Fiber Bragg Grating Sensors for Fatigue Monitoring of Composite

Transcription

1 Fiber Bragg Grating Sensors for Fatigue Monitoring of Composite Fiber Bragg Grating Sensors for Fatigue Monitoring of Composite Zhan-Sheng Guo 1,3, Jiemin Feng 1, Hui Wang 1, Hongjiu Hu 1,3, and Junqian Zhang 2,3 1 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Department of Mechanics, Shanghai University, Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Shanghai University, Summary Fiber Bragg grating (FBG) sensor can be used to monitor the mechanical behavior of composite. The internal strain of composite during a constant stress amplitude fatigue testing process was monitored with FBG sensors in this paper. FBG sensor as a fatigue indicator can reveal the decrease of Young s modulus of the specimen, which is a direct index of damage. FBG sensor can not only be embedded in composite laminates to detect fatigue damage, but also has excellent durability compared with other sensors such as electric strain gauge. After 1 million cycles, the FBG sensor can still keep good sensibility. FBG sensor as a fatigue indicator is a novel sensor to monitor, evaluate and give crash alert for the health state of composite during its whole service life. And also, a new and simple model of stiffness degradation was developed. This model can be used to predict the fatigue life of composite material. 1. INTRODUCTION Composite materials which are composed of two or more kinds of different materials by physical or chemical methods on macro scale have more excellent capability than the individual components which are used alone. Compared with metallic materials, advanced composite materials have higher strength-weight ratio, higher stiffness-weight ratio, good corrosion resistance and antifatigue. It is an inevitable trend to use advanced composite materials to create structures and major project equipment (such as aerospace structures). Researches and engineering applications have shown that composite materials are prone to be damaged because of the tension and compression, impact and fatigue loading during service. It will lead to huge economic losses, casualties, and even disastrous consequences if these injury and damage are not promptly discovered. Therefore, to research and Corresponding author: davidzsguo@shu.edu.cn Smithers Rapra Technology, 2013 develop the sensors which can meet the requirements of composite material engineering is very important 1. Unlike metals, composite materials are inhomogeneous (on a gross scale) and anisotropic. They accumulate damage in a general rather than a localized fashion, and failure does not always occur by the propagation of a single macroscopic crack. The microstructural mechanisms of damage accumulation, including fiber breakage, matrix cracking, debonding, transverseply cracking, and delamination, occur sometimes independently and sometimes interactively. The types of damages may be strongly affected by both materials variables and testing conditions 2. There are many models available to predict the residual stiffness and residual fatigue life. Degrieck and Paepegem 3 provide an excellent review of major fatigue models. Some models are constitutive ones based on physical and mechanical observations, and other models are empirical mathematical descriptions of experimental data gained. They can be classified into three major categories: fatigue life models using S N curves, phenomenological models for residual stiffness/strength, and progressive damage models using variables related to damage. The stiffness degradation model is much more applicable to the practical design of composite structures. From the theories of composite fatigue residual stiffness degradation, the stiffness of materials or structures will continue degradation with the fatigue damage form, development, and failure under the cycle loading. The stiffness degradation during the fatigue can be recorded by the maximum strain change of the structure with the control of load. During the past two decades many researchers have done much work on composite fatigue and obtained much general knowledge of the fatigue behavior of the composite materials 4-8. Sutherland 5 published an extensive review paper on the fatigue properties of materials for wind turbines. In order to verify the models and approve the Polymers & Polymer Composites, Vol. 21, No. 9,

