NDT&E International 45 (2012) 32–38
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NDT&E International
journal homepage: www.elsevier.com/locate/ndteint
Experimental and numerical evaluation of electromagnetic acoustic
transducer performance on steel materials
R. Ribichini a,n, F. Cegla a, P.B. Nagy a,b, P. Cawley a
a
b
UK Research Centre in NDE, Department of Mechanical Engineering, Imperial College, London, SW7 2AZ, UK
School of Aerospace Systems, University of Cincinnati, Cincinnati, OH 45221, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 12 December 2010
Received in revised form
14 August 2011
Accepted 20 August 2011
Available online 1 September 2011
Electromagnetic Acoustic Transducers (EMATs) are an attractive alternative to standard piezoelectric
probes in a number of applications thanks to their contactless nature. EMATs do not require any
couplant liquid and are able to generate a wide range of wave-modes; however these positive features
are partly counterbalanced by a relatively low signal-to-noise ratio and by the dependence of EMAT
performance on the material properties of the test object. A wide variety of steel materials is employed
in many industrial applications, so it is important to assess the material-dependent behaviour of EMATs
when used in the inspection of different types of steel. Experimental data showing the performance of
bulk shear wave EMATs on a wide range of steels is presented, showing the typical range of physical
properties encountered in practice. A previously validated Finite Element model, including the main
transduction mechanisms, the Lorentz force and magnetostriction, is used to evaluate the experimental
data. The main conclusion is that the Lorentz force is the dominant transduction effect, regardless of the
magnitude and direction of the bias magnetic field. Differently from magnetostriction, the Lorentz force
is not significantly sensitive to the typical range of physical properties of steels, as a consequence the
same EMAT sensor can be used on different grades of ferritic steel.
& 2011 Elsevier Ltd. All rights reserved.
Keywords:
Electromagnetic Acoustic Transducers
Magnetostriction
Lorentz force
Steel
1. Introduction
Electromagnetic Acoustic Transducers (EMATs) are able to
generate and detect ultrasonic waves thanks to contactless electromagnetic coupling with the test object, rather than with mechanical
coupling, as in standard piezoelectric probes [1–4]. This feature
makes EMATs an attractive alternative to piezoelectric transducers
in all those applications where contactless inspections are required,
for example when high temperature or moving objects are to be
tested. Moreover, EMATs can excite a wide range of wave-modes and
can be employed as a standard for ultrasonic calibration. However,
EMATs have some disadvantages: the signal-to-noise ratio is relatively low compared to standard transducers and their performance
depends significantly on the material properties of the inspected
sample. A wide range of different kinds of steel materials, with
different physical properties is employed in modern engineering. The
variation of EMATs performance with material properties represents
a major concern for practical applications, since it raises the question
whether the same EMAT probe can be successfully used to inspect
different kinds of steel, or if transducers optimized for each steel
grade have to be developed. For instance, the results of pulse-echo
n
Corresponding author.
E-mail address: [email protected] (R. Ribichini).
0963-8695/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ndteint.2011.08.007
tests performed with the same EMAT transducer on different steel
grades (with no oxidation) is presented in Fig. 1.
When employed on ferromagnetic materials such as steel,
EMATs exploit mainly two different types of transduction mechanisms: the Lorentz force and magnetostriction. When an eddy
current density, Je, induced in a conductive sample by a driving
electric current, interacts with a static bias magnetic flux density, B
produced by a magnet, the Lorentz force arises:
f ¼ Je B,
ð1Þ
where f is a force per unit volume. On the other hand, magnetostriction is due to the fact that ferromagnetic domains tend to align
along the direction of the total magnetic field, causing a net
mechanical strain [5,6]. When the magnetic field has a timevarying component this strain can be exploited to launch ultrasonic waves. Both transduction mechanisms have mechanical to
electromagnetic counterparts, i.e. ultrasonic waves in the testpiece
induce an electrical signal in the transducer so it can be used as a
receiver.
