AN ANALYSIS OF ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR
NONDESTRUCTIVE EVALUATION OF THICK METAL SECTIONS AND WELDMENTS*
C.M. Fortunko and R.E. Schramm
Fracture and Deformation Division
National Bureau of Standards
Boulder, CO 80303
ABSTRACT
A new type of electromagnetic-acoustic transducer (EMAT) has
been developed that may be particularly suitable for use as an
element of ultrasonic arrays. The new transducer can generate and
receive compact ultrasonic pulses that exhibit a component of polarization parallel to the free surface. In the plane of symmetry that
is normal to the free surface and bisects the EMAT (the sagittal
plane), the ultrasonic signals generated by the new transducer are
SH waves. In addition, the new transducer can efficiently receive
ultrasonic signals from a very wide range of direction in the sagittal plane. This property is required to realize very long synthetic
aperture lengths, which are needed to maximize the transverse resolution of ultrasonic inspection systems. The focusing performance
of different linear synthetic array configurations using the new
EMAT is compared analytically with that of a linear end-fire system
using periodic-permanent-magnet (PPM) EMATs that have been used in
the past in weld inspection. The advantages and inherent limitations
of such systems are examined using analytical and numerical methods.
Particular emphasis is placed on the analysis of arrays that can be
focused obliquely with respect to the free surface and the potential
usefulness of such systems in weld inspection.
INTRODUCTION
The use of special ultrasonic probing signals, horizontally
polarized shear waves (SH waves) in nondestructive evaluation (NDE)
*Contribution of the National Bureau of Standards and not subject
to copyright.
283
284
C. M. FORTUNKO AND R. E. SCHRAMM
has been considered in the past by several authors in the context
of weld inspection. 1- 6 Historically, the interest in SH waves was
generated by the fact that the directivity patterns of SH waves produced by elementary sources on the free surface of an elastic halfspace are considerably less complicated than those of vertically
polarized shear waves (SV) waves and longitudinal waves (L waves).7-10
This unique property of SH waves was found to be very useful in the
design of practical inspection configurations. 2 In particular, the
possibility of generating SH wave signals at grazi~g angles was found
to be especially attractive in the inspection of butt welded plates
and shells. 3 ,6,11,12
Interest in the development of nondestructive evaluation techniques based on the use of SH waves was also generated by the realization that SH waves may be more appropriate for the inspection of
certain austenitic stainless steel welds. 4 ,s In this case, it was
determined that SH waves can be used to overcome certain fundamental
limitations imposed by the textured, columnar grain structures of
multipass stainless steel weldments. 13 However, this subject involves a discussion of elastic wave propagation in aeolotropic media
and other concepts that are mainly beyond the scope of this paper.
The propagation and scattering of ultrasonic waves in butt
weldments modeled as isotropic and homogeneous plates can be studied
in two different waves. In plates that are relatively thin compared
to the ultrasonic wavelength in the bulk material, it is often advantageous to represent the ultrasonic signals in terms of propagating
and evanescent plate modes. 3 ,11,12 This approach can often result in
a substantial simplification of the experimental system and less
complicated data processing. 6 However, the plate mode description
is not at all appropriate for thick plates when compact ultrasonic
pulses are used to detect and characterize surface and interior defects. 2 In such cases, the propagation and scattering of the ultrasonic signals is more adequately described using conventional diffraction and ray concepts. 14 ,lS
The propagation of plane SH wave signals in plates is considerably easier to analyze than SV waves and L waves, because SH waves
are completely decoupled upon reflection from signals polarized in
the plane normal to the plate (the sagittal plane).16,17 As a
consequence of this simplification, SH plane waves reflect from the
surface of the plate without a phase shift. 16 Using superposition,
it can then also be shown that the same conclusion holds for all
cases involving two-dimensional diffraction of SH wave signals by
surface and interior defects. However, most practical nondestructive inspection configurations involve three-dimensional diffraction.
In such cases, the reflection coefficient is purely real for certain
symmetrical cases of incidence in the sagittal plane. Nominally SH
wave rays, that do not lie in the sagittal plane, may then generate
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
285
other signals by mode conversion, resulting in an increased ultrasonic background level.
In the past, a number of different weld inspection schemes using
SH wave probing signals have been proposed. 2-4 In the majority of
cases, such schemes relied upon the periodic-permanent-magnet (PPM)
electromagnetic-acoustic transducer (EMAT) configuration, shown in
Fig. 1. 18 Other transducer configurations have also been proposed. 19 ,20
To overcome the inherently low conversion efficiencies, such EMATs
were, in most cases, designed as linear end-fire arrays, which must
be driven with sufficiently long tone bursts to attain maximum
signal-to-noise performance and steer the acoustic beam in the desired direction. Obviously, the resolution along the ray connecting
the center of the transducer with the point of observation (range
resolution) of such transducers is severely limited by the duration
of the ultrasonic signal. The resolution in the plane transverse
to the ray defining the range (transverse resolution) is limited by
the physical length of the array, the direction of propagation, and
the ultrasonic wavelength. In addition, the performance characteristics of PPM and other EMATs of the end-fire type suffer from inadequate sidelobe suppression and inability to independently adjust
important parameters of the ultrasonic beam, e.g., beam width, focal
distance, beam steering angle, etc.
-I 1- 1L
D-
/
2 3
1
Permanent
Magnet Assembly
M
N S N
S N S
N S N
S N S
--------------~
RF Coil
-t - r:::=====r:::::::J=;:==~===f-------c RF
W
, '{I I I I I I
-: - -: -:- -: : :- -:- ~ - :I
I
I
-
,
I
Fig. 1.
I
,
I
I
- -
I
I
--
I
-
Coil
I
-
-
-
-
.- - -
I
A periodic-permanent-magnet (PPM) electromagnetic-acoustic
transducer (EMAT) of horizontally polarized shear (SH) waves.
