Excitation of a Fundamental Shear Horizontal Wave Using a Line Source

Z. Y. Liao, X. T. Cai, Y. Tu, J. H. Jia*, S.T. Tu

Key Laboratory of Pressure Systems and Safety, Ministry of Education, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, P.R.China

Email: jhjia@ecust.edu.cn

KEYWORDS: Guided wave; Fundamental shear horizontal wave; Waveguide bar; Anti-plane shear line source; Nondestructive testing

ABSTRACT

The fundamental shear horizontal (SH0) wave is more and more attractive in the nondestructive testing and structural health monitoring. It is potentially useful in a waveguide bar system to monitor the components working in harsh environment due to its special propagating characteristics. Because the shear horizontal waves normally exists in plates, and the waveguide bars of rectangular cross-section are typical plate-like structures, the waveguide bars of rectangular cross-section are preferred in the waveguide bar system. The rectangular cross-section waveguide bars with large aspect ratios can be considered as line sources. In order to excite pure SH0 wave for specimens, the excitation characteristics of all line sources are investigated and the anti-plane shear line source is selected as the premium loading firstly. And then the matching mechanism of the excitation source and the waveguide source is investigated. Moreover, the transmission efficiency of SH0 wave in the waveguide bar system is analyzed. At last a waveguide bar system is designed and experiments are carried out, and the experimental curve of transmission efficiency agrees quite well with the simulation one. Therefore, the reliability of excitation mechanism for SH0 wave has been validate. The research provides necessary methodology for the design of waveguide bar systems to excite the SH0 wave.

1. Introduction

The initiation and propagation of cracks in high temperature equipment is a fatal factor inducingmajor accidents [1-4]. The guided wave technology has been verified as an effective tool to nondestructively detect cracks [5-9]. Therefore, introducing the guided wave technology into the on-line monitoring of equipment damage is a popular way to keep the health of equipment [10,11]. However, when the ultrasonic transducer is installed permanently on a high-temperature equipment for on-line monitoring, the transducers will depolarize, which limits its application in high temperature [12]. In order to apply guided wave detection technology in high temperature environment successfully, the waveguide bar technology has already been pursued by many researchers. Because the waveguide bar act as a signal transmission medium between the high-temperature specimen and the piezoelectric transducers, the fragile piezoelectric transducer can be isolated from the high-temperature component to ensure the

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transducer to work long-termly. During the development of the waveguide bar, several kinds of waveguide bars have been analyzed and applied recently [13-15]. A thin tapered waveguide bar adding an attenuation cladding outside has been used to suppress unwanted modes of guided waves by Jean et al [16,17]. A spiraled foil bar with the thickness much smaller than the smallest wavelength transmitted in the bar to measure the flow of a hot fluid in a pipe has been proposed by Heijinsdijk et al [18]. A bundle of thin wires has been applied by Lynnworth et al to minimize wave dispersion and obtain a strong signal [19]. Large aspect ratio rectangular strips for the thickness monitoring of a high-temperature wall have been developed by Cegla et al[20]. In addition, Jia et al have investigated a design criteria for rectangular waveguide bar so that the waveguide bar can transmit non-dispersive fundamental shear horizontal (SH0) wave [21]. All these researches focus on avoiding wave dispersion and scattering when waves go through waveguide bars. However, the matching relationship between the excitation source and the waveguide bar have not been reported. The matching mechanism between waveguide bars and wave sources will affect both the energy and the type of the guided waves in the waveguide bar. Similarly, the spatial distribution of guided waves in the test specimen will be influenced by the waveguide source formed by the connection between the waveguide bar and the test specimen. Therefore, in order to excite non-dispersive SH0 wave for the high temperature nondestructive testing specimen effectively, the matching relationshipes among excitation source, waveguide bar, and test specimen are studied in the present research.

