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TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE T |L_ m i = i i Li [—]I i MSU In An Affirmative ActlorVEquel Opportunlly Institution anM-ot The Use of High Frequency Dynamic Information for the Evaluation of Damage in Fiber Reinforced Composite Materials BY James Phillip Nokes A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Metallurgy, Mechanics and Materials Science 1991 ABSTRACT THE USE OF HIGH FREQUENCY DYNAMIC INFORMATION FOR THE EVALUATION OF DAMAGE IN FIBER REINFORCED COMPOSITES BY James P. Nokes This thesis presents details of a dynamic nondestructive inspection (NDI) technique with improved sensitivity to localized damage in fiber reinforced composite materials. The extent of the internal damage was determined using measured changes in the dynamic properties of the system (damping, dynamic stiffness and mode shape). A modal analysis system was developed incorporating both a Laser Doppler Vibrometer (LDV) and an Electronic Speckle Pattern Interferometer (ESPI) to obtain the response information at higher frequencies. The LDV system was used to measure the dynamic characteristics of composite beams over a frequency range extending to approximately 12Khz. ESPI provided a technique for acquiring whole field displacement maps of the various mode shapes. The potential of this system to detect delaminations in fiber reinforced epoxy beams was investigated. As part of the investigation the relationships between the dynamic characteristics and internal damage were examined. A modified data analysis approach was developed to analyze the extended dynamic information. The approach utilized the three dynamic parameters to form a set of linear functions that approximated the relationship between the loss factors and the resonant frequencies. The slopes of these curves were shown to be sensitive to localized damage in composite materials. Experimental verification of the system was done using delaminated cross-ply composites in a cantilever beam configuration. The results of these experiments showed that the best sensitivity to delamination damage is found from changes in the dynamic characteristics of torsional modes of vibration. TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . CHAPTER ONE INTRODUCTION . . . . . . . Overview of NDI techniques . . . . . Overview of Dynamic Testing Methods Organization of Thesis . . . . . . . CHAPTER TWO MODAL ANALYSIS AND INSPECTION . . Dynamic Test Methods . Response Measurement . Displacement . . Acceleration . . Velocity . . . . Excitation Methods . . Acoustic Pressure . . . Piezoelectric Element . Electromagnetic Field . Air Jet . . . . . . . Experimental Evaluation of Ex Po effeeeeeeeeeee 0000000000000 0 erteeeeeoeeeee Data Analysis . . . . Resonant Response . . Material Damping . . Mode Shape . . . . . . . . . Experimental Measurement System . System Excitation . . . . . . . . e e e e e e o e e e e e e e e e e 0 CHAPTER THREE DAMPING . . . . . Introduction . . . . . . Analytical Damping Models . Viscous Damping . . . . Hysteretic Damping . Coulomb Damping . . . Acoustic Damping . . Complex Modulus . . . Energy Formulation . Experimental Measurement of Damping . . Bandwidth of Half-Power Points Quality Factor . . . . . . . . iv nTechniques NONDESTRUCTIVE vi vii \DmHH 12 13 14 15 18 20 21 22 23 23 24 32 32 34 34 38 38 44 44 45 45 46 46 47 48 49 52 55 55 Logarithmic Decay . . . . . . . . . . . . . Curve Fitting . . . . . . . . . . . . . CHAPTER POUR EXPERIMENTAL PROCEDURE . Introduction . . . . . . . . . . Selection of Test Fixture . . . . Specimen Preparation . . . . . . Initial Adjustment of LDV system . Initial Adjustment of ESPI System Data Acquisition . . . . . . . . . Response Evaluation . . . . . . . Damage of the Test Specimen: . . . Validation of Dynamic System . . . Summary of Experimental Procedure CHAPTER FIVE RESULTS/DISCUSSION . . . Evaluation of Data . . . . . . . . . Modified Method of Data Analysis . Test Results . . . . . . . . . . . . Sensitivity Limitations for High Frequency Data Comparison of Different Data Analysis Techniques CHAPTER SIX CONCLUSIONS AND RECOMMENDATIONS . . . APPENDIX A LASER DOPPLER VIBROMETRY (LDV). . . . APPENDIX B ELECTRONIC SPECRLE PATTERN INTERPEROMETRY (ESPI). . . . . . . . . LIST OF REFERENCES . . . . . . . . . . . . . . . . . 