C. M. FORTUNKO AND R. E. SCHRAMM
286
Sm-Co
Magnet
Magnet
Keeper
M=2
Sm-Co
Magnet
Elongated
Spiral Coil ...............
Spacer ....
I
t
Spiral Coil ......... _
Fig. 2.
Two simple permanent-magnet (PM) EMATs.
Recently, a new EMAT configuration has been developed that may
be particularly useful in dynamic and synthetic aperture applications.
Generically, the new EMAT design is derived from the PPM EMAT shown
in Fig. 1, but it uses only one (M = 1) or two (M = 2) pairs of permanent magnets. The M = 1 and M = 2 EMAT configurations are shown in
Fig. 2. The M = 1 EMAT configuration is conceptually similar to a
configuration described earlier in the literature. 21 However, the
earlier EMATs were designed primarily to produce highly collimated
ultrasonic beams propagating along the normal to the plate surface.
In contrast, the M = 1 EMAT of Fig . 1 was specifically designed to
produce signals with a large beam width.
Like the PPM EMAT of Fig. 1, the new EMAT configurations of
Fig. 2 can be used to generate and detect ultrasonic signals that
exhibit a component of polarization parallel to the surface of the
plate (SH waves). Because the new EMATs can be made small along
the intersection of the sagittal plane and the free surface of a
plate as compared to the wavelength, they can be used to generate
and receive compact ultrasonic signals from a wide angular range
(at least in the sagittal plane). These properties are needed to
realize long synthetic aperture lengths (for high beam compression
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
287
ratios) that yield good range resolution performance, especially when
large wavelengths must be used. The new transducers will be referred
to here as permanent magnet (PM) EMATs.
In this paper the subject of beam forming using the more conventional PPM EMATs is considered, first, to illustrate the considerable
shortcomings of linear end-fire transducers in the context of inspection of thick metal sections and welds. Second, some general properties of synthetic aperture systems are reviewed to highlight the most
desirable features of such systems in thick section inspection applications. Third, the directivity patterns in the sagittal plane of
the M = 1 and M = 2, PM EMATs are discussed. Attention is then
focused on the use of the simple PM EMATs in synthetic and dynamic
transducer arrays with better range and transverse resolution performance than the PPM EMATs using a large number of permanent magnets.
The properties of such arrays are studied using analytical and numerical methods. Finally, two possible practical implementations of
arrays using PM SH wave EMATs are discussed.
ULTRASONIC DIRECTIVITY PATTERNS AND RANGE RESOLUTION OF
PERIODIC-PERMANENT-MAGNET EMATs
The factors governing the characteristics of ultrasonic beam
patterns (e.g., directivity) by periodic-permanent-magnet (PPM) EMATs
are considered in detail in References 8, 9 and 18, while the principles of the transduction mechanisms are discussed in References 22,
23 and 24. The directivity pattern in the sagittal plane of the EMAT
depicted in Fig. 1 can be determined approximately from a relationship derived in Reference 18:
DF
(¢)
=
{!. Si~(~Sin¢)} {Sin[~ (1
2
'ITD
(-A-
sin¢)
i)] e-j (M'IT/4)}
sin ¢ 'IT ]
sin 2(~sin¢ - n)
[D 2'IT
(1)
where the angle ¢ is defined by the ray from the center of the PPM
EMAT to an observation point and the normal to the surface of the
plate. As shown in Fig. 1, the PPM EMAT is composed of a periodic
array of M permanent magnets with a period L = 2D and half-width W,
and a spiral wire coil that is always placed b~tween the magnet
assembly and the surface of the metal plate. In practice, a spacer
of thickness S (not shown) is inserted betwen the magnets to reduce
eddy current losses. Then, L = 2(S + D). In Eq. (1) the parameter A
is the bulk ultrasonic wavelength.
An examination of the structure shown in Fig. 1 reveals that
the PPM EMAT is essentially composed of M/2 cells (periods) that are
connected in-parallel electrically and in-series ultrasonically. As
a consequence, the PPM EMAT can be effectively modeled as a linear
288
C. M. FORTUNKO AND R. E. SCHRAMM
end-fire antenna. This fact is reflected in Eq. (1), which can be
interpreted as a product of element ("structure") and array ("form")
factors. (For clarity the element and array factors are isolated
in Eq. (1) using { } braces.) However, to realize narrow beam profiles and maximum transduction efficiencies, the EMAT of Fig. 1 must
be driven electrically by a tone burst of electrical current that is
at least M cycles long. Then, the principal direction (direction of
maximum amplitude) of the ultrasonic beam can be determined from:
~
= arc sin
[~D]
(2)
The end-fire behavior of the PPM EMAT has been verified experimentally using the calibration configuration shown in Fig. 3. (Figure 3
shows a 152 mm radius, 203 mm wide aluminum test block of semicylindrical cross-section.) In the configuration of Fig. 3, the PPM
EMAT under test (transmitter EMAT) is placed symmetrically at the
intersection of the two symmetry planes of the semi-cylindrical test
block. On the curved surface of t.he block, a physically small (D
2.5 mm and W = 5 mm), broadband EMAT of the type shown in Fig. 2
(M = 1) is used as a probe. (It can easily be shown that the M = 1
EMAT of Fig. 2 exhibits maximum sensitivity to SH wave signals propagating along the normal to the surface. 21 The angles e and ~, defining the coordinates of the observation point, are also shown in
Fig. 3.
Using the ultrasonic transducer calibration configuration of
Fig. 3, the directivity patterns for a number of SH wave EMATs were
evaluated. In particular, the radiation patterns of M = 16, D =
3.2 mm, and S = 0.5 mm PPM EMATs were measured in the sagittal plane
at 410 and 550 kHz. The two radiation patterns are shown in Figs. 4
and 5, respectively. Also shown in Figs. 4 and 5 are the directivity
patterns calculated using Eq. (1).
