NDT&E International 45 (212) 32 38 Contents lists available at SciVerse ScienceDirect 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 UK Research Centre in NDE, Department of Mechanical Engineering, Imperial College, London, SW7 2AZ, UK b School of Aerospace Systems, University of Cincinnati, Cincinnati, OH 45221, USA article info Article history: Received 12 December 21 Received in revised form 14 August 211 Accepted 2 August 211 Available online 1 September 211 Keywords: Electromagnetic Acoustic Transducers Magnetostriction Lorentz force Steel abstract 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. & 211 Elsevier Ltd. All rights reserved. 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: remo.ribichini6@imperial.ac.uk (R. Ribichini). 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, J e, 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 J e 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 m r, 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]. 963-8695/$ - see front matter & 211 Elsevier Ltd. All rights reserved. doi:1.116/j.ndteint.211.8.7
R. Ribichini et al. / NDT&E International 45 (212) 32 38 33 Table 1 List of the steel samples under investigation. Designation C [%] Other elements [%] Notes rb.] u de [a r mplitu Am 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 [4,1] 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 Time [µs] 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 34). Two samples of the same grade (L8) were also included for reference. The materials tested are listed in Table 1. All the samples have the same dimensions: 7 3 4 mm. 2.1. Conductivity and permeability measurement 6 12 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 34, CS7, TN8cr3, L8. Oxide layers can significantly increase the signal amplitude due to magnetostriction. The electrical conductivity s and the relative magnetic permeability m r, 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, m r } 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 EN8.32.4.8 Mn Mild steel EN16.3.4 1.5 Mn,.25 Mo Hardenable EN24.3.4.6 Mn,.25 Mo, 1.5 Ni, 1.2 Cr Hardenable EN36.1.5 Mn, 3.5 Ni,.9 Cr Hardenable EN3.16.24.7 Mn Mild steel EN32B.13.18.8 Mn Mild steel BO1.9 1. 1.2 Mn,.5 Cr,.5 W,.22V Tool steel AISI 34.8 9. Ni, 19. Cr Austenitic L8 a.25.3 1.4 Mn..12 Cu, Mo, Cr, Ti Pipe steel L8 b.25.3 1.4 Mn..12 Cu, Mo, Cr, Ti Pipe steel L8SS.25.3 Mo, Cr, Ti Pipe steel TN8cr3.25.3 Mo, Cr, Ti Pipe steel J55.4.5 1. Mn,.17 Cr,.9 Cu, Mo, Ni Pipe steel CS7.65.75.7 Mn Pipe steel 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] l r, ACPD l r, Ferritscope B [mt] EN8 4.12 92 17 753 EN16 3.71 52 11 769 EN24 3.8 65 132 774 EN36 3.3 99 142 762 EN3 4.47 128 166 772 EN32B 4.46 18 15 772 BO1 4.1 9 157 777 AISI 34 1.39 1 1 433 L8 a 4.54 7 143 78 L8 b 4.54 61 139 76 L8SS 4.19 67 126 768 TN8cr3 2.61 86 167 756 J55 4.6 137 164 766 CS7 3.77 59 1 747 4 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 34 is 1.39 MS/m. The measured permeabilities for the ferritic steel samples were between 5 and 14, while AISI 34, being nonferromagnetic, has approximately unit relative permeability. The magnetic permeability was also measured with a Fischer Technology Feritscope MP3E-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 1 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 (3 2 1 mm) was placed in the
34 R. Ribichini et al. / NDT&E International 45 (212) 32 38 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 (B air ) was measured by using a Hall gaussmeter (GM4, Hirst Magnetic Instruments). The magnetic field strength inside the material can then be estimated by acknowledging that H air ¼B air /m and that the boundary conditions for H prescribe the continuity of the tangential component at the boundary between two media, so H steel ffih air. 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 [5,7,1,13]. For comparison, the magnetostriction curve of industrially pure (99.%) 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 Ho2 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. 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 Strain, [ppm] Magnetostrictiv 1-1 -2-3 EN32B EN32 BO1 EN24 nickel -4 2 4 6 8 Static Magnetic Field, H [ka/m] Fig. 2. Magnetostriction curves of four steel grades and industrially pure nickel. Amplitu ude [V V] p [V] Vp-p.3 -.3.3 Extrapolated Value Time [µs] 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. Adjuste ed Sign nal Am mplitude [ V].6.4.2 34 TN8 EN36 EN16 EN24 L8SS acquisitions per steel sample were taken, each resulting from the average of 1 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 field ~ H is superimposed on a large static bias field H, suchthat 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 J55 BO1 EN8 EN32B. 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. L8 2 2 EN3
