Measurement of thickness of layer and sound velocity in multi-layered structure by the use of angular ultrasonic transducers

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1 ISSN ULTRAGARSAS, Nr.1(58). 26. Measurement of thckness of layer and sound velocty n mult-layered structure by the use of angular ultrasonc transducers L. Jakevèus, J. Butkus, A. Vladšauskas Prof. K.Baršauskas Ultrasound Insttute Kaunas Unversty of Technology Abstract: The possbltes of measurement of thckness of layer and the velocty propagaton of ultrasound sgnals n layered structures by the use of the angular electroacoustcal transducers wth known parameters are analyzed. It s shown that, when the velocty propagaton of ultrasound sgnals n the separate layer of structure s unknown, the thckness and the velocty propagaton of sgnals n them may be measured by the use of the sngle measurng channel wth angular ultrasonc transducers. The algorthms for determnaton of thckness of separate layers and ultrasound velocty n them are developed, when the layered structure s radated at a known angle to the surface of structure. The modelng of a measurng channel wth the angular ultrasonc transducers s performed. When modelng the propagaton and reflecton of ultrasound sgnals n duralumn plexglass layered structure and the spatal and temporal dstrbutons of them on the surface of layered structure are revealed. The varaton of temporal and spatal dstrbutons of receved sgnals s nvestgated when the angle of ncdence to the layered structure s changed. It s shown that temporal and spatal dstrbutons of shear and longtudnal waves do not concde to each other and alter dfferently, when the angle of ncdence s changed. The results of expermental nvestgaton are presented. Keywords: ultrasound velocty, angular ultrasonc transducer, layered structure, shear wave, longtudnal wave. Introducton Ultrasonc measurng methods of thckness and other physcal parameters of layered structures are wdely used n ndustry and non-destructve testng [1-4]. But at present the mult-layered structures become more complcated, consstng of materals wth dfferent mechancal and acoustcal propertes, such as plastcs and metals or metals, lquds and plastcs. Dfference of mechancal mpedances of these materals causes many problems. Especally t s evdent when the measurng nformaton must be obtaned only from one sde of the layered structure [5,6]. In ths case not always t s possble to obtan the measurng nformaton about parameters of all layers or some of them. Ths s stpulated by the losses of ultrasound sgnals n separate layers as well as by loses of ultrasound sgnals n the boundares between them. These loses depend on the dfferences of acoustcal mpedances and on the acoustcal propertes of the materals of dfferent layers. Other dffcultes occur because the acoustcal propertes of the materals of dfferent layers often cannot be exactly known. For that reason the measurement of thckness and other parameters of the separate layers s problematc. The problems are related to the fact that the veloctes of propagaton of acoustc waves of dfferent types n the separate layers of structure are unknown. In such a case the determnaton of thckness of separate layer s possble only by usng of two separate measurng channels. At least n one channel the layer must be rradated at an angle to ts surface. Though, when soundng at the angle to the surface of the layer structure, the longtudnal, shear and other types of ultrasound waves are excted [1]. It allows ncrease the measurement possblty by the use of ultrasound wave mode converson. The velocty propagaton of shear waves s about two tmes less than the velocty of longtudnal waves. In ths case the tme of propagaton of acoustcal sgnals n the layer becomes almost twce longer. It enables mprove the resoluton and accuracy of measurement of thckness. But often n mult-layer structures the veloctes of propagaton of dfferent types of waves n separate layers are unknown, especally for ultrasonc shear waves. In that case the angles of propagaton and reflecton of ultrasound waves of dfferent types are not known too. An oblque ncdence method for exctaton of longtudnal and shear waves s very convenent for measurement of an unknown ultrasound velocty and thckness by the use of two measurng channels [6,7]. In both cases two measurements are performed for dfferent dstances and delay tmes. But n analyss presented [6,7] there s no nformaton about ultrasound wave mode converson and about propagaton of shear waves n separate layers of the layered structure. In