COUPLED ELECTRICAL AND THERMAL DAMAGE DETECTION IN CARBON FIBER REINFORCED POLYMERS. A Dissertation. Presented to

Transcription

1 COUPLED ELECTRICAL AND THERMAL DAMAGE DETECTION IN CARBON FIBER REINFORCED POLYMERS A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Jie Wen December, 2011

2 COUPLED ELECTRICAL AND THERMAL DAMAGE DETECTION IN CARBON FIBER REINFORCED POLYMERS Jie Wen Dissertation Approved: Accepted: Advisor Dr. Fred K. Choy Department Chair Dr. Celal Batur Co-Advisor Dr. Zhenhai Xia Dean of the College Dr. George K. Haritos Committee Member Dr. Guoxiang Wang Dean of the Graduate School Dr. George R. Newkome Committee Member Dr. Xiaosheng Gao Date Committee Member Dr. Dale H. Mugler Committee Member Dr. Lindgren L. Chyi ii

3 ABSTRACT Carbon fiber reinforced polymer matrix composites (CFRPs) are widely applicable in various important structural components for aircraft, spacecraft, civil structures and energy generation infrastructures. One of the critical issues in the successful application of CFRPs is nondestructive assessment of damage state in a particular structural component. Electrical measurement is an emerging non-destructive evaluation technology for real-time/on-board damage detection in CFRPs. In this research, electrical potential was measured in an efficient A/D & D/A system to detect the damage in the CFRPs. There were three types of signals generated, DC, Sine wave, and the wavelet signal. To solve the problem of noise influence in the experiment, the wavelet theory has been demonstrated as a remarkable tool for noise reduction by comparing to the traditional signal analysis methods. Another part of this research is the coupled thermal-electrical analysis. To conduct the thermal study, the DC signal was employed to the CFRP sample as a thermal heating source for both experimental and numerical studies. In experimental study, the change of differential electrical potential was investigated to locate the damage and ratios of potential change were used to correlate with the damage size. Two linear relations were developed to evaluate the damage size, the variables of maximum ratio and average ratio of the potential changes. The thermal response was studied with thermography tests and results are compared to indicate the damage on the CFRP using temperature distribution changes. When the iii

4 temperature distributions were compared to those of the electrical measurements, they were in good agreement in locating the damage. In the numerical analysis, the 3D coupled thermal-electrical finite element models have been successfully generated to simulate the electrical potential and the nodal temperature distributions. The experimental results and the numerical results have shown good agreement with each other. iv

5 ACKNOWLEDGEMENTS I would like to express my appreciation to my advisor, Dr. Fred Choy, for his generous guidance and support over last four years. His outstanding insights and encouragement have inspired me to finish this dissertation. I also would like to thank my co-advisor, Dr. Zhenhai Xia, for his valuable advice for my dissertation. He has always been available to help me through my research. I sincerely appreciate his many hours of guidance, even over the long distance. I am also very grateful for all other members of the dissertation committee. I would like to thank Dr. Guoxiang Wang, Dr. Xiaosheng Gao, Dr. Dale Mugler, and Dr. Lindgren Chyi for their time and valuable comments. I would like to show my appreciation to the helpful staffs of ME Department, especially Christina, Stacy, and Cliff. I am grateful to all my colleagues and friends for their help and encouragement, including Peter Shen, Pirapat Arunyanart, Henry Chen, Li Du, Jianbing Niu, Yuerong Chen, Amy Tanya Sujidkul and many others. Special thank to Peter Pan for his help with my thermal experiment. Last but not the least, I would like to thank my husband, my parents, my parentsin-law, uncle Ben and aunt Sherry for their love and faith. My deepest appreciation goes to uncle Ben for his encouragement and being a role model in my life. v

6 TABLE OF CONTENTS Page LIST OF TABLES x LIST OF FIGURES....xi I. INTRODUCTION Statement of problem Objectives Expected results and application of this dissertation Overview II. LITERATURE REVIEW Structure and properties of CFRPs Damage and failure mechanisms of CFRP composites Traditional sensing methods and applications Self-sensing electric resistance and potential measurement Electrical response to fiber damages...18 vi

7 2.4.2 Electrical response to fatigue damages Matrix cracking and delamination damage detection Electromechanical modeling Finite element modeling at the macroscale Analytical solutions for electrical-mechanical behavior Electromechanical modeling at the microscale Signal analysis methods Continuous wavelet transforms and discrete wavelet transforms Application of wavelet transform in composite materials III. METHODS OF ELECTRICAL AND THERMAL MEASUREMENT AND NOISE ELIMINATION Experimental set-up Material preparation A/D and D/A design Thermograph test Summary Noise reduction vii

8 3.2.1 Small random noise effect Large random noise effect A demonstration with experimental data Summary IV. COUPLED THERMAL-ELECTRICAL FEA MODELING OF CFRPS Model creation Electrical potential distribution Temperature distribution Summary V. RESULTS AND DISCUSSIONS OF EXPERIMENTAL AND NUMERICAL STUDIES Experimental results Damage location Estimation of the damage size Summary FEA results FEA results of Electrical Potential viii

9 5.2.2 FEA results of Thermal distribution Summary Correlation of experimental and numerical studies Electrical analysis results Thermal analysis results Electrical versus Thermal Analysis Summary VI. CONCLUSIONS AND FUTURE WORKS Conclusions Limitations Future works REFERENCES 116 ix

10 LIST OF TABLES Table Page 3.1 Errors for 4 sizes of hole SNR and error for DC, sine wave, and wavelet signals Errors for different thresholds Ratios of dimension and potential change (EXP) Ratios of dimension and potential change (FEA)..95 x

11 LIST OF FIGURES Figure Page 2.1 Four types of CFRP structures: (a) Unidirectional composites; (b) Cross-ply composites; (c) 2D woven CFRP; (d) 3D orthogonal woven CFRP Three types of damage in CFRPs: (a) fiber breakage; (b) cross-ply crack; and (c) delamination Electrical resistance measurement methods: (a) Two-probe method; (b) Four-probe method; and (c) Multi-probe method Scheme of specimen with electrodes for one/two-stage electric potential method Normalized resistance change ΔR/R 0 (solid curve) increases with applied strain simultaneously [33] Variation of resistance change ΔR/R 0 with cycle number [35] Response surface methodology [22] Delamination configuration and voltage change distribution xi

12 (a) Delamination monitoring at laminar of [0/90]s;.24 (b) Electric voltage change distribution due to [0/90]s delamination [40] FEA model and the element mesh [45] Electrical resistivity change due to curing temperature [45] Beam-type FEA models: (a) without delamination; and (b) with delamination [46] Comparison between theoretical predictions and experimental results: (a) surface resistance; and (b) oblique resistance between electrodes A2 and A4 [46] Coupled electrical and mechanical models: (a) a real composite; (b) and (d) an electrical network of resistors; (c) and (e) a mechanical network of elastic elements with damage states [49] Transformation of the parallel cell of resistors to a long conductive wire: (a) unit parallel cell with random contact points, and (b) transformation of the unit cell to a long conductive wire over which the electrical nodes are distributed randomly [53] Resistance change as a function of strain: experiment and xii

13 Monte Carlo simulation results for different fiber volume fraction V f [53] Wavelet family (a)pure sine wave; and (b)cwt time-frequency spectrogram (a)sine wave with a pulse; and (b)cwt time-frequency spectrogram Morlet wavelet and CWT time-scaling spectrogram Morlet wavelet with a pulse and CWT time-scaling spectrogram Discrete wavelet transform decomposition tree Noisy sine wave decomposition Denoised signal and original signal (a) CFRP sheet; (b) CFRP sheet with electrodes Scheme of CFRP sheet with electrodes Experimental set-up schematic Experiment Labview code Thermography test setup Small noise effect in DC signal (a) Original sine signal and sine signal with random noise...49 (b) FFT of original sine signal and FFT of sine signal with random noise...50 xiii

14 3.8 (a) wavelet signal without noise and its CWT coefficients; (b) wavelet signal with small random noise and its CWT coefficients Scalogram of top 60% coefficients for wavelet signal (a) without noise; 52 (b) with random noise DWT denoised signal for small random noise effect Large random noise effect at DC signal Partial sine signal without/with random noise FFT of sine signal with large random noise effect The wavelet signal with large random noise The scalogram for wavelet signal (a) without noise; 57 (b) with noise DWT denoised signal for large random noise effect Scalograms for cases of (a) undamged; (b) hole with 1/8 inches diameter;.60 (c) hole with 5/32 inches diameter; (d) hole with 3/16 inches diameter;...61 (e) hole with 1/4 inches diameter (a) Extrusion regions for boundary condition and loading; (b) Electrical ground; (c) Loading region.68 xiv

15 4.2 Mesh size effect Mesh screenshot of 3-dimension model of undamaged/damaged CFRP Loading area effect in FEA model Electrical potential distribution of FEA for undamaged CFRP Electrical potential distribution of FEA for damaged CFRP Nodal temperature distribution of FEA for undamaged CFRP Nodal temperature distribution of FEA for damaged CFRP (a) Schematic of electrodes; (b) Schematic of the differential electrical potential Changes of differential electrical potential for eight sets of input locations Case A thermography Comparison of undamaged and damaged case A Case B thermal images Case C thermal images Case D thermal images Ratio of potential change in experiment Side view of damaged specimen 90 xv

16 5.10 Comparison of dimension ratio R and average ratio of potential change (EXP) Error range of damage size estimation (EXP) Changes of differential electrical potential in FEA Ratio of potential change in FEA Comparison of dimension ratio R and average ratio of potential change (FEA) Error range of damage size estimation (FEA) Schematic of thermal study on Line Temperature distribution of FEA model on Line Schematic of FEA model for Line Temperature distribution of FEA model on Line Test for electrode effect Comparison of experimental and FEA results Comparison of potential change between experimental and FEA results Estimation of damage size in experiment and FEA Comparison of FEA and thermal test for undamaged case xvi

17 5.25 Comparison of FEA and thermal test for damaged case Temperature change ratio in EXP Temperature change ratio in FEA 108 xvii

18 CHAPTER I INTRODUCTION 1.1 Statement of problem Carbon fiber reinforced polymer composites (CFRPs) are manufactured by mixing carbon fibers and plastic resin under certain prescribed conditions for a variety of applications. These materials are distinguished by their high strength and rigidity, low density, excellent damping properties and high resistances to impacting and corrosion combining with modifiable thermal expansion to complement complex characteristics profile. Because of their excellent mechanical properties, CFRP materials have been widely used for critical components and structures, such as aircraft fuselage and wing structures, helicopter rotors and windmill blades, road and marine vehicle body structures, and, bridges and large civil infrastructures. CFRPs can significantly reduce weight while increasing strength and durability which can result in a huge improvement in the efficiency of vehicles and/or structural facilities. Under complex environments and loading states, damage in the form of penetration, delamination and/or transverse cracking may occur in these materials during service. These damages can sometimes lead to catastrophic loss. As an example, the new Boeing 787 structural composition contains over 50% CFRP on the fuselage and wings. A bird strike is a big threat for the aircraft. When the bird strike happens on the wings 1

