A new research method based on vibration testing for the vibration fatigue of FRP was proposed in this paper. Through the testing on a closedloop controlled vibration fatigue test system, the vibration fatigue phenomenon of typical carbonfiberreinforced plastic (CFRP) cantilevered laminate specimens was carefully studied. Moreover, a method based on the frequency response function was proposed to monitor the fatigue damage accumulation of specimens. On the basis of that, the influence factors that affect the vibration fatigue life of CFRP were experimentally studied. The influence of amplitude probability distribution of the vibration load spectrum on the fatigue life was deeply explored. Compared with Gaussian random vibration, the nonGaussian random load has a significant impact on the vibration fatigue life of CFRP. The experimental results also showed that the magnitude of power spectral density (PSD) has a significant effect on the vibration fatigue life of specimens. For Gaussian vibration load, the frequency bandwidth almost has no effects on the vibration fatigue life of CFRP. However, for nonGaussian vibration load, it has a great impact on the fatigue life. When PSD magnitude and frequency bandwidth are constant, the root mean square (RMS) is proportional to the vibration fatigue life of composites.
Fiberreinforced plastic (FRP) has been one of the most widely used composite materials in aerospace, ships, and vehicles, due to its design flexibility and excellent properties which are unmatched by metal materials. For decades, the amount of FRP used in a variety of facilities has been significantly increased. In some equipment, it even accounts for more than 50% of its total weight, such as the US new UAV X47b, which is almost in all composite aircraft. With the large amount of fiberreinforced composite materials used in various types of equipment, the reliability of composite structures in the service process becomes extremely important.
Equipment using FRP always suffers extreme and complex loads during its whole life, and those loads are definitely stochastic. As a result of that, the fatigue of composites is becoming inevitable and may cause catastrophic results. The use of composite materials on the key components of the engineering structure, such as aircraft wings and helicopter rotors, makes fatigue problems more critical. One of the most common fatigue phenomena is vibration fatigue. The FRP has fatigue resistance that is superior to that of a metal material and may be reliably serviced for a long time even after fatigue damage appears. In the early days when people began to use fiberreinforced composites, they were considered to be free from fatigue due to the conservative safe life design of structure. However, with the rapid development of various types of aircraft, ships, and vehicles, the equipment system became more and more complicated, and its service environment and environmental load became more and more extreme. On the other hand, in the aerospace industry, engineering structures are often designed to pursue lighter quality but to carry more severe loads. As a result, the fatigue problem of composite materials gradually becomes unavoidable, and the fatigue problem of composite structures under realistic complex random loads is even more important [
There has been an extremely important and unavoidable question: how do we evaluate the fatigue life of the FRP structure and improve its durability, as well as the life determination and extension of serving facilities? Due to the anisotropy and inhomogeneity of the composites, the fatigue failure mechanism is completely different from that of the metal materials. It is a definitely difficult task to evaluate and predict the fatigue life of composite structures from a theoretical point of view.
For decades, the academic community has done a lot of research on the fatigue of composite materials. However, those studies were almost all carried out based on the fatigue tests under constant amplitude fatigue load. There are several common fatigue life evaluation methods of FRP, such as the experimental method based on SN curve [
For a long time, research on FRP fatigue has focused on a simple fatigue phenomenon under constant amplitude load, such as TensionTension (TT), TensionCompression (TC), and CompressionCompression (CC). However, the fatigue life under the uniaxial load during laboratory experiments is much different from that under realistic and irregular service load [
Currently, there is very little literature on the fatigue life of composite structures under random and complex load. Fawaz and Ellyin explored the fatigue failure model of fiberreinforced materials under general load conditions from a theoretical point of view, taking into account factors such as multiaxial stress, stress ratio, fiber orientation, and load direction [
Engineering structures under complex random vibration loads will suffer from vibration fatigue problems. So far, there have been many researches on the vibration fatigue of metal material structures. Eldoǧan and Cigeroglu and Pothula et al. used a variety of fatigue theories to study the vibration fatigue life of metal cantilever beams [
It is also important to note that it has been pointed out that the composite material is not sensitive to the notch under alternating loads in the literature [
The random vibration load is usually described by the power spectral density (PSD), but only one PSD parameter does not describe all types of random vibrations as the probability density distribution of the random vibrations may be completely different under the same PSD and RMS values [
The amplitude probability density function with the same PSD.
Power spectral density
Amplitude probability density function
For Gaussian random vibrations, the higherorder statistical moments greater than the second order are all zero, so the PSD can completely describe the Gaussian random vibration. However, for nonGaussian random vibrations, the higherorder statistical moments (>2nd) are not constant zero, so both kurtosis and skewness are required. For random vibration
The skewness is defined in
For Gaussian random vibrations,
The conventional research of vibration fatigue for metal structures is usually based on the assumption that the probability distribution of the stochastic vibration load is Gaussian. On the basis of this assumption, a series of signal processing approaches (e.g., cycle counting) were carried out to obtain the structural fatigue life. However, according to the actual investigation by our research team, the probability distribution of realistic vibration load applied on the facilities during their whole life is often subject to nonGaussian distribution. With the hypothesis of Gaussian distribution, the predictive vibration fatigue life of equipment is longer than the realistic fatigue life, which is extremely unfavorable for fatigue life prediction and durability evaluation of composite structures [
The difference between Gaussian and superGaussian random vibration signals.
Gaussian random vibration signal
SuperGaussian random vibration signal
The study on vibration fatigue of FRP under complex vibration load spectra was carried out based on vibration testing in this paper. A series of CFRP (carbonfiberreinforced plastic) cantilevered laminate specimens with holes or notches were intended to be tested by random vibration testing in a developed closedloop controlled vibration fatigue test system. Through the test, the obvious vibration fatigue phenomena can be observed at the risk point of the specimen, which is a predesigned hole or notch and is common in composite material structures. This vibration fatigue phenomenon is much different from conventional theory, which states that the composite is not sensible to risk points. On the basis of that, factors influencing the vibration fatigue life of specimens were explored through the fatigue test of several groups. In addition, the impact of amplitude probability distribution of the vibration load spectra on the fatigue life was also deeply studied. The study also makes a contribution to the establishment of the accelerated degradation test model and vibration fatigue life prediction.
Therefore, the objectives of this paper are as follows: (
The test setup is a typical closedloop controlled vibration fatigue test system, which consists of an industrial computer (vibration control software), vibration controller, power amplifier, shaker, and sensors. The control schematic diagram is shown in Figure
The schematic diagram of the vibration fatigue test system.
The actual vibration fatigue test system.
The industrial computer is the carrier of the vibration control software and also the control core of the test system. The function of the industrial computer is to set the excitation signal parameters and test plan, realtime signal processing, and realtime closedloop control for the shaker. The vibration controller is the medium for the output and receiving signal of the industrial computer. There is a network cable between the computer and the vibration controller for communication.
The vibration controller is the signal source and interface board of the system. The function of it is to generate the vibration control signal according to the instruction of the industrial computer, to receive the feedback and monitoring signal, and to output the driving signal. The vibration controller used in the system is an RC2000 vibration controller (with 8channel input/output) from STI company. It can generate sine, random, and shock signals and is capable of controlling kurtosis, which can be used to carry out nonGaussian random vibration tests.
The main function of the power amplifier is to amplify the drive signal from the vibration controller into a large current drive signal and then transport it to the shaker. The function of the shaker is to generate a stimulus for the test piece mounted on the shaking table base according to the driving signal. The shaker used in this paper is an electromagnetic shaker, which is cooled by an air pump. The power amplifier and shaker chosen in the test are STI D1502 vibration test system. The technical parameters of the D1502 vibration test system are given in Table
The technical parameters of STI D1502.
Item  Parameter 