these artcles no nformaton about the use and selecton of dfferent types of waves and nformaton about the use of angular transducers for that purpose s gven. Therefore the objectve of ths paper s analyss and verfcaton of a new method for thckness and ultrasound velocty measurement n mult-layer structures usng nformaton about parameters of angular transducers. Theoretcal nvestgaton Suppose that we have a medum, whch conssts of n parallel layers wth dfferent physcal propertes. The plane acoustc wave s radated to ths structure at an angle by the use of angular ultrasonc transducer. The velocty of longtudnal wave propagaton n the wedge of the transducer s c. Ths wave at every boundary of layers s transformed to the reflected and refracted longtudnal and shear waves (Fg.1). Wth the purpose do not overburden Fg.1 by nformaton only one from the refracted waves s shown n t. The angle I of propagaton of any wave n the layer s determned by the Snell s law sn sn, (1) c c 2

2 l 1 l 2 ISSN ULTRAGARSAS, Nr.1(58).26. the ultrasound sgnal t n the wedges of electroacoustcal transducers and the tmes of propagaton of the acoustcal sgnal n the layered structure durng whch the sgnal propagates,.e. h l 2 s 1 where c s the velocty of propagaton of ultrasound waves n the medum. Let us consder that the velocty of propagaton of ultrasound waves c and the angle of radaton of waves by the wedge of transducer are known. Then the parameter k, characterzng the transducer wedge, may by ntroduced sn k. (2) c By the use of Fg.1, equaton sn I =l /2s and Eqs.1 and 2 we can obtan the expresson for sgnal path s n the layer l s, (3) 2kc where l s the dsplacement of an acoustcal sgnal n the layer durng the one ptch-catch (Fg.1). On the other hand, the path s of the acoustcal sgnal n the layer may by determned tc s, (4) 2 where t s the propagaton tme of the ultrasound sgnal durng the one ptch-catch. From Eqs.3 and 4 one can obtan the velocty c of propagaton of the acoustcal sgnal n the layer c Fg.1. Propagaton and reflecton of ultrasonc waves n a multlayered structure l. (5) kt From Fg.1 t s seen that the thckness h of the layer l h cot. (6) 2 By the use of Eqs.1, 2 and Eq.5 we can obtan kl arcsn. (7) t Then the thckness h of the layer may be descrbed by equaton l kl h cot arcsn. (8) 2 t In practce usually the tme of propagaton t of an acoustcal sgnal from ts transmsson to recepton s measured. Ths tme conssts of the tme of propagaton of t =t +t 1 +t 2 + +t -1 +t. (9) The dstance l t s convenent to measure between the centers of acoustc axes of transducers l =l 1 +l 2 + +l -1 +l. (1) By the use of expressons (9) and (1), Eq.5 and.8 become lke as l l1 c, (11) k t t 1 l l1 k l l1 h cot arcsn. (12) 2 t t1 The results obtaned show that, when knowng the parameters k and t of transducer wedges and usng the developed algorthms, one can determne the thckness of a separate layer as well as the velocty of propagaton of acoustcal sgnals n t. Modelng of sgnal propagaton Wth the purpose to reveal possbltes of the obtaned algorthms n practce the modelng of spatal and tme dstrbutons of ultrasound sgnals, propagatng n layer structure, was performed. For dervaton of mathematcal equatons Fg. 1 was used. How one can see from Fg.1, an acoustcal sgnal, when propagatng through the n-th layer, s delayed n tme by the value hnc t nm. (13) cnm c cnm sn Here n=1, 2, 3, s the number of the layer; m denotes the type of wave (l-longtudnal, s-shear). Durng ths tme the ultrasound sgnal s propagatng n the layer and passes along the surface of the layer the dstance hnc sn l nm nm. (14) c c sn nm By the use of algorthms (Eq.13 and 14) modelng of sgnal propagaton n the two layer duralumn-plexglass structure was performed. The thckness of each separate layer was 5mm. The exctaton and recepton of ultrasound sgnals was performed from duralumn sde of the layered structure. Wth the purpose to mnmze the number of ultrasound waves, appearng due to mode converson of waves, the angle of ncdence of the ultrasound longtudnal wave excted by the angular transducer was chosen between the frst and second crtcal angles n duralumn. In our case ths angle was changed between 3 and 5. For that reason only the shear waves may be excted n the frst (duralumn) layer. The materal of the wedge of the angular transducer, from whch the ultrasound wave was radated, was plexglass. The velocty of longtudnal waves n t s c l =265 m/s [8]. The frst layer was the duralumn wth the velocty of shear waves c ds =31 m/s. The second boundary of the duralumn layer 21

