Simulation of Angle Beam Ultrasonic Testing with a Personal Computer

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1 Key Engineering Materials Online: I: , Vols. 7-73, pp oi:.48/ 4 rans ech ublications, witzerlan Citation & Copyright (to be inserte by the publisher imulation of gle Beam Ultrasonic esting with a ersonal Computer ung-jin ong, Joon-oo ark, Young. H. Kim, Hak-Joon Kim an Hyunjo Jeong 3 chool of Mechanical Engineering, ungkyunkwan University, uwon, Korea Center for DE, Iowa tate University, Ames, IA 5, UA 3 Division of Mechanical an ystem Design Engineering, Wonkwang University, Korea Keywors: Moel, Multi-Gaussian Beam, urface Breaking Crack, gle Beam Ultrasonic esting Abstract. For the proper performance of angle beam ultrasonic testing of steel wele joints with geometric reflectors such as counter bores an corners, it is necessary to have soun unerstaning on the unerlying physics. o provie such an unerstaning, it is beneficial to have simulation tools for ultrasonic testing. In orer to aress such a nee, we evelop effective approaches to simulate angle beam ultrasonic testing with a personal computer. he simulation is performe using ultrasonic measurement moels base on the computationally efficient multi-gaussian beams. his paper will escribe the evelope angle beam ultrasonic testing moels together with the experimental verification of their accuracy. Introuction he moeling of ultrasonic testing in a rigorous fashion is an extremely ifficult task. o get ri of such a ifficulty, the practical moels that have been propose up to [] now rely on some simplifying assumptions: the paraxial approximation for the beam raiation from the transucer an the small size assumption for scatterers. With these two assumptions moeling of the entire ultrasonic testing reuces to solving two subsiiary problems; evaluation of the ultrasonic beam fiel aroun the flaw, an calculation of the far-fiel scattering amplitue from the flaw. Among various beam moels, in the present stuy the 3-imensional multi-gaussian beam (MGB moels [,3] are aopte to escribe the raiation beam fiel from a transucer. ince this MGB moel has an outstaning capability of calculating reflection beam fiel from interfaces, it is also use to preict the reflection from scatterers with relatively large reflecting surface. In aition, the -imensional ray methos [4] are also aopte to escribe the iffraction beam fiel from the crack eges. o provie the quantitative escription to the ultrasonic testing system, we rely on the system efficiency factor [5] that is a lump sum parameter for the characteristics of the measurement system an can be etermine by an inepenent reference experiment. Implementation of computer program coes can be one straightforwarly, if the quantitative moels are available. In the present work, we propose the angle beam ultrasonic testing moels that are constructe by combining three ingreients (the 3-D MGB moels, -D ray methos, an the system efficiency factor to preict the signals that can be capture from steel wele joints with geometric reflectors. pecifically, presente is the angle beam ultrasonic moel for a surface breaking crack, an the experimental verification of its accuracy. ystem Efficiency Factor he system efficiency factor that is appeare in the evelope moels can be etermine by the econvolution of an experimental reflection signal capture from the circular part of the stanar block by the reference reflector moel [6]. All rights reserve. o part of contents of this paper may be reprouce or transmitte in any form or by any means without the written permission of rans ech ublications, (ID: , ennsylvania tate University, University ark, UA-6/3/6,5:38:33

2 Key Engineering Materials Vols V ( ω ( ω W ( ω ( V ( ω R where V ( ω is the measure voltage by the experiments, V R(ω is the theoretical reference reflection moel an W (ω is the Wiener filter aopte for the esensitization to the noise. Fig. (a shows the signal capture experimentally from the circular part of the B-A block, an (b is the system efficiency factor etermine by Eq.. Amplitue [V] Magnitue ime [µs] (a (b Fig.. (a experimental reference signal acquire from the circular part of the B-A block, an (b the system efficiency factor. Raiation Beam Fiel by the Multi-Gaussian Beam Moel Frequency [MHz] ' x ' x 3 θ x Flui (meium I z θ n I x 3 oli (meium II Fig.. Geometry of the Gaussian beam propagation through a flui/soli interface. When a circular piston transucer of raius a having a uniform velocity, v, on its face raiates a boune beam into flui as shown in Fig., one can have the isplacement (U of the transmitte wave of type (, V which reaches a point in soli from the istance of z after crossing the interface that is locate at the istance of z from the transucer face as: U iω n ibnz + zr ( ( z ik Φ exp : p ( z exp( ikz exp( ik z et G (

