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Evaluation of fatigue damage for FRM with AE method.


Composite materials have the merit that its structure can be designed in accordance with the functional requirement and are widely used as structural members. However, fatigue phenomenon cannot be avoided and mechanisms on the growth of fatigue damage are complicated. The fatigue damage becomes a serious problem in evaluating the reliability of structures. In this report, the parameters for evaluating the fatigue damage of fiber-reinforced metals (FRM) with AE method are proposed. Detected AE signals during fatigue testing were analyzed with weighted-mean-frequency distribution and wavelet transform methods. As the results, the possibility of evaluating the damage by the features of the frequency distribution graphs and the fractal dimension that represented the complexity of the time fluctuation of wavelet coefficient is shown.

Keywords: FRM, Fatigue damage, Weighted-mean-frequency distribution, Wavelet transform,

Fractal theory

1. Introduction

The technology of the composite materials progressed from the development of fiber-reinforced plastics (FRP) to fiber-reinforced metals (FRM), by which the heat-resistance and the fatigue resistance, etc. were improved. The FRM materials are used as structural members under difficult environment and the excellent results are reported. However, it is necessary to establish the monitoring techniques, which can evaluate the fatigue damage. This is essential in order to avoid fatigue breakdown, which causes many of the accidents of the structures. In this study, the information processing techniques (i.e. the weighted-mean-frequency distribution, the wavelet transform and the fractal theory) were applied for analyzing the AE signals (cf. Fig. 1). The features of the frequency components for each fracture mode (i.e., the crack propagation of matrix and the breaking of reinforcement material, etc.) were extracted. After that, the database for evaluating the fatigue damage was constructed by using the features. The damage and the fracture mechanism of FRM are evaluated by comparing the features in the database with the features of the detected signals during the fatigue testing.

2. Analysis Methods of AE Signal

2.1 Weighted-Mean-Frequency Distribution (WMFD)

In the fatigue process of composite materials, extremely numerous AE events are detected and the complicated multiple fracture modes are included in an event. Therefore, it is difficult to judge which type the detected signal belongs to. For this reason, it is necessary to extract the features of the frequency distribution on the basis of the FFT analysis result. In this study, the weighted-mean-frequency distribution (WMFD) method [1] was employed for extracting the features of the distribution. The distribution graph by this method is obtained from the following process: (1) FFT analysis result is divided by the mesh and each mesh is weighted. (2) A frequency distribution graph, in which many analysis results were combined, is shown by adding the weight at every mesh. By applying this method, it becomes possible that the growth of the damage is grasped from the change in the features of the graph in each fatigue stage.


2.2 Wavelet Transform (WT)

The frequency analysis results with FFT are effective for the identification and discrimination of the microscopic destruction factor, and FFT contributes to the solution of the fracture mechanism [2]. However, it is not suitable for the analysis of the signals, whose the statistical properties change with time [3]. Therefore, another method that transforms a signal into a time-frequency domain is needed for analyzing the non-stationary or transient signals such as AE.

Wavelet transform (WT) is one of the methods for supplementing the shortcoming of FFT. The WT of the signal f(x) is defined by:

[WTf](a,b) [[integral].sup.[infinity].sub.[infinity]] [[psi].sup.*](x)f(x)dx (1)

where [[psi].sup.*] is the complex conjugate of the wavelet function [[psi].sub.a, b](x). The function [[psi].sub.a, b](x) is defined by |a [|.sup.-1/2] [psi]((x - b)/a). The function [[psi].sub.a, b](x) is the mother wavelet (e.g., Gabor wavelet) with the scale parameter a and the shift parameter b, and provides a set of localized functions in both frequency and time. The scale parameter a gives the width of window and consequently frequency as the mother wavelet is expanded or compressed in time. The shift parameter b determines the position of the window in the time, and thus defines that which part of the signal f(x) is being analyzed. Therefore, it is possible to make the optional wavelet of the angular frequency wo/a in time b by changing the both parameters, and the optional function is represented by putting the various optional wavelets together (cf. Fig. 2). The wavelet coefficient increases, if [psi]((x - b)/a) resembles f(x), and the intensity is correspondent to the amplitude of f(x) [4]. Therefore, the coefficient shows the activity of the component with the frequency [[omega].sub.o]/a in time b. This becomes effective for the analysis of the AE signals, in which sudden fluctuations and many phenomena are mixed, when the transform result is represented on the plane of b and 1/a. However, the evaluation method of the result is not established yet. Therefore, it is possible to contribute to the grasp of the fracture phenomena and the evaluation of fatigue damage if the features (i.e., the complexity of the time fluctuation waveform of the wavelet coefficient in each frequency component) of the WT result can be evaluated quantitatively. This is very important for grasping each fracture mode by the features of the analysis result. Thus, the fractal dimension that is employed when the various shapes and the phenomena in the nature are quantitatively classified was applied for extracting the features of WT result. This time, the dimension of time fluctuation waveform of wavelet coefficient in each frequency component was found with Box-counting method [5] (cf. Fig. 3).



