Angle Beam Ultraonic Teting Model and Their Application to Identification and iing of Crack NDE00 predict. aure. improve. National eminar of INT Chennai,. 7.. 00 www.nde00.org ung-jin ong*, Hee Jun Jung*, Young H. Kim*, Hak-Joon Kim** and Jae Hee Kim*** * chool of Mechanical Engineering, ungkyunkwan Univerity, 00, Chonchon-dong, Jangan-gu, uwon, Kyounggi-do, 0-76 Korea ** Center for Nondetructive Evaluation, Iowa tate Univerity, Ame, IA 000, UA *** Korea Atomic Energy eearch Intitute, Daejon, Korea Abtract Identification and iing of urface breaking crack uing angle beam ultraonic teting in practical ituation quite often become a very difficult tak due to the preence of non-relevant ignal caued by geometric refl ector. The preent work introduce effective and ytematic approache to take care of uch a difficulty by ue of angle beam ultraonic teting model that can predict the ected ignal from variou target very accurat ely. pecifically, the modelbaed TIFD (Technique for Identification of Flaw ignal uing Deconvolution) i propoed for creening of crack tip ignal from non-relevant geometric reflection ignal. In addition, the model-baed ie-amplitude Curve (AC) i introduced for the reliable iing of urface breaking vertical crack. Keyword: ultraonic, identification of flaw ignal, iing, vertical crack, ultraonic teting model,. Introduction Ultraonic identification and iing of urface breaking crack grown from inner urface of teel pipe uually involve two tep; ) location of the tip and the corner of a crack under interrogation and ) meaurement of a ditance between it tip and corner. Thi procedure ound very imple and traightforward. In many practical ituation, however, it i not o eay due to the preence of non-relevant ignal caued by geometric reflector uch a counter bore and weld root. A a conequence, interpretation of the acquired ignal become a truly difficult tak even to well-trained inpector. To take care of thi difficulty, it i trongly deired to have an efficient and ytematic way to identifying ignal from crack tip and crack corner from captured ultraonic teting ignal. Theoretical ultraonic teting model of which the primary role i to olve the forward problem (that i the prediction of flaw ignal) can alo be applied to thi purpoe. Thi paper decribe our recent effort to develop new approache to addre uch an iue. ecently, we have propoed variou angle beam UT model (Kim and ong, 00, Kim et al, 00) by adopting the multi-gauian beam (chmerr, 000a, 000b). Thee model can predict variou UT ignal that can be acquired from variou reflector or catter uch a the circular part of the TB A- block, large corner of rectangular block, counter bore with variou ie, vertical crack corner, circular crack and pherical void. Baed on thee model, we have developed two approache to quantitative characteriation of crack. The firt approach i related to identification of crack tip ignal, and the econd one to iing of urface breaking crack.
. Angle Beam Ultraonic Teting Model Ultraonic teting model are uually compoed of four ingredient: ) a ytem efficiency factor (Thompon and Gray, 98), ) a radiation beam field from an interrogating tranducer (ong and Kim, 000), ) a cattering (or reflection) field from a target under conideration, and ) a reception of cattered field by a receiving tranducer. Combining thee four ingredient in a rigorou manner i very difficult. However, thi difficulty can be greatly relaxed by adopting ome important aumption uch a the paraxial approximation or iolated catter of mall ie. Taking advantage of thee approximation, we have developed the angle beam UT model adopting the multi- Gauian beam (MGB) (Kim and ong, 00, Kim et al, 00). Here, the key feature of the developed model are dicued briefly.. Multi-Gauian Beam Model In the angle beam UT, ultraonic beam propagate from a olid acrylic wedge to a olid pecimen acro a fluid couplant layer. ince the liquid couplant doe not carry the hear wave, thi propagation can be implified to that with a fluid/olid interface, where the olid wedge i treated a a fluid medium with equivalent material propertie. Then, the multi-gauian beam model (chmerr, 000a and 000b) to calculate the tranmitted beam field, v ( ω,x), at the point x in the olid pecimen (a hown in Fig. ) can be written by Eq. (). ( x ) T ikx [ G ( x )] ik ik x A ; det n p G x v( ω, x) = d T () n= ib n + r where, ω i the circular frequency, A n and individual Gauian beam, ; T p = P, V k, k ( = P, V ) other term including G and ( x ) (000a). B n are height and width factor of r = / ka i the tranmiion coefficient, i the ditance from tranducer to interface, i the ayleigh ditance, are the wave number in the fluid and olid, repectively. Definition of G matrice were dicued in detail by chmerr Tranducer Fluid (Medium ) n T x θ x θ n I x Tran mitted ay oli d (Medium ) FIGUE. Geometry of the multi-gauian beam model with fluid-olid interface.
