EXCESS SCATTERING INDUCED LOSS AT A ROUGH SURFACE

Transcription

1 EXCESS SCATTERING INDUCED LOSS AT A ROUGH SURFACE DUE TO PARTIALLY COHERENT DOUBLE-REFLECTION Peter B. Nagy Department f Welding Engineering The Ohi State University Clumbus, OH James H. Rse and Mehmet Bilgen Center fr NDE Iwa State University Ames, Iwa INTRODUCTION Transmissin (and retransmissin) thrugh rugh surfaes degrades ultrasni flaw detetin and materials haraterizatin. The flaw signal as well as referene signals ( e.g. refletins frm the frnt-surfae r bak-surfae f the speimen) beme diffiult t interpret. In the simplest ase, we make tw assumptins in rder t mdel the ultrasni pulse-eh signal. Our first assumptin is that the satterer is large in the sense that it extends laterally fr many surfae rrelatin lengths. In this ase, the signal has a small variane and is well desribed by its average value that will be referred t as the "speular" signal. Our send assumptin is that the flaw is far frm the surfae, in a sense t be defined belw. Given these tw assumptins, the rugh surfae intrdues a lss that is prprtinal t the square f the rms height, h, and the frequeny,! Further, the lss due t a duble-transmissin, L d, is just twie the lss due t a single-transmissin, L s ' i.e., Ld 2 Ls' In this paper we shw that the signal an be understd using simple physial arguments based n lal hanges in the phase even if the assumptins stated abve are nt satisfied. In partiular, suppse that the send assumptin is vilated and the satterer is near the surfae f the speimen. The initial transmissin, as the ultrasund enters the part, bemes statistially rrelated with the final transmissin, as the ultrasund exits. In this ase the lss is a mpliated funtin f the frequeny, the rms height as well as the surfae autrrelatin length and an be as high as 4 Ls' We shw that speular signals frm subsurfae defets in sht blasted samples an be understd in terms f rughness- Review f Prgress in Quantitalive Nndestrutive Evaluatin. Vl. 14 Edited by D.O. Thmpsn and D.E. Chimenti. Plenum Press. New Yrk

2 indued hanges in the phase. The bserved signals (bth fr the near-surfae and the farsurfae regime) are quantitatively desribed by simple analyti frmulas derived using the phase-sreen apprximatin (PSA) [I]. We will use the wrds "speular" and "diffuse" t desribe the average and randmly varying mpnents f the wavefield. In rder t avid nfusin, we use the wrds "herent" and "inherent" t desribe the presene r lak f rrelatin in the transmissin and retransmissin f ultrasund thrugh the rugh surfae. BASIC IDEA Althugh surfae rughness affets bth the phase and amplitude f the sund wave as it rsses the surfae, the hange in phase dminates the physis sine the phase appears in an expnential, while the amplitude is a slwly varying prefatr. The simplest pssible apprximatin is t ignre the amplitude variatin altgether and t nern urselves entirely with the phase variatin. This idea is expressed via the phase-sreen apprximatin, whih relates the field just befre the surfae, Z = 0 -, t the field just after the surfae, z=o+, as u(r,r,z=o+) = T exp[up(r)]u(r,r,z=o-). (I) Here, r dentes the angular frequeny, r the rdinate parallel t the surfae and <1>( r) the hange in phase due t the lal surfae height variatin at r. Finally, 'Fa dentes the apprpriate plane wave transmissin effiient fr a smth planar surfae. SINGLE-TRANSMISSIONIREFLECTION The rughness-indued lss (single-transmissin r refletin) an be alulated analytially in the PSA fr surfaes desribed by a Gaussian randm press and is given by L = (<I>2> [I]. That is, the lss is prprtinal t the square f the rms value f the phase perturbatin <I>. In this apprximatin the magnitude f the phase perturbatin is always prprtinal t bth the frequeny, j, and the rms rughness, h. Cnsequently, the sattering indued lss fr the refleted Lf and lngitudinal L; and transverse LI transmitted waves an be written in the fllwing general frm (2) where A R, A L, and AT are knwn funtins f the sund velities in the slid and the fluid and the angle f inidene, 8 [2, 3]. Eq. (I) has the interesting feature that the lss depends separately n f 2, h 2 and a funtin f the angle f inidene, A. Lsses fr transmitted waves an be predited ne the lss fr a nrmally inident refleted wave is measured. This fllws frm Eq.(2) and the fat that the A's are simple knwn funtins (tabulated in Ref. 3). The lsses fr the transmitted waves are given by AL,T (8) L;,T (r,h,8) = R Ls (r,h,8 = 0). A (8 =0) R (3) 1846

