EFFECTS OF REFLECTION AND REFRACTION OF ULTRASONIC WAVES ON THE. S. I. Rokhlin, T. K. Bolland, and L. Adler

Transcription

1 EFFECTS OF REFLECTION AND REFRACTION OF ULTRASONIC WAVES ON THE ANGLE BEAM INSPECTION OF ANISOTROPIC COMPOSITE MATERIAL* S. I. Rokhlin, T. K. Bolland, and L. Adler The Ohio State University Department of Welding Engineering Columbus, Ohio 4320 INTRODUCTION Nondestrutive testing of omposite materials by ultrasoni tehniques has severa! speifi features resulting from strong material anisotropy and inhomogeneity. This requires reexamination of old testing methodologies and development of new ones. The latest developments in this diretion were reently reviewed by Henneke and Duke [] and by Bar-Cohen [2]. One of the basi physial onepts in ultrasoni NDE is refletionrefration of ultrasoni waves on a plane interfae. Even the simplest testing proedure requires knowledge of elasti wave refletion and transmission oeffiients, refration angles, and mode onversion [3]. While simple and well-doumented for testing of isotropi materials [3], refration-refletion phenomena for anisotropi materials are muh more ompliated from both physial interpretation and tehnial alulation points of view. In the analysis of the angle beam inspetion method for omposite materials, one first has to address the problem of wave propagation through the interfae between the immersion medium and the omposite material. For example, there is a water-omposite interfae in the immersion tehnique and perspexomposite interfae in the ontat method. Slip boundary onditions must be seleted in the seond ase. Furthermore, for multidiretional plies of fibers, the refletion and transmission of ultrasoni waves from one unidiretional ply to another with a different orientation may be onsidered. From this list, only the problems of liquid-omposite interfaes have been given some attention in a different ontext [4,5,6]. The objetive of this paper is to analyze refletion and refration phenomena between oupling media ontaining an ultrasoni transduer and the omposite material, and between layers with different fiber orientations in the omposite material, both in immersion and ontat variants of ultrasoni tests. For our alulations, we will use a general algorithm [7,8], whih was reently developed for analysis of wave interation with the interfae between two generally anisotropi media. This algorithm was slightly modified to take into onsideration slip interfaes between solids, and if needed, liquid media. *This work was partially sponsored by the U.S. Department of Energy, Basi Energy Sienes Grant, DE-FG02-84ER45057.AOOO. 03

2 STATEMENT OF THE PROBLEM The basi strutural unit of an advaned omposite material is a unidiretional lamina. In suh a lamina, fibers are oriented in a single diretion, parallel to the lamina surfae. A multidiretional omposite material is designed by forming layers with several unidiretional laminas and orienting these layers in desirable diretions. If the thikness of the unidiretional layers is greater than the ultrasoni pulse length, the transmission from layer to layer an be onsidered as transmission through an interfae between two omposite semispaes with different fiber orientations. Therefore, study of ultrasoni wave propagation through the interfae between the immersion medium where the ultrasoni transduer is plaed and the unidiretional omposite lamina, and through the interfae between differently oriented laminas has quite general impliations. Fig. illustrates the ase under onsideration, where the ultrasoni wave is inident from the upper semispae onto a unidiretional omposite medium. The plane of inidene, in general, may be rotated from the fiber diretion. The upper medium may be liquid, solid isotropi, or another unidiretional media with different fiber orientation. It was shown in our previous paper [7] that for haraterization of wave refletion and refration on an interfae, it is very onvenient to use energy flow relations for determination of refletion and transmission oeffiients () where U3 is the projetion of the vetor of this energy flux on the normal to the interfae (axis 3 in this ase), the supersript a haraterizes the type of refleted or transmitted mode, and the supersript o relates to the inident wave. t and r are the energy flow transformation fators; they haraterize the redistribution of the inident energy flux between differen refleted and refrated modes. The diretion of the enery flux vetor U oinides with the diretion of the group (ray) veloity Ug Equation an be written in this form: (2) where Aa and A0 are relative amplitudes of the displaements, p is the density, and vg3 is the projetion of the group veloity on the normal to the interfae. Equation 2 leads immediately to this important onlusion: when the energy of the transmitted wave (or group veloity) is oriented parallel to the interfae (Vg3)a = O, the transmitted oeffiient equals zero independent of the diretion of the wave vetor. For omplete disussion of this ritial angle problem, refer to the authors previous papers [7,8] and.the work of Henneke [9]. The usefulness of the energy transmission oeffiient is illustrated in Fig. 2 where A 0 and At are amplitudes of the inident and transmitted waves. If the transmitted wave is ompletely refleted bak, it will be reeived in the upper medium with oeffiient Ar. The energy transmission oeffiient in one diretion is equal to the forward-bakward transmission through the interfae for amplitude values and equal to the amplitude refletion oeffiient R for the ase shown in Fig. 2. The same energy transmission oeffiient will be equal to the amplitude transmission oeffiient through the plate between two identia! media (transmission through two interfaes). 04

