Determining Limits of Thermal NDT of Thick Graphite/Epoxy Composites

Transcription

1 ECNDT We Deterining Liits of Teral NDT of Tick Grapite/Epoy Coposites Vladiir VAVILOV Institute of Introscopy Tosk Russia Abstract. Te known approac to inspecting tin coposites by using infrared terograpy is etended onto tick grapite/epoy saples were detecting defects at considerable depts requires careful optiiation of a eating procedure and coosing a proper data processing algorit. 1. Introduction Grapite/epoy coposites are widely used in aero space and start to conquer oter application areas suc as autootive industry building sipbuilding etc. Modeling and data processing are indispensable researc stages in developing ost nondestructive testing (NDT) tecniques. In teral NDT ateatical odels allow better understanding te ecaniss wic govern eat transfer in aterials wit subsurface defects tus elping in evaluating detection liits. Analying teral NDT odels enables producing artificial iages wic can serve as references in te verification of data processing algorits including defect caracteriation. In tis paper a closed-up approac to odeling optiiing and data processing is discussed in te application to teral NDT of grapite/epoy coposites.. Higligts of te approac Deterining teral properties of coposites involved. Modeling defect situations. Optiiing an eperiental procedure. Perforing a test. Processing test results. Evaluating teral NDT liits (by studying noise). Caracteriing defects. 3. Deterining coposite teral properties It as been assued tat a grapite/epoy coposite is ortotropic and caracteried by tree coponents of teral diffusivity: y. Te transverse coponent as been deterined by applying bot a rear (R)-surface and front (F)-surface (Parker s) tecnique: = L / τ (F-surface test) (1) = L / (R-surface test) () * in τ1/ 1

2 * were L is te saple tickness τ in is te specific eat transit tie wic specifies te 1/3 F iniu of te artificial function Θ= Fo T Fo = τ/ L is te Fourier nuber τ is te current tie 1/ F R τ is te alf-rise tie specified in T ( τ ) and T ( τ) T ( τ ) are te F- and R-surface teperature evolutions. Te Parker s Eq. () is widely used in deterining teral diffusivity [1] wile Eq. (1) is less known and its efficiency depends on ow noisy is data (bot ultiplicative * and additive noise igt ake difficult finding a τ in value) []. Te grapite/epoy value deterined by te Parker s etod across te etended eated area was /s (see Fig. 1 and Table 1). R IR iage Diffusivity ap a = /s Fig. 1. Converting te R-surface IR iage sequence into te diffusivity ap (TeroFit Pro progra Innovation Ltd Russia) Te details of deterining lateral coponents of grapite/epoy teral diffusivity ave been reported elsewere [3]. Bot spot- and slit-ask tecniques ave been studied and te ost reliable results ave been obtained by using te latter one. Grapite/epoy saples were eated by quart laps troug a slit ask and te R-surface teperature was recorded by a Terovision 570 IR iager wit te acquisition frequency of 6 H. Te algorit applied is illustrated by Fig.. Te spatial Fourier transforation is applied to a recorded IR iage sequence (Fig. a). Due to te presence of te periodical teperature pattern te Fourier spectru clearly reveals te so-called carrier frequency (#5 in Fig. b if a ask contains 5 slits). Te oriontal ( ) teral diffusivity is deterined by te slope of te function wic represents te logaritic ratio LR of two Fourier teperatures obtained for non-ero and ero spatial frequencies [3]: yτ = LR c ( ω y) / ω y (3) were LR = Ln[ T ( ωy τ)/ T (0 τ)] and ω y is te respective spatial frequency. Te eperiental evolution of te LR function is sown in Fig. c and te deterined lateral diffusivities are given in Table 1. Te very convenient feature of Eq. (3) is tat deterining lateral diffusivity is not affected by saple optical sei-transparency and presence of eat ecange on F- and R-surface. If a saple is eated wit a square ask (or wit a laser) bot and coponents can be deterined in a single eperient by analying bot and y spatial directions. In our case te attept of using a powerful Nd laser (pulse duration 1 s) as proven to be inefficient due to dangerously ig teperatures on F-surface and too low teperature on R-surface. Terefore te eating was done wit quart laps for 3 s and only R-surface data were used to calculate diffusivity. Te eperiental procedure was nuerically optiied as described in [3]. y