. eference eflection The reflection ignal from the circular part of the TB-A block wa choen a a reference reflection for the etimation of the ytem efficiency factor, β ( ω ), of an angle beam ultraonic teting et-up a hown in Fig.. Then, the reference reflection model can be written a Eq. (). V ω d () = v ( ω, x) where, ( ω) area, x i an arbitrary point on, and ( ω,x) V i a received average velocity in the frequency domain, i the tranducer v i given by Eq. (). v ω, x An = n = ibn + r T ; p ; T p; ~ ~ () 0 () ( ) ik ik p ik Φ p where, T ; p i the tranmiion coefficient from the wedge to the TB-A block, T ; i the tranmiion coefficient from the TB-A block to the wedge, ; i the reflection coefficient at the circular part of TB-A block.. ytem Efficiency Factor, can be computed by ue of a deconvolution of an erimental ignal captured from the reference reflector (the circular part of the TB-A block) by the reference reflector model (given by Eq. ()), a given by Eq. () The ytem efficiency factor, β ( ω ) β ( ω ) ( ω ) ( ω) V0 = W ( ω ) () V where, V 0 ( ω ) i the meaured voltage by the eriment, ( ω ) voltage by the reference model and ( ω ) V i the calculated W i the Wiener filter (chmerr, 998). ρ,c T T ρ, c FIGUE. Geometrical etup for the calibration of an angle beam ultraonic tranducer.
. Counter Bore eflection When the ie of a counter bore i maller than the beam width, it can be conidered a a catter. In thi cae, the urface of the counter bore can be divided into mall, planar element. And, the individual repone from each element can be evaluated by ue of a well-known ultraonic meaurement model, given by Eq. (). Then, finally, the total repone from a mall counter bore can be obtained by umming up all repone from individual element. V b ; p ; c [ ] c = ik ik T C A ρ β ω ω ω iπfa ρc ω () where, ρ, ρ are denity of the wedge and pecimen, c, c are the P- and -wave peed in the wedge and pecimen, f i the frequency, a i the radiu of tranducer, and the far-filed cattering amplitude, A ; ( ω ), from a planar crack i given by Eq. (6) baed on the Kirchhoff approximation (chmerr, 998): A ; ( δ ln elen) ej πρ ( c ) [ i( k k ) x ] d ( x ) ik C kpljdpnk ω = e e (6) and, the diffraction correction, C ( ω ), i given by Eq. (7): F i r p p A ; p n ik Φ C( ω ) = T (7) n = ib + n det G xr The definition of variou term in Eq. (6) and (7) were dicued in detail by chmerr (998, 000a and 000b).. Corner eflection of a pecimen When the incident beam reflect right at a large corner of a pecimen, the total length of beam travel (a own in Fig. (a)) become that of the cae in Fig. (b), where the beam reflect from the normal plane (to the refracted beam) located right at the corner. F,, ( ) (a) (b) FIGUE. (a) Geometrical etup for corner reflection and (b) geometry of reflection from the normal plane to the incidence wave.
With taking advantage of thi identity, one can calculate the corner reflection, V cr( ω,x), with the model given in Eq. (8) and (9), where the ame reflection coefficient i multiplied twice. V cr β ω ω = vcr ( ω, x) d (8) where, ( ω,x) v cr v i given by: cr An ; p ; ( ω, x) T ( ) = n= ibn + xr T p; det G () 0 ~ ~ det G () 0 (9) p ik Φ ( ik ik ) where, ; i the reflection coefficient at the normal plane to the incidence wave..6 Corner eflection of a urface Breaking Vertical Crack The major contribution of corner trap ignal of a urface breaking vertical crack (a hown in Fig. ) come from two ingredient. The firt one i the reflection at the ide of a vertical crack followed by the reflection at the bottom. The econd one i the reflection at the bottom urface of the pecimen followed by the reflection at the ide of the vertical crack. Thu, the corner trap ignal of a urface breaking vertical crack can be calculated by Eq. (0). D θ f D FIGUE. A chematic repreent ation of the angle beam UT of a vertical crack corner. vc ( ω) = V ( ω) V ( ω) (0) V + ide where, V vc ( ω) i the reflected velocity from the crack corner in the frequency domain, V ide( ω) i the reflected velocity through the vertical crack ide firtly and from the pecimen bottom latly, and V btm( ω) i the reflected velocity through the pecimen bottom firtly and from the vertical crack ide latly. V ide( ω) and V btm( ω) are given by Eq. () and (), repectively. btm
