Abstract

In the present paper, ultrasonic testing of rails (used in railway tracks) with vertical cracks is investigated experimentally and by numerical simulations. For this purpose, four different rail specimens were used. An ideal rail without any crack and three specimens with vertical cracks synthetically generated in the head, neck and bottom of the rail, respectively. The experimental measurements were done with normal piezoelectric longitudinal and shear wave ultrasonic transducers in pulse-echo configuration. For better interpretation of the received signals, wave propagation in the cross section of the rail was modeled numerically using an optimized version of the EFIT code (Elastodynamic Finite Integration Technique) which was adapted to the special testing situation and complex rail geometry. The simulations are in good agreement with the experimental results for all specimens dealt with.

1. Introduction

Fig. 1: Pictures showing rails with real cracks at the bottom (left), the neck (centre) and the head of the rail (right).

One of the possible reasons for the failure of rails in railway tracks is the appearance of vertical cracks in the head, neck or bottom of the rail (see Fig. 1). Therefore, it is necessary to detect such defects at an early stage when the cracks are still of smaller dimensions. For vertical cracks, the results of pulse echo measurements using transient ultrasonic waves are difficult to interpret due to mode conversions at the crack and rail surfaces, respectively. Therefore, for normal incidence not only the attenuation of the primary wavefront but also new echoes due to the converted wave modes can be observed in the ultrasonic A-scan data. For this purpose, the wave propagation in the cross section of the rail was modeled numerically using a special version of EFIT (Elastodynamic Finite Integration Technique) that was optimized for the given testing conditions. By that, all mode conversion effects in the rail were cleared up by comparing the simulations with the experimental measurements.

2. The Specimens

Fig. 2: Specimens used in the measurements. The model cracks were generated synthetically by using electroerosion methods.

Fig. 2 shows three of the four different specimens used for the measurements. The height was H = 169 mm in each case, the width at the bottom W = 154 mm. The cracks were generated synthetically using electroerosion methods so that a crack width of less than 0.3 mm could be realized. In detail
1. Rail A without defects.
2. Rail B with a vertical non-surface breaking crack (length L = 18 mm) in the head of the rail located in 7 mm depth under the top surface.
3. Rail C with a vertical crack (L = 15 mm) in the middle of the rail neck.
4. Rail D with a vertical surface breaking crack (L = 10 mm) at the bottom of the rail.

3. Experimental Setup

Experimental measurements were carried out using a multifunctional ultrasonic flaw detector (USIP-12, Krautkraemer-Branson). Normal piezoelectric longitudinal and shear wave transducers (Panametrics V154) having a circular aperture with a diameter of 12.7 mm were coupled at the centre of the top surface of the rail head. They were used in pulse-echo configuration with a center frequency of f_C = 2.25 MHz. The A-scan-HF data was stored using a digital oscilloscope (LeCroy LC334A).

4. Numerical Simulations

The simulations of the wave propagation processes in the different rails were carried out using the Elastodynamic Finite Integration Technique (EFIT) that was originally developed by Fellinger et al. [1]. The FIT discretization of the integral form of the basic equations of linear elasticity, Hooke's law and the equation of motion, leads to a very stable and efficient numerical code which is applicable for a wide range of NDT problems [2-4]. For reasons of computer capacity, in most cases only two-dimensional simulations are practicable representing a "plane strain" propagation process. Due to this limitation we realized two-dimensional synthetic rail models describing the cross sections of the real specimens (see Fig. 2). For this purpose, the EFIT program of EADQ (developed by F. Schubert and B. Koehler for elastic wave modeling in concrete [3]) was adapted and optimized for the given rail geometries. The result of this modification is the program 'EFITrail' having the following special attributes:
1. Reading of so called "rail-input-files" to realize nearly arbitrary rail geometries. In these "input-files" the cross section of a rail is described in a first step by a simple straight line model. In a second step, each corner of the straight line model is smoothed by an individual smoothing factor. In this way, the synthetic 2D rail models are represented very close to the cross sections of the real specimens.
2. Problem-adapted grid cell management. The EFIT-program usually works with rectangular specimens. If we would put the rail model in such a rectangular environment, more than 2/3 of the grid cells (the grid cells outside the rail region) were found as ineffective cells, that means they were not really necessary but they would occupy the computer memory. The EFITrail program uses only the effective grid cells inside the rail region so that only 1/3 of the original grid cells and hence 1/3 of computer memory is required. Around the effective grid cells, a layer of cells with stress-free boundary conditions was realized.
3. Symmetric boundary conditions. The cross sectional testing geometry was symmetric to the vertical axis of the rail, so that the simulations were carried out in only one half of the rail using symmetric boundary conditions at the axis. With this the number of grid cells is decreased by the factor two.
4. The cracks were assumed as regions with stress free boundary conditions lying exactly on the axis of symmetry.