A comparison of the experimental and theoretical results shown
in Figs. 4 and 5 shows close agreement over a considerable range of
~.
In particular, in Fig. 4 the maximum amplitude is measured at
the grazing angle, ~ = 0°. In Fig. 5, the maximum amplitude is measured at ~ ~ 50°, also in close agreement with the simple theory.
However, the appearance of two major sidelobes in Fig. 4, and the
slight broadening of the principal lobes in Fig. 5 are not predicted
from Eq. (1). These discrepancies are attributed to the contamination of the radiation pattern by higher-order spatial harmonic contributions and end-effects. Clearly, the sidelobes observed in
Fig. 4 are not desirable in many experimental situations. However,
of even greater concern is the temporal duration of the ultrasonic
signals produced by long PPM EMATs.
It is seen from Figs. 4 and 5 that reasonably good transverse
resolution performance can be obtained by using PPM EMATs with a
sufficiently large number of periods M/2. Significantly better
289
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
Transmitter
EMAT
Receiver
EMAT
Fig. 3.
An experimental configuration used in the mapping of
directivity patterns.
E~~T
performance levels can be obtained using linear arrays with nonuniform element spacing. 25 , 2 6 However, to obtain good transverse resolution using the end-fire construction, range resolution performance
must be sacrificed. (For example, 8 rf cycles were required to produce the radiation patterns depicted in Figs. 4 and 5.)
Along the principal direction of the ultrasonic beam, the
range resolution ~r can be determined from Ref. 27:
~r =
v 12M
s
(3)
where v is the bulk shear wave velocity and 6f is the rms system
bandwidEh (pulse-echo operation is assumed). Clearly, PPM EMATs
must sacrifice good range resolution for high directivity. However,
considerable improvement in range resolution can be obtained using
the shorter PM EMATs in conjunction with synthetic aperture and
dynamic focusing techniques, which have recently been made very
practical and cost-effective by significant advances in the field
of digital signal processing. 4
C. M. FORTUNKO AND R. E. SCHRAMM
290
<P
(degrees)
o
,.UTWun.'· 152 mm
SIGNAL (mV)
• Experimental
-
9 =O'
Fig. 4.
Theoretical
M=16
=
0 3 .2 mm
410 kHz
Measured and theoretical SH wave directivity patterns in
aluminum. PPM EMAT with (D + S) = 3.7 rom and M = 16 at
410 kHz.
ENHANCEMENT OF TRANSVERSE RESOLUTION USING SYNTHETIC
APERTURE FOCUSING
Synthetic aperture and dynamic focusing techniques have been
considered by many researchers as a means of improving the performance of medical and nondestructive evaluation systems. 28 ,29 However,
in the past the use of such techniques has generally been evaluated
in the context of piezoelectric-acoustic transducers, whose directivity patterns are significantly different from those of the EMATs.
The purpose of this section is to review certain fundamental constraints of synthetic aperture systems that are directly influenced
by the radiation patterns of the isolated transducer elements used
to build up an array.
Consider a linear array composed of electrically and ultrasonically isolated transducer elements, as shown in Fig. 6. In the
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRA YS FOR NDE
4>
291
(degrees)
SIGNAL (mV)
AkmInum, , . 152 mm
• Experimental
-
8
=O'
Theoretical
M= 16
0 3 .2 mm
=
550kHz
Fig. 5 .
Measured and theoretical SH wave directivity patterns in
aluminum. PPM EMAT with (D + S) = 3.7 rnrn and M = 16 at
550 kHz.
far-field of a single transducer, the effective beam-width is determined only by the bulk wavelength A, the transducer aperture length
L , and the range from the transducer to the defect R. From the
construction of Fig. 6 it then follows that the rnaxigum usable length
L of a synthetic aperture array is given by :
s
AR
L
s
o
(4 )
L
A longer array does not produce further improvements in the
system performance because the defect is no longer in the field of
view of the a dditional transducer elements. It can then be shown
that the best achievable transverse resolution 6L is given by: 27
6L
A
e: - R
L
s
0
e:L
(5)
C. M. FORTUNKO AND R. E. SCHRAMM
292
Scan Direction _
\4--
Fig. 6.
--
L.
- -'Pj
Geometry used to analyze the focusing performance of
synthetic-aperture, ultrasonic inspection systems.
where e: = 1 for a one-way system and 1/2 for a two-way ("pulse-echo")
system using the full synthetic aperture length L. Efficient
synthetic aperture focusing is feasible within th~ near-field of the
array, whose maximum range (R )
is approximately given by:28
L 2
0 max
(Ro) max
=
-f-
(6)
The effect of synthetic aperture focusing using the time-delay
focusing method is to make the synthetic array curved, with R at
the radius of curvature. 29 Beam-steering is also possible byOintroducing appropriate amounts of time-delay as a function of transducer
element position in the array. Both effects are illustrated in
Fig. 7.
The formation of focused ultrasonic beams
spect to the surface is important in practical
the presence of the weld reinforcement (crown)
of specific defects often restricts the use of
at an angle with reapplications because
and the orientation
symmetric arrays.
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
293
"----Free
Surface
Defect below surface
Focal
Point 1
Fig . 7.
Geometry used to define the parameters of synthetic
apertures optimized for oblique focusing.