2. Excitation characteristics analyses of Line sources

There exist two different kinds of guided waves in the plate structure. One is Lamb waves, the other

is SH waves. It is well known that SH0 wave is non-dispersive, and it is less affected by the presence of surrounding media [22-23]. Consequently, it is potentially useful being used in the waveguide bar system to monitor components working in harsh environment. Because the SH0 wave normally exists in plates, and the waveguide bar of rectangular cross-section is a plate-like structure, the waveguide bar of rectangular cross-section is a preferred structure in the waveguide bar system. The junction between the ultrasonic transducer and the waveguide bar is the excitation source for waves in the waveguide bar system, and the connection area of the waveguide bar and the test specimen is the waveguide source for waves to test specimen. Ideally, the excitation source and waveguide source of a rectangular waveguide bar with a large aspect ratio can be approximately considered as a line source [20]. The line source loading types generally includes normal loading, tangential source loading and anti-plane shear loading, as shown in Fig. 1. Different loadings show different excitation abilities.

Figure 1. Schematics of the different line loading types: (a) Normal loading; (b) Tangential shear loading; (c) Anti-plane shear loading[20].

In order to select an appropriate loading to excite the non-dispersive SH0 wave, the finite element analysis of three loading types are carried out using ANSYS software. A 316L stainless steel rectangular plate is applied as a specimen. Its dimensions are 150mm×150mm×1mm. The material parameters are Young’s modulus E = 195 GPa, Poisson’s ratio υ = 0.267 and density ρ = 2700 kg/ m3. The line source lies in the middle of a plate and is supposed as a rectangle area in dimensions of 20mm×0.2mm.The Plate is modeled using the Solid 164 element. The maximum size of the elements is 0.2mm and the time step is selected as 0.05 μs. The excitation signal is a 5-cycle sinusoidal displacement tone burst modulated by a Hanning window and the center frequency fc is 1 MHz. The displacement load is applied according to conditions shown in Fig. 1, respectively. The displacement signals is measured at every 10° to obtain the distribution of the guided waves on the surface of the plate, as shown in Fig. 2.

Figure 2. Layout of the line source and measurement points.

Fig. 3 shows the simulation results of the directivity of guided waves excited by line sources. For waves excited by the normal loading, the SH0 wave is much weaker than the A0 wave, which can be found in Fig. 3(a). Similarly, for waves excited by the tangential shear loading, the SH0 wave is significantly weaker than the S0 wave, as shown in Fig. 3(b). However, for waves excited by the anti-plane shear loading, the SH0 wave is so stronger than the Lamb waves that the Lamb waves can be ignored, which is plotted in Fig. 3(c). And the SH0 wave is perpendicular to the line source with a narrow beam. Therefore, the anti-plane shear loading shows an excellent ability to excite SH0 wave.

Figure 3. Directivity of guide waves excited by different types of line sources on plates: (a) Normal loading; (b) Tangential shear loading; (c) Anti-plane shear loading.

Moreover, the directivity of the SH0 wave excited by anti-plane shear loading on the semi-infinite space is investigated. Fig. 4(a) shows a semi-cylindrical test structure model. The radius r is chosen as 80 mm, and the height h is 80mm too. The line source is loaded in the middle of the upper surface of the target structure and is approximated as a rectangular area with dimensions of 20mm×0.2mm. The signals are measured at every 10° at the edge. The directivity of the SH0 wave in the test structure is

shown in Fig. 4(c). It is found that the anti-plane shear loading can excite omni-directional waves in the semi-infinite space. That is to say, the SH0 wave excited by the anti-plane shear loading can detect defects in all directions of the specimen.

Figure 4. The SH0 wave inside a semi-infinite space: (a) Model of the semi-cylindrical structure; (b) The neutral cross section; (c) Directivity of the wave.

Based on the purity and the directivity of the SH0 wave excited by the line source of anti-plane shear loading, we can conclude that the anti-plane shear loading is the premium line source to excite the SH0 wave.

3. Analysis of excitation sources

The anti-plane shear loading can be easily loaded at the end of a waveguide bar [20,21], as a method shown in Fig. 5(a). The highlighted area represents the excitation source. The width of a waveguide bar is w, and the thickness is d. The width of the excitation source is named as ws, and the thickness is ds.

