DESIGN AND EVALUATION OF PROBE WITH THREE DEGREE- OF-FREEDOM FOR NON-DESTRUCTIVE TEST USING THREE- DIMENSIONAL FINITE ELEMENT METHOD

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1 DESIGN AND EVALUATION OF PROBE WITH THREE DEGREE- OF-FREEDOM FOR NON-DESTRUCTIVE TEST USING THREE- DIMENSIONAL FINITE ELEMENT METHOD Masafumi Aoyanagi Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai, Tsukuba, Ibaraki, JAPAN. Naoto Wakatsuki, Koichi Mizutani and Tadashi Ebihara Faculty of Engineering, Information and Systems, University of Tsukuba, Tennodai, Tsukuba, Ibaraki, JAPAN. A probe having arbitrary sensitive axis is desired to reduce the artifact in the pulse-echo imaging using ultrasonic transducer array for non-destructive testing of solid. The artifact is possibly caused by longitudinal waves generated from shear waves by mode conversion at the boundaries. However, the artifact can be reduced by controlling the direction of the sensitive axis since the directions of vibrational displacement are different by propagation mode. In order to control the sensitive axis, we propose a probe with three degree-of-freedom about vibrational displacements. This probe is piezoelectric plate engraved into a matrix-like shape of truncated pyramid with multiple electrodes. The arrayed probe having arbitrary sensitive axis can form the beams of longitudinal and shear waves on demands. In this paper, the capability of transmission and reception of longitudinal waves and shear waves are confirmed using finite element simulation. As the results, it would be possible to transmit longitudinal or shear waves, selectively. We also found that the use of backing material can enhance the performance of proposed probe. 1. Introduction Non-destructive test (NDT) using ultrasound has widely been used in various fields on the grounds that the following advantages are given as examples. Since it is sensitive to both surface and subsurface discontinuities, the depth of penetration for flaws detection or measurement is superior to other NDT methods. It is also possible to detect flaws from only single-sided access, when the pulseecho technique is used. Accordingly, pulse-echo method is generally used for ultrasonic testing[1]. Elastic wave has longitudinal and shear components in solids, there are inspection techniques using longitudinal wave[], shear wave[3, ] and combination[5, ]. Common probes are dedicated to transmit and receive either longitudinal or shear waves. Also, a non-destructive inspection method for solid using ultrasonic computed tomography (CT) with time-of-flight (TOF) of longitudinal wave was proposed[7, 8, 9]. CT method can visualize the flaws which are difficult to be detected by pulseecho method. In these method, mode conversion is not considered, however, the artifact is generated ICSV, Florence, Italy, 1-1 July 15 1

2 Figure 1: Generation of artifact caused by mode conversion in visualization using transducer array. by mode conversion. Such artifacts can be reduced by controlling the direction of the sensitive axis since the directions of vibrational displacement are different by propagation mode. Therefore, we consider that it is important to study the probe which can discriminate longitudinal component from shear component of elastic waves. For that reason, few inspection techniques use combination of both waves. When either longitudinal or shear waves are input to the solid, additional presence of another wave is generated by mode conversion cause the artifact in visualized image. The artifact is possibly caused by longitudinal waves generated from shear waves by mode conversion at the boundaries. For example, Fig. 1 shows schematic view of the varying additional presence of another wave cause of artifact in visualized image, when arrayed transducer is used. Fig. 1 (a) shows that the refracted direction of the sound beam generated by arrayed probe and propagation direction of echo are the same. In this case, image can be seen in the right location. Figs. 1 (b) and (c) show that the refracted direction of the sound beam generated by arrayed probe and propagation direction of echo are not the same. On the other hand, image cannot be seen in the right direction and to make things worse, image can be seen in the wrong location as artifact. In case of Fig. 1 (b), proposed probe will receive echo of longitudinal wave, which is generated by mode conversion, in sensitive-axis direction of longitudinal wave. The artifact will be generated quite clearly, because longitudinal component of echo is not time-resolved measurement, and direction of sensitive axis and propagation direction of echo are the same. In case of Fig. 1 (c), proposed probe receive echo of shear wave is generated by mode conversion. The artifact is also generated in the similar manner to the previous case but faintly, because direction of sensitive axis and propagation direction of echo are not the same. Therefore, in order to control the sensitive axis, we propose a probe with three degree-of-freedom about vibrational displacements. We reported that it is found that engraved piezoelectric plate in a matrix-like shape of truncated pyramid with multiple electrodes transmit and receive longitudinal and shear wave independently using two-dimensional FEM[1, 11]. In this paper, using three-dimensional FEM, we verify that proposed probe is operated just as operating principle. Also, we verify that it would be possible to transmit and receive longitudinal and shear waves selectively using some electrodes.. Operating principle of probe with three degree-of-freedom.1 Target specification This section describes the target specification of proposed probe. Fig. shows a schematic diagram of proposed probe. In conventional probe for generating longitudinal wave, electric field is applied parallel to polarization axis of the piezoelectric device, and thickness-longitudinal vibration ICSV, Florence, Italy, 1-1 July 15

