ULTRAGARSAS Journal, Ultrasoun Institute, Kaunas, Lituania For all papers of tis publiation lik: www.nt.net/sear/os.pp?mainsoure=7 ISSN 9- ULTRAGARSAS, Nr.(. 00. Investigation of multi-layer strutures by te use of angular ultrasoni transuers A. Vlaišauskas, J. Butkus, L. Jakevičius Prof. K.Baršauskas Ultrasoun Institute Kaunas University of Tenology Abstrat: Pratial aspets of appliation of angular ultrasoni transuers for measurement parameters of multi-layere strutures are analyze. Te algoritms for etermination of tikness of every separate layer in te multi-layere struture, by te use of angular ultrasoni transuers as well as by te use of longituinal or sear waves, are propose. It is sown tat te ratio of tikness of te first layer to te transversal imensions of angular ultrasoni transuers is very important wen te angle of iniene is selete an te parameters of multi-layere strutures are etermine. Te algoritms for etermination of minimal tikness of te first layer, wi may be etermine by te use of angular ultrasoni transuers wit a given transversal imensions, are evelope. Te moeling of epenene of te ratio of minimal tikness of te first layer to te transversal imensions of angular transuers in te plane of iniene was performe, wen te angle of iniene an propagation veloity of ultrasoun signals in te first layer of struture are ange. Te results of moeling are presente an analyze. Keywors: ultrasoun veloity, angular ultrasoni transuer, layere struture, longituinal wave, sear wave, tikness of layer. Introution Reently ultrasoni metos are wiely use for investigation of multi-layer strutures [-]. Tey are espeially useful wen only one-sie aess to a partiular multi-layer struture is possible [, ]. In tis ase iffiulties our beause te aoustial properties of materials of ifferent layers an not be known exatly in avane. For tat reason te measurement of tikness an oter parameters of separate layers is more ompliate. Te problems our beause te propagation veloities of aousti waves of ifferent types in te separate layers are unknown. In su a ase te etermination of tikness of te separate layer an propagation veloity of longituinal or sear waves in it is possible only by te use of two separate measuring annels [, ]. At least in one annel te layer must be irraiate at an angle to its surfae an te angular transuers must be use [7]. Wen te plane aousti wave is raiate at an angle α to te layere struture, tis wave is transforme to te reflete an refrate longituinal an sear waves at every bounary of struture. For tat reason many pulses of sear an longituinal waves may be reeive, wen te istane between te angular transuers is ange [7]. Te isplaement of reflete waves in te istane sale is ifferent from teir isplaement in te time sale [7]. Terefore in pratie it is iffiult to etermine te type of te wave reeive at a given istane an at a given instant. Wit te purpose to minimize te number of ultrasoni waves, appearing ue to moe onversion, te angle of iniene α of te ultrasoun longituinal wave, exite by te angular transuer, is osen between te first an seon ritial angles to te first layer. Terefore, only te sear waves may be exite in te first layer. However, for realization of tis ase in pratie, te veloity propagation of sear an longituinal ultrasoun waves in te first layer of struture must be approximately known in avane. Terefore, wen using te angular transuers, it is very important to know te basi parameters of angular transuers more preisely. Te most important of tem is te angle of te wege of a transuer an te propagation veloity of longituinal ultrasoni waves in te weges. Tese parameters of transuers preetermine te types of ultrasoun waves, wi may be exite in te first layer of a multi-layer struture. Exept tat, tese parameters preetermine te spatial an temporal resolution of ultrasoun waves reeive on te surfae of te layere struture. In tat ase, wen te parameters of weges of angular transuers are known, te first an te seon ritial angles may be alulate an te raiation angles of transuers may be selete. However, te separation of ifferent moes of waves epens not only on te angles of weges of angular transuers. Te transversal imensions of angular transuers in te plane of iniene are very important too. Besies tat, te transversal imensions an te angles of raiation of transuers etermine te minimal tikness of te first layer, wi may be etermine by te separate pair of angular transuers. But in analysis presente in [-7] te relationsip between te angular an transversal imensions of transuers an propagation veloity of waves in te layere struture an in te weges of transuers are not reveale. Terefore, te objetive of tis paper is te evaluation of te relationsip between te parameters of angular transuers an te measure parameters of te layere struture. Teoretial investigation Investigation of a layere struture using te angle beam transuers gives attrative information about te layers if longituinal an sear ultrasoni waves are use. Te exitation of tese waves an be arrie out by te use of transuers of longituinal waves or sear waves. Te bakgroun of tis investigation is a knowlege of parameters of angular transuers. Main of tem are te elay time in te wege, te angle of te wege an te aoustial pat of ultrasoni waves in te wege. Te values of tese parameters an be etermine from te