2 Zhan-Sheng Guo, Jiemin Feng, Hui Wang, Hongjiu Hu, and Junqian Zhang materials used to provide a given fatigue lifetime, extensive testing has focused on design considerations. Yao 6 developed a progressive fatigue damage model to predict the fatigue life of composite laminates based on FEA, in which the stiffness and strength were randomly distributed by using a normal distribution function and based on the experiment. Yashiro 7 investigated damage identification in holed CFRP laminates under cyclic loading by inverse analysis of the reflection spectrum of an embedded FBG sensor. The damage pattern in the laminate and the debonding length were estimated from the reflection spectrum by an optimization technique with numerical analyses. The basic function of the sensors is transforming the change of input energy, in some form, of the object that should be measured into the same form or another form homologous change of the energy (signal). Fatigue monitoring using strain sensors in the composite structures has the advantage of providing additional information on the load history of the composite and, consequently, one can carry out lifetime estimations of the composite structures 9,10. Fiber sensor technology which fast developed with the development of fiber communication technology in the 1970s is a new technology of sensing and transferring the measured signal outside. Mainly because of their lightning safety and neutrality to electro-magnetic interference, fiber-optic (FO) strain sensors are advantageously applied in composite structural health monitoring FBG sensor is a new kind of FO sensor, which is created based on the sensitivity of Bragg wavelength of FBG to temperature and strain. Of the optical fiber sensors reported in the open literature 17, FBG sensors take central stage due to a number of advantages that they offer over other optical sensors. One of the key advantages of these sensors is their inherent signal stability and suitability for multiplexing. As the sensing procedure is based on monitoring shifts in the optical wavelength, FBGs are not susceptible to power fluctuations. Other benefits include their capability for quasi-point sensing as well as nonuniform strain field measurements. They are widely used in civil engineering structure, aeronautics and astronautics industry, shipping industry, electric power industry, petrochemistry industry, nuclear industry, medicine industry etc. 18. FBG sensors have been used to accurately measure strain and temperature. Takeda et al. 19 and Tsuda 20 employed FBG sensors for Lamb wave detection to evaluate impact damage in CFRP laminates. Peters et al. 21,22 and Botsis et al. 23 embedded FBG sensors in various non-homogeneous strain fields and confirmed their response by analytical modeling. Takeda and colleagues 24,25 applied the sensitivity of FBG sensors to non-uniform strain fields to the detection of transverse cracks and delamination in CFRP laminates. Garrett 26 used embedded FBG sensor networks to evaluate local residual post-impact strain of woven composite laminates. However, few studies 13 detected the fatigue properties of composite by using FBG. This paper described an FBG measurement system designed to monitor the fatigue of carbon fiber composite laminates. The strain changing and stiffness degradation were monitored. By using the FBG measurement system, an accurate prediction can be gotten to receive the fatigue lifetime of composite laminates. And also, a new model in a considerably simple form was developed to predict the stiffness degradation during the fatigue life. The model predictions agreed very well with the experimental data. 2. FIBER BRAGG GRATING Fiber grating means the grating effect formed from periodical change of fiber core s refractive index. Hill et al. first discovered the photosensitivity of the Germanium-doped fiber and created the first fiber grating in the world by standing wave method in However, it didn t bring much attention during the decade since it was found until Meltz et al. created the fiber grating by using lateral transverse exposure on fiber to reach the purpose of the refractive index modulation in The fiber grating technology had made a breakthrough since the invention of transversewriting method, and it is always one of the hot issues in the field of fiber communication and fiber sensing all the while. FBG is a new fiber device which actually, as is mentioned above, is a segment of fiber whose core s refractive index changes periodically. The grating