From the construction in Fig. 7, it can be shown that the effective
aperture L is reduced when the focal point does not lie on the
axis bisec~ing the array. As a result, the end of the near-field
region of the obliquely focused array is not as far as in the normal
case. The end of the near-field zone for oblique focusing [R ( ~ )]
o
max
is approximately given by:
(7)
Obviously, to increase [R (~)]
it is necessary to obtain as
long a usable synthetic apertu~e le~£h L as possible. This is
particularly true for cases of large ¢.
further complication is
introduced by the directivity patterns of practical transducers,
which usually exhibit a limited angular beam width. Fortunately,
the special characteristics of the two SH wave EMAT configurations
shown in Fig. 2 can produce plane wave components at all angles ¢
in the sagittal plane and, therefore, permit the realization of
longer synthetic aperture lengths than piezoelectric transducers.
The directivity patterns of the simple EMATs of Fig. 2 and their
effect on the ultimate resolution of practical synthetic apertures
are examined in the following sections.
K
ULTRASONIC DIRECTIVITY PATTERNS AND TRANSVERSE RESOLUTION OF
SIMPLE PM EMATs
.
The dir:cti~ity patterns of the two simple PM EMAT configurat10ns shown 1n F1g. 2 have been measured using the transducer calibration system illustrated in Fig. 3. The measured directivity patterns were then compared with the theory [Eq. (1)]. The measured
294
C. M. FORTUNKO AND R. E. SCHRAMM
and calculated responses of the two simple EMAT configurations of
Fig . 2 are shown in Figs. 8 and 9. The radiation pattern of the
"half-period" (M = 1) and "full-period" (M = 2) SH wave EMATs have
been measured at 520 and 880 kHz, respectively . It is seen from
Figs. 8 and 9 that the correspondence between the theory and experiment is very close. Consequently, it can be assumed that Eq . (1)
can be used to predict the directivity patterns of the two transducer
types at other frequencies.
An examination of the directivity pattern shown in Fig. 8 reveals that the "half-period" (M : 1) EMAT can be used to collect
ultrasonic data from a very wide range of angles. In fact, it can
be concluded that the maximum usable field of view is 180 0 when A
is larger than twice the aperture length L. Experimentally, the
above observation can be related directly ~o the "optical" resolution
~A of a curved array, which is given by :
cP
(degrees)
60
SIGNAL (mV)
Aluminum,
t •
1 52 mm
• Experimental
-
9
Fig. 8.
= O·
Theoretical
M= 1
0 = 3 .2 mm
520 kHz
Measured and theoretical SH wave directivity patterns in
aluminum .
at 520 kHz.
"Half- period" ( M
=
1), PM EMAT
~ith
D
=
3 . 2 mm
295
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
<P
(degrees)
150
SIGNAL (mV)
Aluminum, , • 1 52 mm
• Experimental
-
9
Fig. 9.
M '"
=o·
Theoretical
M=2
=
0 3.2 mm
880 kHz
Measured and theoretical SH wave directivity pattern in
aluminum. "Full-period" (M = 2), PM EMAT with (D + S) =
3.7 mm at 880 kHz.
2sin~/i
(8)
where A is the ultrasonic wavelength and ~ is the viewing angle
(angular aperture) of a synthetic aperture array, as shown in Fig. 7.
(The viewing angle ~ can be directly related to the numerical aperture (f/number) of a curved array.)
From the discussion in the preceding section, it follows that
very long synthetic aperture lengths can be obtained using the halfperiod (M = 1) EMAT of Fig. 2. This fact has an important practical
consequence. Consider a defect positioned just below the free surface, as shown in Fig. 7. Assuming that the sensitivity of the system is not limited by phase errors, electronic noise, and ultrasonic
and electromagnetic interferences, and that the signal amplitudes
C. M. FORTUNKO AND R. E. SCHRAMM
296
are a priori compensated for diffraction and propagation losses, the
effective synthetic aperture length L can be made arbitrarily large.
As a consequence, the viewing angle ~scan be made to approach 90° for
¢ ~ 90°. For ¢ ~ 0°, ~ ~ 180° is theoretically permissible.
The directivity pattern of the "full-period" (M = 2) EMAT of
Fig. 2 is significantly different from that of the M = 1 EMAT. In
particular, the amplitude vanishes for ¢ = 0° for all operating frequencies and is very small for ¢ = ±90° at 880 kHz. The former
effect is a consequence of symmetry and the latter of the A/(2D + S)
ratio at 880 kHz. The directivity pattern of Fig. 9 can be desirable
in certain applications. In particular, it can be used effectively
to reduce resonant reverberation by the ray normal to the free surfaces of a plate. However, the M = 2, PM EMAT does not permit the
realization of as long synthetic aperture lengths as the M = 1 PM
EMAT.
Although the two PH EHATs of Fig. 2 cannot produce radiation
patterns that are altogether independent of ¢ and frequency, the
variations are predictable from Eq. (1). Therefore, it should be
possible to adjust the gains applied to each element of the array
to produce the effect of a lens with widely variable focal length
R and oblique focusing angle ¢. Furthermore, the availability of
expressions for the directivity patterns and diffraction losses permits the modeling of the focusing properties of arrays on the basis
of Huygens principle. This can be accomplished by replacing the
usual ("optical") expression for a Huygens wavelet by the appropriate
directivity function.
CALCULATED RESPONSES OF SYNTHETIC ARRAYS USING PM EMATs
Since a synthetic array is usually focused at a particular
point within an elastic solid, it must be defocused at other points.
Therefore, to understand the focusing performance of a particular
array, it is necessary to describe the ultrasonic fields in the
neighborhood of the focal point. Here, for computational and analytical convenience it is assumed that each element of the array generates a spherical wave ~., which can be represented in the sagittal
1.
plane by:
DF. (¢. ,w)
1.
1.
r
.
-+-+
e
j(kor .-wt)
01.