3 Frequency #5 corresponds to five selected slit ask periods LR N a) b) c) Fig.. Evaluating teral diffusivity by using a slit-ask etod (grapite/epoy saple slit ask period 10 eating tie 3 seconds): N a area of interest Rear surface b - Fourier spectru coponent (N-nuber of iages in sequence) c - LR = Ln[ T ( ωy τ)/ T (0 τ)] as a function of tie Table 1. Eperiental grapite/epoy teral diffusivity values 10-7 /s y 10-7 /s 10-7 /s (±10%) Teral conductivity was easured wit a TPMU-λ-0 unit (Russia) to be λ =0.41 W/(. K). Respectively eat capacity was: Cρ = λ / = J/( 3. K). 4. Modelling defect situations By introducing te deterined values of teral properties over 100 defect situations were odeled using te TeroCalc-6L progra (Innovation Ltd. Russia). Te progra allows odeling a parallelepiped-like si-layer saple wit up to nine parallelepiped-like defects (Fig. 3) uniforly or non-uniforly eated wit a square pulse of a cosen duration (arbitrary eating functions and spatial eating asks are also possible). Te following odel paraeters ave been varied: saple tickness L =5 10 and 15 defect dept l = and 9 defect tickness d = and 0. defect lateral diensions and 5050 eating duration τ =0.01 and 10 s and eating power Q =10 6 and 10 4 W/ respectively. Different carbon fibre lay-outs ave been odelled to siulate tecnologies of producing tick grapite/epoy coposites. Soe eaples of calculated data are presented in Table : Δ T FR - aiu differential signals on F R-surface ( Δ T = Td Tnd Td Tnd-defect and non-defect teperatures) C FR - aiu diensionless running contrasts ( C =Δ T / Tnd ) wit te corresponding optiu observation ties τ. Te data in Table reveals classical relationsips between all involved paraeters tus allowing: 1) optiiing a test procedure by eating power and duration ) evaluating teral NDT liits and 3) developing an inversion algorit for caracteriing defect dept tickness and lateral diensions. 3

4 5. Eperiental set-up and test optiiation Bot F- and R-surface test configurations ave been ipleented to test soe grapite/epoy saples wit ebedded Teflon inserts. R R - surface d b y F F - surface Q ( y τ) Fig. 3. 3D odeling of defects in grapite/epoy coposite Table. Modeling teral NDT of a 5 -tick grapite/epoy coposite l d F F R R F R Δ T τ ( Δ T ) Δ T τ ( Δ T ) F C τ ( C) R o C s C τ ( C) C s s s Flas eating ( τ =0.01 s Q =10 6 W/ ) τ =10 s Q =10 4 W/ ) Square-pulse eating ( Saples were eated wit te eater wic consisted of si tubular quart laps of 5 kw power eac tat allowed eating a area wit power density of about 15 kw/. A typical iage sequence included up to 300 iages captured wit a Terovision 570 IR iager at 0.16 s acquisition interval. An optiied test sould provide a aiu signal to noise ratio SNR =Δ T ( τ)/ σn were σn = σn is te standard deviation of teperature in a nondefect area. It as been sown teoretically tat suc condition is reaced if eating is perfored wit a eat pulse wic is of te Dirac-nature in bot tie and space. However Dirac-like eating is liited by possible destruction of a saple because of a iger 4

5 teperature at te end of pulse. To provide ilder eating a square-pulse test procedure is often used. By a proper cobination of pulse duration and power a coproise between needed SNR values and saple teperature can be acieved. Modelling results suc as given in Table are often used to optiie a test procedure. Calculations are facilitated by te fact tat ecess saple teperatures and differential teperature signals are linearly proportional to eating power i.e. T Δ T Q wile te contrast C is independent on Q. 6. Eperiental results and odel verification Soe illustrations of eperiental results and data processing are presented in Fig. 4 for a 15 -tick grapite/epoy saple wit Teflon inserts. Obviously because of te large saple tickness te F-surface test (Fig. 4 ecept 4c) as proven to provide better defect visibility tan te R-surface test (Fig. 4c). Te Fourier transforation applied to te tie evolution of piel-based teperature functions T( y τ ) as been cosen as a priary processing tecnique intended for aking decision on weter furter processing as to be applied to eperiental results. Defect diaeter 40 Defect dept 3 Defect diaeter 0 Defect dept 1.5 Defect diaeter 0 Defect dept 3 Defect diaeter 40 Defect dept 1.5 a) b) c) d) e) f) Fig. 4. Teral NDT of a 15- tick grapite/epoy saple (10 s eating): a-raw iage at te optiu observation tie (F-surface) b-sae as a) siulation result (TeroCalc-6L progra) c- raw iage at e optiu observation tie (R-surface) d-sae as a) after noraliation e-pasegra f-binary ap by e) By coputer odelling it was iediately revealed tat relatively big teperature signals wic appeared over defects cannot be eplained by te presence of Teflon inserts wic sould be in ideal teral contact wit a ost coposite. By ultiple trial it as been found tat teoretical values atc reasonably tose eperiental if to assue tat 5

