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AE Parameter Analysis for Fatigue Crack Monitoring Dong-Jin Yoon, Juong-Chae Jung, Ki-Bok Kim, Philip Park, Seung-Seok Lee Nondestructive Evaluation Group, Korea Research Institute of Standards and Science Doryong-dong 1, Taejon, 305-600, Korea e-mail: djyoon@kriss.re.kr Contact

ABSTRACT

Acoustic emission technique was employed for the evaluation of fatigue crack activity in steel bridge members. Laboratory experiment was carried out to identify AE characteristics of fatigue cracks for compact tension specimen. The relationship between a stress intensity factor and AE signals activity as well as conventional AE parameter analysis was discussed. Especially, principal component analysis and regression method was introduced to investigate the tendency of AE parameter for stress intensity factor. From the results, the features of three parameters such as the length of crack growth, the AE energy, and the cumulative AE events, showed the almost same trend in their increase as the number of fatigue cycle increased. From the comparisons of several AE parameters, AE energy with stress intensity factor showed a good correlation to the characteristics of crack propagation. It was also verified that the higher stress intensity factors generated AE signals with higher peak amplitude and a larger number of AE counts. Finally statistical approaches such as principal component anslysis and principal component regression might provide a promising method to analyze various AE parameters.
Keywords: Acoustic emission, fatigue crack, steel bridge, stress intensity factor, crack propagation, principal component analysis, principal component regression

1. INTRODUCTION

A number of steel structures are aging and deteriorating due to long time services. Especially, steel bridge members are constantly subjected to a cyclic loading of variable magnitudes. As a result, material fatigue might be experienced. To prevent sudden failures of bridge members and structures, acoustic emission (AE) has been proposed as a passive warning system for detecting fatigue cracking.
Several previous studies have shown the possibility of monitoring fatigue crack propagation by acoustic emission technique.[1-6] A study for continuous monitoring of fatigue crack using acoustic emission had been carried out in the early 1970's. In this study, the detectability of fatigue crack under very low crack growth rate of 10^-6 in/cycle was shown, and the effect of instrumentation gain and sensor frequency for AE measurement was also discussed.[1] Wang et al. investigated AE behaviors for various fatigue crack conditions in structural steel specimens.[2-4] There was a relationship between AE count rate and stress intensity factor. It was found that AE behavior during the crack propagation depended on the specimen orientation. Most of previous works to date have involved studying the characteristics of fatigue crack initiation and propagation as well as crack closure and opening.[5-8]Another study on detecting fatigue crack in both specimen and actual bridge was based on source location technique using wave modes or time arrival method.[9-10] However, neither a useful guideline nor a method of finding crack growth was suggested clearly in the previous studies. To achieve the practical monitoring of AE signals from fatigue cracks with effective noise filtering, it is very important to find out the characteristics of AE signals in various states of crack propagation.
Acoustic emission as a nondestructive evaluation technique and as a useful tool for materials research is a highly sensitive technique for detecting active microscopic events in a material, as well as crack initiation and propagation. Actually, acoustic emission technique was employed for the evaluation of fatigue crack activity in both cases of specimen and actual steel bridge. However, in this paper, the result of laboratory experiment was only introduced and it was carried out to identify AE characteristics of fatigue cracks for the compact tension specimen.
The purpose of this study is to quantify and to characterize the acoustic emission signals emitted from cracks in steel bridge components. This characterization is intended to enhance the existing damage evaluation of highway bridges. The result of this study is targeted at developing AE as a feasible bridge monitoring technique. In addition, this research was aimed at determining the most effective AE parameters necessary for determining the detectability of fatigue crack.

2. RELATIONSHIP BETWEEN AE AND STRESS INTENSITY FACTOR

2.1. Detectability of the AE Technique
Detectability, which decides minimum size of detectable crack, is one of the most important problem for detecting cracks using nondestructive test. Theoretically, as one of the best technique to detect cracks, acoustic emission technique could detect smallest cracks such as separation of atomic unit, if noise signals were completely intercepted. But complete interception of noise signal is practically impossible. The limit of detectability of AE technique would be defined from a threshold, which is determined by background noise level.
In the bridge structure, there is somewhat high level of noise signals because of the existence of various noise sources. The basic method to filter out noises is to acquire only signals that have higher peak amplitude than a given threshold. Therefore, the detectability of AE technique absolutely depends on the threshold value of which the operator choose. Because the value of threshold varies with the conditions of structures, environment and settings of equipment etc., we cannot offer a certain specific value. Accordingly, the experiences of operator is the most important factors to set a threshold.
The AE crack signal is the appearance that some part of released energy due to a crack propagation transformed into elastic wave. From this, we can suppose that the energy of emitted elastic wave is directly proportional to the energy release rate which is a fracture mechanics parameter occurring by crack propagation. Dunegan et al.[11] suggested that N_AE , total cumulative AE count is directly proportional to V_p , the volume of plastic area at the crack tip, (Eq. 1). And Morton et al.[12] reported experimental relationship (Eq. 2) between total cumulative AE count and the stress intensity factor range (D K) for aluminum.