57 57 62 62 62 70 71 73 74 75 75 76 78 80 80 81 94 101 106 117 122 128 133 LIST OP TABLES Tabulation of the Measured Resonance Frequencies Excited using Different Sources3o Comparison of the Loss Factors Measured using Different Sources . . . . . . . . 31 Relative Standard Deviation (%) . . . . 69 Comparison of Loss Factors Measured in Different Studies. . . . . . . . . . . . 77 Comparison of Bending Mode Slopes. . . . 99 Comparison of Mixed Mode Slopes . . . . 100 Comparison of Bending Loss Factor Slope (w/l - 0.32) . . . . . . . . . . . . . . 110 Comparison of Mixed Loss Factor Slopes (w/l = 0.32) . . . . . . . . . . . . . . 111 vi Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure bbé-b-h chub LIST OF FIGURES Comparison of Measured Dynamic Properties Using Accelerometer Data and a Noncontacting Velocity Transducer . . Beam Response to Low Frequency Acoustic Excitation. . . . . . . . . . . . . . . Beam Response to Mid-Range Acoustic EXCitation O O O O O O O O O O I O O O 0 Beam Response to High Frequency Acoustic EXCitatj-on O O O O O O O O O O O O O O 0 Beam Response to Low Frequency Electromagnetic Excitation. . . . . . . Beam Response to Mid-Range Electromagnetic Excitation. . . . . . . Beam Response to High Frequency Electromagnetic Excitation . . . . . . . Beam Response to Low Frequency Piezoelectric Excitation. . . . . . . . Beam Response to Mid-Range Piezoelectric Excitation. . . . . . . . . . . . . . . Beam Response to High Frequency Piezoelectric Excitation. . . . . . . . Representative Frequency Response Function for Cantilevered Beam. . . . . ESPI Image of Beam Vibrating at 3642 hz. . . . . . . . . . . . . . . . ESPI Image of Beam Vibrating at 6175 Hz. . . . . . . . . . . . . . . . Block Diagram of the LDV Dynamic Measurement System. . . . . . . . . . . Block Diagram of ESPI System. . . . . . Photograph of Dynamic Measurement System. . . . . . . . . . . . . . Photograph of ESPI System. . . . . . . Photograph of Electromagnetic Coil used to Drive Specimen. . . . . . . . . . . . Beam Vibrating in x-z Plane . . . . . . Beam Vibrating in x-z and y-z planes. . Bandwidth Method for the Determination of Loss Factors. . . . . . . . . . . . . Use of Real Response to Calculate the Quality Factor. . . . . . . . . . Photograph of 1C-3F Test Fixture. . Photograph of 2C-2F Test Fixture. . Photograph of ZSS-ZF Test Fixture. . Photograph of 4F Test Fixture. . . Comparison of the Loss Factors for the Different Test Fixtures. . . . . . . . Operating Envelope for Dantec LDV Unit . Impact Tester . . . . . . . . . . . . . vii 18 26 26 27 27 28 28 29 29 3O 33 36 37 39 4O 41 41 42 51 52 56 58 64 64 65 66 68 73 76 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure UlU'lUiU'IUIUI Ul U! 01 u N H \Dflflmmh 01 p O 5.11 5.12 5.13 5.14 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 .Torsional Mode Pattern. . . Expected Shift in Loss Factor Curve in Response to Localized Damage. . . . Measured Loss Factor Data for Glass-Epoxy Beam 0 O O O O O O O O O O O O O O 0 Linear Curve Fit of Damping and Frequency Data 0 O O O O O O 0 Bending Mode Pattern. . . Transitional Mode Pattern. Two Cell Torsional Mode. . Three Cell Torsional Mode. . . Relative Magnitude of the Loss Factors Associated with the Different Mode Shapes. . . . . . . . . . . Results of Combined Data Evaluation Technique. . . . . . . . . . . . . . . . SMC Dynamic Characterization. . . . . . Carbon/Epoxy Dynamic Characterization (90 degree ply orientation). . . . . . . Carbon/Epoxy Dynamic Characterization (0 degree ply orientation). . . . . . . Plot of Initial Loss Factor and Resonant Frequency Data for the Glass-Epoxy Beam (l/w =0.22). . . . . . . . . . . . . . . Comparison of I_CP1.22 and D_CP1.22 (10% Delamination) . . . . . . . . . . . Comparison of I_CP4.22 and D_CP4.22 (15% Delamination) . . . . . . . . . . . Comparison of I_CP2.22 and D_CP2.22 (25% Delamination) . . . . . . . . . . . Comparison of I _CP3. 22 and D_ CP3. 22 (50% Delamination) . . Description of Sensitivity Conditions for the Detection of Localized Damage Areas. Expected Loss Factor Response for Small Localized Damage Zones. . . . . . . . Percent Change in Bending Mode Loss Factors (l/w = 0.22).. . . . . . . . . Expected Behavior of Torsional Loss Factors with Localized Damage. . . . . . Percent Change in Torsional Mode Loss Factors (1/w = 0.22). . . . . . . . . . Percent Change in Resonant Frequencies for (l/w =0.22) . . . . . . . . . . . . Initial Loss Factor and Resonance Frequency Data for a Glass-Epoxy Beam (l/w =0.32). . . . . . . . . . . . . . . Comparison of I CP1. 