can be written into the fiber directly through permanent change of the Germanium-doped fiber s refractive index after the fiber is irradiated in ultraviolet rays. FBG reflects the broad-bandwidth incident light selectively and only the narrow-bandwidth light whose central wavelength matches the modulation phase of the fiber core s refractive index will be reflected. It means that only the light wave which meets the Bragg condition can be reflected by the FBG. For a FBG (see Figure 1), the Bragg condition is given by: λ B = 2n eff D (1) where l B is the reflected Bragg wavelength of FBG, n eff is the effective refractive index of the fiber core, and D is the grating spacing. The spacing of the periodic variation of refractive index, which is a function of strain, will be elastically deformed with respect to the external strain on the fiber. Also, due to the strain-optic effect, the effective refractive index will change. These two affect the Bragg wavelength to be shifted for an applied strain. 554 Polymers & Polymer Composites, Vol. 21, No. 9, 2013

3 Fiber Bragg Grating Sensors for Fatigue Monitoring of Composite For a FBG, the change of the effective refractive index is mostly caused by the elastic-optic effect and the thermooptic effect. And the change of the grating spacing is mostly caused by the thermal expansion effect and the strain coming from the stress outside. Therefore, all of the effective refractive index n eff, the grating spacing D and the central wavelength of the reflected light l B are the functions of the temperature T and the strain e. Differentiating the Equation (1), then the following equation can be obtained: Figure 1. Systematic diagram for fiber Bragg gratings Δλ B = 2Δn eff D + 2n eff ΔD Δn eff = n eff Meanwhile ε Δε + n eff T ΔT ΔD = D D Δε +, ε T ΔT D, and ε = D when only axial strain is considered. Consequently: Δλ B = 2( n eff ε Δε + n eff T ΔT)D + 2n ( D eff ε = 2[( n eff ε D + n eff D ε )Δε + ( n eff T D + n eff D Δε + T ΔT) D T )ΔT] = 2[ ( n eff ε 1 n eff D)+ n eff D]Δε + λ B (α f + ξ)δt n eff = λ B [(1 P e )Δε + (α f + ξ)δt] That is, Δλ B = λ B [(1 P e )Δε + (α f + ξ)δt] P e, a f, x in Equation (2) are defined as follows: P e = 1 n eff α n eff ε f = 1, D D T, ξ = 1 n eff n eff T. where Dl B is the wavelength shift of the reflected light, De is the strain, DT is the temperature change of the FBG, P e is the photoelastic constant of the optical fiber, a f is the coefficient of thermal expansion (CTE) of FBG, x is the Bragg grating s thermo-optical coefficient. Therefore, the Bragg wavelength shift due to the strain and the temperature change can be expressed as: Δλ B = K ε Δε + K T ΔT (3) where K e = (1 P e )l B is the sensitive coefficient of strain, K T = (a f + x)l B is the sensitive coefficient of temperature. (2) The response of the FBG strain sensor comes from thermal strain as well as the mechanical strain. When FBG strain sensor is perfectly bonded to a structure, the thermal expansion of the sensor is constrained to take on the CTE of the host structure. Therefore, the thermal expansion of a FBG bonded to or embedded in a material becomes that of the structure itself. When temperature change and strain are applied to structures with an embedded or attached FBG hybrid sensor, the wavelength shift in the capillary tube is changed only by temperature change while external capillary tube is subject to both thermal and mechanical strains of structures. Therefore, we can measure the total wavelength shift by the FBG strain sensors. The strain applied to a structure will be equal to the difference of total wavelength shift and wavelength shift in the capillary tube. That is to say, the wavelength shift caused by applied strain can be expressed as follows: K ε Δε = Δλ ε = Δλ total Δλ T = Δλ total K T ΔT (4) From the Equation (4), we can calculate the strain. The problem that the temperature and the stress are shown in FBG sensors at the same time leads to the cross-sensitivity. The result of that is it can t be distinguished that which Polymers & Polymer Composites, Vol. 21, No. 9,