Generally, the distributions of the anti-plane shear loading in end section of the waveguide bar can be split into two different matching styles. Fig. 5(b) represents an equal width symmetric match (Shorten for EWS). In this case, the excitation source is symmetrically arranged in the middle of the end section. And ws equal to w, and ds is not bigger than d. ds increases from 0.2d to d at an interval of 0.2d during the simulation. Fig. 6(c) represents an equal thickness symmetric match (Shorten for ETS). The excitation source is symmetrically arranged in the middle of the end section. ds equal to d, and ws is not bigger than w. ws increases from 0.2w to w at an interval of 0.2w.

Figure 5. The excitation source locations in the end section of the waveguide bar: (a) A waveguide bar; (b) Equal width symmetric match; (c) Equal thickness symmetric match; (d) Distribution of nodes in

the cross section of the waveguide bar.

For the simulations, four waveguide bars are designed. Their length is 100mm and width is 25mm. Thickness are different which are 0.5mm, 1mm, 6mm and 8mm, respectively. For the waveguide bars with thickness of 0.5mm and 1mm, their frequency-thickness production fds are 0.5MHz⋅mm and 1MHz⋅mm, which are smaller than the first cut-off frequency-thickness production (fd)1=1.6 MHz⋅mm [21]. And for the waveguide bars with thickness of 6mm and 8mm, their fds are 6MHz⋅mm and 8MHz⋅mm which are bigger than (fd)1. The signals are received at nodes in the central lines which are shown in Fig. 5(d). O3O4 line is the center line of the yz cross section of a waveguide bar.

When fds are smaller than (fd)1, a 1mm thick waveguide bar and a 0.5mm thick waveguide bar are analyzed. Fig. 6 shows the waveform of waves excited by the excitation sources with different matching styles in a 1mm thick waveguide bar. The wave signals excited by the EWS are shown in Fig. 6(a) and Fig. 6(b), and the signals excited by the ETS are depicted in Fig. 6(c) and Fig. 6(d). It is noticed that the signals don’t change when the thickness of the excitation source changing from 0.2mm to 1mm. According to the group velocity and the wave structure of SH0 wave, it is easy to know that the wave excited in the waveguide bar is the SH0 wave. This shows no matter how thick the excitation source is, the non-dispersive SH0 wave can always be excited in the waveguide bar. And the wave slightly disperses when width ws is 5mm, as shown in Fig. 6(c). Moreover, the wave dispersion weakens with the increase of the excitation source’s width and the wave dispersion can be ignored when ws is bigger than 9 mm, as shown in Fig. 6(d). The same conclusion can be obtained when the simulation is carried out using a 0.5mm thick waveguide bar. Therefore, 9mm is a critical width value.

Figure 6. Waveforms in 1 mm thick waveguide bars .

When fds are bigger than (fd)1, let’s take the waveguide bar with thickness of 6mm and 8mm as examples. Fig. 7(a) shows that it is impossible to excite the pure SH0 wave if ds is smaller than d. However, it can excite the pure SH0 wave when ds equal to the thickness d, as shown in Fig. 7(b). Moreover, ETS can excite the pure SH0 wave, when ws is bigger than 9 mm, and the wave disperse slightly when ws is smaller than 5mm, as shown in Fig. 7(c) and Fig. 7(d). The same conclusion can be obtained when the simulation is carried out using a 8mm thick waveguide bar. Therefore, 9 mm is the critical width of excitation source.

Figure 7. Waveforms in 6 mm thick waveguide bars.

When we change different simulation frequency, this critical value will change. If the excitation frequency fc is 500kHz, the critical value is 18mm. A lot of simulated value verify that the critical value is 3λ for every frequency. Therefore, when fds are smaller than (fd)1, the width ws of the excitation source should be greater than 3λ, and the thickness is free. And when fds are bigger than (fd)1, ws should be greater than 3λ and the ds equal to d.

4. Analysis of waveguide sources

Once ultrasonic signal has been excited in a waveguide bar based on excitation source match mechanism, the waveguide bar will act as transmitters and receivers of guided waves for test specimens. In fact, a waveguide bar with a large aspect ratio isn’t a strictly line source. In order to determine the critical waveguide source that can be approximately considered as line source, the finite element method is also carried out to investigate the excitation characteristics of the waveguide source. Because the connection area of the waveguide bar and the test specimen is the waveguide source, the thickness and the width of the waveguide source are these of the waveguide bar. Therefore, the thickness of the waveguide source is named as d and the width is names as w.

