Kauno technologijos universitetas

Stanislovas SAJAUSKAS

LONGITUDINAL SURFACE

ACOUSTIC WAVES

(CREEPING WAVES)

Kaunas ✳ Technologija ✳ 2004

UDK 534 Sa79 S. Sajauskas. Longitudinal surface acoustic waves (Creeping waves). Monograph. Kaunas: Technology, 2004, 176 p. Surface acoustic waves of new type, such as surface longitudinal or creeping acoustic waves propagating on the surface of the isotropic solid surface are described in this monograph. The peculiarities of those waves are researched theoretically and experimentally comparing them with transversal surface (Rayleigh) waves. Longitudinal surface acoustic wave application to nondestructive tests, measurements, in UHF electronics, and their seismic evidence are surveyed. Longitudinal surface acoustic waves exciting in ultrasonic frequency band are discussed also; the results of experimental research are given. Reviewers: Prof. Habil. Dr. E. L. Garška (Vilnius University) Prof. Habil. Dr. L. Pranevičius

(Vytautas Magnus University, Kaunas) Prof. Habil. Dr. S. Rupkus (Kaunas University of Technology) Translated into English language by L. Ancevičienė © S. Sajauskas, 2004 ISSN 9955-09-777-9

In memoriam of my Mother

Elzbieta VISKAČKAITĖ-SAJAUSKIENĖ

C O N T E N T S

SYMBOLS 7 PREFACE 11 1 INTRODUCTION 13 2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) 19

2.1 LSAW and TSAW theory 23 2.2 LSAW exciting and receiving methods 34

2.2.1 LSAW exciting by X-cut quartz crystal 34 2.2.2 Y-cut quartz crystal method 35 2.2.3 Periodical mechanical linear structure method 36 2.2.4 Angular method 36 2.2.5 Electromagnetic acoustic method 41 2.2.6 Thermo-acoustic method 42

3 LSAW APPEARANCE AND USE 44

3.1 LSAW usage in nondestructive testing 44 3.2 LSAW application for measurement of physical and mechanical constants 48

3.2.1 Sound velocity measurements 48 3.2.2 Measurement methods of elasticity constants 53 3.2.3 Measurement of surface hardness characteristics

with LSAW 56 3.3 LSAW in seismology 60

3.3.1 Seismic waves and their velocity 60 3.3.2 Simulation of seismic phenomena 63

4 LSAW RESEARCH METHODS 67

4.1 Angular-pulse method 67 4.1.1 Equipment of immersion research 71 4.1.2 Calibration of anglular measurement device 73

4.2 Pulse-time method 75 4.2.1 Experimental equipment for the prism research method 76

CONTENTS 4.2.1.1 Influence of ultrasound attenuation in prism 79 4.2.1.2 Research of angular transducer acoustic contact 83 4.2.1.3 Research of transducer with variable angle 85 4.1.4.4 Constructions of double angular transducers 89 4.1.4.5 Influence of diffraction to the effectiveness of LSAW exciting 90

4.3 Experimental SAW research 95 4.3.1 LSAW and TSAW comparative research 95

4.3.1.1 LSAW and TSAW propagation on the rough surface 99 4.3.1.2 SAW interaction with the corner 106

4.3.2 Research of SAW propagation on the cylindrical surface 111 4.3.2.1 SAW propagation on the convex surface 111 4.3.2.2 SAW propagation on the concave surface 118

4.3.3 Investigations of LSAW excitation by piezoelectric grating 119

4.3.4 Investigations of LSAW and TSAW excitation by pulse laser 127 4.3.5 Lamb waves exciting by LSAW and TSAW transducers 131

4.3.6 Investigation of mechanical tension in sheet products by symmetrical Lamb waves 135

REFERENCES 142

APPENDIXES 151

SUMMARY (In English) 170

SUMMARY (In Lithuanian) 172

7

cLSAWc

cTSAWc

S Y M B O L S Latin A amplitude AL amplitude of bulk longitudinal wave AT amplitude of bulk transversal wave ALSAW amplitude of longitudinal surface acoustic wave (LSAW) ATSAW amplitude of transversal surface acoustic wave (TSAW) cL velocity of bulk longitudinal wave cLW velocity of Lamb wave

sLWc velocity of symmetric Lamb wave

cLSAW velocity of LSAW velocity of LSAW propagating on cylindrical surface

cSAW velocity of surface acoustic waves (SAW) cT velocity of bulk transversal wave cTSAW velocity of TSAW

velocity of TSAW propagating on cylindrical surface

c0 velocity of imerse liquid D diameter d distance; thickness E Young module ELSAW energy of LSAW ETSAW energy of TSAW e = 2.73 natural logarithm base f frequency G shear module h depth I0 light intensity K amplification coefficient k = 2π/λ wave number kL bulk longitudinal wave number kLWs symmetrical Lamb wave number

8

SYMBOLS kT bulk transversal wave number

kSAW SAW number

cylindrical LSAW number

cylindrical TSAW number

l distance ln wave path N pulse number R Earth radius S attenuation t time Ti delay time Txx, Txz, Tzz mechanical tension components Ur

particle displacement vector U voltage, voltage amplitude

LUr

particle displacement vector component along the surface

TUr

particle displacement vector component across the surface vx particle vibration speed along x axis vz particle vibration speed along z axis Z0 comparative acoustic impedance Zp penetration depth of SAW ZLSAW penetration depth of LSAW ZTSAW penetration depth of TSAW Greek α damping coefficient α0 light absorption coefficient

damping coefficient of cylindrical LSAW

damping coefficient of cylindrical TSAW

β angle of corner βL bulk longitudinal wave reflection angle βT bulk transversal wave reflection angle

cLSAWkcTSAWk

cLSAWαcTSAWα

9

SYMBOLS γL bulk longitudinal wave refractive angle γT bulk transversal wave refractive angle ∆ Laplacian operator; absolute uncertainty ϑ SAW incidence angle

Icrϑ first critical angle IIcrϑ second critical angle

Λ laser radiation wavelength λ acoustic wavelength λ’ Leme constant λLs symmetric Lamb wavelength λLSAW wavelengths of LSAW λTSAW wavelengths of TSAW µ Poisson’s ratio ξn particle vibration amplitude square to the surface ξSx tangentiale particle vibration amplitude of Lamb wave ξSz normale particle vibration amplitude of Lamb wave ξt particle vibration amplitude along the surface ξx particle vibration amplitude along x axis ξz particle vibration amplitude along z axis ρ density ρb density of basalt ρg density of granite τi pulse length ϕ potential of longitudinal SAW component ψ potential of transversal SAW component ω angular frequency Abbreviations AFCh Amplitude–Frequency Characteristic BLW Bulk Longitudinal Wave BTW Bulk Transversal Wave FFT Fast Fourier Transformation

SYMBOLS LW Lamb Wave FPRF Finite Pulse Response Filter LSAW Longitudinal Surface Acoustic Waves NDT Nondestructive Testing PC Personal Computer SAW Surface Acoustic Waves SHF Super High Frequency TSAW Transversal Surface Acoustic Waves (Rayleigh Waves) UVH Ultra High Frequency

11

PREFACE Surface acoustic waves (SAW) comprise a class of widely encountered ultrasonic phenomenon in nature. Alfred Nobel Prize laureate Lord Rayleigh was the first to describe them in his work on surface ground motion during seismic events at the end of the 19th century. As a result, SAW propagating on the surface of solids are named as Rayleigh waves. Since Rayleigh’s days, many types of surface waves were discovered. They propagate in isotropic solids, also in crystals, as well as piezoelectric materials, manifesting not only in free surfaces, but also in the boundaries of joined media, when a solid is overlayed with another thin solid, or a liquid film. The theory and practice of SAW that flourished in the second half of the twentieth century were motivated by ultra high frequency (UHF) electronics, inherent possibilities in miniaturization, and demand to create acousto-electronic SAW devices. Useable frequency range for SAW devices in UHF acousto-electronics now exceeds 1010 Hz (10 GHz). The main interest for microelectronics lies in micro-miniaturization. However, the frequency range of interest also turns out to be an impediment to acousto-electronics: the length of waves exceeds the atomic distances of solids some 100 times, resulting in complex technological manufacturing obstacles. The only solution here is to search for new materials and special crystal cuts where SAW would propagate with the higher phase velocity, much greater than that of Rayleigh waves. Promising results in this field were realized at the Kaunas University of Technology (KTU) when new types of SAW, longitudinal surface acoustic waves (LSAW), were shown to exist. LSAW propagate in materials with small Poisson ratios at a maximal phase velocity, exceeding even the content of longitudinal wave velocity. Using pseudo-longitudinal surface acoustic waves by acousto-electronic resonance filter in crystals of lithium niobate (LiNbO3), lithium tantalum (LiTaO3), and lithium tetraborate (Li2B4O7), it was possible at KTU to increase the desired frequency range of the phase velocity to 5 GHz.

PREFACE

This study is the result of an extensive experience at the Prof. K. Baršauskas Ultrasonic Science Center and the Department of Electronics Engineering of the Kaunas University of Technology. I wish to thank my colleagues Dr. Virgilijus Minialga and Dr. Naglis Sajauskas for their assistance while experimenting with LSAW; Dr. Algimantas Valinevičius, the Chair of Electronics Engineering Department; reviewers of the text, Prof. Habil. Dr. Liudvikas Pranevičius, Prof. Habil. Dr. Evaldas Leonardas Garška, Prof. Habil Dr. Stasys Rupkus for their valuable comments and advices. I also convey special thanks to the Chair of the KTU Research Planning Committee, Prof. Habil. Dr. Alfonsas Grigonis, and the Chair of KTU Senate Scientific Committee, Prof. Habil. Dr. Algirdas Žemaitaitis for their significant assistance in publishing this study. I am also very appreciative to my friend A. V. Dundzila for productive discussions and technical assistance translating the book into English language. Prof. Habil. Dr. S. Sajauskas

13

1 INTRODUCTION Surface acoustic waves (SAW) propagating without attenuation in free solid surfaces were discovered and described by Lord Rayleigh (John William Strutt) [1] at the end of the 19th century. Lately they became an irreplaceable instrument in acousto-electronics, material science, nondestructive ultrasonic testing, and seismic research. Since Rayleigh waves are nondispersive (their phase velocity does not depend on frequency), and their attenuation in solids is zero, they are suitable especially in nondestructive testing (NDT). Rayleigh waves are used to discover surface defects, to determine the depth and degree of thermal hardening, residual stresses, and to evaluate the quality of surface finishing. Usually the characteristics of subject materials are determined by measuring SAW velocity and attenuation, two acoustic parameters directly affected by mechanical and chemical surface attributes. Distinct types of SAW were discovered researching SAW propagation in other media than the free solid body surface. A. Love found and described in 1911 transversal SAW on the surface of a solid body covered by a thin layer of material of different acoustic properties. Today they are called Love waves. Dispersion is a significant characteristic of Love waves. Their phase velocity is always less than the velocity of transversal waves in a solid body and greater than the velocity in a solid mass. First described by H. Lamb in 1916, Lamb waves constitute a case of Rayleigh SAW propagating in a thin plate. Although different from Rayleigh waves, they are of dispersive nature. They can be symmetrical or unsymmetrical (flexible), and their velocity depends not only on frequency, but also on the thickness of the plate. In literature Lamb waves sometimes are referred to as normal waves of vertical polarization. Another type of normal waves propagating in plates are the tangential normal waves (of horizontal polarization, transversal), in cases when the plate surface does not deform during propagation.

14

1 INTRODUCTION Another category of electro-acoustic waves named after their founders, J. L. Bleustein and J. V. Gulyaev, differ from Rayleigh waves by propagating in some piezoelectric crystals but to depths of hundreds of wavelengths. The phase velocity here is less than that of transversal waves propagating in the same direction in the piezo-crystals. Surface waves propagating at the junction of two solids were found by R. Stoneley and are named after him. Stoneley waves are nondispersive and their penetration depth is approximately equal to the wavelength. Their phase velocity is always less than bulk longitudinal and transversal wave velocities in boundaries of solid bodies.

The application of SAW in information processing devices (ultrasound signal delay lines, wave band filters, signal branching, phase tommy-bars) stimulated scientists of this sphere to develop broadly scientific research. The subtlest effects, such as features of SAW propagation in irregular surfaces, characteristics of Rayleigh pseudo-waves propagating on the surface bordering with liquid, SAW diffraction’s, reverberation’s regularities were investigated and SAW gyroscopic effect in piezoelectrics was found, SAW wave interferometers were generated and those waves were visualized by the help of laser technique. World famous scientists, such as B. A. Auld [2, 3], G. S. Kino [4, 5], L.M. Brekhovskich [6], W. P. Mason [7], R. M. White [8] and others [9-19] made significant strides here. In Lithuania SAW waves were investigated at the Ultrasonic Research Laboratory established by Professor K. Baršauskas. L. Sereikaitė-Juozonienė was the first to describe in 1972 the new type SAW, different from Rayleigh waves [20, 21]. They were the longitudinal surface acoustic waves (LSAW) in accordance to their physical origin that dominated their longitudinal (tangential) vibration component. Recognizing this distinction, Rayleigh surface acoustic waves could be called transversal surface acoustic waves – TSAW. (The suggestion is made with due respect to Lord Rayleigh’s accomplishments, it simply articulates similarities and differences of the waves). After TSAW discovery for a long time there was an ongoing debate regarding any practical application because of their inherent damping.

15

1 INTRODUCTION For example, I. Viktorov denied SAW existence altogether [22-25]. But significant works by L. Juozonienė and S. Sajauskas (Lithuania) [26-34], J. C. Couchman and J. R. Bell (USA) [35], I. Yermolov, N. Razygraev and others (Russia) [36-42], I. A. Ehrhard, H. Wüstenberg and M. Kröning (Germany) [43-47], Charleswort and J. A. G. Temple (USA) [48] not only demonstrated the new type of surface waves, but also entrenched international acceptance of the new phenomenon. Ultrasonic testing with LSAW presently is included in procedural manuals at most major companies [49] and international standards. Two doctoral theses [50, 51] and a habilitation [52] have been defended on investigations of LSAW properties and usage. Incidentally, many contradictory propositions published by some researchers were either repudiated or confirmed by experiments with enhanced instrumentation and capabilities of personal computers. For example, there were issues regarding the existence of LSAW in materials with the Poisson ratio µ > 0.26 or where LSAW velocity was greater than that of BLW; or because of attenuation in LSAW propagation on a surface covered by a layer of liquid. Possibilities are being investigated to apply LSAW in nondestructive testing that allow examination of coarse surfaces, as well as surfaces inside liquid and gas tanks or pipes, and nuclear reactors. LSAW are less suitable in material science when measuring elasticity constants; also in seismology − with ideal models of earthquakes when evaluating the destructive nature of seismic LSAW around epicentre. SAW main types may be divided into two groups: LSAW in isotropic materials and in monocrystals (Fig. 1.1). This classification is not comprehensive because some pseudo-waves can propagate only in piezoelectric monocrystals, while others also in non-piezoelectric materials. In addition to Rayleigh waves propagating in piezoelectric monocrystals (in literature they are sometimes called pseudo-Rayleigh waves), also pseudo-Love, pseudo-Stoneley, or pseudo-Lamb wave types are known to spawn.

16

1 INTRODUCTION

Fig. 1.1. Classification of surface acoustic waves

In this case, a feature of all acoustic waves in piezoelectric materials should be noted. They cause not only mechanical deformations, but also related changes in electric charge. It can be said that propagating electroacoustic waves may be viewed as a particular field of

SAW PROPAGATING INISOTROPIC SOLIDS

SAW PROPAGATING INMONOCRYSTALS

RAYLEIGH WAVES(TSAW)

LSAW

STONELEY WAVES

LOVE WAVES

LAMB WAVES

PSEUDO-RAYLEIGHWAVES

NORMALWAVES

SEZAWA WAVES

BLEUSTEIN-GULYAEVWAVES

PSEUDO-LOVEWAVES

PSEUDO-LAMBWAVES

PSEUDO-STONELEYWAVES

PSEUDO-NORMALWAVES

17

1 INTRODUCTION acoustoelectronics science. Acousto-electronics evolved after 1965, when R. White and F. Wolmer invented new type converters for exciting SAW on piezoelectric surface [53]. Electrode converters created a revolution in this sphere of research because modern microelectronics technology could be applied in their manufacturing. This permitted to reduce the size and price of acusto-electronic devices, and made them more reliable. High equivalent quality (to 12000, low losses (7-10 dB), and high parameter stability allow using diphase SAW resonators in the design of very stable generators and filters of required frequency characteristics. The frequency passbandwidth of wave band filters can be of 0.01 to 0.5 percent, with their approximate rectangular shape. On the other hand, with the spread of acousto-electronics, the new types of waves were discovered, such as the gap waves which propagate on both sides of a narrow crack in piezoelectric crystal. Their propagation parameters may be managed by imposing an electric field on both sides of the gap. One more type of acousto-electric waves are the Sezawa waves. They are excited by transformation reflecting Rayleigh pseudo-waves. Their phase velocity is much greater than that of pseudo-Rayleigh waves [54, 55]. These waves may be called pseudo-longitudinal surface waves. Depending upon monocrystals (LiNbO3, LiTaO3), their velocity and attenuation may vary. The phenomenon is influenced by monocrystal cut and directional UHF propagation with respect to crystallographic axes. In literature these waves are known as longitudinal surface acoustic waves, surface waves of horizontal polarization, leaky SAW, and others. Besides acousto-electric waves, the acousto-magnetic waves are to be noted. They propagate in magnetic materials where mechanical vibrations are related to movement of magnetic charge. Their properties may be controlled by magnetic field. Also, it should be mentioned that, even in isotropic solids, if their surface is non-planar (cylindrical or spherical), or covered with a layer of other solid (metalization), or a liquid, TSAW (Rayleigh) and LSAW may acquire other properties and become nonhomogeneous, eradiating,

1 INTRODUCTION dispersive. For this reason such waves are called transversal and longitudinal surface acoustic pseudo-waves. Surface acoustic phenomenon in solids varies greatly. Only LSAW propagating in isotropic solids will be considered here, nevertheless touching upon some application possibilities of longitudinal pseudo-waves. Principal attention will be focused in particular on experimental research of LSAW physical properties, and their use in ultrasonic technology.

19

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW)

L. Sereikaitė-Juozonienė was the first to describe the longitudinal surface acoustical waves (LSAW) [20,21]. Measuring velocity of surface acoustic waves (SAW) with an ultrasonic interferometer, she observed a strange side effect. At times apparently a “false” value of surface wave phase velocity differed appreciably from Rayleigh wave velocity and turned out to be near the bulk longitudinal wave (BLW) velocity value. Investigating the reason, it was determined that the fact was due to the surface manifestation associated with the angle of incidence to the solid of BLW. Such incidence angle, also called the first critical angle, is equal to the angle of refracted longitudinal wave. Creeping along the surface of a solid, the BLW excites LSAW. The observed phenomenon was published in the scientific journal “Ultrasound” (In Russian) [20]. This unexpected, apparently “present at the surface” physical manifestation attracted scientific interest from all over the world. However, the phenomenon was not recognized as a discovery in the former USSR [56] because of doubts by an expert I. Viktorov. Nevertheless, such doubts did not mislead other scientists. The “boom” of LSAW research in the world started around 1976 and is continuing to the present day. Independent researchers validated previously published experimental results [35–37], thus confirming the existence of LSAW. Furthermore, they determined LSAW distinct features, such as the phase propagation velocity being near the longitudinal wave velocity value and side bulk transversal wave (BTW) propagation [36]. The discovery of LSAW was explained as an inevitable phenomenon when propagating waves, LSAW, are faster than the waves of some other, transversal, type (the Tcherenkov effect in SAW acoustics). Using ultrasonic angular transducer data was obtained about diffraction influence to the LSAW excitation effectiveness. Similarly, influence of small surface irregularities to LSAW propagation, as well as the longitudinal distance of LSAW

20

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) propagation up to 300 mm was recorded. Subsequently, experimental work yielded transversal wave transformation to the secondary LSAW, excited in the other surface of a flat sample [37]. These experimental results appeared at approximately the same time with theoretical works of I. Viktorov [22–25] the latter arguing that LSAW was only a theoretical fiction, having no practical application because their propagation path length does not exceed one wave length! Naturally, such a case may foster only philosophical discussion. Bitter debate in scientific media showed that conclusions of a famous theoretician were wrong, I. Viktorov having ignored not only results obtained by L. Sereikaitė-Juozonienė but also those announced by other researchers (I. Jermolov, N. Razygraev). Two divergent positions, one expounded by I. Viktorov [24] and another by I. Jermolov [38], about the place of LSAW in the context of surface waves and nondestructive testing appeared. I. Viktorov maintained [24] that the “effluent” surface waves propagate in the boundary with a liquid layer and dissipate rapidly. While I. Jermolov [38] analysed the development and effectiveness of nondestructive, ultrasonic testing theory and practice and LSAW practical application possibilities. L. Sereikaitė-Juozonienė published the article on the LSAW theory in 1980 [27]. With classical wave analysis, using Helmholtz equations and Rayleigh equation solutions, she calculated amplitudes of LSAW normal and tangential vibrations and presented prospects for LSAW applications. Subsequently L. Basatskaja and I. Jermolov in their article [40] (by the way, published before L. Juozoniene’s [27]) solved the same equations with Fourier integrals, calculated longitudinal and transversal LSAW component directional characteristics and their dependence on the product f·D, where f is frequency, D − the diameter of disk piezo-crystal. It was shown that varying this product value, it was possible to alter the LSAW excitation effectiveness and its propagation direction. Presently a number of works appeared dealing with practical LSAW applications, on special LSAW ultrasonic transducers, and describing their construction as well as technical characteristics [41, 42, 54]. These are angular transducers where the prism is made of material featuring a small sonic velocity and damping, e. g., Plexiglass (cL = 2670 m/s).