The simulations were carried out with the following parameters:

• base material of the rails: steel
• acoustic properties: = 7800 kg/m^³, c_L = 5900 m/s, c_S = 3250 m/s
• transducers: shear and longitudinal
• incidence: normal
• sensitivity: Gaussian
• aperture: line, L = 12.7 mm
• center frequency: f_C = 2.25 Mhz
• signal: RC₂ (raised cosine with two cycles)

For the simulations with the longitudinal wave transducer the following discretization parameters were used:

• spatial discretization: x ~ 71.7 µm
• temporal discretization: t ~ 7.8 ns
• number of time steps: 10 260 (t_max ~ 80 µs)
• number of effective grid cells: ~ 765 000
• crack width: 5 grid cells (~ 0.358 mm)

For the simulation with the shear wave transducer we used:

• spatial discretization: x ~ 53.8 µm
• temporal discretization: t ~ 6.3 ns
• number of time steps: 20 600 (t_max ( 130 µs)
• number of effective grid cells: ~ 1 354 000
• crack width: 5 grid cells (~ 0.27 mm)

For each simulation, nine wavefront snapshots were taken at different times corresponding to the wavefront travelling distances 30, 70, 110, 150, 190, 230, 270, 310 and 350 mm, respectively. The snaphots are given as gray scale images representing the absolute value of the particle displacement velocity vector. Additionally HF-A-scans were detected by averaging the signal over all discrete grid points inside the transducer aperture.

5. Results

In the following sections, the ultrasonic wave propagation in the different specimens is discussed in detail by comparing the experimental HF-A-scan measurements with the results of the numerical simulations. The wavefront snapshots are helpful for a better interpretation of the received signals. In this paper, we shall focus on the results for the longitudinal wave transducer. However, results for the shear wave transducer are shortly summarized at the end of this chapter. Any further information on this aspect can be obtained directly from the author.

5.1 Ideal Rail without cracks (Rail A)
Fig. 3 shows EFITrail time snapshots of the wave propagation in the ideal rail without cracks. The longitudinal wave transducer was located at the centre of the top surface of the rail head. The primary wavefront that propagates through the neck of the rail, is further reflected at the bottom and runs back to the transducer where it can be detected about 58 µs after signal input. In the neck of the rail, so called side-echoes are generated due to mode conversions at the rail boundaries (see Fig. 4).

Fig. 3: EFITrail time snapshots of the wave propagation in the rail without cracks. The longitudinal wave transducer was placed at the centre of the rail head. Slide Show =>

Fig. 4: Detailed representation of the mode conversions in the neck of the rail. The longitudinal wavefronts in tow-line of the head-wave cross produce a secondary ultrasonic echo or side-echo that follows the primary wavefront.

The EFITrail snapshots are in a good agreement with experimental schlieren examinations of Hall done at glass model rails [5]. The transformation sequence of the mode conversion is:

primary P-wave   =>   head-waves   =>   secondary P-waves  =>   P-wave side-echo

The head-waves are shear waves with a linear wavefront. After formation of the first side-echo, the second, third, and further side-echoes appear but with rapidly decreasing amplitude. The distance between the different side-echoes and their amplitudes are mainly influenced by the width and the geometry of the rail neck. In this case, the first P-wave side-echo arrives at 62 µs, the second one at 67 µs. The Figs. 5 - 8 show both, measured and modeled HF-A-scans for the given testing situation. They are in an excellent agreement with each other. There are only small differences in the pulse forms due to the fact, that the input signals used in the simulation were slightly different from those used in the measurements.

Fig. 5: HF-A-scan measured at the ideal rail specimen without cracks. The rail bottom echo arriving at about 58 µs and the first side-echo at 62 µs are clearly visible. Fig. 6: HF-A-scan obtained by EFITrail modeling showing good agreement with the experimental result is excellent. In addition to the first side-echo, one can observe the weaker second side-echo at about 67 µs.
Fig. 7: Detailed experimental A-scan showing bottom echo and first and second side-echo, respectively. Fig. 8: Detailed modeled A-scan. The pulse form of the signal is slightly different from that used in the measurements.

5.2 Rail with vertical crack in the rail head (Rail B)


Fig. 9: EFITrail time snapshots of the wave propagation in the rail with a vertical crack in the rail head. Slide Show =>

Fig. 10: Detailed representation of mode conversions at the crack surface showing two head-waves running sideways into the rail head and a Rayleigh wave which can be identified at the crack surface.

