ULTRASONIC VELOCITY CHANGE AND DISPERSION DUE TO POROSITY IN. David K. Hsu and Hyunjo Jeong Center for NDE Iowa State University Ames, Iowa 50011

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1 ULTRASNIC VELCITY CHANGE AND DISPERSIN DUE T PRSITY IN CMPSITE LAMINATES David K. Hsu and Hyunj Jeng Center fr NDE Iwa State University Ames, Iwa INTRDUCTIN Vidsr prsity in carbn fiber reinfrced plastics (CFRP) caused by imprper cur ing, misture in the prepreg and ther reasns can de grade the mechanical prperties f the cmpsite cmpnents [1-3]. Vids caused by trapped air in the layup prcess r vlatile gas released in the cur ing prcess tend t ccur at the interface between the plies f unidirectinal prepregs and are usually elngated alng the adjacent fiber directins [4]. n the ther hand, vids in wven cmpsites tend t be mre spherical. Matrix dminated strengths such as transverse tensile and interlaminar shear strengths are affected the mst by the presence f prsity. Quantitative nndestructive evaluat in (QNDE) methds fr the detectin and characterizatin f prsity in cmpsites are therefre highly desirable. Since vids are strng scatterers fr elastic waves, ultrasund has been a useful prbe fr the detectin and evaluatin f prsity in CFRP. The crrelatin between ultrasnic attenuatin and vid cntent in CFRP is well knwn [5] and has becme the basis fr wide industrial quality assurance practices against prsity. At the Center fr NDE at Iwa State University, measurement prcedures were develped t btain ultrasnic attenuatin as a functin f frequency using bradband pulses. Mdel-based quantitative relatinship between the "attenuatin slpe", r da/dj, and the vlume fractin f prsity has been established fr bth spherical vids and lng cylindrical vids with elliptical crss sectin [6]. The prsity cntent estimatin technique based n the ultrasnic attenuatin has been experimentally tested n varius CFRP systems with encuraging results [7,8]. In this paper we present an experimental study f using ultrasnic,velcity fr the NDE f prsity in CFRP. Cmpared t attenuatin, velcity has been essentially undevelped as a tl fr the NDE f prsity in cmpsites. A cmmn cncern with using velcity has been its dependence n ther material prperties such as variatins f fiber vlume fractin. ne theretical calculat in [9] shwed that the lngitudinal velcity in graphite-epxy changes nly very slightly with fiber vlume fractin in the range f interest. In this paper we use the terms graphite-epxy and carbn-epxy interchangeably. In this wrk lngitudinal velcity was measured as a functin f prsity cntent and frequency in bth wven cmpsite laminates and laminates made f unidirectinal prepreg tapes. 'The velcity measurements were als made with bradband pulses; in fact, the same experimental data were used fr 1567

2 calculating bth the attenuatin and velcity. It was therefre natural t test the Kramers-Krnig relatinship that relates attenuatin and velcity changes. EXPERIMENTAL METHD Ultrasnic velcity in CFRP laminates was measured in an immersin tank using a "substitutin technique" in the thrugh- transmissin mde. The measurement cnfigurat in is shwn in Fig. 1. Tw unfcused bradband transducers were set up t face each ther and separated by a distance f typically 15 cm. The transducers used were 6.35 mm (1/4") diameter prbes with a center frequency f 5 r 10 MHz. The transmitting transducer was driven by a spike vltage pulse. The pulse transmitted thrugh water nly was digitized and stred in the cmputer as the reference signal. The cmpsite panel was then inserted perpendicular t the acustic path. Because the speed f sund in the cmpsite is greater than that in water, the pulse transmitted thrugh the sample appeared earlier in time than the reference signa1. This "sample signal" was als digitized and stred. Frequency dependent attenuatin and velcity were then cmputed frm the FFT f these signals. When the lineshapes f the reference signal and the sample signal are similar, the velcity in the sample Vs may be cmputed frm the time difference 6t between crrespnding pints f the wavefrms using the fllwing simple equatin: where Vw is the speed f sund in water and d is the sample thickness. Equatin (1) can be derived easily frm time f flight cnsideratin. This technique is quite cnvenient fr measuring the sund velcity in thin cmpsite laminates because the reference signal and the sample signal d nt appear at the same time and the time difference between them can therefre be very small withut the cncern fr verlapping. ( 1 ) v,. = Velcity in Waler v, = Velcily in Slid d! = Difference in Pulse Arrival Time Fig. 1. Velcity measurement using the substituting methd. 1568

