The scattering of Rayieigh waves by a two-dimensional groove formed on the surface of an aluminum sample
is investigated experimentally. A complete set of measurements of the scattered-field parameters, including
the elastic characteristics of the scattered longitudinal and shear bulk waves and the reflection and
transmission coefficients of the Rayleigh surface waves, is carried out for a broad range of groove depths

S. Zh. ZharylkaPov (7122965)

Victor V. Krylov (1252356)

English

Loughborough University Institutional Repository

   This item was submitted to Loughborough’s Institutional Repository (https://dspace.lboro.ac.uk/) by the author and is made available under the following Creative Commons Licence conditions.      For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/  scattering of Rayleigh waves by a groove of arbitrary depthS. Zh. ZharylkaPov and V. V. KrylovPhysics Faculty, M. Y. Lomonosou State Uniuersity' Moscow(submitted JanuarY 29, 1981\Akust. Zh. 33. 878-883 {September-Octob€r 1987}The scattering of Rayieigh waves by a two-dimensional groove lormed on the surface of an aluminum sampleisinvestigated.*p".r..truly.Acompletesetofmeasuremeatsofthescattered-fteldparameters'includingthe eiastic characteristics of the scutiered longitudinal and shear bulk waves and the reflection andtransmission coefflcients of the Rayleigh surface waves, is carried out for a broad range of groove depths'The investigation of the specific characteristicsof tn" scaitering"of surface acoustic waves (SAW's);; -;;.fu;" inhoirogeneities in the form of groovesoi cracks is extremeiy important for acoustoelec-ironics and ultrasonic naw detection (see' e'9" the;;;;;;" in Refs. l-5). Scattering,bv shallow;;";;; satisrving the conditions h/ '\ .. 1 and h/a >>i, *n""u h is"thJ groove depth, a ls its width' andi'i. tt" surface wivelength, has been studied intfr"-g"""t".t detail to dat-e' A iarge part of theiii".i"ti""i results has been obtained by various*oA]ii*tio"s of perturbation theory.in this case'r IS"pl;i*."t"f studies of SAW scattering by s.hallow."Jo""" have also been reported for scattering into.:ffi;; *lrr!.i-T's and inio the volume of the medi-11m.8 ,roScattering by flaws with other relations be-tween iire ctraiact,:ristic dimensions has been inves-iinu,"o io a lesser degree' In particular' the case.f'".""t" or slots (a/-r " t) characterized by ra-A.-h/i << t has been analyzed, where the main;;ii; have been obtained by perturbatjon methodst"t"J o" integral reciprocity relations'1r A number;i-tit";li.;" itt trt" fundamental problem of SAW re-ii;ti"; and- transmission at cracks have been ana-i;;;;i;lhe case h/l : 1 as a,r:esult of the solutionn'f-L"tttta""rt integral equationsl2 or by direct nu-;;;;;i-;ft"o,t"J". " surface-wave scattering bvCroo"""'u"a cracks has aiso received scaree atten-iio" "i-tft" experimental levei' only investigations"i'iit" reitection and transmission of Rayleigh wavesat cracks of arbitrary depths have been reportediir"f*-t, 13, and 14), and, to the best of ourt""*1"ag", only onca have the angular characteris-ti;; ;i s--ew scattering into the volume-.of a mediumu"".r-*"t"tred. for * ?""p crack at a fixed value ofitii--=-1i. I (Ref ' 15)- s-ystematic measurements ofSAW scattering ty grooves or cracks of arbitraryA"ptft t """ ev"ideirttly never been performed 'The obiective of the present study is to give -tfte r"s"ft= 6f "*p"rlrn.nts on the characteristics ofRayieigh wave scattering both. into surface wavesand into buik waves at -a vertieai two-dimensionalgtoo,t" over a wide range of values of the param-eter h/1.The experimental arrangement ls shown sche-rnaticallv in Fig. 1. Rayleig6 waves were -generated;;-i;''"";i""""or-"n atiiminirm half-disk of radius1O cm-ana thickness 3 cm by means.of a Plexiglaswedt; (angle-beam transducer), which was bondedto the surface