3 3 Avances in onestructive Evaluation where ; p is the transmission coefficient (base on a velocity ratio to the plane wave of type at the planar flui-soli interface, c ( x3 G ( + x I an. he change in phase experience c G 3 uring the transmission through the interface can be escribe in terms of the matrix, G (. he exact form of the G ( matrix epens on the shape of interface an its orientation. he efinitions of other terms use in Eq. are not given here ue to space limitation, but can be foun in the reference paper [3]. Corner Reflection (of a Vertical urface Breaking Crack or a pecimen Fig. 3 shows the two beam paths with which the secon signal group can be forme. he first path (Fig. 3 (a is corresponing to the beam that reflects at the surface of the vertical crack first, an at the bottom surface of the specimen before reaching to the transucer. he secon path (Fig. 3 (b represents the beam that reflects at the bottom surface of the specimen first, an at the surface of the vertical crack later, an going back to the transucer. he corner reflection from the surface breaking crack can be estimate by summing up these two contributions as: (a (b Fig. 3. A schematic representation of angle beam ultrasonic testing to acquire the signal ue to the ω v ω. reflection aroun crack corner: (a a beam path for v (, an (b a beam path for ( V vc ( ω ( ω[ v ( ω + v ( ω ] s sie sie bottom (3 where, v sie( ω an bottom( ω (b, respectively. Base on the MGB moel, v ( ω an ( ω respectively. bottom v represent the contributions of the beams represente in Fig. 3 (a an sie v can be estimate by Eqs. 4 an 5, bottom v sie ; ; ( ω exp( iks exp( ik s exp( ik s exp( ik s exp( iks ( R ibn z + z w h n c c ( ( s r ( ( s ( ( s ( ( s ik exp Φ ( s hw ; (4

4 Key Engineering Materials Vols v bottom ; ; ( ω exp( iks exp( ik s exp( ik s exp( ik s exp( iks ( R w h n c c ibns + zr ( ( s ( ( s ( ( s ( ( s ik exp Φ ( s hw ; (5 Crack ip Diffraction Fig. 4 (a schematically shows the ultrasonic testing configuration to capture the crack tip iffraction signal prouce by the incient beam reache irectly from the transucer an Fig. 4 (b shows the beam path from which the thir signal group is prouce after reflection from the bottom surface of the specimen. V V δ V (a V Fig. 4. A schematic representation of angle beam ultrasonic testing to acquire (a the irect tip iffraction signal an (b the tip iffraction with reflection. o calculate the iffracte beam fiel, that is generate from the crack tip an propagates through the interface in a -D cylinrical wave, we rely on the geometric ray methos that can provie quantitative escription of iffracte rays generate from the crack. he isplacement of a iffracte ray at a point (with the istance R from the crack tip in the soli specimen can be given by Eq. 6 (b u U ( k R / D ; θ exp( ik R (6 where D θ ; θ is the iffraction coefficient which is given by Eq. 7. ( { E E G E E G } D ; θ κ F + L (7 he efinitions of the terms use in Eq. 7 are not given here ue to the limit of space, but can be foun in [4]. he isplacement fiel prouce at the interface in a soli can be represente by Eq. 7 with the ientity of R s. he isplacement of the transmitte ray in the wege can be calculate by Eq. 8. / ; u U ( / D, θ exp( ikϕ (8

