CRACK LENGTH DETERMINATION BY ULTRASONIC METHODS. D.K. Rehbein, R.B. Thompson and O. Buck Ames Laboratory-USDOE Iowa State University Ames, Iowa 50011

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1 CRACK LENGTH DETERMINATION BY LTRASONIC METHODS D.K. Rehbein, R.B. Thmpsn and O. Buck Ames Labratry-SDOE Iwa State niversity Ames, Iwa INTRODCTION Accurate calculatin f the stress intensity factr n a given cmpnent under lad relies n an accurate size determinatin f the flaws present in the cmpnent The challenge t the NDE cmmunity has been develpment f reliable techniques t prvide that accurate size determinatin. Many research grups have investigated this prblem using ultrasnic methds with summaries f their techniques and results prvided by varius authrs [1-3]. In general, the techniques develped fall int three general categries; (1) determinatin f crack length frm signal amplitude measurements, (2) determinatin f crack length frm time-f-flight measurements, and (3) determinatin f crack length using diffracted waves. Sketches f representative techniques in each categry are shwn in Figure 1. (1 ) (2) Figure 1. Representative techniques used fr determining crack length. (1) Signal Amplitude (Ref. 4). (2) Time f flight (Ref. 5). (3) Diffracted wave mdulatin (Ref. 6). (3) Review f Prgress in Quantitative Nndestructive Evailllin, Vl. 12 Edited by D.O. Thmpsn and D.E. Chimenti, Plenum Press, New Yrk,

2 Crack Len~ Frm Si~al Amplitude Figure 1 (1) is a sketch f the technique develped by Lumb and cwrkers [4]. They used a cmpressin wave t mnitr the grwth f a thrugh-the-thickness crack. A calibratin curve f the ultrasnic signal amplitude versus crack depth was develped using milled slts and destructive measurements f part-thrugh fatigue cracks t determine the depth f penetratin f inservice cracks. They claim measurement f grwth increments accurate t +/ mm and larger amunts f grwth accurate t +/-0.25 mm. Particular prblems cncerning this technique were determined t be the stability f the cupling and temperature induced drift due t attenuatin and velcity in the wedges. Additinally, crack clsure cntributes t inaccuracy f the crack depth measurement since cntact between the crack faces allws additinal energy t be transmitted that wuld be blcked if the crack were cmpletely pen. Crack Length Frm Time-f-Flight Crack length measurement using the technique shwn in Figure 1 (2) as develped by Silk [5] determines the crack length by the time f flight f the wave diffracted by the crack tip and the wave reflected frm the back surface. The crack length a is calculated accrding t where Cl is the acustic velcity f the wave and t is the time f flight. This result can be checked by using where dt is the difference in flight time f the waves diffracted frm the crack tip and reflected frm the back surface. It is recgnized that any inaccuracies in the measurements f the separatin distance f the receiver frm the crack r the acustic velcity wuld be reflected in the calculated crack length. It is recmmended that the technique be calibrated using saw slts cut int the material f interest in rder t crrect fr pssible texture changes. It is als pssible that clsure in the crack wuld effectively braden the diffracted wave being received since diffractin wuld be ccurring at mre than ne psitin in the crack, rendering the time measurement mre difficult. If the structure is under lad, it is pssible t measure the crack depth t +/-0.2 mm. Crack Length Frm Diffracted Waves Achenbach and cwrkers [6] have utilized the elastdynarnic ray thery [7] t predict the scattering field fr the situatin shwn in Figure 1 (3). In this cnfiguratin, the crack is cmpletely subsurface and the first arriving wave at the receiving transducer is due t the interference f the lngitudinal rays diffracted at the crack tips. This wave exhibits a mdulatin in the frequency dmain with perid, p, (1) (2) p = rc/a [cs 8 - sin 8 0 ] (3) Since bth a and 8 0 are unknwn, tw measurements at different angles are necessary t quantify the crack parameters but with inclusin f the apprpriate attenuatin values, agreement between their mdel and the experiment was almst perfect. It is imprtant t nte, hwever, that ne f the bjectives f the riginal theretical wrk was t generate a better understanding f the scattering at the tips f fully pen cracks embedded in the bulk f a material. Clsure in such a crack will cntribute additinal lw 2160