where, C, A and l are experimentally determined constants.
The energy of AE signal can be expressed by an area of triangle that consisted of a width of signal duration and a height of peak amplitude. Therefore, if the energy of AE signal increased according to crack growth, the peak amplitude would increase as well as AE count rate. In the present paper, based on this assumption, characteristics of AE signal according to crack growth condition is experimentally investigated to provide a basic data associated with the detectability of AE technique.

2.2. Energy Release Rate, Stress Intensity Factor and Crack Growth Rate
Fatigue is a mechanism of crack growing.[13] Fatigue cracks occur by cyclic load under lower stress condition than allowable stress, and fatigue cracks spend most of life on subcritical crack growth. For assuring safety of steel structure, we should detect and monitor cracks in the period of subcritical crack growth.
Fatigue crack growing process is classified to three regions according to the change of fatigue crack growth rate (da/dn). Region I is a state of crack initiation. The value of stress intensity factor(K) is as low as fatigue threshold(K_th) and crack growing speed is very slow. In region II, crack growing speed increases according to the crack length. Stress intensity factor and crack growth rate show the relationship of direct proportion. It is well known as Paris' equation (Eq. 3).[14] The crack growing condition in region II is so called stable crack growth. In region III, crack growth rate quickly increases and the member is about to failure. It is called unstable crack growth. A boundary between region II and region III is called transition point(K_Tr)[15] and stress intensity factor at failure is called fracture toughness(K_c).


where, C and m are experimentally determined constants.
Elastic energy release rate, G has a relationship of Eq. 4 with stress intensity factor, K. Stress intensity factor defines the amplitude of the crack tip singularity[16] and is a function of applied nominal stress(s ), crack length(a) and geometric function(F) as shown in Eq. 5. Therefore, if detectability of AE technique was expressed by using stress intensity factor, it would be applicable to various stress range and crack length.

where, E is modulus of elasticity.

2.3. Application of Detectability to Fatigue Estimation
If there are enough data about AE signal characteristics according to the change of stress intensity factor, a detectability, K_AE can be obtained from threshold determined by background noise level. Fatigue estimation methods by applying AE technique are suggested in case that K_AE is given.
Eq. 6 and Eq. 7 is derived from Eq. 5 and K_AE. If an applied stress is known, detectable crack length can be obtained by Eq. 6. In opposite case, when a crack size to be detected is given, we can determine a load to be applied in the field test by using Eq. 7.

where, D s _test is applied nominal stress range and a_AE is detectable crack length.
In addition, by using an idea of Eq. 3, the remaining life of detectable crack can be predicted. Eq. 8 is a modified Paris' relationship suggested by Klesnil and Lukas[17] to consider the effect of fatigue threshold.

Eq. 9 can be derived from Eq. 8. From Eq. 9, we can obtain the number of remaining fatigue cycles, n.

where, D K_eq is equivalent stress intensity factor range and a_cr is critical crack length for failure.

3. EXPERIMENTS

3.1. Preparation of Specimen
SWS490B steel, which is most popular for bridge construction, was used in this study. Standard compact tension (CT) specimens were machined from rolled plate of 250 mm thick. Three kinds of thickness with 9, 12, 20 mm were prepared for considering the effect of thickness. Two types of L-T and T-L associated with rolling direction for each thickness were also prepared. In this investigation, however, L-T specimen was only used. Shevron notch was introduced with 5 mm long in the middle of the notch. Different load ratio was applied for introducing pre-crack before each test.