3 These angle-dependent nrmalized lsses an be easily alulated fr bth lngitudinal and transverse waves frm the knwn sund velities in the slid and the fluid [3]. DOUBLE-TRANSMISSION Rughness-indued lsses fr transmitted waves are desribed in a remarkably simple and useful way by Eq. (3). Experimental tests f this equatin are reprted in Ref 3 and a shrt synpsis f these experiments is as fllws. We measured the lsses fr refleted and dubly-transmitted waves fr a series f sht-blasted aluminum plates, whih are desribed in greater detail in Ref 3. The duble-transmissin lss was measured in a pulse-eh arrangement by plaing the speimen between a 112-inh-diameter transduer and a plane refletr app. 500 mm apart. That is, the experiment was arefully prepared s that the assumptins f the first paragraph were mpletely satisfied and nsequently the lsses fr duble-transmissin are expeted t be just twie the lss fr single-transmissin. The results are shwn in Fig. 1, whih shws that Eq.(3) is quantitatively aurate fr thse values f the frequeny and the angle f inidene that are shwn. Nte that Eq. (3) will fail near the ritial angle and that it is expeted t be best fr samples whse rms height is muh less than the surfae autrrelatin length. It has been reently regnized, that the tw-way phase-perturbatin is nt neessarily the inherent sum f the tw ne-way perturbatins if the prpagatin distane between the tw interatins is small [4,5]. Clearly, partial herene between the tw interatins an signifiantly inrease the duble-transmissin lss. In the ase f mpletely herent interatins, the rms value f the mbined phase-perturbatin is twie as muh as ,..., b. 24 :: ;:l :: Cl) < Figure 1. Sattering lss as a funtin f frequeny fr the refleted and dubletransmitted waves at given angles f inidene (h = 25.6 lm, aluminum). The slid lines are theretial preditins based n the phase-sreen apprximatin and the symbls represent the experimental data. 1847

4 that fa single interatin, i.e., <l>d = 2<1>s. Sine the lss f the speular mpnent is prprtinal t the square f the rms value f the mbined phase-perturbatin, the ttal lss aused by the duble-interatin is fur times higher than the lss f the singleinteratin, i.e., Ld = Yz<<I> > = 4 Ls. In mparisn, in the ase f mpletely inherent interatins disussed abve, the rms value f the mbined phase-perturbatin is nly <l>d =..fi <l>s, and therefre the ttal lss aused by the duble-interatin is twie the lss f the single-interatin, i.e., Ld = Yz <<I> > = 2 Ls. The transitin between mpletely herent interatins at lse distanes t mpletely inherent interatins at large distanes is demnstrated by Figure 2, whih shws the alulated duble transmissin lss f the lngitudinal wave at nrmal inidene fr an aluminum speimen immersed in water. The rms rughness and the herene length f the speimen were h = 20 J..Lm and 1.5 mm, respetively. Bth Gaussian and expnential aut-rrelatin funtins were nsidered. These alulatins were made by using the phase-sreen apprximatin and assuming a Gaussian beam prfile f a = 10 mm radius and an peratin frequeny f f= 10 MHz. Fr this mbinatin f parameters, the refletin lss, La' at nrmal inidene is 12.2 db. The nrmalized lngitudinal transmissin lss fr aluminum in water is The duble-transmitted lss an be estimated frm the refletin lss in the inherent repetitin apprximatin as LJ(8 = 0) 3.69 db (dashed line in Fig. 2). At very large depths belw the rugh surfae, the lss f the duble-transmitted signal asympttially apprahes this "inherent" limit. Hwever, at smaller depths, the atual lss is muh higher. Fr example, the exess lss with respet t the inherent apprximatin is app. 2 db at 5 mm belw the surfae. At very small depths, the lss f the duble-transmitted signal apprahes the "herent" limit f LJ(8 = 0) 7.38 db, i.e., twie the value f the inherent limit. en 6 en...:l.9 en. 4 en E--< Q ::g 2 Q , -- Gaussian Expnential i "Inherent" estimatin frm refletin lss Depth [m] Figure 2 Calulated duble-transmissin lss f the lngitudinal wave at nrmal inidene fr an aluminum speimen immersed in water (h = 20 Lm, rrelatin length = 1.5 mm, a = 10 mm, and f= 10 MHz). 1848

