Magnetic hysteresis and magnetic flux patterns measured by acoustically stimulated

electromagnetic response in a steel plate

Hisato Yamada, Kakeru Watanabe, and Kenji Ikushima*

Department of Applied Physics, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, JapanE-mail: ikushima@cc.tuat.ac.jp

Received March 5, 2015; accepted April 30, 2015; published online July 2, 2015

Magnetic hysteresis loops are measured by ultrasonic techniques and used in visualizing the magnetic-flux distribution in a steel plate. Thepiezomagnetic coefficient determines the amplitude of acoustically stimulated electromagnetic (ASEM) fields, yielding the hysteresis behavior ofthe intensity of the ASEM response. By utilizing the high correspondence of the ASEM response to the magnetic-flux density, we image the specificspatial patterns of the flux density formed by an artificial defect in a steel plate specimen. Magnetic-flux probing by ultrasonic waves is thus shownto be a viable method of nondestructive material inspection. © 2015 The Japan Society of Applied Physics

1. Introduction

All ferromagnetic materials exhibit hysteresis in the variationof flux density B with magnetic field H. Hysteretic properties,such as permeability, coercivity, remanence, and hysteresisloss are known to be sensitive to such factors as stress, strain,grain size, and heat treatment. Because hysteresis measure-ments yield a number of independent parameters of materials,they have been used in the determination of materialproperties, in stress sensor applications, and in nondestructiveevaluation (NDE) of large-scale structures.1–3) For instance,the leakage flux techniques with magnetic sensors are oftenused to detect a defect or flaw from anomalies in magneticflux.1) In the conventional techniques, however, the distancebetween the sensor and an object (lift-off) should typically beless than 1mm and maintaining a constant lift-off is difficultfor a complex structure or rough surface.

Recently, we presented a magnetic detection techniquethat incorporated ultrasonic inspection.4,5) The principle ofthis technique is based on the generation of acousticallystimulated electromagnetic (ASEM) fields through magneto-mechanical coupling. An advantage of the ASEM method isthat it is compatible with conventional ultrasonic pulse–echosensing, and can be used for evaluating the magneticproperties of a material even in optically opaque objectssuch as a human body, plastic, and concrete.5) In addition,unlike the leakage flux techniques, the intrinsic magnetic fluxflowing inside the target materials is visualized through RF-ultrasonic excitation. Another feature of the ASEM method isthat the distance between the RF-receiver antenna and thetarget sample (typically 1–5 cm) does not affect the spatialresolution; it is determined by the size of the ultrasonic focalspot. Therefore, centimeter-scale lift-off is acceptable in thismethod. This allows the difficulty of constant lift-off to bereduced. To make the ASEM method practical for NDEapplications, however, it is important to clarify the hysteresisproperties of the ASEM response. In this paper, we show thehysteresis loop of the ASEM response and demonstrate thedetection of anomalies in magnetic flux caused by a defect ina steel plate specimen.

2. Theoretical background

To complete the description of magnetic hysteresis in stressfields, there must be a constitutive relation between themagnetic field H, the magnetic flux density B, and the stress

T. The B should be expressed by a nonlinear function,B = F(H,T ) = μ0H + M(H,T ). The phenomenon of hystere-sis implies that the magnetization M(H,T ) is not a single-valued function of H and T. For small reversible changes inthe linear response regime, magnetostriction is phenomeno-logically equivalent to piezomagnetism.6) The piezomagneticcoefficient djm can be defined by

djm ¼ ð@Bj=@TmÞH ¼ ð@Mj=@TmÞH; ð1Þwhere μ0 is the space permeability, j = 1, 2, and 3, and m ¼1; 2; . . . ; 6. When stress Tm(t) is applied through acousticirradiation, the magnetic flux density Bj in the material istemporally modulated by the following formula:3)

dBj

dt¼ @MjðHj; TmÞ

@Tm

� �H

dTm

dt¼ djmðHÞ dTm

dt: ð2Þ

In the ASEM method, the near-field components of theRF magnetic fields emitted to the surrounding environmentare detected. We should note that the ASEM responsearises from the intrinsic flux confined in ferromagneticmaterials and not from leakage flux from the surface ofthe materials into the air; this latter type is detected by thestandard flux leakage technique for NDE. Therefore,correction of the demagnetizing fields, which depends onthe shape of the specimen, is not required in the ASEMmethod.