V V btm ide + D An P ( ik ) ( ik ) ( ik ) ( ik ) T ; ; ω = β( ω) ( ) det G f w 0 n= ibn + r ~ ~ ~ ~ det G () 0 ik Φ de D / tanθ An ; P = ( ik ) ( ik ) ( ik ) ( ik ) T ( ; ω β ω ) det G w f 0 ib n n = + r ~ ~ ~ ~ ik where, f i the ie of the crack, θ i the refracted angle of the beam, D Z i the ditance from tranducer to the interface, i the ditance from the interface to the vertical crack urface, i the ditance from the vertical crack urface to the pecimen bottom, i the ditance from the pecimen bottom to the interface and i the ditance from interface to the tranducer. The definition of other term can be found in Kim and ong (00)..7 Iolated Flaw ignal The ultraonic teting ignal that can be obtained by an angle beam tranducer from iolated flaw uch a a circular planar crack, a pherical void and a ide-drilled hole can alo be calculated by uing Eq. (7). In the calculation of iolated flaw ignal, however, one hould adopt proper far-field cattering amplitude. For example, the far-field cattering amplitude for a circular crack, A cr ( ω ), obtained by adopting the Kirchhoff approximation i given by Eq. () (chmerr, 998). A cr p p p p l n j kplj p k p p p p; p ( c ) ei e re p p p p; p [ k e e r ] Φ de a d w a d T w P; () T P; () ib e e e C D n ( ω ) = J i e () ρ where, b i the radiu of a penny-haped crack. The detailed definition of individual term can not be addreed here due to pace limitation, but can be found in chmerr (998). Baed on the Kirchhoff approximation, the far-field cattering amplitude for a pherical void, A V (ω ), can be obtained by Eq. (). ( k b) b in ( ω ) = ( ik b) ( ik b) () k b A V where, b i the radiu of the pherical void. The correponding far-filed cattering amplitude for a -dimenional ide-drilled
hole of the length of L, A (ω DH ), can be given by Eq. () uing the Kirchhoff approximation with the aumption of mall ie in it diameter (chmerr and edov, 00). ik ( ω ) = b A ( ) + ( ) DH L H k b ij k b () π where, b i the radiu of the ide-drilled hole, and H and J i the truve and Beel function of the firt order, repectively..8 Experimental Verification of the Model It i worthwhile to note that the ytem efficient factor hould be defined for the erimental verification of the propoed model in time domain. For thi purpoe, the reflection ignal from the circular part of the TB-A block wa captured by ue of a planar tranducer with the center frequency of MH and the diameter of 0.7 inch a hown in Fig. (a). Then, the ytem efficient factor for a given ultraonic teting ytem wa determined a hown in Fig. (b). (a) (b) FIGUE. (a) The erimental reference reflection ignal, and (b) the ytem effi ciency factor for a MH center frequency, 0.7 inch diameter tranducer with the refracting angle of degree in the TB-A block. Once the ytem efficiency factor i defined, the time domain waveform ected to acquire can be predicted by the invere Fourier tranform of the ultraonic teting model preented above. Fig. 6 how the comparion between the erimentally meaured ignal (with the ame et-up a that for Fig. ) and the predicted time domain ignal from a mall counter bore (with the width of mm) and the corner of the pecimen. The excellent agreement between the theory and the eriment demontrate the accuracy of the propoed model. The further comparion between the model prediction and the erimental meaurement for other reflector and catter are not hown here due to pace limitation, ince they can be found elewhere (Kim and ong, 00, Kim et al, 00). In fact, they howed very good agreement demontrating the high accuracy of the propoed model.