3 T. At ot" Ao T Ar to"at R-& - Ao Fig.. Position of the plane of inidene relative to fiber diretion. Fig. 2. where: t energy transmission oefllient Relation of the energy flow from transmission oeffiient to the amplitude value. Material parameters used in this study were seleted from the paper of Kriz and Ledbetter [0). They are listed in Table. Several angles of rotation of the inident plane relative to the fiber diretion (Fig. ) were onsidered: 0, 30, 45, 70, and 90. The angle of inidene was varied in the 0-90 range. Due to paper length limitations, we onsider only several typial examples of the alulations. TABLE. Elasti onstants in GPa and density in g/m3 for graphite-epoxy omposite material. u =Czz C33 l2 u=z3 44=55 66=<u-lz)/2 p RESULTS AND DISCUSSION The unidiretional graphite-epoxy omposite material an be onsidered as transversely isotropi. In suh a material, three elasti waves an propagate in an arbitrary diretion: quasi-longitudinal, quasi-transverse, and pure transverse. The displaements of all three waves must be orthogonal. In the plane of inidene, oinident with the fiber diretion ( 8 = 0 where 8 is the angle of rotation, see Fig. ), the pure transverse wave will have displaement per pendiular to the plane of inidene independent of the angle of propagation in this plane, so it may be alled SH wave. The seond transverse wave will be a quasi-sv wave. The phase veloity of the SH wave is less than the veloity of the SV wave. Only in the diretion of fibers do both speeds have the same value. In this plane of inidene, mode onversion ours only to the two transmitted waves, quasilongitudinal and quasi-sv, at any angle of inidene from the liquid or isotropi solid. The same situation ours when the plane of inidene is e = 90 ; this is the plane of isotropy (plane perpendiular to the fiber diretion). The SV wave has displaement laying in this plane, and therefore has displaement perpendiular to the fiber diretion. The SH wave will have displaement i n the fiber diretion and will be faster than the SV wave. If the angle of rotation is ontinuously hanged, one will observe that the slow pure transverse wave whih is SH in the plane of fibers ( 8 = 0 ) beomes an SV wave at 8 = 90 and vie-versa for the quasi-transverse wave. 05

4 Woter / Composite 45 Water / Composife I.Of- or o - o o.).) - u 0.6 j.!! o Qj 0.5f- a: a:,.,.. O> O> 0.4 >. > ,.. r v-- j 0. r- 0. ) zo eo 90 0 Inident woe veor Angle It. d :i: :!:... ::a::.! :r:!i "h 3: ::. J3! :.! =x::j:::.a:: IU (),$ {3, :. : Woter / Composite 45 : t!: J; :;:! Water / Composile 70 I.Or, , -... o.ro 0.9- / - i -----; /...!! <.> u.), i, 0.6-, -, o... : : : :i,,...,..., : e e 0.6 : ,,,., Î 6 f,,, : : o J F,. 0.5 f- 0.5 fi,,,. :,: 0.4 f i It " w rl : w 0.3-.: - 0.3,,,.._, 0.2f- / ,, N l 0.00,...,." zo Inident Wove Vetor Angle Fig. 3. Energy refletion and transmis sion oeffiients for liquid/omposite interfae. 06