21

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) It should be noted that while researching LSAW, LSAW application ideas were being patented quickly as well. The first inventions using LSAW for nondestructive testing were registered in 1975 [26, 57]. Several inventions were announced by L. Sereikaitė-Juozonienė and S. Sajauskas on LSAW applications to materials science in measurements of physical mechanical constants [29, 30, 32, 34] and velocities of acoustic waves [28, 31, 33]. The group of A. Erhard, H. Wüsterberg, M. Krönung, E. Shulz and others began their work on LSAW in 1981 in Germany. Having patented a LSAW transducer, they broadly researched LSAW use in nondestructive testing, quality control of austenitic welding seams [45–47], described the secondary LSAW energized on inner surfaces of vessels, and researched applications for inner surfaces of nuclear reactor component's [44]. For their work A. Erhard and M. Krönung were awarded the prestigious Berthold prize in 1984. Surface longitudinal wave applications by other authors are known on nuclear reactors and inner pipe walls [49, 57–59]. Practical issues of LSAW usage, such as LSAW transducers [61–64], wave testing methodology [65–68], development of standards [69] subsequently received appreciable attention by world scientists. Research of LSAW forms generated some nuisances in communication due to redundant but different terminology for the same phenomenon, e.g. longitudinal surface acoustical waves. Thus the term “creeping waves” got entrenched in Western literature [43–48, 57, 58, 63–68], denoting the wave characteristic to propagate not on the surface as Rayleigh waves do, but a bit deeper and with weaker surface interaction. Meanwhile, other authors tended to emphasize maximal LSAW velocity, calling them Kőpfwellen in German, golovnyie volny in Russian [36, 38, 41, 42]. This term was borrowed from seismology where the fastest seismic signal pulses are known as primary waves. Interestingly, in other publications the same authors call LSAW as longitudinal pre-surface waves (prodolnyje podpoverchnostnye volny in Russian). Still several others call them LCR critically reflected longitudinal waves [70]. Even though inside solids LSAW eradiated BTW in certain acute angle [22–24], but to call them leaky surface acoustic waves

22

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) (vytekajushchiesia poverchnostnyje volny in Russian) is a gross misnomer. The issue remains that LSAW are not the only ones to lose energy (by eradiating, leaking) during propagation; energy losses are manifested also in other heterogeneous surface waves. For instance, Rayleigh type waves, TSAW, propagating through either uneven or smooth surface that borders with a liquid or its layer, propagate longitudinal waves sidewise and this is also leaking process. Precisely because of such a peculiarity Rayleigh waves propagating on the surface bordering with a liquid are called pseudo-Rayleigh waves. Moreover, it may be noticed that the English term “leaky surface acoustic waves”, leaky SAW, also are called SAW. They propagate in certain cut anisotropic piezoelectric monocrystals of LiNbO3, LiTaO3, Li2B4O7. The term “creeping waves” (Kriechwelle in German, polzuchie volny in Russian) precisely brings to mind one − albeit not essential − characteristic to propagate near the surface. However, since “to creep” is to move slowly or timidly, a mistaken impression about the velocity is produced as well. On the contrary, these surface waves propagate most rapidly, their phase velocity cLSAW can be even greater than that of cL, velocity of the BLW. For no other reason in this work we will use the term longitudinal surface acoustic waves, LSAW, emphasizing the underlying difference of such waves from the others − such as Rayleigh’s, the transversal surface acoustic waves (TSAT). In addition, this essential distinction underlines the differences in main physical properties of LSAW and Rayleigh (TSAW) waves, such as phase velocities (cLSAW ≈ cL; cTSAW ≈ cT , where cT is the BTW velocity) and excitation angles (the first critical angle I

crϑ by LSAW and the second critical angle II

crϑ by TSAW). Let it be noted that LSAW are mostly applied in nondestructive testing, using experimental research in SAW excitation, signal identification, acoustic geometry, and other practical considerations. Meanwhile, LSAW physical characteristics were researched only theoretically and there are almost no publications on experimental phase velocity and attenuation measurements, LSAW transformation into other type

23

2.1 LSAW and TSAW theory waves, and research about other types of propagation. There are no attempts to employ experimental methods to metrology, material science, nor seismology. In seismic events these waves manifest a startling destructive force near the epicentre when the seismic focus is not deep. Typically in scientific literature LSAW are not uniquely identified; they are enfolded with BLW, denoted by the letter P (in English primary wave), mostly called head wave. Thus, according their origin and behaviour, LSAW are similar to TSAW (Rayleigh waves) and, in particular, constitute a Rayleigh wave antipode because of many opposite characteristics. In order to underline physical similarities and differences, in this book Rayleigh waves will be called transversal surface acoustic waves (TSAW), the term better suited for comparative analysis.

2.1 LSAW and TSAW theory Theoretically LSAW and TSAW are described analyzing bulk longitudinal waves (BLW) refraction in solid body. Generally, when incident wave is plane and does not diffract, in the boundary between two solid body forms not only reflected from the boundary and refracted in the second body longitudinal waves are composed but also transversal waves (Fig. 2.1) with the propagating angles described by the Snell’s law:

Fig. 2.1. Transitions of BLW in the boundary of two solid bodies

γT γL

βL

βTϑ

'TA

"TA

'LA

"LA

First solid body

Second solid body

24

LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW)

where ϑ is the longitudinal wave incidence angle, βL and βT are the angles of reflected BLW and excited bulk transversal waves (BTW) in the first solid body; γL and γT are the angles of refracted BLW and excited BTW in the second solid body; '

Lc and 'Tc are the velocities of

BLW and BTW waves in the first body; ''Lc and ''

Tc are the velocities of BLW and BTW in the second solid body. The total reflection can occur in the second solid body if '''''

LTL ccc >> , when refracted wave (BLW or BTW) creeps along the boundary line (Fig. 2.2). The total reflection incidence angle of BLW is called the first critical angle I

crϑ and is equal to

;arcsin ''

'

=

L

LIcr

ccϑ (2.2)

the total reflection angle of BTW is called the second critical angle II

crϑ and is equal to

.arcsin ''

'

=

T

LIIcr

ccϑ (2.3)

The condition '''''

LTL ccc >> always fulfilled in immersion case (when

the first material is liquid, 0' =TA ). If two bodies are solid, the first body is usually from organic material where the sound propagates in low speed (organic glass, polystyrene, kind of nylon) [71]. The additional condition to the first solid body, essential in ultrasonic wave band is minimal sound damping.

(2.1) ,sinsinsinsin''''''

T

T

L

L

T

T

L ccccγγβϑ

===

25

2.1 LSAW and TSAW theory The longitudinal wave that has fallen in the first solid body to the first critical angle I

crϑ , BLW creeping along the surface of the second solid body, excites LSAW in it (Fig. 2.2 a). Similarly, the longitudinal wave that has fallen to the second critical angle II

crϑ , BTW creeping along the surface of the second body, excites TSAW there (Fig. 2.2 b).

a)

b)

Fig. 2.2. Diagrams of LSAW (a) and TSAW (b) exciting by angular method

The harmonic wave of ω frequency propagation along the surface of homogeneous ideal isotropic solid body bordering with vacuum (Fig. 2.3) would be studied further.

Icrϑ

'TA

'LA

''

TA

AL0

βT

βL

γT

ALSAW First solid body

Second solid body γL = 90°

'LA

'TA

AL0

βT

βL

γT = 900

IIcrϑ

ATSAWFirst solid body

Second solid body

26

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW)

Fig. 2.3. Co-ordinate system on the solid surface The motion of such body is described by the equation [72, 73]

( ) ,2

2UdivgradGUG

tdU rrr

++=∂ λ∆ρ (2.4)

where U

r is the particle displacement (shift) vector; t is the time, ρ −

density; λ’ is Leme constant; G is shear module, 2

2

2

2

2

2

zyx ∂

∂+

∂

∂+

∂

∂=∆

is the Laplacian operator. Having resoluted shift vector TL UUU

rrr+= into two components: LU

r

along the surface and TUr

across the surface, associated with scalar ϕ and vectorial ψ potentials

,ϕgradUL =r

(2.5)

,ψrotUT =r

(2.6) two independent equations [70]

Solid body

Vacuum y x

z

27

,12

2

22

2

2

2

tczx L ∂

∂=

∂

∂+

∂

∂ ϕϕϕ

2.1 LSAW and TSAW theory

( ) ,02'2

2=+−

∂

∂L

L UGtU rr

∆λρ (2.7)

02

2=−

∂

∂T

T UGtU rr

∆ρ (2.8)

are obtained from Eq. (2.4). Potentials ϕ and ψ are the solutions [73] of wave equations

(2.9)

(2.10)

Potentials ϕ and ψ on the surface of free solid body depend only on co-ordinates x and z and are expressed by equations [6, 73]:

(2.11)

(2.12)

where

GkL 2' +

=λ

ρ is the number of BLW,

.12

2

22

2

2

2

tczx T ∂

∂=

∂

∂+

∂

∂ ψψψ

( ) ;exp 22

−+−−= txkikkzA L ωϕ

BTW, ofnumber theis G

kTρω=

( );exp 22 tkxikkizB T ωψ −+

−=

28

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) kL < k < kT , ω is the angular frequency, A = const, B = const. The amplitudes of solid body particles vibration along x and z axes are:

,zxx ∂

∂−

∂∂

=ψϕξ (2.13)

xzz ∂

∂+

∂∂

=ψϕξ . (2.14)

Having solved those wave equations, the natural (Rayleigh) equation of the sixth order [27] is got and has the form

(2.15)

where

Tkkm =

(2.17)

As it is shown in [27], this equation for the real solid bodies has only one real radical

22

TSAW

T

T cc

kkm == (2.18)

(2.16)

( ) ( ) ,018328116 24262 =−+−+− mmrmr

L

T

T

Lcc

kkr ==

BLW, ofnumber theis

BTW. ofnumber theis

29

2.1 LSAW and TSAW theory that describes TSAW, propagating in solid bodies (0.26 < µ < 0.5) and one complex radical

LSAW

T

T cc

kkm ==1 (2.19)

that corresponds LSAW; where 211 innm += ,

LSAWTT cckkn == 11 , k2 is the TSAW number; cTSAW is the TSAW phase velocity; cLSAW is the LSAW phase velocity;

( )11 αicc LSAWLSAW += , 12 nnLSAW =α is the standard attenuation coefficient for the wavelength λLSAW. The complex character of phase velocity LSAWc shows that LSAW even in perfect material is the damped surface wave. This “natural” LSAW attenuation is induced by BTW eradiation into solid body propagating along the surfaces. LSAW attenuation coefficient depends on Poisson’s ratio µ, when µ > 0.26 and grows together [27]. The vibration velocity components of solid surface layer along x and z axis on the LSAW are described by formulae [27]:

( ) +

−+−−= tkxikkzAkiv Lx ω22exp

( ) ,2exp2

2 2222

2222

−+−

−

−−+ txkkkizA

kk

kkkkkT

T

TL ωv

v (2.20)

( ) −

−+−−−−= txkikkzAkkv LLz ω2222 exp

.exp2

2 2222

222

−+−

−

−− txkkkizA

kk

kkkT

T

L ω (2.21)

30

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) The surface tensions in LSAW are:

( ) ( )[ ]

( ) +

−+−−×

×−−−=

txkikkzA

kGkkGTxx

T

LL

ω

λ

22

2'22

exp

22

( )

,exp

2

4

22

22

22222

−+

−×

×−

−−+

txkkkziA

kk

kkkkkiG

T

T

LT

ω

−

−+−−= 2222 exp2 kkztxkikkAkiGT TLxz ω

( ) ,exp 22

−+−−− txkikkz L ω (2.23)

( )[ ] ( ) −

−+−−+−= txkikkzAkGkGT LLzz ωλ 2222 exp22

( )

.exp

2

4

22

22

22222

−+

−×

×−

−−−

txkkkziA

kk

kkkkkiG

T

T

LT

ω

(2.22)

(2.24)

31

2.1 LSAW and TSAW theory The material point of surface body surface (z = 0) in LSAW propagating in ideal solid surface is described by (2.20) and (2.21) formulae. It moves in ellipse trajectory with major axis pointed parallel to the surfaces; so tangential (to the direction of x axis) vibration component ξx is bigger than normal (to the direction of z axis) component ξz (Fig. 2.4, a).

a) b) c) Fig. 2.4. Movement trajectory of the surface point (a) and its vibration

amplitude dependence on depth z during LSAW propagation by the normal (b) and tangential (c) directions

LSAW penetration depth in z axis direction does not exceed 2λL; so LSAW energy is concentrated in the layer of particular thickness near the surface of solid body. It is dependent to LSAW that maximal density of acoustic energy (ELSAW)max is not on the surface wall (z = 0), but a bit deeper. The material surface point moves in the ellipse trajectory when TSAW propagates on the surface of ideal isotropic body surface, but its major axis differently than in LSAW case is perpendicular to the surface, so the amplitude of normal vibrations is bigger than tangential (ξz >ξx) (Fig. 2.5, a).

z z

ξ z ξ x

ξ z

ξ x

32

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) TSAW maximal density of acoustic energy (ETSAW)max is on the surface of solid body (z = 0) and so it differs from LSAW. Theoretical research shows that LSAW phase velocity cLSAW is Poisson’s ratio µ function also to the materials with µ < 0.32, cLSAW >cL. The penetration depth of the LSAW and TSAW commonly does not exceed surface wavelength ( LSAWLSAW zx

z λξ ≈→0,,

TSAWTSAW zxz λξ ≈

→0,).

a) b) c) Fig. 2.5. Movement trajectory of the surface point (a) and its vibration

amplitude dependence on depth z during TSAW propagation by the normal (b) and tangential (c) directions The main characteristics of LSAW and TSAW (given in comparative Table 2.1) allow understanding the differences of those waves that determine the sphere of their use and availability for solving different acoustic problems.

z z

ξ z ξ x ξ z

ξ x

33

2.1 LSAW and TSAW theory

Table 2.1. The main LSAW and TSAW characteristics

N

Property LSAW TSAW

1

2

3

4

5

6

Angular exciting conditions(ϑmax) Propagation nature: − direction − localization − attenuation − wave interaction with the surface Trajectory of particle vibration Components of the surface particle vibrations Velocity Vibration amplitude change character, receding from the surface

ϑmax = Icrϑ

LSAW

ELSAW

λLSAW

z

BTW

Solid body

ELSAWαLSAW > 0

x

αLSAW > 0, when 0.26 < µ < 0.5 αTSAW → 0, when µ → 0 Weak Ellipse with the major axis perpendicular to the surface ξx > ξz cLSAW ≈ cL Exponential attenuation, penetration depth

TSAWLSAW

LSAW zxz

λλξ

>≈

≈→0,

ϑmax = IIcrϑ

TSAW

λTSAW z

ETSAW

αTSAW = 0

ETSAW

x

αTSAW ≈ 0 Strong Ellipse with the major axis parallel to the surface ξx < ξz cTSAW ≈ cT Exponential attenuation, penetration depth

LSAWTSAW

TSAW zxz

λλξ

<≈

≈→0,

34

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW)

2.2 LSAW exciting and receiving methods LSAW in isotropic solids can be excited in the same ways as TSAW [9, 73], but the efficiency of LSAW and TSAW exciting differs greatly. LSAW has “natural” attenuation depending on solid body properties (Poisson’s ratio, solidity, fragility), the most active methods and rather sensitive ultrasonic transducers must be used for their exciting. The classical ultrasonic frequency band SAW exciting methods are:

exciting by X-cut quartz crystal attached to the edge of solid body; exciting by Y-cut quartz crystal having acoustic contact

with the surface; exciting by the oscillating periodical line structure; exciting by the angular transducer; exciting by electromagnetic acoustic method; exciting by thermo-acoustic method.

2.2.1 LSAW exciting by X-cut quartz crystal

The vibrant quartz surface excited edge in the range of the right angle propagates spherical transversal and LBW that propagating along the free surface can excite not only TSAW but also LSAW, when X-cut quartz crystal will be attached to the edge of the right angle (Fig. 2.6 a).

a) b) Fig. 2.6. SAW exciting by X-cut quartz crystal P

45°SAW

SAW

SAW P P

35

2.2 LSAW exciting and receiving methods Unfortunately, only rather weak LSAW can be excited by this method because only a small part of piezo-crystal acoustic energy becomes LSAW energy [74]. The efficiency of exciting is the biggest when quartz crystal makes 45° angle with the surface, but because of the small contact area and small vibration amplitudes of quartz piezo-crystal, such case of exciting is not sufficiently efficient and is used rarely. Sometimes for enlargement of piezoelectric transducer vibration amplitude are used more effective piezo-crystals (lithium niobate LiNbO3, barium titanate BaTiO3, or plumbum-zirconium-titanate piezoceramics PZT). Exciting by piezo-crystal, attached to the right angle wall near the edge perpendicular to the exploratory surface is one version of the use of this method (Fig. 2.6, b) [75]. Yet even having used the modification of this method for special LSAW exciting [25], the authors could not register LSAW on the free surface of quartz sand [76]. So, X-cut quartz method, as non-efficient, does not fit for LSAW exciting. 2.2.2 Y-cut quartz crystal method Two SAW propagating into opposite sides (x and –x directions) are excited near the edge quivering Y-cut quartz crystal acoustically contacting with the solid body (agglutinated, edged through the viscous liquid, e.g., epoxy) (Fig. 2.7).

Fig. 2.7. SAW exciting by Y-cut quartz crystal P Such SAW (TSAW and LSAW) exciting method is non-efficient because in this case the most part of acoustic energy falls on the BTW.

SAW SAW

x

BTW

z

P

36

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) 2.2.3 Periodical mechanical linear structure method SAW transducer formed from piezo-crystal and periodical linear structure is used for LSAW exciting by this method (Fig. 2.8). Electrodic SAW type exciting method in piezo-materials is simulated by such transducer. Periodical mechanical stresses with dimensional frequency are equal to surface wavelength λSAW and are formed on isotropic solid body by such transducer.

Fig. 2.8. SAW exciting by linear periodical vibration structure, where

P is piezo-crystal, and PS is periodical structure Nevertheless, the great progress in the sphere of precision mechanics allows producing precise periodic structures, suitable for exciting SAW of hundreds of megahertz frequency [77]; the energetic efficiency of such transducers is small because of inevitable losses associated with diffractive bulk wave propagation into solid body. Besides, LSAW and TSAW are excited at the same time using this method, so the acoustic energy is lost and its efficiency diminishes. 2.2.4 Angular method Periodical mechanical stresses on the solid surface are designed by angular method just in the same case as by periodic linear vibration system but much more simpler. The angular methods can be:

immerse (liquid prism); solid body prism.

PS P

SAW SAW

x

z

37

2.2 LSAW exciting and receiving methods Solid body, analyzed by immerse method, is plunged into a liquid (e.g. water) and a plane ultrasonic wave is oriented to its surface by acute angle ϑ. So, the periodical mechanical tension area with the length depending on the dimension of piezo-crystal and fixed incidence angle ϑ are formed on the solid surface. SAW (LSAW and TSAW) are exited on the surface if the ultrasonic incident critical angles ( I

crϑϑ = or ( II

crϑϑ = ) are set. The advantage of immerse method is that the ultrasonic incidence angle to the surface can be easily changed. The ultrasonic velocity in liquids is always less than BLW velocity in solids (in water c = 1480 m/s, when T = 20°C), so not only LSAW but also TSAW can be excited almost in all solids (also in plastics). One of the mentioned advantages is less ultrasonic wavelength in liquid; so ultrasonic wave diffracts less (is more “plane”) when piezo-crystal has constant transverse dimension of invariable frequency. Such directional characteristic of ultrasonic transducer is narrower and this is very actual carrying out angle research. The immerse method has several shortcomings also. One of the major shortages is that ultrasonic attenuation in liquids is bigger than in solids and for this reason the efficiency of SAW in high (megahertz) frequency exciting is becoming weaker. TSAW excited on the surface of plunged into liquid investigative solid body (product) becomes inhomogeneous wave (pseudo-Rayleigh wave), eradiating side bulk waves into immerse liquid in its propagation path. The damped TSAW loses the main advantage with regard to LSAW. The angular transducers with liquid prisms are constructed for the elimination of those shortcomings. This is the combination of immerse and prism methods useful because BTW do not propagate in liquid prism and the inner reverberations of transducers can be easier reduced. The construction of such prisms is complex, especially when prism has the variable angle. The working principle of solid body prism method is similar to immerse method, but the triangular solid body prism with the attached

38

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) piezo-crystal on one edge and creating plane BLW is used there. The other prism edge is attached to the solid surface through thin liquid layer (usually motor oil) that makes the acoustic contact in the place where SAW is excited (Fig. 2.9). It would be simple to achieve h << λ (where h is the thickness of the layer, λ is the bulk wave length in liquid) in the case when the research is carried out in comparably low ultrasonic frequency range (megahertz) and then the coefficient of bulk acoustic wave crossing the liquid layer becomes close to zero. In order to excite LSAW, prism must be made from the material with the longitudinal wave velocity '

Lc lower than longitudinal wave velocity in investigative solid ''

Lc . The condition '''TL cc < must be met in order to

excite TSAW. Prism is usually made of plastics (cL of Plexiglass is 2680 m/s, cL of nylon is 2680 m/s, cL of polystyrene is 2320-2450 m/s) [76] and this allows exciting not only LSAW but TSAW also.

Fig. 2.9. SAW angle exciting method, where N is bulk wave incidence point and d is the cross size of piezo-crystal

The appropriate angles of LSAW and TSAW exciting by prism method are the same as if exciting by immerse method. The maximal TSAW transducer sensibility is achieved when piezo-crystal’s front point of eradiated BLW projection to the surface coincides with the prism angle (Fig. 3.9) as prism surface damps TSAW. While it is not relevant to LSAW because it weakly interacts with the surface propagating not on

cL

z

ϑ

d

SAW

x

Piezo-crystalPrism

N

39

2.2 LSAW exciting and receiving methods the surface but a bit deeper and the attached prism has a little influence (does not damp). While, SAW is excited not only to the x direction but to the opposite also, but practically TSAW amplitude to the –x direction is 30-40 dB and in the case of LSAW is 25 dB less than to +x direction. The transducers with variable angle must be used for exciting LSAW and TSAW in unknown or with different acoustic properties solids having the same transducer. Having evaluated the sound velocity dependence change in solids on temperature, the variable angular transducer would allow the precise fixing of the most effective exciting angles of LSAW and TSAW after the change of the temperature. The variable angular transducers are especially useful for NDT or measurements alternately using SAW of different type (LSAW and TSAW) [26, 28, 32]. The transducers of different structure variable angle are used in practice [51, 65]. The cylindrical polystyrene prism with the polystyrene slipper and adjusted piezo-crystal can be used for the change of ultrasonic incidence angle (Fig. 2.10).

Fig. 2.10. Prism SAW transducer with variable angle

This transducer is superior because acoustic wave access to solid body point N does not change its place changing the incidence angle ϑ. It is especially convenient for measurement the distances by SAW. But it has several shortcomings. The principal shortages are:

SAW

ϑ

Slipper l(ϑ)

Piezo-crystal

N

Prism

40

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW)

• changing the position of the slipper 2, the couplant (motor oil) removes under it, and the quality of acoustic contact changes; that determines instability of research for SAW and reduces the reliability of the results;

• the front part of solid prism with the thickness d acoustically damps SAW (especially TSAW);

• the prism damping part area l depends on incidence angle ϑ (l = l(ϑ)), so SAW attenuation varies without forecast if SAW excitation angle ϑ is changed.

Variable angular SAW transducer of better construction (simplified company’s Krautkramer-NDT transducer’s [65]) is shown in Fig. 2.11 [51].