19 of the aircraft, the damage will usually issue as a hole shape within the composite structure. In general, to ensure the safety and reliability of CFRPs during their lifetime, non-destructive evaluation (NDE) has become one of the critical issues in the successful application of CFRPs. NDE can be used in damage detection and accurate prediction of the remaining service life of the CFRP components, thus provides life extension control or damage mitigation. Presently, there are various NDE methods that can be used for the assessment of the damage state. Most conventional NDE techniques such as ultrasonic C- scan [1], x-ray [2], thermography [3] and eddy current [4] are not on line based techniques, and they usually require the targeted component to be taken out of service for a prolonged period of time for post-damage inspection and assessment. Other techniques, such as piezoelectric sensor [5], optical fiber [6], can be used for on-line health monitoring of CFRP structures but they all involve the attachment of external sensors or additional fiber inputs in CFRPs. CFRPs are electrically conductive because of the high conductivity of carbon fibers. CFRPs are multifunctional materials in which the damage is coupled with the material electrical resistance, which provides the possibility of real-time information about the damage state through monitoring of resistance/electric potential. The uniqueness of this resistivity technique lies in its capability of in-situ self-sensing of damage criticality of composite materials without any additional sensors to be embedded within composites. Currently, most of the experimental work has been conducted relying on the electrical conductive characteristics of carbon fibers for damage detection in CFRPs. By comparing with classical non-destructive evaluation techniques such as acoustic emission, it has been shown that resistance measurement allows the monitoring 2

20 of the in-situ evolution of various internal damage nucleation and growth phenomena such as fiber fractures, interply matrix cracks and interply delamination [7, 8]. Changes in electrical resistance of carbon fiber composite damages have been established by a number of experimental studies in the last decade [5, 9]. One of the difficulties in measuring small changes of electrical signal due to failures in the carbon fibers is the contamination of induced noises during the measuring process. A signal analysis technique has been adopted in recognition of materials failure. In traditional signal analysis procedures, the Fast Fourier Transform (FFT) is often used. FFT is a perfect tool to analyze signals in frequency domain, but it is incapable to show the precise time that particular frequency components occur. To overcome this drawback, wavelet transform has attracted much attention in the signal analysis field during the last 40 years. As a time-frequency signal analysis tool, wavelets offer simultaneous interpretation of the signal in both time and frequency domains which leads to wide applications in transient signal analysis, image analysis, communications systems, and many others. Wavelets are also an effective tool for noise reduction. In any sensing environment, signal acquired by electro-mechanical or electronic is degraded because of the noise. Reducing noises is one of the priorities in experiments. The infrared thermography has been widely used in detecting the damage of composites materials [10-13]. The electrical source produces the thermal response of the CFRP, which conducts the coupled thermal-electrical analysis. Only the constant DC signal is suitable for the coupled thermal-electrical analysis, as it is difficult to produce the temperature changes by applying any waveform signal. The experiment and FEA 3

21 simulation are executied to study the coupled thermal-electrical characteristic of the CFRP. 1.2 Objectives Two major objectives of this dissertation are the noise reduction and accurate measurement of electrical signals due to material damages and nondestructive damage detection of the CFRPs using the coupled thermal-electrical analysis in both experimental and numerical studies. The newly developed experimental system will conduct the generation of the electrical signal and acquisition of the electrical response signal simultaneously. As noise effect is always the big issue for electrical measurement of CFRPs, the current research applies the wavelet transform technologies in reducing the noise as well as enhancing the electrical signal for damage detection in CFRPs. Based on the material properties of the CFRPs, the coupled thermal-electrical analysis is also conducted to solve the inverse problem of locating the damage and estimating the damage size. Flexible electrodes patterns have been designed to locate the damage. The multi-scale FEA models are created to verify to the experimental study and also to offer further investigation of the damage detection in CFRPs. The specific objectives of this dissertation are listed as follows: Testing the damage on the CFRP is described in a small scale for the proof of concept, the specific objectives can be described as follows: Multiple-probe method is used in this research. Because the traditional two-probe method is sensitive to the quality of the electrical contacts. In the four-probe method the outer two contacts are for current, and the inner two are for voltage measurement. By using four contacts, the resistance of 4

22 voltage contacts is not included in the resistance between the voltage contacts. But the four-probe method leaves a lot to be desired because of the high anisotropic properties of carbon fiber composites. The input and output electrodes have to be coincident on a straight line. Both A/D and D/A functions are assembled on one Data Acquisition System. This technique not only reduces the operating steps, but also increases the variety of input signal function. Thus the experiment is more flexible to conduct. National Instrument DAQ system is adopted in this research, which is accompanied to LabVIEW (Laboratory Virtual Instrumentation Engineering Workbench). LabVIEW contains a huge amount of libraries including signal generation and wavelet design, which are employed to produce the analog input signal in this research. D/A to generate three signals: DC, sine wave, and wavelets Programming in Labview is adopted to generate the continuous signals, with maximum amplitude 0.1V for the above three cases. The generated signals are supplied at 8 sets of input electrodes. A/D to acquire the signals Acquiring the signals with sampling rate of 2 KHz, using 16 single-end channels. Totally 8 sets of input combinations for each type of signals, and 10k data of each channel are collected every time Reducing the noise. Since the experiment is lab based, the noise can be ignored. However, CFRPs are often employed under harsh and dangerous environments. 5

23 The unpredictable noises are a big issue. It is desirable to filter out the noises and monitor the potential damages. Three types of signals are reduced random noise by three different methods. For the purpose of demonstrating the use of DC signal with averaging of the data, sine wave signal with FFT, wavelet signal with wavelet transforms, two conditions are imported into the study: Small random noise effect Large random noise effect Estimation for the location of damages can be acquired by comparing the electrical potential distributions, which is used to limit it within a quarter section of specimen including: 8 sets of input patterns on the edge of CFRP are applied to produce the different electrical potential distributions Each electrode obtains a different potential under each input set, thus the approximate location can be estimated. Estimate the size of damages by comparing the potential changes through calculating of the ratio of electrical potential change for every single electrode Thermography study is conducted for the thermal characterization analysis. The thermal image has been collected by another cooperating group. FEA simulation is the numerical confirmation which provides parametric study. FEA modeling results, as an insight for experimental set up, are used for the correlation with verification of experimental results 3D thermal-electrical model is created 6

24 Apply the electrical load, and calculate the electrical potential and the nodal temperature at the corresponding points The model with a hole is created to simulate the damaged case and verify the experimental results 1.3 Expected results and application of this dissertation As the objectives proposed above, the multi-probe measurement in the advanced A/D & D/A system is expected to be more efficient and easier to operate than traditional methods. The application of the wavelet transform technology will enable noise reduction during the denoising process. The analysis of electrical response is able to identify the damage location of the CFRP sample. The damage size can be quantitatively estimated. The coupled thermal-electrical FEA models can effectively simulate the damage detection of the CFRP, and was also verified with the experimental study. The results have shown the A/D & D/A system is capable of generating and acquiring data efficiently. Signals with different properties were generated, including constant DC signal, sine wave signal, and wavelet waveform signal. The system responded swiftly and precisely when receiving the signals from the measurement system. The wavelet transform technique has been proved as the best denoising approach by comparing with other methods in this research. The demonstration has shown that the wavelet transform can successfully recognize the damage on CFRPs. The damage location and the damage size on the CFRPs can also be estimated by analyzing the electrical potential changes. The 3D coupled thermal-electrical FEA models have been developed and have agreed with the experimental results. 7

25 1.4 Overview Chapter II gives the background and literature review of the CFRP in both experimental and numerical analysis. The basic knowledge of wavelet theory and its denoising application will be introduced. Chapter III presents the details of the experimental study including the electrical measurement, thermography test, and the demonstration of the wavelet transform application in noise elimination. Chapter IV introduces the FEA modeling creation including the electrical potential study and the thermal study. Results of both experimental and numerical analysis will be discussed in Chapter V. Chapter V also presents the approach of detecting damage location by comparing the differential electrical potential and estimating damage size by creating the linear relationship of potential change ratio to the damage dimension ratio. The correlation of experiment and FEA results will be discussed for both electrical and thermal studies. The difference between electrical study and thermal study is also included in chapter V. Chapter VI concludes this research and makes suggestions for the future work. 8

26 CHAPTER II LITERATURE REVIEW 2.1 Structure and properties of CFRPs The simplest structure of CFRPs is unidirectional composites in which all fibers run in the same direction parallel to each other in polymer matrix, as shown in figure 2.1 (a). The most common form of CFRPs is the cross-ply laminate, such as laying up a sequence of unidirectional plies. Usually the cross-ply laminates, as shown in figure 2.1 (b), suffer from the complex damage processes involving debonding of the fiber-matrix, transverse cracks, delamination and fiber failure. In other structural models such as woven CFRPs shown in figure 2.1 (c), the fibers are braided with each other. This special structure improves the damage tolerance of the composites. In addition, the threedimensional orthogonal woven CFRPs, as shown in figure 2.1 (d), has also been developed, in which fibers are placed in three orthogonal directions with each other. Due to the cross-over pattern, this multi-directional structure endows the CFRPs a better delamination resistance. Besides the reinforcement, carbon fiber, the other composition in CFRPs is epoxy matrices. Epoxy matrices fix the pattern of CFRPs and play a part to transfer loads within 9

27 the composites. Epoxy matrix has been widely used due to the high heat resistance and high strength. It is an insulator because of the low electrical conductivity. (a) (b) (c) (d) Figure 2.1 Four types of CFRP structures: (a) unidirectional composites, (b) cross-ply composites, (c) 2D woven CFRP, and (d) 3D orthogonal woven CFRP CFRPs are widely used in many areas because of their excellent mechanical properties. This material has a very high elastic modulus and high tensile strength of approximately 7GPa. Low density and low thermal expansion are also the reasons of its popular use. In addition, CFRPs have high chemical inertness and can serve under the 10

28 corrosive environment. Although failure under fatigue loading can sometimes be observed, CFRPs have better fatigue behavior than metals. The CFRPs endurance limit reaches about 60-80% of the fracture stress, but the metals endurance limit only reaches about 30% of the fracture stress [9]. However, the CFRPs are relatively brittle compared with metallic materials. During fatigue, delamination may occur in CFRPs. A study, discussing the influence of moisture on CFRPs, was carried out [10]. The mechanical properties of CFRPs become worse due to moisture. CFRPs are electrically conductive because of the high conductivity of carbon fibers. Although the epoxy matrix has high electrical resistivity, which can be taken as an insulator, the fiber-fiber contact in the matrix forms an electrical network, which makes the CFRPs conductive in transverse and through-thickness directions. The electrical resistance in CFRPs relys on the volume fraction, the loading and the size of carbon fibers and the laminate sequence. The resistance change is linearly proportional to strain due to the conductive fibers. However, fiber fracture in CFRPs results in sudden increasing of resistance because of breakage of electrically conductive fibers [9]. The resistance change increases dramatically with an increase of the strain due to the damage of the fibers. The CFRPs are electrically anisoreopic. The conduction on different directions within the composite is various with different structures of CFRPs. For unidirectional CFRPs, the conductivity in the longitudinal direction is much higher than that in the transversal direction. For cross-ply laminates, more fiber contacts result in similar conductivity on 0 o and 90 o directions. But the through-thickness resistivity is much 11