While the Lorentz force mechanism is linear and relatively
insensitive to material properties such as electric conductivity s
and relative magnetic permeability mr, magnetostriction is highly
non-linear, depends significantly on the physical properties of the
sample and is a function of the applied magnetic field, stress state,
magneto-mechanical loading history and surface conditions [7].
R. Ribichini et al. / NDT&E International 45 (2012) 32–38
33
Am
m plit u de [a rrb.]
Table 1
List of the steel samples under investigation.
0
60
Designation
C [%]
Other elements [%]
Notes
EN8
EN16
EN24
EN36
EN3
EN32B
BO1
AISI 304
L80a
L80b
L80SS
TN80cr3
J55
CS70
0.32–0.40
0.30–0.40
0.30–0.40
0.10
0.16–0.24
0.13–0.18
0.90–1.00
0.08
0.25–0.30
0.25–0.30
0.25–0.30
0.25–0.30
0.40–0.50
0.65–0.75
0.80 Mn
1.50 Mn, 0.25 Mo
0.60 Mn, 0.25 Mo, 1.50 Ni, 1.20 Cr
0.50 Mn, 3.50 Ni, 0.90 Cr
0.70 Mn
0.80 Mn
1.20 Mn, 0.50 Cr, 0.50 W, 0.22V
9.00 Ni, 19.00 Cr
1.40 Mn. 0.12 Cu, Mo, Cr, Ti
1.40 Mn. 0.12 Cu, Mo, Cr, Ti
Mo, Cr, Ti
Mo, Cr, Ti
1.00 Mn, 0.17 Cr, 0.09 Cu, Mo, Ni
0.70 Mn
Mild steel
Hardenable
Hardenable
Hardenable
Mild steel
Mild steel
Tool steel
Austenitic
Pipe steel
Pipe steel
Pipe steel
Pipe steel
Pipe steel
Pipe steel
120
Time [µs]
Fig. 1. Pulse-echo signals from a spiral coil EMAT on a range of different steel
grade samples with equal thickness: from top down EN24, AISI 304, CS70,
TN80cr3, L80. Oxide layers can significantly increase the signal amplitude due to
magnetostriction.
For this reason, it is fundamental to determine, which transduction mechanism dominates for a given EMAT configuration as it
affects the behaviour of the transducer when used on materials
with different properties. Previous research has established that
magnetostriction is the leading phenomenon in those EMAT
configurations where the bias field is parallel to the surface of
the sample [3]. However, when the static field is normal to the
sample, some authors state that the Lorentz force dominates
[3,8,9], while others [4,10] claim that magnetostriction is the
major effect for most practical cases.
This paper presents an experimental study of bulk shear wave
EMAT performance on a wide range of steel materials commonly
used in engineering. The experimental results are compared with
simulations from a previously validated Finite Element model in
order to obtain a physical interpretation of the data. An analysis of
the relative importance of the transduction mechanisms is performed and practical conclusions are drawn.
2. The experimental study
The steel grades under investigation are among the most
commonly used in modern engineering, ranging from mild steel
to tool and alloy steel, and including pipe steel and an austenitic
steel (AISI 304). Two samples of the same grade (L80) were also
included for reference. The materials tested are listed in Table 1.
All the samples have the same dimensions: 70 30 4 mm.
2.1. Conductivity and permeability measurement
The electrical conductivity s and the relative magnetic permeability mr, of each sample were measured with the alternating
current potential drop (ACPD) technique. A pair of electrodes
injects an alternating current in the testpiece and a second pair
of electrodes measures the resulting potential drop; the resistance
can then be computed as the real part of the ratio between the
potential difference and the current. Resistance varies with frequency due to the electromagnetic skin depth effect; once the
geometric configuration of the probe and the thickness of the
sample are known, analytical solutions [11] can be employed to
compute the couple {s, mr} that minimizes the root mean square
error between theoretical and experimental data. The resistance of
each sample was measured in the frequency range between 2 and
Table 2
Measured electromagnetic properties. Relative magnetic permeability was estimated via ACPD technique and a Feritscope instrument. The electric conductivity
was measured with ACPD. The static magnetic flux density B when the spiral coil
EMAT is applied to each sample, measured at the centre of the transducer and on
the surface of the sample, is also given. Data accuracy 75 mT.