3.2. Fatigue Test and AE Measurement
Fatigue cycle loading test was conducted on a MTS closed loop hydraulic loading machine. All of the test specimens were subjected to constant amplitude cyclic loading for three types of cyclic frequency of 1, 2, and 4 Hz. In order to reduce the hydraulic noise from loading system, extensional rod with sound isolation tape was connected to the each clevis. The pin was also taped to reduce noise. Consequently, total reduction of about 10 dB in noise level could be obtained.
Crack length measurement were made optically using a micro-zoom lens to observe the polished surface of the specimens which had been scribed with grid lines spaced 1 mm apart. This image was fed into CCD camera, and then connected to both video monitor for observing and camcorder for recording as shown in Fig. 1. Crack lengths were estimated to within 0.1 mm.
The measurement of AE signals was conducted using multi-channel commercial AE equipment, MISTRAS 2001 (PAC). Two sensors were used in all cases, one with a resonant frequency at 300 kHz (R30) and the other with a broad-band frequency at maximum sensitivity of -60 dB at 550 kHz (WD, 100-1,000 kHz). A preamplifier gain of 60 and a fixed threshold of 32-48 dB range were used. The preamplifier output was also fed into 4 channel digital oscilloscope (Model 9354A, LeCroy). Each waveform was digitized into 2,500 samples at a sampling rate of 2.5 MHz. After acquisition and storage of AE waveforms, post-analysis of waveforms and frequency spectrums were carried out. The schematic diagram of overall experimental setup is shown in Fig. 1.

Fig 1: Schematic diagram of experimental setup.

4. THE CHARACTERISTICS OF AE PARAMETERS

4.1. AE Peak Amplitude vs. Fatigue Cycle
Fig. 2 shows AE peak amplitude and stress intensity factor range as a function of fatigue cycle. Fig. 2 indicates the result of LT specimen of 20 mm thick for each cycle frequency (1, 2, 4 Hz). As shown in figures, on the whole, AE peak amplitude increases with the number of fatigue cycle. It was found that the peak amplitude of 20 mm thick specimen was higher than that of 12 and 9 mm specimen, relatively. However, the peak amplitude did not increase continuously according to the increase of stress intensity factor. That is, there was some irregularity in the change of peak amplitude. This trend can give an erroneous criterion for evaluating the detectability of AE signals. From the results, it can be seen that AE peak amplitude was distributed from 45 to 80 dB approximately and that AE signals from crack propagation could be detected at over 22 in stress intensity factor range. This implies that it is possible to evaluate the existence of crack propagation by measuring AE events in the concerned area, if we have an information for the relation between a stress intensity factor and AE peak amplitude. Of course, this approach doesn't give absolute solution, because there might be unexpected AE activity due to material characteristics or environmental conditions. If we can collect more reliable database for the relation between AE peak amplitude and stress intensity factor, this approach will provide a good information for evaluating both the existence of crack and the minimum detectable size of crack.

Fig 2: AE peak amplitude and stress intensity factor range as a function of fatigue cycle (12 mm thick)

4.2. AE Energy vs. Fatigue Cycle
In order to examine the relations between AE energy and AE peak amplitude, the AE energy vs. fatigue cycle was plotted in Fig. 3. This figure indicates the result of LT specimen of 20 mm thick for each cycle frequency (1, 2, 4 Hz). This result shows a very different feature compared with Fig. 2, which are a time history of peak amplitude. It was found that AE energy increases constantly as fatigue cycle increases. Although AE peak amplitude of the individual AE event has a different magnitude, total AE energy for each AE events increases gradually. In other words, this implies that there exist several kinds of AE event with different peak amplitude during fatigue crack propagation. Especially, in case of LT-20 specimen by 1 Hz cyclic loading, there was a big AE energy compared with other specimen as shown in Fig. 3(a). It is thought that a large number of AE event with small amplitude, which exceeds barely a given threshold, was attributed to making a series of big energy. This parameter, AE energy, is similar to AE count which was popular in AE analysis for fatigue crack growth rate. That is, this analysis may be used for assessing the relation between AE parameter and crack activity. From this result, the change in the AE energy with fatigue cycle was shown to be one of the effective parameter to estimate the activity of crack propagation.

Fig 3: AE energy and stress intensity factor range as a function of fatigue cyclic (12 mm thick)

4.3. Cross Plot of AE Peak Amplitude and Event Duration
Fig. 4 shows the results of a cross-plot of the AE signal amplitude and duration for each specimen. The cross-plot is an effective tool to analyze the entire AE signal for the purpose of distinguishing signal characteristics. Each point indicates the feature of AE signal, which shows both amplitude and duration of each signal. Fig. 4 corresponds to the results of LT specimen with 2 Hz loading cycle according to the change of thickness (9, 12.5, 20 mm). Generally, the feature of cross-plot moves to up and right side according to increase of specimen thickness as shown in Fig. 4. On the other hand, not shown here, there was not a clear difference in cross-plot result according to the change of loading cycle. It can be also found that there were a lot of AE signals with high amplitude and long duration as memtioned in Fig. 3(a). It is believed that these large energy AE signals attributed to a number of signals generated from the last stage of the test as shown in Fig. 2. This result might affect partially in the plot of AE energy vs. fatigue cycle as previously mentioned in Fig. 3.