4.1 Excitation characteristics of waveguide sources with different thicknesses

A series of waveguide sources with different thickness are investigated at 1MHz. Their widths are 20 mm. And the thickness are 0.4mm, 0.8mm, 1mm, 2mm, 3mm, and 4mm, respectively. Fig. 8 shows the simulation results of the directivity of the guided waves excited by the waveguide sources with different thicknesses on the surface of the plate. It is noted from Fig. 8 that the amplitude of Lamb wave’s components increases with the increase of the thickness d. And the interference of Lamb waves cannot be ignored, although the SH0 wave are dominant along the propagation direction. The directivity of the SH0 excited in the semi-infinite space are shown in Fig. 9. It is obvious that the beam width becomes narrower when d increases. And the SH0 wave radiates omni-directionally when d is smaller than 0.5mm, as shown in Fig. 9(a). Therefore, 0.5mm is the critical thickness of waveguide source to excite the preferred waves, which is pure and omni-directional , when the exciting frequency fc is 1MHz.

And then the exciting frequency fc is changed to 500 kHz, simulation results show that the preferred wave can be excited when d is smaller than 1mm. Hence, 1 mm is the critical thickness when the fc is 500kHz. A lot of simulation validate that the critical thickness is 1/6λ for every frequency. Therefore, it can conclude that the waveguide source can be approximated as a line source to excite the preferred wave when the thickness d of the waveguide source is smaller than 1/6λ.

Figure 8. Directivity of the guided waves excited by different thickness waveguide sources on the surface of the plate.

Figure 9. Directivity of the SH0 wave excited by different thickness waveguide sources in the semi-infinite space.

4.2 Excitation characteristics of waveguide sources with different widths

A series of waveguide sources with different widths are studies at 1 MHz. Their thickness is 0.4 mm. And the widths are 3 mm, 6 mm, 10mm, 12 mm, and 20 mm, respectively. Fig. 10 shows the simulation results of the directivity of the guided waves excited by waveguide sources with different widths on the surface of the plate. It is found that the amplitude of Lamb wave’s component increases with the decrease of w. In this case, the interference of Lamb waves cannot be ignored, which can be seen in Fig. 10(a) and Fig. 10(b), and the Lamb waves can be ignored in Fig. 10(c). The directivity of the SH0 wave excited by different w in the semi-infinite space are shown in Fig. 11. The beam width doesn’t change with the changing of w.

Moreover, a lot of simulation using different frequency verify that the interference of Lamb waves can be ignored when w is wider than 3λ, and the directivity of the SH0 wave is good, Therefore, a necessary condition of the waveguide source can be approximated as a line source is that the width w of the waveguide source is bigger than 3λ.

Figure 10. Directivity of the guided waves excited by different width waveguide sources on the surface of the plate.

Figure 11. Directivity of the SH0 wave excited by different thickness waveguide sources in the semi-infinite space.

Therefore, when the thickness of the waveguide source d is smaller than 1/6λ and the width w is bigger than 3λ, the waveguide source can be approximated as the line source to excite the SH0 wave.

5. Transmission efficiency of SH0 wave

Once the ultrasonic signal is excited and propagate along the waveguide bar, only a part of waves can transmit into the specimen for defect detection. In order to transmit the SH0 wave into the test specimen effectively, it is necessary to investigate the transmission efficiency of the SH0 wave. As the result analyzed in Section 4.1, the variation of the thickness of the waveguide source could significantly affect the directivity of the SH0 wave in the semi-infinite space. That is to say, the thickness d affect the wave energy transmitted into the specimen. Therefore, the influence of waveguide bar thickness on the transmission efficiency is analyzed by the ANSYS simulation and experiment.

5.1 Simulation of the transmission efficiency

A waveguide bar is installed perpendicular to a test plate by a special tool. A waveguide bar and a test plate is called a waveguide system. The dimensions of the test plate is 150 mm×1500 mm×10 mm. For the purpose of analyzing the thickness effect on transmission efficiency, a series of waveguide bars with different thickness has been designed. The length is chosen as 50mm in the convenience of simulation and the width is selected as 25mm in non-dispersive consideration according to the reference [21]. Thicknesses chosen here are from 1mm to 4mm with the step 1mm. The excitation displacement signal is applied on the excitation area and signals are measured at a point in the center of the waveguide bar at the excitation area, as shown in Fig. 12(a).