5 DOUBLE-REFLECTION The partial hereny between subsequent phase-perturbatins experiened by the ultrasni wave upn repeated interatin with the same rugh surfae is bviusly a general phenmenn affeting bth refleted and transmitted waves. Of urse, in typial NDE appliatins we are mainly interested in the transmitted wave. In the mmnly used pulse-eh mde f peratin the transmitted wave always interats twie with the same rugh surfae; first time as it enters the speimen and send time when it leaves it. An analgus phenmenn urs when multiple-refletin takes plae between parallel refletrs. We fund that the effet f partial hereny between repeated interatins with a rugh surfae an be mre easily studied experimentally using the refleted part f the wave than n the transmitted mpnent. The asymptti behavir f the duble-refletin lss an be readily predited frm simple physial nsideratins fr either very lw r very high values f standff distane, frequeny and autrrelatin length. It is muh mre diffiult t quantitatively desribe the transitin frm dminantly inherent repetitin t dminantly herent repetitin. Hwever, the phase-sreen apprximatin prvides simple expliit results fr bth Gaussian and expnential rrelatin funtins [5]. EXPERIMENTAL TECHNIQUE AND RESULTS Figure 3 shws (a) the shemati diagram f the experimental arrangement used t investigate the effet f hereny n the sattering indued lss f the duble-refleted speular wave frm a rugh surfae and (b) the multiple ehes reeived frm the smth and rugh sides f the speimen. One f the main advantages f this arrangement is that the standff distane Z an be varied easily ver a wide range. Details f the experimental setup and sample preparatin and haraterizatin are given in Ref. 5. A 1I2"-diameter llimated-beam bradband immersin transduer was used in the measurements. The transduer had a 1I2"-lng glass buffer whih plays an essential part in this experiment. The perfetly smth, plished water/glass interfae enuntered by the bak refleted ultrasni waves frm the surfae f the speimen ats like an ideal mirrr. The sattering indued lss f the first and send (r any higher rder) refletin an be easily measured by mparing the spetra f the same signal frm the smth and rugh sides as the speimen is flipped ver. Of urse, the refletin effiient f the water/glass bundary is nly abut 80% but, beause f the way we measure the sattering indued lss f the speular signals, this small frequeny-independent lss has n effet n ur results. In rder t measure the speular and nly the speular mpnent f the refleted signal, we shuld measure the refletin frm a large number f speimens and alulate the ensemble average. Instead, we did spatial averaging ver the whle 2"-by-2" rughened area f the speimen. Measurements f the sattering-indued lss f the singly- and dubly-refleted speular waves were made n an aluminum speimen f h = 5.2 Lm rms rughness and 730 m rrelatin length. The measurements were made fr six standff distanes f2.5, 5.25, 8, 11, 16, and 22 mm between 5 MHz and 50 MHz (subjet t a dynami range f app. 40 db). Figure 4 shws the measured lss as a funtin f frequeny fr different standff distanes. The slid lines shw the best fitting j2 urves mathed t the frequenydependent lss f the first refletin. The tw dtted lines simply shw twie and fur times this best fitting lss spetrum t indiate the inherent and herent limits f the duble- 1849

