J. C. Moulder,1 P. J. Shull,1 and T. E. CapObianc02

Transcription

1 UNIFORM FIELD EDDY CURRENT PROBE: EXPERIMENTS AND INVERSION FOR REALISTIC FLAWS* INTRODUCTION J. C. Mulder,1 P. J. Shull,1 and T. E. CapObian02 1Frature and Defrmatin Divisin 2Eletrmagneti Tehnlgy Divisin Natinal Bureau f Standards Bulder, Clrad Unifrm field eddy urrent (UFEC) prbes perate by interrgating flaws with a spatially unifrm eletrmagneti field. Their use in quantitative NDE is partiularly attrative beause theretial mdels f the field-flaw interatin are greatly simplified by the assumptin f a unifrm field. This in turn leads t muh simpler invers in prtls fr determin ing flaw sizes frm measurements. A thery fr the interatin f a unifrm interrgating field with three-dimensinal surfae flaws in the limit f small skin depth (a/6» 1) has been develped by B. A. Auld and his -wrkers at Stanfrd University [1-3J. Last year, E. Smith reprted the first quantitative measurements n fatigue raks and EDM nthes with an "essentially" unifrm field eddy urrent prbe, demnstrat ing exellent agreement between thery and experiment [4J. We reprt here the results f an extensive series f measurements t evaluate in detail the use f unifrm field eddy urrent prbes fr quantitative NDE. As desribed in a mpanin paper [5), we designed and built tw UFEC prbes that perate in the frequeny ranges f 0.5 t 4 and 2 t 8 MHz. The prbes were alibrated with either ylindrial r part-spherial reesses frmed by eletrial-disharge mahining. We used these prbes t study a number f surfae-nneted, semielliptial EDM slts and atual fatigue raks in a variety f materials, inluding 7075 A1, Ti-6A1-4V, and Haynes 188 allys. Beause f the limited spae available, we reprt nly the results fr high-frequeny measurements n EDM nthes and fatigue raks in Ti-6A1-4V. Flaws ranged in length frm 0.5 t 3.0 mm and in depth frm 0.25 t 1.5 mm. AII. measurements and alibratins were perfrmed with an autmati netwrk analyzer. We mpare measured flaw signals with the preditins f Auld's unifrm field thery, and the limits f appliabillty f the thery are determined. We als explre the auray with whih flaw depth an be determined uslng a simple leasţ-squares invers in algrithm. *Cntributin f the Natinal Bureau f Standards; nt subjet t pyright in the United States. 601

2 THEORY The general âz thery fr the interatin f a spatially unifrm magneti field with tw- and three-dimensinal flaws has been develped by Auld et al. [1-3]. In the limit f small skin depth, the hange in prbe impedane aused by a flaw an be represented as (1) where H/I is the magneti field strength per unit urrent, a is the ndutivit" 2 is the flaw length, âu is the flaw width, 6 is skin depth. IO and Iare shape fatrs that depend nly n a/ (a is flaw depth); they must be alulated fr the partiular flaw gemetry. The three terms in Eq. 1 rrespnd rughly t resistive lsses at the rak rners, the wall impedane f urrent flwing ver the flaw surfaes, and Faraday indutin due t the vlume enlsed by urrents enirling the flaw [2]. It is lear frm Eq. 1 that the flaw signal âz is prprtinal t the square f the magneti field strength and inversely prprtinal t the ndutivity f the wrkpiee. âz depends n frequeny nly thrugh the skin depth 6 = {2/~wa. âz depends strngly upn the flaw length, but depends n flaw depth nly thrugh IO and 11 The I's apprpriate t ret angular and semi-elliptial flaws were alulated numerially last year at Stanfrd University and published in referene [3]. This year it was disvered that the values fr IO fr semi-elliptial flaws published last year are in errr fr values f a/ > These were realulated this year by Steve Jefferies at Stanfrd and the new values are shwn in Table 1. Fr use in the invers in f flaw signals, the numerially alulated values f IO and 11 were fit t plynmials by a nnlinear least-squares predure, giving and 2 ~O = (~) (~) (~) (~) (~) (2) (3) Table 1. Values fr the shape parameter IO used in Eq. 1. Curtesy f S. Jefferies, Stanfrd University. a/ I O