Designation
r [MS/m]
lr, ACPD
lr, Ferritscope
B [mT]
EN8
EN16
EN24
EN36
EN3
EN32B
BO1
AISI 304
L80a
L80b
L80SS
TN80cr3
J55
CS70
4.12
3.71
3.80
3.03
4.47
4.46
4.01
1.39
4.54
4.54
4.19
2.61
4.06
3.77
92
52
65
99
128
108
90
1
70
61
67
86
137
59
170
110
132
142
166
150
157
1
143
139
126
167
164
100
753
769
774
762
772
772
777
433
780
760
768
756
766
747
400 Hz and a two-variable fit with the analytical formula was
performed to deduce the electromagnetic properties (Table 2). The
measured conductivity of the ferritic steels falls within the range s
A [2.5; 4.5] MS/m while the conductivity of austenitic AISI 304 is
1.39 MS/m. The measured permeabilities for the ferritic steel
samples were between 50 and 140, while AISI 304, being nonferromagnetic, has approximately unit relative permeability.
The magnetic permeability was also measured with a Fischer
Technology Feritscope MP30E-S. This instrument measures an
engineering parameter, the equivalent ferrite content, from which
permeability can be estimated using an approximated relationship
found in the literature [12]. While ACPD employs low-intensity
currents, in the order of a few milliamperes, the Feritscope induces
much larger currents in the sample. The EMATs used in the
experimental study were driven by an approximately 10 A peak
to peak pulse, and the currents used by the Feritscope are closer to
the actual experimental conditions than the ACPD ones, however,
this instrument gives much less accurate values, reported in
Table 2.
2.2. Magnetostriction measurement
The magnetostrictive curves, i.e. magnetostrictive strain
against magnetic field strength, of four steel grades (EN3, EN24,
EN32B, BO1) were measured in order to determine the magnetostrictive parameters to be fed in the numerical model. In each
measurement, a small sample (30 20 1 mm) was placed in the
R. Ribichini et al. / NDT&E International 45 (2012) 32–38
2.3. EMAT wave amplitude measurement
Two commercial transducers (Sonemat Ltd.) have been used:
a spiral coil EMAT and a linear racetrack coil EMAT. Both transducers generate shear waves, with radial and linear polarization,
respectively, propagating in the bulk of the material. The static
magnetic field is normal to the surface of the sample and is due to a
permanent magnet (NdFeB), while the coil generates eddy current
and dynamic magnetic fields parallel to the surface of the sample.
The transducers are driven by a broadband pulse, whose centre
frequency is around 2.5 MHz. The result of a typical pulse-echo test
is shown in Fig. 3 (a): the ultrasonic pulse travels across the
thickness of the sample and the reflections from its back-wall are
received by the transducer. For each type of transducer, five
Magnetostrictiv Strain, [ppm]
10
0
-10
EN32B
EN32
-20
BO1
EN24
nickel
-30
-40
0
20
40
60
80
Static Magnetic Field, H [kA/m]
Fig. 2. Magnetostriction curves of four steel grades and industrially pure nickel.
