Prüflings als Bezugskörper. Ermittlung von Fehlergrößen im Fernfeld und im Nahfeld. Anwendung von Prüfköpfen besonderer Bauart bei der Durchführung des Verfahrens im Nahfeld. Berücksichtigung, des Einflusses gekrümmter Oberflächen.
Article
A study is made of the ultrasonic field produced by a circular quartz crystal transducer and the integrated response of a quartz crystal receiver with the same dimensions as the transducer. The transducer and receiver are taken to be coaxial, and it is assumed that the transducer behaves as a piston source while the integrated response is proportional to the average pressure over the receiver area. Computations are made for cases of interest in the megacycle frequency range (ka=50 to 1000; a=piston radius; λ=wavelength; k=2π/λ). The results contain features of use in identifying and correcting for diffraction errors. These features which apparently have been missed in previous investigations are compared with available experimental data. Finally correction formulas to account for diffractioneffects in the accurate measurement of attenuation are discussed. It is shown that the order of magnitude of the diffractionattenuation is given by one decibel per a 2/λ.
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This paper discusses the problem of estimating the size of flaws using ultrasound. A solution to the problem, for various targets, is suggested that uses Krautkramer's method of similarity for a disc reflector. Examples are worked out for different conditions.