3 When the cmpsite laminate is thicker r cnta ins prsity, the thrugh-sample signal will have a different lineshape than the reference signal. This is a result f the frequency dependence f the attenuatin and velcity in the sample which changes the spectral cntent and hence lineshape f the pulses. In this case the measurement f t becmes ambiguus and ne shuld measure the velcity as a functin f frequency using a phase spectrscpic technique [10]. In the phase spectrscpic methd the phase velcity f the lngitudinal wave prpagating perpendicular t the cmpsite laminate plate is btained by calculating the phase difference '.(Ul)-'r(Ul) between the sample signal and the reference signal. This phase 0.40 Effect f 271' Errr 0.36 'Iii' Gr/, Wven Lminte (0.0 % Vids) E 'u i > 0.28., cn.r: " ' Fig Frequency (MHz) Methd fr remving ambiguity in phase. difference, t within an uncertainty f ±2nm, m being an integer, is btained by perfrming a decnvlutin f the tw signals. The phase uncertainty f an integer multiple f 2n arises because the spectral cntents f the pulses d nt extend all the way t zer frequency. The phase velcity v(vu) is given by v( Ul) = [l/v w - {,.( Ul) - 're Ul) ± 2nm}/Uldf I (2) where vu is the angular frequency and the subscripts s and r refer respectively t the sample signal and the reference signal. The crrect value f m can usually be determined by cmpar ing the phase spectral velcity v(vu) and the apprximate velcity btained frm a simple time-f-flight measurement. Figure 2 shws the effects f errrs f 2n n the phase velcity in a vid-free graphite laminate. The center curve is the velcity with n errr in the integer m in Eq. (2) and the upper and lwer curves are respectively the results with an errr f +2n and -2n in the phase. The slid dts are the time-f-flight results using three different transducers. It is clear that any errr in the phase can be eliminated by cmparing with the time-f-flight result. 1569

4 RESULTS T study the effects f prsity n ultrasnic velcity, measurements were made n fur cmpsite systems: wven graphite-epxy with - 5% vids, wven graphite-plyimide with 0-11% vids, quasi-istrpic graphite-epxy with 0-4% vids and unidirectinal graphite-epxy with 0-6.5% vids. Figure 3 shws the phase velcity f lngitudinal waves prpagating nrmal t wven graphite-epxy laminates cntaining up t 5% vids. T demnstrate that the measured velcity results d nt depend n the particular type f transducers used, Fig. 3 shws the measurement results btained with bth 10 MHz transducers and 5 MHz transducers. As can be seen, the agreement is gd. Results in Fig. 3 shw that the velcity decreases with increasing vid cntent and the velcity dispersin is greater fr laminates with mre vids. The velcity data btained with the phase spectral technique were cmpared with pint-by-pint tneburst measurements made at different frequencies. The agreements were very gd. Measurements were als made in quasi-istrpic graphite-epxy laminates cntaining % vids, the results are similar t that in Fig. 3. The crrelatin f decreasing velcity with increasing prsity was als bserved in a set f 10 wven graphite-plyimide laminates. T make a quantitative crrelatin between the velcity change and vid cntent, the fractinal velcity decrease v/v (expressed in percents) with respect t the velcity in a vid-free sample was pltted against the vid cntent. Figure 4(a) shws the results fr three cmpsite systems at a frequency f 8 MHz. As a cmparisn, the same plt was als ma de fr a frequency f 4 MHz, as shwn in Fig. 4(b). A review f the results at different frequencies revealed that at higher frequencies the different systems fllwed almst the same slpe; at lwer frequencies, hwever, each material system seemed t fllw a different slpe. The explanatin f the prsity-induced velcity changes in cmpsites still awaits mre theretical mdeling. Althugh theries are available fr ultrasnic velcity dispersin in therwise hmgeneus slids cntaining prsity [11], the same has nt been develped fr cmpsites. 320 Ultrasnic phase velcity in wven carbn/epxy laminates 300 'Cii' { E 280 u Qi > <Il <Il a ".. #, " Trnsducers used Slid lines - 5 MHz Dashed lines - 10 MHz Fig Frequency (MHz) Phase velcity f lngitudinal waves prpagat ing perpendicular t wven graphite-epxy laminates as a functin f frequency and vid cntent

5 30 25 L:::. V/V vs. Vid cntent at 8 MHz "-../ > <J Cr/Epxy, Quasi-istrpic Cr/Epxy, Wven 6 Cr/plyimide, Wven.6" " /" " :4t/ :>'.,.. 6 " 6ţ;,,1-. " " ",,5' a Vid cntent (%) A V/V vs. Vid cntent at 4 MHz... "-../ > <J Cr/Epxy, Quasi-istrpic Cr/Epxy, Wven 6 Cr/plyimide, Wven 5 Fig. 4. b Vid cntent (%) Velcity change versus vid cntent f cmpsites at 8 MHz (a) and at 4 MHz (b). 1571