A
Amplitu
ude [V
V]
0.3
-0.3
0
20
Time [µs]
0.3
Vp-pp [V]
air gap of a magnetic circuit. Two electromagnets driven by an
adjustable DC current generated the bias field, the resulting
magnetic field being proportional to the driving current. The
magnetic flux density generated at the surface of the sample, in
a direction parallel to the surface (Bair) was measured by using a
Hall gaussmeter (GM04, Hirst Magnetic Instruments). The magnetic field strength inside the material can then be estimated by
acknowledging that Hair ¼Bair/m0 and that the boundary conditions
for H prescribe the continuity of the tangential component at the
boundary between two media, so Hsteel ffi Hair. Since the magnetostrictive strain to be measured is relatively small (less than
8 ppm) four strain gages (Kyowa) in a full bridge configuration
were employed. Two gages on the opposite arms of the Wheatstone bridge were parallel to the static bias field, while the other
two gages were perpendicular to it. Two gages orthogonal to each
other were on each side of the sample; this configuration maximizes the sensitivity to the strain in the bias field direction while
cancelling out any bending strain or thermal expansion strain. The
resulting magnetostriction curves, shown in Fig. 2, are consistent
with data available in the literature [5,7,10,13]. For comparison,
the magnetostriction curve of industrially pure (99.0%) nickel is
also shown [14]. In the steel samples the application of a magnetic
field initially causes a positive strain (i.e. an expansion) along the
direction of the field. The deformation reaches a maximum for
Ho20 kA/m and turns into a compressional strain for higher bias
fields. Even though the shapes of the four curves are similar, the
position and magnitude of the maxima differ significantly for each
grade because of the presence of alloy elements and due to
thermal treatments. Conversely, nickel shows a monotonic contraction whose amplitude is significantly larger than the strain
observed in any steel.
Extrapolated Value
0
20
0
Time [µs]
Fig. 3. (a) Signal received by an EMAT transducer in a pulse-echo test. The peak to
peak amplitudes of the back-wall reflections have been interpolated via an
exponential fit (b). It is then possible to estimate a theoretical attenuation-free
amplitude for zero time of flight.
0.6
A
Adjuste
ed Signnal Am
mplitudee [ V]
34
J55
TN80
L80SS
L80
EN36
EN16
0.4
EN3
EN32B
EN24
BO1 EN8
304
0.2
0.0
1
2
3
4
5
Fig. 4. Experimental EMAT amplitudes on different steels plotted against their
electric conductivity. The amplitudes are attenuation compensated and squarerooted to account for the wave generation process only.
acquisitions per steel sample were taken, each resulting from the
average of 1000 time traces. The peak to peak amplitudes of the
first seven reflections were measured and were fitted with an
exponential function, in order to extrapolate the theoretical amplitude for zero time of fight (Fig. 3 (b)). This is necessary in order to
compensate both for diffraction effects and for the ultrasonic
attenuation, which is different for each kind of steel. Since the
tests used the EMAT in pulse echo mode, the square root of the
values obtained was taken in order to account for the generation
mechanism only, on the assumption that reciprocity holds. Being
magnetostriction highly non-linear, it is in general non-reciprocal.
However, a linearization can be employed when a small dynamic
~ is superimposed on a large static bias field H, such that
field H
~
Hb H. This assumption is normally satisfied in EMATs, as the bias
field due to the magnet is usually much larger than the timevarying field caused by the driving current.
The experimental results are shown in Figs. 4 and 5 for the linear
coil transducer. The adjusted signal amplitudes are plotted against
electric conductivity s (Fig. 4) and against magnetic permeability
R. Ribichini et al. / NDT&E International 45 (2012) 32–38
A
Adjuste
ed Signnal Am
mplitudee [ V]
0.6
0.4
0.2
0.0
40
70
100
130
Magnetic permeability, r
160
Fig. 5. Experimental EMAT amplitudes on different steels plotted against their
magnetic permeability as measured with ACPD technique (AISI 304 not shown in
this graph as mr ¼ 1). The amplitudes are attenuation compensated and squarerooted to account for the wave generation process only.
(measured with ACPD technique), mr (Fig. 5). Error bars show the
experimental standard deviations of the quantities under investigation for each steel grade. Analogous graphs were obtained from the
spiral coil EMAT. The data show that the signal amplitudes do not
have a large scatter and are not obviously correlated with the
electric conductivity and magnetic permeability. Even using the
permeabilities values measured with the Feritscope there is no
better correlation between EMAT amplitudes and permeabilities.