ny an epoxy resin layer' A vertical."uit""ing-g"oorr" *ith-a cbnstant width a = 1 mmand a semicircular bottom was machine-cut into theflat end of the half-disk.The scattered SAW's were received by meansof an identical Plexiglas wedge, which was mounted"itn"" to the right Jr to the left of the groove (de-olnaine on whelher the Rayleigh-wave transmission;;';;fi;"ti"n coefficient was to be measured) ' Lon-git"Ji"Lf-*ode piezoelectric ceramic wafers of diam-Eter 1.5 cm with a resonance frequency of' 2'04 MHz*ere monnted on both wedges' The losses in re-"ip*".f transduction in thii case were r 50 dB 'The scattered bulk-wave field was recorded bymeans of a specially designed transducer ln theiorm of a Plexigias- slab with a rounded base to en-sure reiiable co--ntact with the cylindrical surface ofitt" s.mpte. Piezoelectric ceramic wafers weremounted alternately on the siab by- means of salol';;-; -; io"git"al"ar-mode wafer of diameter 1'5 cm*iitt " *"rorr"u.,"" frequency of 2'04 MHz for the re-""ptlo" of scattered lbngitudinal-waves, and a trans-""-."11."a" wafer of diameter 1' 5 cm and thickness1.0 cm with a resonance frequency of 5 MHz for thereception of scattered shear waves ' As in the caseof the angle-beam transducers, mechanical contactwas estabished between the buik-wave transducer;; 6;;;"faee of the sample through epoxy resin'which ensured the possibility of its free movementaiong the Perimeter'The scattered bulk waves were measured aftertne inpul of rf voltage pulses wifh- a center frequen-"v.f-i.tj+ rvriz atta i duration of 5 ps to the radiat-inq anaie-beam transducer (the shear-wave trans-;;";';;;uJ itt trt" nonresonant reg:ime in this;*i. -Tn. u"gorar scattering functions Ds(0) andOif e I of iongrtudinal and shear bulk waves werer.i"ri*"a for"a fixed g?oove depth h' The measure-re.ri" of D[(s) anO Di(o) were then repeated foralii""""t .tulrr"" of the g?oove depth' which wasFIG. 1. Experinental alrangeo€nt' 1) Alminu[ sarple; 2) ra-diating ilgle-bem (vedge) transducer; 3) receiving angle-bezntransduceri 4) scattered-bulk-vave transducer; 5) video pulsegenerator; 6) modulaied harnonic sigml Senerator; 7) widebandmplifier; 8) oscilloscope; 9) spectnrn atalyzet'Sov.phys.Acoust.33(5),September-october1987 OO38'562X/87/O5O5O9-03$03'40 olgsSAmericanlnstituteoiPhvsics509.o*, ( e)60FIG. z. Angularscatteringpatt.erns of longiLudj,nal (a) andshear(b) bulkwaves forvarious depttrs h of grooves havinga const'ntwidth a =1 m; frequencY 2.04 MHz.deg160t20100804020120/00varied from 0.5 to 4 mm in 0.25 mm steps in the ex-periments. The measurements were repeated severaliimes (the scatter of the expe"imental data was" iOZ) 'for each value of the depth h and the angleof observation 0, and the results were averaged sta-iistically. The radiated SAW amplitude was held con-stant anrit g this process ' The measurement resultsio" it" larg"est muxima of each series of Dt(e) andblf g I ",r"i". are shown in Fig. 2' , The level Dc' =1 coruesponds to "v 63 dB insertion losses in conver-sion of ihe eiectrical input signal into SAWrs and in"catt"rittg and conversion of the scattered iongitudi-nal wave"into an electrical signal, and the level Dt =1 coresponds to analogous t 67 dB losses for thescattered shear waves. The relatively low level ofthe scattered shear-wave signal is attributable tothe nonresonant operation of the given transducer'The field of scattered surface waves (reflectedand transmitted) was measured by a co-nventionaiprocedure (see, e'g., Refs. 2 and 9) for each of theibove-indicated deplhs h' Measurements were alsoperformed for h = 4 mm by an ultrasonic spectro-I""pi" pt""edure.lr The iatter entailed the input ofu "-hotf voltage video pulse to the radiating angl-e-beam transduter with the resulting generation ofSAW's over a wide range of frequencies' The prop-agating SAW was then recorded by the-receiving.igt.