If H, B, and M are axial vectors parallel to the 3-axis inferromagnetic materials, then the nonzero piezomagneticcoefficients will be limited to d31 = d32 and d33 in the uniaxialsymmetry of a polycrystalline medium. When the wavevector k of longitudinal ultrasonic waves is parallel to the1-axis in the present setup [Fig. 1(a)], the signal voltageVsig(H, t), detected by a tuned loop antenna, can be expressedas5)

VsigðH; tÞ / � 1

2�r3d31ðHÞ _T1ðtÞ; ð3Þ

where r is the distance between the locally modulated mag-netization and the observation point. Consequently, the fielddependence of the signal intensity can be identified with thatof the piezomagnetic coefficient d31(H ) = (∂B3=∂T1)H.

3. Experimental setup and samples

ASEM measurements have been performed by the probemethod [Fig. 1(a)].4) As the reference data of magnetization,

Japanese Journal of Applied Physics 54, 086601 (2015)

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we also measure the leakage flux density Bleak using acommercial Hall sensor (Lakeshore MFT-3E03-VH). Aspecimen (JIS G 3101 SS400; size: 50 × 50 × 0.8mm3) issubjected to external magnetic fields along the direction ofone edge of the plate (the 3-axis) using a commercial elec-tromagnetic coil. The Bleak is detected along the 3-axis [theinset of Fig. 1(a)]. The ultrasonic focal point (focal spot size:0.8mm) is scanned over the whole area of the specimenby moving the transducer with an integrated pick-up loopantenna (tuned frequency: 8.9MHz; diameter: 10mm) whileholding the distance r constant (r ’ 15mm). The steel platespecimen with an artificial defect (a 1-mm-diameter hole) isplaced in the focal zone at a distance of about 40mm froma 10MHz transducer (diameter: 20mm). Accordingly, thetarget signal is temporally separated from the transducerexcitation noise signals.4) The ASEM response is shownin Fig. 1(b), where the signal is amplified by 80 dB andaveraged over 10000 pulses at a repetition frequency of1 kHz. The two signals coincident with the excitation t = 0µsand the echo t = 53 µs (≡ τecho) signals are attributed to theelectromagnetic noise signals generated by the transducer.We observe a signal starting at the midpoint t = 26.5 µsbetween the excitation and the echo pulses [Fig. 2(a)]. Thisis identified as the ASEM response emitted by the steelplate. The slight deviation of the ASEM delay time fromτecho=2 (about 160 ns) is attributed to the presence of low-

and high-pass filters incorporated into the ASEM measure-ment setup.

The ASEM waveform indicates that the phase is invertedin the opposing field direction [Fig. 2(a)], suggesting that thedirection of magnetic polarization can be determined duringphase-sensitive heterodyne detection in the ASEM method.4)

In the Fourier analysis of the waveform, we observe the mainpeak at the tuned frequency of the antenna (8.9MHz) andtwo satellite peaks at 7.6 and 11.5MHz [Fig. 2(b)]. Thesatellite peaks correspond to the thickness modes of onewavelength and three-quarter wavelength resonances in thesteel plate, respectively. Thus, the confined elastic wavesyield a long tail of electromagnetic radiation, as seen inFig. 2(a).

4. Results and discussion

Figure 3(a) shows the initial magnetization curve and ahysteresis loop in the ASEM intensity and the leakageflux density Bleak. Under the initial condition, the sampleis demagnetized by applying alternating current to themagnet (AC demagnetization method). The ASEM intensityj �Vsigj is here defined as the integral of signal voltageVsig(t):

j �Vsigj ¼ 1

��

Z �echo=2þ��

�echo=2

jVsigðtÞj dt / jd31ðHÞj; ð4Þ

(a)

(b)

Fig. 1. (Color online) (a) Schematic of the experimental setup formeasuring the ASEM response.4) The inset shows the setup of the Bleak

measurements. The dashed arrow indicates the active direction of the Hallsensor. (b) Typical time traces obtained for a steel plate: (i) acoustic echosignal and (ii) ASEM signal.

(a)

(b)

Fig. 2. (Color online) (a) Time trace of ASEM and echo signals in twoopposing magnetic fields, H > 0 and H < 0. The phase of ASEM signalsdepends on the direction of magnetic polarization. (b) Fourier spectrum ofthe ASEM signals.

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where Δτ is the integrated time. As shown in Fig. 2(a), thevalue of Δτ is set to 500 ns to avoid interference by elasticwaves from additional signals emitted distantly from thefocal spot. No distinct phase change of the ASEM signals isobserved in this experiment. The component of Bleak parallelto the surface is measured at a position distant from the hole(the R region; this is shown in Fig. 4).