A(w)
(9)
01.
where k is the wave-number (2rr/A), w is the angular frequency, r .
is the distance from the particular array element to the observa~ion
point, and A(w) is the spectrum of the ultrasonic signal. DF.(¢.,w)
is the directivity function, which may also include the effecEs 6f
lift-off and changes in inductive coupling as a function of material
parameters. For simplicity, Eq. (1) may be used to approximate DF
(¢,w).
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
297
At the focal point of the array the total response is given by:
()()
(10)
Then. for points in the neighborhood of the focal point x f • Eq. (11)
takes the form:
00
1jJ
(x o ,t)
(r f 1.-r.)
-jwt A( w)
01 e
(11)
where r f . is the distance from the i'th EMAT element position to the
focal point f of the array, as shown in Fig. 10. Vs is the bulk
shear wave velocity.
x
An approximate solution to Eq. (11) can be obtained by assuming
a Gaussian spectrum A(w):
1
_~
A(w) = ~w 12n e
(W-W o)
\-z;-
2
(12)
Position Of i'th Array Element
1+1
1-1
r - r I
Focal Point
Observation Point
Fig. 10.
Geometry used for calculating responses of synthetic PM
EMAT arrays in the sagittal plane.
C. M. FORTUNKO AND R. E. SCHRAMM
298
The integrals in Eq. (11) can then be readily evaluated using
the saddle-point method of integration. 3D The saddle-point occurs at:
(13)
w
0) and
When all the signals are correlated at the focal point xf(t
W
»(l1w)2 (rf.-r .)/v
o
1
1jJ
(x 0 ,t) ~L
i
01
S
DF. (¢. ,w )
110
2nr
oi
ej
w
0
v
s
(rf·-r
.) e -!:2
1
01
~:Y
(r f .-r .) 2
1
01
(14)
Equation (13) can be used to study the focusing properties of
synthetic arrays at maximum correlation. It is interesting to note
that in the limit as I1w approaches 0, Eq. (14) is the same as for a
monochromatic array.
Since in many practical applications it is not possible to center the synthetic array directly above a defect, e.g., in weld inspection, it is of interest to examine the focusing properties of
arrays that are focused obliquely with respect to the free surface.
Oblique focusing is also required because SH waves propagating at
right angles with respect to the free surface and polarized along
the long defect dimensions are insensitive to planar defects that
are oriented normal to the plate surfaces. In practice such defects
are most likely to precipitate failure because of their orientation
relative to the applied and residual stress fields. For this reason, cases of normal (on-axis) and oblique (off-axis) focusing were
studied.
Using Eq. (13), the focusing performance of different synthetic
arrays using the PM EMATs of Fig. 2 was investigated. In particular,
Fig. 11 shows contour maps of three ultrasonic field distributions
(log scale) produced by a 50-mm-long array of M = 1 PM EMATs with
d = 3.2 mm and w /2n = 550 kHz focused at a depth of 25 mm below
the free surface? In Fig. 11, three representative cases are shown:
(1) the focal point located directly below the center of the array,
(2) the focal point located directly below the first element of
the array, and (3) the focal point 25 mm in front of the first element of the array. The array shown in Fig. 11 has 2.5 mm elementto-element spacing and is driven by a tone burst with I1w/w = 33%.
The amplitudes of the correlated signals are indicated foroeach
focal point, in relation to the case of focusing directly below the
center of the array. The focusing performance of the same physical
299
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
~
0.48
0.80
\.00
~
•
C>
_
@]
C>
E ...
.§
;!:
"-
...
Q
C>
..
2
1-0.55 MHz
C· ...... . . . . . . . . . . . . . .
- 50
o
db • c.nl ..
-1 db
-2 db
-3 db
- 6 db
-1 0 db
-20 db outer
,
~ ' O 3J
-20
- 30
- 40
- 10
0
SURfACE POSITION
E MAT lotal i on'
Fig. 11.
CONTOUR INTERVALS
50 In m .per IUIO
2.5 mm ,pa cing
M' I
.,I
~
10
30
20
&
40
50
Imml
Focusing performance of a 50-rum-long array of M = 1, PM
EMATs focused at three different points 25 rum below the
free surface. The array operates at w /2TI = 50 kHz and
has 33 % fractional band\vidth.
0
0 .38
0 .72
0 .94
•
C>
-E
.§
..
...
CONTOUR INTERVALS
o db • clnUr
-I db
- 2 db
- 3 db
-6 db
- 10 db
- 20 db ' OUI"
50 mm aperlur.
2.5 mm spacing
. . .. .......
..- ~----~------~--~~~--~------~-----c.~--~
so
_ 40
- 20
- 10
10
20
~ ' o . JJ
- 30
r-- • • • • • • • • • •
LEMAT lOCllions
Fig. 12.
SURfACE POSITION
30
40
50
Imml
Focusing performance of a 50-mm-long array of M = 1, PM
EMATs focused at three different points 25 rum below the
free surface. The array operates at w /2TI = 850 kHz and
has 33% fractional bandwidth.
0
300
C. M. FORTUNKO AND R. E. SCHRAMM
array, but operated at 850 kHz, is shown in Fig. 12. From the plots
shown in Figs. 11 and 12 it can be verified that the transverse resolution ~ increases with frequency in accordance with Eq. (8), and
decreases with ~, because the effective array length is shorter.
For comparative purposes, it is useful to examine the focusing
performance of an array similar to that shown in Fig. II, but with
a significantly longer element-to-element spacing. Figure 13 shows
a contour map of the ultrasonic field produced by a sparse (undersampled) EMAT array at w /2TI = 550 kHz when 12.5-mm element-toelement spacing is used. o A comparison of Fig. 11 with Fig. 13 shows
that the contours of the main lobe, centered in the vicinity of the
focal point, are essentially the same. However, in Fig. 13 the
appearance of two large (grating) sidelobes can be observed. In
this case, the broad spatial extent and high amplitude of the sidelobes defeats the main purpose of synthetic aperture focusing.