29 higher than those on 0 o and 90 o directions. For the woven CFRPs, the through-thickness resistivity is 1000 times higher than the in-plane resistivity [14]. 2.2 Damage and failure mechanisms of CFRP composites There are three major types of damages in CFRPs under loading conditions. Fiber breakage, as shown in figure 2.2 (a), is one of the basic types of damage. The broken fibers lose their stress capabilities and transfer loads to the unbroken fibers. The discontinuation of electrical conductivity due to the broken fibers results in a general increase of electric resistivity along the fiber direction. The second form of damage is the matrix structural damage which is more common than the fiber breaking damages. Since fibers strength is substantially stronger than the matrix, damage usually involves in the matrix earlier than those in the fibers for laminate composites. Two major types of matrix damages were commonly observed [7]. One form of matrix damages causes more fiber contacts with each other which results in decreasing of electrical resistance. Another form is the damage from cross-ply crack within fiber plies, which results in through-thickness resistance increasing as shown in figure 2.2 (b). The third type of damages, as shown in figure 2.2 (c), is delamination of CFRPs in which the local separation of the fiber plies occurs due to matrix cracking between the layers and/or debonding at the fiber-matrix interface. The delamination affects the reliability of composites and is very difficult to detect using conventional NDE methods. 12

30 Fiber breakage Cross-ply crack Delamination (a) (b) (c) Figure 2.2 Three types of damage in CFRPs: (a) fiber breakage; (b) cross-ply crack; and (c) delamination 2.3 Traditional sensing methods and applications As online structural health monitoring becomes critically desired, a variety of procedures using embedded or attached sensors, such as acoustic emission, lamb wave method, piezoelectric, optical fiber, sonic infrared imaging technique, and fiber Bragg grating sensors have been applied for structure health monitoring. Belchamber et al. [15] has developed a series of pattern recognition techniques for collecting acoustic emission (AE) from composite materials, and acoustic emission has been used as an efficient tool to acquire in-situ information on damage. However, although acoustic emission allows damage infliction sensing, it does not allow strain/stress sensing in the absence of damage [16-18]. The application of Lamb waves method is a convenient approach to evaluate composite laminates as the waves can propagate through long distance to detect transverse cracks and delamination [19, 20]. Based on acoustic wave principles, piezoelectric sensors and actuators have been applied successfully for monitoring 13

31 structural damages [21]. Fiber-optical sensors have been used for monitoring the damage of the composites and their optical interference signals are sensitive to specimen damages [6]. Sonic infrared imaging technique applies a series of short pulses of sound wave to infuse the material and an infrared camera captures the temperature rise at the crack location[22]. The fiber Bragg grating sensor is developed to be embedded in composite materials for detection of the delamination in carbon fiber reinforced plastic cross-ply laminates. The sensor measures the length of the delamination through spectrum changes and the intensity ratio in the spectrum is used as an indicator for the prediction of the delamination length [6]. However, all the embedded and attached sensors are usually expensive, not durable, and difficult to repair. Some other inspection procedures such as ultrasonic, x- ray, and magnetic particle have problems in detecting small-size damages. Since the carbon fiber composites are electrically conductive, it can provide the self-sensing capabilities for detecting damages in addition to its reinforcement properties. Based on the principles that carbon fiber breakage or delamination in the structural materials will lead to electrical resistance increase, this method of self-sensing is attractive and has the ability of sensing the entire volume of the composite while most embedded or attached sensors are only able to sense the local volume. 2.4 Self-sensing electric resistance and potential measurement The electrical resistance measurement method has been widely employed for damage sensing. Basically, two-probe method and four-probe method are commonly used in electrical resistance measurement for self-sensing in carbon fiber polymer-matrix composites. The two-probe method uses two electrical contacts which serve both current 14

32 and voltage measurements shown in figure 2.3 (a). This method is simple and convenient; however, it is sensitive to the quality of the electrical contacts. In the four-probe method shown in figure 2.3 (b), four contacts are applied. The outer two contacts are for current, and the inner two are for voltage measurement. By using four contacts, the resistance of voltage contacts is not included in the resistance between the voltage contacts. Wang and Chung proved that the four-probe method is more sensitive, more accurate, and more precise than the two-probe method by sensing impact damage in CFRPs using electrical resistance measurements [23]. However, care should be taken when applying the fourprobe method to anisotropic materials. Angelidis et al. showed that the four-probe method is not perfect because of the high anisotropic properties of carbon fiber composites. From the finite element analysis, the damage or poor electrical contact at the electric current electrodes can cause wrong measurement [24]. The multi-probe electric potential method has high reliability for measurements of slight electric resistance changes of composite materials. It is similar to the two-probe method, but a different way to charge the electric current and measure the electric potential as shown in figure 2.3 (c)[25]. 15

33 Figure 2.3 Electrical resistance measurement methods: (a) Two-probe method, (b) Four-probe method, and (c) Multi-probe method In-situ detection of damage in CFRPs was performed by using both DC and AC electrical property measurements. It seems that DC electrical conduction allows detecting fiber failure, but AC measurements are more suitable for monitoring matrix cracks, delamination, fiber/matrix debonding or transverse cracks [26]. The DC and AC electrical methods are possible to monitor strain and failure as well as to classify different failure mechanisms in static and dynamic load conditions. For CFRPs, the response of DC resistance due to damage is better than that of AC resistance [27]. In situ detection of damage for unidirectional CFRPs under the monotonic and cyclic flexural tests has been carried out by means of electrical resistance measurements. Results demonstrate AC and DC methods are suitable for the detection of the development of damage by resistance changing [28]. Finally, electric capacitance is also used to determine the damage in CFRPs. Monotonic tests under post-buckling bending conditions have been performed on cross ply laminates. The monitoring of electrical resistance and capacitance changes, 16

34 which are linked to the modifications of the conduction paths in the composites and occurrence of voids during loading, allowed the detection of damage growth. The electric resistance method offers high analytical accuracy, however it requires multiple electric charges to measure the resistance between electrodes. For the four-probe method, the current path and the potential gradient path must be coincident [29]. Also for the two-probe method, the contact resistance between the electrodes and carbon fibers highly affects the result. The electric potential measurement has been employed to resolve these problems. The damage of the CFRP can be detected by measuring changes in the electric potential field on the surface. The current path is modified because of the fiber breakage and delamination, which results in changes around the damage zone [30]. In this method, two current electrodes and several voltage electrodes are attached on the surface of the specimen to adopt a four-probe method. But it has a disadvantage that the electric current perpendicular to the surface disappears at the center segment of the current electrodes. To overcome this problem, a two-stage electric potential method has been created in both numerical analysis and experiment. Figure 2.4 shows the configuration of the specimen. Electrodes A and D in the two-stage potential method are current supply instead of electrodes A and G. This two-stage electric potential method involves two stages, which are estimating the delamination at the center segment of the current electrodes and charging electric current between center electrode and endelectrode [31-33]. Figure 2.4 Scheme of specimen with electrodes for one/two-stage electric potential method 17

35 2.4.1 Electrical response to fiber damages By using the electrical resistance measurement, the self-sensing of composites has been presented to predict the damage from uniaxial tension, flexure, impact, and fatigue loading. When the composites are under uniaxial static tension loading, the electrical resistance linearly increases with fiber strain increasing until the fiber breaks(9), as shown in figure 2.5. Under the cyclic longitudinal tension loading, the fractional resistance changes increase in transversal direction and decrease in longitudinal direction due to the increase of the degree of fiber alignment [34]. The same results were obtained from applying current in both longitudinal direction and transversal direction, which the resistance change fraction in the former case was lower than that in the latter case [24]. Flexure is more complicated than uniaxial tension because the stress/strain is not uniform. The two surfaces are under compression and tension, respectively. By separately measuring compression, tension surface, and volume resistance, the resistance of the compression surface decreases, but the tension surface resistance and volume resistance increase. The resistance of surfaces is more sensitive than the volume resistance to the low deflection since the strain is higher at the surface. When major damage occurs, the resistance on both surfaces and the volume resistance increase abruptly [35]. 18

36 Figure 2.5 Normalized resistance change ΔR/R 0 (solid curve) increases with applied strain simultaneously [36] To investigate the self-sensing ability of carbon fiber composites by measuring electrical resistance away from the damaged region, an impact test has been done by Wang and Chung. The resistance is measured in different locations and directions of the composite materials before and after local impact. Through-thickness and volume resistance are more effective to indicate the damage than longitudinal resistance. Furthermore, while distance from the impact point is increased, the through-thickness resistance decreases more than the volume resistance [37]. Both two-probe and fourprobe methods were applied to sense impact damage of both 8-lamina and 24-lamina specimens [23]. As discussed before, the four-probe resistance is more sensitive than the two-probe resistance for both specimens. The increasing of resistance change in 8-lamina composite reduces along the distance increasing from the impact section. However, for 24-lamina composite, the resistance in the closest area to the impact section decreases in a certain extent. A special case, the damage in the carbon fiber polymer-matrix composite cylinder was investigated by measuring electrical resistance. The four-probe method was applied to measure axial, radial, oblique, and the circumferential resistance. The 19

37 circumferential resistance was found most sensitive to impact among these resistances [23]. The comparison of the electrical resistance and potential measurement for an impact test has been demonstrated [29]. Due to studies on 8-laminae, 16-laminae, and 24- laminae, the resistance method was more sensitive than the potential method for 16 and 24 laminae. For the 8-laminae composite the potential method was more effective than resistance Electrical response to fatigue damages Fatigue loading causes various types of damage of structural materials. To detect fatigue damage, online electrical resistance measurement has been proved an efficient approach to replace the traditional prediction by using past experience. The longitudinal resistance is measured to monitor the fatigue damage in composites. The resistance decreases reversibly upon tensile loading in every cycle, which offers dynamic strain monitoring shown in figure 2.6. The peak resistance in a cycle irreversibly increases when the fiber breakage occurs. According to research data, the fiber breakage can be detected at 50-55% of fatigue life. When 18% of fibers are broken, structural materials occur disastrous failure. The delamination occurs rapidly at 62% of the fatigue life [38-39]. Experiments prove that the change of electrical resistance increases 10-15% due to the stiffness changes of material during fatigue loading [40]. Under the repeated tensile loading in the fiber direction, it was found that the major damage of CFRPs turned increasing of the through-thickness resistance to decreasing with strain reversibly [7]. 20