As shown in Fig. 3(b), the minimum (at Hmin ’ �2:0kA=m) is not observed in the initial magnetization curve.In addition, the minimum values in the hysteresis loop arecomparable to the ASEM intensity under the demagnetizedinitial condition. It follows that the minimum observed in thehysteresis loop indicates a demagnetized condition; Hmin

corresponds to the so-called coercivity Hc. The Bleak curveshows an inflection point at Hmin [Fig. 3(c)], but no signi-ficant difference is observed between the initial magnetizationcurve and the hysteresis loop. This is reasonable because thepresence of remanent magnetization is not detected inthe Bleak measurements. At H > ∣Hmin∣, the ASEM intensityincreases as the magnetic field is increased and shows amaximum value at around ∣H∣ = 20 kA=m.

We here offer a simple explanation for the H-dependenceof the ASEM intensity. Under the demagnetized condition,microscopic domains are aligned to reduce the macroscopicmagnetization to zero (to decrease magnetostatic energy).The net temporal modulation of Bj by acoustic pressure willvanish when statistically averaged over a focal spot sizeof about 1mm; this results in a minimum of j �Vsigj at Hmin

(= Hc). In the process of increasing magnetization atrelatively low fields, the domains can be easily rearranged

when the stress is applied.7,8) Above a critical field, thedomain-wall movement will be completed, and the stresssensitivity of magnetization decreases as the magnetic fieldis increased. In the high-field limit (∣H∣→ ∞), the magneticalignment becomes sufficiently stable; in this case, theRF fields driven by acoustic pressure on the order of 101

kilopascals will be absent. It follows that the ASEM responseshows a maximum in the H-dependence. In the linearresponse regime,5) the ASEM intensity corresponds to theslope of the magnetostriction curve, as observed in thetransmitter properties of EMAT techniques,9,10) becausedjm = (∂Bj=∂Tm)H = (∂Sm=∂Hj)T = dmj.

Hysteresis measurement by ultrasonic techniques shouldfind interesting applications in material evaluation and NDE.Figures 4(a) and 4(b) represent a numerically calculatedimage and an ASEM image for an artificial defect (1-mm-diameter hole) in a steel plate specimen, respectively. Weobserved a specific pattern of the ASEM intensity around thedefect. Under the experimental conditions, the applied H is40 kA=m, where the field dependence of the ASEM intensityhas a negative slope in Fig. 3. Therefore, the contrast of theASEM image [Fig. 4(b)] is reversed for the distribution ofthe calculated intrinsic flux density. To quantitatively confirmthat the contrast of the ASEM image originates from thefield dependence, as shown in Fig. 3, we first numericallycalculated the relative ratio of Bleak around the defect. Usingthe Bleak = 32mT experimentally obtained in the R regionof Fig. 4, we estimated Bleak to be 9.6 and 35mT, in the P andQ regions, respectively. Therefore, the leakage flux densitiesin the P and Q regions correspond to field conditions of14 and 46 kA=m, respectively, from the Bleak curves inFig. 3. Accordingly, the ratio of the ASEM intensity betweenthe P and Q regions is evaluated to be about 1.7 from thedata in Fig. 3. The result derived from the field dependencein Fig. 3 is in agreement with the intensity ratio betweenthe P and Q regions of about 2, as evaluated from imagingresults.

Figure 5(a) shows the ASEM image in a defect-freespecimen. The root-mean-square deviation of the ASEMintensity over the scanned area is about 1.5V in the specimenwithout a defect [Fig. 5(a)], while a clear contrast of theASEM intensity is widely observed in the plate with adefect [Fig. 5(b)]. This result indicates a magnification effect

(a)

(b) (c)

Fig. 3. (Color online) Initial magnetization curve (black circles) andhysteresis loop (red triangles and blue squares) of the ASEM intensity andBleak. (a) The red triangles and blue squares represent the upward anddownward field data of the ASEM intensity, respectively. The solid red andblue lines represent the upward and downward curves of Bleak, respectively.The solid (red) and dashed (blue) arrows indicate the upward and downwardfield directions, respectively. (b) and (c) show that the system isdemagnetized at jHj ¼ Hc ’ 2:0 kA=m (shown by the dotted lines), whichcorresponds to the inflection point of Bleak and the minimum of the ASEMintensity.

Fig. 4. (Color online) Magnetic flux distribution around a 1-mm-diameterhole in a steel plate. (a) Numerically calculated image of magnetic fluxdensity (JMAG-Studio). Flux densities in the P and Q regions (shown by thedotted circles) are suppressed or enlarged, respectively, in comparison withthe average value in the R region. The diameter of these regions correspondsto a focal spot size of 0.8mm. (b) ASEM image around the hole atH = 40 kA=m. Because of the negative slope for the field dependence of theASEM intensity at around H = 40 kA=m, the contrast of the ASEM image isreversed for the flux density.