6 a) II L.L... "- Immersin Transduer with Glass Buffer [::i ,._-----""'....., _--,.. _ b) smth side: rugh side: # 1 st \ \ J L * 2nd h ) Figure 3 Shemati diagram f (a) the experimental arrangement used t investigate the effet f hereny n the sattering-indued lss f duble-refletin frm a rugh surfae and (b) the multiple ehes reeived frm the smth and rugh sides f the speimen. refletin lss. The pen bxes indiate the measured single-refletin lss, while the pen irles shw the measured duble-refletin lss. The duble-refletin lss is fur times the single-refletin lss either fr small standff distanes r high frequenies, i.e., when herent repetitin urs. Figure 4a is fr ur smallest standff distane f2.5 mm. As an be seen, the measured duble-refletin lss is nearly fur times higher than the singlerefletin lss ver the whle frequeny range. On the ther hand, Figure 4f shws the results fr ur largest standff distane f22 mm. In this ase the measured dublerefletin lss is apprximately twie the single-refletin lss ver the whle frequeny range. Fr intermediate standff distanes, the duble-refletin lsses are twie the singlerefletin lsses fr lw frequenies but swith t fur times the single-refletin lsses at high frequenies. 3rd 1850

7 30r _, a) z = 2.5 mm : : 20.b.0. a Q) 10 D " 30r b) z = 5.25 mm? 0,' q' :::;: , Q) ,-----,---.,.0 J:) ) z = 7.9 mm '0 0 '0.'0 '0 '0... 0,' '0.0,'! ;::; , L) 30r d) z = 11 mm !"--:---:'--, e) z = 16 mm a Q) , , t) z= 22 mm O.j...-..&l;l-._ I """""<;: Figure 4 Measured lss as a funtin f frequeny fr six different standff distanes (see explanatin in the text). 1851

8 CONCLUSIONS The sattering indued lss f a speular ultrasni wave interating with a rugh surfae is prprtinal t the square f the rms rughness-t-austi-wavelength rati. Under mst rdinary irumstanes, a send interatin with the same rugh surfae is inherent with respet t the first ne and the lsses an be simply added. Hwever, when the send interatin urs within the herene length f the sattered diffuse field frm the first interatin, the ttal sattering indued lss is nt twie but fur times the lss inurred during a single interatin. As a first experimental step in studying the generi prblem f partially herent duble-interatin with a rugh interfae, we measured the sattering indued lss f singly- and dubly-refleted speular waves frm a arefully prepared rugh speimen. We varied the degree f hereny between the tw interatins by hanging the prpagatin distane and the frequeny. Our experiments shw that at lse distanes and high frequenies, when the interatins are herent, the dublyrefleted wave is fur times mre attenuated than the singly-refleted ne. In mparisn, at large distanes and lw frequenies, when the interatins are inherent, the dublyrefleted wave is tw times mre attenuated than the singly-refleted ne. It has been shwn reently [5], that the transitin regin between herent and inherent interatins as either the prpagatin distane r the frequeny varied an be used t haraterize the autrrelatin funtin f the surfae and assess the autrrelatin length. ACKNOWLEDGEMENT This wrk was supprted in part by the FAA Center fr Aviatin Systems Reliability, perated by the Ames Labratry, USDOE fr the Federal Aviatin Administratin under Cntrat N. W-7405-ENG with Iwa State University REFERENCES 1. C. Ekhart, J. Aust. S. Am. 25, 556 (1953). 2. P. B. Nagy and Laszl Adler, 1. Aust. S. Am. 82, 193 (1987). 3. P. B. Nagy and 1. H. Rse, 1. Appl. Phys. 73, 566 (1993). 4. Bilgen and Rse, in Review f Prgress in QNDE, Vl. 13B, eds. D. O. Thmpsn and D. E. Chimenti (Plenum, New Yrk, 1994) p H. Rse, M. Bilgen, and P. B. Nagy, 1. Aust. S. Am. 95, 3247 (1994). 1852