38 Figure 2.6 Variation of resistance change ΔR/R 0 with cycle number [38] Thermal cycling results in matrix molecular movement, thus the electrical resistance changes upon the length changing of composites at the various temperatures. The measurement of electrical resistance was applied to thermal analysis of carbon fiber polymer-matrix composites [41]. Interlaminar thermal damage can be detected by changing of resistivity during the thermal cycling. Both thermoset-matrix composite and thermoplastic-matrix composite were tested under two modes of thermal cycling, which are cycles with fixed temperature amplitude and cycles with gradually increased and decreased temperature amplitude. The resistivity at the interlaminar interface increased for thermoset-matrix composite and decreased for the thermoplastic-matrix composite due to matrix damage [8] Matrix cracking and delamination damage detection As mentioned in the previous section, matrix damage is more common than fiber damage. One type of matrix damage allows fibers to touch each other, which results in a decrease in the resistivity as presented in short carbon fiber polymer-matrix [42]. Also for 21

39 continuous fiber polymer-matrix composites [7], the longitudinal resistance decreased due to minor laminar damage between fibers and through-thickness resistance increased at first step followed by decreasing due to major damage between adjacent laminae. Delamination is another type of matrix damage that commonly occurs in the composites. Delamination causes low reliability for composite laminates. Usually, delamination is invisible and very difficult to detect by visual inspections. Electrical resistance measurement is an efficient way to identify the delamination in CFRPs. The through-thickness electrical resistance measurement was presented for sensing the delamination during fatigue loading [39]. When the electric current flows in the fiber direction, the delamination can be detected with electric resistance change. When the current flows in the transverse direction, delamination cannot be detected, because of the different electric conductance in the through-thickness and transverse directions [43, 44]. The two-stage electric potential change method has been presented for delamination detection experimentally [33]. A prediction of delamination locations and sizes from electric resistance changes is an inverse problem. Comparing to the artificial neural network, the response surface methodology, an inverse problem solver, can approximately solve the inverse problem without consideration of modeling, as shown in figure 2.7. Also the approximated response surfaces can be evaluated by using statistical tools [25, 44-46]. The wireless detection using oscillating frequency changes has been proposed by Matsuzaki et al. in 2006 [47]. They also adopt the CFRPs themselves as a sensor, in addition, a ceramic oscillating circuit is attached to the structure. The resistance change results in a frequency change according to self-sensing of composites, thus the 22

40 delamination is detected. This approach avoids wired measurements; however, it requires the attached circuit. Figure 2.7 Response surface methodology [25] 2.5 Electromechanical modeling Many computational methods, for instance, macroscale modeling which is based on finite element analysis, microscale modeling, analytical modeling, and multiscale modeling, have been developed to simulate the mechanical damage in CFRPs. For damage detection, researchers pay more attention to the modeling of electric resistance response to composite damages. Coupled electrical and mechanical models were therefore developed to predict electromechanical behaviors of the CFRPs and to extract mechanical damages from electrical measurements Finite element modeling at the macroscale Finite element analysis (FEA) is one of the most popular numerical analysis tools in science and engineering. Since the diameter of fibers is small, the CFRP materials are assumed to be homogenous orthotropic. Along with experiments, Todoroki et al. applied 23

41 FEA to study the effect of measured orthotropic electric conductance on delamination [43]. They used measured orthotropic electric conductance for FEA with the ANSYS auto mesh generation system. Double nodes are created on the delamination crack surface, and then dispatched to represent electric current insulation. The artificial neural networks and response surfaces were adopted to solve this inverse problem of achieving delamination location and size. Figure 2.8(a) shows the delamination monitoring of beam type specimens at [0/90]s, in which the delamination lies between electrodes A and B. Figure 2.8(b) is electric voltage distribution results of three cases of the fiber volume fractions V f. The electric voltage change is observed at a large fiber volume fraction. (a) (b) Figure 2.8 Delamination configuration and voltage change distribution (a) Delamination monitoring at laminar of [0/90]s; and (b) Electric voltage change distribution due to [0/90]s delamination. [43] 24

42 The electrical resistance measurement has also been used for predicting the curing of CFRPs [48]. In this research, FEA evaluated the equivalent stress. Figure 2.9 shows the FEA model and the element mesh. The Von Mises criterion addressed the relationship between stress components and equivalent stress by converting all stress components on both fiber and matrix into von Mises stress. Figure 2.10 shows the change of electrical resistivity for single carbon fiber/epoxy composites with curing temperature during the curing process. The electrical resistivity change after curing increased with curing temperature increasing. Figure 2.9 FEA model and the element mesh [48] 25

43 Figure 2.10 Electrical resistivity change due to curing temperature [48] Figure 2.11 Beam-type FEA models: (a) without delamination; and (b) with delamination. [49] Resistance and voltage changes of a beam-type specimen with and without damage were simulated by FEA modeling [49]. The brief modeling schemes are shown in figure Their FEA results show that the four-probe method is only valid when the through- 26

44 thickness conductivity is big enough compared to the longitudinal conductivity shown in figure (a) (b) Figure 2.12 Comparison between theoretical predictions and experimental results: (a) surface resistance, and (b) oblique resistance between electrodes A2 and A4 [49] Analytical solutions for electrical-mechanical behavior An analytic electromechanical model for fiber damage evolution in CFRPs has been presented by Park et al. [50]. This model is based on the Global Load Sharing concept (48) and Weibull fiber strength distribution. The Global Load Sharing model assumes that the load lost by a fiber at some axial position, due to breakage, is transferred to all unbroken fibers in the cross-sectional plane. Their novel concept, electrical ineffective length, which is the length over which a broken fiber recovers current carrying capacity because of fiber contacts, was proposed. Thus the relationship between the mechanical damage and electrical resistance change was developed as follows. (2.1) 27

45 where ΔR is the change of electrical resistance in the composite, R 0 is the initial composite resistance, α is the proportionality constant, ε is the applied strain, L 0 is a reference length, L is the gage length of the tested specimen, E f is the tensile stiffness of the fiber, m and σ 0 are the Weibull shape and scale parameters. Xia et al. [52] developed an analytic model for the transverse electrical resistance of pristine and damaged unidirectional composites complementing earlier work on the longitudinal resistance. They found that the ratio of transverse to longitudinal resistance for undamaged materials provides a direct measure of the internal density of fiber fiber electrical contacts, a key material parameter in linking to the response of damaged materials. Under uniaxial loading with evolving fiber breakage, the normalized transverse resistance versus strain is predicted to have exactly the same form as that for the longitudinal resistance. Numerical studies show this agreement for uniform fiber fiber contact distributions but, for random contact distributions, the longitudinal resistance is larger than predicted while the transverse resistance is smaller; these differences are shown to arise as a result of the statistically-preferential breaking of longer fiber segments Electromechanical modeling at the microscale From the microscale, electric current flow in fibers determines the sensing and detectability of mechanical damage in composite materials. A composite ply consisting of more-or-less well-aligned carbon fibers exhibits a finite electrical resistance associated with the resistance of the carbon fibers. Under increasing applied load, the carbon fibers break at the locations of flaws in the fibers. Each fiber break interrupts the electric current flow through the broken fiber and increases the resistance of the composite. Since 28

46 electric current flows along the fibers, a coupled electro-mechanical model at the microscale is needed to describe how the electric current interacts with damages in the composites. Such micromechanics models, developed from fundamental damage mechanisms, can predict the relationships between the fiber damage and the electrical resistance. As discussed previously, the macroscale modeling is a large-scale calculation and does not have good ability to detect the local damage, while the microscale models focus on the local simulation [50]. According to the electrical properties of CFRPs, the electrical model has successfully been created. With the resistance change, the local damage of fibers or matrix is able to be detected directly [52]. Xia et al. [52] created coupled electrical and mechanical models to describe the electrical resistance change due to fiber breaks in CFRPs, shown in figure A numerical electrical resistor network model is coupled to the fiber breaks predicted by a shear-lag model. The shear-lag model is commonly used for estimating stress distributions, stress concentrations, and failure in fiber-reinforced composites. In this model, the fibers are regarded as one-dimensional spring elements. The matrix is treated as a material that transfers tensile loads among fibers via shear deformation only without carrying tensile loads. The stresses and fiber breaks predicted by the shear lag model are then input into an electrical resistance model which consists of a fiber resistor network due to fiber-fiber contact. The resistance of the resistors in the electrical network is adjusted based on the fiber stress and damage information from the mechanical model [54]. This coupled model offers a distinct relationship between the electrical ineffective length and the density of fiber contacts. Furthermore, the coupled model provides the description of local damage in both mechanical behavior and electrical response. Their 29

47 study shows that both longitudinal and transverse resistance changes are sensitive to composite damage. Additionally, this model has been developed to predict damage under cyclic loading [55]. The model has also been developed to study the resistance change from the mechanical damage in ceramic matrix composites [56, 57] Figure 2.13 Coupled electrical and mechanical models: (a) a real composite; (b) and (d) an electrical network of resistors; (c) and (e) a mechanical network of elastic elements with damage states.[52] To consider the random distribution of the fiber contacts, a Monte Carlo simulation was employed, in which the fiber fragmentation process combines to the concept of the electrical ineffective length [58]. A long conductive wire was considered as shown in figure 2.14, in which the dark lines stand for conductive carbon fiber and thin lines stand for contact between fibers. 30

48 (a) (b) Figure 2.14 Transformation of the parallel cell of resistors to a long conductive wire: (a) unit parallel cell with random contact points, and (b) transformation of the unit cell to a long conductive wire over which the electrical nodes are distributed randomly.[58] The resistance change was given by where l 0 is the initial length of conductive wire and l eff is the remaining effective conductive path at the strain level of ε. The simulation results are consistent with the experimental data, as shown in figure Figure 2.15 Resistance change as a function of strain: experiment and Monte Carlo simulation results for different fiber volume fraction V f. [58] 31

49 2.6 Signal analysis methods Signal analysis methods have been applied in material damage detection for many years [59-61]. The Fast Fourier Transform (FFT) is one of the most widely used signal analysis methods. It is a perfect tool to extract the frequency information. But when the signals have oscillation in the time domain, the FFT is not able to obtain the location where it occurs. This drawback can be overcome by time-frequency methods. There are currently a number of time-frequency methods, such as the short time Fourier transform (STFT), Wigner-Ville distribution (WVD) [62], Choi-Williams distribution (CWD) [63] and the continuous wavelet transform (CWT). Among these methods, CWT is the most favored because it has no cross-talk terms which are observed in WVD and CWD. Also window of variable width is employed in the CWT, which offers a more flexible way to observe simultaneously time and local spectral information than the STFT. Unlike Fourier analysis, which is limited to sinusoid-based feature, wavelet methods have various wavelet functions. According to different morphological signals, a suitable wavelet function can be selected. Discrete wavelet transforms (DWT) adopt the digital filtering techniques to obtain the time-frequency representation. It is widely used in signal compression and de-noising. In this section, the basic concept of wavelets will be presented, and followed by some applications of the wavelet transforms Continuous wavelet transforms and discrete wavelet transforms Wavelet transforms basically have two distinct classes [64, 65]: continuous wavelet transforms (CWT) and discrete wavelet transforms (DWT). The definition of CWT is: 32

