# Use of Surface Acoustic Waves for Crack Detection on Railway Track Components--Laboratory Tests
## 3 Results  
### EFIT Visualization of Surface Wave Propagation in a Rail  
The results of the numerical simulations provide a guidance for the signal processing, which is otherwise inconclusive if complex geometries, complex waveforms and mode conversions are involved. It is inevitable that simultaneously to the intended Rayleigh surface waves, bulk waves were also introduced by the comb transducer (sender) at the left bottom of the rail head. Figure 7 shows chronologically ordered snapshots of the magnitude of the velocity field over time. While the Rayleigh waves follow a simple path along the surface, the bulk waves show a complex behavior due to multiple scattering and mode conversion. In the first row a pressure wave (marked with \"P\") is seen to propagate towards the top of the rail head. The oblique reflection leads to a partial conversion of the pressure wave into a shear wave (marked as \"S\"), as can be seen in the second row. The lower left figure at 10.08 \(\upmu\)s shows an additional low-amplitude Rayleigh wave, caused by interference where the P- and the S-waves meet the surface. This is an example of the simulations conducted, which allowed optimization of the sender and receiver placement, so that the expected signal originating from interactions with the crack was well separated from undesired additional wave modes when arriving at the sensor. In the following, we examine in more detail the signals caused by these travelling waves at different positions of the rail head. Figure 6: Three different crack geometries as modelled in the simulations. The rail cross-section corresponds to the standard 60E1 (UIC60) profile (EN 13674–1). Figure 7: Simulated ultrasonic wave propagation in an undamaged rail head after introducing a wave corresponding to excitation with a comb transducer. The magnitude of the velocity field is shown for subsequent snapshots in time. The red arrow marks the position of the Rayleigh wave, “P” marks the pressure wave and “S” stands for the shear wave. EFIT Calculation of the Wave Signals Received at Specific Circumferential Points of the Rail-Wave Reflection  
First, we investigated a setup with the receiver at the left side of the rail head just before the gauge corner (position HL), i.e., between the sender and the cracks; the receiver signal was thus expected to show first the wave coming from the sender, followed by the wave reflected at the cracks. In this setup the signal from the surface wave interaction with the cracks was well separated in time from bulk wave contributions. Figure 8 shows the simulated surface normal velocity component at position HL for the four crack configurations illustrated, viz., without cracks, with one, two, and three cracks, respectively. The passage of the pristine interrogation wave (initiating at 5 \(\upmu\)s) and subsequent reflections of the surface wave (encircled in red) caused by the presence of the cracks can be clearly distinguished. The proposed main factors influencing the reflected signal portion are the number of cracks and the crack depth with respect to the wavelength, whereas in these simulation studies the variations of crack inclination were neglected. The simulation results in Figures 9 and 10 show the waveform of the surface wave (first wave packet on the left side) followed by a signal generated by reflections at the cracks with different depth and crack numbers. Apart from subtle differences, the expectations from the theoretical considerations in Section 2.3 are confirmed: The amplitude of the reflection is not very sensitive in the range of crack lengths (see Figure 4d) of highest interest (e.g., 0.5-1 mm). Going beyond this statement, in the case of the longer cracks with 1 mm depth the reflected signal is to a high extent determined by the reflection at the first crack that the wave encounters. In comparisons, the reflected signals for the 0.5 mm cracks showed stronger differences between the one-, two-, and three-crack cases.