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IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 Non-contact evaluation of thickness reduction of plates and pipes using EMAT-generated guided wave Ik-Keun Park, Yong-Kwon Kim and Jin-Hyuk Lee Seoul National University of Technology Seoul, 139-743, Korea +82-970-6332 +82-977-4507 [email protected] Yong-Sang Cho Korea Electric Power Research Institute Daejeon, 305-380, Korea Jun-Hyun Lee Pusan National University Pusan, 609-735, Korea Abstract The evaluation of thickness reduction in structures such as plates and pipes by guided waves is presented. Ultrasonic guided wave techniques have been widely studied and successfully applied to various non-destructive applications with the advantage of long range inspection. Non-contact methods for ultrasonic wave generation and detection have been of a great concern and highly demanded in the guided wave techniques due to their capability of wave generation and reception on surface of high temperature or on rough surface. A non-contact EMAT (Electro-Magnetic Acoustic Transducer) technique for guided waves is illustrated with some applications on monitoring of corrosion simulated thickness reduction in structures. The EMAT technique is successfully applied for the non-contact generation and detection of guided waves in the structures. Promising features based on the dispersive behavior of selected wave modes are found to quantify thickness reduction. The experimental results show that the mode cutoff measurements provide a qualitative scheme to measure thinning defect while the change in group velocity can be used as a quantitative parameter. 1. Introduction It has been reported that in 1968, Wallance developed a non-contact technique using EMAT (Electro Magnetic Acoustic Transducer) to generate and receive ultrasonic waves in a metallic material with the lift-off of several mm from the surface of the test material. In 1970 and 1980s, the technical advance and various applications of EMAT

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  • IV Conferencia Panamericana de END

    Buenos Aires – Octubre 2007

    Non-contact evaluation of thickness reduction of plates and pipes using

    EMAT-generated guided wave

    Ik-Keun Park, Yong-Kwon Kim and Jin-Hyuk Lee

    Seoul National University of Technology

    Seoul, 139-743, Korea

    +82-970-6332

    +82-977-4507

    [email protected]

    Yong-Sang Cho

    Korea Electric Power Research Institute

    Daejeon, 305-380, Korea

    Jun-Hyun Lee

    Pusan National University

    Pusan, 609-735, Korea

    Abstract

    The evaluation of thickness reduction in structures such as plates and pipes by guided

    waves is presented. Ultrasonic guided wave techniques have been widely studied and

    successfully applied to various non-destructive applications with the advantage of long

    range inspection. Non-contact methods for ultrasonic wave generation and detection

    have been of a great concern and highly demanded in the guided wave techniques due to

    their capability of wave generation and reception on surface of high temperature or on

    rough surface. A non-contact EMAT (Electro-Magnetic Acoustic Transducer) technique

    for guided waves is illustrated with some applications on monitoring of corrosion

    simulated thickness reduction in structures. The EMAT technique is successfully

    applied for the non-contact generation and detection of guided waves in the structures.

    Promising features based on the dispersive behavior of selected wave modes are found

    to quantify thickness reduction. The experimental results show that the mode cutoff

    measurements provide a qualitative scheme to measure thinning defect while the change

    in group velocity can be used as a quantitative parameter.

    1. Introduction

    It has been reported that in 1968, Wallance developed a non-contact technique using

    EMAT (Electro Magnetic Acoustic Transducer) to generate and receive ultrasonic

    waves in a metallic material with the lift-off of several mm from the surface of the test

    material. In 1970 and 1980s, the technical advance and various applications of EMAT

  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 2

    have been carried out by other researchers such as R.B. Thomson (3) and B.W. Maxfiled

    (5, 6).

    EMATs are able to generate and receive ultrasonic waves without contacting the surface

    of test materials by the interaction of magnetic field and Eddy current which are induced

    from magnets and coils into the test material. Thus, EMATs do not require any pre-

    process or removal of coating or insulation on the test surface. But, it has been reported

    that the effective lift-off should be less than 2 mm due to the rapid exponential decay of

    the electromagnetic force from the surface.

    Also another advantage with EMATs is that various wave modes can be generated

    easily by change in the arrangement of magnets and coils. For example, shear horizontal

    wave (SH wave) is not easy to generate with conventional PZT transducers due to the

    coupling problem. But, this problem can be overcome easily by using EMATs since

    EMATs do not require any coupling media between the transducer and the test material.