Fig. 9 shows EFITrail time snapshots of the wave propagation in the rail specimen with a vertical crack in the rail head. The mode conversions at the crack (Fig. 10) produce two significant shear waves running sideways into the head of the rail. Moreover, a Rayleigh wave is generated immediately at the crack surface [6]. The shear waves are reflected at the rail head boundaries and turn back to the transducer where a new echo can be detected at about 31 µs. Due to the mode conversions described above, the bottom echo and the first side-echo are significantly attenuated in comparison to the case of an ideal rail without cracks. This fact can be easily noticed in the modeled and measured A-scans as shown in Figs. 11 -14. Again there is a good qualitative agreement between experiment and simulation but there are quantitative differences in the relative amplitudes of the different echoes. This is obviously caused by the fact that the simulations were two-dimensional (i.e. strip-like transducer aperture in the direction of the longitudinal axis of the rail) while the measurements were three-dimensional (circular transducer aperture). Moreover, another fact that cannot be excluded is, that the modeled cross section was slightly different from the cross section of the real rail specimen. Furthermore, there were some inaccuracies in the measurements due to unstable coupling conditions.

Fig. 11: HF-A-scan measured at the rail specimen with a vertical crack in the rail head. Besides the attenuation of the bottom echo (in comparison to the case of an ideal rail without cracks) one can observe the head-wave reflex at about 32 µs. Fig. 12: HF-A-scan obtained by EFITrail modeling. Again, there is a good qualitative agreement with the experimental result with differences in the relative amplitudes of the echoes.

Fig. 13: Detailed measured A-scan showing the crack tip echoes and the head-wave reflex. Fig. 14: Detailed modeled A-scan. All crack tip echoes which can be seen in the measured A-scan can also be found in the simulation result.

5.3 Rail with vertical crack in the rail neck (Rail C)


Fig. 15: EFITrail time snapshots of the wave propagation in the rail with a vertical crack in the rail neck. Slide Show =>

Fig. 16: Detailed representation of the mode conversions at the crack and rail surfaces in the neck of the rail. A new side-echo is produced lying exactly between the bottom echo and the (first) side-echo known from the case of an ideal rail without cracks (compare Fig. 4).

Fig. 15 shows EFITrail time snapshots of the wave propagation in the rail with a vertical crack in the rail neck. From the case of an ideal rail without cracks it is known that different side-echoes are generated. Their amplitudes and the distances to each other and to the rail bottom echo depend on the geometry and width of the rail neck, respectively. In this case, the crack in the neck bisects this rail region into two parts having only half the width of the original neck without cracks. Therefore, a new side-echo with a high amplitude is generated directly between the bottom echo and the former first side-echo (Fig. 16). It can also be found in the modeled and measured A-scans (Figs. 17 - 20). Again, the agreement between experiment and simulation is qualitatively good but there are differences in the relative amplitudes. It should be mentioned that the rail specimen in this case was somewhat different from those used in the other measurements (compare Fig. 2). In particular, the height of the rail was bigger so that all echoes arrived about 1 µs later than in the other cases.

Fig. 17: HF-A-scan measured at the rail specimen with a vertical crack in the rail neck. The new side-echo at about 61 µs lying between the bottom echo at 59 µs and the (former) first side-echo at 63 µs is clearly visible. Fig. 18: HF-A-scan obtained by EFITrail modeling. The new side-echo can also be seen here. Again, there are some quantitative differences to the measurement concerning the relative amplitudes of the echoes.

Fig. 19: Detailed measured A-scan. Fig. 20: Detailed modeled A-scan. The qualitative agreement with the measured data concerning the arrival times of bottom echo and side-echoes is good.

5.4 Rail with vertical surface-breaking crack at the bottom of the rail (Rail D)


Fig. 21: EFITrail snapshots of the wave propagation in the rail with a vertical surface-breaking crack in the bottom of the rail. Slide Show =>

Fig. 22: Detailed representation of the mode conversions at the crack showing head-waves produced at the crack surface propagating sideways into the bottom of the rail. Therefore, they cannot be detected by the transducer.

Fig. 21 shows EFITrail snapshots of the wave propagation in the specimen with a surface-breaking crack at the bottom of the rail. Similar to the case in which the crack was located in the rail head, also here two significant head-waves are generated (Fig. 22). They propagate sideways into the rail bottom and therefore they cannot be detected by the transducer. Consequently, only the attenuation of the bottom echo and the first side-echo can be observed in the A-scans (Figs. 23 - 26). The arrival times of the different echoes in simulation and experiment are nearly identical but the attenuation of the signals in the EFITrail calculation is less significant than in the measurement.