R. Ribichini et al. / NDT&E International 45 (212) 32 38 35 Adjuste ed Sign nal Am mplitude [ V].6.4.2. 4 7 1 13 Magnetic permeability, μ r Fig. 5. Experimental EMAT amplitudes on different steels plotted against their magnetic permeability as measured with ACPD technique (AISI 34 not shown in this graph as m r ¼1). The amplitudes are attenuation compensated and squarerooted to account for the wave generation process only. (measured with ACPD technique), m r (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 41mT for AISI 34, against an average of Bffi77mT 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 34 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 S H ~s þd H ~ ~B ¼ d T ~s þm s H ~, ð2þ 16 where ~e and ~s are the strain and stress tensors and B ~ and H ~ are 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 S H (measured for constant H) and permeability matrix m s (measured at constant stress), coupling terms, proportional to the magnetostriction matrix d, (and its transpose d T ) 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 bias field approximation, Hb H, ~ it is possible to derive all the 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: d 15 ¼ 3e ð3þ H The magnetostriction model (and its underlying assumptions) has been quantitatively validated for SH wave generation in a nickel plate [14]. The model predicted the wave amplitude from first principles, without any adjustable parameters, with a 72% accuracy over a 2 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 J j. These interact with the vertical component of the static flux density B z producing a Lorentz body force f r ¼ J j B z 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 pd 15 Hr ~ ð4þ where d 15 is the magnetostrictive coupling matrix component involved in shear wave generation and ~ H r is the radial component of the dynamic magnetic field strength. The other magnetostriction contributions are proportional to the normal component of the dynamic field, ~ Hz, and are considerably lower as the magnetic field ~ H below the coil is mostly parallel to the surface of the 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.6 mm. The coil is driven by a 1 A current oscillating at a frequency f¼2 MHz. The mesh consists of approximatively 15, triangular elements. The elastic properties used were the same for all the grades of steel: Young s modulus 2 GPa, Poisson s ratio.33, mass density 785 kg/m 3. 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. 9z944d, 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
36 R. Ribichini et al. / NDT&E International 45 (212) 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 ¼ðpfsmÞ 1=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 B z ) is continuous, while the perpendicular component of H is discontinuous. In other words, we know accurately the value of B z from experimental data, but we can only estimate H z using FE models. For the case under study it was found that H z A [6, 15] ka/m. The maximum values of the magnetostrictive constant d 15 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 B z was assumed to be the same for all the samples and was set to the experimental value: B z ¼ 77mT. 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 3% of the Lorentz force for three samples, and reaches 7% for EN24 (Fig. 7). For comparison, the simulations were also performed on nickel. The material properties used were: Young s modulus 2 GPa, Poisson s ratio.29, mass density 89 kg/m 3, electric conductivity 14.3 MS/m, and assuming the most favourable operation point for magnetostriction on nickel, i.e. 2 ka/m, relative permeability 24, and magnetostrictive constant d 15 ¼4.9 nm/a. It has also to be noted that the bias magnetic flux density in nickel is B ¼ 6mT 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, ent [arb.] Displaceme 2. Lorentz Magnetostriction 1.5 1..5. 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 d 15 of four steel samples in the range H z 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 f¼2 MHz. Data on nickel are also shown for reference. Material d 15 [nm/a] Exp. Amp. [OV] MS/LOR 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. EN32B 1.3.411 27.5% EN3 1.44.417 25.7% BO1 1.23.427 35.6% EN24 1.71.413 7.4% Nickel 4.9 173.5%
R. Ribichini et al. / NDT&E International 45 (212) 32 38 37 i.e. magnetic domains, it is likely that the value of d 15 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 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 the total induced current: F L pb R JdA, whereas the total magnetostrictive force is proportional to the integral of the dynamic R magnetic field: F MS pd 15 ~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 m r 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 m r because not only does the distribution of the dynamic magnetic field H ~ along the 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 m r ; however, there is 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 EMATprobeonawiderangeofgrades.Largeamplitudevariations 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. 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 [4,1] 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 [4,1], 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. Normalized Amp litude [arb.] 1..8.6 4.4.2. 1 2 3 4 5 Conductivity, σ [MS/m] 1..8.6 4.4.2. 4 7 1 13 16 Magnetic permeability, μ r Fig. 8. Total induced current ( R JdA, dashed line) and total dynamic magnetic field ( R ~ HdA, continuous line) plotted against (a) electric conductivity and (b) magnetic 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 m r.
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