3. Specimens and Experimental Methods

Figure 4 shows the dimensions of the specimens and material details. The fatigue test was carried out under the load control (i.e. the stress amplitude ([[sigma].sub.a]) 52 MPa, the loading frequency = 2 Hz and the stress ratio R [equivalent to] 0). The emitted signals from the specimen were detected by a wideband AE sensor (NF 900S-WB) and they were recorded on two computers using Mistras system (cf. Fig. 1). The following experiments and data analyses were carried out in order to elucidate the fracture mechanism and to evaluate the fatigue damage from the detected signals.

(a) Features of AE signals on the damage (i.e. the crack propagation of matrix and the fiber breaking, etc.) were extracted from the two testing that were the fatigue test of aluminum alloy and the tensile test of carbon fiber. The database for evaluating the damage was structured by using the features.

(b) By comparing the features in the database with the detected AE signals during the fatigue testing of FRM, the elucidation of fracture mechanism and the evaluation of fatigue damage are carried out.



4. Experimental Results and Discussion

4.1 Features of AE signals of matrix and fiber

Figure 5 shows the result of the fatigue test for the matrix (i.e., the aluminum alloy: A5052). In this figure, the analysis results (i.e., the WMFD and WT) of the AE signals are superimposed on the relationship between the crack propagation rate da/dN and the stress intensity factor range [DELTA]K. From this result, it is understood that the features of the frequency distribution of the signals depend on the rate da/dN. In short, though the frequency components 100 to 150 kHz are active when da/dN is slower than 4 x [10.sup.-7] mm/cycle, the components over 300 kHz are active when da/dN is faster than 4 x [10.sup.-7] mm/cycle. Therefore, it is possible to discriminate the difference of the rate da/dN. However, it is difficult that each fracture mode is discriminated with the WMFD when we considered Fig. 6 that shows the analysis results on the fiber pullout and the fiber breaking because the frequency component of the fiber pullout is 100 to 150 kHz and the component of the fiber breaking is near 300 kHz. Thus, the application of the fractal dimension m of time fluctuation waveform of wavelet coefficient in each frequency was tried for extracting the features of each fracture mode. The results are shown in Fig. 7 and the following can be considered from the figure.



(1) The fluctuations of the dimension m of each frequency for the fiber pullout and the fiber breaking are comparatively smaller than the fluctuations of the crack propagation of the matrix.

(2) The dimension m around 100 kHz is high when the propagation rate da/dN of the matrix is slow, and the dimension m of 250 to 300 kHz rapidly increases when the rate da/dN is fast.

(3) By using WT, it became possible to discriminate the differences of each fracture mode, in which it is difficult to discriminate the mode with the WMFD. One is the discrimination between the fiber breaking and the fast crack propagation, and the other is the discrimination between the fiber pullout and the slow crack propagation. The dimension m of 125 and 350 kHz were noticed because the difference between two dimensions is large.

The obtained dimension m for discriminating each mode by the consideration of the above is shown in Table 1.

4.2 Relationship between Fracture Modes and Fatigue Damage

From the results (i.e. the AE event rates, the AE amplitude distribution and the crack initiation point) of the fatigue test of FRM specimen, the fatigue phenomena were divided in 4 stages as shown in Fig. 8. These stages are the early stage (i.e. the range of many AE events right after the test starts), the middle stage (i.e., the stable range of the event rates until crack initiation point), the late stage (i.e., the crack propagation range) and the stage before fracture (i.e., the range of many AE events again), respectively. The feature extraction in each stage was tried by considering the results of the WMFD graphs, the behavior of the fractal dimension m on the time fluctuation of wavelet coefficient and Table 1.



Figure 9 shows the relationship between the analysis results (i.e. the WMFD graphs and the behavior of the fractal dimension m) and the fatigue damage %. As the results, the following became clear.