Fig. 2.11. Simplified SAW transducer’s construction of variable angle

This SAW angular transducer consists of Plexiglass prism with the hole where the cylindrical figure piezo-crystal header from the same material is set. The plane is milled in the header till the axial line with the agglutinated piezo-crystal made from PZT piezoceramics. The entire empty cavity and a narrow gap between the body (prism and cylindrical header) are filled with couplant (silicone oil). The bulk plane ultrasonic wave crosses the cylindrical insert into prism almost without losses because acoustic contact is made between two concentric cylindrical surfaces of the same material and the thickness of the

cSAW

Scattering surfacestructure

Couplant

Piezo-crystal

Cylindrical body

PrismLateral bulk wave

N

ϑ

41

2.2 LSAW exciting and receiving methods couplant layer is << λ. Exciting SAW by the angular method a part of bulk acoustic wave reflects to the solid prism and attenuates propagating in it or is scattered because of multiplex reflection on the structures formed on the prism surface. The described SAW transducer has several advantages, such as: good acoustic contact persistent stable changing incidence angle ϑ; minimal acoustic energetic losses because of the change of incidence angle ϑ; right geometry. The only shortage is the dependence of acoustic energy access to the researched solid surface point N of incidence angle ϑ that yet has no reason when the measurements are conducted in the same solid; so, the acoustic properties remain constant when the fixed optimum incidence angle is ϑ = const. It should be noted that the efficiency of LSAW exciting by universal angular transducer couldn’t be optimal, because angle is always

IIcr

Icr ϑϑ < (cT < cL). The transducer’s sensibility material of prism should

be chosen so that =Icrϑ 45° for maximal LSAW.

2.2.5 Electromagnetic acoustic method

The non-contact electromagnetic acoustic method is broadly applied for SAW exciting in magnetic materials. Using this method the coil is set in magnetic field near the surface and it is excited by alternating electric current. Generated alternating magnetic field on the surface of metal creates vortex current that interacting with extra-enclosed constant magnetic field excites SAW because of acoustomagnetic phenomenon [78]. The surface of electrically nonconducting materials is metallized for exciting vortex SAW [79]. This method is broadly applied in NDT for the railing and carriage wheels [80]. The biggest shortcomings of electromagnetic acoustic transducers are that the sensibility in comparison to piezoelectric transducers is in two ranks less and the resistance to electromagnetic interference is small.

42

2 LONGITUDINAL SURFACE ACOUSTIC WAVES (LSAW) 2.2.6 Thermo-acoustic method

Thermo-acoustic method originated and had spread together with lasers that can establish electromagnetic (luminous) fluxes of concentrated high energy. They can heat the solid surfaces locally and during the very short time. The solid surface (e.g. metal) during few nanoseconds can be heated even to the melting point when the electromagnetic density is high. Very high temperature and mechanic stress gradients generating metal deformations propagating in solid body in the shape of sound (ultrasonic) waves [81–84] are designed by short pulse (duration τi = 10…30 ns) of pulsed lasers (e.g. Nd:YAG laser, wavelength Λ = 1.06 µm, ruby – Λ = 0.694 µm). Linear optical lattice [85], composed of unique width transparent and non-transparent tapes set alternately and after lightening by powerful laser with the periodical mechanical tensions can be used for exciting harmonic SAW. Harmonic SAW is excited on the surface by this method if the lattice period is equal to the surface wavelength. Space laser pulse is designed on solid surface while mechanical tension (pressure) pulse in non-modeled; its shape is shown in Fig. 2.12. If τi << l/α0 c, where α0 is the surface light absorption coefficient, c is sound velocity in solid body, so the intensity of Gauss form laser pulse is

( ) ( )[ ] ,/exp 200 itItfI τ−=

where f is the frequency; t is the time; τi is laser pulse duration. Pressure pulse front length ~l/∆ f is designed on the solid surface, if α0 = const in broad frequency range ∆ f (Fig. 2.12, curve 1). Pressure pulse front on the dielectric surface is described by exponent exp(α0 c τi) (Fig. 2.12, curve 2).

(2.25)

43

2.2 LSAW exciting and receiving methods The advantage of acoustic wave exciting by laser method in comparison to others is that the analysis can be done in a distance, even in transparent environment without the influence on the exploratory surface. The precise acoustic measurements on NDT in hostile environment and also in vacuum placed objects can be done by it. But in many cases of pulse measurements, several types of acoustic waves (BLW, BTW, LSAW and TSAW) with the signals that can coincide regarding the time are exited simultaneously; the signals of slower waves can be summed with the inner reflections of faster waves. This deforms the dimensional signal form and for this reason the precision of the measurements becomes lower. Besides, the problems of signal interpretation and identification in small or complex objects can arise.

Fig. 2.12. Pressure gradient form induced by pulse laser on the solid surface [86]: 1 – highly mechanically damping surface; 2 – free dielectric surface

In this regard LSAW in many cases being the quickest wave has great advantage because its signals come into recipient the first and LSAW measurements cannot be disturbed. Laser exciting method allows performing precise comparative LSAW and TSAW velocity and attenuation measurements.

44

3 LSAW APPEARANCE AND USE According to theory (Chapter 2), velocities on solid isotropic surfaces essentially differ from velocities previously attributed to TSAW, Rayleigh waves. Until LSAW discovery, LSAW were registered only in seismograms, and were viewed rather disapprovingly as potentially destructive mechanical energy. Nowadays LSAW are used as handy SAW, generated by special means, such as ultrasonic transducers or laser pulses. Unique LSAW features facilitate quantitatively different results in otherwise traditional SAW applications, such as nondestructive ultrasonic testing. LSAW also opened new fields offering original, qualitative findings. More expansive LSAW use, in conjunction with bulk acoustic waves (longitudinal, transversal) and also with SAW of a different type, such as TSAW, opens new possibilities. Just as TSAW (Rayleigh waves) are used widely in microelectronics for novel UHF devices, LSAW use in this area is also promising [87–93]. UHF-type LSAW devices are of bigger parameters because of high LSAW propagation speed in piezoelectric materials (cLSAW > cTSAW); it allowed broadening the range of device processing to 2,5–5 GHz [89, 90, 94]. By the way, analogous LSAW waves in crystals UHF in SAW technique frequently are called pseudo-Rayleigh waves (pseudo-SAW) or leaky SAW. At times, rarely they are called longitudinal leaky SAW [91, 92]. Since the object of our research lies in isotropic solids, propagation of LSAW in crystals will not be considered to any extent in this work.

3.1 LSAW usage in nondestructive testing NDT with LSAW is based on their distinct properties as compared to TSAW. As can be seen in Table 2.1, LSAW and TSAW differ in many properties and propagation characteristics. Phase velocity is an important parameter here: the value of TSAW phase velocity is close to

45

3.1 LSAW usage in nondestructive testing BTW value while LSAW velocity is similar to that of BLW. The fact is due to different LSAW and TSAW excitation conditions. In solids, LSAW-impacted surface particles move with trajectory of ellipse which semimajor axis is parallel to the solid surface (Fig. 2.4). While in the case of TSAW the semimajor axis of ellipse is square to the surface (Fig. 2.5). Very important LSAW characteristic in NDT practice is self-eradiation. LSAW loses a part of its energy (i.e. damps) because propagating LSAW even in free solid surface eradiates BTW receding from the surface deeper into the solid. Otherwise, this property is used for exciting secondary LSAW (LSAW II) by side waves in the other (inner) surface of exploratory shell (Fig. 3.1).

Fig. 3.1. Registration of inner surface defects by secondary LSAW II on an inner surface of a solid shell

It is known that SAW penetration depth is ∆ zp ≈(1.2-1.4)λp; where index p signifies surface wave. ≈97% of wave acoustic energy is concentrated in the layer of ∆ zp thickness. SAW propagates deeper

d

LSAW II

Icrϑ

LSAW I

BTW DefectShell

Angular transducer

46

3 LSAW APPEARANCE AND USE than TSAW because cLSAW > cTSAW and λLSAW > λTSAW. Energetic maximum in LSAW is not on the surface but in particular depth (≈0.1λLSAW). This is one more fundamental difference between TSAW and LSAW that can give new LSAW application opportunities. The assumption to use LSAW for the NDT of near surface layer is LSAW property to propagate near the surface layer. LSAW is not sensitive to the surface mechanical state (coarseness, corrosion, and paint) because of this property and this is especially useful while exploring coarse thread surfaces (Fig. 3.2).

a)

b)

c)

Fig. 3.2. NDT using LSAW: a) the pre-surface defect; b) the crack under the welding seal; c) the defect under the thread surface

Thread surface

LSAW transducer

DefectDEFECTOSCOPE

LSAW

Solid surface

DefectLSAW

LSAW transducer

DEFECTOSCOPE

LSAW Defect

Welding seal

LSAW transducer

DEFECTOSCOPE

47

3.1 LSAW usage in nondestructive testing The place of surface defect can be fixed even in those objects where phase velocity is unknown when LSAW and TSAW are used together for the NDT [26]. In this case having measured LSAW and TSAW signal maximal reflection from defect angles ϑ1 = I

crϑ , and ϑ2 = IIcrϑ ,

and the time interval between those signals (Fig. 3.3).

Fig. 3.3. Schematic of measurement of the distance to the defect by SAW

The distance from LSAW and TSAW introduction point M to the defect is

;

sinsin1sin2

2

12

0

−

=

ϑϑϑ

∆tcd (3.1)

where: c0 is sound velocity in prism; ∆ t is time interval between LSAW and TSAW signals.

Icrϑ

IIcrϑ

LSAW, TSAW

Defect

Angle beamtransducer

d

GENERATOR

AMPLIFIER OSCILLOSCOPE

M

48

3 LSAW APPEARANCE AND USE

3.2 LSAW application for measurement of physical and mechanical constants

3.2.1 Sound Velocity Measurements The material BLW and BTW phase velocity cL and cT necessary for defining the inner defect co-ordinates and material elasticity constant can be calculated as it is shown in [27, 28]. Such possibility is useful when the exploratory object has only one smooth surface, or only one surface is available. Method appeals to theoretical (2.18) and (2.19) connections obtained after solving Rayleigh equation:

,22

TSAW

T

T cc

kkm == (3.2)

,11

LSAW

T

T cc

kkm == (3.3)

it makes the relation

.1

2nm

ccs

TSAW

LSAW == (3.4)

After calculation of theoretical dependencies

the parameters r, n1, and m2 are estimated graphically (Fig. 3.3, Fig. 3.4, Fig. 3.5) according to the measured relation cLSAW /cTSAW . Then velocity of the bulk waves is calculated according to formulae

,,, 21

=

=

==

TSAW

LSAW

TSAW

LSAW

TSAW

LSAW

L

Tccfm

ccfn

ccf

ccr

49

3.2 LSAW application for measurement of physical and mechanical constants ,21 TSAWLSAWT cmcnc == (3.5)

.21r

cmr

cnc TSAWLSAWL == (3.6)

Fig.3.3. Theoretical ratio r = ct /cL dependence on cLSAW /cTSAW

Fig. 3.4. Theoretical Rayleigh equation radical n1 dependence on ratio s = cLSAW /cTSAW

0.30

0.350.40

0.45

0.50

0.55

0.60

2.0 2.1 2.2 cLSAW / cTSAW

r

0.48

0.49

0.50

0.51

0.52

0.53

2.0 2.1 2.2 cLSAW /cTSAW

n1

50

3 LSAW APPEARANCE AND USE

Fig. 3.5. Theoretical Rayleigh equation radical m2 dependence on ratio s = cLSAW /cTSAW

Fig. 3.6. Theoretical cLSAW/cTSAW dependence on Poison’s ratio µ Ratio s = cLSAW/cTSAW depends on Poison’s ratio µ (Fig. 3.6) connected to cTSAW by known empirical Bergman’s equation [9]

1,05

1.06

1.07

1.08

1.09

1.10

2.0 2.1 2.2 cLSAW / cTSAW

m2

2.05

2.07

2.09

2.11

2.13

2.15

2.17

0.27 0.32 0.37 0.42 µ

c LSA

W/c

TSAW

51

3.2 LSAW application for measurement of physical and mechanical constants

( ) .1

12.187.0121

12.187.0µ

µµρµ

µ++

=++

+= TTSAW cEc (3.7)

After simple calculation it is obtained that cLSAW also depends on µ. The dependencies cLSAW /cT and cTSAW on Poison’s ratio µ are calculated and shown in Fig. 3.7 and Fig. 3.8.

Fig. 3.7. Theoretical cLSAW /cT dependence on Poison’s ratio µ

Fig. 3.8. Empirical cTSAW / cT dependence on Poison’s ratio µ

1.89

1.94

1.99

2.04

0.27 0.32 0.37 0.42 µ

cTS

AW /c

T

0.92

0.925

0.93

0.935

0.94

0.945

0.95

0.27 0.32 0.37 0.42 µ

cTS

AW/c

T

52

3 LSAW APPEARANCE AND USE Having compared the dependencies in Fig. 3.7 and Fig. 3.8 we can see that cLSAW much more (about three times) depends on materials Poison’s ratio than cTSAW. LSAW velocity in many materials with µ < 0.33 is bigger than longitudinal wave velocity (cLSAW > cL) and grows when µ is getting less. One of practical LSAW and TSAW speed measurement in solid surface schemes is shown in Fig. 3.9. Angle immerse method and two identical piezoelectric transducers (emitter and receiver) are used there. The mechanism used for measurements is composed from two articulately jointed plates P1 and P2 with the ultrasonic emitter E and receiver R fastened to them. The bearings are used for the smooth change of angle ϑ and relief of mechanical friction with researched solid surface. The specific angles ϑLSAW = I

crϑ and ϑTSAW = IIcrϑ are measured by the

protractor when maximal signal amplitude received by receiver R according which cLSAW and cTSAW are calculated when the sound velocity c0 is known. Solid surface Poisson’s ratio value µ is obtained according to the ratio s = cLSAW /cTSAW from the diagram in Fig. 3.6. Then bulk wave velocities cL and cT are set from theoretical diagrams (Fig. 3.7, Fig. 3.8 and Fig. 3.3)

Fig. 3.9. Schematic of angle measurements by two types of ultrasonic waves: P1 and P2 are plates

P1

PULSEGENERATOR

FIRSTAMPLIFIER

SECONDAMPLIFIERINDICATOR

BLW

P2

Square

Icrϑ

ReceiverEmitterLSAW

A

Solid body

53

3.2 LSAW application for measurement of physical and mechanical constants 3.2.2 Measurement methods of elasticity constants The main elasticity constants (shear modulus G and Young modulus E) can be determined using theoretical Rayleigh equation radical m1 and m2 dependencies on ratio s = cLSAW /cTSAW and the relationship of this ratio with Poisson’s ratio µ according to the measured vales of the angles ϑLSAW = I

crϑ and ϑTSAW = IIcrϑ . The ratio sinϑTSAW /sinϑLSAW must

be measured by sine potentiometer for the increase of angle measurement accuracy when the object of research has only one smooth surface or there is no possibility to reach the other surface. It must be noted that even the shortcoming of those waves (natural attenuation in the way of propagation) has no influence on the reliability of angle measurements of LSAW results. As

,sinsin s

cc

TSAW

LSAW

LSAW

TSAW ==ϑϑ (3.9)

so according to measured ratio s and having estimated m1, m2, and µ given theoretical reliance in Fig. 3.4, Fig. 3.5 and Fig. 3.6, shear and Young modules are calculated from formulae

;sinsin

202

2

202

1

=

=

TSAWLSAW

cmcnGϑ

ρϑ

ρ (3.10)

( ) ( ) ( ) =+=+

=+= µµ

ϑρµ 121

sin212

202

1 GcnGELSAW

where ρ is the solid body density, c0 is the sound velocity in immerse liquid or prism.

(3.11) ( ),1sin

22

022 µ

ϑρ +

=

TSAW

cm

54

3 LSAW APPEARANCE AND USE Time intervals can be measured in practice more precisely than angles and their sinus, so time method is used for measurement of tension constant in the objects with right configuration (in special samples) [39]. By this method two types of waves (LSAW and BLW) are excited in solid body of right configuration and the terms tLSAW and tL of pass through the sample of length d are measured. The process of measurement can be automatic, synchronically switching ELSAW and EL emitters near the output of pulse generator and receiver RLSAW and RL near the amplifier input.

Fig. 3.10. Schematic of tension constants measurement

Having measured crossing time tLSAW and tL in both channels, according to the ratio tLSAW / tL = cL /cLSAW shear and Young modulus are calculated by processor

,22

2r

tdG

Lρ= (3.12)

( )µρ += 12 22

2r

tdE

L. (3.13)

RLSAWELSAW

EL

d

PULSEGENERATOR

FIRSTCOMMUTATOR

SECONDCOMMUTATOR

PROCESSOR

LSAW

Synchronization

tLSAW; tL

RL

AMPLIFIER

BLW

55

3.2 LSAW application for measurement of physical and mechanical constants µ and r are set in usual case from theoretical dependencies given in Fig. 3.11 and Fig. 3.12. Significant physical parameter of material is the velocity cT of transversal waves and is calculated according to equation

.L

T tdrc = (3.14)

Fig. 3.11. Theoretical r(tLSAW / tL) dependence

Fig. 3.12. Theoretical r(tLSAW /tL) dependence

tLSAW / tL

0.30 0.35 0.40

0.45 0.50 0.55 0.60

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

r

0.27

0.32

0.37

0.42

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

µ

µ(tLSAW / tL)

56

3 LSAW APPEARANCE AND USE 3.2.3 Measurement of surface hardness characteristics with LSAW

The surface hardening by chemical, mechanical, or thermal influence is broadly used for the increase of mechanical surface resistance. Its resistance to wear and other mechanical influences are increased almost not changing the elasticity features (fragility, flexibility, flow, and resistance to fatigue). Usually the surface hardness (micro hardness) is measured recording the interaction of indenter with the exploratory surface in the particular small sphere. The big scattering is typical to the results obtained by local measurement methods depending on the surface structure and coarseness. The hardness measurements by mechanical indenters impressed into the exploratory surface is frequently unacceptable because of the violation of surface solidity. So, sometimes the integral surface characteristics and also the hardness measurement methods are more useful. Material hardness boundary σmax is related with acoustic material properties and is defined by formula

χρσ

42

maxck

= , (3.15)

where: k and χ are the coefficients depending on the properties of material, and c is the sound velocity.

Experimentally measuring IIcrϑ and I

crϑ by angular method [96, 97], it was estimated that integral hardness of hardened and partially free steel surface determines cTSAW and cLSAW. Obviously, measuring in different frequencies, the law of hardness change in the direction of z co-ordinate can be estimated considering that SAW penetration depth is close to the wavelength. Otherwise, probing the surface layers of 0.3 < z < 1.5 mm, the ultrasonic velocity must be measured in 11 > f > 2 MHz range of frequency [97]. The angle measurements of real analysis objects in such high frequencies without special treatment of the surface subject are rather difficult and could not be very exact because of the propagation induced by the surface coarseness.

57

3.2 LSAW application for measurement of physical and mechanical constants The method for measurements [98] performed by the lowest frequency of LSAW by spot sensor, measuring the dependence of received signal amplitude on the depth z and LSAW propagation path length x, was created as alternative (Fig. 3.13).

Fig. 3.13. LSAW schematic of hardened surface research The maximum LSAW energy is concentrated not on the very surface but by the certain acute angle βLSAW in the bordering surface layer with the thickness depending on material’s Poison’s ratio µ and wave length λLSAW. For this reason LSAW output through the final surface point co-ordinate is zmax ≠ 0. Thereby, zmax depends on the depth of surface hardening. In CT.3 steel products, processed by shot flow method (lifetime is 300 s, diameter of shots is 1 mm) was experimentally measured. Normalized ∆U/∆x dependence on z was measured while changing LSAW propagation way x and having measured depth zmax in the condition of point sensor where the LSAW signal amplitude received by the sensor ∆U is maximal (Fig. 3.14). LSAW propagation velocity as depth z function is calculated deflecting LSAW sensor lengthwise wave propagation way by the distance ∆x and digitally having measured the change of delay ∆ tLSAW (Fig. 3.15):

x z

HRCz

∆ x

AMPLIFIER

AMPLITUDEINDICATOR

PROCESSORPULSEGENERATOR

Solid body

LSAW transducer

Point sensor

βLSAW

Icrϑ

58

3 LSAW APPEARANCE AND USE

( ).HRCFt

xcLSAW

LSAW ==∆∆ (3.16)

The change of steel depth mechanical properties (hardness) in the level of 3 dB was evaluated to ≈1.5 mm according the curve in Fig. 3.15. The measurer for the solid surface measurement in absolute HRC units was calibrated in the same mark of steel in calibrated hardening samples of 40 × 30 × 60 mm (Fig. 3.16). It should be noted that the empirical relation between cLSAW and hardness was not estimated, because those parameters also depend on other physical and mechanical constants associated with hardness, e.g., density ρ.

Fig. 3.14. Experimental normalized LSAW signal relative amplitude dependence on depth

0.2

0.4

0.6

0.8

1.0

0.5 1.5 2.5 3.5 4.5

z, mm

maxxU

xU

∆∆

∆∆

59

3.2 LSAW application for measurement of physical and mechanical constants

Fig. 3.15. Experimental ∆ cLSAW dependence on depth

Fig. 3.16. Calibration dependence ∆ cLSAW on hardness in standard sample of CT.3 steel

0

2

4

6

8

10

12

14

0 1 2 3 4 5 z, mm

∆c L

SAW, m

/s

5000

5010

5020

5030

5040

5050

5060

5070

40 45 50 55 60 65 HRC

∆cLS

AW, m

/s

60

3 LSAW APPEARANCE AND USE

3.3 LSAW in seismology 3.3.1 Seismic waves and their velocity LSAW are registered in seismograms during the Earthquake as primary seismic waves (Fig. 3.17). The truth is that they were treated as longitudinal waves propagating terrenely.