Figure 12. A waveguide system: (a) The model of the waveguide system; (b) A signal travel path.

Figure. 12(b) shows the signal travel path when the wave excited and transmitted partly into the plate. The dashed line depicts the end reflection wave and the solid line is about the first backwall echo. The time-domain signal waveforms in a 1mm thickness waveguide bar are drawn in Fig. 13. It is clear from the picture that the first received signal is the end reflection signal and then followed by some echoes from the backwall. The amplitude AT of the first backwall echo signal and the amplitude AR of the end reflection siganl are compared. The ratio can qualitatively indicate the transmission efficiency η:

T

R

Aη=A

(1)

The transmission efficiency η of waveguide bars with different thickness are calculated. The curve of the transmission efficiency η versus thickness is shown by the black solid line in Fig. 14, which is a monotonically increasing curve line. The curve shows that the thicker the waveguide is, the more energy of the SH0 wave is transferred into the test plate for damage detection.

Figure 13. A time-domain signal of the waveguide system.

Figure 14. SH0 wave transmission efficiency versus waveguide thicknesses.

5.2 Experimental verification

In order to verify the transmission efficiency of SH0, an experiment system is set up. Some waveguide bars and a test plate has been fabricated. The structure and material are same with simulation. The picture of the experimental system is shown in Figure 15, which is composed of an oscilloscope, a function generator, a power amplifier, a piezoelectric transducer, a test plate and some waveguide bars. During testing, five-cycles tone bursts modulated by a Hanning window are generated at 1 MHz. The transmission efficiency η versus thickness of the waveguide bar is shown by the stars in Fig. 14. The experimental results agree quite well with the simulation results.

Figure 15. The experimental system.

The monotonically increasing line depicts that the thickness of the waveguide bar should be designed big enough, in order to effectively transmit the SH0 wave from the waveguide bar into the test specimen. However, it is also found in section 4 that the directivity of the SH0 wave in the plate will deteriorate, and the Lamb wave component will be dominant when the waveguide bar is too thick. And the beam of the SH0 wave in the semi-infinite space becomes narrow, and the effective detection scope reduces, which is an undesirable phenomenon for nondestructive testing. Therefore, both wave quality and transmission efficiency should be considered simultaneously. When we design the waveguide bar, the thickness of the bar is the thicker the better to generate the higher wave energy, and the excitation source and the waveguide source should satisfy the requirements of the line source.

6. Conclusions

In order to excite non-dispersive SH0 waves using a waveguide bar system, the excitation mechanism of SH0 wave using line sources is studied. Firstly, line source excitation characteristics with different loading conditions is analyzed. And the anti-plane shear loading line source is verified as the optimum one for the SH0 wave excitation. Secondly, the matching mechanism for excitation source and waveguide source is investigated. About the excitation source, when the frequency-thickness product of the corresponding waveguide bar is less than its first cut-off frequency, the pure SH0 wave can be excited only if the length of the excitation wave source is greater than 3λ. And when the frequency-thickness product of the bar is bigger than its first cut-off frequency, the SH0 wave can be excited on the condition that the length of the excitation wave source is greater than 3λ and the thickness of the excitation wave source equal to the thickness of the waveguide bar. About the waveguide source, the wider and the thinner of the waveguide source are, the easier the SH0 wave can be excited. At last, a waveguide bar system is designed and transmission efficiency experiments are carried out. The experimental curve of transmission efficiency agrees well with the simulated curves. And it is better to select a thicker waveguide bar to generate the higher wave energy, on the condition that the SH0 wave can be excited. As a result, the excitation of SH0 wave using the anti-plane shear line source has been validated reliability. It provides important theories for the design of an ideal waveguide bar system to generate the SH0 wave.

Acknowledgments

The authors are grateful for the support provided by the National Key R&D Program of China

(No.2018YFC0808800) and Shanghai Natural Science Foundation (No. 18ZR1408800).

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