Traditional Method Based on Crack Propagation Induced AE Waves. The Paris' law [12] describes a critical relationship between fatigue crack growth rate.
Detection and Quantification of Fatigue Cracks in Rail Steel Using Acoustic Emission Technique D. LI, K.S.C. KUANG and C.G. KOH
ABSTRACT Acoustic emission (AE) technique has a promising application for crack detection in rail tracks. However, it is still a challenging task to identify the size of fatigue cracks from AE signals. This paper proposes an index based on wavelet coefficients to accurately distinguish AE waves induced by crack propagation and crack closure, and a novel method of crack quantification based on crack closure induced AE waves. A higher count rate of crack closure induced AE waves indicates a larger crack size. The performance of the proposed method was validated by a three-point bending fatigue test on the rail steel specimen. In contrast with the traditional method, which is based on crack propagation induced AE waves and good at detecting crack growth rate, this method estimates the crack size without using the cumulative AE information, and is thus applicable to crack quantification of both new and existing structures. These two methods can be used to complement each other leading to a more efficient approach for crack detection, which has the potential for condition monitoring of rail tracks in the field.
INTRODUCTION Condition monitoring of rail tracks aims to identify defects in advance and to ensure smooth and safe operation [1]. Acoustic emission (AE) technique is a nondestructive testing (NDT) method that has a promising application for crack detection in rail tracks [2, 3]. AE refers to the generation of transient stress waves within the material due to sudden release of elastic strain energy during processes such as plastic deformation, crack, impact, friction, and others [4]. Compared with other ultrasonic NDTs, it is more sensitive to crack initiation and propagation, less influenced by the geometry of structure and more capable of long-distance detection. AE technique has been shown to be able to detect the presence of defects and locate their positions in various materials and structures. However, it is still a challenging task to quantify the size of defects, especially cracks, based on AE signals [5].
Department of Civil and Environmental Engineering, National University of Singapore, Block E1A, # 07-03, 1 Engineering Drive 2, Singapore 117576, Singapore
When fatigue cracks grow in metals, AE hits occur in two main processes, i.e. crack propagation and crack closure [5, 6]. The crack propagation process includes plastic deformation, crack extension and fracture events within the plastic zone. It happens mostly near the peak load regions of fatigue cycles. The crack closure process mainly refers to the friction between crack surfaces. It happens mostly in the unloading periods. Traditionally, the crack quantification relied on crack propagation induced AE waves, which were extracted during the top 10% or 20% of load range. A good correlation was obtained between the corresponding AE count rate and crack growth rate on various specimens [5-7]. The crack length was then estimated by cumulative AE information, e.g. cumulative counts or energy. It is applicable for continuous monitoring of newly built structures with an undamaged initial state, but not existing structures already with some unknown cracks. While, crack closure induced AE waves were used to measure the closure load and closure level [8]. In order to apply AE technique to the condition monitoring of rail tracks, this paper brings forward an index based on wavelet coefficients to accurately distinguish AE waves induced by crack propagation and crack closure, and a novel method of crack quantification based on crack closure induced AE waves. It is believed that more closure induced AE waves per load cycle indicates a larger crack