5 3 Avances in onestructive Evaluation where, is the principal raius of curvature of the reflecte wave at the point x R, is the ; principle raius of curvature of the transmitte ray on the point of transmission, is the transmission coefficient of plane wave through the interface from soli, an ϕ is the phase of the iffracte ray at the point of x R in the wege. Having Eq. 8, we can calculate the velocity of the iffracte ray on the face of the receiving transucer, v. hen, the average velocity prouce by the iffracte wave on the face of transucer, v (ω, can be calculate by integrating the normal component of v to the face of transucer over the transucer face, an taking the average of the result, as given in Eq. 9. v ( ω v n( s (9 If the system efficiency factor is available, the voltage output corresponing to the first signal group is given by Eq.. V ( ω ( ω v ( ω ( he moel to preict the tip iffraction with reflection can be constructe quite similarly to that of the irect tip iffraction, with the only ifference of incluing the reflection from the bottom surface of the specimen. Due to the space limitation, the etaile erivation for the voltage output of the receiving transucer for this case is not presente here, but the final result is given by Eq.. v ( / / δ iωu p p δ D, θ exp( ikϕ ( where U iω n exp( ik ibns + zr s exp( ik : s exp( ik s ( ( s ik Φ ( s exp ( ( s ( v ( / / δ iωu p p δ D, θ exp( ikϕ (3 he specimen use in this stuy is a steel plate (with the thickness of mm having a surface breaking crack with the size of mm. For the angle beam ultrasonic pulse-echo measurements, a circular plane transucer (with the center frequency of 5 MHz an the iameter of.375 inch was mounte on an acrylic shoe (which was mm in the central istance to the interface, an prouce the refracte shear wave with the refracting angle of 45 egrees in steel. Fig. 5 shows an example of the comparison between the moel preiction an the experimental measurement with aiming the axis of central beam to the crack tip irectly, an emonstrates the high accuracy of the evelope moel for the preiction of all three signal groups generate by a vertical, surface breaking crack. In fact, excellent agreements between the theory an experiments at the ifferent probe positions have been observe in the present stuy. However, ue to the space limitation they are not presente here.

6 Key Engineering Materials Vols mm steel 45 mm Amplitue [V] Amplitue [V] (a (b (c Fig. 5. Comparison of preicte surface breaking crack signals with experimental ata on the aiming crack tip irectly (a Geometry of the soli specimen corner, (b multi-gaussian beam moel, an (c the experimental signal. ummary In the present stuy, we have propose the theoretical moels to preict the angle beam ultrasonic testing signals for surface breaking crack corners, an crack tips those are most frequent abnormalities occurre in steel wele joints. hese moels have been constructe by combining three ingreients: raiation an reflecte beams by the 3-D MGB moels, crack tip iffraction signals by -D ray methos, an 3 the system efficiency factor etermine by the reference experiment. he accuracy of the moels has been verifie by the experimental comparison. he excellent agreement observe in the present work emonstrates the high potential of these moels as effective tools for proviing the unerstaning of the unerlying physics relate to the ultrasonic testing. In fact, the application of these moels for ientification an sizing of surface breaking cracks are explore in a separate paper [7] in this volume. In aition, these moels are very computationally efficient so that the computer coes in which the propose moels are implemente can be run on an orinary personal computer. Acknowlegements he authors are grateful for the support provie by a grant from o. R---3- from the Basic Research rogram of the Korea cience & Engineering Founation (KOEF. References ime [µs] [] chmerr, L. W., Funamentals of Ultrasonic onestructive Evaluation A Moeling Approach, lenum, 998. [] J. J. Wen an M. A. Breazeale: J. Acoust. oc. Am. Vol. 83 (988, p. 75. [3] L. W. chmerr: Materials Evaluation Vol. 58 (, p.88. [4] Achenbach, J. D., Gaustesen, A. K an McMaken, H. Ray Methos for Waves in Elastic olis, itman Avance ublishing rogram, Boston, 98. [5] hompson an Gray, J. Acoust. oc. Am. Vol. 74 (988, p ime [µs] [6] Kim, H.-J. an ong,.-j., reiction of angle beam ultrasonic testing signals using multi-gaussian beams, in Review of rogress in Quantitative DE, es. D. O. hompson an D. E. Chimenti (AI, ew York,, vol., p [7].-J. ong, H.-J. Jung, J.-. ark, H.-J. Kim, Y. H. Choi, Moel-base Interpretation of gle Beam Ultrasonic esting ignals from Wele Joints ACD 3, in this volume.

7 Avances in onestructive Evaluation.48/ imulation of gle Beam Ultrasonic esting with a ersonal Computer.48/