-"b"u* transducer, whose electrical output sig-,ruf *a. sent to a spectrum anaiyzer' The fre-q;.""V response of the seattering g"oo-ve in thiscase could be determined by dividing the spectrumoi tn" electrieal signai from the scattered wave bythe signal spectrum coresponding to Rayleigh-wavetransm"isslon from the radiating to the receivingtransducer in the absence of ihe seattering flaw'The duration of the input video pulse waschosen so that the direct (unseattered) signal spec-trum comesponding to the product of the spectrumof the original reciangular video pulse and the trans---:fer functidn of the two transducers would be suf-ficiently smooth over as wide a frequency ?ange aspossible. The optimum duration of the video pulseio. our transducers with resonance frequencies of2.04 MHz was found to be equal to 0.5 irs' Thespectrum of the direct (referenee) signai was locai-ized in the interval 0.4-2-2 MHz.The moduli of the surface-wave reflection coef-ficient R and the transmission coefficient T areplotted as a function of the parameter h/I in Fig'- 3'("rr".t"" 1) accord.ing to resuits obtained by the-rfpulse method. Also shown for comparison sre theialues of R(h/r) and T(h/r) obtained by the ultra-sonic spectroseopic technique for h = 4 mm (curves2). The quantitative discrepancy between thecurves obtained by the two procedures in the givensituation eharacterizes the influence of the finitegroove width (a = 1 mm), which was comparableiitn the Rayleigh wavelength at 2.04 MHz (l =1.4 mm) in the rf pulse measurements. In the spec-troscopic measurements, on the other hand, thegroove wid.th a was commensurate with l only at theipper end of the SAW spectrum and was consider-ably smailer than ,tr at the lowest frequencies of the"p"-"ttrrt. This situation is typieal of SAW seatter-ing by nar?ow siots or cracks, for which measure-rJnts- by both of the indicated procedures giveidenticai dependences on h/). (see, e.g., Refs' 2'13, and 14).We now discuss the resuits.S. K. Zharylkapov and V. V. KrylovIt is evident from5105 l O Sov. Phvs. Acoust. 33{5), September-October 1 987=*&F0.4FIG. 3. Reflection (a) md trilsnission (b) coefficientsfor Rayleigh waves at a groove vs paraneler h/'l ' measuredby: 1) the rf Pulse method at a fr€quency of 2'04 |dlz; 2)by the ultrasonic spectroscopic technique for a groove ofdepthh=4nn.In conclusion we note that the experimental dataottainea-nere snouid be useful not only for direct.,r'".ti"af apDlications, but also to check numericalI;;r*;t";At"iutio"t in the interval h/r : 1' r{ore-il;,'il5y-;;;"y itfot*"uon about sAW scatteringbv a sroove over a wide range of depths and angiesJf ot"'"-""ution and should therefore be of interesti"o* ti," standpoint of the formulation and solutionof-itt""t"" .oota-.".iiering problems in solids'18rR, c. williaoson, "Reflection grating filters''i in: Surfacewave Filters Design, Constnction' md Use' H' f4aLthews (ed')rtJiley, Nes York (1977)' P' 381'2I. A. viktorov, ecoustic- surface waves in Solids [in Russi'm]'Nauka, Moscow (1981)'3c. S. KLno, 'INDI with Raylei'gh and optical waves'rr in: Proc'Int. Sytrp. Rayleiglr t'iave Theory and Application' E' A' Ash andE. G. S. Paige (eds'), Springer-Verlag' Berlin (1985)' p' 300'aYr. v. Golyt"v md V. P' Plesskii, Radiotekh' Elektron' !!'r.55e (1980).sA. D. L.pi., Alqrst. zh. 29' z:Iz (19s3) [Sov' Phys" Acoust' ?9t123 (1983)1.6J. P. Parekh ad H'-s. Tttr, J' APPI' Phys' 48' 994 (L917)'75. v. Bityttov' Akust. zt.' 26t 494 (1980) [sov' Phys' Acoust'?9,272 (1e8o)1.