50 (2.3) where (t) is the complex conjugate of the analyzing wavelet function (t) (mother wavelet), x(t) is a continuous time signal, a is the scaling parameter (corresponding to frequency), b is the shifting parameter (corresponding to time), and W(a,b) is a set of coefficients that is mapped by scaling parameter and shifting parameter. CWT is the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet. The basic process starts with selection of the mother wavelet and compared to a section at the beginning of the original signal. The mother wavelet determines the characteristics of the resulting CWT in order to produce an effective wavelet transform, an appropriate mother wavelet has to be chosen. Generally speaking, the good choice of mother wavelet is the one with a similar shape to the original signal. The closer the similarity is, the more significant the coefficients obtained. Then the wavelet is shifted to the right over the full domain of the analyzed signal. Repeated process is carried on for the entire signal. Then the wavelet is scaled/stretched for the same comparison as described above. Eventually, the coefficients are generated at the different scales for different sections of the original signal. The coefficients can be presented in a 3D plot. Scale corresponds to frequency. The relationship between them is defined as (2.4) where a is scale, f c is the center frequency of the wavelet, and is the sampling period. There are a number of basic functions being used as the mother wavelet in wavelet family, such as Haar, Daubechies, Biorthogonal, Morlet, and Mexican Hat 33

51 showed in figure The Haar wavelet is the simplest wavelet. Daubechies wavelets are the most popular used wavelets. Biorthogonal, Morlet, and Mexican Hat wavelets are symmetric in shape. These wavelets are chosen to be used in a particular application. (a) Haar (b) Daubechie (c) Biorthogonal (d) Morlet (e) Mexican Hat Figure 2.16 Wavelet family In figure 2.16(a), a series of sine wave is given. The CWT by using Mexican Hat wavelet shows the 3D time-frequency scalogram shown in figure 2.17(b). Figure 2.18(a) shows that the sine wave with a pulse at the middle of the period which leads to obvious spike from coefficients change at CWT time-frequency scalogram as shown in figure 2.18(b). 34

52 Figure 2.17 (a)pure sine wave; and (b)cwt time-frequency scalogram Figure 2.18 (a) Sine wave with a pulse; and (b)cwt time-frequency scalogram In order to demonstrate the proper selection of a mother wavelet based on morphological characterization, the signal with a mother wavelet in shape is calculated in the CWT by the same wavelet function. A Morlet wavelet is created in figure 2.19(a), 35

53 followed by the CWT time-scaling scalogram as shown in figure 2.19(b). This illustrates that the high frequency occurs at the middle of period where the original signal has the peak in amplitude. When a pulse occurs as shown in figure 2.20(a), a downwards spike is produced at the low scaling/ high frequency range. From these examples above, CWT express the efficiency and accuracy in time-frequency analysis. Figure 2.19 Morlet wavelet and CWT time-scaling scalogram 36

54 Figure 2.20 Morlet wavelet with a pulse and CWT time-scaling scalogram Discrete Wavelet Transform (DWT) is sampled CWT. In DWT, the signal is analyzed at different scales. The DWT is computed by a series of high pass and low pass filtering of the signal. Then the decomposition at each level is represented by approximated and detailed coefficients until the signal is fully decomposed. The process can be demonstrated in a tree structure as shown in figure These coefficients can be reduced or set to zero to emphasize the particular feature of the signal. The popular threshold method is usually adopted in this step. A proper value is chosen as the threshold (T), and all detailed coefficients are set to zero if their absolute values are less than T. In the end, reconstruction of the coefficients will be achieved. This is actually a signal denoising process. Figure 2.22 shows a noisy sine function. The mother wavelet db5 is applied to this function with 5 levels of decomposition. S is the original signal, followed by a 5, the approximated coefficients, and d 5, d 4,, d 1, the detailed coefficients at each level. After selecting a threshold of 0.85, the coefficients were constructed. In figure 2.23, 37

55 the black smooth curve is the de-noised signal after reconstruction, accompanied with the original signal. It is clearly a demonstration that the wavelet transform is an effective tool to signal de-noising. Figure 2.21 Discrete wavelet transform decomposition tree Figure 2.22 Noisy sine wave decomposition 38

56 Figure 2.23 Denoised signal and original signal Application of wavelet transform in composite materials The wavelet-based acoustic emission (AE) analysis technique has been presented to detect the fracture behavior of glass fiber reinforced composites(61). As wavelet transform feature characterization, the relationship between stress and stress intensity factor is approximated efficiently. The approach has been applied to detect the different modes of damage on glass/polyester composite materials [67]. AE signals were obtained and decomposed in many various levels. By using energy concept, the specific frequency ranges were successfully obtained. The wavelets method was introduced to ultrasonic non-destructive evaluation of composites material [68]. An interpretation procedure has been created by the selection of wavelet coefficients and a windowing process, which doesn t require signal reconstruction. Another application of wavelet analysis in composite materials was the initial crack detection using embedded piezoelectric 39

57 actuators/sensors. The wavelet transforms method was able to decompose the energy variation of structural vibration response to detect the initial crack [61]. 40

58 CHAPTER III METHODS OF ELECTRICAL AND THERMAL MEASUREMENT AND NOISE ELIMINATION 3.1 Experimental set-up In this section, the experimental set-up and procedure are presented in detail. The material preparation will be presented first, which is followed by the detailed description of the test procedure. Besides the electrical testing, the thermography test is also presented to show the temperature distribution under the electrical load Material preparation The specimen is carbon fiber reinforced epoxy polymer with a size of 2.83*2.83*0.02 in. Figure 3.1(a) shows the picture of the specimen. The surface of this CFRP sample was sanded first for the purpose of connecting carbon fibers with the electrodes well. Tiny holes were drilled at specific locations of the sheet to produce the appropriate electrodes. Silver Conductive Epoxy was deposited in all the holes with connecting wires as shown in figure 3.1(b). This silver conductive epoxy is a mixer of pure silver epoxy adhesive, which provides a good combination of the adhesive properties of epoxy with the electrical properties of the silver. Even though the resistance of the silver conductive epoxy is low, it still has a little influence on the resistance of CFRP, which will be discussed in detail in chapter V. 41

59 Figure 3.1 (a) CFRP sheet; (b) CFRP sheet with electrodes There were 24 electrodes being used in this experiment. Eight of them were used for electrical generation, which connects to the Analog Output (AO) channels as red dots in figure 3.2. The rest were connected to the Analog Input (AI) channels for the electrical signal acquisition, which are shown as blue dots in figure 3.2. All the electrodes are named with numbers shown as the figure 3.2, such as PT1, which is used throughout this dissertation Figure 3.2 Scheme of CFRP sheet with electrodes 42

60 3.1.2 A/D and D/A design National Instrument DAQCard-6062E is used in this experiment. This DAQCard consists of 16 Analog Input channels with 12-bits resolution and 500kS/s sample rate, and 2 Analog Output channels. The voltage range for all the channels are ±10V. The desktop connector NI SCB-68 was connected between the CFRP sheet and DAQCard. The experimental set-up schematic is demonstrated in figure 3.3. Figure 3.3 Experimental set-up schematic National Instrument data acquisition system, which is accompanied to LabVIEW (Laboratory Virtual Instrumentation Engineering Workbench), assembles both Analogto-Digital (A/D) and Digital-to-Analog (D/A) functions. Based on this application, the combined operating system including both A/D and D/A has been created in this research. This technique not only reduces the operating steps, but also increases the variety of input signal function. The input signals can be designed accordingly to fit further analysis. 43

61 Thus the experiment is more flexible to conduct. In this research, three types of signals were generated; they are constant DC, sinusoid signal, and wavelet waveform. Individual Labview graphic codes were created for the three signals as shown in figure 3.4. Figure 3.4 Experiment Labview code 44

62 AO channels serve as D/A convertor for generating the electrical signal to the CFRP sheet through the 8 input locations marked in red dots in figure 3.2. These 8 locations paired up into 2-12, 4-10, 6-16, and For instance, 2-12 is chosen to be the input location, and the electrical signal is applied between 2 and 12. All 16 locations marked in blue dots are connected to AI single ended channels, and the electrical response signal is collected. Since either point 2 or point 12 is grounded, making a switch of these two input locations provides another set of response signals. The same procedure is repeated for the other pairs of input locations; they are 4-10, 6-16, and There are 8 total sets of input combination. The purpose of multiple inputs is to locate the existing damage. The collected signals from 16 AI channels are varied because of different electrical input locations. The closer AI channels are to the input locations, the more sensitive response signals will be produced. Holes were introduced in the undamaged sheet in order to detect the damage. Four holes were drilled with diameters 1/8 in, 5/32 in, 3/16 in, and 1/4 in. When damage occurs, the corresponding signals are affected, which provides the information for estimating damage location Thermographic test Because of the thermal property of the CFRP, the electrical signal is capable of producing heat in the specimen. The thermal characteristic is observed for both undamaged case and damaged case. An IR camera placed on a stand captured images of the thermal response of the CFRP specimen as when the electrical source was applied. Figure 3.5 shows the test setup that was used for the analysis. 45

63 IR Camera Power Source Thermal Imaging Software Labview Software CFRP Sample Figure 3.5 Thermography test setup The infrared camera used in this experiment to record the thermal images was a MikroSpecRT thermal imaging camera with a resolution of 0.06 C at 30 C, a measurement accuracy of + 2 C of reading, and 320 x 240 dpi. The Camera was set to record 300 frames at 1 second per frame. The temperature range was set to -40 to 120 C, and the emissivity was set at The power supply was set at 1.5V. The obtained images present the temperature distribution. The images acquired during the thermal test were taken by another group in the Southern Illinois University. Four cases were studied in the thermographic test. Case A is that PT2 is grounded along with positive input at PT12. Case B is PT4 is grounded along with positive input at PT10. Case C is PT6 is grounded along with positive input at PT16. Case D is PT8 is grounded along with positive input at PT14. Temperature distribution pictures were shot for all cases. And then a hole with ¼ in diameter was drilled between PT17 and PT24. The same procedure was conducted for four cases. 46

64 3.1.4 Summary In this section, the experimental set-ups for both electrical and thermography test are introduced. The novel A/D & D/A system is created to conduct the generation of the electrical signal and acquisition of the electrical response signal simultaneously. This system only requires the DAQ card to conduct the measurement without any outside power supply. The operation procedure is easy to control. The signal generation functions offer a large range of customized signal designs, which leads to multiple options of further analysis. Three types of signal, DC, Sine wave, and wavelet signal were generated in the current study. The thermography test quickly provides temperature information without any contact measurement. The heating and cooling periods are able to be recorded. However, the A/D &D/A system has difficulty in timing control. The multiple input combinations are applied to obtain the different electrical potential distributions. The generation and acquisition functions in this measurement system share the same timing clock. Thus switching the input positions have to be done by hand. The thermography test requires very expensive equipment. It is hard to conduct the test if the thickness of the specimen is too large. 3.2 Noise reduction CFRPs usually serve in a harsh environment. The surrounding noise is a huge obstacle for the measuring process. There are many types of noises, such as general engine noise, unexpected electrical/magnetic field, acoustic, vibrations, and severe weather. Reducing the noise is one of the top priorities. In this section, an approach of de- 47

