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CHARACTERIZATION OF PLANE DEFECT IN A RAIL Chong Myoung Lee1, Younho Cho2, and J. L. Rose1 1 The Pennsylvania State University, Engineering Science & Mechanics Department, University Park, PA, USA; 2 Pusan National University, School of Mechanical Engineering, Pusan, South Korea. Abstract: This paper presents the theoretical phase velocity dispersion curves and wave structures of a rail. For the characteristics of multiple modes of a rail, the wave structure is an important factor for practical application. The result of this study could help to establish the guideline for the experimental design. Introduction: Concern on nondestructive testing has increased over decades. Especially, the application of NDE in a nuclear power plant or to a mass transportation system such as a train is more essential since failure can cause a serious disaster. For this reason, many nondestructive testing methods have been developed as a consequence of a great effort of engineers and researchers. Ultrasonic testing using guided wave is a very promising technique because the guided wave can propagate long distance along the structure. The defects are found by detecting reflected waves. The sensitivity can be improved by proper mode and frequency selection. Practical applications of guided waves for pipes were performed by Rose et al., Lowe et al., and Alleyne and Cawley[1-4]. The applications to the rail are also carried out by Rose, Cawley and Hayashi[5-8]. In this paper, the phase velocity dispersion curves and wave structures for a rail is presented. The experimental data of a vertical crack in the rail head using pulse-echo and through transmission techniques are also discussed. Numerical Results of a Rail : The phase velocity dispersion curves of a steel rail are calculated using the SAFE technique[9-10]. For the calculation of phase velocity dispersion curves, 68 elements and 101 modes were used. Figure 1 shows the cross-section and meshes of a rail and the phase velocity dispersion curves are represented in figure 2. Fig. 1 Cross-section of a rail 10000 8000 ) e c s m/ 6000 k y ( ci t Ve o l
4000 e Phas 2000 00 20 40 60 80 Frequency (kHz) 100 Fig. 2 A phase velocity dispersion curve of a traction free rail. As it is shown in figure 2, the multiple modes exist in a rail. Comparing with the phase velocity dispersion curves of a plate, the phase velocity dispersion curves of a rail show more complex patterns. For this reason, the wave structure becomes important because it shows whether the energy is at some portion of a rail to be inspected or not. It will provide us with improved insights into wave propagation in a rail for determination of special excitation regions for best sensitivity. Figure 3 shows the displacements in the x, y, and z direction at 10 kHz and a phase velocity of 4.45mm/sec. (a) displacement x (b) displacement y (c) displacement z Fig. 3 Wave structure diagrams for a rail Experimental Result of a Rail : Figures 4 and 5 show the experimental results of vertical defects with various crack depths. The guided waves are generated with 60kHz shear horizontal EMAT transducer located 14' apart from the defect. In pulse-echo technique, the amplitudes of reflected signals are increased with the crack depth. On the contrary, the amplitudes of the transmission signals are decreased with the crack depth. 180 160 140 120 100 80 60 40 20 Am plit ude Expected response 7 ft. 14 ft. 14 ft. 0 0 5 10 15 20 25 30 3 5 % of rail cut depth Transmitter Receiver Fig. 4 Experimental result for pulse-echo evaluation of 60 kHz SH EMATs Cut plane 250 200 150 100 50 Expected response % of rail cut depth 7 ft. 7 ft. 7 ft. 14 ft. 00 20 40 60 80 100 Cut plane Transmitter Receiver Fig. 5 Experimental result for through transmission evaluation of 60 kHz SH EMATs Concluding Remarks: The phase velocity dispersion curves and wave structures of a rail are theoretically calculated and presented in this paper. The reflected and transmitted signals are experimentally obtained with 60kHz EMAT transducers. The wave structures could be a guideline of experimental design and data acquisition. References: [1] J. L. Rose, J. J. Ditri, A. Pilarski, J. Zhang, F. T. Carr, and W. J. McNight, "A Guided Wave Inspection Technique for Nuclear Steam Generator Tubing", Nondestr. Test. 92, 191-195, 1992 [2] J. L. Rose, K. M. Rajana, and F. T. Carr, "Ultrasonic Guided Wave Inspection Concepts for Steam Generator Tubing," Mater. Eval. 52(2), 307-311, 1994 [3] M.J.S. Lowe, D.N. Alleyne and P. Cawley, "The Mode Conversion of a Guided Wave by a Part-Circumferential Notch in a Pipe", J. Appl. Mech., 65, 211-214, 1998 [4] D.N. Alleyne and P. Cawley, "Long Range Propagation of Lamb Waves in Chemical Plant PipeWork", Materials Evaluation, 55, 504-508, 1997 [5] J.L. Rose, M.J. Avioli and W.-J. Song, "Application and potential of guided wave rail inspection", Insight, 44(6), 353-358, 2002 [6] J.L. Rose, M.J. Avioli and Younho Cho, "Elastic Wave Analysis for Broken Rail Detection", Review of Quantitative Nondestructive Evaluation, 21, 1806-1812, 2002 [7] P. Cawley, M.J.S. Lowe, D.N. Alleyne, B. Pavlakovic and P. Wilcox, "Practical Long Range Guided Wave Testing : Application to Pipes and Rails", Materials Evaluation, 61(1), 66-74, 2003 [8] T. Hayashi, W.-J. Song and J.L. Rose, "Guided Wave Dispersion Curves for a Bar with an Arbitrary Cross-Section, a Rod and Rail Example", Ultrasonics, 41, 175-183, 2003 [9] H. Taweel, S. B. Dong, and M. Kazic, "Wave Reflection from the Free End of a Cylinder with an Arbitrary Cross-Section," Int. J. Solids and Structures, 37, 1701-1726, 2000 [10] H. Bai, A. H. Shah, N. Popplewell, and S. K. Datta, "Scattering of Guided Waves by Circumferential Cracks in Composite Cylinders," Int. J. Solids and Structures, 39, 4583-4603, 2002 |
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