Figure 14 shows the focusing performance of a 50-mm-long, 550 kHz
array with ~w/w = 33% and 2.5-mm element-to-element spacing that
uses the M = 2 ~M EMAT elements. The performance of this array
should be compared directly to that shown in Fig. 11. It is seen
that the performance of this array is not quite as good as that
using the M = 1 PM EMATs. However, this array may be useful in
practice, because the M = 2 PM EMATs produce a significantly smaller
ultrasonic background level that reverberates between the free surfaces of a plate. In certain applications this may be a distinct
advantage.
To study the effect of array length on the focusing performance,
the field distributions of a 50-mm-long and 250-mm-long M = 1 PM
EMAT array , operating at 500 kHz, were compared. The results are
shown in Fig. 15 for the case of focusing at a point 25 mm below the
free surface and directly below the first element of the array. In
Fig. IS, the amplitudes of the signals correlated at the focal point
are not pre-emphasized to compensate for the effects of diffraction.
It is seen that the total amplitude of the ultrasonic signal evaluated at the focal point is smaller (0.80) for the shorter array than
for the longer array (1.51). However, the additional gain is not
commensurate with the greatly increased array length. Also, the
range and transverse resolution in the two cases are not significantly different
An evaluation of the results shown in Figs. 11-15 reveals that
the transverse resolution ~ agrees qualitatively with the simple
theory of Eq. (8). The effect of the large angle ~ on the transverse resolution ~A is especially pronounced in Fig. 15. The quantitative differences between the simple theory of Eq. (8) and the
actual transverse resolution determined directly from Figs. 11-15
(using the l/e criterion) are attributed to the effective apodization
301
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
.....
0.2)
-..
~~
E
~
:z:
.......
lL
~
CI
CONTOUR INTERVALS
~
iJ
..- so
4M:T
o
M'I
50 mm ape' lure
1' 0.55 MHz
~ ' 0 . 33
- 10
12.5 mm spacing
•
- 30
- 20
locll i ons
Fig. 13.
db - unlar
- I db
- 2 db
-) db
- 6 db
- 10 db
- 20 db - Oull,
o
-10
•
10
20
so
10
30
SURFACE POSITION Imml
Focusing performance of a 50-mm-long, undersampled array
of M = 1, PM EMATs focused at two different points 25 mm
below the free surface. The array operates at w /2n
550 kHz and has 33 % fractional band~Tidth.
0
.....
o.so
0.14
0.50
-.
CONTOUR INTERVALS
o
db - •• nu,
-I db
- 2 db
- ) db
50 m m Iporlun
2.5 mm spicing
c· . · . · · . . .. . . . . .
1' 0.55 MHz
-so
- 40
[MAT lO"l i o.s
Fig. 14.
~ ' O 33
-30
-20
-1 0
. ..
- 6 db
-10 db
- 20 db - oute,
10
20
30
10
SURFACE POSITION Imml
Focusing performance of a 50-mm-long array of M = 2, PM
EMATs focused at three different points 25 mm below the
free surface. The array operates at w /2n = 550 kHz and
has 33% fractional bandwidth.
0
so
C. M .FORTUNKO AND R. E. SCHRAMM
302
5\
0
....
.
.
0
0
E
oS
...
E
oS
0
0
...co :::
l-
a..
a..
~
Mq
..• • .
I • 0.
55 MHz
- --.
~
50 mm .plrturl
2.5 mm spicing
"0.55 MHz
- ..... . • • •
-10
10
4MAT LDClt i Dns SURFACE POSITION
250 mm .p"rture
2.5 mm spacing
M' I
~ ' O . JJ
- 10
Fig. 15.
...
CONTOUR INTERVALS
o db • cent ..
-I db
-2 db
- J db
-6 db
-10 db
-20 db - Duter
:z:
:z:
...co :::
I-
0
1.51
0.80
..
~ ' 0 . 33
0
SURFACE POSITION
(mml
10
(mml
Comparison of focusing performances of two arrays, 50-mmlong and 250-mm long, of M = 1, PM EMATs focused at a
point 25-mm below the free surface and directly below the
first element. Both arrays operate at 500 kHz with 33%
fractional bandwidth. The correlated signals are not preemphasized to compensate for diffraction effects .
(taper) of the arrays by diffraction effects and the dependence
of the EMAT directivity function [Eq. (1)] on the angle~. Under
certain circumstances it may be possible to compensate for such
effects by varying the gain of each element as a function of element
position in the array. (Analytically, this can be done by evaluating
Eq. (13) with the factors DF.(¢., w )/r . set to unity.)
J.
J.
0
oJ.
For comparative purposes the focusing performance of the array
shown in Fig. 11 was evaluated in the limit as ~w approaches O. The
resulting contour plot is shown in Fig. 16. An examination of Fig.
16 shows that the contour patterns of Figs. 11 and 16 are considerably different. The major differences between Figs. 11 and 16 are
caused by the time-limited nature of the signals used to dr'ive the
array in Fig. 11. As a consequence, it can be expected that the
synthetic aperture approach can offer significant improvements in
practical systems. In particular, this approach promises a significant reduction of the importance of multiple echoes caused by reverberation between the free surfaces of a plate. This follows directly
from the fact that the dimensions of the resolution cell, ~ r and ~A
estimated from Figs. 11-15, are smaller than the thicknesses of
practical plate weldments.
303
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
.
'"
1.00
..
a
_..
E ...
.§
.........z:
a:::
1If/&/
/"
CONTOUR INTERVALS
o db • Clnlor
- I db
-2 db
-3 db
- 6 db
SO mm apellu,"
..