65 noising by using the wavelet transform is introduced for electrical measurement of CFRPs damage detection. The laboratory based experiment is carried out in this research. There is no significant noise to affect the experimental procedure. Considering the possible noise in a real environment, the random noise was forced to mix with actual results obtained in the experiment. This section demonstrates the comparison of noise reduction approaches for three types of signals, DC, Sine wave, and wavelet signals. The applied random noises have two different amplitudes, ±0.03V and ±0.5V, in order to discuss how the different denoising approaches work for the signals with various levels of noises. The denoising methods discussed in this section are data averaging for constant DC case, FFT for sine signal, and wavelet transforms for the wavelet signal. In section 3.2.1, a signal denoising comparison is presented for small noise (±0.03V) effect. Large noise (±0.5V) effect is given in section Small random noise effect The noise with equal or smaller amplitude than the original signal is regarded as a small noise in this research. For DC case, the original data is 0.03 V continuous signal. The random noise with the amplitude range of ±0.03 V is applied to influence the signal as shown in figure 3.6. The noise is reduced by averaging the data. The error of denoised data to original signal is 1%. Since the random noise is unpredictable, the average of the signal can produce a large error. The same noise is used in the sine signal, too. The original sine signal is 200 Hz with 0.03 V of peak amplitude as shown in figure 3.7(a). The frequency domain analysis is applied for filtering. First the FFT of the original signal 48

66 at the top one of figure 3.7(b) indicates the high amplitude at 200 Hz. When small amplitude of random noise, the FFT is able to filter out the noise and shows the significant amplitude at 200 Hz which is demonstrated in bottom plot of figure 3.7(b). The error is 1.3% at 200 Hz. Figure 3.6 Small noise effect in DC signal (a) 49

67 (b) Figure 3.7 (a) Original sine signal and sine signal with random noise (b) FFT of original sine signal and FFT of sine signal with random noise The original wavelet signal is db10 in shape with maximum amplitude 0.03V as shown in figure 3.8(a). The color graph in figure 3.8(a) indicates the coefficients of the CWT with scales of 1 to 500. The wavelet db10 is chosen for the transform, which is the same as the wavelet signal. In general the coefficients illustrate the similarity of the analyzing signal to the chosen wavelet for transform. So using the same wavelet is to obtain the high coefficient. High coefficients of the signal stand for the high similarity to the wavelet at the current scale. The wavelet signal with small random noise and its wavelet coefficients are given in figure 3.8(b). The small random noises result in fluctuation, but the high coefficients still can be observed. 50

68 (a) (b) Figure 3.8 (a) wavelet signal without noise and its CWT coefficients; (b) wavelet signal with small random noise and its CWT coefficients 51

69 As the region with high coefficients indicates the important information of the signal, 60 % of the maximum coefficients were selected as the standard section to avoid the noise affected coefficients at the other sections. The wavelet coefficients are collected at the same standard section for the signal with noise. During this procedure, all values outside of the standard section have been filtered out, and only those significant coefficients are left. The scalograms are given in the figure 3.9 for signals without and with random noise. These two scalograms present the percentage of the energy for each wavelet coefficient, which is also given the visualized denoising results. The error is found as 0.17%. It is hard to see the difference between these two scalograms since the random noise is too small to make tremendous influence. But this brings an idea that comparing the CWT coefficients is capable of observing the noise influence with few errors. (a) 52

70 (b) Figure 3.9 Scalogram of top 60% coefficients for wavelet signal (a) without noise; (b) with random noise Figure 3.10 DWT denoised signal for small random noise effect 53

71 The other wavelet transform, DWT, offers the denoising technique of decomposing data into many levels and reconstructing the data. DWT by db10 is applied in this case. The denoised signal is obtained after 6 levels of decomposition and signal reconstruction. As shown in figure 3.10, the signal with small random noise effect can be denoised and reverted to the similar shape to original signal Large random noise effect Figure 3.11 shows the DC signal with large random noise. The amplitude of original DC signal is 0.03V, which stands for the data obtained from one channel. The range of random noise is within ±0.5V. The signal becomes big fluctuated from the noise effect. By averaging the data, the error is found as 14%. It can be larger since the random noise effect is unpredictable. Figure 3.11 Large random noise effect at DC signal 54

72 The same noise is added to the sine signal. The original sine signal has 0.03 V in amplitude with 200 Hz in frequency. There are total 5000 samples. Figure 3.12 shows the part of the sine signal without and with the random noise. Frequency domain analysis method, FFT, is applied for filtering the noise in frequency domain. As shown in figure 3.13, the significant peak occurs at the 200 Hz for the original sine signal. However, in the FFT of the signal with large random noise, there appears no remarkable high amplitude at 200 Hz. A comparison has been made to find the error ratio, 16%, at 200 Hz for both without and with noise signals V is obtained for data without noise while V is for signal with noise. It is impossible to identify the frequency of original signal when the noise level is too high. Figure 3.12 Partial sine signal without/with random noise 55

73 Figure 3.13 FFT of sine signal with large random noise effect The same large random noise is applied to the wavelet form signal. Figure 3.14 indicates the huge influence of random noise to the original signal. It is really hard to tell the original shape of the signal. As the same procedure with small noise case, top 60% of CWT coefficients in magnitude at the standard section were selected and investigated. Comparing the coefficients in the standard section for both signals, the error is 1%, which is much less than the errors in the DC and FFT cases. The scalograms are presented in figure The differences between two graphs in figure 3.15 can be observed because of the large random noise effect. 56

74 Figure 3.14 The wavelet signal with large random noise (a) 57

75 (b) Figure 3.15 The scalogram for wavelet signal (a) without noise; (b) with noise DWT is also conducted in the large random noise case. The wavelet db10 as original wavelet signal was selected for DWT. After 6 levels of decomposition, the signal was reconstructed as shown in denoised signal of figure It is obviously big change in shape of the denoised signal to the original one. 58

76 Figure 3.16 DWT denoised signal for large random noise effect A demonstration with experimental data As discussion in the last two sections, the wavelet transform method provides a large amount of choices in the signal denoising. In this research, the wavelet signal in db10 shape was generated from a D/A system. The CWT is applied to demonstrate the analysis for both undamaged and damaged cases. The studied electrical data are obtained from two channels which connect to two electrodes where the hole exists in between, referring to electrode 17 and 24 in figure 3.2. The differential electrical potentials are calculated for the undamaged case and four damaged cases. The damaged cases refer to the CFRP specimens with 4 different diameters of a hole. Then the 5 sets of differential electrical potentials are carried on the CWT. The top 60% of CWT coefficients are partitioned. The scalograms for all cases are given in the figure It can be seen that the scalogram has changed in damaged cases compared to the undamaged case. To investigate the size of the damage, the errors of each damaged case to the undamaged 59

77 case are obtained and listed in table 3.1. The errors illustrate that the coefficients are influenced by different sizes of damage and can be adopted for damage detection. The error increases with damage enlarging. (a) (b) 60

78 (c) (d) 61

79 (e) Figure 3.17 Scalograms for cases of (a) undamged; (b) hole with 1/8 in diameter; (c) hole with 5/32 in diameter; (d) hole with 3/16 in diameter; (e) hole with 1/4 in diameter Table 3.1 Errors for 4 sizes of hole Diameters of hole 1/8 in 5/32 in 3/16 in 1/4 in Error 0.96% 1.19% 1.5% 2.39% Summary This section demonstrates the wavelet transform application in the noise reduction of the electrical measurement. When a small random noise affects the signal, both FFT and wavelet transforms can filter out the noise in either frequency or time-frequency domain. Even though, FFT and CWT are able to denoise the signal when noise is small enough, the DWT is recommended since the signal can be reconstructed. Thus, the denoised signal can offer more information to compare to the original signal. The CWT is recommended when the random noise is large. Although it can t revert to the original signal, the coefficient comparison offers valuable information to tell the damage 62

80 occurring. Signal-to-noise ratios (SNR) for these three types of signals are calculated and compared with errors from both small noise case and large noise case. Table 3.2 SNR and error for DC, sine wave, and wavelet signals Small Noise Large Noise SNR Error SNR Error DC % % Sine wave % % Wavelet % % In this research, the top 60% of the wavelet coefficients is taken as the threshold of forming the standard section. In table 3.3, different thresholds are demonstrated for parametric study. The threshold can be varied when the different wavelets are used to meet the requirement. Table 3.3 Errors for different thresholds Threshold 40% 50% 60% 70% 80% Small Noise 0.005% 0.09% 0.17% 0.3% 0.7% Large Noise 0.5% 0.8% 1% 2.6% 5.5% The wavelet transform has been applied for damage detection in CFRPs by using Lamb wave [69, 70], and first been adopted for the electrical signal measurement in this research. The signal generation function provides the wavelet form signals, which results 63

81 in more accurate analysis in further wavelet transform application. The morphology of the wavelet signal is coincident with the mother wavelet of the wavelet transform to get the large coefficients. One of the most important advantages of the wavelet application is the powerful denoising technique. Noise reduction by using the wavelet transforms is a distinguished accomplishment in the real industry. It is desirable that the wavelet method can be widely involved in damage detection in the CFRPs by electrical measurement. 64

82 CHAPTER IV COUPLED THERMAL-ELECTRICAL FEA MODELING OF CFRPS 4.1 Model creation Finite Element Analysis can simulate the electrical and thermal fields by dividing the structure into a grid of elements and creating a model of the real structure. Every element is simple in shape, either square or triangle. And these elements are connected by nodes. In the present research, the FEA model is created in commercial software ABAQUS 6.9. The element type is the thermal-electrical element since the CFRP has both thermal and electrical properties. The coupled thermal-electrical element model has been developed to analyze the composite sheets [71] and the effect of impact damage in composite structures [72]. The electrical potential distribution on the CFRP specimen can be simulated by FEA with applying a current load and boundary conditions. The objectives of the modeling section in this research are to simulate the electrical potential distribution and thermal distribution for undamaged and damaged CFRP. ABAQUS [73] offers a fully coupled thermal-electrical analysis to solve both electrical potential and temperature at the nodes simultaneously. The electric field is governed by Maxwell s equation as shown in equation

83 where V is control volume, S is the surface, J is the electrical current density, n is the outward normal to S, and r c is internal volumetric current source per unit volume. where E is the electrical field intensity, φ is the electrical potential, is the electrical conductivity matrix, θ is the temperature, f is predefined field variable, The governing equation of the finite element model is: The 3D geometry model is 2.83 in*2.83 in*0.02 in in size. Since the carbon fibers are braided with each other, the structure on the fiber plane is symmetric. So the FEA model is assumed to be homogeneous [74]. However, the electrical conductivity is affected by the fiber contacts. The electrical conductivities are measured according to the Ohm s law for circuit theory. The resistance, R, is defined by the length (L), the resistivity (ρ), and the cross sectional area (A) of the sample, as shown in equation