6 Teflon inserts are surrounded by air gaps wit tickness fro 0.06 to 0.1 (Fig. 5). Te IR iages calculated by suc odel resebled eperiental IR terogras very uc (Fig. 4). It is wort entioning tat a siilar odel was proposed in te earlier paper were also te possibility of a sligt odification of coposite teral properties over Teflon inserts was assued [4]. Air ( ) Teflon (0.1 ) l Fig. 5. Te odel of defects in a grapite/epoy coposite (Teflon inserts surrounded by air gaps) Te coparison between eperiental and calculated data is given in Table 3. A relatively good atc between tese values favours te ypotesis of air-filled gaps between Teflon inserts and a ost aterial. Table 3. Coparing eperiental and odelling data for a 15 -tick grapite/epoy saple (Teflon inserts are surrounded by air gaps according to Fig. 6) Defect #1 Eperient Teory # Eperient Teory #3 Eperient Teory #4 Eperient Teory Δ o C τ ( Δ T ) s C = [ Δ T( τ)/ T( τ)] τ ( Δ T ) s T Noise and defect detection liits in teral NDT Studying noise is crucial in deterining defect detection liits. As entioned above defects sould produce a signal-to-noise ratio iger tan unity ( S 1). Often te noise is classified for additive (IR detector noise and reflected abient radiation) and ultiplicative (structural noise). Ten te above-entioned detection condition can be separated for te following ones: 1) a differential teperature signal ΔT ust be iger tan te teperature resolution ΔTres of a used IR terograpic syste i.e. ΔT Δ Tres (te condition iposed by IR detector additive noise in te absence of reflected radiation) and ) a running contrast C ust be iger tan a noise running contrast C noise i.e. C =ΔT / Tnd Cnoise (te condition iposed by ultiplicative noise). Te second detection condition requires tat a saple teperature ust be under te teperature of aterial destruction T destr i.e. T < Tdestr. Since a saple ecess 6

7 teperature is linearly proportional to te absorbed energy W tis condition liits eiter eating power Q or eating duration τ (note tat W = Qτ ). Finally IR terograpic systes can be caracteried by teir tie resolution i.e. by te iage acquisition rate f wic ust be ig enoug to ensure a reasonable nuber of iages stored before an optiu observation tie τ is reaced. Tis condition can be rougly assued as follows: f (5...10) / τ. In any teral NDT cases detection liits are conditioned by saple structural noise. By oter words eac aterial can be caracteried by te noise contrast C noise. Tis kind of noise ainly coes fro variations in saple eissivity/absorptivity. Te iniu C noise value of about 1-% appears in case of unifor non-etals and/or aterials covered wit black coatings suc as soot grapite enael oil paints etc. Te 1% tresold as been applied to all calculated data (see eaple in Table ) to produce Table 4 were detection liits are presented for two saple ticknesses and bot flas and square-pulse test procedures. Table 4. Teoretical liits in detecting air-filled defects in grapite/epoy coposite (detection liit is assued to be 1% by running teperature contrast) Miniu detectable defects * L=5 L=15 F-surface R-surface F-surface R-surface Flas eating l=4 At any dept l=5 l> ~ 4 (D =10 d=0.1 ) (D =10 d=0.1 ) (D =10 d=0.5 ) (D =10 d=0.5 ) l=3 (D =5 d=0.1 ) At any dept (D =5 d=0.1 ) l< (D =5 d=0.5 ) l> ~ 10 (D =5 d=0.5 ) l=3 (D =10 d=0.05 ) At any dept (D =10 d=0.05 ) l< (D =10 d=0.5 ) l> ~ 5 (D =10 d=0.5 ) Square-pulse eating l=4 (D =10 d=0.1 ) l=4 (D =10 d=0.1 ) l=5 (D =10 d=0.5 ) At any dept (D =10 d=0.5 ) l=3 (D =5 d=0.1 ) l=3 (D =5 d=0.1 ) l< 5 (D =5 d=0.5 ) l> (D =5 d=0.5 ) l=3 (D =10 d=0.05 ) l=3 (D =10 d=0.05 ) l< (D =10 d=0.5 ) At any dept (D =10 d=0.5 ) * l - defect dept counted fro F-surface D - defect diaeter d - defect tickness Te following conclusions are iplicated by te data in Table 4. In practical cases te predictions in Table 4 sould be odified by two oter detection conditions wic ave been discussed above. For eaple available eat energy igt be not enoug to create a detectable Δ T signal. Ten a reasonably ig teperature contrast ay not be supported by an adequate differential teperature signal. Suc situation is ore likely on R-surface in case of ticker saplers and sorter eat pulses. Furterore on F-surface a eat pulse of a particular energy ay overeat a saple tus aking test destructive. Miniu detectable defects are caracteried by a cobination of dept tickness and lateral sie. Siply suc defects can be deep but laterally etended or sall but tick etc. In tin coposites (L~5 ) a two-sided test allows detecting defects troug wole saple tickness but in tick coposites (L~15 ) even a two-sided test requires defects to be located closer to R-surface. In all cases te efficiency of a one-sided (F) test strongly depends on defect dept. 7

