·Table of Contents
AE Parameter Analysis for Fatigue Crack MonitoringDong-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
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. suggested that NAE , total cumulative AE count is directly proportional to Vp , the volume of plastic area at the crack tip, (Eq. 1). And Morton et al. reported experimental relationship (Eq. 2) between total cumulative AE count and the stress intensity factor range (D K) for aluminum.
2.2. Energy Release Rate, Stress Intensity Factor and Crack Growth Rate
Fatigue is a mechanism of crack growing. 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(Kth) 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). 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(KTr) and stress intensity factor at failure is called fracture toughness(Kc).
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, KAE can be obtained from threshold determined by background noise level. Fatigue estimation methods by applying AE technique are suggested in case that KAE is given.
Eq. 6 and Eq. 7 is derived from Eq. 5 and KAE. 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.
test is applied nominal stress range and aAE 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 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 Keq is equivalent stress intensity factor range and acr is critical crack length for failure.
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.|
4.1. 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)|
|Table 1: Eigenvalues and cumulative to each factor|
|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.
Fig 5: The results of calibration and validation plot in predicting the SIF for he AE parameter by PCR model|
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