32 to D_ CP1. 32 (15% Delamination) . . . . . . . . . . Comparison of I _CP2. 33 to D_ CP2. 22 (10% Delamination) . . . . . . . . . . . viii 83 84 85 86 87 88 88 89 89 91 92 92 93 95 97 98 98 99 102 103 104 105 105 106 108 108 109 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 5.28 5.29 5.30 Comparison of I _CP3. 33 to D_ CP3a. 33 (10% Delamination) . . . . . . . Comparison of I_ CP3. 33 to D_ CP3b. 33 (10% Delamination) . . . . . ESPI Image of’Mode Shape Before and.After Damage (8560 hz) . . . . . . . . . 2nd Bending Mode (700 Hz) . . Torsion Mode (3000 hz). . . . 6th Bending Mode (8000 hz). . Torsion Mode (9000 hz) . . . . Michelson Interferometer . . . The Effect of Pre-shifting the Reference O O O O O Beam on Direction Discrimination. . . ESPI System . . . . . . . . . . . . . ix 109 110 112 114 114 115 115 122 126 129 INTRODUCTION Advanced composite materials are becoming increasingly important for high volume industrial applications. The use of these specialized composite materials can provide elegant solutions to difficult engineering problems. Unfortunately the physical characteristics of composite materials present problems for the accurate detection and evaluation of internal flaws. These difficulties have created a need for NonDestructive Inspection (NDI) techniques optimized specifically for fiber reinforced materials. Overview of NDI techniques NDI techniques appropriate for these materials can be divided into two classes: 1) Spatial methods, where the actual physical attributes of the damage zone are measured; and 2) indirect methods, where damage is inferred from changes in global material properties. Both methods are useful for efficient testing of composite materials. Spatial methods provide a detailed geometric description of a damage zone. The specific information on the location and size of damage zones is necessary for the visualization of the internal flaws and as input for 1 2 analytical evaluation techniques. The recording of spatial information is often obtained at the expense of test complexity and speed. Among the more important spatial methods are: Ultrasound - Ultrasound is an important NDI method which is sensitive to a wide range of flaws found in composite materials. When used as a spatial technique, ultrasonic inspection utilizes variations in reflected ultrasonic pulses to map the physical extent of internal flaws (1,2,3). Radiography - Radiographic methods use directed high energy radiation to detect density changes within the material. These techniques have a limited sensitivity to internal damage in composite materials. In addition there are safety and cost issues that must be evaluated (4,5). Thermography - Thermography is a relatively new technology that creates a map of the external temperature of a body. By detecting discontinuities in either the temperature contours or the heat flow, internal damage can be detected. There'are two common modes of operation. The first utilizes remote heating of the test object and then evaluates the resulting thermal conduction. The second, known as SPATE (Stress Analysis by Thermal Emission), utilizes the thermoelastic effects in 3 materials to detect thermal gradients during cyclical loading. SPATE is a powerful technique for identifying regions of high stress. The sensitivity of thermography is extremely dependent on the material and the component thickness (6,7). Holography/Speckle Interferometry - - These techniques use the coherence properties of laser light to create fringes that indicate lines of constant surface displacement. For NDI applications, fringe discontinuities (surface displacement) can be used to indicate sub-surface flaws. Interferometric techniques have a number of advantages over other spatial techniques: (1) they are non-invasive; (2) a whole field image of the displacement is generated in close to real time; and, 3) they are sensitive to a wide array of loading techniques. The benefits of the interferometric techniques have traditionally been offset by severe vibration isolation requirements, extended film processing times and difficulties in the qualitative evaluation of the recorded images. Computer based image processing systems have provided a means for minimizing the impact of these experimental difficulties. In particular, Electronic Speckle Pattern