The only exception is the case of austenitic steel whose lower
amplitude is due to the fact that since this material is not
ferromagnetic the magnetic flux density is significantly smaller
than in the case of ferromagnetic steels. Indeed, measurements
indicated that B ¼ 410 mT for AISI 304, against an average of
B ffi 770 mT for all the other samples (Table 2); this reduces the
resulting amplitude by a factor of about 2, as the Lorentz force is
linear in B (Eq. (1)). If we compensate the amplitude of AISI 304 for
this effect, all the experimental points have similar amplitudes. This
strongly suggests that the transduction is mainly due to the Lorentz
force, whose magnitude does not depend significantly on conductivity or permeability; if magnetostriction were dominant, a much
larger scatter would be expected because of the observed differences in the magnetostriction curves of the various grades. In order
to test this hypothesis and shed light on the experimental results
numerical simulations were carried out.
3. Finite element simulations
An EMAT numerical model has been developed using a Finite
Element (FE) commercial software, COMSOL Multiphysics [14].
The program solves simultaneously the electrodynamic problem,
accounting for eddy-current induction, and the elastic problem,
accounting for wave generation. The magnetomechanical coupling is achieved by adding the Lorentz force and magnetostriction. The Lorentz force is implemented using its definition: the
input force of the elastic problem, a mechanical effect, is caused
by electrical quantities i.e. the vector product of eddy current
density and static magnetic flux density (Eq. (1)). Modelling
magnetostriction requires a modification of the constitutive
equations in a way analogous to piezoelectricity:
(
e~ ¼ SH s~ þdH~
,
ð2Þ
~
B~ ¼ dT s~ þ ms H
35
~ are
where e~ and s~ are the strain and stress tensors and B~ and H
the magnetic flux density and the magnetic field strength,
respectively. Dynamic components of physical quantities are here
indicated with a tilde as opposed to the static components
denoted by a bar. Together with the usual elastic compliance
matrix SH (measured for constant H) and permeability matrix ms
(measured at constant stress), coupling terms, proportional to the
magnetostriction matrix d, (and its transpose dT) are present. The
first equation accounts for direct magnetostriction, i.e. strain
caused by the application of a magnetic field, whereas the second
equation describes inverse magnetostriction, used in the detection process, when a stress produces magnetic flux density
changes that can be picked up by the transducer. Under the large
~ it is possible to derive all the
bias field approximation, Hb H,
components of the magnetostrictive coupling matrix d from a
single experimental curve of the magnetostrictive strain versus
the applied bias field H, which is characteristic of the ferromagnetic material under investigation. All the non-zero terms of the
matrix are either proportional to the derivative of the magnetostriction curve at the operation point, i.e. the bias field H, or to the
ratio between the total magnetostrictive strain, e and the corresponding static bias field. The latter is usually the most relevant
for magnetostrictive wave generation; Ogi and Hirao [4] have
shown that it can be computed as:
d15 ¼
3e
H
ð3Þ
The magnetostriction model (and its underlying assumptions)
has been quantitatively validated for SH0 wave generation in a
nickel plate [14]. The model predicted the wave amplitude from
first principles, without any adjustable parameters, with a 720%
accuracy over a 200 kHz range and over a wide range of bias field
strength.