Early stage: From the result of the WMFD graph, it is clear that the activities of the frequency components 150, 250 and 300 kHz are high. Since the dimension m at 125 and 350 kHz shows 1.25 and 1.35, respectively, it appears that the fiber pullout and the fiber breaks are taking place. It is also likely that many causes of the fatigue fracture intermingle in an AE signal and many signals are emitted from the stress concentration zones of the defects inside the specimen.

Middle stage: In addition to the activity of 300 kHz, the activities of 120 to 200 kHz are strong. The fractal dimension m of 350 kHz is higher than that of 125 kHz. However, the dimension m of 125 kHz shows the increasing tendency, while the dimension m of 350 kHz gradually decreased from 1.35. From these, it seems that the activity of the fiber breaks gradually decreases, and the activity of the matrix damage increases. Therefore, even if the crack is not found on the surface of the specimen, it is likely that the main fracture mode inside is changed from the fiber breaks to the matrix damage.

Late stage: The dimension m comes to show the high value beyond 1.35 and the occurrence ratio of 300 kHz increase. From this, it can be judged that the main factor in this stage is the rapid crack propagation.

Before fracture: The main frequency component of the detected signals is near 100 kHz, and the dimension m of 125 and 350 kHz is converged to 1.25 and 1.30, respectively. In this stage, it is the high possibility that the main factor of the fatigue phenomenon is not the crack propagation of matrix but the fiber pullout if the rate of crack propagation was high in the last stage. From the above, it can be predicted that the fatigue process approaches the end when the dimension m rapidly decreases.

4.3 Application to Evaluation of Fatigue Damage

In order to find a parameter that describes the relationship between the behavior of the dimension m and the fatigue damage, we defined the parameter F as follows;

F = m350kHz - m125kHz (2)

Here m350kHz and m125kHz is the fractal dimension of 350 and 125 kHz, respectively. Figure 10 shows an example of the evaluation on fatigue damage by the parameter F. From this result, it can be seen that the parameter F appears to show different stages of the fatigue damage.

5. Conclusion

Composite materials have the merit in fulfilling its structural design requirement with comparative ease. However, the fracture mechanism and the fatigue damage of the materials are complicated. Therefore, the establishment of the technique, which evaluates the reliability and the safety of the structure materials, is desired. The following became clear from the experiments for establishing the evaluation technique of the fatigue damage of FRM with AE method.

(1) The WMFD is possible to grasp the features on the frequency distributions of the detected AE signals from the fracture phenomena.

(2) Fractal property was recognized in the time fluctuation waveform of wavelet coefficient in each frequency component after the WT of the signals. The possibility of evaluating the fracture mode and the fatigue damage by the dimension m is shown.

(3) By the frequency analysis of AE signals, it is possible to relate matrix damage by the fracture of the reinforced fiber with the final fatigue fracture.


The authors are grateful for valuable assistance of Yoichiro Koyama of Kansai University. This research was supported by a grant from Life Cycle Engineering Working Group in ORDIST (Organization for Research and Development of Innovative Science and Technology) of Kansai University.


[1] T. Asano and S. Somiya: Prepr. of Jpn. Soc. Mech. Eng., (1994), 74.

[2] Y. Ichida, K. Kishi and Y. Hasuda: J. Jpn. Soc. Prec. Eng., 58(5) (1992), 841.

[3] Q.Q. Ni, Y. Misada, K. Kurashiki and M. Iwamoto: Proc. National Conference of AE, (1997), p. 173.

[4] H. Inoue: J. Soc. Mat. Sci., 45 2(1996), 1353.

[5] M. Kurose, M. Tsuda, T. Sasaki, Y. Hirose, Y. Yoshioka: J. Soc. Mat. Sci., 43(1) (1994), 1489.


Faculty of Engineering, Kansai University, Yamate, Suita, Osaka 564-8680, Japan.
Table 1 Frequency components on each fracture mode of specimen.

Feature/Fracture mode     Peak of weight   Fractal dimension m of
                          mean frequency   time fluctuation of
                          distribution     wavelet coefficient
                          graph            350kHz      125kHz

Crack propagation speed
of aluminum: Fast         250~300kHz       1.34~1.40   Nearly 1.30

Crack propagation speed
of aluminum: Slow         100~150kHz       1.20~1.25

Fiber breaking            270~390kHz       1.29~1.33

Fiber pullout             120~150kHz       1.27~1.29   Nearly 1.20

Fiber debonding           180~240kHz       1.23~1.27
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Author:Takuma, Masanori; Shinke, Noboru
Publication:Journal of Acoustic Emission
Date:Jan 1, 2005
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