Interferometry (ESPI) systems using Helium-Neon lasers provide a video - rate measurement of out-of-plane displacements with a 4 sensitivity of better then 0.5 microns. The ‘development of more efficient image processing and evaluation algorithms is an area of active research (8,9,10,11). These spatial techniques provide a wide range of measurement tools for locating internal flaws within a composite specimen. Indirect NDI techniques utilize the measured changes in specific material characteristics to indicate damage. The indirect methods are typically faster and better adapted to field work than spatial techniques. The widespread application of the indirect approach to NDI has been moderated by the complexities of evaluating internal damage from global properties. The availability of inexpensive and powerful computer systems has generated renewed interest in the development of the indirect NDI techniques described below. Acoustic Emission - Acoustic Emission (AE) testing evaluates the material condition by measuring characteristics of the internal stress waves released during loading. AE has not seen widespread industrial use because of difficulties in analyzing the recorded information. A notable exception is in the manufacture of fiberglass storage tanks, where an acoustic emission inspection standard has been established (12,13). Acoustic-Ultrasonics This is a variation of the acoustic emission technique. Instead of using an applied load to release the stress waves, an ultrasonic signal is input into the system to simulate a stress wave. This pseudo-stress wave can then be evaluated in a manner similar to AE. Acoustic- Ultrasonics has good potential for the NDI of composites and is the subject of a number of research efforts (14,15). Dynamic/Vibration Technique This method utilizes changes in the dynamic characteristics, (frequency,damping and mode shape), of a system to detect damage. The dynamic method has been used to detect a wide variety of flaws typical with composite materials. In its current state of development it has a limited ability to detect small localized damage areas. By integrating combinations of indirect and spatial methods, a multi-stage NDI program can be developed that is optimized for the detection of specific damage conditions. The first stage of an optimized NDI program would consist of a screening procedure to quickly detect flaws. Based on the results of the first stage, a decision would be made to either continue through the manufacturing process or to direct the part to additional inspection processes. The second stage would use the more time-consuming spatial NDI 6 techniques to provide the information required to accurately locate and define the flaw. A preliminary examination of dynamic NDI procedures shows them to be nonintrusive, capable of fast data acquisition, and sensitive to a wide range of flaw types. These characteristics would make dynamic NDI an excellent candidate for an industrial screening method. In this thesis a detailed investigation into some of the dynamic NDI methods was conducted. The goal was to address performance limitations that are found in current dynamic NDI test systems. The most serious of these limitations is a lack of sensitivity to localized damage zones such as delaminations. Researchers have taken different approaches to solving the analytical and experimental difficulties of dynamic testing. Much of their work has focused on measuring changes in either the system damping or dynamic stiffness and correlating the change to internal damage. In the following paragraphs selected milestones in the development of dynamic NDI will be discussed. Overview of Dynamic Testing Methods In the late 1970's Cawley (16) developed a finite element model that utilized measured changes in the dynamic stiffness to locate regions of damage in a two dimensional structure. Variations of the dynamic stiffness were .indicated by the frequency shift in a resonant mode between 7 the initial and damaged condition. In later experiments, Cawley and Theodorakopoulos (17) used Cawley's earlier work as the basis of a membrane resonance method. The membrane resonance technique attempts to identify the dynamic characteristics of the damage zone. This method has intriguing possibilities for NDI of composite materials. Tracey and Padroen (18) used both finite element models and experimental techniques to examine