The model was used to help to understand the results of the
experiments on the steel samples discussed above. An axisymmetric two-dimensional model in a cylindrical reference system
{r,z,j} of an EMAT has been developed. The driving current in the
coil is modelled as a zero cross-section current sheet, flowing in
the circumferential direction above the metal, that induces eddy
currents Jj. These interact with the vertical component of the
static flux density Bz producing a Lorentz body force fr ¼ Jj Bz in
the radial direction that generates shear waves. Magnetostriction
also contributes to the wave generation since it can be shown
from Eq. (2) that shear strains e~ rz are produced by the dynamic
magnetic field:
e~ rz pd15 H~ r
ð4Þ
where d15 is the magnetostrictive coupling matrix component
~ r is the radial component
involved in shear wave generation and H
of the dynamic magnetic field strength. The other magnetostriction contributions are proportional to the normal component of
~ z , and are considerably lower as the magnetic
the dynamic field, H
~ below the coil is mostly parallel to the surface of the
field H
sample. The outer and inner diameters of the coil are 34 mm and
6 mm, respectively; the distance between the coil and the sample
(lift-off) is 0.6 mm. The coil is driven by a 1 A current oscillating at
a frequency f¼2 MHz. The mesh consists of approximatively
150,000 triangular elements. The elastic properties used were
the same for all the grades of steel: Young’s modulus 200 GPa,
Poisson’s ratio 0.33, mass density 7850 kg/m3. Just below the coil,
full magnetostrictive constitutive equations are employed to
simulate the transduction process. For a depth larger than a few
skin depths d, i.e. 9z9 44d, the dynamic magnetic field becomes
negligible and no transduction occurs. For this reason, purely
elastic constitutive equation can be used to describe wave
propagation saving significant computational time. In order to
R. Ribichini et al. / NDT&E International 45 (2012) 32–38
simulate the operation on a half-space, an absorbing region with
finite damping constant surrounds the elastic domain, to avoid
back-reflections from the boundaries of the model. The result of a
typical FE simulation is shown in Fig. 6.
The displacement amplitudes produced separately by the
Lorentz force and by magnetostriction were computed for four
of the steel samples (EN3, EN24, EN32B, BO1). In turns, the sole
Lorentz force was applied, without any magnetostriction, and then
the simulation was repeated with purely magnetostrictive effects
and no Lorentz force, in order to evaluate the contribution of each
mechanism. The magnetostrictive and magnetic properties were
obtained from the experiments discussed above. In order to test
the hypothesis that the Lorentz force is the dominant effect, the
most favourable conditions for magnetostriction were taken into
account to assess its maximum contribution. The magnetic permeabilities used in the simulations were those measured via
ACPD, which are lower than those estimated with the Feritscope.
Lower permeabilities imply a larger skin depth as d ¼ ðpf smÞ1=2 ,
~
that is, there is a larger region where a significant dynamic field H
is present. In other words, this means that the area over which Eq.
(4) has to be integrated is wider hence the effect of magnetostriction is stronger. Moreover, the magnetic bias field in the material
H, which determines the operation point cannot be estimated
without a degree of uncertainty. This is a consequence of the fact
that at the boundary between two media the perpendicular
component of B (in our case Bz ) is continuous, while the perpendicular component of H is discontinuous. In other words, we know
accurately the value of Bz from experimental data, but we can only
estimate Hz using FE models. For the case under study it was
found that Hz A [6, 15] kA/m. The maximum values of the
magnetostrictive constant d15 falling in this range were considered
to assess the largest possible impact of magnetostriction on wave
generation. For the Lorentz force computations the static bias field
Bz was assumed to be the same for all the samples and was set to
the experimental value: Bz ¼ 770mT. Remembering that the
values for magnetostriction are to be considered an ideal upper
limit, the simulations indicate that for the investigated steels,
the Lorentz force is the main transduction mechanism and that the
contribution of magnetostriction is never larger than 30% of the
Lorentz force for three samples, and reaches 70% for EN24
(Fig. 7).
For comparison, the simulations were also performed on nickel.
The material properties used were: Young’s modulus 200 GPa,
Poisson’s ratio 0.29, mass density 8900 kg/m3, electric conductivity
14.3 MS/m, and assuming the most favourable operation point for
magnetostriction on nickel, i.e. 20 kA/m, relative permeability 24,
and magnetostrictive constant d15 ¼4.09 nm/A. It has also to be
noted that the bias magnetic flux density in nickel is B ¼ 600 mT
due to magnetic saturation. Nickel is significantly more magnetostrictive than steel, thus in this case magnetostriction is the larger
effect, the resulting displacement being 1.7 times the one due to the
Lorentz force mechanisms. These results are summarized in Table 3.