-50
2.5 m m .pie in g
- 40
- ]0
r- • • • • • • • • • •
LE MAT Lata! i on.
Fig. 16.
. . . . . ... .. .
-20
- 10
SURFACE POSITION
10
- 10 db
-20 db · oulor
,
20
]0
40
50
(mm)
Focusing performance of a 50-mm-long, 550-kHz, monochroma·tic array of M = 1, PM EMATs focused at two different
points 25 rom below the free surface .
DISCUSSION
An array can be viewed as an aperture excited in localized areas
by isolated elements that, in general, exhibit nonisotropic radiation
characteristics and may be driven by generators of unequal strength.
Upon reception, the gain of the receiver preamplifiers may also vary,
depending on the time and spatial coordinates of the elements. General methods needed to calculate the responses of practical arrays
are found in the literature. 27 ,31,3 2, 33
In ultrasonic nondestructive evaluation, the ability of an
array inspection system to detect and characterize a potential defect is limited principally by the resolution. High resolution can
be attained either by forming an intersecting family of focused,
monochromatic beams that can be scanned across the defect by applying
appropriate phase shifts to individual elements, or by using timelimited ultrasonic signals that can be made to correlate at a partiular point within an elastic solid by time-delay techniques. Recent
technological advances in the fields of digital processing of ultrasonic signals and electromagnetic-acoustic transducer design have
made the latter approach particularly attractive . 4 For this reason
the synthetic aperture alternative to improved resolution has been
explored in this paper.
304
C. M. FORTUNKO AND R. E. SCHRAMM
In practical applications, it is often necessary to aim a linear
array at an oblique angle and, then, to scan the ultrasonic beam over
a range of angles in the sagittal plane. For example, in weld inspection it is often not possible to place an array directly above
the region to be inspected because of the presence of certain geometrical obstacles (e.g., the weld crown). Since the angular scanning
range is restricted primarily by the element beamwidth, it is advantageous to build up the array using elements with broad angular radiation patterns. In this paper, this problem has been addressed by
building up the arrays using SH wave electromagnetic-acoustic transducers with a small aperture length in relation to the ultrasonic
wavelength. The use of SH waves is advantageous because the radiation patterns of elementary SH wave line-sources are omnidirectional
in the sagittal plane. whereas those of shear waves polarized in the
sagittal plane (SV waves) and longitudinal waves are very complicated. 7 '8 The use of SH waves has also other important practical
advantages in defect detection and characterization. 3-6
Because of its inherent complexity, the subject of ultrasonic
scattering from defects was omitted in this paper. Instead, it was
implicitly assumed that the scatterers were ideal line or point
targets. However, this idealization must not be considered a major
limitation, because of the recent emphasis on long-to-medium wavelength inversion techniques in defect characterization, particularly
in weld inspection.3'~'6'11
In this paper, the focusing and beam steering properties of
several arrays of practical dimensions have been studied using a
combined analytical-numerical approach. The performance of the
arrays was simulated numerically on the basis of the empirically
determined response of a new type of array element with a broad beam
width. The results of the study strongly suggest that it may be
feasible to fabricate practical arrays using SH wave EMATs that,
although operating at relatively low frequencies (large wavelengths),
would outperform in resolution and scanning range the conventional,
unfocused ultrasonic inspection systems. (This implication is particularly important in weld inspection and nondestructive evaluation
of thick section structures.) In practice, such arrays could either
be implemented by mechanically scanning simple transmitter and receiver EMATs over the surface of the part to be evaluated, or by
using physical arrays composed of many individual EMAT elements.
The former approach involves essentially in-series processing of the
ultrasonic data, while the latter is essentially an in-parallel signal processing approach.
The main practical limitation of the in-series signal processing scheme may be caused by phase errors associated with the mechanical scanning of the single transmitter and receiver EMATs.
This
approach may also be limited by the total ultrasonic power that
can be concentrated in the neighborhood of a defect. Although the
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
305
in-parallel approach can produce higher ultrasonic power densities
(albeit at higher cost), it suffers from the disadvantage of rather
sparse element-to-element spacing, imposed by the physical configuration of the EMATs. (This limitation is easily overcome in the inseries approach.) However, in the in-parallel approach the relative
element positions are fixed. This raises the possibility of utilizing the phase information (interferometry), which can lead to even
better resolution than that defined by "optical" relationships. A
definitive choice between the two approaches can only be made after
having taken into account the details of the expected scattering
mechanisms, specimen geometry, and the cost factors related to a
specific hardware implementation.
ACKNOWLEDGEMENT
The authors would like to acknowledge S.A. Padget who fabricated
prototype SH wave EMATs and collected much of the experimental data
used in this paper. This work was supported by the Center for Advanced Nondestructive Evaluation, operated by the Ames Laboratory,
US DOE , for the Naval Sea Systems Command and the Defense Advanced
Research Projects Agency under Contract No. W-7405-ENG-82 with Iowa
State University and by the National Bureau of Standards.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
C.M. Fortunko, C.F. Vasile and R.B. Thompson, "Electromagnetic
Transducers for Weld Inspection," presented at 37th National
Fall Conference of the American Society for Nondestructive Testing, Detroit, MI, October 3-6, 1977.
C.M. Fortunko, "Ultrasonic Inspection of Weldments Using Frequency Scanned SH Waves," in Proc. 1979 Ultrasonic Symp., J.
deKlerk and B.R. McAvoy, eds., IEEE, New York, 1979.
C.M. Fortunko, R.B. King and M. Tan, "Nondestructive Evaluation
of Planar Defects in Plates Using Low Frequency SH Waves,"
J. Appl. Phys., 53, 3450, 1982.
R.K. Elsley and C.M. Fortunko, "Improvements in Flaw Detection
in Austenitic Stainless Steel Weldments," Proc. 1981 Ultrasonics
Symp., B.R. McAvoy, ed., IEEE, New York, 1981.
