NUMERICAL MODELING OF AIR-COUPLED ULTRASOUND WITH EFIT M. Rudolph, P. Fellinger and K. J. Langenberg Dept. Electrical Engineering University of Kassel 34109 Kassel, Germany D. E. Chimenti Center of Nondestructive Evaluation Iowa State University Ames, Iowa, USA INTRODUCTION In this paper the Elastodynamic Finite Integration Technique (EFIT) [1] is applied to an isotropic, inhomogeneous, three media acoustic-elastic problem. We consider three media: an acoustic medium, air, above an elastic layer of acrylic, and another layer of air below the elastic layer. Numerical integration results are presented for various values of the simulation parameters. We generate simulated data by variation of the transducer angle and the presence of planar defects in the acrylic. We compare and discuss the results for both the wavefront images and simulated A-scan data from a second transducer located in the lower acoustic medium. GEOMETRY OF THE SIMULATION The geometry of the experiment is shown in Figure 1. All simulations are performed in two dimensions. The transducer has a width of 19 mm and a center frequency of 1MHz. It is located in the center of the test body, as shown in Figure 1. For the three layer problem we assume the following dimensions: The width of the test region is 45 mm, and its total height is 12 mm. The thickness of the air regions is 2.5 mm, while the acrylic layer is 7 mm thick. A small air region is essential to minimize the transit time across this medium, since the wavespeeds can differ by a factor of 10, or more. The simulation parameters are collected in table 1. Review of Progress in Quantitative Nondestructive Evaluation, Vol. 14 Edited by D.O. Thompson and D.E. Chimenti, Plenum Press. New York, 1995 1053
I x" I Z First Layer : Air Second Layer: Acrylic I Third Layer : Air f -------, -- / '" X,/ Crack ~ Receiving Transducer t Z L Figure 1. Geometry of the experiment Table 1: Parameters for the simulation. I Air I Acrylic Pressure Velocity [m/sec] 342 2670 Shear Velocity [m/sec] none 1220 Rayleigh Velocity [m/sec] none 1143.94 Density [kg/m 3 ] 1.8 1180 ZERO-DEGREE INCIDENCE WITH CRACK In Figures 2 through 7 time-domain wavefront sequence frames of the propagating sound field are presented. In the upper air layer, shown in Figure 2, we observe the geometrical acoustical pressure wavefront and two cylindrical pressure wavefronts generated by the edges of the transducer. Figures 3 and 4 show the diffraction of the pressure wavefront and the excitation of the mode-converted shear wavefront in the acrylic specimen. Furthermore, the reflection and diffraction of the pressure and the shear waves at the crack are visible. In Figures 5 though 7 the pressure wave propagates into the lower air layer. We can observe a small minimum in the amplitude of the transmitted pressure wavefront in the lower air layer below the crack owing to the crack shading. 1054
The transducer radiates a pulse with a center frequency of 1 MHz in the air layer. The frames are shown for different delay times. The numbers on the right-hand side of the figures represent the maximum values of the magnitude of the displacement velocity in arbitrary units. In order to permit visualization of the waves in the three media simultaneously, this scaling of the wave amplitudes is essential. f--- \:~7111111. IIIIiIIII..._ \:... t!!.1~ l0.530. 10 4 Figure 2. EFIT time sequence of acoustic waves in an air/solid/air structure; tl 7.28/18 after initial excitation. 0.49. 104 2.01 Figure 3. As in Fig. 2, t2 = 8.76/18... ~, ~ 0' I ),. ~ " 0.5.10 4 2.4 Figure 4. As in Fig. 2, t3 = 10.24/18. '-- -'4.01 Figure 5. As in Fig. 2, t4 = 11.72/18. 1055
1---'~;'::;;:====:;;::'~J---10.52. 10 4 Figure 6. As in Fig. 2, ts = 13.2Jls.. 104 Figure 7. As in Fig. 2, t6 = 14.68Jls. 1 2 3 t Figure 8. A-Scan as averaged amplitudes over the receiving aperture. The A-Scan of the 15 mm receiving transducer, located in the center of the lower air layer (Figure 1) is shown in Figure 8. The first large pulse, annotated 1, is the pressure wavefront directly transmitted from the transducer through the specimen and into the lower air layer. The second pulse, labeled 2, is the first reflection of the pressure wavefront at the lower interface which has been downward reflected by the crack. The third pulse, labeled 3, is the reflection of the pressure wave front at the lower interface being downward reflected by the upper interface. 1056
FIVE-DEGREE INCIDENCE Here we model the wave propagation for the case of a wave incident at five degrees. The time sequences for the different times are shown in Figures 9 through 14. Figure 15 displays the time history of the A-scan. The crack and the receiver are in the same location as in the previous simulation. [====S:\..~Z: ~ ;;;;;~::~====~0.547. 10 4 Figure 9. Efit time sequence of acoustic waves in an air/solid/air structure; tl = 7.28J18 after initial excitation. [====~::Z:::;;;;~~====~O.94.10 4 2.47 Figure 10. As in Fig. 9, t2 = 8.76J18. "II!!!!!!!!!!!~~=--- -J0. 36 10 4 2.37 Figure 11. As in Fig. 9, t3 = 10.24J18... O. 36.10 4 ~~----------~ 4 L--- ----l1.63 Figure 12. As in Fig. 9, t4 = 11. 72J18. 1057
L- ----' 1.6 Figure 13. As in Fig. 9, t5 = 13.2Jls. Figure 14. As in Fig. 9, t6 = 14.68Jls. Figure 15. A-scan as averaged amplitudes over the receiving aperture. The detailed time history of the recorded A-scan is more difficult to interpret than the one in the previous example, since it is complicated by shear wave mode conversion effects in the elastic layer. 1058
TEN-DEGREE INCIDENCE WITH CRACK In this case the transducer radiates into the upper air medium at an angle of ten degrees. The frames are shown in Figure 16 through 21. In the acrylic we observe only the plane mode-converted shear wave, since the longitudinal critical angle has been exceeded. However, we can recognize a weak cylindrical longitudinal wave in the acrylic generated by the edge of the incident beam, similar to the cylindrical pressure wave in the air generated at transducer edges. [====:s:\. -:J~;;~~:::=====]0.545. 104 Figure 16. EFIT time sequence of acoustic waves in an air/solid/air structure; tl 7.28/18 after initial excitation. [====S:::Z::;;;~~~:=======]0. 719.104 2.76 Figure 17. As in Fig. 16, t2 = 8.76/18. I----~-=::~--:::===-~-----IO. 23.104 4.37 Figure 18. As in Fig. 16, t3 = 10.24/18. I--------~~::~-~~::::::Ir----------~O. 23.104 2.6 '-- ---'0.352 Figure 19. As in Fig. 16,; t4 = 11.72/18. 1059
5.2 '-- ---.J 0.356 Figure 20. As in ig. 16, ts = 13.211. Figur 21. ig. 0.35 Figure 22. A-Scan as averaged amplitudes over the receiving aperture. REFERENCES 1. P. Fellinger: Ph. D. Thesis, University of Kassel, Germany 1991. 2. S. Klaholz, K. J. Langenberg, P. Baum and F. WaIte: Elastic Wave Pmpagation and Scattering in Austenitic Steel, QNDE 1994, in these Proceedings. 3. R. Marklein, R. Biirmann, K. J. Langenberg: The Ultrasonic Modeling Code EFIT as Applied to Inhomogeneous Dissipative Isotropic and Anisotmpic Media, QNDE 1994, in these Proceedings. 1060