ISSN 9- ULTRAGARSAS, Nr.(. 00. analysis of transuers esign or by te experimental investigation. Te elay time t 0 in te wege of transuer is given by 0 tan α 0 t0 =. ( 0 Here 0 is te istane between te enter of piezoelement an te lower bounary of te wege; α 0 is te angle of te wege; 0 is te veloity of a longituinal wave in te wege. Te seme of measurement of te elay time in te layere struture is sown in Fig.. α 0L α L α S α L αs α L 8 9 0 α S x Fig.. Te measurement seme of te elay time in te layere struture It onsists of two transuers plae on te surfae of te layere struture. Te piezoelement of te transuer raiates te longituinal wave into te wege. Two refrate ultrasoun waves are exite in te first layer: te longituinal wave an te sear wave. After te refletion from te bounary wit te seon layer an after te moe onversion tere will be four waves: two longituinal (, two sear (8 an (after te moe onversion longituinal sear (0 an sear longituinal (9 waves. Te elay time in te weges of bot transuers (t 0 an te time of a full skip (t for te sear (t S an longituinal (t L waves in te first layer will be t = t0 +, ( were t =t L an t =t S are te sums of te elay times of waves propagating in te weges of te transuers an in te first layer for longituinal or sear waves, orresponingly; = L an = S are te veloities of longituinal or sear waves in te first layer; α =α L an α =α S are te refration angles of longituinal or sear waves in te mentione layer, respetively. Te angle α L as well as te angle α S are efine by te Snell s law sin α 0 sin α = ( 0 Ten te tikness of te first layer an be alulate for longituinal or sear waves ( t t0 =. ( Ultrasoni waves after te moe onversion (longituinal sear an sear longituinal were not onsiere ere. Te elay time of ultrasoni waves in te 7 weges of te transuers an in te first an seon layers of te struture is given by t w t = 0 + w + w, ( w were t w =t L an t w =t S are te sums of te elay times of longituinal or sear waves in te weges of te transuers an in te first an seon layers, orresponingly; w = L an w = S are te veloities of longituinal or sear waves in te seon layer; α L, α S are te refration angles of longituinal an sear waves in te seon layer, respetively. Te tikness of te seon layer for bot types of waves is ( tw t0 Δt w w =. ( Here Δt =Δt L an Δt =Δt S are te elay times of longituinal or sear ultrasoun waves in te first layer, respetively. In te same manner te tikness of te tir layer may be etermine. Ten te tikness of te k-t layer may be etermine as k tkw t0 t iw kw Δ kw i = k =. (7 Te subsripts kw an iw must be ange to kl an il for longituinal waves an to ks an is for sear waves, respetively. Te auray of tis meto igly epens on te auray of measurement of parameters of te first layer. Terefore, a more eep investigation of interation of ultrasoni waves wit a layere struture an espeially wit te first layer is neessary. For tat reason let us suppose tat we ave two iential angular ultrasoun transuers, te imensions of wi in te plane of iniene is, te angle of iniene is α, an te istane between te external ege of te transuer an te bounary of external enlosure of te transuer is l (Fig.. α p β l Fig.. Displaement of angular transuers for realization of te pitat of ultrasoun signals Let us etermine te minimal tikness of te layer, wi may be measure by te use of te first skip of ultrasoun wave, exite by te angular transuer. How one an see from Fig., te minimal tikness of te first layer may be fixe, wen te ousings of te ultrasoun transuers are presse lose togeter. Ten one an obtain b + l = ot( β. (8 b