Frequency range  5–4500 Hz 
Max. exciting force  150 kgf 
Max. displacement  25 mm (PP) 
Max. velocity  2 m/s 
Max. acceleration  75 g 
Max. load  70 kg 
The sensor used in the test system is an accelerometer. The function of accelerometers is to collect monitoring and feedback vibration signal. Accelerometer 1 was mounted on the shaking table base and collected the signal to monitor the state of the excitation signal in real time to ensure that the actual vibration of the shaking table matches the preset excitation signal parameter. Accelerometer 2 was mounted on the test piece and collected the feedback signal to obtain the vibration response of the test piece under the excitation signal. These two signals were sent to the computer through the vibration controller for further processing. The frequency response function of the test piece can be obtained based on signal processing. The accelerometers are B&K 4508B with 0.3–8 kHz working frequency range and ±71 g peak range.
For the metal material, because of its isotropic nature and homogeneity of the material, fatigue damage can be described by the process of a dominant crack’s derivative, propagation, and fracture. However, due to the completely different properties of FRP, the fatigue damage mechanism is very complex and cannot be described by a dominant crack. Currently, the commonly used composite material damage detection method is generally offline, such as radiographic testing, ultrasonic testing, infrared imaging, and acoustic emission. And it is difficult to monitor the fatigue damage of composite materials online. Besides, it is pointed out that the fatigue damage of the composite laminates is not sensitive to the risk point of the structure (notch, hole), and it is difficult to observe and judge the occurrence of fatigue damage with the human eye. The above reasons undoubtedly make it difficult to monitor the vibration fatigue damage of the composite in the test in real time, and it is also difficult to define the critical point of fatigue failure of the specimen, which makes it difficult to study the fatigue problem of the composites.
The relationship between the modal parameters and the fatigue damage of the structure was studied by Adams et al. [
Frequency response function.
The main objective of this paper is divided into two aspects.
The first is to verify whether there is a vibration fatigue phenomenon in the composite structure under complex random vibration load and to study whether the fatigue damage of the composite structure under alternating load is sensitive to the risk point. By designing a typical composite cantilever test piece with different risk points, the vibration test was carried out under the same load conditions. In the course of the test, whether there is vibration fatigue damage at the location of risk point should be observed and its derivative law should be explored. In addition, the difference of the vibration fatigue phenomena of the two specimens with different ply sequences under the same load condition was compared by carrying out the vibration test with crossply and unidirectional ply specimens with the same risk point.
The second is to study the load influence factors on the vibration fatigue life of the composites on the basis of the verification of the vibration fatigue phenomenon in Test 1. By changing the parameters of the load, the variablecontrolling method is used to carry out the vibration test of the same specimen to explore the influence of the different parameters of the random vibration load on the vibration fatigue damage of the composite material, which will lay the foundation for the future study.
The load in the vibration fatigue test is random vibration load, which is completely different from those of the conventional composite fatigue test. As shown in Figure
The constant amplitude load of fatigue test for composite materials.
The typical cycling load
The load with different stress ratio
The random vibration load of fatigue test for composite materials.
The PSD of a random vibration load
The time domain signal of a random vibration load
T300 carbon fiberreinforced epoxy resin composite laminates, which are widely used in the aerospace, vehicle, and ship industry, were chosen to carry out the tests in this paper. The mechanical property parameters of materials are presented in Table
Mechanical property parameters.
Item  Parameter 