3 CALIBRATION Fr quantitative measurements alibratin is extremely imprtant sine, t alulate ~Z fr a partiular prbe, it is neessary t knw H/I. Fr air re prbes, ne may alulate this quantity using the results f Ddd and Deeds fr a vertial il [6] r Burke fr a hrizntal il [7]. But fr ferrite re prbes like the NBS UFEC prbe, analytial expressins fr the field strength are nt available and the field strength must either be measured r alulated numerially. We hse t use a predure first suggested by B. A. Auld [8J and used last year by Smith [4J. The methd nsists f measuring the impedane hange ~z aused by a ylindrial reess f depth greater than the skin depth and alulat ing H/I frm the expressin ~z 2 i (L) 2 (4) 1 where A is the surfae area f the reess and d is its depth. This frmula was adapted by Auld frm a mirwave perturbatin thery slutin fr a smth dimple in the surfae f a perfet ndutr [8J. Smith fund that t btain agreement f alulated and measured flaw signals, the numerial fatr f.2 in Eq. 4 had t be replaed by a fatr f 1 [4J. We nfirmed his result this year in aur measurements n ylindrial reesses in Ti-6A~-4V ( = 5.9 x 105 S/m). Fr a reess 0.78 mm in diameter and 0.83 mm deep (d/ > 2), the values f H/I alulated using the fatr f 1 in Eq. 4 gave exellent agreement f alulated and experimental ~Z values fr a ser ies f EDM nthes. These results are shwn in Fig. 8 f referene [5J. Fr anther reess 0.77 mm dia. x 0.40 mm deep (d/ = 1), a fatr f 1.2 in Eq. 4 gave gd agreement f alulated and measured flaw signals. Sine these reesses had t be quite deep ta meet the riterin d/ > 2, the disrepany between Eq. 4 and measurement may be related t the fat that the ylinders very little resemble a smth dimple. T apprximate mre lsely the theretial assumptins, we made reesses in the shape f a spherial ap in the same titanium ally. Calibratin with a reess that was deeper than the skin depth (1.46 mm surfae diameter, 0.89 mm radius, and 0.37 mm depth) gave exellent agreement f thery and experiment fr the same EDM slts when a fatr f 2 was used in Eq. 4 and with the apprpriate vlume substituted fr Ad. Fr a spherial ap apprximately the same depth as the skin depth (0.67 mm surfae diameter, 0.42 mm radius, and 0.19 mm depth), a fatr f 4 gave the best results. Thus, we find that Eq. 4 may be generalized t (5 ) where V is the vlume f the reess (either ylindrial r spherial) and C is an empirial shape fatr whse value depends an the shape and depth f the reess relative ta O, as desribed abve. Reently, R. Cllins and his lleagues at University Cllege Lndn have derived analytial expressins fr the eletri and magneti fields inside axisymmetri surfae flaws (inluding ylinders and spherial aps) interrgated with a unifrm field in the small skin depth limit [9, 10J. This raises the pssibility f alulat ing ~Z exatly fr ylindrial and spherial-ap reesses. 603

4 Anther pssible alibrat in methd is t measure âz fr an EDM nth f knwn dimensins, then t determine H/I by fring the alulated flaw signals int agreement with experimental signals. Results f alibrating the NBS UFEC prbe using these different methds are shwn in Figure 1. Agreement is exellent amng the different alibrat in predures, exept at the lwest frequenies, where d/~ < 2 fr tw f the artifats. EXPERIMENT As desribed in the mpanin paper [5], ali measurements were made with a mputer-ntrl led autmati netwrk analyzer that measured prbe impedane at 401 disrete frequenies distributed unifrmly ver the frequeny range f 2 t 8 MHz. Eah measurement was the result f signal averaging 64 times; n fewer than five independent measurements n eah flaw were smthed with a ten-pint running average and then averaged t btain the final result. A measurement nsisted f measuring the impedane f the prbe n and ff the flaw ver the stated frequeny range, and then mputing the vetr differene f the tw impedanes. The prbe was psitined by a mputer-ntrl led x-y psitiner. Liftff in the z diretin was ntrlled with a manual mirpsitiner; tilt in the x-z and "y-z planes uld be independently adjusted. As desribed in referene [5], the prbe was extreffiely sensitive t hanges in tilt r liftff during the measurements and it was neessary t ntrl these parameters very lsely. A series f five semi-elliptial EDM slts were prepared in a speimen f Ti-6AR.-4V 7.5 m wide, 21" m lng, and 1 m thik. They ranged in length frm 0.5 t 2.5 mm and in depth frm 0.33 t 1.05 mm; their exat dimensins are given in Table 2 f referene [5]. The fatigue raks that we studied were grwn in similarly sized speimens f Ti-6Ai-4V by W. Rummel and wrkers [11]. They were grwn in antilevered bending. The lengths and estimated depths f these flaws are shwn in Table 2. Lengths were measured ptially during grwth f the raks; depths were estimated frm the lengths using the expeted aspets rati f al = Three additinal fatigue raks in a Ti-6A~-4V speimen 3.5 m x 23 m x 0.6 that were measured are als shwn in Table 2 (MM2A-C). RESULTS The magnitude and phase" f âz fr fur f the semi-elliptial EDM slts are shwn in Fig. 2 and 3, where they are mpared with alulated signals btained using the spherial-ap alibratin methd t determine H/I. Crrespnding results btained using a ylindrial reess t alibrate the prbe are shwn in Fig. 8 f referene [5]. Fr bth alibratin methds the agreement between the alulated and measured magnitude f âz is exellent fr the larger flaws (within ±5 perent). Fr frequenies less than 3 MHz, thery and experiment diverge smewhat wing t the fat that d/~ fr the alibratin reesses fell belw 2.0 at these frequenies. The effet is mre prnuned in the ase f the ylindrial reess alibrat in. The agreement between thery and experiment fr the phase f âz is better fr the spherial alibratln methd, and this is the alibrat in methd we use in the remainder f this paper. Fr the smallest flaw shwn in Figure 2, NBS15D, thery and experiment diverge fr frequenies belw 7 MHz, but at this frequeny a/6 fr this flaw is nly 1.6. This shws that the limits f appliability f the thery extend t a/~ = 1.6, whih is less nservative than the usual estimate f 604