(a) (b) FIGUE 6. Comparion of erimentally meaured ignal to predicted time domain ignal for a) a mall counter bore in the pecimen and b) a corner of the pecimen. (olid line: erimental ignal, Dotted line: calculated ignal uing multi-gauian beam model).. Model-baed Identification of Crack Tip ignal For the identification of the crack tip ignal from complicated UT ignal, the TIFD (Technique for Identification of Flaw ignal uing Deconvolution) ha been propoed previouly (ong et al, 00a, 00b). The TIFD identifie flaw ignal uing a imilarity function defined from the deconvolution of a target ignal by a reference ignal. The TIFD howed great potential to identify variou practical ignal. Unfortunately, however, the TIFD propoed in the previou work i not eay to implement in practical application, ince it require many reference ignal. Obviouly, it will be very difficult to acquire variou reference ignal in many ituation. Here, we introduce an enhancement of the TIFD baed on the angle beam ultraonic teting model in order to relax the requirement of acquiring variou kind of reference ignal. Furthermore, the feaibility of the enhanced approach for the identification of crack tip ignal i addreed. The enhanced approach adopt only one reference ignal, which i the pecular reflection from the circular part of the TB-A block a hown in Fig. a). The deconvolution pattern of three different target (a counter bore, a vertical crack corner and a crack tip a hown in Fig. 7) are predicted uing the propoed ultraonic teting model. 0 mm mm 0 mm teel mm 0 mm teel mm (a) (b) (c) FIGUE 7. chematic repreentation of acquiition of ignal from (a) a counter bore, (b) a vertical crack corner, and (c) a vertical crack tip. Fig. 8 how the calculated time-domain waveform uing the propoed angle beam UT model for three target a hown Fig. 7 by ue of the teting et-up whoe efficiency factor i hown in Fig. b). Here, it hould be noticed that the crack tip ignal (in Fig. 8(c)) wa taken a the firt group of the circular crack ignal, ince the crack tip ignal could not be calculated accurately by the Kirchhoff approximation. Fig. 9 how the calculated reult of deconvolution pattern for three flaw ignal (a hown Fig. 8) by adopting the pecular reflection from the circular part of the TB-A block (a hown in Fig. (b)) a the reference ignal. The time domain waveform a hown
in Fig. 8 can not be ditinguihed from each other. The deconvolution pattern hown in Fig. 9, however, can be clearly ditinguihed even with a naked eye. A hown in Fig. 9 (a) the deconvolution pattern of the counter bore reflection ignal how the poitive impule-like pattern, while that of a corner reflection ignal the negative impule-like pattern (Fig. 9(b)). On the other hand, the deconvolution pattern of the crack tip ignal how the bipolar pattern, a hown in Fig. 9 (c). The deconvolution pattern of a crack tip ignal i quite different from thoe of the geometric reflector (uch a the counter bore and the corner). Thu, it i poible to identify the crack tip ignal from geometric reflection uing the model-baed TIFD approach. (a) (b) (c) FIGUE 8. Calculated time domain waveform for (a) a counter bore, (b) a vertical crack corner, and (c) a vertical crack tip. (a) (b) (c) FIGUE 9. Deconvolution pattern of the calculated ignal for (a) a counter bore, (b) a vertical crack corner, and (c) a crack tip. To demontrate the viability of thi approach, the erimental ignal were acquired from three target a hown in Fig. 7 uing a MH tranducer (whoe ytem efficiency factor i hown in Fig. b)). Fig. 0 how the deconvolution pattern of the erimental ignal, from which a very good agreement to the theoretical prediction (in Fig. 9) can be cleanly found. (a) (b) (c) FIGUE 0. Deconvolution pattern of the erimental ignal for (a) a counter bore, (b) vertical crack corner, and (c) a vertical crack tip.
. Model-baed iing of urface Breaking Vertical Crack The iing of a urface breaking vertical crack i, in fact, equivalent to the meaurement of the ditance between the crack tip and the crack corner. Thu, for iing of crack, it i eential to capture the crack tip ignal. Unfortunately, however, the crack tip ignal are uually very tiny o that it i not eay to acquire. On the contrary, the corner trap ignal (that i the reflection from the corner of a urface breaking crack) i eay to capture, ince they are much higher in amplitude. Therefore, if it i poible to etimate the crack ie from the corner trap ignal it would be very beneficial not only for the direct iing of the crack but alo for the location of the crack tip. In the preent work, we propoe a quantitative iing method for urface breaking vertical crack baed on the angle beam UT model. If we define the amplitude ratio (named a amplitude-area (Aa) factor and defined in time-domain) of the crack corner trap ignal (that can be predicted by Eq. (0)) to that of the pecimen corner ignal (which can be calculated by Eq. (8)), it would be given by Eq. (6). P - P( Vvc () t ) a = 00 (% ) (6) P - P( V () t ) A cor where, A a i the Aa