136.00 GPa 

9.80 GPa 

4.70 GPa 

5.20 GPa 

0.280 

0.150 

1540 kg/m^{3} 
The eightlayer laminates with a single layer thickness of 0.125 mm and a total thickness of 1 mm were selected. In addition, two kinds of laminates with different ply stacking sequences
The specimen dimensions are shown in Figure
The specimen of vibration testing.
Specimen 1
Specimen 2
Specimen 3
The top view and profile map of specimens.
Specimens
Unidirectional
Crossply
In order to study the vibration fatigue of specimens with different ply angles, two kinds of CFRP laminates with different ply sequences were selected. One is crossply and the other is unidirectional. The top view of the three kinds of specimens and the profile map of the two different materials are shown in Figures
The fixtures of specimens, tip mass, and accelerometers.
A complete vibration test procedure is as follows.
According to the test objective in Section
The test conditions of Test 1.
Specimen  Lower frequency (Hz)  Upper frequency (Hz)  PSD bandwidth (Hz)  Acceleration PSD magnitude (g^{2}/Hz) 

Kurtosis 

Unidirectional  5  100  95  0.01  0.974676  3 
Crossply  5  100  95  0.01  0.974676  3 
The test conditions of Test 2.
Item  Lower frequency (Hz)  Upper frequency (Hz)  PSD bandwidth (Hz)  Acceleration PSD magnitude (g^{2}/Hz) 