5 At an arbitrary rotation angle (e 0 or 90 ), neither of these waves will have SV or SH harater, and both of them will have displaement omponents in and out of the plane of inidene. So we distinguish them as fast (with higher speed) whih will be quasi-transverse and slow whih will be pure transverse. Due to deviation of the displaement of all three waves from the plane of inidene for an arbitrary rotation angle, the inident wave from liquid or isotropi solid will be onverted on the interfae to three transmitted waves. This is illustrated in Fig. 3 for angles of rotation 45 and 70. It is seen that for the 45 inident plane, there exist three ritial angles for the quasi-longitudinal and both quasi-transverse waves, while for 70, only two ritial angles exist sine the speed of the slow wave beomes less than the speed in the water. Another interesting observation is that the positions of the first and seond ritial angles move in opposite diretions on the inident angle axis when the angle of rotation hanges. In the upper part of the figures for the transmission oeffiient, the angles of refration both for the ray (ultrasoni beam) and the wave vetor are shown. Therefore, these sales give the angle of deviation of the ultrasoni beam from the wave normal. The ultrasoni beam deviates not only in the plane of inidene, but out of the plane also. This is illustrated for a quasi-longitudinal wave in Fig. 4 for rotation angle 45. From this figure, one an see that the beam of the quasi-longitudinal wave tends to deviate to the fiber diretion (out of plane omponent is lose to 45 ) and strongly deviates toward the material surfae even at small angles of inidene (loser to the fiber diretion). As shown in Fig. 3, when the wave vetor has a refration angle Bti(w.v) equal to 23 ; the angle of refration for the beam Btt (ray) is equal to 72 (deviation in the plane of inidene an be around 50, Fig. 4). These very large deviations in omposite materials were observed experimentally [,2]. If the ultrasoni beam for the quasilongitudinal wave tends not to penetrate to the material (deviates to the surfae), the ultrasoni beam for the fast quasi-transverse wave at rotation angle 45 behaves differently. At small angles of inidene, it very strongly deviates from the wave normal, ompare the anfle for the wave normal Bft(w.v) = 6.9 and the refrated angle for the beam 8 t(ray) = 52.. At larger angles of inidene, the ray refration angle dereases and beomes less than the wave normal angle. The deviation angle of the slow transverse wave is positive. For rotation angle 70, the angle of deviation for the fast quasi-transverse wave does not hange sign. - j , ! 0 > Q o o f out of plane -inplane Fig. 4. Angle of deviation of group veloity from wave normal for quasi-longitudinal wave. 07

6 For modeling of angle beam ontat transduers, slip boundary onditions must be seleted on the interfae. These onditions onsist of ontinuity of the normal displaement and stresses on the interfae and vanishing of the tangential stress omponents. Physially suh boundary onditions orrespond to a thin, low-visosity liquid layer on the interfae [3]. The ase for an angle beam ontat transduer (perspex wedge) is illustrated in Fig. 5. The plane of inidene is rotated by 45 from the fiber diretion. First, it is useful to note the very high transmission at normal inidene (the parameters of materials are very similar in this diretion). For the material parameters under study, only one ritial angle for the quasi-longitudinal wave may be observed. As in the ase of the water-omposite interfae, at the ritia! amplitude, the refletion oeffiient sharply reahes unity. It seems that unity of the refletion oeffiient at the ritia! angle is a general property for liquid-solid interfaes and solidsolid interfaes with slip boundary onditions. The results of the alulations for the same pair of materials but with rigid boundary onditions are shown in Fig. 6. The refletion oeffiient for this ase is about ten times less at the ritia! angle and does not tend to unity. Another interesting differene from the slip boundary onditions ase is that the SH refleted wave appears in the refleted field, but the slow transverse wave disappears in the transmitted field. The dependene of the ritial angle on the rotation angle is shown in Fig. 7. It hanges from about 7 in the fiber diretion to 70 in the diretion perpendiular to the fiber. Two examples for refletion transmission on a omposite-omposite interfae are shown in Fig. 8 and Fig. 9. The ase of inident plane oinident with the fiber diretion in the upper medium and 45 rotated in the lower medium is shown in Fig. 8. First of all, it is useful to note the relatively higher refletion oeffiient for the longitudinal wave above 20 inident angle. Note also, the very strong deviation of the ultrasoni beam : Y. f- :w. -r-r-r-r "E " (j u.2 e CI) CI) e CI) - >- e " w Perspex /Composite 45 Slip Boundory Condition 7, Perspex / Compslte 45 Slip Boundory Condilion o!-=;,o""zo!;,J.::--:40!::---:t;:!O::--:;so Ioeident Wave Veetor Arlgle Fig. The refletion and transmission oeffiients for the perspex/omposite interfae. Slip boundary onditions. ;:;--;ro::--;;:;=.,o: 08