factor, P - P( V vc () t ) i the peak-to-peak amplitude of the vertical crack corner trap ignal in the time-domain, P - P( V cor () t ) i the peak-to-peak amplitude from the pecimen corner reflection ignal in the time-domain. Uing the Aa factor we can plot a theoretically contructed curve, named a the ie-amplitude curve (AC), from which the vertical crack iing can be performed quantitatively. Fig. how two example of the AC contructed for the pecimen with the height of 0 mm and mm. A hown in Fig., the AC are very imilar in pite of the difference in the pecimen height. DX X `c cx \/ Z / ^^ FIGUE. ie-amplitude Curve (AC) for two pecimen with different height: tranducer: MH center frequency, 0.7 inch diameter, and degree diffraction angle. To demontrate the iing performance uing the theoretically contructed AC, we performed iing of a urface breaking vertical crack (with unknown ie) in a pecimen with a height of mm. Fig. (a) how the corner trap ignal captured from the vertical crack corner, of which the peak-to-peak voltage i meaured to be. mv. For the iing of the urface-breaking crack uing the AC, we need to etimate the peak-to-peak voltage of the pecimen corner. Fig. (b) preent the reult of the theoretical prediction (uing Eq. (8)) of which the peak-to-peak voltage i calculated to be 6. mv. Then, we can calculate
the A a factor, which i turned out to be.8% in thi particular example. Then, finally, we can etimate the unknown vertical crack ie from the AC, a hown in Fig. (c), to be.8 mm. Conidering the fact that actual ie of the crack i.0 mm, one can recognie that the accuracy of the AC iing i very good. :7 /^ 7 /^ Aa (%) Aa:.8.9 mm Crack ie (mm) (a) (b) (c) FIGUE. (a) An erimentally meaured corner trap ignal from the mm vertical crack, (b) A predicted corner reflection ignal from the mm height pecimen, and (c) etimation of the vertical crack ie uing the AC: Tranducer MH center frequency, 0.7 inch diameter, and degree diffraction angle.. Concluion Identification and iing of a urface breaking crack by angle beam ultraonic teting involve two tep; identification of the crack tip ignal and the corner trap ignal, and the meaurement of the ditance between them. Performing thee tep ound very imple and traightforward. In many practical ituation, however, it i not o eay ince the angle beam ultraonic teting ignal are quite often captured together with non-relevant ignal caued by geometric reflector uch a corner, counter bore and weld root. To take care of thi difficulty, we have propoed efficient and ytematic approache to the identification of the crack tip ignal and the ucceive iing of the urface breaking vertical crack by ue of the angle beam ultraonic teting model. A the firt approach, the model-baed TIFD (Technique for Identification of Flaw ignal uing Deconvolution) ha been propoed for the creening of the crack tip ignal from the non-relevant geometric reflection ignal, epecially, counter bore ignal and corner trap ignal. A the econd, the model-baed ie-amplitude Curve ha been contructed for the reliable iing of urface breaking vertical crack. The performance of the propoed approache wa verified in the initial eriment demontrating the high poibility of their application in practice. ererence Kim, H. J. and ong,. J. (00) Prediction of Angle Beam Ultraonic Teting ignal Uing Multi-Gauian Beam, in: D. O. Thompon and D. E. Chimenti (Ed.), eview of Progre in quantitative Nondetructive Evaluation, Vol. A, American Intitute of Phyic, Melville, New York, pp. 89-86. Kim, H. J., ong,. J. and Kim, Y. H. (00) Quantitative Approache to Flaw iing Baed-on Ultraonic Teting Model, eview of Progre in Quantitative Nondetructive Evaluation, Bellingham, Wahington, July -9. chmerr, L. W. (998) Fundamental of ultraonic nondetructive evaluation A Modeling
Approach, Plenum, New York. chmerr, L. W. (000a) A Multigauian Ultraonic Beam Model for High Performance imulation on a Peronal Computer, Material Evaluation, Vol. 8, No. 7, pp. 88-888. chmerr, L. W. (000b) Lecture Note on Ultraonic NDE ytem Model and Meaurement, ungkyunkwan Univerity, uwon, Korea. ong,. J. and Kim, H. J. (000) Modeling of adiation Beam from Ultraonic Tranducer in a ingle Medium, Journal of the Korean ociety for Nondetructive Teting, Vol. 0, No., pp. 9-0 (in Korean). ong,. J., Kim, J. Y. and Kim, Y. H. (00a) Identification of Flaw ignal in the Angle Beam Ultraonic Teting of Welded Joint with Geometric eflector, in: D. O. Thompon and D. E. Chimenti (Ed.), eview of Progre in quantitative Nondetructive Evaluation, Vol. A, American Intitute of Phyic, Melville, New York, pp. 69-698. ong,. J., Kim, J. Y. and Kim, Y. H. (00b) Identification of Flaw ignal Uing Deconvolution in Angle Beam Ultraonic Teting of Welded joint, Journal of the Korean ociety for Nondetructive Teting, Vol., No., pp. -9 (in Korean). Thompon,. B. and Gray, T. (98) A Model elating Ultraonic cattering Meaurement through Liquid-olid Interface to Unbounded Medium cattering Amplitude, Journal of Acoutical ociety of America, Vol. 7, pp. 79-90.