Kurtosis 

A1  5  100  95  0.01  0.974676  3 
A2  5  100  95  0.01  0.974676  5 
A3  5  100  95  0.01  0.974676  7 
B1  5  35  30  0.01  0.54681  3 
B2  5  65  60  0.01  0.774595  3 
B3 (A1)  5  100  95  0.01  0.974676  3 
C1  5  35  30  0.01  0.54681  5 
C2  5  65  60  0.01  0.774595  5 
C3 (A2)  5  100  95  0.01  0.974676  5 
D1 (B2)  5  65  60  0.01  0.774595  3 
D2  5  65  60  0.015  0.94868  3 
D3  5  65  60  0.02  1.09544  3 
E1 (C2)  5  65  60  0.01  0.774595  5 
E2  5  65  60  0.015  0.94868  5 
E3  5  65  60  0.02  1.09544  5 
In Test 1, in order to verify the presence or absence of vibration fatigue of the composite laminates and to explore the sensitivity of vibration fatigue damage to risk points under random loads, Specimen 1 with the same geometrical dimensions but different layers (crossply and unidirectional) and crossply Specimen 2 and Specimen 3 were, respectively, tested on the shaker with the same test conditions.
The purpose of Test 2 is to explore the influence of PSD, RMS, frequency bandwidth, and kurtosis on the vibration fatigue life of composite materials. Crossply Specimen 1 was selected as the object to carry out the test. The test conditions are shown in Table
The purpose of Group A is to investigate the influence of kurtosis on the vibration fatigue life of composite materials, while that of Group B is to explore the impact of Gaussian random vibration frequency bandwidth on fatigue life. Group C was designed to study the effect of superGaussian random vibration frequency bandwidth on the fatigue life of specimens. The purpose of Groups D and E was to investigate the effect of the Gaussian and nonGaussian random vibration PSD on the vibration fatigue life, respectively. The RMS value of the random vibration load is affected by both bandwidth and PSD; it is not the main influence factor.
It can be seen from Table
The load in the test is a random vibration load with a flat PSD spectrum, which means the PSD spectrum of the load is flat. The realtime autopower spectral density of test condition A1 is shown in Figure
The autopower spectral density of vibration load.
According to the test conditions in Section
The vibration fatigue of specimens.
Notched specimens
Specimen with a hole
The vibration fatigue damage of different specimens.
As shown in Figure
The difference of vibration fatigue between specimens with different overlays.
Crossply specimen
Unidirectional specimen
The FEA result of Specimen 1.
Crossply Specimen 1 was selected to carry out Test 2 according to the test conditions in Section
Some of the damaged test specimens.
The test results of Group A are shown in Table
The test results of Group A.
Specimen  Resonant frequency  

Initial value (Hz)  Ultimate value (Hz)  Reduction (Hz)  The time of the last decrease (min)  
A1  7.8906  7.6563  0.2343  183.25 
A2  8.1250  7.8125  0.3125  181.33 
A3  7.9688  7.5000  0.4688  101.75 
The variation and fitting curves of resonant frequency in Group A.
The test results of Groups B and C are shown in Table
The test results of Group B&C.
Specimen  Resonant frequency  

Initial value (Hz)  Ultimate value (Hz)  Reduction (Hz)  The time of the last decrease (min)  
B1  7.4158  7.1411  0.2747  159.33 
B2  8.1482  7.8735  0.2747  166.75 
B3  7.8906  7.6563  0.2343  183.25 
C1  7.9651  7.5989  0.3662  130.33 
C2  8.0566  7.7820  0.2746  171.83 
C3  8.0469  7.8125  0.2344  181.33 
The variation and fitting curves of resonant frequency in Group B.
The variation and fitting curves of resonant frequency in Group C.
The purpose of Group B is to explore the effect of different frequency bandwidths on the fatigue life of the composite material under the condition of Gaussian random vibration load, and the purpose of Group C is to explore the influence of frequency bandwidth on vibration fatigue under nonGaussian random vibration load. As can be seen from Table
Table
The test result of Group D&E.
Specimen  Resonant frequency  