Fig. 23: HF-A-scan measured at the rail specimen with a surface-breaking crack at the bottom of the rail showing significant attenuation of the bottom echo and the first side-echo. Fig. 24: HF-A-scan obtained by EFITrail modeling. Again, the qualitative agreement with the measurement is good with attenuation of the bottom echo being less significant.
Fig. 25: Detailed measured A-scan. Fig. 26: Detailed modeled A-scan. The arrival times of the different echoes are nearly identical with the measurement.

5.5 Shear wave results
In this section, we give a short summary (without figures) of the results obtained using the shear wave transducer on the same specimens used above. In order to compare measurement and numerical calculation, only shear waves polarized in the plane of the rail cross section were investigated. The qualitative agreement between experiment and simulation was found good with only differences in the amplitudes of the different echoes. The most important difference between the longitudinal and the shear wave results is the fact that the interaction between the primary shear wavefront and the crack or rail surfaces does not produce new significant wavefronts like the head-waves or the side-echoes as described before. Only Rayleigh waves are generated by mode conversion and therefore in the corresponding A-scans, the attenuation of the shear wave bottom echo can only be observed. The results for the different crack configurations can now be summarized as follows: If the crack is in the head or in the neck of the rail, it is better to use longitudinal transient signals instead of shear waves because in these cases the crack can be clearly identified not only by the attenuation of the bottom echo but also by the appearance of new mode-converted reflexes. If a surface-breaking crack is at the bottom of the rail, shear waves are preferable because in this case the attenuation of the rail bottom echo is found to be stronger than for longitudinal waves.

6. Conclusions

The good qualitative agreement between the measurements and the numerical simulations for the different testing situations shows the accuracy of the developed EFITrail program. With the help of the simulations, all mode conversions at the crack and rail surfaces were definitely cleared up which leads to a better understanding and interpretation of the received signals. A significant attenuation of the rail bottom echo for the three different crack locations were found for both, shear and longitudinal waves. The mode conversions of the longitudinal waves additionally produce head-wave echoes and side-echoes which can be detected by the transducer if the crack is located in the head or the neck of the rail. Consequently, vertical cracks in rails can be detected with both wave types, shear and longitudinal waves. The actual wave type which is preferable in a given testing situation mainly depends on the crack location. It should be mentioned that the method using piezoelectric shear wave transducers is unpracticable for fast testing of real rails in railway tracks due to coupling-problems. But this can be solved using EMA-transducers. Further investigations should involve more realistic crack geometries and various crack parameters (width, length, depth, orientation, surface roughness and so on), different frequencies and moreover shear waves with a polarization plane perpendicular to the rail cross section. For the latter problem, real three-dimensional simulations are essential. However, a broader future perspective of the investigations should involve a classification of typical defects using both, shear and longitudinal waves, in the pulse-echo mode of ultrasonic testing.

References

1. P. Fellinger, R. Marklein, K.J. Langenberg, S. Klaholz, "Numerical modeling of elastic wave propagation and scattering with EFIT - elastodynamic finite integration technique", Wave Motion 21, 47-66 (1995).
2. R. Marklein, R. Bärmann, K.J. Langenberg, "The Ultrasonic Modeling Code EFIT as applied to Inhomogeneous Isotropic and Anisotropic Media", Review of Progress in QNDE, Eds. D.O. Thompson and D.E. Chimenti, Plenum Press, New York, Vol. 14, 251-258 (1995).
3. F. Schubert, B. Koehler, "Numerical Modeling of Ultrasonic Attenuation and Dispersion in Concrete - The Effect of Aggregates and Porosity", in: Proceedings if the Int. Conf. 'Nondestructive Testing in Civil Engineering', Liverpool, 143-157 (1997).
4. F. Schubert, B. Koehler, "Numerical Modeling of Elastic Wave Propagation in Random Particulate Composites", Proceed. 8th Int. Symp. on Nondestructive Characterization of Materials, Boulder, Colorado, USA, June 15-20, 1997, to be published in May or June 98.
5. K.G. Hall, "Visualization Techniques for the Study of Ultrasonic Wave Propagation in the Railway Industry", Materials Evaluation 42, 922-933 (1984).
6. V.P. Lochov, "Investigation of Rayleigh wave diffraction on the edge of the crack", Defektoskopiya 3, 39-47 (1989).

Authors

Frank Schubert*, Bernd Koehler
Fraunhofer-Institute Non Destructive Testing (IzfP)
Branch Lab EADQ, Kruegerstrasse 22
D-01326 Dresden (Germany)
Email: schubert@eadq.izfp.fhg.de
On NDTnet: Q Net Stand
Olga Sacharova
Railway University St.Petersburg (Russia).


* Frank Schubert received the Ernst Schiebold coin awarded in Dresden 1997