Fig. 3.17. The seismogram of the Earthquake in Isle of South Sandwich on

January 30, 1963. The seismogram was registered in Scot seismic station [99] (the focal depth was 33 km, strength was 6.8 point according to Richter scale): P is direct longitudinal wave; PP is longitudinal wave reflected from the Earth surface; S is transversal wave; PS is transversal wave transformed by reflection from the surface longitudinal wave; SS is transversal wave, reflected from the surface; SSS is transversal wave reflected twice; LR is surface Rayleigh wave (TSAW)

The semantic difference of the concepts “longitudinal acoustic waves” and “longitudinal waves propagating on the surface” seems small, but it is essential. It shows that the acoustic (infrasound) phenomena going on the Earth surface were interpreted and modelled wrongly. Having not evaluated surface mechanical oscillation, when the longitudinal surface waves propagate along the surface, the resistance of building constructions to such waves and the character of geotectonic processes could not be exactly forecasted. It is relevant for the research of seismic motion near the surface Earthquake epicentre (focal depth up to 30 km), because the destructive force of LSAW horizontal component is the biggest. LSAW energy is maximal near the epicentre; it is not

61

3.3 LSAW in seismology diminished because of irradiation of side longitudinal seismic wave irradiation when LSAW propagates along the surface. It must be noticed that very small Poisson’s ratio (µ = 0.17−0.22) [99] on which depends LSAW strength is typical to the constituents of the Earth crust (granites ρg ≈ 2.8 g/cm3, basalt’s ρb ≈ 3.0 g/cm3). Fig. 3.18 shows the scheme of the Earth cut and it explains the seismogram shown in Fig. 3.17. It was set that sound velocity changes (Fig. 3.19) and the biggest value of 8100 m/s reaches in the upper layer of the mantle (below the limit of Mochorovich situated in the depth of 30−33 km) because of solid density and compressibility change in the deeper layers pressed by the upper ones.

Fig. 3.18. Seismic wave trajectories, when the distance between the

Earthquake focus and seismic station is big The attention was focused on the strange phenomenon while exciting seismic waves by explosion on the Earth surface [99]. It was observed that the measured longitudinal surface wave velocity excited by the artificial blow was greater than the velocity of seismic waves at the same place. Considering that seismic waves propagate not on the surface but deeper, the result was likely opposite.

Earth core

RE ≈ 6370 km

Seismic station

PS PP, SS SS

P, S

O

Mantle

LR

Seismic focusK

F

62

3 LSAW APPEARANCE AND USE

Fig. 3.19. Hypotethic depending This “mysterious” result is easily explained by LSAW properties in solid bodies with the Poisson’s ratio µ < 0.26. It is known that cLSAW > cL. The different conditions of the research must be mentioned as the main reason for the mistake. Usually the Earthquakes happen not near the seismic station, so the structure of registered signals reflect many bulk wave transformations formed in seismic focus. While during the experimental explosion transducers can be near the modelled focus of seismic blow for the exact measurement of the primary wave velocity, attenuation, explore their spectra and other characteristics. Seismic wave scheme near the surface explosion epicentre is shown in Fig. 3.20.

5000

5500

6000

6500

7000

7500

8000

8500

0 10 20 30 40Depth, km

Soun

d ve

loci

ty, m

/s

63

3.3 LSAW in seismology

Fig. 3.20. Trajectories of seismic waves situated near of explosion focus, where F is the explosion focus, E is the epicentre, K is the place for registration of signals (seismic station)

The quickest wave (LSAW) signal is registered the first, and the last registered signal is of the slowest (TSAW) wave when the focus depth is h << x and cLSAW ≥ cL (µ < 0.26). It was set that seismic waves are dispersive because of the character (change of physical and mechanical properties depending on depth) of the Earth upper layers (crust, mantle). So, the form and spectrum of seismic pulse signal changes and it is difficult to interpret seismograms. Seismic waves induced by the earthquakes allowed to set the structure of the Earth abyss (to find the liquid Earth core and the solid phase in the centre), but to use them for the seismic prospects of minerals are rather difficult. For this purpose seismic waves were excited artificially (e.g., exploding, or by shocks to the surface) [99, 100]. Artificially made seismic waves are used for the scientific purposes simulation the Earthquakes. 3.3.2 Simulation seismic phenomena Seismic processes are usually simulated and explored in the ultrasonic frequency range in laboratory conditions. The simplest Earth crust seismic model designed for the research of the waves propagating on the surface is shown in Fig. 3.21. This is the glass plate with a soldered light-adsorbing gasket A in the particular depth. The gasket can be

Fx

hBLW, BTW

BTWBTW

ELSAW TSAW

K

64

3 LSAW APPEARANCE AND USE spherical, cylindrical, tetrahedron, cubic, or of irregularly shaped form depending on simulation seismic phenomena and waves. Seismic blow (push) in such a model is excited by the pulse laser with the light focused to the gasket.

Fig. 3.21. The flat ultrasonic model of the Earth crust (the ultrasonic wave receivers are not shown) The pulses of the excited by ultrasonic longitudinal, transversal, surface waves (LSAW, TSAW, Love waves) are received by broadband piezoelectric or optic receivers of appropriate waves. Wave reflections from the upper plate surface and their transformations simulate the reflection of seismic waves from the Mochorovich line, where mechanical and physical properties of the Earth deep saltatory changes (the density and bulk waves velocity cL and cT grow). But in this case the phase change mark during the reflection is not considered because waves reflect from the boundary with the acoustically soft material (air). The experiments with pulse laser (ruby; Λ0 = 0.694 µm, τi ≈ 1 µs) exciting the ultrasonic waves on the surface of glass plate were performed for the checking the model. The received signal by 1.8 MHz angle converter with the registered LSAW and TSAW pulses is shown in Fig. 3.22.

A h

BLW d

BTW BTW BLW

Glass

Linse

Light pulse

LSAW TSAW TSAW LSAW

65

3.3 LSAW in seismology

Fig. 3.22. Ultrasonic signals excited by two laser pulses and received on glass plate near the exciting point (“focal”)

The ultrasonic frequency band cylindrical Earth seismic model evaluating the curvature of the Earth surface better suits for the simulation of the seismic phenomenon. The minimum attenuation in materials with the particularly small Poisson’s ratio is the precondition for the use of LSAW. The Poisson’s ratio of the Earth deep rocks (basalt and granite) is µ ≤ 0.3, so the fastest wave of the seismic phenomenon usually is called the primary and is identified as LSAW. The research of LSAW is relevant because those fastest waves are responsible for the first destroys. At the same time they are the first information source about the forthcoming much more strong TSAW (Rayleigh) waves. Their simulation in the range of ultrasonic frequency can be very effective taking into account the occasional character and particularly low frequencies.

3 LSAW APPEARANCE AND USE Seismic wave propagation on the surface of the ocean is relevant seismic occasion. It is known that TSAW propagating on the surface bordering with the liquid excites longitudinal waves there and they propagating into the liquid bring the most part of the acoustic energy. So, the TSAW damps. Otherwise, analyzing Stoneley waves in the boundary between solid body surface and liquid, I. Viktorov made the deduction [24] that in the thick liquid layer situated near the solid surface the slow wave (c < cliq) with the energy concentrated in the liquid propagates on the bottom of the ocean during the Earthquake. LSAW propagation on the Earth surface layer under the ocean bottom is the other seismic wave propagation mechanism. As it is experimentally set (Chapter 4.3.1.1), LSAW weakly interacts with the solid surface, so the surface state (roughness, contact with the liquid) almost has no influence on their propagation (attenuation). So, LSAW can propagate in big distances and raise the first destructions on the coast.

67

4 LSAW RESEARCH METHODS In order to establish an envelope of application and usefulness, principal LSAW characteristics are of interest to research. They are the phase velocity and its dependence on physical parameters and the configuration of the solid, as well as the attenuation inside the material. The angular pulse and pulse methods in LSAW velocity measurements are the most efficacious in such work. They are used to determine attenuation as well.

4.1 Angular-pulse method The angular-pulse method co-ordinates the advantages for the measurement of pulse method time intervals and wave velocities, and the angular method for SAW exciting also. Plane wave piezoelectric transducers must be used to excite surface ultrasonic waves by the angular method. In NDT a flat frontal longitudinal wave is radiated by transducers, with the aperture of transducers S much greater than the acoustic wavelength (S0 >> λ) and with equal oscillation distribution in aperture. Usually it is assumed that those conditions for the accepted in practice precision are fulfilled in the range of megahertz, if S0 ≥ 10λ. Incidence angle of a plane frontal wave is determined with respect to the surface normal, though practically the direction of this normal not necessarily coincides with that of the transducer surface. For this reason the normal direction will be taken along the bearing where the frontal acoustic wave reflects from a smooth surface with the maximal amplitude. Thus the incidence angle of a plane frontal acoustic wave will be determined with respect to the direction of maximal reflection from the surface. As is known, because of unavoidable acoustic wave diffraction, angular-amplitude characteristic of a transducer has a finite

68

4 LSAW RESEARCH METHODS width. As a result, the maximal directional angle ϑ0 of the signal is set with a particular uncertainty, which is not equal to zero. For more exact estimation of the angle ϑ0 the “fork” method is adopted. Here, taking the assumed flat, symmetric, directional characteristic of the transducer, two angles ϑI and ϑ2 corresponding to the fixed amplitude of the signal (usually it is 0.7) are measured on both sides of the incidence angle ϑ0 (Fig. 4.1) and is calculated as the average of the angles.

Fig. 4.1. Incidence angle λ0 estimation using the received signal amplitude

However, satisfactory results are not always obtained using the “fork” method. This is due to the lack of precision when measuring the angles ϑ1 and ϑ2. Besides, in such measurements the maximal amplitude value must be known. Schematic for the incidence angle indicator is shown in Fig. 4.2; it makes use of flat ultrasonic waves, it is automatic [101]. Activated electric motor starts to rotate the ultrasonic transducer around axis, located on the surface of the tested solid body. With rotation of the transducer, the contacts are connected and first electronic key is supplied. At that time, radio pulses from a high frequency generator and pulse modulator are sent through the first commutator and the first electronic key to initiate the transducer.

ϑ0

U/Umax

ϑ1 ϑ0

0.7

1.0

ϑ2

69

4.1 Angular-pulse method

Fig. 4.2. Schematic for incidence angle indicator

The ultrasonic pulses U1 irradiated for transducers (Fig. 4.3 a) are reflected from the surface of the solid, and, in case of the incidence angle ϑ ≈ 0, are received by the same transducer; subsequently the reflected pulses are directed through the amplifier and amplitude noise limiter (Fig. 4.3 a) to the voltage envelope detector. The dependence of the voltage U2 in the output of the envelope detector on time and angle ϑ is the same (Fig. 4.3 b). Rectangular electric pulse U4 (Fig. 4.3 d) formed by the second comparator sets the time interval when the zero level comparator can function. The voltage is given into its signal input

d

Transducer ϑ

FIRSTELECTRONIC

KEY

SECONDELECTRONIC

KEY

FIRST COMMUTATOR

AMPLIFIER

SECOND COMMUTATOR

TRIGGER

ELECTRICMOTOR

PULSEGENERATOR

NOISELIMITER

REDUCER

ENVELOPEDETECTOR

DIFFEREN−TIATOR

ZERO LEVELCOMPARATOR

ANGLEINDICATOR

REVOLIUTIONCOUNTER

a

b

c

e

Solid body

Contacts

E

LSAW

70

4 LSAW RESEARCH METHODS obtained after differentiation of envelope voltage U3 (Fig. 4.3 c). The zero value voltage U3 corresponds the maximal amplitude instant (incidence angle) of ultrasonic pulse, thus the produced pulse U5 (Fig. 4.3 e) at the output of zero comparator coincides with the time instant when the ultrasonic pulses reach the surface perpendicularly (ultrasonic transducer incidence angle ϑ = 0°). This pulse opens the switch to the second electronic key to initiate the counting of revolutions. For this purpose in the schematic there is an electro-optical revolution counter with the identifiable angle markings (pulses) to be counted. The pulses are counted while the ultrasonic transducer rotates, till the position where it excites in a solid body and receives the reflected LSAW pulses of maximal amplitude.

Fig. 4.3. Time (angular) diagrams: a) received and reinforced acoustic signals; b) the voltage of pulses envelope; c) differentiated voltage of pulse envelope; d) output voltage of zero comparator; e) pulse, corresponding the maximum of pulse envelope

ϑ, t

ϑ, t

ϑ, t

ϑ, t

ϑ, t

ϑ= 0°

E0

e)

d)

c)

b)

a)

U1

U2

U3

U4

U5

0

Icrϑϑ =

71

4.1 Angular-pulse method This happens in the position of sensor in marked by the dotted line when the pulse obtained in the zero position of comparator output disconnects the second electronic key and breaks the counting of angle markings. The number of pulses registered by the counter is proportional to the LSAW excitation angle (ϑLSAW = I

crϑ ). Having set contacts into the other position where the pulses of maximal amplitude in the output of noise limiter are obtained, the other typical incidence angles, such as the TSAW excitation angle ϑLSAW = II

crϑ , can be measured. The control of the contact position can be monitored visually from the screen of the oscilloscope (not shown in the schematic of Fig. 4.2). It is to be noted that the precision of the described incidence angle indicator does not depend upon speed stability of the electric motor. Increasing the reduction coefficient N and the number of angular markings in the optic-electric sensor may improve the precision. Practically it is not at all problematic to obtain from 60 to 90 angular markings per revolution. In this case, when N = 100, the incidence angle measurement error is ≤ 4’.

4.1.1 Equipment for immersion research Transformation of longitudinal waves into transversal followed by subsequent excitation of SAW, is used in NDT with angular pulse waves excitation and reception. However, such practice is not without problems. They are rooted in the methods of time interval measurement, attributes of angular measurements, and measurement instrumentation. In the situation on hand, measurements yield the best precision when the impulse immersion method is employed. The immerse measuring device reported in [102] is used for that purpose. It measures LSAW speed in the samples with the fixed dimension, mechanically changing the position of the transducer for excitation longitudinal ultrasonic waves. Changes in the transducer position should be such that the longitudinal wave incidence to the

72

4 LSAW RESEARCH METHODS surface point would not be altered. This is accomplished by matching the rotation centre of the ultrasonic transducer with the surface of the sample under investigation and turning on an axis of the transducer in a plane perpendicular to the sample surface. Schematic for the device to determine angular measurements of immersed bodies is shown in Fig. 4.4. SAW are excited in the sample immersed in a distilled water tank by a revolving ultrasonic transducer which is connected to a standard ultrasonic defectoscope.

cLSAW

Sample

Tank

Transducer

ϑMOTOR,REDUCER,GEAR

PULSEGENERATORAMPLIFIEROSCILLOSCOPE

OPTICAL SENSOROF THE ANGLESIGNAL

PROCESSOR

MONITOR NLSAW, I

crϑ , cLSAW

KEYBOARD

Reverser signalPC

H2O

ULTRASONIC DEFECTOSCOPE

Fig. 4.4. Schematic of the experimental device for LSAW velocity measurements

The angle ϑ of the ultrasonic transducer is managed mechanically. The output of an electric motor through a double reducer is slowed down 1.6⋅105 times from 3000 rot/min for the task. A digital optic-electrical sensor providing rotational angle markings at the output reads the

73

4.1 Angular-pulse method resulting shaft revolutions. A special electronic indicator was designed to read such rotational values of the output shaft, in turn connected to a personal computer, programmed to calculate and display parameters of interest [101]. With such set up not only the revolution count NLSAW at the reducer output, but also the positional angle of the transducer ϑLSAW, and the energized LSAW velocity cLSAW in the sample are calculated with the formula (4.1) and displayed.

( ) ,

*sinsin LSAW

liqIcr

liqLSAW N

ccc

ψϑ== (4.1)

where cliq is sound velocity of the immersion liquid; Ψ is constant of the ϑLSAW positioning system; NLSAW is the number of pulses corresponding to the deflection angle ϑLSAW of the transducer. 4.1.2 Calibration of angular measurement device

The precision of measuring depends much on the work of mechanical system of angle change. The influence of axle angle freedom grows evaluating big coefficient of engine axle rotation reduction coefficient. The angle sensor must be connected not with the reducer but with the engine axle in order to obtain minimal errors of measurement. The angle backlash of reducer axle is the systematic error of angular measurement. The transducer of speed measurement is turned in the same direction for its removal as in the case of fixing zero position of the converter where the ultrasonic pulses of maximal amplitude having reflected from the smooth sample surface are received. The other important systematic error is the calibration error of angle measurement. It depends on calibration methodology and the precision. The angle signal sensor is calibrated counting the number of pulses obtained turning the ultrasonic transducer by 360° (Fig. 4.5). 2,5 MHz frequency transducer П111-2,5-K12-002 was used for the measurements. The zero position of the transducer is fixed when ultrasonic pulses amplitude is maximally reflected from the surface.

74

4 LSAW RESEARCH METHODS The number of indicated on monitor value (N = 0) is fixed in this position and the engine is switched on. After the transducer turns 360° the engine is stopped in the same position fixed according to the maximal ultrasonic pulses (seen on the monitor of defectoscope) amplitude. The experimental dependence from angle ϑ [102] of reflected pulses amplitude from the surface is shown in Fig. 4.6.

Fig. 4.5. Schematic of angle device calibration

Fig. 4.6. Angular dependence of normalized amplitude of reflected ultrasonic pulses

0-1-3 -2 1 2 3 4-4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

A/A

m

ϑ °

ϑ1 ϑ2ϑ0

∆ϑ

A

ULTRASONICDEFECTOSCOPE

MONITORNLSAW., ϑLSAW , cLSAW

ϑ

O

d = 20 mm

Transducer

Plane solid surface

75

4.1 Angular-pulse method This dependence reflects the ultrasonic diffraction wherefore the width of ultrasonic transducer’s directivity characteristics is ∆ϑ0.5 = 2.4° and it determines the setting uncertainty of ultrasonic transducer zero position measuring the angle according to the maximum of the signal. The ultrasonic transducer’s position determination uncertainty is connected with the sharpness of dependence A/Am(ϑ) close to zero in the zone of ϑ ≈ 0°. In the described case this uncertainty reaches ± 0.2°; for its reduce the “fork” method is used; the position of maximum is calculated according two measurements in the spheres of the biggest curve sharpness. The exact value of the maximal angle ϑ0 = (ϑ1 + ϑ2)/2 is calculated having measured the values of the angle ϑ1 and ϑ2 obtained in the position of the transducer where the signal amplitude is equal to A/Am = 0.5. Using the described technique of angle measurement, such calibration results were obtained: the impulses N360 = 137166 were counted after the ultrasonic transducer has turned by 360°; calibration constant, showing the angular value of one impulse; Ψ = 9.449”, the mechanical angular backlash of the axle ∆ϑ = ± 2.36°.

4.2 Pulse-time method

SAW Phase velocity is measured using pulse method exciting frequency f acoustic pulses and measuring their propagation time t according which they propagate the distance l according classical equation

tlcSAW ∆

∆= . (4.2)

The difficulties for setting SAW pulse exciting time moment and wave propagation distance l conditioned by the SAW pulse exciting point uncertainty on the solid surface rises SAW pulses exciting by angular method, e.g. prism transducer. In this case SAW pulse exciting by the focused pulse laser light is more superior.

76

4 LSAW RESEARCH METHODS 4.2.1 Experimental equipment for the prism research method The digital signal analyzer PCS64i [103] (Appendix 1) was established for the measurement of the form of LSAW pulse signals and spectrums. The structural schematic of the ultrasound pulses analyzer is shown in Fig. 4.7. The problem how to emit topical acoustic pulse from the complicated signal seen in the analyzer’s screen is met while measuring in SAW (Fig. 4.8). Besides useful component, residual excitation pulse induction is in this signal also and the side reflections of the BTW and BLW are possible in the prism of angular transducer and in measuring sample. All the side pulses are emitted using rectangular electric pulse (time “window”) with the length τi and delay Ti with the regard to exciting electric pulse is exactly regulated. It controls the electronic key: the pulse signal reflected from the exploratory defect penetrates through it and accesses the digital analyzer, when the electronic key is conductive.

Fig. 4.7. Schematic of SAW pulse signal analyzer

PULSEFORMER

PULSEGENERATOR

ELECTRONICKEY ATTENUATOR AMPLIFIER

SIGNALANALYZER

PCS64i

PC

ϑ

Defect

SAW

Angulartransducer

Sample

77

4.2 Pulse-time method

Fig. 4.8 Typical ultrasonic pulse signal on the screen of the digital analyzer Triple electronic key is switched for the avoidance of side electric disturbances and for the effective repression of exciting signal induction ( > 60 dB) beyond the time “window” borders. Besides, it is constructed so that the input of analyzer is additionally electrically shortly connected in the zone beyond the time “window”. The time strobing principle of the exploratory LSAW signal is described by the schematic (Fig. 9) and time diagrams (Fig. 4.10). Pulse generator is started by the synchronized pulse Ug of defectoscope and forms two electric pulses, where the second is delayed by time Ti. Those two impulses start and stop multivibrator forming the rectangular pulse Um where the second front starts multivibrator generating the pulse of τi time ruling the electronic key. The term τi is set longer than the time desirable to distinguish SAW signal Us. So, the signal analyzer measures only proper SAW impulse parameters (time, amplitude, and spectrum). The possibilities of LSAW signal analyzer are determined by such parameters of digital analyzer PCS64i as: digitizing frequency 64 MHz, minimal time interval ∆ tmin = 0.01 µs/division, input sensibility Umin = 10 mV/division, frequency range 0-16 MHz, maximum readout error 2.5 % (Appendix 2).

78

4 LSAW RESEARCH METHODS

Fig. 4.9. Simplified structural schematic for digital ultrasound

LSAW signals analyzer

Fig. 4.10. Time diagrams of LSAW pulse signal strobing

Emitter

ReceiverLSAW

Electromagneticinduction

DEFECTO −SKOPE

PULSEGENERATOR

TIME DELAY

ELECTRONICKEY

AMPLIFIERSIGNAL

ANALYSERPCS64i

τi t

t

t

t

t

Ug

Ui

Um

Us

Ul

InductionLSAW

Ti

TSAW

79

4.2 Pulse-time method SAW pulse signal form, measured time “window” parameter τi (µs) and the chosen actual level (amplitude, mV) is seen on the screen of personal computer, recorded in its memory and can be printed, when the signal analyzer works in the schedule of signal form analyzing. The form of signal spectrum is recorded, the essential (resonant) frequency (MHz) is measured, and the level of spectrum component (dB) is marked in the schedule of spectrum analyzing. The scale of frequencies can be set as linear or logarithmic. Digital ultrasonic signal analyzer is universal and can be used as ultrasonic defectoscope for the NDT and measurements of any ultrasonic waves, for the measurement of their velocity, attenuation, thickness of the product, for the observations of echo signals, analyzing and recording in the memory of PC. 4.2.1.1 Influence of ultrasonic attenuation in prism

Theoretically, usually the precondition is made that exciting SAW by the angular method the ultrasonic oscillation amplitude scattering on the solid surface plane is equal. In such a case, the work efficiency of SAW angular transducers depends only on the geometric parameters of piezo-crystal and prism, and the peculiarities of their construction conditioning the reverberations of the transducer (Fig. 4.11).