ISSN 9- ULTRAGARSAS, Nr.(. 00. Here b is te lengt of te surfae of te wege, wi is ontating te layere struture in te plane of iniene; β is te angle of te propagation iretion of ultrasoun wave in te first layer of te struture. After te trigonometri reonstrution may be written ( b + l sin ( β sin( β =. (9 If is te veloity propagation of ultrasoni waves in te layer uner investigation an p is te veloity propagation of ultrasoun waves in te wege of te angular transuer, ten, after te use of Snell s law an geometrial relation s = /, from Eq., one an obtain [ + l os( α ] p sin ( α sin( α =. (0 In orer to reue te number of variables te relative quantities n=, m=l/ were introue. Ten te relative tikness / may be obtaine: [ + m os( α ] n sin ( α n sin( α =. ( Tis expression esribes te minimal tikness of te layer, wi may be measure by te use of ultrasoni transuers wit te speifi parameters, wen te first pit-at signal is fixe. Wen analyzing tis expression one an etermine te optimal parameters of angular ultrasoni transuers, wi may be use for investigation of layere strutures of speifi materials. Te analysis of te obtaine expression sowe tat in an ieal ase te istane between te external ege of te transuer an te bounary of its ousing soul be l=0. Ten te first pit-at signal may be fixe on te surfae of te first layer wit te tikness not less tan te normalize value Matematial moeling sin ( α ( α n =. ( n sin Wit te purpose to reveal te possibilities of te propose algoritms, te matematial moeling was arrie out. Te moeling of ange of te ratio of te minimal tikness of te first layer to te transversal imensions of angular transuers in te plane of iniene was performe. During moeling te angle of iniene an te propagation veloity of waves in te layere struture were ange. Te results of moeling are presente in Fig.. How one an see from Fig., wen te veloity of ultrasoni waves in te layere struture is bigger tan te propagation veloity in te weges of angular transuers (n= <, te minimal tikness of te layer in omparison wit te imensions of transuers, is rapily ereasing, wen te angle of iniene is inrease. In tat ase te angle of iniene α of longituinal waves may be inrease only till te first ritial angle. By analogy, te angle of iniene of te sear waves may inrease only till te seon ritial angle too. / m=0 m=0. m= n=0. C 0 n= B A 8 7 n= 9 n=. n= 0 0 0 0 0 0 0 eg Fig.. Angular epenenies of te relative minimal tikness / of te first layer at ifferent relations of propagation veloities in te layere struture an in te weges of transuers 7
ISSN 9- ULTRAGARSAS, Nr.(. 00..8. 9...0 0. 0..9.9 0...8.7.7... 0. 0 0 0 0 0... 0..0.... 0. 0 0 0 0 0 a... 9 0. 0. 0 0 0 0 0. 7.0.9..8. 0 0 0 0 0. b 0. α 0, eg 0.....9 7. 8..7. 0. 0 0 0 0 0...0...9...8 0 0 0 0 0 e f Fig.. Te epenene of te relative tikness / of te first layer on te angle of iniene an on te relative veloity propagation of signals at ifferent relations m: a, b m=0;, m=0.; e, f - m=; a,, e - te ratio < ; b,, f te ratio > Wen te veloity of ultrasoni waves in te first layer of te struture is less tan te veloity in te weges of angular transuers (n= < an te angle of iniene α<0, te measurements of tikness are possible only wen te tikness of te layer is onsierably bigger tan te iameter of te piezoelement of te transuer (urves -, Fig.. Tis onition is often satisfie, wen te sear waves are applie, but te tikness of te layer must be at least twie bigger tan te iameter of te transuer (point A, Fig.. Te minimal tikness of te first layer, wi may be measure by te angular transuers wit te given transversal imensions, is ereasing wit te angle of iniene. But tis erease ontinues till te optimal value of te angle of iniene is aieve. In tis ase te minimal tikness of te first layer may be fixe. After tat te minimal tikness, wi may be measure by te use of angular transuers wit te given parameters, begins to inrease wit te angle of iniene. On te oter an, te possibilities of measurement of a tikness of a separate layer epen on te istanes between te weges of transuers an teir ousings (istane l, Fig.. In te best ase, wen m=l/=0 an n=/ 0 = (urve 9, Fig., te tikness of te first layer an be smaller tan te iameter of te transuer if te 8
ISSN 9- ULTRAGARSAS, Nr.(. 00. iniene angle α 0 >0. Terefore te istane l in te ultrasoni transuer soul be minimize. Wen te iniene angle is between te first an seon ritial angles (for example α 0 =0, longituinal an sear waves may be exite in te layer an may be use for measurement of its tikness. However, te minimal tikness of te first layer may be fixe wen longituinal waves are use an te iniene angle is α 0 = (point B on te urve 9, Fig.. In tis ase te same transuer, loate on te surfae of te first layer, will reeive longituinal an sear waves, but at ifferent time instants. Slow sear waves in te first layer ause iffiulties to reeive waves of oter types, reflete from ifferent layers of te layere struture. Witin te range of te iniene angles from 0 to 70 sear waves an be use wit te best avantage. In tis ase, wen n=, te tikness of te layer may be less tan te iameter of te piezoelement (urves 7-9. Wen te veloity of ultrasoun waves in te layer is more tan te veloity in te wege, te angle of iniene is restrite (urves 0-. For example, wen n=/ 0 =, te angle of iniene an not be bigger tan (te seon ritial angle for longituinal waves. Insie te range of te angles of iniene from 0 to te istane l influenes signifiantly. Te possibilities of measurement of te layer tikness epen onsierably on te iniene angle. Near te ritial angle it is possible to measure te tikness of te layer wi ompile 0. 