in the structure. A three-point bending fatigue test will be carried out on the rail steel specimen to validate the performance of the proposed method. The results, advantages and disadvantages of both traditional and novel methods will be compared and discussed. AN INDEX TO DISTINGUISH DIFFERENT TYPES OF AE WAVES Crack propagation and crack closure induced AE waves are usually separated artificially depending on the load [5-7]. However, they may happen at the same load levels. It is difficult to get real-time loading information and determine the threshold in terms of percentages of load range. Thus, an index based on wavelet coefficients is established to distinguish different types of AE waves. Continuous wavelet transform (CWT) can fully characterize AE signals in the time-frequency domain [9]. The CWT of a signal x(t ) of time t is defined as
WT a, b x t a,b (t ) dt
(1)
Here, a ,b (t ) t b / a / a ( a 0 ) is a series of wavelet functions, which are dilated and translated from a mother wavelet (t ) . a is the scale parameter, b is the translation parameter, and “*” denotes the complex conjugation. In this study, the complex Morlet wavelet [10] is selected as the mother wavelet, which provides excellent resolution in both of the time and frequency domains. Its function (t ) is
t2 exp i 2 f c t exp (2) fb fb where fb is the bandwidth parameter, fc is the central frequency of the wavelet, and i is the imaginary unit. It is considered admissible for 2 f c 5 . The Shannon entropy of wavelet coefficients is introduced to determine the values of fb and fc for the sake of an optimal mother wavelet [11]. Assuming that wti ( i 1, 2,..., n ) is a set of wavelet coefficients, its Shannon entropy is defined as
t
1
SWT i 1 pi log pi n
pi
where
wti
2
n
wt j j 1
(3)
2
with in1 pi 1 , and pi log pi 0 for pi 0 . An optimal mother wavelet would produce a coefficient matrix with the minimum Shannon entropy, i.e. the highest energy concentration. Using AE waves obtained in a laboratory fatigue test (which will be introduced in the “Experimental test” section), the optimal complex Morlet mother wavelet was found to the function with fb=0.5 and fc=4. The two types of AE waves, acquired respectively from the top 5% and bottom 5% load period in the fatigue test, were analyzed. The waveforms and WT plots of two examples are shown in Figure 1 and 2. The energies of both types of AE waves are found to be all concentrated mainly in the frequency range of [100-350] kHz. Crack propagation induced AE waves also have a notable portion of energy in the higher frequency range of [350-800] kHz. However, the wave energy of crack closure induced AE waves in the higher frequency range is almost negligible compared to that in the lower frequency range. Based on these observations, the wavelet coefficients in the two frequency bands, B1 = [100-350] kHz and B2 = [350-800] kHz, are extracted. The ratio between the two peak values, P1 and P2 , respectively in B1 and B2 is considered as the index to distinguish the two types of AE waves: 0.5
Crack propagation
5
Voltage (V)
Voltage (V)
10
0 -5 -10 0
Crack closure
0.25 0
-0.25
0.5
1
1.5 Time (ms)
2
2.5
-0.5 0
3
0.5
1
1.5 Time (ms)
(a)
10
600 400
5
200 0.5
1
3
1.5 Time (ms)
2
2.5
3
Crack closure
1000
0
Frequency (kHz)
Frequency (kHz)
800
0 0
2.5
(a) Crack propagation
1000
2
1
800
0.8
600
0.6
400
0.4
200
0.2
0 0
0.5
1
1.5 Time (ms)
2
2.5
3
0
(b)
(b)
Figure 1. Crack propagation induced AE wave (a) waveform and (b) WT.
Figure 2. Crack closure induced AE wave (a) waveform and (b) WT.
TABLE I. INDEX CALCULATION OF AE WAVES. P2 R AE waves Amp (V) P1
P1
P2
R
0.33
1.069
0.183
0.17
C2
0.36
0.819
0.264
0.32
0.81
C3
0.46
1.121
0.298
0.27
5.074
0.67
C4
0.58
1.373
0.446
0.32
12.698
11.879
0.94
C5
0.71
1.507
0.643
0.43
18.039
10.282
0.57
C6
0.80
1.761
0.702
0.40
AE waves
Amp (V)
P1
0.35
0.537
0.437
0.81
C1
P2
0.76
1.071
0.794
0.74
P3
1.27
1.822
1.467
P4
5.30
7.531
P5
8.25
P6
9.91