    Ultrasonic guided waves have been noted as an effective method to inspect joints or

    weld in plates and pipelines. It has been reported that the guided wave techniques are

    successfully applied to inspection of the airplane (12)

    . In the inspection of the corrosion

    in a aluminum plate using guided waves, it is found that many features of the Lamb

    waves such as the cutoff frequency, group velocity, and transmission and reflection

    factors are sensitive to the thickness reduction of a plate (13).

    In this paper, the use of EMAT is proposed as a new efficient non-contact NDE tool to

    monitor the thickness variation of corrosion-simulated plates and pipes.

    2. Understanding on the Ultrasonic Guided Wave Technique

    As well known from earlier works, elastic waves propagating along thickness, d=2h of a

    plate satisfy the Rayleigh-Lamb frequency equation.

    1

    22

    24

    )tan(

    )tan(±

    −−=

    kq

    pqk

    qh

    ph................................................................................................. (1)

    Where the signs “+” and “-” on the right hand side are for symmetric and anti-

    symmetric modes, respectively. p and q in eqn.(1) represent the corresponding wave

    vector components of the partial longitudinal and shear modes in thickness direction as

    illustrated in the equation below.

    2

    2

    2 kC

    pL

    =

    ω............................................................................................................. (2)

    2

    2

    2 kC

    qT

    =

    ω............................................................................................................. (3)

    Where ω is the angular frequency and k is the wave number (11). Dispersion curves for a plate are numerically obtained from the eqn. (1). Fig. 1 shows

    the phase and group velocity dispersion curves of a steel plate. Mode cutoff regions are

  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 3

    also shown. Cp, Cg, f and d denote the phase velocity, group velocity, frequency and

    thickness, respectively.

    Fig. 1 Dispersion curves for a steel plate (CL=5.8mm/sec, CT=3.2mm/sec), S=

    symmetric modes, A=antisymmetric modes.

    Thickness reduction of plates can be detected based on the measurement of various

    dispersion characteristics of guided wave modes. Especially, the phase velocity of a

    narrow band signal, which is a function of the wavelength of EMAT, is a key

    experimental parameter to select a desired mode at a given frequency. Alternatively,

    other modes can also be generated by frequency tuning. The propagation characteristics

    of guided wave modes need to be carefully observed to quantitatively evaluate various

    thickness reductions. In this paper, among those features (13)

    , the mode cutoff and group

    velocity changes are used to assess the thickness reduction.

    3. Principles and Features of Lamb-EMAT

    The EMAT generation and reception of ultrasonic waves involve the three following

    mechanisms: the Lorentz's effect, the magnetic effect and the magnetostrictive effect.

    The Lorentz's effect exists in a conductive material while the magnetostrictive effect

    appears in a ferro-magnetic material.

    When the magnetic field, B, and Eddy current, Je, induced by the coil near the surface

    are applied to the conductive material, Lorenz force is generated in the normal direction

    to both magnetic filed and Eddy current. This force moves the material particle in the

    direction that the force is applied. By applying the alternative current, the force

    direction is also changed alternatively and consequently, the stress waves are generated

    and propagated. (Fig. 2)

    N

    S

    N

    S

    N

    S

    Jc

    Je F

    BF = Je × B

    Fig. 2 Wave generation mechanism of the EMAT

    0 1 2 3 4 5 60

    1000

    2000

    3000

    4000

    5000

    6000

    7000

    8000

    9000

    AAAA0000

    SSSS0000

    AAAA1111

    SSSS1111

    SSSS2222

    fd[MHzfd[MHzfd[MHzfd[MHz·mm]mm]mm]mm]

    AAAA2222

    0 1 2 3 4 5 60

    1,000

    2,000

    3,000

    4,000

    5,000

    6,000

    fd[MHzfd[MHzfd[MHzfd[MHz·mmmmmmmm

    AAAA0000

    SSSS0000

    AAAA1111

    SSSS1111

    SSSS2222

    AAAA2222

    mode cutoff

    region

    Cg[m

    /sC

    g[m

    /sC

    g[m

    /sC

    g[m

    /s

    Cp[m

    /s]

    Cp[m

    /s]

    Cp[m

    /s]

    Cp[m

    /s]

  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 4

    In order to generate Lamb waves with EMATs, the coil and permanent magnets are

    arranged as shown in Fig. 2. A permanent magnet is located above the meander coil

    which is designed to have alternative direction of the current flow in each turn. The

    center frequency of the EMAT is determined by the spacing of the coil. Usually, the

    spacing of coil is 1/2 of the wavelength. This arrangement of the coil and magnets

    results in Lamb wave in the conductive materials in which, the particle movement is

    parallel to the surface.