The predictions made for magnetostriction are essentially an
upper limit; not only have we considered the maximum magnetostrictive constant for a given steel and the lowest measured
permeability, also an implicit assumption has been made: that
magnetostrictive constants are frequency independent. The
magnetostriction curve of each material was measured in dc
conditions, applying a static bias field and the resulting magnetostrictive constants were used for ac simulations. This assumption
was made simply because assessing the frequency dependency of
magnetostriction is a very complex experimental task, and in the
literature there is a lack of dynamic magnetostriction properties.
However, it is likely that when a dynamic magnetic field oscillating
at frequencies in the order of hundreds of kilohertz is applied to a
ferromagnetic material, not all the magnetic domains are able to
follow the driving input, resulting in a reduction of the magnetostrictive coefficients. This hypothesis is strongly supported by the
fact that magnetic permeability significantly decreases with
frequency [15,16]; since permeability and magnetostriction are
macroscopic effects caused by the same microscopic structures,
2.0
Displacemeent [arb.]
36
Lorentz
Magnetostriction
1.5
1.0
0.5
0.0
EN32B
EN3
BO1
EN24
Ni
Fig. 7. Simulated displacements caused by the Lorentz force and magnetostriction
in four steel grades and nickel. The amplitudes are not necessarily in phase. The
same unit driving current oscillating at 2 MHz was used for all the simulations.
Table 3
Maximum magnetostrictive constants d15 of four steel samples in the range
Hz A [6, 15] kA/m. The corresponding EMAT signal amplitudes (experimental), for
the wave generation process only, are also shown. The last column displays the
percentage ratio of the displacement caused by magnetostriction against the one
due to the Lorentz force as predicted by the FE model for f¼ 2 MHz. Data on nickel
are also shown for reference.
Fig. 6. Axisymmetric FE model of spiral coil EMAT. The displacement in the r
direction generated by the transducer is represented by the colour plot. The
dynamic magnetic field produced by the coil is represented by the contour lines.
Material
d15 [nm/A]
Exp. Amp. [OV]
MS/LOR
EN32B
EN3
BO1
EN24
Nickel
1.30
1.44
1.23
1.71
4.09
0.411
0.417
0.427
0.413
–
27.5%
25.7%
35.6%
70.4%
173.5%
R. Ribichini et al. / NDT&E International 45 (2012) 32–38
some scatter in the experimental data. This is mainly due to the
contribution of magnetostriction, together with experimental
uncertainties in the measurement of magnetic flux density B
and of the driving current I, which were quantified to 73–6%
uncertainty of the signal amplitudes.
From a practical point of view, since the measured amplitudes on
different kinds of steel are similar, it is possible to use the same
EMAT probe on a wide range of grades. Large amplitude variations
have been observed in the field while inspecting steel components.
Such variations are probably due to the presence of highly magnetostrictive oxide layers. In those cases, at the frequencies and
permeabilities considered in this study, the transduction is mostly
confined in the oxide layer, and magnetostriction is the dominant
mechanism, as in the case of nickel, significantly increasing the
overall signal level. It can be concluded that normal bias field EMATs
do not show large variations in the performance when operating on
steel with a range of different material properties, except when a
highly magnetostrictive oxide layer is present.
i.e. magnetic domains, it is likely that the value of d15 used in our
computation is overestimated. This is experimentally hinted at by
the fact that there is no correlation between the magnetostrictive
constants measured and the EMAT wave amplitudes.
4. Discussion
No rmalize d Amp l itude [a rb.]