R
max wti wti B2
max wt j wt j B1
P2 P1
(4)
TABLE I lists some selected results, where P1-P6 are AE waves induced by crack propagation, and C1-C6 are AE waves induced by crack closure. As can be seen, the indexes of crack propagation induced AE waves are all above 0.5, while those of crack closure induced AE waves are below 0.5. Therefore, the ratio between the maximum wavelet coefficients from the two representative frequency bands could be considered as an effective index to distinguish different types of AE waves by a threshold of 0.5. QUANTIFICATION OF FATIGUE CRACKS Traditional Method Based on Crack Propagation Induced AE Waves The Paris’ law [12] describes a critical relationship between fatigue crack growth rate da / dN and stress intensity factor range K : da m da C0 K or log (5) m log K log C0 dN dN
where a is the crack length, N is the number of fatigue cycles, and C0 and m are assumed to be material constants. The absolute energy of AE waves is considered proportional to the total energy released due to crack propagation. Thus, a similar relationship between the count rate of AE waves induced by crack propagation dc p / dN and K is widely used [6, 7]. dc p n C1 K dN
dc p or log dN
n log K log C1
(6)
where cp is the AE counts induced by crack propagation, and C1 and n are material constants. After eliminating K , the relationship between dc p / dN and da / dN , linear in the log-log sacle, is deduced dc p da log (7) q log log C2 dN dN where C2 and q are also material constants. Then, the crack length can be determined by accumulation of AE counts from the uncracked initial state to the present cracked state. This is only applicable for those cases that AE sensors are installed before any damage occurs and fixed on the structure to continuously record data. Novel Method Based on Crack Closure Induced AE Waves
The crack closure concept has been considered important in assessing the fatigue life of structures under fatigue loads. Here, it mainly refers to the friction between crack surfaces. When there is a fatigue crack in the structure, the two crack surfaces can contact each other during unloading periods due to a variety of mechanisms [6, 8]. Obvious phenomenon of crack closure could be found provided the load ratio is below 0.45 [13]. Similar to the crack propagation, the friction of crack surfaces would also generate prominent AE hits, which are related to the area of surfaces, material
properties and load levels. It is reasonable to believe that, under certain load range, a larger number of crack closure induced AE waves in a load cycle indicate a larger crack size, i.e. a longer crack length, exiting in the structure. That is to say, there is an approximately linear relationship between the absolute crack size and count rate of AE waves induced by crack closure dcc / dN : dcc k a a0 g (8) dN where cc is the AE counts induced by crack closure, a0 is the notch depth, (a a0 ) is the absolute crack length due to fatigue load, and k and g are assumed to be material constants. The size of a fatigue crack can be quantified by the count rate of crack closure induced AE waves in one or several load cycles. It requires no cumulative AE information, and thus is applicable to both continuous monitoring and scheduled inspection of new and existing structures. EXPERIMENTAL TEST
A three-point-bending fatigue test was carried out on a rail steel specimen in the laboratory (Figure 3). The specimen was cut from the head of CHN 60 kg/m rail. Its dimensions were 200 mm 40 mm 20 mm. A notch of 8 mm was machined at the bottom. The universal testing machine (INSTRON MODEL 1334) was used to generate a sinusoidal load with peak load of 25 kN, load ratio of 0.1, and load
Figure 3. Experimental setup
Figure 4. Final fracture of specimen.
Amplitude (dB)
100 90 80 70 60 50 0
Figure 5. Crack length versus load cycles.
2000
4000 6000 Time (s)
8000
10000
Figure 6. Different AE waves acquired.