3 amplitude diffracted waves in the clsure regin, making the determinatin f the crack length virtually impssible. Extended Clsure Previus wrk [8] has shwn the existence under certain grwth cnditins f a greatly extended clsure regin, up t several mm. This extended clsure regin necessitates the applicatin f a tensile lad t pen the crack in rder fr the earlier techniques t make a determinatin f the psitin f the crack tip. The wrk currently underway is an attempt t address this prblem and determine the crack tip psitin withut the necessity fr the applicatin f tensile lading. CRRENT WORK Cnsiderable effrt has been made t characterize varius aspects f the gemetry present at the tip f a fatigue crack using a mdificatin f earlier methds suggested by Thmpsn and Fiedler [9]. This methd in cnjunctin with the "distributed spring mdel" f Baik and Thmpsn [10] characterizes the cnditins in the clsure regin near the crack tip by the use f a brad-band pitch-catch transducer system with stepper mtr translatin f the cracked sample. This cmbinatin allws characterizatin f the transmissin respnse f a fatigue crack as shwn in Figure 2. The left side f the figure is a sketch f the experimental apparatus with tw sets f experimental results shwn n the right side. The tp graph is the respnse frm a saw slt while the bttm figure shws the respnse f an actual fatigue crack grwn at cnstant M<.. TRANSMIT x RECEIVE FATIGE CRACK e- ~ 1.0 E r.l 0.8 () 0.6 ~ 0.4 Sl fq 0.2 ~ e- ~ 1.0 ~ _ 0.8 () 0.8 ~ 0.4 Sl fq 0.2, \, ~,, \~ - 4!1Hz - - 6!1Hz !1Hz e- 0.0 L--,--"",---,---,---,---I:."""';;:;"';;::=:s:::::.=l a DISTANCE. em \ - 4!1Hz - - 6!1Hz Hz ~ 0.0 L...-.I--"~--'---'---'---i:..."'-"-.::;...;;J a W DISTANCE. em Figure 2. Experimental arrangement and typical respnse frm saw slt (tp) and fatigue crack (bttm). 2161

4 The actual differences between the tw transmissin respnses are rather subtle in Figure 2 but are caused by dramatic differences in the samples themselves. The tp respnse, that frm a saw slt, shws a crss-ver f the curves at a transmissin cefficient f 0.5 due t the verlapping f the effective spt sizes at the tip f the cmpletely pen slt. Each spt is half n and half ff the slt at the same psitin leading t a transmissin cefficient f 0.5 fr each frequency at that psitin. Hwever, because f clsure, the crack shws a transmissin cefficient f 0.5 that changes psitin with frequency due t the changes in transmissin characteristics with frequency. The crss-ver therefre is elevated abve 0.5. In additin, there is a mre gradual change frm perfect transmissin (T=1.0) t n transmissin (T=O.O) in the respnse frm the fatigue crack. Characterizatin f the clsure in the transmissin respnse curve has been accmplished using the distributed spring mdel based n the wrk f Baik and Thmpsn [10]. Mdeling the cntact in the clsure regin leads t the expressin -00 (4) 00 where rn is the transmissin thrugh a given psitin nrmalized by the transmissin thrugh the uncracked ligament, C is a cnstant cntaining infrmatin n the material parameters and the transducer characteristics, x 1 is the center psitin f the transducer and w is the effective radius f the ultrasnic beam. a(x) is characterized accrding t a(x) = ltpvf/x:(x) (5) with p being the material density, v the acustic velcity and f the frequency. x:(x) is the distributed spring cnstant applied in the cracked regin f the sample and is expressed by x: is equal t K() at the crack tip and decreases accrding t the decay cnstant ~ as the beam mves deeper int the crack. In rder t fully characterize the crack, then, it is necessary t accurately determine the crack tip psitin in rder t begin applying Eq. (6) ver the prper regin. (6) EXPE~ENTALRESLTS Figures 3 and 4 shw experimentally determined transmissin respnse curves frm cracks in three different samples with n external lading. Figure 3 shws tw respnses frm fatigue cracks grwn in 2024-T6 aluminum using a cnstant M<. The material was in the as-rlled cnditin with the crack in the left-hand graph grwn parallel t the rlling directin, i.e., parallel t the elngated grains while the crack in the right-hand graph was grwn perpendicular t the elngated grains. Als shwn are crack tip psitins determined by varius ther means. The psitin labeled ptical was determined n the utside surface f the sample where the crack intersected the surface. A clip gauge was attached at the starter ntch pening with the crack psitin determined by that means labeled. The crack tip psitin labeled fracture was determined by physical measurement f the furthest extent f the crack after fracture f the sample. The x-axis values shwn n Figures 3 and 4 are determined by registratin f the sample using a reflectin scan n a cmer f the sample. This scan is similar t that shwn in the tp f Figure 2 in that the crss-ver f all frequencies ccurs at the same psitin (when the beam is half n the sample) and prvides an accurate determinatin f the sample cmer. The x-axis values then represent the remaining uncracked ligament f the sample. 2162

5 w ~ w z :::> '-' w z '-' :::> 0:: 0 <{ 0:: 0 <{ :::> (Il :::> (Il f- <{ '-' f- <{ '-' 0:: a.. u 0:: 0..- <{ f- f- <{ f- _f- 0::...J :i a.. a::...j...j.. u.. :::> u 0 u.. ::J u ~ w z. -~':::':""''''''', rii ", rii u " u s:: --,=-~... - ~ ~ ~ rii rii \!\,,. 0 0, FREQENCY FREQENCY I ' " ;::?;l "... ;::?;l, 4 MH 4 MH I' 6 MH 6 MH 0:: 10 MH 0:: 10 MH Figure 3. Transmissin respnse and crack tip psitin determined by varius means in 2024-T6 aluminum samples. w '-'w ::J:: 0 <{::J (Il "I- <{.. u 0:: { l- I-...JO::...J a.. u.. ::J ~, FREQENCY 1.0 I! ~. REQENCY \ rii \ rii... 1 I I \ 1", 4 MH 4 MH I".,' 0.6 MH s:: 0.6., 6 MH ~ ~, ', rii 10 MH rii 10 MH c s::, 6 Cil 0.4 i... " _---- " i , ~~ :: :: I ' Figure 4. Transmissin respnse shwing extended clsure and crack tip psitin determined by varius means fr fatigue crack in Mnel. 2163