3 Thickness longitudinal mode (z) Thickness shear mode (y) Thickness shear mode (x) Poling axis Poling axis Poling axis Vibratiom mode (z) Vibratiom mode (y) Vibratiom mode (x) Figure : Schematic view of the propesed probe. is generated. Also, in conventional probe for generating shear wave, electric field is applied normal to polarization axis of the piezoelectric device, and thickness-shear vibration is generated. Since the relation between the polarization axis and the direction of electrical field is fixed, the conventional probe can only generate either longitudinal or shear mode. Then, we propose three-degree-of-freedom probe, for generating both longitudinal and shear vibration, those are dynamically selective. We intend to apply this probe for non-destructive inspection methods such as pulse echo. In the proposed probe, both electric field parallel to the polarization axis and one normal to the axis can be arbitrarily applied, hence the proposed probe has three degree-of-freedom with ingenuity of structure and multiple electrode. In the pulse-echo like inspection methods, the probe is required to have flat frequency response.. Operating principle Figure 3 shows operating principle of proposed probe which is used as a transmitter or a receiver. In order to transmit longitudinal and shear waves, selectively, a probe that has multiple channels is devised. When in-phase voltages are applied to all the electrodes except for, the top of probe vibrate in z-direction as shown in Fig. 3 (a), because the direction of electric field and polarization axis are roughly parallel to each other. Anti-phase voltages are applied to electrodes I and II, or III and IV, the probe causes thickness-shear vibration in x- or y-direction as shown in Fig. 3 (b). In this case, the direction of electric field and polarization axis are orthogonal each other. On the other hand, if x or y-axis force F x, F y is applied to proposed probe, the voltages of electrodes I and II, or III and IV are anti-phase with respect to a pair of opposite electrodes. Similarly, when force in z-direction F z, is applied to the bottom of probe, the voltages on electrodes I to IV are in-phase. By using the above mentioned vibration modes, longitudinal or shear waves are selectively transmitted and received to target direction. This section describes to transmit and receive elastic wave in target directions. After selecting longitudinal or shear waves as identified in Fig. 3 (c). Arrayed proposed probe transmit or receive longitudinal or shear wave to target direction using array signal processing. Target direction θ is determined by velocity of elastic wave c, delay time of excitation D t and pitch of arrayed proposed ICSV, Florence, Italy, 1-1 July 15 3

4 Transmitter (a) (b) (c) In-phase driving Anti-phase driving Thickness-longitudinal driving (z) Thickness-shear driving (x), (y) v I Receiver Elastic wave v II v III v IV v Iv II v III v IV Anti-phase(x) Anti-phase(y) All In-phase(z) Shear wave Longitudinal wave Longitudinal wave Shear wave z Longitudinal wave Shear wave Elastic wave Figure 3: Operation principle of proposed probe. 5 mm 1 mm z y y x 5 mm All slanted electrodes are connected every -x/+x/-y/+y side electrodes x, respectively v I Electrode v IV IV I v II II III v III Figure : The overview of proposed probe using FEM. probe P, using following equation. (1) θ = sin 1 cd t P 3. Evaluation of proposed probe using finite element method (FEM) 3.1 Simulation conditions Figure shows the overview of proposed probe. The probe has the shape of x truncated pyramids. The electrodes are placed on bottom surface and every slanted surfaces. The proposed probe consists of monolithic piezoelectric device with 5 electrodes. The material of the probe was assumed as piezoelectric ceramic (PZT-), which is polarized in z-direction. Proposed probe was modeled using FEM. To simulate characteristics of the only proposed probe, since the characteristics of the probe are affected by the material in contact, boundary condition around the probe was free. Mechanical quality factor Q of PZT-, silicone and tungsten, is attached to the top of probe, are set to be 5, 1 and 1 using a Rayleigh damping, respectively. Silicone was used for backing material of the probe to achieve wide frequency range. Tungsten was also used for heavy material to fix the top of proposed probe. When proposed probe is driven in Z-direction, electric voltage v I and v II, v III and v IV are 1 V. When the proposed probe is driven in x-direction, electric voltage v I and v II are -1 V and 1 V, respectively. ICSV, Florence, Italy, 1-1 July 15