frequency of 5 Hz. A crack opening displacement (COD) gauge was used to calibrate the crack length. PAC WD AE sensors with wide operating bandwidth of 125-1000 kHz, were fixed onto the side surface of the specimen. AE signals acquired by the sensors were amplified via preamplifiers with 40 dB gain. PAC AEwin® and MATLAB® softwares were used for data acquisition and analysis. The sampling rate was 5 MHz, the analog band-pass filter was 100 – 1000 kHz, and the threshold for trigger-mode acquisition was set to 50 dB after a series of trials and calibration. RESULTS AND DISCUSSIONS Crack Length Calibration and AE Waves Separation
According to the ASTM standards E1820 and E647 [14, 15], crack length were calculated using the measurements of COD gauge, as shown in Figure 5. Due to the high peak load applied, a macroscopic crack initiated from the notch around 5000 cycles, and propagated gradually afterwards. After reaching certain length (marked by the red arrow in Figure 4), the crack propagated rapidly until specimen fractured with a total number of about 40,000 cycles. The plot can be divided into three regions: region I (threshold), region II (Paris) and region III (rapid fracture). A period with crack length from 8.4 to 12.0 cm will be focused, which falls into the region II. Using the index based on wavelet coefficients, the AE hits acquired were separated into two groups (Figure 6), crack propagation induced AE waves marked by red points and crack closure induced AE waves marked by blue circles. The amplitudes of AE waves induced by crack propagation vary from 50 dB to 100 dB, while the amplitudes of AE waves induced by crack closure are all below 80dB. Crack Quantification Using Two Methods
Considering the crack propagation induced AE waves only, the cumulative AE counts are plotted versus load cycles in Figure 7. Consistent with the crack length, it successively experiences the slow increase, stable increase and rapid rise periods. Figure 8 shows the relationship between the corresponding AE count rate dcp /dN and crack growth rate da /dN in the log-log scale. Equation (7) is then calibrated to be x 10
5
dcp/dN (counts/cycle)
4
AE counts
3 2 1 0 0
10
2
10
1
10
0
-1
1
2 3 Cycles (N)
4
5 x 10
4
Figure 7. Cumulative AE counts induced by crack propagation
10 -5 10
-4
10 da/dN (mm/cycle)
10
Figure 8. Relationship of crack propagation induced AE count rate and crack growth rate
-3
x 10
4
6 dcc/dN (counts/cycle)
AE counts
15
10
5
0 0
1
2 3 Cycles (N)
4
5 x 10
4
4
2
0 8
9
10 a (mm)
11
12
Figure 9. Cumulative AE counts induced by crack Figure 10. Relationship of crack closure induced closure AE count rate and crack length
dc p da da dc p log (9) 1.21log 5.36 or log 0.49 log 4.19 dN dN dN dN The count rate of AE waves induced by crack propagation directly reflects the crack growth rate, which presents the status of crack. However, the crack length needs to be estimated by its relationship with the cumulative counts of corresponding AE waves, which turns to be nonlinear. It is difficult to be applied to fatigue cracks in structures other than test samples with standard shapes. Considering the crack closure induced AE waves only, the cumulative AE counts are plotted versus load cycles in Figure 9. Also consistent with the crack growth, it successively experiences the slow increase, stable increase and rapid rise periods. As shown in Figure 10, the crack closure induced AE count rate dcc / dN does linearly increase along with the growth of crack. Equation (8) is calibrated as dcc dc 0.79 a a0 0.08 or a 0.88 c 0.74 a0 (10) dN dN where a0 = 8 mm in this study. This line almost passes through the origin. It means no AE waves would arise when there is no crack. Based on this relationship, the crack length can be estimated by recording the count rate of crack closure related AE waves. This empirical equation does not rely on the Paris’ law, and is thus applicable to the three regions of crack growth as along as the load ratio is low enough to make the crack surfaces contact during unloading periods. Additionally, it has the potential to quantify fatigue cracks of complex modes, e.g. the rolling contact fatigue cracks of rail tracks. CONCLUSIONS
This paper investigated the detection and quantification of fatigue cracks in rail steel using AE technique. An index based on wavelet coefficients was established to accurately distinguish the different types of AE waves, respectively induced by crack propagation and crack closure. For the WT of AE waves, the Shannon entropy was introduced to select the optimal mother wavelet. Then, a novel method of fatigue crack quantification was developed based on crack closure induced AE waves, the count rate of which is linearly related to the crack size. Its performance was validated by a three-
point bending fatigue test on the rail steel specimen. The traditional crack quantification method, which is based on crack propagation AE waves and Paris’ law, is good at to detect the initiation and growth rate of fatigue crack, however needs complicated calibration and cumulative AE information for identifying crack size. In contrast, this novel method no longer needs the cumulative AE information, and is thus applicable to crack quantification of both new and existing structures. Furthermore, these two methods can be used to complement each other leading to a more efficient approach for crack detection, which has the potential for condition monitoring of rail tracks in the field. ACKNOWLEDGEMENT
This study is supported by the National University of Singapore Academic Research Fund (Grant No. R-302-000-097-112). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
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