Fig. 4.11 LSAW signal received by the angular transducer of variable angle; f = 3.0 MHz

80

4 LSAW RESEARCH METHODS Ultrasound diffraction in prism is very weak when the transversal dimension d > 10λ and when there is equal oscillation amplitude distribution in the structure of piezo-crystal aperture, the BLW of rather plane front is obtained. But oscillation amplitude distribution on the solid surface because of the BLW attenuation in prism becomes uneven in the band of higher (megahertz) frequencies. Amplitude A of acoustic field vibrant pressure on the solid surface plane becomes equal to

nlAe α− , where α is the coefficient of liquid damping, ln is the distance to the solid surface (Fig. 4.12) and because of that, the efficiency of SAW transducer worsens.

Fig. 4.12. Influence of ultrasonic attenuation in prism to the piezo-crystal’s acoustic field on the solid surface

The transducer with the controlled aperture amplitude distribution is used for the return of the even character for the acoustic field on the plane of solid surface. Piezo-crystals grating made of n parallel band piezo-crystals or obtained respectively sectioning the piezo-crystal electrodes of rectangular profile can be the example of such a transducer. The voltage of grating transducer (Fig. 4.14 a) piezo-crystals exciting is set inversely proportional to the wave attenuation in the path length ln. This is obtained while introducing the correction of exciting pulse amplitude Sn=B em⋅ln; (4.2)

ln

l1

Ae-αl1 Ae-αln

Piezo-crystal

81

4.2 Pulse-time method where B = const and m = const are coefficients; ln is the propagation way of BLW in prism. The distribution of excited ultrasonic signal pressure amplitude in the plane M of piezoelectric grating and in the plane N of solid surface in this case is shown in Fig. 4.13 b.

a)

b)

Fig. 4.13. Schematic of grating SAW angular emitter (a) and the exciting level law in aperture M and pressure distribution

in plane N (b)

x

l1

11

mlBeS =

nml

n BeS =

PULSEGENERATOR

SAW N

n

1

M

ϑ ln

x

n=1 SM(x)

PN(x)

x1 xn

n

x

82

4 LSAW RESEARCH METHODS The amplification of separate piezo-crystal signals is changed for the equalization of SAW grating received signals of amplitude distribution as shown in Fig. 4.14.

a)

b)

Fig. 4.14. Schematic of grating SAW angular receiver (a) and aperture distributions of pressure in section M and signal

amplitude Us(x) The amplification of every element signal is defined Kn = D eg⋅ln, (4.3) where D = const and g = const are coefficients.

ϑ

1SU

nSU

SAW

l1

Us(t)

n

1

ln

K1=D⋅eg⋅l1

Kn=D⋅eg⋅ln

AMPLIFIER

M

Σ

x

xn x1 x

PM(x)

Us(x) x

n =1

n

83

4.2 Pulse-time method Signal amplitude correction Sn(x) (exciting SAW) and amplification Kn(x) (receiving SAW) functions depend on angle ϑ using the described method for SAW transducer of variable angle. This variation is evaluated automatically using PC connected to the automatic variation system of angle ϑ. Having changed the angle ϑ the appropriate coefficient values Bn(ϑ) and Dn(ϑ) are defined programmely or can be changed by the key board, visually observing the obtained result (the variation of output signal Us(t) form (amplitude) during the experiment). It should be noted that such control system of aperture distribution could be effective only when the crystal transversal dimension of piezo-grating is quite big in comparison to the wave length (dn /λ >1), so it means in frequency band (megahertz). 4.2.1.2 Research of angular transducer acoustic contact Analyzing by SAW excited in angular method, the exploratory surface is moistened by the liquid (usually by the motor oil); so for the formation of acoustic contact the liquid layer of particular thickness d is formed between the angular transducer and the surface of sample. It is known that [2] when kd << 1 and λ >> d, sin kd ≈ 0 and acoustic wave transmitting coefficient Kp in the direction perpendicular to the surface (ϑ = 0°) does not depend to the impedance Z0 and is maximal:

,2

31

31max ZZ

ZZK p +

≈ (4.4)

where k = 2π/λ is the wave number, Z1 and Z3 are acoustic impedancies of piezo-crystals and solid body. If sin kd ≠ 0, acoustic waves are transmitted the best, when 312 ZZZ = (4.5)

.

84

4 LSAW RESEARCH METHODS It is more complicated to calculate coefficient of acoustic wave transmitting when the layer of contact liquid is of thickness d in the case of angular measurements (ϑ > 0), because coefficients of acoustic wave reflection and transmitting coefficients are the functions of incidence angle ϑ. Besides, in practice the acoustic impedance Z0 of contact liquid is frequently not known. So, the influence of liquid layer thickness was researched experimentally [104]. Measured ultrasonic dependence of surface wave attenuation S ~ 1/Kp on liquid layer between the angular transducer and sample surface thickness d is shown in Fig. 4.15. The measurements were conducted using the motor oil for acoustic contact (sound velocity c = 1140 m/s) [76] in the frequencies of 1.8 MHz and 2.5 MHz (λ1.8 = 0.78 mm; λ2.5 = 0.56 mm).

Fig. 15. Damping dependence of surface waves on the thickness of the motor oil layer between the angular transducer and the sample

85

4.2 Pulse-time method It is evident that those dependencies are of interference character and signal amplitude is maximal when the liquid layer thickness is of the particular thickness dmin. This effect allows obtaining acoustic “brightening” that is analogous to broadly used for optical device brightening in optics covering the surface of the lens by the interferential film. The dependencies shown in Fig. 4.16 allow constructing the maximal sensitive angular transducer of SAW exciting through the contact liquid layer dopt = dmin (Fig. 4.16). The acoustic contact of SAW transducer is made of the viscous liquid, e.g., silicone oil that with the help of gravity flows from the cell inside the body (the electric contacts and liquid flow speed regulator are not shown in the figure).

Fig. 4.16. The construction of angular transducer with the acoustic contact layer of optimal thickness

Such transducers are useful researching solid bodies by SAW, especially by LSAW that have great “natural” attenuation. 4.2.1.3 Research of transducers with variable angle As it was shown experimentally, the best results are obtained using transducer with variable angles. Three identical kits of symmetric emitters and receivers working in different frequency bands (1.8; 3.0, and 4.0 MHz) were produced (Fig. 4.17). The LSAW pulses and their spectra were obtained (Fig. 4.19 b) when the incidence angle ϑ = I

crϑ = 25° and the transducers are functioning as the pair emitter – receiver (Fig. 4.18).

Viscous liquid

dopt

Piezo-crystal

Contact layer

86

4 LSAW RESEARCH METHODS

Fig. 4.17. Variable angle symmetric transducers pair (f0 = 3.0 MHz)

Fig. 4.18. LSAW signal registration by the pair of angular transducers

Though SAW almost does not diffract, a small amount of energy can be radiated backwards by the angular transducers. The backward propagation signal is interfering and can raise the outside signals; when they are summarized with the direct signals, big measurement mistakes can occur. The body of the transducer greatly damps TSAW because TSAW propagates on the very surface of the solid surface. While LSAW, propagating not deeply under the surface and so are damped weaker by the body of the transducer, and the backward propagation becomes even more actual.

IIcrϑ

Icrϑ

b

PULSEGENERATOR

SIGNALANALYZER

PCS64i

Emitter Receiver

Sample

LSAW

TIMEDELAYBLOCK

87

4.2 Pulse-time method

a)

b)

Fig. 4.19. LSAW signals of variable angular transducers in the samples of duralumin and their spectra when the central frequency of the transducer is: a) 1.8 MHz; b) 3.0 MHz

Emitter was turned round while researching the backward propagation (Fig. 4.20). It was measured that TSAW signal amplitude decreased by 16 dB (1.8 MHz) and by 19 dB (3.0 Hz); LSAW signal amplitude has decreased by 24 dB (1.8 MHz) and by 21 dB (3.0 MHz). The level of reverberation noise of transducer with 3.0 MHz and 4.0 MHz is almost equal, but when the amplitude ratio A3.0/A4.0 ≈ 8 dB, the reverberation ratio level of 3.0 MHz transducer is the smallest and equal to (Ar

/A3.0)LSAW ≈ −15 dB (Fig. 4.19 b).

88

4 LSAW RESEARCH METHODS

Fig. 4.20. Schematic of backward propagation measurement

Evaluating those results it must be taken into account that SAW exciting sphere is closer to the front prism edge. So SAW, propagating backward are damping by prism surface for the longer distance; so they are damped more than SAW propagating in the direct direction. This factor can be especially meaningful for the level of TSAW. TSAW signal and spectrum obtained after determination of incidence angle ϑ = II

crϑ = 59° are given for the comparison (Fig. 4.21). TSAW signal (Fig. 4.21 b) in comparison to LSAW signal (4.19 b) is delayed because cLSAW > cTSAW.

Fig. 4.21. TSAW signal and its spectrum (f = 3.0 MHz)

IcrϑI

crϑ

dLSAWbLSAW

Receiver Emitter

89

4.2 Pulse-time method 4.2.1.4 Constructions of double angular transducers The natural need to excite and record signals of both types at one time arise while researching two types of SAW, especially performing comparative analysis of LSAW and TSAW. The double transducer of constant angle composed of biprism with two identical piezo-crystals (Fig. 4.22) and two angles equal to ϑ1 = I

crϑ

and ϑ2 = IIcrϑ must be used for the NDT of known acoustic property

products. Using transducer of that construction, the maximal sensibility of LSAW and TSAW is obtained because the created ultrasonic field edges of both piezo-crystals (LSAW and TSAW) are superposed with the front edge of biprism. The configuration of biprism front part has the form of ultrasonic “catcher” and for the sake of reverberation reduction it is made as diffusive and is coated by the absorbtive compound (grained rubber, epoxy resin, and mixture of wolfram powder).

Fig. 4.22. Double LSAW and TSAW angular transducer

Transducer of such construction must be used for the precise measurements where the LSAW and TSAW piezo-crystal signal introduction points M and N must be superposed. The LSAW signal level will reduce fractionally because of such LSAW piezo-crystal

IIcrϑ

Icrϑ

LSAW TSAW Biprism

Compound

LSAW piezo-crystal

TSAW piezo-crystal

N M

90

4 LSAW RESEARCH METHODS change of the position to TSAW piezo-crystal as LSAW are not sensitive to the mechanical state of sample surface and to the damping by the front part of the transducer prism. Double transducer LSAW and TSAW of variable angle (Fig. 4.23) is multipurpose and can be used to sent and receive LSAW and TSAW signals and for the complex exciting of one type of wave (LSAW or TSAW) pulses, and for the receiving of pulses (TSAW or LSAW) transformed to the other type of waves. LSAW or TSAW interaction with the various profile objects can be researched with such transducer.

Fig. 4.23. The double transducer of LSAW and TSAW variable angle

By the way, this double different transducer of SAW type can be used as tandem, i.e., as double transducer of some one type of surface wave (LSAW or TSAW), where the appropriate waves are excited by one piezo-crystal and received by the other. 4.2.1.5 Influence of diffraction to the efficiency of LSAW exciting Till now LSAW were mostly used for the NDT. As practical results show [45–47], not LSAW, but the whole of two waves: LSAW propagating on the surface and BLW propagating in a small angle to

TSAWLSAW

Diffuser

LSAW piezo-crystal

TSAW piezo-crystal

Plexiglass prism

N M

IIcrϑ

Icrϑ

91

4.2 Pulse-time method the surface are outlined by German term Kriechwelle (Eng. Creeping wave) (Fig. 4.24). Together with LSAW side BTW with a velocity of cT also propagate as inevitable satellites.

Fig. 4.24. Acoustic field of angular LSAW transducer

The origin of BLW propagating together with LSAW is diffraction as inevitable phenomenon existing when the ratio of transversal dimension of piezo-crystal with the length of acoustic wave d/λL < ∝. It was also set that when the ratio d/λL is increased, BLW propagating angle in the solid body (900−β) can be reduced. But, as it is shown in [47], even when d/λL = 40, the angle 90°−β ≈ 6° remains. Otherwise, the BLW propagating angle β < 90° can mean that BLW propagating in prism has the set incidence angle I

crϑϑ ≠ ; so LSAW wave exciting is not optimal. In general, three cases are possible: 1 – when I

crϑϑ < ;

2 – when Icrϑϑ = ;

3 – when Icrϑϑ > .

β

Ikrϑ

γ BTW

BLW Solid body

Piezo-crystal

LSAW

Prism

92

4 LSAW RESEARCH METHODS In the first case (Fig. 4.25 a) LSAW exciting is not optimal because of BLW diffraction and BLW propagation in solid body besides LSAW in the angle β. In the second case (Fig. 4.25 b) LSAW maximal amplitudes are excited and besides them as inevitable lateral phenomenon propagate residual BLW. In the third case (Fig. 4.25 c) LSAW is excited not in maximal amplitude, when BLW interacts with the solid surface and because of diffraction weaker than in the second case residual BLW propagate. It is evident that not deeply from the surface the defect can be found by the angular transducer where LSAW and BLW are excited at the same time in the solid body (Fig 4.25) because cLSAW ≠ cL. The exact fixing of the defected place is associated with the indetermination of reflected from the defected place acoustic waves. It is necessary to separate LSAW from BLW while researching LSAW physical characteristics and applying them in metrology (e.g. for measurement of physical and mechanical constants of solid bodies). But it must be taken into account that Poisson’s ration µ depending on material can be cL ≤ cLSAW or cL ≥ cLSAW. So, if the signals LSAW and BLW are not separated, phase wave velocity concept cannot be used for the complex characterization of two different types of wave beam. TSAW transformation into LSAW can be used as one of the methods how to get “clear” LSAW (Fig. 4.26) [105, 106]. TSAW effectively transforms into LSAW on the corner of solid body (projection into the plane of the figure is point A), because its transversal component of the amplitude z

TSAWξ on the perpendicular surface beyond the corner A becomes LSAW longitudinal component x

LSAWξ , and LSAW longitudinal component x

TSAWξ becomes zLSAWξ .

93

4.2 Pulse-time method

a)

b)

c)

Fig. 4.25. Influence of BLW diffraction to LSAW exciting efficiency (BTW on the solid body are not shown):

a) Icrϑϑ < ; b) I

crϑϑ = ; c) Icrϑϑ > .

βmax

ϑ

LSAW

BLW

Piezo-crystal

Solid body

Prism

LSAW

Icrϑ

BLW

Piezo-crystal

Solid body

Prism

ϑ

LSAWBLW

Piezo-crystal

Solid body

Prism

94

4 LSAW RESEARCH METHODS

Fig. 4.26. LSAW exciting when TSAW crosses the corner of 90°

The other possibility to excite “clean” LSAW is to use refracted BTW on the solid body exciting the secondary LSAW on the other plane of parallel solid surface (Fig. 4.27).

Fig. 4.27. Schematic of secondary LSAW exciting

(side BTW is not shown) This method is used for the ultrasonic NDT for tanks (boilers, bodies of nuclear reactors) [107].

Icrϑ

γ

Piezo-crystal

Solid body

Primary LSAW

Prism

BTW Secondary LSAW

LSA

W

ATSAW

IIcrϑ

BTW

95

4.3 Experimental SAW research

4.3.1 LSAW and TSAW comparative research LSAW is the antipode of TSAW according to its physical origin, so their similarities and differences can be shown the best during the comparative researches. They can be excited and received by the angular method by the same transducers of variable angle (Chapter 4.2.1). The most useful application spheres of those waves can be evaluated by the comparative methods. The useful comparative characteristics are:

• phase velocity; • attenuation; • form of pulse signal; • spectra of pulse signal.

The following technique used for LSAW or TSAW phase velocity measurements is described below. The particular body K of calibrated thickness d is set-in between the SAW impulse generating emitter E and receiver R (Fig. 4.2.1) and time interval between analyzer’s sweep starting pulse and received LSAW pulse is measured.

Fig. 4.28. SAW velocity measurement schematic

ϑϑ

d

PULSEGENERATOR

SIGNALANALYZER

PCS64i

Emitter Receiver

Solid bodySAW

Calibre

DELAYSCHEME

96

.d

tcPAB∆

=

4 LSAW RESEARCH METHODS After that, the calibre is taken away and the emitter is compacted with receiver; so SAW path between the emitter and receiver is shortened by the dimension d and the deflection of SAW signal in time scale ∆ t is measured and the velocity is calculated according

(4.67)

SAW propagating in solid bodies attenuate because of different reasons, such as energy dissipation, scattering surface roughness, transducers’ acoustic field diffraction; LSAW damps additionally because of transformation to the side BTW. Attenuation is expressed by logarithmic attenuation coefficient

,ln 0d

AAdSAW =α (4.7)

where A0 is the amplitude of a signal when the distance between the angular transducers d = 0; Ad is the signal amplitude when d > 0. The form of impulse signal is indicated in the screen of digital analyzer and register in PC memory. The analyzing informative signal must be emitted while analyzing LSAW or TSAW spectra of impulse signals from total signal that has not only necessary informative signal but also lateral signals (inner reflections in prism, in exploratory object, signals of electric interference) (Fig. 4.8). Exploratory signal is distinguished, i.e. time selection is provided by electronic key (Chapter 4.2.1). But because of “window” time selection component with the period depending on “window” duration and equal to ∆ f = l/τi can occur as lateral phenomenon in signal spectrum. This lateral component can be filtered programmable using e.g. digital finite pulse responce filters (FPRF) [51, 103]. They are steady because pulse characteristic of FPRF is of finite length. Their phase frequency characteristics can be linear and Fast Fourier Transformation (FFT) is used for their realization and it is applied to calculate exactly the succession of finite length.

97

( )

<−<−≤≤

=.1,0when,0

10when,1nNn

Nnnw

4.3 Experimental SAW research Amplitude-frequency characteristic of FPRF:

ψπ

Θωωπ

πω deWeHeH jj

ij )( )(

21)( )( −

−∫= [108]; (4.8)

where W(ejω) is FFT of “window” function w(n); n is the number of n-th element of numerical sequence. “Window” function:

(4.9) Standard Bartlett, Hamming, Kaizer “windows” with the functions shown in Table 4.1 [108] were used while experimental influence of time “windows” to the spectrum of filtered pulse signal.

Table 4.1. “Windows” and their functions w(n)

Window

Function w(n)

Bartlett Kaizer Hamming

−≤≤−

−−

−≤≤

−= Nn N

Nn

NnN

n

nw1

21 ,

122

,2

10 ,1

2

)( (4.10)

10 ,

21

21

21

)(

0

22

0

−≤≤

−

<

−

−−

−

= NnNI

NnNI

nw

a

a

ω

ω(4.11)

10 ,

12cos46.054.0)( −≤≤−

−= NnN

nnw π (4.12)

98

4 LSAW RESEARCH METHODS Pulse signal and its spectra processed by different FPRF are shown in Fig. 4.29.

a)

b) c)

d) e)

Fig. 4.29. Digital signal (a), its spectrum (b) and spectra of this signal obtained by Bartlett (c), Kaizer (d), and Hamming (e) filters

99

4.3 Experimental SAW research The best of used filters in this case is Kaizer’s filter that almost eliminates periodical disturbances of signal spectrum induced by time “window”. Signal spectral analysis can be very informative and useful to the research of ultrasonic surface waves interaction with coarse surface. Resonance scattering is obtained during such interaction with the efficiency depending on the average surface roughness ratio with the SAW length. 4.3.1.1 LSAW and TSAW propagation on the rough surface The propagating not on the surface of solid body but in the deeper layer is important and exceptional LSAW propagation feature. It is evident that for this reason LSAW interaction with the surface must be different than TSAW. The character of this interaction is set the best while measuring the attenuation of the appropriate SAW and it is evaluated by the ratio of amplitude decline to the unit of length. Analysis was accomplished by digital SAW defectoscope. Its structural scheme is shown in Fig. 4.30.

Fig. 4.30. Schematic of defectoscope for the SAW pulse signals

PULSEGENERATOR

τi

ELECTRONICKEY

SPECTRUMANALYZER

PCS64i

ϑEmitter

Sample SAW

PC

ϑReceiver

Surface structure

ULTRASONICDEFECTO-

SCOPEAMPLIFIER

DELAYCIRCUIT

Ti

100

4 LSAW RESEARCH METHODS The relief profiles of known depth h of triangular and rectangular were made on the surface of duralumin sample for the quantitative research of the surface roughness and the SAW interaction (Fig. 4.31 a, b) [109, 110]. Rectangular electric pulse of τi duration (time “window”) exciting with the regard to electric pulse delayed by time Ti was made by pulse generator on purpose to avoid multifold ultrasound reflections from the edge of the sample and exciting pulse lateral induction influence to the spectrum of signal. Electronic key becomes conductive only to the time interval when exploratory SAW signal passes through it. This is achieved by the exact regulation of the pulse duration τi and delay time Ti. This signal comes into the digital oscilloscope.

Fig. 4.31. Rough surfaces of rectangular (a) and triangular (b) profiles

Fig. 4.32. Duralumin sample with a structure of rectangular profile

SAW

SAW

a)

b)l2=25 mm

h2=1.2 mm

l1=30 mm

h1=1.0 mm

101

4.3 Experimental SAW research The measurement methodic of SAW signal attenuation on the surface structure is described below. SAW signal amplitude Ani is calculated and then the sensors in the same position are transferred on the smooth surface and the signal amplitude A0i is calculated having estimated the distance between the angular transducers equal to the length l of the surface structure. Then the transducers are anticipated (l = 0), their amplitude A0 is measured and SAW attenuation coefficient on the smooth surface is calculated according to formulae

( )

lAA l 00

0/ln

PAB−=α ; (4.13)

on the surface structure calculated by

( )

lAAnl

n0/ln

PAB −=α . (4.14)

Measuring in the rectangular profile structure is n = 1, and in triangular profile structure is n = 2. From the formulae could be seen that SAW signal having propagated the distance l on the surface weakens by

l

l

PABeAA 00 α= (4.15)

times, therefore, according formulae (4.13) and (4.14) calculated logarithmic attenuation coefficient αSAW shows that waves damps e times propagating the distance equal to l/αSAW. SAW pulse and their spectrum were registered researching the influence of duralumin sample surface unevenness to SAW characteristics. The attenuation of two types of surface waves (LSAW and TSAW) was measured by three pairs of angular transducers with different frequencies (1.8 MHz; 2.5 MHz, and 4.0 MHz). Typical TSAW pulses propagated through the sample surface with the

102

4 LSAW RESEARCH METHODS rectangular profile (Fig. 4.31 a) structure are shown in Fig. 4.33. It must be mentioned that quicker LSAW pulse propagating in the velocity cLSAW >cTSAW occurred against TSAW pulse. This shows that during TSAW interaction with the surface structure, a part of its energy transformed into propagating more quickly LSAW.