Initial value (Hz)  Ultimate value (Hz)  Reduction (Hz)  The time of the last decrease (min)  
D1  8.1482  7.8735  0.2747  166.75 
D2  7.9651  7.6904  0.2747  150.38 
D3  7.6904  7.4158  0.2746  137.27 
E1  8.0566  7.7820  0.2746  171.83 
E2  7.5989  7.2327  0.3662  144.35 
E3  7.6904  7.2327  0.4577  140.17 
The variation and fitting curves of resonant frequency in Group D.
The variation and fitting curves of resonant frequency in Group E.
The RMS value is affected by the frequency bandwidth and the PSD magnitude, which is not a critical factor in itself. However, the test results show that, for the nonGaussian random vibration load, when the RMS value is larger, the structural vibration fatigue damage accumulates faster. For the Gaussian random vibration load, when the frequency bandwidth is the same, the larger the RMS value, the smaller the structural vibration fatigue life. This is mainly due to the fact that the vibration fatigue life of the composite material is mainly affected by the magnitude of the vibration at the resonant frequency.
Figures
In addition, the fitting curve is also similar to the curve of residual stiffness in the related literature, which is about conventional fatigue of composites under constant amplitude load. This shows that the peak frequency of the frequency response function can be used as a parameter to reflect the fatigue damage accumulation. The decreasing curve in the vibration fatigue test is similar to the traditional
There was an another interesting phenomenon in the test. No matter under any test condition, with the increase of the test time, the peak frequency of the response function declined to a certain degree, and then it would not decrease for a long time until the delamination damage emerged. This phenomenon was observed in all the tests in this paper, and the initial decline of resonant frequency was generally about 0.3 Hz. It can be seen as a fatigue threshold for delamination damage.
According to the previous literature [
In this paper, the fatigue life evaluation and prediction methods of FRP were summarized and reviewed firstly. It was pointed out that the fatigue of composites under complex load still needed to be deeply developed. The concept of vibration fatigue of FRP was proposed and verified through the experiment. A closedloop controlled vibration fatigue test system suitable for CFRP and typical CFRP cantilevered laminate specimens was designed. The influence factors of vibration fatigue of CFRP were explored through the vibration testing.
The test of this paper verified that the composite material had obvious vibration fatigue phenomenon, and the damage first emerged at the risk point of structure. The vibration fatigue damage is sensitive to the notch and throughhole. In addition, the vibration fatigue damage of CFRP with different ply sequences is also different. Secondly, the effects of load parameters such as frequency bandwidth, PSD magnitude, kurtosis, and RMS on the vibration fatigue life of CFRP were investigated. For the Gaussian random vibration load, when the frequency bandwidth of the load covers the natural frequency of the structure and the other load parameters are the same, the PSD magnitude is inversely proportional to the vibration fatigue life of the composite structure, and the frequency bandwidth almost has no effect on the fatigue life. For nonGaussian random vibration loads, when the frequency bandwidth of the load covers the natural frequency of the structure and the other load parameters are the same, the frequency bandwidth is proportional to the vibration fatigue life of the composite structure, while the PSD magnitude is inversely proportional to the vibration fatigue life. When the frequency bandwidth and kurtosis are constant, the RMS value is inversely proportional to the vibration fatigue life of the composite structure.
During the test, it is found that the decreasing trend of the resonant frequency of the structure satisfies the inverse power law, and there is an obvious fatigue threshold for delamination damage. This can provide a new point of view and effective auxiliary method for online evaluation of vibration fatigue life of composite materials.
Additionally, due to the good fatigue resistance performance (compared with metal materials) and greater dispersity of fiberreinforced composites, it is necessary to perform longterm tests to obtain fatigue life data and to perform a large number of tests to obtain sufficient samples for a confident result, which undoubtedly makes the test cost very high and the test cycle very long. Fortunately, the accelerated life test can overcome such shortcomings. Through the accelerated test, the test cycle can be effectively compressed, and the cost is also reduced, which is particularly beneficial for the study of composite fatigue. Accelerated test can be used to evaluate the fatigue life of composite structures as an effective and reliable method. The superGaussian random vibration load has a significant acceleration effect on the structural vibration fatigue damage accumulation. If the acceleration effect of the superGaussian random vibration load can be quantitatively studied, it can be used as an effective load condition in the accelerated test.
The above research results could be used as a basis for the subsequent study on the evaluation of the fatigue life of composites under complex load. The load influence factors and their influence laws of vibration fatigue of FRP laid the foundation for the future research, which aims at the prediction and evaluation of vibration fatigue life of FRP based on accelerated testing.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was sponsored by the National Natural Science Foundation of China (Grants no. 50905181 and no. 51405501) and the National Key Laboratory Foundation of China with Grant Agreement 9140C710104140C71002. The financial support received is gratefully acknowledged. Thanks are due to Feng Zhao and Junwen Liu, who have offered great help in the experiment as laboratory technicians. Thanks are also due to Dr. Dezhi Wang, who has offered great help with the paper writing.