D.S. Kupperman and K.J. Reimann, "Ultrasonic Wave Propagation
and Anisotropy in Austenitic Stainless Steel Weld Metal, \I
IEEE Trans. Sonics & Ultrasonics, 27:7, 1980.
C.M. Fortunko and R.E. Schramm, "Nondestructive Evaluation of
Butt Welds Using Electromagnetic-Acoustic Transducers," Weld.
J., 61:39, 1982.
G.F. Miller and H. Pursey, "The Field and Radiation Impedance
of Mechanical Radiators on the Free Surface of a Semi-Infinite
Isotropic Solid," Proc. Roy. Soc. London, Ser. A, 223:521, 1954.
W.J. Pardee and R.B. Thompson, "Half-Space Radiation by EMATs,"
J. Nondestructive Eval., 1:157, 1980.
306
9.
10.
11.
12.
l3.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
C. M. FORTUNKO AND R. E. SCHRAMM
A. V. Kharitonov, "Progress and Problems in the Theory of Normal
Waves in Ultrasonic Flaw Detection," Defectoskopiya, 7:59, 1979.
R.B. Thompson, "The Relationship between Radiating Body Forces
and Equivalent Surface Stresses: Analysis and Application of
EMAT Design," J. Nondestructive Eval., 1:79, 1980.
S .K. Datta, C.M. Fortunko and R.B. King, "Sizing of Surface
Cracks in a Plate Using SH Waves," Proc. 1981 UltJ;asonics Symp.,
B.R. McAvoy, ed., IEEE, New York, 1981.
N.N. Egorov and A.V. Kharitonov, "Diffraction of Shear Normal
Modes by a Surface Crack in an Elastic Plate," Sov. Phys.
Acousticis, 25:34. 1979.
B.L. Baikie, A.R. Wagg, M.T. Whittle and D. Yapp,"Ultrasonic
Inspection of Austenitic Welds," J. Br. Nucl. Energy Soc., 15:
251, 1976.
L.M. Brekhovskikh, "Waves in Layered Media, Sec. Ed.," Academic
Press, New York, 1980.
S.K. Datta, A.H. Shah and C.M. Fortunko, "Diffraction of Medium
and Long Wavelength SH Waves by Edge Cracks," J. Appl. Phys.,
53:2895, 1982.
B.A. Auld, "Acoustic Fields and Waves in Solids, Vol. II," WileyInterscience, New York. 1973.
L. Niklas, "Group Propagation Time and Beam Displacement in
Inclined Reflection: Their Effect on Practical Ultrasonic Testing of Materials" (in German). MaterialprUfung, 7:281, 1965.
C.F. Vasile and R.B. Thompson, "Excitation of Horizontally
Polarized Elastic Waves by Electromagnetic Transducers with
Periodic Magnets," J. Appl. Phys., 50:2583, 1979.
J.F. Martin and R.B. Thompson, "The Twin Magnet EMAT Configuration for Exciting Horizontally Polarized Shear Wave," Proc. 1981
Ultrasonics Symp., B.R. McAvoy, ed., IEEE, New York, 1981.
R.B. Thompson, "New Configurations for the Electromagnet Generation of SH Waves in Ferromagnetic Materials," Proc. 1978 Ultrasonics Symp., J. deKlerk and B.R. McAvoy, eds., IEEE, New York,
1978.
B.W. Maxfield, M. Linzer, W.B. McConnanghey and J.K. Hulbert,
"Design of Permanent Magnet Electromagnetic Acoustic Wave Transducers (EMATs)," Proc. 1976 Ultrasonics Symp., J. deKlerk and
B.R. McAvoy, eds., IEEE, New York, 1976.
R.B. Thompson, "A Model for the Electromagnetic Generation of
Rayleigh and Lamb Waves," IEEE Trans. Sonics & Ultrasonics,
20:340, 1973.
R.B. Thompson, "Mechanisms of Electromagnetic Generation and
Detection of Ultrasonic Lamb Waves in Iron-Nickel Alloy Polycrystals," J. Appl. Phys., 48:4942, 1977.
R.B. Thompson, "A Model for the Electromagnetic Generation of
Guided Waves in Ferromagnetic Metal Polycrystal," IEEE Trans.
Sonics & Ultrasonics, 25:7, 1978.
W.L. Weeks, "Antenna Engineering," McGraw-Hill, New York, 1968.
R.H. Duhamel, "Optimum Patterns for End-fire Arrays," Proc. IRE,
41:652, 1953.
ELECTROMAGNETIC ACOUSTIC TRANSDUCER ARRAYS FOR NDE
27.
28.
29.
30.
31.
32.
33.
307
A. Rihaczek, "Principles of High-Resolution Radar," McGraw-Hill,
New York, 1969.
E.B. Miller and F.L. Thurstone, "Linear Ultrasonic Array Design
for Echosonography," J. Acoust. Soc. Am., 61:1481, 1977.
G.S. Kino, D. Corl, S. Bennett and K. Peterson, "Real-time Synthetic Aperture Imaging Systems," Proc. 1980 Ultrasonics Symp.,
B.R. McAvoy, ed., IEEE, New York, 1980.
A. Papoulis, "The Fourier Integral and Its Applications," McGrawHill, New York, 1962.
B.D. Steinberg, "Principles of Aperture and Array System Design,"
Wiley-Interscience, New York, 1976.
U. Aulenbacher and K.J. Langenberg, "Analytical Representation
of Transient Ultrasonic Phased-Array Near- and Far-Fields,"
J. Nondestructive Eval., 1:53, 1980.
H.F. Harmuth, "Acoustic Imaging with Electronic Circuits,"
Academic Press, New York, 1979.