Fig. 4.33. Regarding TSAW interaction with the surface structure the occurred LSAW pulse is received earlier than having “created” it TSAW signal

The results of TSAW and LSAW velocities and attenuation measurements in duralumin samples obtained by the converters of 1.8 MHz and 4.0 MHz are given in Table 4.1 and Table 4.2. Relational measurement errors originated from time interval measurement of 0.03 µs discretion and signal amplitude measurements of 10 mV discretion are shown in the tables. It can be seen from Table 4.1 and Table 4.2 that because of LSAW natural attenuation in smooth free surface α0LSAW >> α0TSAW . While because surface structure more damps TSAW than LSAW by measuring with 4.0 MHz transducers αnTSAW > αnLSAW. So, the surface roughness interacts more with TSAW than LSAW. This can be explained by LSAW wave feature to propagate not on the very surface but a bit deeper. This LSAW feature can be especially useful for NDT of the corroded, coarse, or threaded surfaces.

103

4.3 Experimental SAW research

Table 4.1. Measured TSAW velocity and attenuation coefficient values in duralumin

f = 1.8 MHz f = 4.0 MHz

Surface structure

cTSAW, m/s

αTSAW, 1/m

cTSAW, m/s

αTSAW, 1/m

Smooth surface 2880±10 1.9±0.6 2854±6 2.9±0.6

Rectangular profile structure 2790±10 27.0±6.0 2820±10 71±3.0

Triangular profile structure 2970±7 134±2.0 2858±6 135±2.0

Table 4.2. Measured LSAW velocity and attenuation coefficient values in duralumin

f = 1.8 MHz f = 4.0 MHz

Surface structure

cLSAW, m/s

αLSAW, 1/m

cLSAW, m/s

αLSAW, 1/m

Smooth surface 6840±36 19±2 6800±35 32±2

Rectangular profile structure 6350±50 21±2 6350±50 37±2

Triangular profile structure 6760±35 65±5 6730±35 126±2

104

4 LSAW RESEARCH METHODS TSAW damps because of big scattering of those waves on the coarse surface interacting with the surface roughness (Fig. 4.34). Scattering of TSAW is extremely intensive because of maximal TSAW energy concentration on the very surface (Chapter 2.1, Table 2.1).

Fig. 4.34. Illustration of TSAW scattering on the rough solid

body surface As it is seen from given TSAW signal characteristics (Fig. 4.35 a, b) (pulse form and its spectrum), not only the signal amplitude, but also its form changes. LSAW almost does “not react” also to the other surface state changes, such as the change of liquid layer thickness because of weak interaction with solid body surface. But TSAW pulse signal amplitude greatly depends on liquid layer thickness (Fig. 4.36).

Surface

TSAWDiffusive energy

105

4.3 Experimental SAW research

a)

b)

Fig. 4.35. 1.8 MHz TSAW pulse signal and its spectrum propagating on: a) smooth aluminium surface (δ << λ); b) transversal

rectangular profile surface structure (h3 = 1,0 mm)

106

4 LSAW RESEARCH METHODS

Fig. 4.36. Normalized amplitude experimental dependence on liquid layer relational thickness of 1,8 MHz TSAW signal in aluminium: 1 is the smooth surface; 2 is transversal rectangular profile surface structure (h3 = 1,0 mm)

It must be noted that the influence of liquid thin layer to TSAW attenuation is interferential. 4.3.1.2 SAW interaction with the corner The interaction of surface waves with the corner of rectangular form sample has the great influence to the NDT practice. The scheme shown in Fig. 4.37 is used for the research of this interaction [105]. SAW excited there by the angular transducer (emitter) is received by the other angular transducer (receiver). Measurements by two transducers allow to avoid generator’s electric induction exciting in the signal circuit and research the waves that have propagated a small distance; also to avoid the influence of multiple reflections when the samples are small. Modified scheme where one angular transducer excites and receives ultrasound pulses were used for the research of SAW reflection from the exterior corner. It must be noted that research schematic can be

107

4.3 Experimental SAW research re-co-ordinated so that one type of surface waves are excited (TSAW, by the angle ϑTSAW = II

crϑ ) and received SAW signals of other type (LSAW, by the angle ϑLSAW = I

crϑ ). Two transducers arranged one after the second so that the further transducer excites LSAW and the nearer receives TSAW in the research of LSAW transformation to TSAW reflecting from the angle.

Fig. 4.37. Research schematic of surface wave interaction with the corner: l1, l2 are the distances between the front edge of

transducers and the sample corner B But the inverse scheme where the further from the angular transducer excites TSAW and the nearer receives LSAW for the exact research does not fit because LSAW receiver mechanically damps TSAW propagating under it.

Sample

LSAW

Icrϑ

β

l2

l1

DELAYSCHEME

ELECTRONICKEY

SIGNALANALYZER

PCS64i

Emitter

BPC

Icrϑ Receiver

PULSEGENERATOR

AMPLIFIER

SYNCHRO −NIZING

GENERATOR

108

4 LSAW RESEARCH METHODS The sample of special form of 55 mm thickness and 65 × 75 mm of duralumin size was researched for the determination of SAW reflection (conversion) dependence from the corner.

Fig. 4.38. Duralumin sample with different β angles

The bigger duralumin sample of 300 × 740 × 20 mm was used for the research of LSAW because cLSAW > cTSAW. TSAW signals of 1.8 MHz reflected from β = 85° (the first pulse) and β = 95° (the second pulse) angles are shown in Fig. 4.39.

Fig. 4.39. TSAW pulses reflected from the sample corner with

different angles The normalized amplitude measurement results of SAW signals are given in Table 4.2 and Table 4.3.

100°

80°

95°

85°

109

4.3 Experimental SAW research

Table 4.2. Normalized amplitudes of LSAW signals reflected from the corner and crossed it

Angle β°

85

90

95

(Upl/Upl max )refl

1.00

0.34

0.18

(Upl/Upl max )cr

0.74

0.83

1.00

Table 4.3. Normalized amplitudes of TSAW signals reflected from the corner and crossed it

Angle β°

80

85

90

95

100

(Ups/Ups max)refl

0.53

0.76

0.84

0.93

1.00

(Ups/Ups max)cr

1.00

0.94

0.88

0.78

0.65

As it is seen from Table 4.2 and Table 4.3 the corner with right angle has a big influence to the reflection and crossing of LSAW and TSAW and those waves differently (contrarily) reflect and crosses interacting with the corner. It must be noted that calculation of reflection and crossing ratios according to those results would be incorrect as a part of the energy because of interaction with corner becomes the surface wave of the other type; so without the ratios of reflection and crossing the transformation ratio must be calculated also. LSAW better reflect from the corner with more acute angle because the energy of LSAW concentrated on the layer of two wave length thickness under the surface is reflected according to the law of geometric acoustics. While because of TSAW with the energy maximum on the surface interaction with the corner, the edge line B is excited. The excited line B radiates waves of both types in both perpendicular surfaces.

110

4 LSAW RESEARCH METHODS So, surface waves of one type (TSAW) because of the interaction with the corner transforms into surface waves of the other type (LSAW). Exciting and receiving transducers are matched in different angles (for the first and the second critical angles) during the research of SAW wave transformation into the SAW of the other type. For this case the obtained SAW signals are shown in Fig. 4.40.

Fig. 4.40 Signals received by TSAW transducer over the corner with

angle of 90° and excited before the corner by LSAW transducer. f = 1.8 MHz; l1 = l2 = 40 mm (Fig. 4.34)

There the first pulse is the direct LSAW signal received by TSAW transducer because of piezo-crystal diffraction and matched for the second critical angle. Delayed pulse is LSAW signal transformed into TSAW pulse because of interaction with the corner. Normal component becomes tangential and tangential becomes normal because TSAW normal vibration component is bigger than tangential after vibrating the edge B in the perpendicular surface (to the direction of z axis) (Fig. 4.41). So TSAW transforms into LSAW propagating on the other surface making angle β. It is obvious that TSAW transforms into LSAW more effectively because LSAW propagates in a deeper layer and excites edge B weakly.

111

4.3 Experimental SAW research

Fig. 4.41. TSAW and LSAW motion trajectories of surface particles: ξn, ξ0 are normal and tangential oscillation component amplitudes

The researched surface wave transformational mechanism allows stating that LSAW can be excited transforming TSAW because of the interaction with corner. In materials with big Poisson’s ratio (µ > 0.4) this LSAW excitation method may be more effective than excitation with angular transducer. 4.3.2 Research of SAW propagation on the cylindrical surface 4.3.2.1 SAW propagation on the convex surface It is theoretically shown [111] that TSAW propagating on the homogeneous free curved (cylindrical) surface of isotropic solid body becomes disperse waves. Scalar and vectorial potentials ϕ and ψ in the system of cylindrical co-ordinates r, Θ, z (Fig. 4.42) are described in wave equations

(4.16)

Transformation on

90oangle corner

ξτ

ξn ξn

ξτ

LSAWTSAW

=+∂

∂+

∂∂

∂∂

=+∂

∂+

∂∂

∂∂

.011

011

22

2

2

22

2

2

ψθψψ

ϕθϕϕ

T

L

krr

rrr

krr

rrr

112

4 LSAW RESEARCH METHODS

Fig. 4.42. Co-ordinate system of cylindrical body Shift components Ur, UΘ and tensions Trr, Tθ r are described by formulae [111]:

(4.17)

(4.18)

(4.19)

(4.20)

r

θ

R

Cylindrical body

z

,1θψϕ∂∂

+∂∂

=rr

Ur

,1rr

U∂∂

−∂∂

=ψ

θϕ

θ

( ) +

∂∂∂

+∂∂

−∂

∂+=

θψ

θψϕλ

rrrrGTrr

2

22

2' 112

,11112

2

2

2

2'

∂∂

+∂∂

+∂∂

∂−

∂

∂+

θψϕ

θψ

θϕλ

rrrrrr

,121222

2

2

2

∂∂

+∂∂

−∂

∂+

∂∂∂

=rrrrrrr

GT rψ

θϕψ

θϕ

θ

113

4.3 Experimental SAW research where λ’ is Leme constant and G is shear module in equations (4.20) and (4.21). The solution of equation system (4.17) to the cylindrical body in the most common case is similar to [111] the described:

where A = const, B = const; Jp(kLr) and Jp(kTr) are the Bessel’s functions of p range, p = kpR = 2πR/λp is the angle number of waves, R is the cylinder radius, λp is surface wavelength on the surface of cylinder. It must be noted that the range of Bessel’s function in this case may be whatever, not only the whole number. The equation system (4.21) has many solutions; two of them match two types of different SAW: LSAW (λp = λLSAW) and TSAW (λp = λTSAW). Strictly estimating, LSAW and TSAW propagating on the free surface of the cylindrical surface are different than LSAW and TSAW. LSAW and TSAW are only limitary cases of appropriate cylindrical SAW, when R → ∝. So the parameters of SAW propagating on cylindrical surface will be marked with the superscript index C. Besides, the number of cylindrical LSAW and phase velocity are complex and this means that the loss of acoustic energy occurs because of BTW eradiation. The SAW propagation characteristics on the cylindrical surface are: phase velocities c-c

LSAW and ccTSAW (wave length λc

LSAW and λcTSAW),

attenuation coefficients αcLSAW and αc

TSAW, oscillation amplitudes to the direction r and Θ (ξc

rLSAW, ξcΘ LSAW and ξc

rTSAW, ξcΘ TSAW) also are the

functions of angular wave number p = kpR and ratio R/λ. This shows that cylindrical surface waves are dispersal, so their phase velocities are:

(4.21)( )[ ] ( )

( )[ ] ( )

=

=

−

−

;

,

rkJeB

rkJeA

Tptpi

Lptpi

ωθ

ωθ

ψ

ϕ

114

,LSAWLSAWcLSAW cc δ−=

;TSAWTSAWcTSAW cc δ−=

,cLSAW

cLSAWc

LSAWcLSAW

cgrLSAW d

cdccλ

λ−=

4 LSAW RESEARCH METHODS

,constck

cLSAW

cLSAW ≠=

ω (4.22)

constck

cTSAW

cTSAW ≠=

ω (4.23)

where δLSAW and δTSAW are appropriate LSAW and TSAW phase velocity corrections depending on Poisson’s ratio µ and curvature radius R of cylinder material. The pulse signal propagation velocity of disperse acoustic waves are more exactly outlined by the group numbers

The experimental research was made with the glass cylindrical samples PI-120, PI-100, PI-80 (cL = 5795 ± 5 m/s) and with the special samples from 6063-T6 mark of duralumin (µ = 0.345; cL = 6370 ±5 m/s) was measured (Fig. 4.43). Measured SAW velocity values are given in Table 4.4 and Table 4.5.

(4.24)

(4.25)

(4.26)

(4.27) .cTSAW

cTSAWc

TSAWcTSAW

cgrTSAW

ddc

ccλ

λ−=

,

115

4.3 Experimental SAW research

a) b)

Fig. 4.43. Glass (a) and duralumin (b) cylindrical samples for the SAW research

Table 4.5. SAW velocities, calculated in the glass cylindrical samples (Fig. 4.43 a)

R, mm

R/λLSAW

c cLSAW, m/s

R/λTSAW

c cTSAW, m/s

40 50 60 ∞

27.6 34.5 41.4 ∞

9670 8380 7980 6290

48.7 60.9 73.0 ∞

3830 3330 3280 3160

Table 4.5. SAW velocities, calculated in the duralumin cylindrical sample (Fig. 4.43 b)

R, mm

R/λLSAW

c cLSAW,

m/s

R/λTSAW

c cTSAW,

m/s

15 25 30 ∞

10.4 17.3 20.7 ∞

7650 6920 6740 6160

19.4 32.3 38.7 ∞

3470 3350 3130 3105

LSAW signals of 3.0 MHz frequency, registered in the duralumin sample are shown in the Fig. 4.44.

116

4 LSAW RESEARCH METHODS

a)

b)

c)

Fig. 4.44. LSAW pulses, when: (a) angular transducers are compacted; (b) crossed the cylindrical surface; (c) propagated the same distance by the smooth surface

117

4.3 Experimental SAW research cLSAW measurement method is the following. At first the signal propagation in cylindrical surface is measured (Fig. 4.44 b). Then, the path distance in cylindrical and smooth surfaces is measured. Having measured cLSAW on the smooth surface of the sample (Fig. 4.44 c), the velocity cLSAW

c can be calculated. Specific LSAW characteristics can explain LSAW phase velocity changes depending on the curvature of cylindrical surface (Table 4.4 and Table 4.5). According to theoretical calculations [111], SAW propagating on the curved convex surface penetrates less comparing with the smooth surface; it sorts out to the surface. So, phase velocity grows when the curvature radius is reduced. Besides, the less influence to the LSAW propagation on cylindrical surface has the BLW diffraction of angular transducer (Fig. 4.45).

Fig. 4.45. LSAW propagation on the cylindrical surface

Comparing LSAW and TSAW velocities measured changing the curvature radius R the similarity (phase velocity of two waves quickly grows while the curvature radius R is reducing) is seen.

ϑ

R

BLW

1

2

3O

BTW

118

4 LSAW RESEARCH METHODS 4.3.2.2 SAW propagation on the concave surface It is obvious from the theory that TSAW propagating on the conclave cylindrical surface obtains LSAW characteristics to loose acoustic energy radiating side bulk waves. So, the extra wave attenuation proportional to the ratio R/λ-c

TSAW occurs (superscript index −C will mark the conclave cylindrical surface). The angle wave number of such wave is complex

where p1TSAW and p2TSAW are the real and imaginary components of angle wave number. In this case phase velocity is

So, wave velocity in concave cylindrical surface is less than in smooth free surface. Velocity change δ is of the same size as in the convex surface (with the opposite sign) and also depends on ratio R/λc

p. An LSAW specific with the concave cylindrical surface is such that its longitudinal composite propagating receive from the concave surface. Therefore the acoustic energetic losses grow and LSAW attenuates more. It is obvious that this phenomenon could be seen better when the ratio R/λc

LSAW is less. Because of this effect during experimental measurement of waves propagating in the concave cylindrical duralumin sample of 3.0 MHz LSAW inclination for 90° with the curvature radius R = 20 mm was not registered. The conclusion that LSAW, propagating in concave cylindrical and even more in spherical surfaces, in practice has no important meaning because easily can become BLW.

(4.29)

(4.30)

( ) ,1 21 TSAWTSAWc

TSAW ippp ++=− δ

( ).1 δ−=−TSAW

cTSAW cc

119

4.3 Experimental SAW research

4.3.3 Investigations of LSAW excitation by piezoelectric grating SAW are usually excited in isotropic solids using angular transducers, when the incident angle of BLW is equal to the first critical angle. The critical angle depends on a sound velocity both in the prism and in the solid. That is the reason why the prism angle transducer with constant incidence angle can not be universal, and it can be used to excite LSAW only in solids, where sound velocities are known and matches to the sound velocity in a prism. In order to make LSAW angular transducers more universal, angular transducers with a variable angle are used. Incidence angle of longitudinal waves in the mentioned transducers can be selected from the interval (0°-90°) to obtain the maximum angle of LSAW excitation, i. e. the first critical angle in a solid. The mentioned drawbacks of angular transducers must be solved in the other way. Using NDT efficiency of LSAW excitation becomes very important. LSAW are weaker in comparison to the TSAW. The attention on theoretically described process of excitation of TSAW was paid using periodical vibratory linear structure. Estimating similarity of LSAW and TSAW propagation features it could be expected to use piezoelectric gratings for LSAW excitation. This conclusion comes from the latest experiments, when LSAW are excited thermo-acoustically, using pulse laser to create mechanical strains on the solid surface. Experimental results show that LSAW and TSAW are excited at the same time efficiently. Strip-shaped piezo-crystal (Fig.4.46) with l >> h, l >> d is mechanically attached to the solid surface.

Metallization

dl

hP

Fig. 4.46. Elementary strip-shaped piezo-crystal

120

4 LSAW RESEARCH METHODS The piezo-crystal excited by a thickness mode of oscillation emits semispherical BLW a(r, t) (Fig. 4.47), described by equation

( )

−=

Lcrt

TAtra π2sin, , (4.31)

where A is the wave amplitude, T is the period; t is the time; r is the radius; cL is the velocity of BLW.

x

Qx0

Fig. 4.47. Spot source of acoustic waves on the surface of isotropic solid plane

If there are m spot sources on the surface (piezoelectric grating, which consisting of m elementary strip-shaped piezo-crystals, arranged at distance ∆ x), and these spot sources are excited in-phase (Fig. 4.48), then the wave generated at the surface spot Q, is given by

( ) ( )∑=

∆−+−=

m

n Lcxnx

tT

Atxa1

00

12sin, π , (4.32)

where x0 is the distance between the last piezo-crystal and the surface spot Q. The piezo-crystals (Fig. 4.48) are excited in-phase, when ∆x = cLSAW /ω = λLSAW, where ω is the angular frequency, cLSAW ≈ cL and λLSAW ≈ λL are the phase velocity and the length of LSAW; cL and λL are the phase velocity and the length of BLW.

121

4.3 Experimental SAW research

x0

1 2 m

∆ x

Q a(x,t)

GENERATOR

Fig. 4.48. In-phase excited grating consisting of m piezo-crystals The length of grating can be reduced and quantity of piezo-crystals is the same when LSAW transducers are operating in a low frequency. Then piezo-crystals must be arranged at the distance λLSAW/2 between them and excited in phase opposition, or excited in phase, but polarization direction is changed contrarily. The shape of oscillations, generated by piezoelectric grating, was mathematical simulated. There are m = 4 piezo-crystals in the grating. It is assumed that piezo-crystals are made of piezoceramics CTS-19, h = 0.5 mm, l = 15 mm >> h. The thickness resonant frequency f0 = 3.3 MHz, because the velocity of BLW in the piezoceramics CTS-19 is cL=3300 m/s. The LSAW are excited in duralumin, where cL=6320 m/s and λL ≈ λLSAW = 1.92 mm. Each piezo-crystal is excited using burst with the duration of 10T, where T is the period of an excitation voltage. The normalized amplitude of the pulse is 1 (Fig. 4.49 a). The acoustic wave, generated at the surface spot Q (Fig. 4.49 b) was calculated accepting that damping of wave is deniably small. The distance m between the spot Q and the piezo-crystal is x0 = 5λLSAW.

122

4 LSAW RESEARCH METHODS

a) 0 1 2 3 4 5 6

1

0

1

t, mkst, µsa(

x 0,t)

b) 0 1 2 3 4 5 6

5

0

5

t, mkst, µs

a(x 0

,t)

Fig. 4.49. Finite duration excitation pulse (a) and acoustic wave on surface spot Q (b)

If can be seen that the acoustic wave is amplified, delayed and has ramp-up and ramp-down fronts. The shape of acoustic wave may be restored (Fig. 4.50 b) if the shift circuits (Fig. 4.50 a) with a delay equal to the period T = 0.33 µs are used.

a) x

Q∆T∆T ∆TGENERATOR

b)

0 1 2 3 4 5 65

0

5

t, mkst, µs

a(x 0

,t)

Fig. 4.50. Excitation of piezoelectric grating using shifted elements (a) and the waveform (b)

123

4.3 Experimental SAW research The acoustic wave fronts are sharp. The fronts of the excited signal are nearly linear (Fig 4.51 b), when exciting pulses are not delayed and the piezoelectric grating is excited using the pulse with the exponent ramp-up and ramp-down fronts (Fig 4.51 a). The excited signal has almost the same waveform, when the exciting pulses are delayed (Fig 4.51 c) using the shift circuit (Fig. 4.50 a).

a)

0 1 2 3 4 5 61

0

1

t, mkst, µs

a(x

0,t)

b)

0 1 2 3 4 5 65

0

5

t, mkst, µs

a(x 0

,t)

c)

0 1 2 3 4 5 65

0

5

t, mkst, µs

a(x0

,t)

Fig 4.51. Finite duration excitation pulse (a) and the waveforms of signal at the surface spot Q, when the exciting signals are not delayed (b) and are delayed (c)

124

4 LSAW RESEARCH METHODS Comparing Fig. 4.51 b and Fig 4.51 c, we see that the waveform and amplitude are similar, but the delay time differs notably. Piezoelectric gratings (m = 1, 2, 3, 4) were made in order to perform the research. Strip-shaped piezo-crystals (made of the piezoceramics CTS-19, l = 15 mm, h = 1.0 mm, d = 1.5 mm) were glued to the duralumin sample using an epoxy resin. The piezo-crystals were excited at the resonant frequency of the thickness mode. The emitted LSAW pulse signal was received using the angular transducer with a variable angle, when the angle matched the maximal received signal amplitude (the first critical angle). The piezo-crystal, used in the angular transducer, was made of the piezoceramics CTS-19 (l = 11 mm, h = 1,0 mm, d = 8 mm), the prism – of Plexiglas. Signals were registered using the digital signal analyzer. Experimental set-up is shown in Fig. 4.52 a.