0. from te iameter of transuer. Tis onition an be easily fulfille by exiting te sear waves an using te angles of te weges between α=0 an α=0. Te epenenies of te minimal relative tikness / of te layer on te angle of iniene an on te relative veloity of soun veloity in te layer an in te weges of transuers at ifferent relations m=l/ are presente in Fig.. How one an see from Fig., wen te ratio is onstant, te relative minimal tikness of te layer, in omparison wit te transversal imensions of transuers, is rapily ereasing wit te angle of iniene. Espeially it is evient wen te propagation veloity of signals in te layere struture is bigger tan te veloity of waves in te weges of angular transuers (Fig. b,, f. Wen te veloity of ultrasoun waves in te first layer of struture is less tan te veloity in te weges of angular transuers, te minimal tikness of te first layer is ereasing, wen te angle of iniene is inrease. However, tis erease ontinues only till te optimal value of te angle of iniene is aieve. In tis ase te minimal tikness of te first layer may be fixe at given ratios an l/ (Fig. a,, e. Conlusions Te analysis of pratial aspets of appliation of angular transuers sows tat wen measuring parameters of layere strutures te ratio of tikness of te first layer to te transversal imensions of angular transuers is very important, wen te angle of iniene is selete. Te algoritms for etermination of a minimal tikness of te first layer, wi may be etermine by te use of angular transuers, wit given transversal imensions, are propose an moeling is performe. Wen te veloity of ultrasoni waves in te layer struture is bigger tan te veloity propagation in te wege of an angular transuer, te minimal tikness of te first layer, in omparison wit te transversal imensions of te transuers, is rapily ereasing wen te angle of iniene is inrease. Wen te veloity of ultrasoun waves in te first layer of struture is less tan te veloity in te weges of transuers, te optimal raiation angle of transuers may be selete an te layers of minimal tikness may be investigate. Referenes. Guyott C. C. H., Cawley P. Te measurement of troug tikness plate vibration using a pulse ultrasoni transuer. J. Aoust. So. Am.., 988. Vol. 8. No. P. -.. Hsu D. K., Huges M. S. Simultaneous ultrasoni veloity an sample tikness measurement an appliation in omposites. J. Aoust. So. Am.. 99. Vol. 9. No.. P. 9-7.. Greo e Sousa A., Maao J. C., Pereira C. A. Ultrasoni araterization of stratifie meia wit inepenent measurement of wave veloity an tikness. IEEE ultrasoni symposium. 00. P.8-8.. Cotter D. J., Miaels J. E., Zang Z., Gabour E, Nelligan T., Abbate A., Kass D. an Elfbaum G. Hig frequeny ultrasoni tikness an aousti veloity measurement metos for avane material an omponent araterization. NDT.net-Otober 00. Vol.7. No.0.. Caroiskey T. J., Meyer P. A. Tikness measurement in materials of unknown aousti veloity. NDTnet-Otober 997. Vol.. No.0.. Siegel M. Measurement issues in quantitative ultrasoni imaging. IEEE transations on instrumentation an measurement. 998. Vol.7. No.. P. -8. 7. Jakevičius L., Butkus J., Vlaišauskas A. Measurement of tikness of layer an soun veloity in multi-layere struture by te use of angular ultrasoni transuers. Ultragarsas. 00. Nr.(8. P.0-. A. Vlaišauskas, J. Butkus, L. Jakevičius Daugiasluoksnių struktūrų tyrimas nauojant ultragarsinius kampinius keitiklius Reziumė Analizuojami ultragarsinių kampinių keitiklių nauojimo augiasluoksnių struktūrų parametrams matuoti praktiniai aspektai. Pasiūlyti algoritmai kiekvieno sluoksnio storiui augiasluoksnėje struktūroje nustatyti nauojant ultragarsinius kampinius keitiklius ir išilgines arba skersines ultragarso bangas. Parooma, ka, matuojant augiasluoksnių struktūrų parametrus ir pasirenkant bangų kritimo kampą, labai svarbu yra pirmojo sluoksnio storio ir kampinio keitiklio skersinių matmenų santykis. Pateikiami pirmojo sluoksnio mažiausio storio, kuris gali būti išmatuotas nauojant tam tikrų skersinių matmenų kampinius keitiklius, nustatymo algoritmai. Atliktas pirmojo sluoksnio mažiausio storio santykio su kampinio keitiklio skersiniais matmenimis kritimo plokštumoje moeliavimas, kai keičiamas ultragarsinių signalų kritimo kampas ir signalų skliimo greitis pirmajame struktūros sluoksnyje. Pateikiami ir analizuojami moeliavimo rezultatai. Pateikta spauai 00 0 9