7 Perspex / Compose 45 Rigid Boundory Condition eo 90 Angle of Material Rotation Fig. 6. The refletion oeffiient for the perspex/omposite interfae in a ase of rigid boundary, onditions. Fig. 7. The dependene of the ritial angle on the rotation angle. Composite o /Compose 45 of,_,. S!:ia 52. &2" j f I.O &.9 6f9 & Pt w.v 3.4 & u.e u!.! ! 4.s J.a Dl Ao 7.2 7, !53.7 S6.4!8.2!5! o ll: fjf /,V l 0 0 o o Inident Wove vetor Angle Inident Wove Vetor Angle Fig. 8. Energy refletion and transmission oeffiients for 0 /45 omposite interfae. suh that the refleted beam is very lose to the interfae (this deviation is greater than for the 45 rotated plane). There is no deviation of the refleted beam.from the plane of inidene. The onversion to the quasitransverse refleted wave is very small. All three waves appear in the transmitted spetrum while the quasi-longitudinal wave is dominant. The inverse situation is shown in Fig. 9. Here the upper medium is a 45 rotated omposite and in the lower medium, the fibers lie in the inident plane. The ritia! angle phenomenon is observed in this ase for the trans- 09

8 . J y,, "r 60 "r o "" r r " , ), {3, w.v _ !! ,J.3 2.3,._ o ! QO , J: :: J.: :-: Composite 45"/CompositeOO Fig. 9. Energy refletion and transmission oeffiients for 45 /0 omposite interfae. mitted quasi-longitudinal wave. The general rule in both ases is that below 5 inident angle, very small refletion and mode onversion our for the quasi-longitudinal wave when it rosses interfaes in the multidiretional omposite. On the other hand, beam deviation from the wave normal is very signifiant even at these small angles. REFERENCES. E. G. Henneke, II and J. C. Duke, Jr., Mater. Eval. 43, (985). 2. Y. Bar-Cohen, Mater. Eval. 44, (986) J. Krautkramer and H. Krautkramer, "Ultrasoni Testing of Materials," 2nd Ed. (Springer-Verlag, Berlin-New York, 977). 4. W. R. Sott, "Wave Propagation in Anisotropi Layered Media," Report No. NADC , 980. Naval Air Development Center, Warminster, PA. 5. J. D. Ahenbah and J. Qu in "Review of Progress in Quantitative NDE," Vol. 5B, D. O. Thompson and D. E. Chimenti, eds., (Plenum, New York, 986) A. 7. s. 8. s. 9. E. 0. R.. R. 2. w. l3. s. H. Nayfeh, these Proeedings. I. Rol<hlin, T. K. Bolland, and L. Adler, J. Aoust. So. Am. 79, (986). I. Rokhlin, T. K. Bolland, and L. Adler, J. Appl. Phys. 59, (986). G. Henneke, II, J. Aoust. So. Am. 5, 20 (986). D. Kriz and H. M. Ledbetter, "ElastiRepresentation Surfaes of Unidiretional Graphite/Epoxy Composites," in Proeed. of 2nd US-Japan Conf. on Composite Materials (ASTM, Philadelphia, 985), D. Kriz and W. W. Stinhomb, Exper. Meh. 9, 4-49 (979). R. Rose, S. I. Rokhin and L. Ader, these Proeedings. I. Rokhlin and D. Maron, J. Aoust. So. Am (986). o