6 'Iii' E 'u Qj :;> II) '".r CMPARISN F VELCITY GR/PLYIMIDE, WVEN LAMINATES VID % :::.:=.::... :::""" 2.36 :.. :::::::::: SLID lines - MEASURED DASHED lines - THRUGH K-K Fig L-.l.-..l-...L......J... -L.. --J Frequency (MHz) Cmparisn f measured velcity in graphite-plyimide cmpsites with prsity and calculated velcity using Kramers-Krnig relatin and w.=5 MHz. la THE RELATINSHIP BETWEEN ATTENUATIN AND VELCITY CHANGE --THE KRAMERS-KRNIG RELATIN It is well knwn that ultrasnic attenuatin and velcity are related by the Kramers-Krnig relatin. In the general Kramers-Krnig relatin the velcity change is prprtinal t an integrat in ver frequency frm zer t infinity f a(w)/w 2 A simpler frm f the Kramer-Krnig relatin, knwn as the lcal apprximatin, relates the velcity change and the attenuatin ver a finite frequency range [12]. (3) where C(w) and C(w) are respectively the velcities at frequencies w. and (A). In this wrk the lcal apprximatin is applied t the attenuatin and velcity f cmpsites cntaining prsity. Figure 5 shws the phase velcity in wven graphite-plyimide cmpsites with 0-9.7% vids as measured by 5 MHz transducers. Als shwn in Fig. 5 are the calculated velcity using the Kramers-Krnig relatin and a reference frequency w. f 5 MHz. This calculat in used frequency dependent attenuatin data btained previusly (8) and the cmparisn is "nrmalized" at w. = 5 MHz. These results shw that the lcal apprximatin f the Kramers-Krnig relatin hlds in prus cmpsites where the velcity dispersin is quite large. CNCLUSIN Phase spectrscpic methd is applied t bradband thrugh-transmissin ultrasnic measurements in cmpsites cntaining prsity. The measurements yield frequency dependent velcity ver the effective band f the transducers used. The vid cntents in CFRP are fund t crrelate with changes in the ultrasnic phase velcity. With increasing vid cntent, the velcity decreases substantially. In additin, the velcity in CFRP cntaining vids is fund t be mre 1572

7 dispersive than that in vid-free cmpsites. Fina11y, the re1atinship between the u1trasnic attenuatin and the ve10city change is cmpared t that described by the lcal apprximatin f the Kramers-Krnig re1atin. ACKNWLEDGEMENT This wrk was supprted by the Center fr NDE at Iwa State University and was perfrmed at the Ames Labratry. Ames Labratry is perated fr the U. S. Department f Energy by Iwa State University under Cntract N. W-7405-ENG-82. REFERENCES 1. N. C. Judd and W. W. Wright, "Vids and their effects n the mechanica1 prperties f cmpsites -- an appraisa1", SAMPE Jurna1, JanjFeb pp G. W. Brasse11, J. A. Hrak and B. L. But1er, "Effects f prsity n strength f carbn-carbn cmpsites", J. f Cmpsite Materia1s, 2, (1975). 3. H. Yshida, J. gase and R. Hayashi, "Statistica1 apprach t the re1atinship between ILSS and vid cntent f CFRP", Cmpsites Science and Techn1gy,, (1986). 4. David K. Hsu and Kevin M. Uh1, "A mrph1gica1 study f prsity defects in graphite-epxy cmpsites", Reviewf Prgress in Quantitative NDE, VI 6, D.. Thmpsn and D. E. Chimenti, eds., (P1enum press, New Yrk, 1987), pp D. E. W. Stne and B. C1arke, "U1trasnic attenuatin as a measure f vid cntent in carbn fiber reinfrced p1astics", Nndestructive Testing, VI. 8, pp S. M. Nair, D. K. Hsu and J. H. Rse, "U1trasnic characterizatin f cy1indrica1 prsity -- a mdel study", Review f Prgress in Quantitative NDE, VI. 6, D.. Thmpsn and D. E. Chimenti eds., (P1enum press, New Yrk, 1987) pp D. K. Hsu and S. M. Nair, "Evaluat in f prsity in graphite-epxy cmpsites by frequency dependence f u1trasnic attenuatin", ibid, pp D. K. Hsu, "U1trasnic measurements f prsity in wven graphite-p1yimide cmpsites", Review f Prgress in Quantitative NDE, VI. 7, (P1enum press, New Yrk, 1988) pp B. G. Martin, "U1trasnic wave prpagatin in fiber reinfrced slids cntaining vids", J. App1. Phys., (1977). 10. J. F. Muratre and H. R. Car1etn, "Phase spectrscpy in lssy media", IEEE U1trasnic Sympsium, pp C. M. Sayer and R. L. Smith, "The prpagat in f u1trasund in prus media", U1trasnics, Sept pp M. ' Dnne11, E. T. Jaynes and J. G. Mi11er, "Kramers-Krnig re1atinship between u1trasnic attenuatin and phase ve1city", J. Acust. Sc. Am. (3), (1981). 1573