8 8. Enancing defect visibility Particular coponents of noise corrupting teral NDT results can be subdued by proper data treatent. For eaple teperature resolution of an IR syste tat represents te ultiate detection liit in teral NDT can be iproved by averaging teperature readouts (wit a respective loss of acquisition speed). Uneven eating can be seriously reduced by noraliation (copare iages in Fig. 4a and 4d). Surface penoena largely disappear in pasegras (Fig. 4e). Certain discriination between defects can be done by applying polynoial fitting to teperature evolutions in tie. A possible gain in SNR values cannot be predicted in advance and requires a special study by statistically coparing identification results by different processing algorits [5]. In addition to te aboveentioned tecniques principal coponent analysis and neuron networks start to be effectively applied in teral NDT. Using advanced data processing algorits igt iprove te detection liits presented in Table Defect caracteriation A great deal of inversion algorits ave been proposed to evaluate defect lateral sie dept l and tickness. A deeper analysis of tese tecniques is done in []. Defect lateral diensions can be deterined by: 1) siply viewing defect surface footprints tat typically ensures accuracy of about 10-30% ) easuring te spatial etension of a Δ T signal at te alf of aiu aplitude (FWHM - Full Widt Half Maiu tecnique) 3) differentiating Δ T signal in space. For deterining l and d soe peculiarities in tie evolution of Δ T or C are typically used (apparent effusivity log-log data presentation etc.). In tis study we ave used te following inversion forulas derived by fitting te data suc as in Table []: l = L Fo C [ ] [ τ ( τ)] (1 λd / λ) ( / λ) ; R K W = L Fo C d[ ] 4.368[ τ ( τ)] (1 λd / λ) ( / λ) (4) were λ d is te teral conductivity of a defect Rd = d/ λd is te teral resistance of a defect. Te accuracy of using Eq. (4) is typically better tan 0% and 60% for l and R d respectively. 10. Conclusions Ipleenting teral NDT in te inspection of particular aterials requires fulfilling soe teoretical and eperiental steps to optiie bot a eating/recording protocol and data processing. Tese steps are: 1) deterining teral properties of aterials ) odeling defect situations 3) optiiing an eperiental procedure 4) perforing a test 5) processing test results 6) evaluating teral NDT liits (by analying noise) 7) caracteriing defects. Defect situations are typically siulated nuerically tus obtaining direct relationsips between defect paraeters suc as lateral diensions dept and tickness and teperature signals (optiu observation ties) caused by defects. 8

9 Defect detection liits are deterined by cobinations of soe conditions wic require tat: 1) a signal-to-noise ratio calculated by eiter differential teperature signals or diensionless contrasts or bot ust eceed unity ) saple teperature during test ust be under aterial destruction level 3) acquisition frequency ust be ig enoug to ensure reliable teperature recording and data processing at optiu observation ties. Signal-to-noise ratio can be enanced by applying soe advanced processing algorits suc as pulse pase terograpy principal coponent analysis polynoial fitting neural networks etc. In tin coposites (L~5 ) a two-sided test allows detecting defects troug wole saple tickness but in tick coposites (L~15 ) even a two-sided test requires defects to be located closer to R-surface. In all cases te efficiency of a one-sided test strongly depends on defect dept and in ost cases it does not eceed 4. Te fact of reliable detection of Teflon inserts in any eperiental reference coposite saples can be eplained by te presence of air-filled gaps between inserts and a ost aterial Proposed inversion forulas allow deterining dept and teral resistance of defects in grapite/epoy coposites wit te accuracy better tan 0% and 60% respectively. Conclusions [1] W.J. Parker R.J. Jenkins C.P. Butler and G.L. Abbot Flas etod of deterining teral diffusivity eat capacity and teral conductivity J. Appl. Pysics Sept Vol. 3 p [] V.P. Vavilov Teral NDT NDT series ed. Russian NDT Soc. Vol p. (in Russian). [3] V.P. Vavilov and D.D. Burleig Deterining teral diffusivity coponents in tick anisotropic coposites by using IR terograpy SPIE Proc. Terosense-XXVIII Vol pp [4] V.P. Vavilov D.D. Burleig and A.G. Kliov Advanced odeling of teral NDT probles: fro buried landines to defects in coposites Proc. SPIE Terosense XXIV Vol pp [5] V.P. Vavilov Evaluating te efficiency of data processing algorits in transient teral NDT Proc. SPIE Terosense XXVI Vol pp