{- nornetLeiv ad J. Souquet, [suface to bulk wave scaEterlngfron grooves,'t in: IEEE 1975 Ultrasonics syap' Proc'' IEEE'Nev York (1975), P. 279'9s. v. Korolev, v. A- Icasilinikov, 4nd v' v' rcylov' Akust' zh-:!, 138 (1985) [Sov. Phys' Acoust' 31' 8L (1985)]'tfa- e"tot, M. De Billy' and G' Quentin' Rev' Phys' ApPl' ?9'369 (1e85).t1r. g. Itto, S. Ayter' ild M' Tan, "Theory of scattering of Ray-leigh waves by surface breaking cracks'r' in: IEEE 1978 Ultra-soni.c= synp. Proc'' IEEI' New York (1978)' p' 384'12Y. c. engel and J. D' Achenbach" J' Acoust' soc' Am' 12' 313( 1e84) -r3lt. Hi.rao ad H. Fukuoka' J' Acoust' soc' An' 7z' 602 (].982)'lav. q. vu and v. K. Ki'nrat "APplication of ultrasonic specLros-copy to scattering of Rayleigh wave j'n a halfspacet" in: Rev'Prog:r. Quantitative Nondestructive Evalution' Pr*' Ninth Am'Rev., San Diego' cA, 1982' vol' 2A' Ne{ York (1983)' p' 539'th- tittnann, L. A. Ahlberg, ajrd A' K' I'b1' lraiterent du sig-nar a, 443 (1985).16e. f. Gautesen, wave Motion gr 27 (1986).r7w- Paiewski and t{. Szalewski, Arch' Acoust' q' 3 (1983)'lfu. A. Buroo, A. A' Goryunov' A' v' saskovetst and T' A'Tlkhonov, Akust. Zh. 32' 433 (1986) [Sov' Phys' Acoust' 3e'273 (re86)l'Translated by J. S. Wood,'.i:.rlr,rl_i!::*.: i::'}-!::,$i,Aiis l,n.ti:iii .')i::,:.,;.Fig. 2a that the angular scattering diagrams forioigitrrairr.t \4/aves varv considerably with the ratio^r rho drnove denth h to the Rayleigh wavelength;: '?h;^t-";";J ii"ld is distributea fairlv uniformlv*ittt-"""p*t to the angte" 0 for small values of h/l'consistent witn previou-s theoreticai,and experiment€l;;;;iG;;;,1' fo; shallow groove.s (h/r.<< 1)' Foris-r-;-varues of h/I (correiponding to I = gl **;e;" the experimenial conditions) ' a ,tendencyf"*."a staUllation of the scattering diagram al]d a"o""""t""tion of the scattered-field energy in the;i;;-"ti"" of angles g t 1350 (in the backscattering;;;;l't" ooser.iea. This fact agrees with the re-."tt" .f existing numerical calculationst6 and ex-rru"im"nt"tt on"the scattering of a Rayleigh wave byil;^;;;of a g0o elastic wedge (quarter-space)'iir" ""?ir"-"a ii"ra exhibits J complex behavior iniir" ittt".tn"diate range of vaiues of h/r; the curvesoi-tttu scattered-wavZ amplitudes vs h'/ '\ tend to"".iii"t" at fixed values of tn" angle I smaller thann, 1100.The angular scattering diagrams for shear*u""" irigl-zb; evolve soriewhal differently withlru"iutio" 5f tn. parameter h/I' They are consistent;ih t# th";;t For "man values of h/ ^ and then be-;;;; ;;;y l;t."g"larlv in the intermediate rang-e (h =0.?5-1.25 mm), "*p.'"it""ing oscillations as a func-;i"".f tti l, ui'fixia values-of the angie 0' Thep"ii"*" tto." or less stabilizes as hi I is increased';;fli ;ifi"rs from the longitud'inal-wave case in that;iie* ;;";t";;;g-maxirrum is iow formed in the vicinitvoi-e-"g0", i]e., in the direction of the normal tothe surface. The aUovtltetttioned concentration ofscattered transverse-*"t" "t"tgy i1 tle vicinity ofitt"-rro**ut has aiso been observea in Ref' 15 fordaW- ""utt"ting by a nar?ow slot of fixed depth(h/,r. = 12.3).The surface-wave reflection (R) and transmis-.ion fij coefficients otialnea by lh: rf puise methodi;;il;'iilFG". 3a and 3b, which are the onlvones that can be "otp"t"a wiin ttre above-discussed;;ik-;;;" scattering diagrams) are- also character-i*J u:r osciuations "as a Tunction of the depth'pa-rameter and'r B'f,e qualitativeiy similar to the analogous;;;;;torl ,r"*to,i slots2' 13''14 (see also curves 2i"-FG. sa .nA aU)--:frre existing quantitative dif-i;.;;?;, as mentioned, is attribut;ble to the influ-";;; ;i'the finite groove width' The,oscillatory -behavior of the ouserved curves in all. the investi-g;il';;";; is-couutiess associated mainly with reso-i-""""-"i nuyt*gfl waves propagating along the sur-face of the groove.5115 I 1 Sov. Phys' Acoust. 33(5), Septemb€r-october 1 987 S. K. ZharylkaPov and V. V. Krylovff;4 I r'::i*i'r' '"jt' - "t*'iiTt;

Scattering of Rayleigh waves by a groove of arbitrary depth

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Scattering of Rayleigh waves by a groove of arbitrary depth

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