5 Cylinder - Sphere Sphere 2 - EDM Slt 'E ~ I 10.0 O ~.O 8.0 Frequeny Fig. 1. Calibrat in urves f magneti-field intensity per unit urrent fr unifrm field eddy urrent prbe, btained using three different types f artifats. Fig. 2. : N 10.0 <1 -;; Ql 'C :l...,... O> ::>: '" NBS 15A - N8S 15B NBS 15C - NBS 15D Frequeny (MHz) Measurements (slid lines) f the magnitude f the flaw signals frm fur different semi-elliptial EDM slts in Ti-6Ai-4V mpared with theretial preditins (symbls) C Ql E N <l ;; Ql <f) r A - B " - C - O b') 40 ~ Frequeny (MHz) Fig. 3. Measurements (slid lines) f the phase f the flaw signals frm fur different semi-elliptial EDM slts in Ti-6A~-4V mpared with theretial preditins (symbls). 605

6 Table 2. Ti-6A~-4V Fatigue Craks Speimen Length Estimated ID ( mm) Depth (mm) NBSF1A NBSF1B NBSF2A NBSF2B NBSF3A NBSF3B NBSF4A NBSF4B NBSF5A NBSF5B MM2A MM2B MM2C wuld have required perating the prbe at 15 MHz. The exellent agreement between thery and experiment is very enuraging, beause n adjustable parameters were used in alulating flaw signals. A mparisn f measured and alulated flaw signals fr five fatigue raks in Ti-6A~-4V is shwn in Figure 4. Flaw dimensins used fr the alulatins were the ptially measured lengths and estimated depths shwn in Table 2. Flaw width was arbitrarily set t 1 pm. Changing the rak width t 10 pm inreased ~Z by nly 3-4 perent. As shwn in Figure 4, the agreement between thery and experiment is exellent fr these fatigue raks, whih ranged in length frm 1.0 t 1.5 mm. Fr the smallest fatigue raks we examined (NBSF2A and B, results nt shwn) the nditin al > 1.6 uld nt be attained. A similar mparisn fr fur f the larger fatigue raks (2 = mm) is shwn in Figure 5. Fr these fur flaws the measured flaw signal was nsistently lwer than the flaw signal alulated using estimated flaw sizes. The differene in depth neessary t aunt fr the disrepany ranged frm 32 t 42 perent, as determined by using the inversin predure desribed belw. These differenes are disussed mre fully in the next setin. INVERSION With the exeptin f the puzzling results shwn in Figure 5, the agreement between thery and experiment is exellent fr bth EDM slts and fatigue raks. This suggests that a simple invers in predure may be devised t determine the flaw sizes frm eddy urrent measurements. Pssible apprahes t the mplete invers in prblem have been nsidered befre [2J. In priniple, it is pssible t derive bth the length and depth f a fatigue 606