84 In the FEA model, the electrical conductivities are 3600/Ω m in x-axis, 1500/ Ω m in y-axis, and 3000/ Ω m in z-axis. The thermal conductivity is 12 W/m K, which is adjusted by referring to [75]. The specific heat is 1 J/K. The models of four damaged cases are created by modifying a hole with four diameters; they are 1/8 in, 5/32 in, 3/16 in, and 1/4 in. Eight input locations are precisely assigned along the edges. Concentrated current was applied on single nodes at input locations of each simulation. Because of the symmetric geometry of the model, only one set of modeling is demonstrated, which is the case with ground electrode PT2 and positive input electrode PT12 (refer to figure 3.2). Two tiny extrusions connected to the PT2 and PT12 to apply boundary condition and electrical load as shown in figure 4.1(a). The two boundary conditions are: One is the initial electrical potential at the surface of one extrusion next to PT2 shown in figure 4.1(b), and the other boundary condition is the room temperature 20 o C at the top and the bottom edges. Concentrated current was applied at four nodes of the extrusion next to PT12 as shown in figure 4.1(c). Mesh type is 8-node linear coupled thermalelectrical brick. The mesh size effect is investigated by applying different values as shown in figure 4.2. The result indicates that is better to choose for the mesh size in this research. Mesh screenshots for both undamaged and damaged models are shown in figure 4.3. The meshes become irregular shape near the extrusions and the damage location. 67

85 (a) (b) (c) Figure 4.1 (a) Extrusion regions for boundary condition and load; (b) Electrical ground; (c) Load region 68

86 Electrical Potential (V) 4.00E E E E E E E E E+00 Mesh size effect Electrode Location Number mesh mesh mesh Figure 4.2 Mesh size effect Figure 4.3 Mesh screenshot of 3-dimension model of undamaged/damaged CFRP The area of loading can affect the modeling result as well. Since the electrodes in the experiment may have defects, some uncertain factors have to be considered in the model creation. According to the different size of electrodes, the amount of loaded nodes may be varied in order to obtain optimal simulation results as close as possible to the experimental results. As shown in figure 4.4, when the amount of loading points changes 69

87 Electrical Potential (V) from 4 down to 2, even though the power supply remains the same, the electrical potential at the output electrodes drop. The reason is that large loading area results in large current on the surface and increases the electrical potentials at output electrodes. 4 points loading offers bigger region than 2 point loading. In this model, loads are applied at 4 points of the extrusion. Loading area effect 4.00E E E E E E E E E Electrode Location Number 4 points loading 2 points loading Figure 4.4 Loading area effect in FEA model The FEA model, which simplifies the complicated experimental procedure, is capable of conducting convenient studies without any troublesome effect that is accompanied to the experiment. The material manufacturing defect is one of the effects. Especially the carbon fibers contacts in the CFRPs directly influence the electrical conductivity and the thermal conductivity. Any loose contacts or gap between carbon fibers result in decreasing of both electrical and thermal conductivities. The modeling study can avoid this defect. The loading section is also possible to have a defect in the experiment, as the electrodes are handmade and hard to be perfectly attached to the 70

88 surface to conduct the loads. But this thermal-electrical FEA model provides full control on the loading sections. 4.2 Electrical potential distribution In this section, the electrical potential distribution is presented by the simulation of the thermal-electrical FEA model. This offers a direct visualization of the electrical potential changes resulting from the damage in the form of hole. Corresponding to the CFRP specimen for electrical potential experiment, the load applied in this model is equivalent to 0.1V at the input electrodes. The geometry of the model has two extrusions (0.04 in*0.02 in*0.04 in) at the input locations to weaken the electrodes effect. The undamaged model has 5,433 elements and 11,165 nodes. The electrical potential distribution of undamaged model is shown in figure 4.5. The electrical potential reaches the highest value at the loading point and gradually decreases. The close region shows more sensitive electrical response, especially between the two input locations, PT2 and PT12. Four models were created with holes in different diameter sizes. With increasing the diameter of holes, the electrical potentials indicate different patterns. The damaged model has 5,572 elements and 11,450 nodes. As shown in figure 4.6, the electrical potential distribution changes with the damage increasing around the damage region. 71

89 Figure 4.5 Electrical potential distribution of FEA for undamaged CFRP Figure 4.6 Electrical potential distribution of FEA for damaged CFRP 72

90 From the distributions for all cases shown in this section, the damage effects of the electrical potential on the CFRP as expected. The electrical current goes to an alternative route when a hole occurs, which leads to the changes of electrical potential around the hole. 4.3 Temperature distribution The coupled thermal-electrical FEA model is adopted for the thermography simulation. Using the same study as in the electrical potential distribution, the temperature distribution is simulated under the idealized situation. Thus damage leads to significant temperature change. The load applied in this model is equivalent to 1.5V at the input electrodes as in the experimental study. The geometry of the model has two different sizes of extrusions: one is 0.04 in*0.02 in*0.015 in at PT12 side and the other is 0.04 in*0.02 in*0.03 in at PT2 side. The reason is that the two electrodes in CFRP sample for thermal test are accidently different in size. The undamaged model has 5,424 elements and 11,146 nodes. The nodal temperature distribution is presented in figure 4.7. The temperature at PT2 is higher than that at PT12 because of the high resistance at PT2. And the far regions from the input locations illustrate low temperature as room temperature. The damaged model has 5,560 elements and 11,436 nodes. The nodal temperature of the damaged case is given in figure 4.8. It is clear to see the temperature decreases around the hole. 73

91 Figure 4.7 Nodal temperature distribution of FEA for undamaged CFRP Figure 4.8 Nodal temperature distribution of FEA for damaged CFRP 4.4 Summary This chapter introduces the numerical analysis by the 3D thermal-electrical FEA modeling. The visual results are shown in the predictive resolutions for both electrical distribution and temperature distribution. As a great tool for parametric study, the FEA modeling is capable to simulate various problems by adjusting the parameters. The proposed coupled thermal-electrical FEA models have provided the foundation of 74

92 electrical potential analysis in CFRPs. The CFRP sample is assumed to be modeled in the solid part without considering its braided structure. The assumption shows convincing results for modeling the CFRP with woven structure. By doing this, the procedure of building the model is simplified, and the calculation time is reduced as well. The external extrusions used in these models reduce the input electrodes effect as expected. This idea can be brought into any simulations involving electrical loading and measurement. After all, the 3D coupled thermal-electrical FEA modeling successfully simulates the electrical and thermal response to the damage in the CFRP. The numerical analysis can be easily conducted by using this type of model. 75

93 CHAPTER V RESULTS AND DISCUSSIONS OF EXPERIMENTAL AND NUMERICAL STUDIES 5.1 Experimental results In this section, only constant DC input signal is presented to conduct the thermalelectrical analysis, as the waveform signal is found difficulty to generate the constant heat for the thermal study. Two major aims of the experiments in this research are to locate the damage and estimate the size of the damage. Section presents the results of different electrical input configurations, and both electrical and thermal test results are given for damage allocation. The estimation of damage size is investigated in section Damage location Locating the damage is one of the biggest challenges in NDE. In CFRPs, fiber breakage leads to the electrical and thermal properties changes. The damage influences the electrical response and the temperature distribution. In this section, the electrical potential at all output electrodes on the CFRPs are discussed. The differential electrical potential of every input combination are able to evaluate the approximate location of the damage. The temperature changes because of the damage are also presented. The electrical potential distributions are various because of the different input configurations. The fibers are braided each other in the woven structure of CFRP as 76

94 discussed in chapter II. The input current route does not go only along the fibers, since the fiber contacts form the current bridging. The electrodes near the input electrodes are more sensitive to the electrical response. If the damage occurs on or close to the fibers between input electrodes, nearby electrical potentials exhibit big changes. The differential potentials of every neighborhood electrodes illustrate evident influence from the damage. Figure 5.1(a) is the scheme of the CFRP with all electrodes and the hole, in which all numbers stand for the name of electrodes, such as electrode 2 is PT2 and electrode 12 is PT12. Figure 5.1(b) is the schematic diagram of differential electrical potentials. All numbers stand for the name of the differential potentials. Arrows indicate the differential potential is obtained by subtracting the potential at the starting electrode to the potential at the ending electrode. These numbers in two schematic diagrams will be used as the identification of the following results. The equation of differential electrical potential is: where is differential electrical potential at Location A, Location A is one of the numbers in figure 5.1(b), and are the electrical potentials at Points a and b, and PT a and PT b are two of points in figure 5.1 (a). For example, the differential electrical potential at Location #1 is obtained by subtracting electrical potential at PT15 to that at PT1, which is. 77

95 Figure 5.1 (a) Schematic of electrodes; (b) Schematic of the differential electrical potential Figure 5.2 (a-h) shows the experimental results of all 8 cases, which features 8 combinations of input locations. The title 2GD means that PT2 is connected to ground with 0 volt electrical potential and PT12 is connected to the positive electrode of power supply. X-axes are the location number/ name of the differential electrical potential refer to figure 5.1(b). Y-axes are the changes of the differential electrical potential when damage occurs. It is obtained by subtract the differential potentials for undamaged case from that for the damaged cases. Four curves in each figure stand for the four diameter holes affecting the differential potential. The equation of differential potential change is given as: where is the differential potential change at the location A for undamaged case. 78

96 As stated above, the hole locates between PT17 and PT24. Figure 5.2 (a) and (e) are 2GD and 12GD, respectively. The hole lies on the route of these two input locations. Considering the fiber direction along the input locations, the results of 2GD and 12GD are relatively more sensitive to the damage than other cases. Thus the changes of differential potential are greater than other cases. Also the changes at Locations #3, 16, and 17 are higher than the ones at other locations. Thinking of detecting damage location inversely, comparisons of the differential potential changes are firstly carried on for 8 sets of input combinations, and then the damage location is narrowed down to the top half of the CFRP specimen near to PT2 and PT12. The differential potential changes are found higher at certain locations, which provide more precise information of locating the damage. The differential potential at Location #3 is calculated by potentials at PT24 and PT17. Similarly, Location #16 and #17 are determined by PT24 and PT15, and PT24 and PT20 respectively. So an estimation made in this case is that damage locates at the lefttop part of the specimen where the hole actually is. (a) 79

97 (b) (c) 80

98 (d) (e) 81

99 (f) (g) 82

100 (h) Figure 5.2 Changes of differential electrical potential for eight sets of input locations In this research, small scaled specimen is studied to prove the concept. To solve the problem with large scale and more complex structure, it will be valid to increase the input combinations and the output locations. The damage location estimation of this research is a quarter of field. It can be varied with the different electrodes patterns. Figure 5.3 (a) shows the thermal distribution of undamaged CFRP when electrical power is applied. The highest temperature is at the ground point PT2, appearing in red zone on the image. Line 1 starts from positive region PT12 to ground region. The thermal image of damaged case A is shown in figure 5.3(b). The temperature curves for Line 1 are shown in figure 5.3(c) and (d). Two input regions illustrate higher temperature gradient than the center regions for both undamaged and damaged cases. In figure 5.3(d), the temperature fluctuation displays at the 100 pixels in Line 1 which corresponds to the location where the hole occurs. 83