Piezoelectricgrating

ϑ

PULSEGENERATOR

SIGNALANALYZER

PCS64i

Angular transducer

Sample

LSAW

DELAYCIRCUIT

a)

b)

Fig. 4.52. Piezoelectric grating investigation schemating (a) and photograph of piezoelectric grating together with the

angular transducer (b)

125

4.3 Experimental SAW research The piezoelectric grating consisting of four piezo-crystals (m = 4) was excited using a shock voltage. Acoustic signal was received at the distance x0 = 20 mm. The received pulse signal and its spectrum are shown in Fig. 4.53.

The acoustic signal generated by the piezoelectric grating (Fig. 4.53 a) consists of LSAW corresponding to the thickness mode of vibration (1). There are two different frequency pulses of TSAW that match thickness (2) and transverse modes of vibration (3).

a) b)

Fig. 4.53. Typical acoustic signal (m=4) (a) and its spectrum (b)

The thickness mode resonant frequency in the signal spectrum is 2.05 MHz and the transverse mode resonant frequency is 1.24 MHz. Other generated LSAW signals are shown in Fig. 4.54. The LSAW, generated by an elementary piezo-crystal (m = 1) is shown in Fig. 4.54 a (x0 =20 mm). The LSAW, generated by the piezoelectric grating of four elements (m = 4), is shown in Fig 4.54 b (x0 = 20 mm). The obtained results can be compared with the generated signal using the angular transducer (Fig. 4.54 c). The signal amplitude dependence upon quantity of piezo-crystals is shown in Fig. 4.55. The dependence shows that sensitivity of the angular transducer is less than sensitivity of the two piezo-crystals (m = 2) grating.

126

4 LSAW RESEARCH METHODS

a)

b)

c)

Fig. 4.54. LSAW signals, generated using one piezo-crystal (a), grating when m=4 (b), and the angular transducer (c)

127

4.3 Experimental SAW research

050

100

150

200

250

0 1 2 3 4m

,A, m

V

Fig. 4.55. Dependence of signal amplitude on quantity of piezo-crystals in the grating. Dotted line shows the pulse amplitude, generated using the angular transducer

Experimental investigations show that a piezoelectric grating is more sensitive than the angular transducer, when grating consists of m ≥ 2 piezo-crystals. Piezoelectric gratings generate the LSAW together with the TSAW or the TSAW. That does not interfere to carry out measurements and NDT using the LSAW, because the velocity of the LSAW is the fastest.

4.3.4 Investigations of LSAW and TSAW excitation by

pulse laser LSAW excitation by pulse laser can be useful for the practical

purposes especially for measurements, because short ultrasonic pulses can be excited in this way and the SAW exciting point on the surface is fixed precisely.

LSAW excitation possibilities were researched by the

experimental equipment; its schematic is shown in Fig. 4.56 [112, 113].

Pulse ruby laser generating light pulse (Λ = 0.694 µm) was used for exciting SAW on solid surface (Fig 4.56). The run of equipment is synchronized by light pulse (Fig. 4.57 a) registered by photodiode.

128

4 LSAW RESEARCH METHODS

Fig. 4.56. Experimental schematig for the measurements of SAW excited by pulse laser

The pulse duration τi ≈ 3.44 µs and front length τf ≈ 0.5 µs are enlarged because of narrow band width of photosensor sensitivity frequency characteristics and are observed in oscillogram at the level of −6 dB. According to technical certificate the ruby laser generated pulse duration τi ≈ 1 µs. LSAW and TSAW are excited on the solid surface because of thermo-acoustic effect and are received by the 1.8 MHz angular transducer of variable angle when the angle I

crϑ < ϑ < IIcrϑ .

So, at the same time both types of SAW can be registered on the screen of spectrum analyzer (Fig. 4.57 b). LSAW pulse propagating in maximal speed is the first and then goes TSAW pulse and reverberation signals in prism of the angular transducer. For the increase of signal exciting sensitivity, laser beam was focused on the sample surface to the line segment by cylindrical lens and gap diaphragm (Fig. 4.58). The width of focused beam is d ≈ 0.2 mm, and the line segment length is ≈ 15 mm.

TSAW

Photosensorϑ

PULSELASER

DELAYBLOCK

SIGNALANALYZER

PCS64i

LSAW

SAW receiver

Solid body

SYNCHRONIZER

129

4.3 Experimental SAW research

a) b)

Fig. 4.57 Form of laser pulse received by photosensor (a) and SAW pulses excited in duralumin sample (b)

a)

b)

Fig. 4.58. Laser beam cylindrical focusing (a) and the fragment of investigation device (b)

z

Cilindrical lens Gap diaphragm Sample

Laser beam

Collimator

d

130

4 LSAW RESEARCH METHODS Pyroceram sample CO-115M of 120 × 60 × 30 mm was used for measurements where cL = 6508 m/s, cLSAW = 7030 m/s; 1.8 MHz, LSAW length λLSAW = 3.9 mm, I

crϑ = 23°. Surface of the sample lightened by laser beam was blackened for the larger laser beam energy absorption and LSAW exciting efficiency also.

Fig. 4.59. Schematic for measurement LSAW penetration depth For the research of LSAW penetration depth the distance h was changed by a step ∆ h = 1 mm (Fig. 59) and LSAW signal amplitude was registered. The measured dependence is shown in Fig. 4.60. It can be seen that maximal amplitude signal is obtained when h ≈ 5 mm = 1.28λLSAW, differently as in the case of TSAW when maximal amplitude signal is obtained when h = 0.

Fig. 4.60. Dependence of LSAW signal ratio amplitude on the distance h. Pyroceram CO-115M, f = 1.8 MHz

h

LSAW receiver Icrϑ

Solid body

LSAWLaser beam

131

4.3 Experimental SAW research It is also seen that signal amplitude change has the oscillation character. It corresponds the theoretical conclusions obtained in work [35] where measured LSAW penetration depth is between λLSAW and 2λLSAW. 4.3.5 Lamb waves exciting by LSAW and TSAW

transducers LW are SAW in thin plates. The plate has two surfaces, so their vibrations because of a small thickness interact resonantly and LW are disperse. Besides, many different modes can be excited and also several types of LW (Table 1.1) and their phase velocity is not equal to the group velocity of energy transfer. LW can be also excited and received by angular transducer, as it is shown in Fig. 4.61.

Fig. 4.61. LW exciting on the solid body plate. Full lines show BLW

and dot lines show BTW So, LW is the result of BLW and BTW interaction with plate surface; its mode, phase and group velocities depend on slice thickness d, velocities cL and cT in the material of the surface and frequency ω. As it is seen from Fig. 4.61, LW structure receding from exciting source in the most general case are obtained as the combination of different origin of acoustic pulses becomes more complicated (Fig. 4.62 a). This reflects in its spectrum (Fig. 4.62 b), so it is relevant to determine the regularities and conditions when LW propagate as the resonant process of maximal amplitude.

d

ϑ

BTW

BLW LW

Angular transducer Plate

132

4 LSAW RESEARCH METHODS

a) b)

Fig. 4.62. LW excited by the angular transducer in the duralumin plate of 3 mm thickness (a) and its spectrum (b)

For practical purposes it is very important to know the exciting sensitivity, how it depends on angular transducers of exciting angle, to investigate LSAW and TSAW transducer characteristics by exciting LW in plates. Experimentally analyzing LW in special samples made of 6063-T6 duralumin alloy (Fig. 4.63) it was determined that LSAW and TSAW transducers established LW pulse signals and their spectra are different even exciting ultrasonic pulses of the same form and duration (Fig. 4.64, Fig. 4.65). This obvious result is commented by different LSAW and TSAW interaction with the slice surface and different structure of transducers acoustic field. TSAW transducer (ϑ = II

crϑ ) excites in the plate creeping on the surface transversal wave causing harmonic vibrations and LSAW transducer (ϑ = I

crϑ ) creates on the plate not only the wave component but also side BTW and because of it multiple reflection from the surface, BLW occur also (Fig. 4.64). So, pulse signal form of LW excited by LSAW transducer is more complicated (pulse is of interferential character, longer).

133

4.3 Experimental SAW research

a)

b)

c) Fig. 4.63 LW pulses and their spectra excited by 3.0 MHz LSAW transducer in duralumin plates. Thickness of the plate:

a) 20 mm; b) 2 mm; c) 1 mm

134

4 LSAW RESEARCH METHODS

a)

b)

c)

Fig. 4.64. LW pulses and their spectra excited by 3.0 MHz TSAW transducer in duralumin plates. Thickness of the plate: a) 20 mm; b) 2 mm; c) 1 mm

135

4.3 Experimental SAW research The attention to the different signal velocities (time delay, having spread the equal distance between radiation and receiving transducers equal to 75 mm) must be pointed out. TSAW does not interact with the other sample surface when sample thickness d ratio with the wavelength is d/λTSAW > 1 (Fig. 4.64 a) and such a wave can not be called LW yet. It must be mentioned also that LW excited by TSAW signals are of bigger amplitude than excited by LSAW.

LW are broadly applied to the NDT of shells (plates, pipes, thin wall profiles), constructing transducer of echolocation systems operating in acoustically soft environment (air). LW attenuate considerably less and their vibration amplitudes are much bigger than TSAW or LSAW. They are easily excited and propagate not only in plates, but in the shells also.

It should be noticed that LW and acoustic resonance systems oscillating in those waves are broadly applied in sound frequency band. Namely LW propagating in sounding board of stringed instruments (guitar, grand piano) provide pleasant specific sound and allows to increase the sound power. 4.3.6 Investigation of mechanical tension in sheet products by symmetrical Lamb waves LSAW excited on the surface of isotropic solid surfaces by the first critical angle are characterized by the bigger longitudinal component of surface material point of vibrant amplitude than transversal component. This determines their property to propagate in phase velocity close to the BLW phase velocity depending also on the Poisson’s ratio of the solid. The prediction that LSAW phase velocity must depend on solid surface layer mechanical state can be made. It was theoretically proved that in sheet products with the thickness of h << λLW (λLW is the length of the LW) the dispersal symmetric (s0) and antisymmetrical (a0) LW waves of zero order can be excited. Experimentally it was set that in sheet products by the angle transducer matched for the first critical angle, the excited wave on the sheet is symmetric LW of a zero mode.

136

( )( ),

22sh

ch2

2sh

ch 2/22

πωξ −−

⋅+

−= txki

S

S

SsLW

SS

S

SsLWSSx

sLWehs

zs

sk

sqhq

zqkA

4 LSAW RESEARCH METHODS The purpose of this work was to investigate experimentally the properties and the dependence on the mechanical stress of the sheet of symmetric s0 LW excited by LSAW transducer. The material point moves in the trajectory of the ellipse with the longitudinal component ξ x > ξ z (where ξz is normale component; λL is BLW length) in the BLW excited by the I

crϑ . Tangential ξ x and normal ξ z vibration components in symmetric wave are described by the equation [73]:

where: AS = const; ( ) ;222LLWS kkq −= ( ) 22

TsLWS kks −= ;

sLW

sLW chk 2/ω= is the number of symmetric LW, kL and kT are the

numbers of BLW and BTW; h is the thickness of the plate; ω =2πf, f is the frequency; s

LWc is the phase velocity of symmetric LW. Symmetric LW are dispersal and cLWs depends not only on the thickness of the sheet h, but also on the sound velocity in sheet material and

changes from the meaning ( )21/ µρ −E to the cTSAW (Fig. 4.65); where E is Young module; ρ is the density; µ is Poisson’s ratio; cTSAW is the phase velocity of TSAW [73].

(4.33)

(4.34)

( )( )

( ),2

sh

sh2

2sh

sh22

2txki

S

S

SsLW

sLW

S

SSSSz

sLWehs

zs

sk

khq

zqqA ωξ −

⋅+

−−=

137

4.3 Experimental SAW research

Fig. 4.65. Theoretical dependence of symmetrical LW (s0) phase velocity on TSAW velocity [73] It excites symmetric LW s0, with dominating longitudinal component in acoustically thin sheets (h << λL) because of LSAW interaction with both free sheet surfaces. Physical origin of such wave determines that the features of s0 wave more depend not on the transversal but on longitudinal component propagation determining factors. One of such factors is the mechanical tension of the material changing the material density and Poisson’s ratio µ. Special form strip-shaped samples with the broadened ends for better fixing in stretch mechanism (Fig 4.66) were made from bronze sheet for the research of excited LSAW s0 mode symmetric LW. The thickness of the sheet was h = 0.09 mm.

Fig. 4.66. Form of the sample The sample is fixed in the stretch mechanism and the signal of symmetric LW is excited in its narrowed part by LSAW angle transmitter received by the analogues LSAW receiver situated in the distance l0 from the transmitter.

l

dd0

2.0

1.5

1.00 1.0 2.0 3.0

/cTsLWc

ωh/cT

138

4 LSAW RESEARCH METHODS

Fig. 4.67. Research schematic The received s0 mode LW ultrasound signal is indicated by digital signal analyzer and synchronized by the delayed pulses of electric pulse generator (Fig. 4.67). Its amplitude and the position in time axis are measured at the same time. As it is seen from the theoretical disperse dependence (Fig. 4.65), phase velocity of symmetric s0 mode LW quickly changes in the limits cTSAW < s

LWc < 2cTSAW, when ωh/2cT changes from 2.5 to 1. Strip-shaped sample is in the range of strong symmetric LW dispersion, when the ultrasound signal frequency f = 2 MHz, bronze sheet thickness h = 0.09 mm, and parameter ωh/2cT ≈ 1.88 (cT ≈ 3000 m/s). s0 mode dispersal LW phase velocity is calculated having changed the distance between transducer by the dimension ∆ l0 = 32 mm and having measured the shift of the received signal in time axis ∆τ = 7.69 µs, when mechanical tension W = 0 ( s

LWc = ∆l0/∆τ = 4160 m/s). The dependencies ∆AS(W) and ∆τ(W) were measured during the research changing the mechanical tension W = F/dh (in our case F is the sample dragging power in the direction x (Fig. 4.66) and recording the change of received ultrasound amplitude ∆AS and time shift ∆τs. Ultrasound signals, spread by the bronze strip-shaped sample, registered in the screen of spectrum analyzer PCS64i discreetly changing mechanical tension W, are shown in Fig. 4.68 [115].

DELAYBLOCK

T∆

PULSEGENERATOR

SIGNALANALYZER

Emitter Receiver

LWTENSION

MEASURER

139

4.3 Experimental SAW research

a)

b)

Fig. 4.68. Ultrasound pulse s0 mode LW signals excited and received by the angular LSAW transducer, when a ) W = 0;

b) W = 92.6 N/mm2

It was noticed that when the mechanical tension increases, s0 mode LW signal amplitude AS and phase propagation velocity s

LWc decrease. LW attenuation calculated according measurement results dependencies AS/(AS)max(W) and s

LWc (W) of s0 mode are shown in Fig. 4.69 and Fig. 4.70.

140

4 LSAW RESEARCH METHODS Stretching strip-shaped sample changes as the amplitude of the signal (attenuation) as the phase velocity, but the dependence s

LWc is comparatively weak, so it is recommended to control mechanical tension and the state of strip-shaped construction measuring s0 mode LW attenuation.

-14

-12

-10

-8

-6

-4

-2

00 10 20 30 40 50 60 70 80 90 100

W ,N/mm2

Fig. 4.69. s0 mode LW signal amplitude dependence on

mechanical tension

05101520253035404550

0 10 20 30 40 50 60 70 80 90 100

W, N/mm2

Fig. 4.70. s0 mode LW phase velocity dependence on mechanical tension

A S /(

A S) m

ax ,

dB

cs LW, m

/s

4.3 Experimental SAW research The angle transducers in this case do not fit the best because the measurements of signal amplitude (attenuation) are sensitive to the stability of transducer acoustic contact. Strip-shaped piezo-crystals or their gratings would be more promising for the exciting and receiving s0 mode LW [114]. It was theoretically and experimentally shown than symmetric LW can be excited effectively in acoustically thin sheet by the angular ultrasound angle matched for the first critical angle. The attenuation of those waves strongly depends on the mechanical stress of the sheet and the measurements of the attenuation of symmetric waves can be effectively used for the mechanical state research of sheet materials by NDT method.

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Pulse Signal // Scientific Materials of the International Conference „Elektronics-2000“. Kaunas: Technology (2000): p.74-76 (In Lithuanian).

104. Sajauskas S., Sajauskas N. Experimental Research of Surface Waves Angular Exciting Method // Materials of the International Conference „Electronics'98“. Kaunas: Technology (1998): p. 112-114 (In Lithuanian).

105. Sajauskas S., Minialga V. Experimental Investigation of Interaction of Longitudinal Surface Acoustic Waves or Transversal Surface Waves and External Corner // Ultrasound. N. 1(42) (2002): p. 42-45 (In Lithuanian). 106. Sajauskas S. The Problem of Excitation of Longitudinal-surface acoustic waves // Ultrasound. N. 2(43)(2002): p. 17-20 (In Lithuanian). 107. Möhler P., Röhrlich H. Rechnergesteuerte Ultraschall-Prüftechnik zur automatischen Untersuchung von Kernreaktor-Komponenten im Rahmen der Fertigungsprüfung // Materialprüfung. B. 25. Nr. 3. (1983): S. 66-69. 108. Krivickas R. Digital Signal Processing. Vilnius: Mokslas, (1984): 126 p. (In Lithuanian). 109. Sajauskas S., Minialga V., Sajauskas N. Comparative Investigation of Rough Surfaces by Transversal Surface Waves and Longitudinal Surface Waves // Ultrasound. N. 3(36) (2000): p. 33-35 (In Lithuanian). 110. Minialga V., Sajauskas S., Sajauskas N. Influence of Liquid on the Propagation of Ultrasonic SAW on the Rough Surface // The e–Journal of Non-Destructive Testing. Proceedings of the 15th World Conference on Non-Destructve Testing (WCNDT). 15-21 October 2000 in Rome (Italy). Materials and Instrumentation. – *http:www.ndt.net*, idn.727. 6 p. 111. Viktorov I. A. Sound Surface Waves in Solid Surface. Moscow: Science (1981): 287 p. (In Russian). 112. Minialga V., Sajauskas S. Generation of Longitudinal Surface Acoustic Waves by Laser Pulse // Proceedings of the 5th International Conference on Vibration und Measurements by Laser Technique. Advance and Applications. Ancona, Italy. (18-21 June 2002): p. 219-223. 113. Sajauskas S., Minialga V. Investigation of Generation of Surface Acoustic Waves by Pulsed Laser // Ultrasound. N. 4(45). (2002): p. 18-21 (In Lithuanian).

REFERENCES 114. Sajauskas S., Vilpišauskas A. Investigation of Excitation of Longitudinal Surface Acoustic Waves by Piezoelectric Grating // Ultrasound. N. 2(51) (2004): p. 13-16. 115.Sajauskas S., Valinevičius A., Klimavičius D. Investigation of Mechanical Tension in Sheet Products by Symmetrical Lamb Waves // Ultrasound. N. 3(52) (2004): p. 18-20. 115. Diedrich R. Nondestructive Testing Encyclopedia, UT Formulae, NDT net.

APPENDIXES

153

Appendix 1

Technical data of digital signal analyzer PCS64i General • Two separate channels • Input impedance: 1 MOhm/30 pF • Input bandwidth: 13 MHz • Maximum input voltage: 100V • Maximum readout error: 2.5 % • Vertical resolution: 8 bit • Real time sampling frequency: 32 MHz (max) • Oversampling: 64 MHz Minimum system requirements • IBM compatible PC • Windows 98 • 480 Kb free conventional memory • Arithmetic coprocessor needed for RMS readout and spectrum analyzer Oscilloscope • Timebase: 100 ns to 100 ms per division • Trigger source: CH1, CH2 or free run • Trigger edge: rising or falling • Trigger level: adjustable in steps of ½ division • Step interpolation linear or smoothed • Markers for voltage and frequency • Input sensitivity: 10 mV to 5 V/division • True RMS readout Spectrum analyzer • Frequency range: 0 - 800 Hz to 16 MHz • Linear or logarithmic timescale • Operating principle: FFT (fast Fourier Transform) • FFT resolution: 2048 lines • FFT input channel: CH1 or CH2 • Zoom function • Markers for amplitude and frequency

154

Appendix 2

a)

b)

Signal form (a) and its spectrum (b) in the screen of digital analyzer PCS64i

155

Appendix 3

Physical and electrical constants of materials The tables of main parameters, illustrating the properties of some usually in ultrasound technique used materials (isotropic solid bodies, monocrystals, liquids, and plastic) are given in this appendix. The exceptional attention is given to piezoelectric materials (Table 1) whereof the ultrasound converters for the exciting of SAW are produced. The data in literature [4, 27, 65, 105] and also A. Selfridge, R. and G. Diedrich data published in Internet [71, 116] are used for the formation of the tables. The author has measured a part of TSAW and LSAW velocity values. The attention that the values of different alloys, glasses, polymeric compounds or piezoceramic acoustic parameters in literature varies and can differ by types or names in different countries must be taken into account. It is noticed that the values of piezoceramic (CTS) parameters made in Russia in handbooks are shown with the dispersion of ±10%.

156

APPENDIXES

Table 1. Physical ratio of piezoelectrics

Piezoelectric cL (cT), m/s

Density ρ, g/cm3

Dielectric Permitti-

vity ε

Ratio of Electrome-

chanical Coupling, kT

Barium Titanate, BaTiO3

Zinc Oxide, ZnO

Quartz, X-cut

Lithium Iodide, LiJ

Lithium Niobate, LiNbO3:

Z-cut

Y-cut

Lithium Sulphate, Li2SO4

Y-cut

Lithium Tantalate, LiTaO3

Seignette Salt, KNaC4H4O6

Lead Zirconate Titanate:

PZT-2

PZT-4

PZT-5A

PZT-5H

PZT-8

CTS-19

CTS-21

CTS-22

CTS-23

CTS-24

5640

6100

5750

4100

7730

(3800)

5460

7300

3080

4410

4600

4350

4560

3400

3300*

3650*

3800*

3200*

3200*

5.55

5.64

2.65

4.54

4.64

4.64

2.06

6.16

1.77

7.6

7.5

7.75

7.5

7.6

7.45

7.0

7.0

7.4

7.4

1200

11,0

4.5

8.2

-

-

10.3

45-63

70

450

1300

1700

3400

1000

1880*

625*

900*

1075*

1075

0.46

0.41

0.095

0.5-0.6

0.49

0.55

0.38

0.31

0.56

0.38

0.51

0.45

0.39

0,29

0.4

0.2

0.2

0.43

0.45

* Parameter mean value.