4 Zhan-Sheng Guo, Jiemin Feng, Hui Wang, Hongjiu Hu, and Junqian Zhang part of wavelength shift is caused by strain and which part is caused by the change of temperature by the single wavelength shift. In this paper, the strain is considered only. In order to eliminate the effect of temperature, temperature compensation should be carried out. There are many common temperature compensation methods, such as reference FBG method, etching FBG method, dual-wavelength FBG method, FBG harmonics method, FBG and long-period fiber grating (LPG) hybrid detection method, polymer packaging method, FBG and Polarization-Rocking Filter (PRF) superposition method etc. 29,30. Among these methods, the reference FBG method was simple, practical, convenient and economical. Therefore the reference FBG method was also used to consider the influence of temperature in this paper. 3. EXPERIMENTS 3.1 Fabrication of Specimen The laminate was made of T300/5222A (Carbon/Epoxy) prepreg and the stacking sequence of the laminates were [0] 16 and [0/90] 4S, respectively. The size of the laminate was 300 mm 300 mm. The size of specimen was 250 mm 25 mm and the number of specimen was 6 for unidirectional laminate and 2 for cross-ply laminate. During the cutting laminate, FBG signals of a cross-ply specimen were lost, so this specimen was not used. FBG sensors were embedded parallel to the reinforcing fibers. Two K-type thermocouples were adhered to the surface of specimen in order to monitor the temperature during fatigue test and to serve as a reference source for the temperature. 3.2 Experimental Apparatus The experiments were carried out at the high frequency fatigue machine (PLG 200C, Changchun Research Institute for Testing Machines). The apparatus of the PLG 200C is shown in Figure 2. The reflected signals of the FBGs were acquired through a DAQ board, and processed and saved by a signal-processing program written in LabVIEW software. Figure 2. Photograph of the fatigue testing system 3.3 Static Experiments In order to obtain the stress-strain relationship and strength of this material, the quasi-static tensile test was carried out. The experimental results of unidirectional and cross-ply laminate are shown in Figure 3. The tension strength of [0] 16 and [0/90] 4S are 1270 MPa and 566 MPa, respectively. The FBG strain sensor was embedded in the composite laminate specimen and the electrical strain gauges (ESG) were bonded on the specimen surface during fatigue experiments. Figure 4 shows the strain results measured by FBG sensor and ESG. It is found that these results agree well. It also indicates Figure 3. Quasi static tensile test results 556 Polymers & Polymer Composites, Vol. 21, No. 9, 2013

5 Fiber Bragg Grating Sensors for Fatigue Monitoring of Composite that the FBG strain sensor can measure internal strain of composite accurately. 3.4 Experimental Parameters PLG 200C high frequency fatigue testing machine is designed based on the principles of resonance. When the specimen was installed in the head cards, then the testing machine was started, the resonant frequency was 66 Hz. The load was supplied by load control method during fatigue testing. The experiments were carried out at room temperature. During the fatigue monitoring process, when fatigue numbers reached 50,000 (or 100,000), stopping the fatigue testing, static experiment was applied on the specimen. The FBG wavelength signals of maximum load, minimum load, and average load were recorded. The strain could be calculated by the strain sensitivity coefficient of FBG strain sensor. A reference FBG sensor as temperature compensation was set in order to remove the influence of ambient temperature. Fatigue strains of specimens of No. 1 and 2 were monitored respectively. The ply sequence and experimental parameters are shown in Table 1. Stress ratio is the ratio of minimum and maximum stress during experiments. Table 1. Experimental parameters for one step cycles loading fatigue tests Specimen Lay up Stress ratio Maximum stress (MPa) Average stress (MPa) Minimum stress (MPa) 1 [0] (40%) [0/90] 4S (65%) Figure 4. Comparison between strains measured by FBGs and electrical strain gauges ( ESG) Figure 5. Typical stiffness degradation curve for a wide range of fiber-reinforced composite materials 4. RESULTS AND DISCUSSION 4.1 Theory of Stiffness Degradation It is commonly accepted that for the vast majority of fiber-reinforced composite materials, the stiffness decay can be divided into three stages: initial decrease, approximately linear reduction and final failure shown in Figure 5. The damage development of carbon/ epoxy specimens with stacking sequence [0/90] 4s during tensiontension fatigue was thoroughly studied by Schule 31. The process of fatigue was distinguished by three distinctive stages. The initial region (stage 1) has a rapid stiffness reduction of 2-5%. The development of transverse matrix cracks dominates the stiffness reduction ascertained in this first stage; An additional 1-5% stiffness reduction occurs in an approximately linear fashion with respect to the number of cycles in the intermediate region (stage 2). Predominant damage mechanisms are the development of edge delaminations and additional longitudinal cracks along the 0º fibers. Stiffness reduction occurs in abrupt steps ending in specimen fracture in a Polymers & Polymer Composites, Vol. 21, No. 9,