    4. Thinning Defect Monitoring

    Fig. 3 shows the experimental setup for detection of thinning defect in aluminum, steel

    plate and steel pipes using the Lamb wave. Fig. 4 shows a pair of EMATs and coils

    used to generate and receive the Lamb waves.

    Fig. 3 Schematic of Lamb-EMAT system for detection of thickness reduction in

    specimens

    Fig. 4 A pair of EMATs and coils

    In order to consider the case of thickness reduction, the EMATs were placed on the

    opposite side of the simulated corrosion defects. One of the EMATs was used as a

    transmitter and the other was used as a receiver. The distance between the EMATs is

    250 mm. The test specimens are shown in Fig. 5. In case of an aluminum plate whose

    thickness is 2 mm and whose size is 1200 x 400 mm as shown in Fig. 5a, three artificial

    defects to simulate thickness reduction due to corrosion were machined. The area of

    each defect is 50 x 50 mm and the depths of the defects are 10, 20 and 30% of the plate

    thickness. In case of steel plates whose thickness is 1 mm and whose size is 800 x 300

    mm as shown in Fig. 5b, eight artificial defects simulating different thickness reductions

    in the range between 3% and 20% of the plate thickness were machined. In case of

    carbon steel pipes whose thickness is 4.5 mm and length is 2000 mm as shown in Fig.

    5c, various defects were machined. The circumferential width of all defects is 30 mm.

    The lengths of the defects are 30, 40, 50, 60 and 70 mm, and the thicknesses are 3, 5, 7,

    10, 15, 20, 25 and 30% less the pipe thickness.

  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 5

    50mm*50mm△d

    △d/d=10%

    △d/d=20%

    △d/d=30%

    50mm*50mm△d

    △d/d=10%

    △d/d=20%

    △d/d=30%

    (a) (b) (c)

    Fig. 5 Dimensions and locations of simulated hidden corrosion defects in three

    specimens.

    The mode cutoff is one of the characteristics of the Lamb wave: a wave mode

    disappears or its amplitude decays with the thickness reduction. In order to enhance the

    detectibility of thickness reduction with mode cutoff, it is ideal to choose the Lamb

    wave modes near mode cutoff regions (Fig. 1). The experiment results of mode cut-off

    due to increasing thickness reduction are shown in Fig. 6. In case of an aluminum plate,

    S1 was chosen as a mode sensitive to thickness reduction in terms of the mode cut-off.

    Fig. 6a shows the waveforms of S1 mode at the center frequency of 1.4 MHz in the 2

    mm-thick aluminum plates with no defect, 10, 20, and 30% thickness reduction,

    respectively. In case of steel plates and pipes, A1 was chosen as a mode sensitive to

    thickness reduction in terms of the mode cut-off. Fig. 6b and 6c show the waveforms of

    A1 mode. The center frequencies are 1.8 MHz and 0.49 MHz in the 1 mm-thick steel

    plates and 4.5 mm-thick pipes, respectively.

    As shown in Fig. 6, it is found that the S1 and A1 modes disappear when the thickness

    is sufficiently reduced. Therefore, S1 and A1 modes turn out to be useful modes to

    detect the presence of thickness reduction in the plate and pipe considered here.

    However, the mode cutoff cannot provide any quantitative evaluation of thickness

    reduction (8, 9, 10 and 13)

    .

    Since the phase and group velocities of guided waves change as functions of frequency

    and specimen thickness, the change in group velocity can be used for the evaluation of

    thickness reductions described below.

    In order to obtain a correlation between the change in group velocity and thickness

    reduction, it is better to select the mode whose group velocity is discernibly changed

    due to thickness (Fig. 1). Therefore, S0 and A1 modes were selected for evaluation of

    thickness reduction.