7 O)... Fig O Thery - Experi.llnt 0. 1 L ~ N < 'O ~ :: a. 10. O I Frequeny (MHz) Cmparisns f thery and experiment fr five fatigue raks grwn in Ti-6Ai-4V. AII r aks were less than 1.5 mm lng. Fig ~ N <l -:; :.. :: '" 'O Z 100 la ţ- 1 t Best Flt 4tual Fie", Silit - EXl:ler l l1ent 6 n N8SF "~ 1 la l NBSFtB 100 "... n u MM l- a a a a a "... NBSFIA Frequeny (MHz) Cmparisn f measured and predited flaw signals fr fur fatigue raks in Ti-6H-4V. All raks were greater than 2.0 mm lng. I

8 rak frm measurements at three r mre frequenies. Hwever, as shwn in Eq. 1, ~Z depends strngly n flaw length, but nly indiretly n flaw depth thrugh the dependene f IO and 11 n ale. Rather than attempting a full invers in, we assumed that the length f the flaw uld be determined easily with a nventinal, nnunifrm field prbe using the imaging nepts suggested by Auld t determine flaw length frm the shape f the flaw prfile btained frm a se an dwn the length f the flaw [12J. lf the flaw length is knwn, it is quite simple t invert the measurements t btain flaw depth. This is the apprah we tk. Flaw length was assumed t be the atual length f the flaw in the ase f the EDM nthes r, in the ase f fatigue raks, the' ptially measured length. Flaw depth was then determined by minimizing the rt-mean-square differene between measured and alulated flaw signals. This was amplished n a prtable mirmputer using a mmerial spread sheet prgram t demnstrate the simpliity f the invers in predure. Results f using this invers in methd t estimate the depths f the EDM nthes we measured are shwn in Fig. 6a. In ali but ne ase the predited depths are within ±O.l rm f the atual depth. Results fr the invers in f the fatigue rak meas urements are shwn in Fig. 6b. Fr the smaller flaws (a < 0.5 rm), the invers in results are als exellent, but fr the Iar ger flaws the dis repanies firs t shwn in Fig..5 are evident. The nature f the disrepany in the invers in results is suh that measured flaw signals underpredit the flaw depths by up t 42 perent. Beause this an have serius impliatins when using eddy urrent methds t size flaws, we brke pen fur flaws, three f whih exhibited serius disrepanies, t determine their atual sizes. The results are listed in Table 3; they shw that in ali ases the atual flaw dimensins were lse t the estimated dimensins. The flaw lengths listed in Table 3 under the heading "NBS Preditin" were determined by ething the speimen surfae and then measuring the flaw length with the speimen in an unladed nditin, us ing a traveling mirspe. Flaw depths were then alulated by using this length as an input t the invers in predure desribed befre. This methd E D - NBS15 D - Brken D - MM4 D - Unbrken E 1.00 ~ S.OO C. II> Q) a 'D 'C Q) Q) D <..> <..> ; ; Q).. a.... a E D O 0.00 ~ Fig. 6. -L ~ ~ -L L- ~ ~ -'-_--L ~_-L I-.,_~ Atual Depth (mm) b A tua 1 Depth (nun) Inversin results fr (a) semi-elliptial EDM slts and (b) fatigue raks in Ti-6A~-4V. Flaw depths predited by the invers in predure are pltted against the atual depths, r, in the ase f unbrken fatigue raks, the estimated depth. 608

9 Table 3. Ti-6A~-4V Fatigue Crak Results Speimen MM Estimate NBS Preditin Atual Per ent ID 2 a 2 a 2 a Differene (mm) (mm) (mm) (mm) (mm) (mm) ( Depth) NBSF1A % NBSF1B % NBSF5A % NBSF5B % underestimated the flaw depths by up t 42 perent.- Fr ne f the flaws that was brken (NBSF5A), the predited depth was nly 0.1 mm less than the atual depth; this is nsidered aeptable agreement. The disrepany in inverted flaw depths is diffiult t explain. The exellent agreement between thery and experiment fr EDM slts and smaller fatigue raks wuld seem t indiate the thery is valid as lng as the nditin a/6 > 1.6 is met. There is n reasn t expet the thery t break dwn fr fatigue raks, sine we fund gd agreement in sme ases. It is diffiult t asribe the prblem t measurement errrs, sine the disrepany arises fr larger flaws, where. the signal-t-nise rati is highest. It als seems unlikely that randm errrs wuld.result in unifrmly underestimating flaw sizes. One pssible explanatin that is nsistent with the bservatins is that lsure fres n the rak faes aused partial ntat, shrt-iruiting the eddy urrents flwing arund the flaw. That this shuld nly ~r fr the lnger raks is nsistent with the fat that the lnger raks had a greater stress intensity fatr dur ing grwth. This uld ause greater plasti defrmatin at the rak tip, leading t greater lsure fres. But, befre this an be nsidered a valid explanatin f the bserved disrepanies, a mre nlusive experiment needs t be perfrmed demnstrat ing that 6Z hanges when the rak is pened under lad. CONCLUSIONS A UFEC prbe was designed and fabriated at NBS and used t study a series f semi-elliptial EDM slts and fatigue raks in Ti-6A~-4V. Frm this study the fllwing nlusins emerge: Calibrat in f a UFEC prbe an be arried ut with any f three alibrat in artifats -- ylindrial reess, spherial ap, r EDM slt. Empirial shape fa trs needed t alulate H/I were determined fr ylindrial and spherial reesses. Measurements n ali EDM slts and thse fatigue raks less than 1.5 mm lng were in exellent agreement with the preditins f Auld's unifrm field thery fr a/6 > 1.6. Fr larger fatigue raks, measurements underestimated flaw depth by up t 42 perent. Crak lsure fres ating n the lnger raks is ne pssible explanatin that is nsistent with experimental bservatins. A simple methd fr inverting UFEC measurements t btain flaw depth when the length is knwn was demnstrated. Predited depths were within ±O.1 mm in the absene f pssible lsure effets. 609