3 ISSN ULTRAGARSAS, Nr.1(58). 26. t, s 25 l, mm 3 2 4l 15 4l 3sl 3ls 2s 2 3ls 3sl 2l 2s 1 ls 2l ls deg Fg.2. Varaton of propagaton tme of ultrasound sgnals n two layer duralumn-plexglass structure when the angle of ncdence s changed deg Fg.3. Varaton of dstance between the ponts of transmsson and recepton of ultrasound waves on the surface of layered structure when the angle of ncdence s changed s the nterface wth the plexglass, wth the velocty of longtudnal waves c pl =265 m/s and the velocty of shear waves c ps =1335 m/s [8]. The results of modelng, whch show spatal and temporal dstrbuton of ultrasound sgnals propagatng n the two-layer structure, when the angle of ncdence s changed between 3 and 5 are shown n Fg.2 and Fg 3. Wth the purpose to smplfy the desgnaton of ultrasound sgnals, propagatng n the layered structure, the shear wave n duralumn was labeled by the ndex t. The shear and longtudnal waves n the plexglass layer were labeled by ndexes s and l correspondngly. The number before the ndex shows the number of transtons of correspondng wave through the layer. The frst two symbols n ndex concern the frst layer (duralumn) and two subsequent the second plexglass layer. How t was menton above only the shear wave s excted n the duralumn layer. Part of ts energy s reflected from the nterface duralumn-plexglass and the shear wave returns to the recevng transducer (the frst ptch-catch n Fg.4). The shear waves n Fg.4 are shown by sold lnes and the longtudnal waves - by the dotted lnes. Another part of energy of ths wave on the boundary duralumn-plexglass s transformed to the shear and longtudnal waves, transmtted to plexglass. Durng the reflecton from the nterface plexglass-ar the part of energy of the shear wave s transformed to a longtudnal wave. By analogy the part of energy of the longtudnal ls 2l 2s t, ìs Fg.4. Spatal dstrbuton of ultrasound waves n two layer duralumn-plexglass structure 22

4 ISSN ULTRAGARSAS, Nr.1(58).26. á 2s ls w2t2l á 1s á 2l á 2s l, mm Fg.5. Temporal dstrbuton of ultrasound waves n two layer duralumn-plexglass structure wave s transformed to the shear wave. After the refracton on the nterface plexglass-duralumn these waves are receved at a dfferent dstances from the pont of transmsson (the waves 2s, ls and s l n Fg.4). The part of energy of the longtudnal wave, reflected from the plexglass-ar nterface, on the boundary plexglassduralumn s converted to the shear wave and s receved as 2s wave. But the shear wave n the plexglass layer, between the duralumn and gas meda, may be reflected two or more tmes and s receved as wave. In the smlar way the shear wave n duralumn, between the boundares wth plexglass and angular transducer, may be reflected 3 or more tmes and receved at a suffcently bg dstances (the wave after the second ptch-catch n Fg.4). In the tme scale (Fg.5) lke as n the dstance scale (Fg.4) the frst receved wave s the shear wave reflected from the duralumn-plexglass nterface. But the dsplacement n the tme scale of other reflected waves s dfferent from ther dsplacement n the dstance scale. For that reason n practce t s dffcult to determne the type of wave receved at a gven dstance or at a gven nstant. Therefore, the modelng of sgnal propagaton n multlayer structure s necessary before the measurements n real condtons. Expermental results and dscusson An expermental nvestgaton of the measurng method was performed usng angular transducers wth an angle of ncdence of sgnal to the layer structure =44.7. The wedges of ultrasound transducers were made of plexglass. The velocty of longtudnal waves n the wedges of transducers was c pl =265 m/s [8]. For calbraton of the measurng channel the wedges of transducers were pressed face to face to each other and maxmal ampltude of the sgnal was receved. Durng ths experment the delay tme of the ultrasonc sgnal n the wedges of the transducers t =6.9s and the dstance l =1mm between the acoustcal axes of transducers were determned. The frequency of the broadband ultrasonc transducers was 5. MHz. The thckness of the frst duralumn layer, to whch the transducers were pressed, was 5.14 mm. The second layer was plexglass glued to the frst layer by epoxy resn. The thckness of the plexglass layer was 4.9 mm and thckness of glue 21-6 mm. The results of calculatons and expermental nvestgatons are presented n Table 1. Sx mpulses of shear and longtudnal waves were receved when the dstance between the transducers was changed. By the use of the results of measurement the delay tme and the ultrasound velocty n the layers were calculated. Every measurement of the delay tme and the dstance between ultrasonc transducers was performed n a skp poston accordng to the mpulse ampltude. The parameter k of the transducer wedges, for the angle =44.7 and the ultrasound velocty n them c p =265 m/s, was.2654*1-3. Table 1. The delay tme and the dstance between acoustcal axes of transducers Reflected Theoretcal Expermental wave t, s l, mm t, s l, mm sl l s For calculatons of the thckness of layers and the ultrasound velocty n t the Eqs.11 and 12 were used. The results of calculatons of thckness of layers and the veloctes propagaton of shear and longtudnal waves are presented n the Table 2. 23