6 Zhan-Sheng Guo, Jiemin Feng, Hui Wang, Hongjiu Hu, and Junqian Zhang Figure 6. Maximum strain vs. fatigue loading cycles with load control final region (stage 3). In this stage, a transfer to local damage progression occurs, when the first initial fiber fractures lead to strand failures. 4.2 Experimental Results of Stiffness Degradation Figure 6 shows the relationship between maximum strains and fatigue loading 11. From this figure we can find that the maximum strain changes continually under the control load condition. The maximum strain change is like the profile of stiffness degradation of composite 12. It also could be divided into three stages. So we can use the change of maximum strain to describe the stiffness degradation of composite during fatigue. Figure 7. Strain increment vs. cycle loading If the fatigue modulus F(N) = s(n)/e(n) is the residual stiffness of composite laminate during fatigue, the degradation of the residual stiffness during fatigue can be expressed as follows 13 : ( ) ( ) = σ max ε( N) E N E 0 ( ) = ε ( 0 ) ε( N) (5) σ max ε 0 The relationships of the increment of maximum/average/minimum strain of No. 1 and 2 with the load cycle numbers are shown in Figure 7. It can be found that the maximum/average/minimum strains increase with the cycle number under the tension-tension fatigue control load. The strain curves are similar although the lay-up and stress levels are different. In the initial stage of fatigue, strain increases fast with a nonlinear trend. The strain increases as the linear trend and the growth speed is slow at second stage which makes up the bulk of the total cycle time. The specimen of No. 1 is imposed by a lower stress level during fatigue testing; the maximum stress is only 40 percent of ultimate strength. This is why the strain increases slowly. At the end of the testing (cycle numbers equal 50,000), the increment of maximum strain is about 30με. The stress level of specimen 2 is higher (60 percent of ultimate strength), so the 558 Polymers & Polymer Composites, Vol. 21, No. 9, 2013

7 Fiber Bragg Grating Sensors for Fatigue Monitoring of Composite strain increases fast and reaches 203 με at the end of the testing (cycle numbers equal 100 million). According to the strain measured by FBG sensor, the normalized residual stiffness can be calculated using Equation (5). Figure 8 shows the results. It can be found that the residual stiffness decays continually during fatigue testing. Stiffness decays slowly at low stress level and quickly at high stress level. Under the certain stress level, the degradation of the stiffness shows distinct two stages. At first, the residual stiffness decays quickly and then slowly at a constant rate. Only stage 1 and 2 were represented in this paper. This is done to avoid difficulties with modeling stage 3 as a function of cycles because of the large variability in lifetimes. Because we are interested in predicting remaining strength prior to final failure of the composite, neglecting stage 3 should not be very significant in the results. The stiffness degradation experimental data are shown in Figure 8 along with the predictions from our model. Model prediction agrees very well with the experimental data. The stiffness degradation shows distinct two stages. In the first stage, the microcracks of matrix of transverse layer or oblique layer that cause the decrease of stiffness. This stage is generally over when the crack density of the matrix reaches a saturated state which is called characteristic damage state (CDS). Debonding and/or lamination of the interface of matrix and fiber are the main cause of the stiffness degradation in the second stage. 