5 (i) Shear-driving(X) (ii) x x component (m/v) x x component (m/v) (iii) Longitudinal-driving (Z) (iv) x1-11 x z component (m/v) -15 z component (m/v) Figure 5: Simulation results of state of vibration during shear(x) and longitudinal(z) driving :(i) and (iii) proposed probe (ii) and (iv) proposed probe attached silicone and tungsten for backing material 3. Operational evaluation of proposed probe Frequency characteristics of the proposed probe was evaluated by analyzing vibration of the probe using FEM. Figure 5 shows the simulation results of state of vibration at 5 khz. Figs. 5 (i) and (ii) show frequency characteristics of only piezoelectric device, and frequency characteristics of piezoelectric device attached silicone and tungsten, in shear driving. According to Fig. 5 (i), the top surface vibrates larger amplitude than bottom surface. In order to reduce the movement of the top surface and enlarge that of the bottom surface, a tungsten plate is attached on the top surface. Silicone is filled in the groove to extend the bandwidth. In contrast, Fig.5 shows that it can be seen that the bottom surface vibrates with larger amplitude than that of the top surface. Also, Fig. 5 (iii), (iv) show piezoelectric device attached silicone and tungsten, in longitudinal driving. According to Fig.5 (iii) and (iv), it was found that the flexural vibration is generated in longitudinal-driving. It is due to the growth vibration in x-direction by transversal effect. Figure shows the frequency response of displacement of the bottom surface. According to Fig. (i) with (iii), the probe attached silicone and tungsten shows reduction of resonance and to obtain larger displacement. Also, according to Fig. (ii) and (iv), the similar results are obtained in the driving. It was confirmed the probe is vibrate just as principle and displacement is increased by attaching a tungsten plate as weight. From the above, proposed probe was suggested that a probe could transmit and receive longitudinal and shear wave independently.. Conclusions In this paper, we designed the probe, which can select the vibration mode: thickness-longitudinal mode (z), thickness-shear mode (x) or (y). As a result, proposed probe was verified to vibrate just as operating principle. It was also confirmed that the amplitude was increased using a combination of silicone and tungsten for backing materials. From the above, proposed probe was suggested that ICSV, Florence, Italy, 1-1 July 15 5

6 1 x Z component (Hz) x 1 5 (iii) 1 x Z component (i) (Hz) x x Z component (Hz) (iv) x x Z component (ii).5 1 (Hz) 1.5 x 1 5 Figure : Simulation results of state of vibration during shear driving (i) proposed probe in X-driving, (ii) proposed probe in Z-driving, (iii) proposed probe attached silicone and tungsten in X-driving, (iv)proposed probe attached silicone and tungsten in X-driving. a probe can transmit and receive longitudinal and shear wave independently. In our future works, proposed probe received longitudinal and shear wave, independently. The array of proposed probes is expected to transmit longitudinal or shear waves to target direction using array signal processing. REFERENCES 1. M. Abe, T. Fujioka, and Y. Nagata, Location of a defect in a concrete block by a non-destructive technique. Acoustical Science and Technology, (). M. Lang, and H. Ermert, Linear Synthetic Aperture Modes for Ultrasonic Pulse-Echo Imaging Biomedical Engineering / Biomedizinische Technik (1997) 3. F. Honarvar1, A. N. Sinclair, Scattering of an obliquely incident wave by a transversely isotropic cylinder. Journal of the Acoustical Society of America99 8 (199). A. Pilarski, J. L. Rose, A transverse wave ultrasonic oblique incidence technique for interfacial weakness detection in adhesive bonds, Journal of Applied Physics (1988) 5. Angle, Y. C. and Achenbach, J. D., Reflection and transmission of obliquely Incident Rayleigh waves by surface breacking crack., Journal of the Acoustical Society of America 75 (198). Y. Bar-Cohen, Ultrasonic NDE of conposites Solid Mechanics Reserch for Quantitative Non-Destruction Evaluation, (1987) 7. H. Mitsui, K. Mizutani, and N. Wakatsuki, Interval of Observation Plane in Visualization of Region near Defects in Billets Using Ultrasonic Computerized Tomography Method Japanese Journal of Applied Physics 8 (9) 7GD5. 8. Y. Norose, K. Mizutani and N Wakatsuki, Speeding Up of Nondestructive Inspection for Shape-Distorted Billet by Simultaneous Measurement of Time of Flight, Japanese Journal of Applied Physics 5 (13) 7HC9. ICSV, Florence, Italy, 1-1 July 15

7 9. K. Kakuma, Y. Norose, K. Mizutani and N Wakatsuki, Interval of Observation Plane in Visualization of Region near Defects in Billets Using Ultrasonic Computerized Tomography Method, Japanese Journal of Applied Physics 5 (13) 7HC1. 1. M. Aoyanagi, N. Wakatsuki, K. Mizutani and J. Takarada, Three Degree-of-Freedom Ultrasonic Contact probe for Imaging Inside of Solid Material, Proceedings of Symposium on Ultrasonic Electronics, 3 (13) 11. M. Aoyanagi, N. Wakatsuki, K. Mizutani and T. Ebihara, Probe with three degree-of-freedom for ultrasonic test using longitudinal and shear waves, Proceedings of Symposium on Ultrasonic Electronics, 35 (1) ICSV, Florence, Italy, 1-1 July 15 7