5 ISSN ULTRAGARSAS, Nr.1(58). 26. Table 2. The ultrasound velocty and the thckness of layers Shear wave Longtudnal wave c, m/s h, mm c, m/s h, mm Frst layer Second layer Conclusons By the use of angular transducers wth known parameters of wedges the new measurement method of the thckness of layers and the velocty propagaton of ultrasound sgnals n t s presented. The method s based on the measurement of the dstance between the acoustcal axes of transducers (on the surface of a layer) and the delay tme of sgnals n skp. The modelng of propagaton of ultrasound sgnals n a two-layer duralumn-plexglass structure s performed. The peculartes of temporal and spatal dstrbutons of ultrasound sgnals and dependences of these dstrbutons on the angle of exctaton of waves are analyzed. The results of modelng show that the sequence of receved ultrasound sgnals on the dstance axs not concde wth the sequence of correspondng sgnals on the tme axs. For that reason the dffcultes occur, when measurng the thckness of the layer and the ultrasound velocty n multlayered structures. Wth the purpose to ncrease the possbltes of measurement and facltate the selecton of measurng sgnals t s expedent to mnmze the transformatons of ultrasound waves n the frst layer. They depend on the acoustcal propertes of a layer as well as on the angle of the wedge of electroacoustcal transducers, whch must be chosen between the frst and second crtcal angles of the layer. References 1. Guyott C. C. H., Cawley P. The measurement of through thckness plate vbraton usng a pulsed ultrasonc transducer. J. Acoust. Soc. Am Vol. 83. No 2. P Hsu D. K., Hughes M. S. Smultaneous ultrasonc velocty and sample thckness measurement and applcaton n compostes. J. Acoust. Soc. Am Vol. 92. No. 2. P Greco de Sousa A., Machado J. C., Perera C.A. Ultrasonc characterzaton of stratfed meda wth ndependent measurement of wave velocty and thckness. IEEE Ultrasonc Symposum. 22. P Cotter D. J., Mchaels J. E., Zhang Z., Ghabour E., Nellgan T., Abbate A., Kass D. and Elfbaum G. Hgh frequency ultrasonc thckness and acoustc velocty measurement methods for advanced materal and component characterzaton. NDT net, October 22. Vol.7. No Carodskey T. J., Meyer P. A. Thckness measurement n materals of unknown acoustc velocty. NDT net, October Vol. 2. No /caro 2.htm. 6. Vlkckas M., Kažys R. Thckness measurement at ndvdual layers n sandwch structures wth unknown ultrasound velocty. Ultragarsas. 23. Nr.4(49). P Segel M. Measurement ssues n quanttatve ultrasonc magng. IEEE transactons on nstrumentaton and measurement Vol.47. No. 6. P Hung B. N., Goldsten A. Acoustc parameters of commercal plastcs. IEEE Trans. Soncs Ultrason Vol. SU-3. No.4. P L. Jakevèus, J. Bukus, A.Vladšauskas Sluoksno storo r ultragarso greèo matavmas daugasluoksnëje struktûroje naudojant kampnus ultragarsnus ketklus Rezumë Ištrtos galmybës sluoksnø storá r ultragarsnø sgnalø skldmo gretá sluoksnuotose struktûrose matuot naudojant žnomø parametrø kampnus elektroakustnus ketklus. Parodyta, kad, esant nežnomam ultragarsnø sgnalø skldmo greèu struktûros sluoksnuose, šø storá r garso gretá juose galma šmatuot naudojant ven¹ ultragarsná matavmo kanal¹ r žnomø parametrø kampnus elektroakustnus ketklus. Sukurt algortma sluoksnø storu r ultragarso greèu juose nustatyt, ka sluoksnuotoj struktûra zonduojama ultragarsnus sgnalus spnduluojant žnomu kampu á jos pavršø. Be to, sumodeluotas toks ultragarsno matavmo kanalas su kampnas ultragarsnas ketklas. Modeluojant akustnø sgnalø skldm¹ r atspndžus duralumnoorganno stklo sluoksnuotoje struktûroje, atsklestas lakns r erdvns sgnalø passkrstymas sluoksnuotos struktûros pavršuje, štrtas jo ktmas dël sluoksnuotos struktûros zondavmo kampo pokyèo. Parodyta, kad lakns r erdvns skersnø r šlgnø bangø passkrstymas neattnka venas kto r skrtnga knta keèants sluoksnuotos struktûros zondavmo kampu. Patekam ekspermentno tyrmo rezultata. Patekta spauda