5. CONCLUSIONS The residual stiffness of composite laminates will decay while the strength of composite will not reduce immediately due to the damage accumulation during cycle loading. This trend can be reflected by the strain increasing under the cycle control loading. FBG sensor can be embedded in the composites directly; the strain changes can be obtained during the fatigue. In other words, the residual stiffness profile due to damage accumulation can be obtained. FBG sensors can be used as a new means and tool to monitor internal strain of composites. It is possible to monitor damage online, detect damage in service, and predict the residual service life of composites. FBG sensors will show their advantages greatly if FBG sensing net can be formed though appropriate multiplexing approach. A new and simple model for the degradation of stiffness was developed. The model prediction showed excellent agreement with our own experimental results. Figure 8. Stiffness degradation curves of the specimen during fatigue test 4.3 Modeling of Stiffness Degradation In this paper, a new model with very simple form is presented to describe the degradation of composite materials. This model accurately explains the rapid stiffness degradation in the first stage and slow linear degradation in the second stage. The proposed function is of the form: E(N) ) + e A(k2N+b2 ) ) = ln(ea(k1n+b1 E 0 A (6) Where E(N) is the cyclic stiffness after N cycles, E 0 is the initial stiffness before fatigue, N is the number of applied loading cycles, A, k 1, b 1, k 2, b 2 are material dependent parameters. The parameters k 1, b 1, and k 2, b 2 can separately be determined by the linear part of stage 1 and stage 2. The parameter A which controls the nonlinear segment between the stage 1 and stage 2 can be determined by fitting the experimental data. Polymers & Polymer Composites, Vol. 21, No. 9,

8 Zhan-Sheng Guo, Jiemin Feng, Hui Wang, Hongjiu Hu, and Junqian Zhang ACKNOWLEDGMENTS The authors gratefully acknowledge the support of this research by the NSFC (No , ), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and Shanghai Leading Academic Discipline Project (Project Number: S30106). REFERENCES 1. Wang Y.N., Study on the Theory and Design Technology of CFRP Fiber Bragg Grating Sensor. Wuhan University of Technology (2008). 2. Harris B., In Fatigue in Composites. Edited by B. Harris, Woodhead Publishing Ltd (2003). 3. Degrieck J., Paepegem W.V., Appl. Mech. Rev., 54 (2001) DOE / MSU Composite Material Fatigue Database. Version 16.0 (2007). 5. Sutherland H.J., Wind Energy, 3 (2000) Lian W., Yao W.X., International Journal of Fatigue, 32 (2010) Yashiro S., Okabe T., Composite: Part A, 42 (2011) Colombo C., Vergani L., International Journal of Fatigue, 33 (2011) Kensche C.W., International Journal of Fatigue, 28 (2006) Kong C., Kim T., Han D., Sugiyama Y., International Journal of Fatigue, 28 (2006) Schroeder K., Ecke W., Apitz J., Lembke E., Lenschow G., Meas. Sci. Technol., 17 (2006) Zetterlind III V.E., Watkins S.E., Spoltman M.W., IEEE Sensors Journal, 3 (2003) Wu Z.J., Wan L.B., Zhang B., Zhao H., Acta Materiae Compositae Sinica, 21 (2004) Vallons K., Zong M., Lomov S.V., Verpoest I., Composites Part A, 38 (2007) Silva-Munoz R.A., Lopez-Anido R.A., Composite Structures, 89 (2009) Ang J., Li H.C.H., Herszberg I., et al., International Journal of Fatigue, 32 (2010) Kuang K.S.C. and Cantwell W.J., Appl. Mech. Rev., 56 (2003) Jiang D.S., He W., Journal of Optoelectronics Laser, 13 (2002) Takeda N., Okabe Y., Kuwahara J., Kojima S. and Ogisu T., Compos. Sci. Technol., 65 (2005) Tsuda H., Compos. Sci. Technol., 66 (2006): Peters K., Pattis P., Botsis J., Giaccari P., Opt. Laser Eng., 33 (2000) Peters K., Studer M., Botsis J., Iocco A., Limberger H. and Salathe R., Exp. Mech., 41 (2001) Botsis J., Humbert L., Colpo F. and Giaccari P., Opt. Laser Eng., 43 (2005) Okabe Y., Yashiro S., Kosaka T. and Takeda N., Smart Mater. Struct., 9 (2000) Takeda S., Okabea Y. and Takeda N., Compos. Part A, 33 (2002) Garrett R.C., Peters K.J. and Zikry M.A., Aeronaut J., 113 (2009) Hill K.O., Fujii Y., Johnson D.C., et al., Appl. Phys. Lett., 32 (1978) Meltz G., Morey W.W., Glenn W.H., Opt. Lett., 14 (1989) Yun B.F., Theoretical and Experimental Study of Fiber Bragg Grating Sensors. Southeast University (2006). 30. Sun M., Health Monitoring of Engineering Structures Using Fiber Bragg Grating Sensing Technology. Sichuan University (2005). 31. Schulte K., Reese E. and Chou T.W., Sixth international conference on composite materials & Second european conference on composite materials, Volume 4, pp , 1987, Proceedings, London, UK, Elsevier. 560 Polymers & Polymer Composites, Vol. 21, No. 9, 2013