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through magnetic flux distribution. We should note that theminimum detectable size of flaws is not determined by thesize of the ultrasonic focal spot (0.8mm diameter in thecurrent setup) in this method. The flux anomaly caused by thepresence of a flaw is normally extended to a region largerthan the actual geometric size of a defect [typically 5 times asseen in Fig. 5(b)], which is beneficial for NDE.1) Further-more, the flaw to be detected may be a grain of lowerpermeability (that is insensitive to echo signals). If thepermeability of the grain is sufficiently lower than that of thehost ferromagnetic substrate, a similar specific ASEM patternis expected. In this experiment, a relatively large hole withspace permeability is used in the demonstration, but the

ASEM method has the potential to exceed the applicablescope of the standard echo inspection.

To further confirm the origin of the specific pattern, wealso measure the normal components of the ASEM fields ina static magnetic field of H = 40 kA=m (Fig. 6). The ASEMresponse is larger at four diagonally opposite areas around thehole [Fig. 6(c)], which is reasonable given the amplitudeof the field components projected in the detection direction[Fig. 6(b)]. In addition, these results indicate a specificadvantage of the ASEM method: individual vector compo-nents of the intrinsic flux confined in the material can beindependently measured by varying the configuration ofantennas.11)

5. Conclusions

We showed the magnetic hysteresis behavior of the ASEMresponse and applied it to the magnetic-flux imaging of asteel plate. The properties obtained by the ASEM method are(1) the direction of magnetic polarization, determined by thephase of the waveform; (2) the coercivity, obtained as theminimum of the hysteresis behavior of the ASEM intensity;(3) the individual vector components of the intrinsic fluxdensity, selectively measured by adjusting the antenna con-figuration;11) and (4) the spatial distribution of the intrinsicflux density by ultrasonic scanning, yielding a magnificationeffect of a flaw. This method will be also applicable formaterial evaluation because the local B–H characteristics forthe intrinsic flux can be obtained.

Acknowledgments

We thank Mr. J. Yotsuji of JFE Steel Corporation for samplepreparation and helpful discussion. This work was financiallysupported by JSPS KAKENHI Grant Number B22360037.

1) D. Jiles, Introduction to Magnetism and Magnetic Materials (Taylor &Francis, London, 1998) 2nd ed., p. 439.

2) L. Vandenbossche and J. Melkebeek, J. Appl. Phys. 99, 08D907 (2006).3) O. Hubert and K.-J. Rizzo, J. Magn. Magn. Mater. 320, e979 (2008).4) K. Ikushima, S. Watanuki, and S. Komiyama, Appl. Phys. Lett. 89, 194103

(2006).5) H. Yamada, K. Takashima, K. Ikushima, H. Toida, M. Sato, and Y.

Ishizawa, Rev. Sci. Instrum. 84, 044903 (2013).6) D. A. Berlincourt, D. R. Curran, and H. Jaffe, Physical Acoustics (Academic

Press, New York, 1964) Vol. 1, Part A, p. 169.7) R. M. Bozorth, Ferromagnetism (IEEE Press, New York, 1951) p. 595.8) K. J. Stevens, NDT&E Int. 33, 111 (2000).9) T. Yamasaki, S. Tamai, and M. Hirao, in Nondestructive Characterization

of Materials VIII, ed. R. E. Green, Jr. (Plenum, New York, 1998) p. 733.10) R. Murayama, Ultrasonics 37, 31 (1999).11) Selective measurement in the direction of intrinsic flux flow inside materials

is usually difficult in standard magnetic measurements because the directionis restricted by the arrangement of the coil wound around the measurementobject. For a similar reason, the measurement of local B–H curves for theintrinsic flux (not leakage flux) is almost impossible in the standard method.In particular, hysteresis behaviors in the low-field region below themagnetic saturation condition are not clearly probed by leakage fluxtechniques.

Fig. 5. (Color online) ASEM image for a steel plate (a) without and(b) with an artificial defect. The circle (diameter: 5mm) in (b) indicates thedetectable size magnified by magnetic flux distribution.

(a) (b)

(c)

Fig. 6. (Color online) Measurements of the normal field components.(a) Schematics of experimental conditions. (b) Numerical calculation: thevector field components projected in the RF-detection direction are indicated.(c) ASEM image at H = 40 kA=m.

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