101 Temperature Temperature (a) (b) 40 Line 1 40 Line Number of Pixels in Line (c) Number of Pixels in Line (d) Figure 5.3 Case A thermography: (a) thermal image of undamaged case A; (b) thermal image of damaged case A; (c) temperature curve of line 1 in (a); (d) temperature curve of line 1 in (b) Figure 5.4 presents the comparison of case A. Temperature at two input electrodes are unstable. This can be seen in the figure 5.3 (a) and (b). The reason is that the process of making electrodes is not defects free when deploying the conductive epoxy. The electrodes may contain air or other impurities. Therefore, to identify the location of the damage, the subtraction is made by temperatures in middle section of Line 1 as presented 84

102 Temperature change (Celcius) Temperature (Celcius) in figure 5.4 (b). The peak of the curve stands for the big temperature drop at the edge of damage when there is a hole on the specimen Thermal distribution Case A no hole with hole Number of Pixels in Line 1 (a) Temperature change Case A Number of Pixels in Line 1 (b) Figure 5.4 Comparison of undamaged and damaged case A The similar studies have been done with the other cases as shown in figure 5.5, 5.6, and 5.7. The Line 1 is located at the same position for all cases. However the 85

103 Temperature change (Celcius) comparison of undamaged and damage cases doesn t illustrate any huge temperature change. So it is hard to detect damage if the load position is far away from the damage. (a) (b) Temperature change Case B Number of Pixels in Line 1 (c) Figure 5.5 Case B thermal images: (a) undamaged; (b) damaged; and (c) temperature change between (a) and (b) 86

104 Temperature change (Celcius) (a) (b) Temperature change Case C Number of Pixels in Line 1 (c) Figure 5.6 Case C thermal images: (a) undamaged; (b) damaged; and (c) temperature change between (a) and (b) 87

105 Temperature change (Celcius) (a) (b) 3.0 Temperature change Case D Number of Pixels in Line 1 (c) Figure 5.7 Case D thermal images: (a) undamaged; (b) damaged; and (c) temperature change between (a) and (b) By presenting the thermal images and temperature changes of all cases in figure 5.5, 5.6, and 5.7, the damage location can be identified in case A. So electrical loads with multiple patterns are necessary to solve the inverse problem of locating the damage. In this thermal study, the loading seems not enough to make the temperature change in all areas. Thus the visual recognition is hard to be conducted, which leads to a lack of information for solving the inverse problem. This research doesn t include thermal loading application, but it could be a good way to have thermography study by doing it. 88

106 5.1.2 Estimation of the damage size Besides the estimation of damage location, the size of the damage is another important issue to be studied. Comparing to the response surface method [25], which is a statistical analysis used for estimating damage size, the method presented here is easier to conduct. Figure 5.8 presents the ratio of the differential potential change for four diameter holes to the undamaged case. It only demonstrates the ratio for 11 locations of differential potential. The reason is that the differential potential on these 11 locations are determined by the pairs of electrodes along x-axis, which are in the same direction with the input electrodes, referring to the locations with horizontal arrows in figure 5.1 (b). Figure 5.8 shows the ratio of potential change increases with enlarging the diameter of the hole. When damage increases, more fibers are broken which leads to large potential change. The ratio of potential change is given as followed: 89

107 Figure 5.8 Ratio of potential change in experiment L PT2 D PT12 Figure 5.9 Side view of damaged specimen Simplifying the damaged specimen, the side view is given in figure 5.9, where D stands for the diameter of the hole and L is the original fiber length between two input electrodes PT2 and PT12. The dimension ratios of D to L are calculated and listed in table 5.1. The average ratios of potential change are also given for damaged cases with four diameter holes in table 5.1. Comparison of both ratios is carried on and presented in figure The average ratio of potential change can be regarded as the approximate dimension ratio of damage. Figure 5.11 presents the estimation limit based on the average ratio of potential change. Conservatively speaking, 20% is taken as the acceptable range 90

108 of estimation. The dimension ratios in this study are all satisfying. The estimation is more conservative for large damage size. Table 5.1 Ratios of dimension and potential change (EXP) D (Diameter of hole) R=D/L (L=2.83 in) MAX R (Maximum ratio of potential change) AR (Average ratio of potential change) 1/8 in 5/32 in 3/16 in 1/4 in % 10.00% 8.00% 6.00% 4.00% R Ave of Ratio 2.00% 0.00% Figure 5.10 Comparison of dimension ratio R and average ratio of potential change (EXP) 91

109 14.00% Damage size estimation (EXP) 12.00% 10.00% 10.7% 8.00% 7.74% 6.00% 5.65% 4.00% 3.80% 2.00% 0.00% Figure 5.11 Error limits of damage size estimation (EXP) Summary In the above sections, experimental results have been presented in details; two major targets of the damage detection have been achieved: locating the damage and the estimation of damage size. The differential electrical potential is easy to be calculated by the electrical potential obtained from the electrical measurement. The comparisons between all input combinations illustrate the different regions sensitiveness to the damage. The damage location can be directly recognized from the quantitative comparison. For the results of the thermal test, the temperature change at the specific locations can be used to identify the damage location. The estimation of the damage size is linearly correlated with the ratio of the potential change. 92

110 The electrical analysis offers easy and convincing method to locate the damage and estimate the damage size. But the thermal analysis is difficult to solve the inverse problem to locate the damage. Both methods are not visually detected. The thermography test is supposed to be visualized. Because the small area of electrical loading results in less heat generated at the region far away from the loading electrodes, the damage can only be seen in the image with high contrast. 5.2 FEA results FEA studies in this research including two major sections: electrical potential distribution and temperature distribution. As mentioned in previous chapter, the coupled thermal-electrical element was employed in this FEA model. Section presents the results of electrical potential analysis. The thermal distribution is discussed in section FEA results of electrical potential FEA is an effective tool to simulate the CFRP thermal-electrical characteristic. Many factors affect the results in the experimental study, while the FEA model is capable to provide a much more accurate resolution. Similar to the experimental results, the investigation of electrical potential change for FEA is given. The changes at Location #3, #14, #16, and #17 are larger than other locations as shown in figure These locations are closer to the damage than others. And the change increases as the severity of damage increase. For instance, the potential change is very little at location #3 when the diameter of the hole is 1/8 in, and become 93

111 about 8 times higher when the size of hole reaches 1/4 in of diameter. Location #3 is where the hole exists, which results in the significant change of electrical potential. Figure 5.12 Changes of differential electrical potential in FEA Ratio of potential change was calculated for the horizontal locations, which is similar to the analysis of experiment, as shown in figure Location #3 illustrates evident trend for four sizes of holes. However, location #8 and #9 show high ratio irregularly, especially for 1/4 inch diameter of hole. The potentials for both damaged and undamaged cases at these two locations are small because of the longer distance to the input location. So the value of ratio is affected by the small values of potential changes. Average ratio of potential change is calculated as presented in table 5.2. The comparison of average ratios of potential change and dimension ratio is given in figure To be a little bit conservative, 50% is taken as the acceptable range of the estimation. The error range of the estimation is presented in figure

112 Figure 5.13 Ratio of potential change in FEA Table 5.2 Ratios of dimension and potential change (FEA) D (in) Diameter of hole R=D/L (L=2.83 in) MAX R (Maximum Ratio of potential change) AR (Average ratio of potential change) 1/ / / /

113 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% R Ave of Ratio 2.00% 0.00% Figure 5.14 Comparison of dimension ratio R and average ratio of potential change (FEA) 25.00% Damage size estimation (FEA) 20.00% 15.00% 10.00% 5.00% 0.00% Figure 5.15 Error range of damage size estimation (FEA) FEA results of thermal distribution To explain the FEA results of thermal distribution, a schematic figure 5.16 is given. Figure 5.17 presents the temperature distribution on the Line 1 from positive input point to ground point. The temperature at ground electrode is slightly higher than the one on the positive input electrode. The reason is that CFRP specimen consists larger 96

114 electrode connecting to the ground than the one to the positive input source. To be more accurate in the modeling study, the extrusion on the side of the ground was thicker than the other side of extrusion. They are 0.03 in at PT2 and in at PT12 in x-axis. For the damaged case, the temperature dropping displays between 0.04 m and 0.05 m where the hole locates. The temperature around the hole is influenced, which leads to temperature gradient increasing correspondingly. The temperature at hole reduces to the room temperature. Ground Line 1 X-axis V Figure 5.16 Schematic of thermal study on Line 1 97

115 Temperature (Celcius) Temperature on Line 1 (FEA) undamaged FEA damaged FEA Distance in x-axis (m) Figure 5.17 Temperature distribution of FEA model on Line1 Figure 5.18 Schematic of FEA model on Line 2 98

116 Temperature (Celcius) Temperature on Line 2 (FEA) Distance in y-axix (m) damaged FEA undamaged FEA Figure 5.19 Temperature distribution of FEA model on Line 2 One more model was built to analyze the temperature distribution to locate the damage. The input locations were defined along y-axis as shown in figure The temperature on Line 2 is given in figure According to the simulation results, the damage can be detected by applying electrical loads at different directions. The damage occurs at the crossed section where the temperature curves have big changes at both directions Summary The FEA models successfully simulate the electrical response and the temperature change because of the damage. Similar to the experimental analysis, the trend of the differential electrical potential of the FEA results are found coincident to the experimental results. The linear relation is observed between the damage dimension ratio 99

117 and the average ratio of the potential change. The temperature distribution easily indicates the damage location on the CFRP model by analyzing the specific locations. The 3D coupled thermal-electrical FEA model successfully serves as the simulation tool in this research. Besides the visualized results discussed in chapter IV, the detailed analysis for electrical potential and the temperature provides the more convincing results. The extrusions used in these models reduced the electrode effect. It offers wide applications of the parametric study. 5.3 Correlation of experimental and numerical studies The verification of experimental and numerical analysis results is conducted in this section. The electrical analysis results are compared in section 5.3.1, and followed by the thermal analysis results in section Section presents the discussion of the differences between electrical and thermal analysis Electrical analysis results In experiment, the electrodes were made from the silver conductive epoxy which has its own electrical resistance. During the preparation process of CFRP specimen, the epoxy was deposited to make all electrodes. The voltage supply 0.1V was not 100% used in the CFRP because of the consuming at the input electrodes. Load in FEA model varies to make the equivalent supply. In this FEA study, the voltage at the input electrodes was adjusted to 0.07 V equivalently. A simple test was taken to measure the electrode resistance. As shown in figure 5.20, the resistance for the left sample (7 mm*2 mm*1 mm) and the right sample (3 mm*1 mm*1 mm) are 0.5 ohm and 0.1 ohm respectively. The electrodes made in this research were within this range. 100

118 Electrical Potential (V) Figure 5.20 Test for electrode effect The electrical potential collected in experiment at 16 channels is compared to the data in modeling analysis. Figure 5.21 (a) presents the results of undamaged (no hole) and figure 5.21(b, c, d, and e) presents the cases with four holes of different diameter sizes. The good matches can be noticed in the following figures no hole 2GD Number of electrode EXP FEA (a) 101