    As shown in Fig. 7, it is found that S0 and A1 modes change the group velocity due to

    increasing thickness reductions. In case of an aluminum plate, S0 mode was chosen as a

    mode sensitive to thickness reduction. Fig. 7a shows the waveforms of S0 mode at the

    center frequency of 1.21 MHz in the 2 mm-thick aluminum plate with no defect, 10, 20,

    and 30 % thickness reductions, respectively. In case of steel plates and pipes, A1 mode

    was chosen as a mode sensitive to thickness reduction in terms of the change in the

    group velocity. Fig. 7b and 7c show the waveforms of A1 mode. The center frequencies

    are 2.09 MHz and 0.62MHz in the 1 mm-thick steel plates and 4.5 mm-thick pipes,

    respectively (8, 9, 10 and 13)

    .

  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 6

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    Defect-free

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    dd /∆ =10%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    dd /∆ =20%

    x 10-3

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    dd /∆ =30%

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    Defect-free

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    Defect-free

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    dd /∆ =10%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    dd /∆ =10%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    dd /∆ =20%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    dd /∆ =20%dd /∆ =20%

    x 10-3

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    dd /∆ =30%

    x 10-3

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    dd /∆ =30%dd /∆ =30%

    Time [sec.]

    Am

    plit

    ude [

    V]

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    Defect-free

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    dd /∆ =10%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    dd /∆ =20%

    x 10-3

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    dd /∆ =30%

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    Defect-free

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    -0.15-0.1

    -0.05

    00.050.1

    0.150.2

    0.250.3

    Defect-free

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    dd /∆ =10%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    dd /∆ =10%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    dd /∆ =20%

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.250.3

    0.35

    dd /∆ =20%dd /∆ =20%

    x 10-3

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    dd /∆ =30%

    x 10-3

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    -0.15-0.1

    -0.050

    0.050.10.150.20.250.30.35

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    dd /∆ =30%dd /∆ =30%

    Time [sec.]

    Am

    plit

    ude [

    V]

    (a) (b) (c)

    Fig. 6 Change in the amplitude of mode due to increasing thickness reductions in

    (a) aluminum plate (S1 mode), (b) steel plates (A1 mode) and (c) pipes (A1 mode)

    x 10

    0.25-0.2- 0.1-0.05

    00.050.10.150.20.25

    0.25-

    - 0.1-0.05

    00.050.10.150.20.25

    0.25

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    - 0.1-0.05

    00.050.10.150.20.25

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    0.150.2

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    0.150.2

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    0.150.2

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    0.150.2

    0.25

    -0.4

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    0

    0.1

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    0 1.2 1.4 1.6 1.8

    x 10

    -0.4

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    x 10

    0 0.2 0.4 0.6 0.8 1.0

    x 10-6

    Defect-free

    dd /∆ =10%dd /∆ =10%

    dd /∆ =20%dd /∆ =20%

    dd /∆ =30%dd /∆ =30%

    Time [sec.]

    Am

    plit

    ude [

    V]

    2

    x 10

    0.25-0.2- 0.1-0.05

    00.050.10.150.20.25

    0.25-

    - 0.1-0.05

    00.050.10.150.20.25

    0.25

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    - 0.1-0.05

    00.050.10.150.20.25

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    0.150.2

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    0.050.1

    0.150.2

    0.25

    -0.25-0.2

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    0.050.1

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    0.150.2

    0.25

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    0.150.2

    0.25

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    -0.050

    0.050.1

    0.150.2

    0.25

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    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.25

    -0.25-0.2

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.25

    -0.25-0.2

    -0.15-0.1

    -0.050

    0.050.1

    0.150.2

    0.25

    -0.4

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    -0.2

    -0.1

    0

    0.1

    0.2

    0.3

    0 1.2 1.4 1.6 1.8

    x 10

    -0.4

    -0.3

    -0.2

    -0.1

    0

    0.1

    0.2

    0.3

    -0.4

    -0.3

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    0

    0.1

    0.2

    0.3

    0

    x 10

    0 0.2 0.4 0.6 0.8 1.0

    x 10-6

    Defect-free

    dd /∆ =10%dd /∆ =10%

    dd /∆ =20%dd /∆ =20%

    dd /∆ =30%dd /∆ =30%

    Time [sec.]