The numerical and experimental results lead to the conclusion
that the Lorentz force mechanism is the dominant one in steel,
while magnetostriction plays a less significant role. This conclusion can be interpreted via the physics of the two transduction
mechanisms. As long as the eddy current penetration depth is
much smaller than the acoustic wavelength, it is found by
integrating Eq. (1) that the total Lorentz force is proportional to
R
the total induced current: F L pB JdA, whereas the total magnetostrictive force is proportional to the integral of the dynamic
R
~
magnetic field: F MS pd15 HdA.
By using an electromagnetic FE
model, or analytical solutions [17], we can compute the dependencies of these quantities on electrical conductivity and magnetic permeability. The results are shown in Fig. 8, normalized on
the y-axis in order to show the relative variations of the integrals
with the electromagnetic properties. The Lorentz force is not very
sensitive to changes in s and mr because highly conductive
materials show a shielding effect: the eddy currents tend to equal
and mirror the driving current, regardless of their spatial distribution, which is governed by conductivity and permeability
[3,5]. For this reason, the total eddy current, and thus the Lorentz
force, is relatively insensitive to conductivity and permeability
changes in highly conductive materials. On the other hand,
magnetostriction is highly affected by s and mr because not only
~ along the
does the distribution of the dynamic magnetic field H
depth of the material change, but also its amplitude. This means
that the integral of the magnetic field, and thus magnetostriction,
is strongly affected by the electromagnetic properties of the
material. The overall conclusion is that if the Lorentz force
mechanism is dominant, a small variation of signal amplitudes
with conductivity and permeability is to be expected, while if
magnetostriction is the main transduction mechanism, large
variations in the amplitudes should be observed. The relatively
small variation of signal amplitudes in the experimental data
supports the argument that Lorentz force is the dominant
transduction mechanism for this EMAT configuration [3,8,9], in
agreement with FE predictions. A purely Lorentz force mechanism
would give virtually no variation with s and mr; however, there is
5. Conclusions
Electromagnetic Acoustic Transducers operate on ferromagnetic materials via two physical phenomena: the Lorentz force and
magnetostriction. Previous research on bulk shear wave EMATs
has established that when the magnetic bias field is parallel to the
surface of the sample magnetostriction is the dominant effect,
while when it is normal to the surface diverging conclusions have
been drawn. Some authors stated that the Lorentz force is the
main effect [3,8,9], while others [4,10] claim that magnetostriction
is up to two orders of magnitude larger than the Lorentz force.
Experimental tests and numerical simulations undertaken in this
study indicate that the Lorentz force is the largest transduction
mechanism on steel materials, regardless of the level of magnetic
bias field employed, while the Lorentz force and magnetostriction
are of the same order in nickel. This finding is in contradiction
with relatively recent claims [4,10], but agrees with previous
studies [3,8,9]. This conclusion is of practical importance because,
unlike magnetostriction, the Lorentz force is relatively insensitive
to the range of material properties of steels. This implies that using
the same EMAT probe on various grades is possible and yields
similar performance. However, signals will increase when a highly
magnetostrictive oxide is present so magnetostriction becomes
significant, while the performance on austenitic steels is poorer
than ferritic steels because of the reduced bias magnetic field.
1.0
1.0
0.8
0.8
0.6
0.6
00.4
4
0.4
04
0.2
0.2
0.0
1
2
3
4
Conductivity, σ [MS/m]
37
5
0.0
40
70
100
130
160
Magnetic permeability, r
R
R ~
continuous line) plotted against (a) electric conductivity and (b) magnetic
Fig. 8. Total induced current ( JdA, dashed line) and total dynamic magnetic field ( HdA,
permeability. Since the Lorentz force is proportional to the total induced current and magnetostriction is proportional to the total dynamic magnetic field, these plots show
the dependency of the two transduction mechanisms on material properties. The values on the y-axis are normalized to show the relative variations with s and mr.
38
R. Ribichini et al. / NDT&E International 45 (2012) 32–38
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