Fig 4: Cross-plot of peak amplitude and event duration (2 Hz cycle)

5. PRINCIPAL COMPONENT REGRESSION MODEL

Principal component regression (PCR) method was used to evaluate the relationship between stress intensity factor and AE parameters. Usually this statistical approach is very useful for analyzing the multivariate data having various response variables such as AE parameters. The principal components (factors) consisted of smaller number of new variables were derived from a large number of variables by principal component analysis (PCA). Since all the principal components are orthogonal to each other, there is no redundant information. Each of the principal component is a linear combination of original variables of AE parameters such as rise time (RT), ring-down count (RC), energy (EN), event duration (ED) and peak amplitude (PA). Thus the principal component can be defined as the eigenvectors of a variance-covariance matrix. They provide the direction of new axes, or new variables, onto which data can be projected. The size and length of these new axes containing the data of AE parameters is proportional to the variance for the new variable. With the results of the principal component analysis, the PCR model was developed. AE parameters for the specimen (12mm thick, 4 Hz) was only used to calibrate and to verify. From the results, it showed that there were high correlation between SIF value and AE parameters. In this analysis, the mean value of each AE parameters for each SIF values was used. The results of principal component analysis are summarized in Table 1 and Table 2.

Factor	Eigenvalue	Cumulative value
1	9.9665	0.99758
2	0.0240	0.99998
3	0.0001	1.00000
4	0.0000	1.00000
5	0.0000	1.00000
Table 1: Eigenvalues and cumulative to each factor

Variable	Factor1	Factor 2
RT	0.40755	-0.73477
RC	0.90050	0.40654
EN	0.97709	0.16330
ED	0.93533	-0.28478
PA	0.04360	0.92142
Table 2: Factor score

From the Table 1, it is found that the eigenvalue of first factor(principal component) is very high compared with others. Especially, AE energy has largest value among the five variables in factor 1 as shown in Table 2. This gives a good agreement with previous analysis for the relation between AE energy and SIF (Fig. 3). Therefore, the following equation may be proposed to evaluate the relationship between SIF and AE parameters. In this equation, the first principal component is used and the coefficients represent the eigenvectors of the AE parameters of the first factor.

Factor1 = 0.0272RT + 0.0042RC + 0.0036EN + 0.9996ED - 0.0006PA

(10)

The known data sets of 42 were used to develop PCR model and the unknown data sets of 41 were used to verify the developed model. As shown in Fig. 5 the correlation coefficient and standard error of calibration (SEC) for the result of calibration were 0.875 and 3.541, respectively. The correlation coefficient, bias and standard error of prediction (SEP) for the result of validation were 0.841, 0.0048 and 3.269, respectively. As a results, the PCR model may provide a promising method to evaluate the relationship between stress intensity factor and AE parameters.

(a) Calibration	(b) Validation
Fig 5: The results of calibration and validation plot in predicting the SIF for he AE parameter by PCR model

6. CONCLUSIONS

Based on the preliminary results presented in this paper the following conclusions can be made.
1. The approach suggested in this study implies that it is possible to evaluate the existence of crack propagation by measuring AE events in the concerned area, if we have an information for the relation between a stress intensity factor and AE parameters. If we can collect more reliable database for the relation between AE parameters and stress intensity factor, this approach will provide a good information for evaluating both the existence of crack and the minimum detectable size of crack.
2. From the result of AE parameter analysis, the change in the AE energy with fatigue cycle was shown to be one of the effective parameter to estimate the activity of crack propagation. The AE energy analysis may be used for assessing the relation between AE parameter and crack activity.
3. From the principal component analysis, it was found that AE energy has largest value among the five variables in first factor. This also gives a good agreement with AE parameter analysis for the relation between AE energy and SIF. The quation for evaluating the relationship between SIF and AE parameters was proposed. As a results, the PCR model may provide a promising method to evaluate the relationship between stress intensity factor and AE parameters.

REFERENCES

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