6 Knwledge f the initial uncracked ligament befre crack grwth then yields a measurement f the crack length. In btl)cases shwn in Figure 3, the ultrasnic determinatin f the crack tip psitin lies clsest t the actual psitin as measured n the fracture surface. The discrepancy between the acustically determined crack length and the actual crack length is within 0.5 mm in each case as cmpared t 1.0 mm by the ther means. The apparent shrtening f the crack as determined acustically is cnsidered t be due t the curvature present in the crack frnt in these samples. The acustic beam may nt be cmpletely illuminating the linear prtin f the crack frnt resulting in an apparently shrter crack than is actually present. The curvature undubtedly results in the greater inaccuracy in the tip psitin as measured by the clip gauge r ptically n the surface. The left side f figure 4 shws the full respnse curve fr a crack grwn in K -Mnel with an expanded view f the respnse immediately arund the crack tip shwn in the right side. This crack exhibits a cnsiderable regin f extended clsure deep int the crack. The crack tip was again measured by varius means with the results shwn. This crack exhibits cnsiderably less curvature in the crack frnt, thereby yielding mre accurate results. In this case, the acustic measurement is within 0.25 mm f the actual psitin again yielding an apparently shrter crack. The clip gauge results shw a smewhat lnger crack than is actually present due t the inherent nise in the measurement. The significance f Figures 3 and 4 lies, hwever, in that the acustic measurements were taken in the unladed cnditin with clsure present in all f the cracks and an extended clsure regin present in the Mnel. This is in direct cntrast t all f the ther measurements f crack tip lcatin (ptical, clip gauge, fracture) being accmplished with the crack in the fully pen cnditin r brken. Other techniquys such as were shwn earlier were als able t measure crack length t within 0.5 mm but in all cases were much mre accurate with the crack in the laded cnditin since these techniques culd nt take clsure int accunt. The distributed spring mdel and experimental technique shwn here explicitly cnsider clsure in the determinatin f the crack length. CONCLSIONS nder the restrictin f being able t perate in thrugh transmissin with fcussed transducers, it has been shwn that the lcatin f the tip f a fatigue crack can be determined t within 0.5 mm in thse cases where curvature f the crack frnt is significant with crrespndingly better accuracy as the curvature decreases. Lcatin f the crack tip is accmplished thrugh use f the distributed spring mdel and als yields infrmatin n the residual stresses due t clsure. The technique used is able t determine the crack length t within +/- 0.5 mm in the unladed cnditin in cntrast t mst f the wrk dne previusly, remving the necessity fr applicatin f a lad sufficient t fully pen the crack. ACKNOWLEOOEMENT Ames Labratry is perated fr the. S. Department f Energy by Iwa State niversity under cntract W-7405-ENG-82. This wrk was supprted by the Office f Basic Energy Sciences. REFERENCES 1. J.M. Cffey, in The Measurement f Crack Length and Shape During Fracture and Fatigue, edited by C. J. Beevers (Chamelen Press, Ltd., Lndn, 1980) p O. Buck and B. R. Tittman, in Advances in Crack Length Measurement, edited by C. J. Beevers (Chamelen Press, Ltd., Lndn, 1982) p

7 3. O. Buck, in Fracture Mechanics: Micrstructure and Micrmechanisms, edited by S. V. Nair, J. K. Tien, R. C. Bates and O. Buck (American Sciety fr Metals, Metals Park, OH, 1987) p R. F. Lumb, R. J. Hudgell and P. Winship, in Prceedings 7th Internatinal Cnference n NDT, Paper H-01, Warsaw, M. G. Silk, in Research Techniques in Nndestructive Testing, Vl.3, Academic Press, Lndn and New Yrk, 1977, p J. D. Achenbach, L. Adler, D. K. Lewis and H. McMaken, J. Acust. Sc. Am., 66, 1979, p F. C. Karal and J. B. Keller, J. Acust. Sc. Am., 31, 1959, p D. K. Rehbein, L. Van Wyk, R. B. Thmpsn and O. Buck, in Review f Prgress in Quantitative Nndestructive 7B, edited by D. O. Thmpsn and D. E. Chimenti (Plenum Press, New Yrk and Lndn, 1988) p R. B. Thmpsn and C. J. Fiedler, in Review f Prgress in Quantitative Nndestructive Evaluatin 3A, edited by D. O. Thmpsn and D. E. Chimenti (Plenum Press, New Yrk and Lndn, 1984) p J.-M. Baik and R. B. Thmpsn, J. Nndestruct. Eval., 4,1984, p