10 ACKNOWLEDGMENTS This wrk was spnsred by the Center fr Advaned Nndestrutive Evaluat in, perated by the Ames Labratry, USDOE, fr the Air Fre Wright Aernautial Labratries/Materials Labratry under Cntrat Number W ENG-82 with Iwa State University. Fatigue raks were prvided by W. Rummel, B. Christner, and D. Lng f Martin Marietta Denver Aerspae. We thank W. Rummel fr numerus helpful disussins n eddy urrent methds and fr his ntinuing interest in this wrk. We are grateful t S. Jefferies f Stanfrd University fr ntributing new alulatins f the shape fatr used in Eq. 1. We espeially thank B. A. Auld f Stanfrd University fr ntinuing enuragement and fr prviding many useful insights int the theretial mdel and the alibrat in methds used here. We als thank E. Smith f Lkheed-Sunnyvale fr helpful disussins n the experiment. We were aided in this study by the skilled prgramming f S. Ciira and by the areful measurements ntributed by C. Cherne. REFERENCES 1. B. A. Auld, F. G. Muennemann, and D. K. Winslw, J. Nndestrutive Evaluatin 2, 1 (1981). 2. B. A. Auld, F. G. Muennemann, and M. Riaziat, Quantitative mdeling f flaw respnses in eddy urrent testing, in: "Researh Tehniques in Nndestrutive Testing, VI. VII," R. S.Sharpe, ed., Aademi Press, Lndn (1984). 3. B. A. Auld, S. Jefferies, J. C. Mulder, and J. C. Gerlitz, Semielliptial surfae flaw EC interatin and inversin: thery, in: "Review f Prgress in Quantitative Nndestrutive Evaluatin 5A,"" D. O. Thmpsn and D. E. Chimenti, eds., Plenum Press, New Yrk (1986). 4. E. Smith, Appliatin f unifrm field eddy urrent tehnique t 3-D EDM nthes and fatigue raks, in: "Review f Prgress in Quantitative Nndestrutive Evaluatin 5A:" D. O. Thmpsn and D. E. Chimenti, P. C. S. B. R. R. W. B. eds., Plenum Press, New Yrk (1986). J. Shull, T. E. Capbian, and J. C. Mulder, Design and haraterizatin f unifrm field eddy urrent prbes, these' preedings. V. Ddd and W. E. Deeds, J. Appl. Phys. 39, 2829 (1968). K. Burke, J. Phys. D: Appl. Phys. 19, 1159 (1986); A. Auld, Stanfrd University, Stanfrd, CA 94305, private mmuniatin. Cllings, D. Mi rshekar-syahkal, and D. H. Mihael, Pr. R. S. Lnd. A393, 159 (1984). Cllins, D. H. Mihael, D. Mirshekar-Syahkal, and H. G. Pinsent, J. Nndestrutive Evaluatin 5, 81 (1985). D. Rummel, B. K. Christner, and D. L. Lng, Cmparative respnses frm raks and EDM slts as measured by eddy urrent methds, these preedings. A. Auld, G. MFetridge, M. Riaziat, and S. Jefferies, Imprved prbeflaw interatin mdel ing, invers in pressing, and surfae rughness lutter, in: "Review f Prgress in Quantitative Nndestrutive Evaluatin 4A,n-D. O Thmpsn and D. E. Chimenti, eds., Plenum Press, New Yrk (1985). 610