    Am

    plit

    ude [

    V]

    2

    (a) (b) (c)

    Fig. 7 Change in the group velocity due to increasing thickness reductions in (a)

    aluminum plate (S0 mode), (b) steel plates (A1 mode) and (c) steel pipes (A1 mode)

    (a) (b) (c)

    Fig. 8 Results of the thinning defect monitoring: (a) aluminum plate, (b) steel

    plates, and (c) steel pipes

    1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.51

    1.5

    2

    2.5

    3

    3.5

    4Group velocity

    Gro

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  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 7

    The observed changes in group velocity caused by thickness reduction are plotted on

    dispersion curves (Fig. 1) in Fig. 8. The theoretical and experimental results show

    similar trends. According to the experimental results of Fig. 7 and Fig. 8, it is possible

    to evaluate thickness reduction by the comparison between change of group velocity

    and theoretical group velocity. However, the dispersion curves of the structure to be

    tested should be determined prior to the field test because the Lamb wave velocity is

    highly dependent on the geometry and material properties.

    5. Conclusions

    In this paper, the thickness reduction in thin plates and pipes using a non-contact guided

    wave technique was evaluated. The EMATs were successfully utilized to generate and

    receive Lamb waves in an aluminum plate, steel plates and steel pipes. The dispersive

    behavior of S1, S0 and A1 modes are used for evaluation of thickness reduction. The

    experimental results show that the mode cutoff of S1 and A1 modes provide a

    qualitative measurement to detect the presence of thinning defect and it is also possible

    to evaluate the thickness reduction quantitatively by measuring the change in the group

    velocity of S0 and A1 modes.

    References and footnotes

    1. B Y Ahn, Y J Kim, Y G Kim and S S Lee, ‘Development of an EMAT System for Detecting Flaws in Pipeline’, Journal of KSNT, Vol 24, No 1, pp 15-21, 2004

    2. M Hirao and H Ogi, ‘EMATs for Science and Industry Noncontacting Ultrasonic Measurements’, Kluwer Academic Publisher, 2003

    3. J S Lim and R B Thompson, ‘Precise velocity measurement using EMATs’, KSNT/SC0009, pp 54-58, 2002

    4. J H Lee, I K Park, Y K Kim, Y S Cho and D H Kim, ‘Health Monitoring of Gas Pipes using Noncontact Lamb-EMAT’, KSNT/SC0044, pp 252-256, 2007

    5. B W Maxfield and C M Fortunko, ‘Design and Use of Electromagnetic Acoustic Wave Transducers(EMATs)’, Materials Evaluation, Vol 41, No 12, pp 1399-1408,

    1983

    6. B W Maxfield, A Kuramoto and K Hulbert, ‘Evaluating EMAT Designs for Selected Applications’, Materials Evaluation, Vol 45, No 10, pp 1166-1183, 1987

    7. R Murayama, ‘A Survey of Electro- magnetic Acoustic Transducer’, J. JSNDI Vol 52, No 2, pp 63-67, 2002

    8. I K Park, Y K Kim, Y Cho, Y S Ahn and Y S Cho, ‘A Study on the Behavior of Ultrasonic Guided Wave Mode in a Pipe Using Comb Transducer’, Journal of

    KSNT Vol 24, No 2, pp 142-150, 2004

    9. I K Park, T H Kim, H M Kim, Y K Kim, Y S Cho and W J Song, ‘Evaluation of Hidden Corrosion in a Thin Plate Using a Non-Contact Guided Wave Technique’,

    Journal of Key Engineering Materials, Vol 321-323, pp 492-496, 2006

    10. I K Park, Y K Kim, T H Kim, W J Song and Y S Cho, ‘Sizing Evaluation of Thinning Defects Using Noncontact EMAT Technique’, The 7th Far-East

    conference on Nondestructive Testing, pp 203-209, 2006

    11. J L Rose, ‘Ultrasonic Waves in Solid Media’, Cambridge University Press, 1999

  • IV Conferencia Panamericana de END Buenos Aires – Octubre 2007 8

    12. J L Rose and L E Soley, ‘Ultrasonic Guided Waves for Anomaly Detection in Aircraft Components’, Materials Evaluation, Vol 58, No 9, pp 1080-1086, 2000

    13. D Tuzzeo and F Lanza di Scalea, ‘Noncontact Air-Coupled Guided Wave Ultrasonics for Detection of Thinning Defects in Aluminum Plates’, Res. Nondestr.

    Eval., Vol 13, No 2, pp 61-77, 2001

    14. W Zhu, Rose, J N Barshinger and V S Agawala, ‘Ultrasonic Guided Wave NDT for Hidden Corrosion Detection’, Res. Nondestr. Eval., Vol 10, No 4, pp 205-225, 1998