157

APPENDIXES Table 1. (continued) Physical ratio of piezoelectrics

Piezoelectric cL (cT), m/s

Density ρ, g/cm3

Dielectric Permitti-

vity ε

Ratio of Electrome-

chanical Coupling, kT

K180

K270

K350

K500

K550

Lead Metaniobate, PbNb2O6:

K-81

K-83

K-85

Lead Titanate, PbTiO3:

KNTA

KN3B

Tellurium, Te:

X-cut

Y-cut

Tourmaline, Z-cut

PVDF

4000

4060

3960

3960

4080

3050

5480

3350

4170

4270

2410

(1470)

7150

2200

7.7

7.5

7.7

7.6

7.8

6.2

4.5

5.7

7.5

7.65

6.24

6.24

3.1

1.78

425

1300

1700

2700

3000

300

175

80

170

215

346

53

7.5

12

-

-

-

-

-

0.30

-

-

-

0.51

-

-

-

0.098

0.2-0.3

158

APPENDIXES

Table 2. Acoustic parameters of metals and alloys

Metals and Alloys cL, m/s cT, m/s cTSAW, m/s

cLSAW, m/s

Density ρ, g/cm3

Poisson’s Ratio µ

Aluminum, Al

Tin, Sn

Gold, Au

Beryllium, Be

Bismuth, Bi

Brass

Bronze (phosph.)

Chromium, Cr

Zinc, Zn

Zirconium, Zr

Duralumin

Gallium, Ga

Iron, Fe

Germanium, Ge

Inconel

Cadmium, Cd

Constantan

Manganese, Mn

Cupronickel

Molybdenum, Mo

Monel

Nickel, Ni

Platinum, Pt

6320

3320

3240

12900

2180

4280

3530

6650

4170

4650

6400

2740

5900

5410

5820

2780

5240

4660

4760

6250

5400

5630

3960

3130

1670

1200

8880

1100

2300

2230

4030

2410

2250

3120

-

3230

-

3020

1500

1040

2350

2160

3350

2700

2960

1670

2900

1560

1120

7870

1030

2200

2010

-

2220

2660

3100

-

2790

-

-

1400

-

-

-

3110

1960

2640

1570

6020

3250

2140

-

2100

4170

-

-

-

-

6160

-

6160

-

-

2870

-

-

-

-

-

5720

3350

2.70

7.29

19.32

1.82

9.80

8.56

8.86

7.0

7.1

6.47

2.8

5.95

7.69

5.47

8.28

8.64

8.88

7.39

8.4

10.2

8.82

8.88

21.4

0.345

0.31

0.44

0.046

0.33

0.378

0.38

0.21

0.25

0.35

0.335

-

0.29

0.31

0,31

0.30

0.327

-

0.37

0.29

0.33

0.30

0.377

159

APPENDIXES

Table 2 (continued). Acoustic parameters of metals and alloys

Metals and Alloys cL, m/s cT, m/s cTSAW, m/s

cLSAW, m/s

Density ρ, g/cm3

Poisson’s Ratio. σ

Steel

Steel (austenit.)

Radium, Ra

Silver, Ag

Lead, Pb

Tantalum, Ta

Titanium, Ti

Uranium, U

Vanadium V

Copper, Cu

Tungsten, W

5900

5660

8220

3600

2160

4100

6070

3370

6000

4660

5180

3200

3120

4110

1590

700

1140

3310

1980

2780

2260

2870

-

-

4030

1480

630

-

3200

-

-

1930

2650

-

-

-

3170

1440

-

-

-

-

4430

-

7.9

8.03

5.0

10.3

11.4

16.6

4.50

18.7

6.03

8.93

19.25

0.298

-

-

0.367

0.44

-

0.32

0.24

0.36

0.34

0.27

160

APPENDIXES

Table 3. Acoustic parameters of solids

Solid cL, m/s

cT, m/s

Density ρ, g/cm3

Poisson’s Ratio µ

Boric Carbide, B6C

Diamond

Faience (pottery)

Granite

Silica (fused), SiO2

Corundum, SiC

Ice, H2O

Marble

Porcelain

Sapphire, Al2O3

Glass:

- flint

- crown (reg.)

- crown (heaviest)

- quartz

- window

- Pyrex

Titanium Carbide, TiC

11000

17500

5600

6500

5960

13060

3990

6150

5900

11100

4260

5660

5260

5700

6790

5640

8270

-

-

3600

2700

3760

7270

1980

3810

-

6040

2690

3520

3260

3520

3400

3280

5160

2.40

3.52

2.4

4.1

2.20

3.22

0.92

2,7

2.3

3.99

3.60

2.60

-

2.60

2.6

2.24

5.15

-

-

0.23

-

0.17

-

0.34

-

-

-

-

0.24*

0.28

-

-

-

0.24

-

161

APPENDIXES

Table 3 (continued). Acoustic parameters of solids

Plastics, rubbers cL, m/s

cT, m/s

Density ρ, g/cm3

Poisson’s Ratio µ

Cellulose Acetate,

HO⋅C6H7O(CH3⋅COO)2

Epoxy resin

Resin

Acrylic

Silicone

Rubber

Kapron

Nylon 6,6

Plexiglas

Polyamide

Polyethylene (low density)

Polyethylene (high density)

Polyisobutylene

Polymethylacrylate

Polypropylene, Profax

Polystyrene

Polyvinyl Butyrall

Polyvinylchloryde, PVC

Teflon

2450

2650*

2730

1027

1600

2640

2600

2730

2400*

1950

2430

1490

1260

2740

2340

2350

2395

1350

-

1100

1430

-

-

-

1100

1430

1150*

540

-

-

-

1050

1150

-

1060

550

1.30

1.17*

1.18

1.05

-

-

1.12

1.18

1.1-1.2

0.92

0.96

-

-

0.88

1.06

1.11

1.34

2.2

-

0.37

-

-

-

2.9

0.39

0.40

-

0.46

-

-

-

-

0.35

-

-

-

162

APPENDIXES

Table 4. Acoustic parameters of liquids

Liquid cL, m/s Density ρ,

g/cm3

Acoustic

Impedance Z0, g/cm2⋅s

Acetone, (CH3)2CO

Oil:

Olive

Fluorosilicone

Motor

Paraffin

Castor, C11H10O10

Silicone

Linseed

Transformer

Carbon Tetrachloride, CCl4

Benzol, C6H6

Gasoline

Diesel Oil

Ethylene Glycol, CH2OH⋅CH2OH

Mercury, Hg

Glycerine, CH2OH⋅CHOH⋅CH2OH

Honey

Petroleum

Alcohol:

Butyl, C4H9 OH

Ethyl, C2H5 OH

Methyl, CH3 OH

Prophyl (i), C3H7 OH

1170

1430

760

1740

1420

1480

1350

1770

1390

930

1330

1250

1250

1660

1450

1920

2030

1290

1240

1180

1120

1170

0.790

0.948

-

0.870

0.835

0.969

1.11

0.992

0.92

1.595

0.878

0.803

0.8

1.11

13.53

1.26

1.42

0.825

0.810

0.789

0.792

0.786

0.924

1.36

-

1.51

1.19

1.43

1.50

1.76

1.28

1.48

1.17

1.00

1.00

1.84

19.6

2.42

2.88

1.06

1.00

0.93

0.887

0.920

163

APPENDIXES

Table 4 (continued). Acoustic parameters of liquids

Liquid cL, m/s Density ρ, g/cm3

Acoustic

Impedance Z0, g/cm2⋅s

Turpentine

Water:

H2O (20° C)

D2O

Sea

Kerosene

1280

1480

1400

1530

1320

0.893

1.00

1.104

1.025

0.81

1.14

1.48

1.55

1.57

1.07

164

Appendix 4

Angle beam probes of Panametrics Company (USA)

Table 1

Probe

Prism

Diameter of Piezo-crystal,

mm

Frequency, MHz

A539S-SM, V539-SM AS40S-SM, V540-SM A545S-SM, V545-SM A541S-SM, V541-SM A547S-SM, V547-SM A548S-SM A549S-SM, V549-SM A550S-SM, V550-SM A551S-SM, V551-SM A552S-SM, V552-SM A542S-SM, V542-SM A546S-SM, V546-SM A543S-SM, V543-SM A544S-SM, V544-SM A534S-RM, V534-RM A536S-RM, V536-RM A538S-RM, V538-RM A533S-RM, V533-RM A535S-RM, V535-RM A537S-RM, V537-RM

ABWML-5T *

− − −

ABWM-5ST *

ABWM-7T * −

− −

ABWM-7ST *

ABWM-4T * −

− ABWM-4ST *

ABWML-5 * − ABWML-5S *

ABWML-4 *

− ABWM-4S *

13 − − − −

10 − − − −

6 − − −

13 − −

6 − −

1.0 2.25 3.5 5.0 10.0 1.5 2.25 3.5 5.0 10.0 2.25 3.5 5.0 10.0 2.25 5.0 10.0 2.25 5.0 10.0

* Prisms are produced of 30°, 35°, 45°, 60° and 70°

165

APPENDIXES

Table 2

Probe

Prism

Diameter of piezo-

crystal, mm

Frequency, MHz

A420S-SB A421S-SB A422S-SB

ABWS-6 *

− −

15×15

15×18,5 18×18,5

2.25 − −

* Prisms are produced of 45°, 60° and 70°

Table 3

Probe

Prism

Diameter of piezo-

crystal, mm

Frequency, MHz

A414S-SB, V414R-SB A407S-SB, V407R-SB A408S-SB, V408R-SB A411S-SB A409S-SB, V409R-SB A402S-SB, V402-SB A404S-SB, V404-SB A415S-SB A406S-SB. V406-SB A413S-SB, V413-SB A401S-SB, V401-SB A403S-SB, V403-SB A412S-SB A405S-SB, V405-SB

ABWSL-3 * − − − − ABWSL-1*

ABWSL-2 * −

25 − − − −

13

− − −

13×25

− − −

0.5 1.0 2.25 3.5 5.0 1.0 2.25 3,5 5.0 0.5 1.0 2.25 3.5 5.0

* Prisms are produced of 30°, 35°, 45°, 60°, and 70°

166

APPENDIXES

Table 4

Probe

Prism

Diameter of piezo-

crystal, mm Frequency,

MHz A5033 A5037 A5038

OP-4 * − −

6

− −

2.25 3.5 5.0

* Prisms are produced of 45°, 60°, and 70°

Table 5

Probe

Prism

Diameter of piezo-

crystal, mm

Frequency, MHz

A430S-SB A431S-SB A432S-SB

ABWS-8 * − −

15×15

15×18,5 18×18,5

2.25

− −

* Prisms are produced of 45°, 60° and 70°

167

Appendix 5

Angle beam probe of Krautkramer-NDT Company

(Germany)

Table 1

Probe Diameter of

Piezo-crystal, mm

Frequency, MHz

Radiation Angle

K0,5S+KSY45S K1S+KSY45 K1SM+KSMY45 K1SC+KSMY45 K2SC+KSMY45 WRY45 WRY60 WRY70 WSY45-2 WSY60-2 WSY70-2 WSY45-4 WSY60-4 WSY70-4

34 34 28

24 24

24 24 24

10 10 10 10 10 10

0.5 1.0 1.0

1.0 2.0

1.5 1.5 1.5

2.0 2.0 2.0 4.0 4.0 4.0

45°

45° 45°

45°

45°

45°

60°

70°

45°

60°

70°

45°

60°

70°

Table 2

Probe Dimensions of Piezo-crystal,

mm

Frequency, MHz Radiation Angle

SMWK45-5 SMWKB60-5 SMWK70-5

3×4 3×4 3×4

5.0 5.0 5.0

45°

60°

70°

168

APPENDIXES

Table 3

Probe Dimensions of Piezo-crystal,

mm

Frequency, MHz Radiation angle

SWB45-2 SWB60-2 SWB70-2 SWB45-5 SWB60-5 SWB70-5 WK45-1 WK60-1 WK70-1 WK45-1 WK60-1 WK70-1 SWK45-2 SWK60-2 SWK70-2 MWB35-2 MWB45-2 MWB60-2 MWB70-2 MWB80-2 MWB35-4 MWB45-4 MWB60-4 MWB70-4 MWB80-4 MWK45-2 MWK60-2 MWK70-2 MWK45-4 MWK60-4 MWK70-4

14×14 14×14 14×14 14×14 14×14 14×14

20×22 20×22 20×22 20×22 20×22 20×22

14×14 14×14 14×14

8×9 8×9 8×9 8×9 8×9

8×9 8×9 8×9 8×9 8×9

8×9 8×9 8×9 8×9 8×9 8×9

2.0 2.0 2,0 5.0 5.0 5.0

1.0 1.0 1.0 2,0 2.0 2.0

2.0 2.0 2.0

2.0 2.0 2.0 2.0 2.0

4.0 4.0 4.0 4.0 4.0

2.0 2.0 2.0 4.0 4.0 4.0

45°

60°

70°

45°

60°

70°

45°

60°

70° 45° 60°

70°

45° 60°

70°

35°

45°

60°

70°

80°

35°

45°

60°

70°

80°

45°

60°

70°

45°

60°

700

169

APPENDIXES

Table 4

Probe Dimensions of Piezo-crystal,

mm

Frequency, MHz Radiation Angle

WB45-1 WB60-1 WB70-1 WB35-2 WB60-2 WB70-2 WB80-2 WB45-2 WB35-4 WB45-4 WB60-4 WB70-4

20×22 20×22 20×22

20×22 20×22 20×22 20×22 20×22

20×22 20×22 20×22 20×22

1.0 1.0 1.0

2.0 2.0 2.0 2.0 2.0

4.0 4.0 4.0 4.0

45°

60°

70°

35°

60°

70°

80°

45°

35°

45°

60°

70°

Table 5

Probe Dimensions of Piezo-crystal,

mm

Frequency, MHz Radiation Angle

MUWB 2N MUWB 4N

8×9 8×9

2.0 4.0

0…90°

0…90°

170

Appendix 6

Angle beam probe of company “Volna” (Moldova)

Probe Frequency, MHz

The Width of the Frequency

Band, MHz

Radiation Angle

П121-1,25-300-002 П121-1,25-400-002 П121-1,25-500-002 П121-1,25-700-002 П121-1,8-300-002 П121-1,8-400-002 П121-1,8-500-002 П121-1,8-700-002 П121-2,5-300-002 П121-2,5-400-002 П121-2,5-500-002 П121-2,5-700-002 П121-4,0-300-002 П121-4,0-400-002 П121-4,0-500-002 П121-4,0-700-002

1.25 1.25 1.25 1.25 1.8 1.8 1.8 1.8 2.5 2.5 2.5 2.5 5.0 5.0 5.0 5.0

0.25 0.25 0.25 0.25 0.35 0.36 0.36 0.36 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0

30°±2 40°±2 50°±2 70°±2

30°±2 40°±2 50°±2 70°±3

30°±2 40°±2 50°±2 70°±3

30°±2 40°±2 50°±2 70°±3

171

LONGITUDINAL SURFACE ACOUSTICAL WAVES (CREEPING WAVES)

By Prof. Habil. Dr. Stanislovas SAJAUSKAS

S U M M A R Y This book is intended to contribute to ongoing work on Longitudinal Surface Acoustic Waves (LSAW) in isotropic solids. Discovered in 1972 by L. Sereikaite-Juozonienė at the Kaunas University of Technology (Lithuania), they are the antipodes of Rayleigh waves. The author recapitulates the discovery, provides a literature survey, and notes the ensuing problem with the acceptance of the discovery by the scientific community. A synopsis of research results obtained in Lithuania, Germany, Russia, and the USA as well as potential applications are included. The author performed some of the reported research himself. LSAW are analyzed by comparing them to Rayleigh waves. Considering the physical nature of Rayleigh waves the author calls them the Transversal Surface Acoustic Waves (TSAW). The comparison disclosed the differences between and identified the similarities of LSAW and TSAW, thus articulating their unique characteristics. It was shown theoretically and substantiated experimentally that LSAW differ from TSAW in a number of features. The phase velocity of LSAW is approximately two times higher than that of TSAW. LSAW attenuation is more pronounced, being conditioned by emissions of sidelong bulk acoustic waves. Also, LSAW are manifested by deeper penetration into solids. Finally, different excitation environments for the two types of waves are evident. It was demonstrated that LSAW can be excited using the angular method by directing bulk longitudinal waves to the surface at the first critical angle while TSAW are typically excited at the second

SUMMARY (In English) critical angle. Also, previously reported statements about the non-existence of LSAW were shown experimentally to be incorrect; previous claim that the path of LSAW does not exceed more that one wavelength, and that they can only be excited in solids with Poisson’s ratio of µ < 0.26, proved to be in error. Numerous experiments with duralumin (µ = 0.345) aliquots were conducted by the author. Various possibilities exist for use of LSAW in non-destructive testing of rough, mechanically unfinished surfaces while searching for inner surface defects of boilers or nuclear reactors. A design of computerized digital spectrometer, enabling one to study LSAW and TSAW effects is described. They include reflection and transformation of waves emanating across cylindrical surfaces in ultrasonic 1.8–4.0 MHz range. Concluding observations include the efficiency of the angular excitation in ultrasonic non-destructive testing and the availability of the laser excitation for studies in precision. The monograph extends current research work in acoustics. Suggestions for NDT, measurement of physical parameters of solids, and modeling of seismic phenomenon appear to offer interesting possibilities here.

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PAVIRŠINĖS IŠILGINĖS AKUSTINĖS BANGOS (ŠLIAUŽIANČIOSIOS BANGOS)

Prof., Habil. Dr. Stanislovas SAJAUSKAS

S A N T R U M P A

Knyga skirta naujo tipo paviršinių akustinių bangų, sklindančių izotropiniuose kietuosiuose kūnuose, teoriniams ir eksperimentiniams tyrimams. L. Sereikaitės-Juozonienės 1972 m. Kauno technologijos universitete atrastos bangos, pavadintos paviršinėmis išilginėmis kustinėmis bangomis (PIAB), yra Reilėjaus bangų antipodas. Neardančiųjų bandymų srityje šios bangos neretai vadinamos ir šliaužiančiomis bangomis (angl., creeping waves). Knygoje aprašyta šių bangų atradimo istorija ir pasaulinio pripažinimo sunkumai, atlikta literatūrinė analizė, pateikti jų tyrimų Lietuvoje, Rusijoje, Vokietijoje ir JAV rezultatai, atskleistos jų panaudojimo sritys ir galimybes. Tiriant paviršines išilgines akustines bangas jos sugretintos su Reilėjaus bangomis. Panaudojus lyginamąjį metodą ir atsižvelgus į Reilėjaus bangų fizikinę prigimtį autorius jas įvardijo paviršinėmis skersinėmis akustinėmis bangomis (PSAB). Tai įgalino įtikinamai atskleisti šių dviejų tipų paviršinių bangų – PIAB ir PSAB – panašumus ir skirtingumus, lemiančius jų panaudojimo galimybes. Teoriškai ir eksperimentiškai parodyta, kad PIAB esminiai skiriasi nuo PSAB daugeliu savybių: apie dukart didesniu faziniu sklidimo greičiu, didesniu slopimu, sąlygojamu šoninių tūrinių skersinių bangų išspinduliavimu, gilesniu įsiskverbimu į kietojo kūno paviršių, skirtingomis sužadinimo sąlygomis. Teoriškai ir eksperimentiškai parodyta, kad PIAB gali būti sužadinamos kampiniu metodu, tūrines išilgines bangas nukreipiant į kietojo kūno paviršių pirmuoju kritiniu kampu. Tuo tarpu PSAB efektingai sužadinamos antruoju kritiniu kampu. Išskirtine PIAB savybe yra galimybė tūrinėmis skersinėmis

SUMMARY (In Lithuanian) bangomis sužadinti antrines PIAB neprieinamame, pavyzdžiui, vidiniame kevalo (rezervuaro sienelės) paviršiuje. Knygoje pateikta daugelio eksperimentinių tyrimų duraliuminio (µ = 0,345) bandiniuose rezultatai, parodytos galimybės PIAB panaudoti ultragarsiniams neardantiems gaminių bandymams, jų tarpe šiurkštiems, mechaniškai neapdorotiems paviršiams, rezervuarų (garo katilų, branduolinių reaktorių elementų) vidinių paviršių defektams tirti, lakštų mechaniniam įtempiui matuoti. Čia aprašyta sukurtoji tiksli skaitmeninė spektrometrinė aparatūra, leidusi atlikti PIAB ir PSAB sklidimo efektų – atspindžio, transformavimosi į kito tipo paviršines bangas, sklidimo cilindriniais paviršiais − lyginamuosius tyrimus ultragarsiniame 1,8…4,0 MHz dažnių diapazone, pateikti jų rezultatai. Atlikus PIAB sužadinimo metodų analizę, padaryta išvada apie kampinio sužadinimo metodo efektyvumą ultragarsiniams neardantiems bandymams, parodyti sužadinimo pjezoelektrinėmis gardelėmis ir impulsiniu lazeriu naudingumas tiksliems tyrimams. Išsamiu naujo tipo paviršinių akustinių bangų − PIAB − pristatymu monografija praturtina akustikos mokslą, atskleidžia jų praktinio taikymo perspektyvas ultragarsiniams neardantiems bandymams, kietųjų kūnų fizikiniams parametrams matuoti, seisminiams reiškiniams modeliuoti.

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Briefly about the author Stanislovas SAJAUSKAS was born in Marijampolė district (LITHUANIA) on February 25, 1946

Education Marijampolė high school, 1963 Kaunas Polytechnical Institute (KPI),

Electronics Department, 1968

Professional experience Scientific researcher at Kaunas Politechnical Institute

Prof. K.Baršauskas laboratory for ultrasound problems, 1968-1972 PhD studies at KPI, 1972-1975 Doctor of electronics, 1975 Visiting professor at Halė M. Liuther University, Germany, 1979-1980 Associate Professor, 1994 Habilitated Doctor, 1994 General scientific researcher at Kaunas University of Technology, 1995 −

Present Professor at Kaunas University of Technology, Electronics Engineering

Department, 1997 − Present

Scientific Work Professor S. Sajauskas works in ultrasonic measurement, SAW, NDT, acousto-optics and holography. He is the author of 3 monographs, 70 inventions, the manager and leader of 45 scientific research works; he has authored or co-authored over 120 refereed papers and over 55 reports in scientific symposiums and conferences, invited lectures at Halė M. Liuther University in Germany in 1998, Merzeburg higher technical school in Germany in 2000. Awards Graduated high school with a silver medal, 1963 KPI diploma with honour, 1968 Bronze medal in the exhibition of Folk Economy Achievement, Moscow, 1984 The diploma of Lithuanian Scientific Technical Society Presidium, 1986 Award of Kazimieras Baršauskas established by Lithuanian Science

Academy, 1998

Address Varpo g. 10-9, LT-50238, Kaunas, Lithuania e-mail: Stanislovas.Sajauskas@tef.ktu.lt

Leidyklos „Technologija“ knygas galima užsisakyti internetu www.knygininkas.lt

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Stanislovas Sajauskas

LONGITUDINAL SURFACE ACOUSTIC WAVES (CREEPING WAVES)

Monografija

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