the damage-induced changes in the resonant frequencies of a composite plate. An important result of their study was to show an increase in the sensitivity of the resonant frequency to internal damage if the damage was located in regions of high shear strain. Other researchers have evaluated changes in the internal damping of a structure to indicate damage. In one study, Gibson and Suarez (19) compared the changes in the of system damping and natural frequencies due to matrix cracking. Gibson and Suarez showed that the system loss factor was more sensitive then the resonant frequency to distributed damage. Lee et a1 (20) used artificial delaminations in composite beams to investigate the sensitivity of the dynamic method to localized damage. The projected area of the damage in the beams ranged from 10 to A 50 percent of the total beam area. Lee used an eddy current probe and an impulse hammer to measure the dynamic response «of the beams. Lee found that the change in the loss factor ranged from 1.5 - 40 percent over a frequency range 8 extending to approximately 1500 hz. For the smaller damage areas, the changes in the loss factor measurement did not provide adequate sensitivity to the delaminations. In his conclusions Lee postulated that the sensitivity to localized damage could be increased by evaluating the dynamic information at higher frequency modes. The potential of higher frequency information to enhance the sensitivity of the dynamic method was reported in other studies as well (21). To date the experimental and analytical techniques needed to verify the potential of high frequency dynamic testing have not been developed. As a result, the data reported in the damping studies mentioned above was limited to the first three normal vibration modes. Research Goals This thesis will describe a new approach to enhancing the sensitivity of dynamic testing techniques to small scale damage. Building on the published literature, the major focus of this research is the development of a dynamic test system capable of measuring dynamic properties over an extended frequency range. After development of the experimental system, the increase in sensitivity due to extension of the testing frequency can be investigated. In order to use the higher frequency information properly, an investigation into the techniques for analyzing the dynamic 'information will be presented. Other aspects of dynamic NDI 9 that will be investigated are the relationships between the dynamic properties and damage. Organization of Thesis Chapter Two Modal Analysis and Nondestructive Inspection. Chapter Three This chapter details the performance objectives of the proposed dynamic analysis system. Critical aspects of this system are examined for applicability to an NDI system. This evaluation includes the performance tradeoffs between different vibration transducers and an experimental evaluation of different methods for system excitation. In addition, the use of Electronic Speckle Pattern Interferometry (ESPI) for the measurement of mode shapes at critical resonant frequencies is described. Damping. This chapter presents an overview of the experimental and analytical background necessary for the appropriate evaluation of the modal data. Chapter Four Chapter Five Chapter six Appendix A. 10 Experimental Procedure. Chapter four details the experimental methodology used in this study. After discussing the experimental procedures a comparison is be made between data measured using the optimized NDI system developed in this study and modal NDI systems utilized by other researchers. Results/Discussion. This chapter has a compilation of the measured dynamic properties for both undamaged and damaged Glass/Epoxy materials. These results are then be used to support a discussion and the associated conclusions regarding the different aspects of dynamic NDI using higher mode information. Conclusions. The conclusions drawn from this study will be formally presented in this chapter. It also includes potential extensions of the research. Details the operating theory of the Laser Doppler Interferometer. 11 Appendix B. Presents a detailed description of the theory utilized by the Electronic Speckle Pattern Interferometer (ESPI) system. CHAPTER TIO MODAL ANALYSIS AND NONDESTRUCTIVE INSPECTION Dynamic Test Methods Current methods for the measurement and evaluation of dynamic properties in complex structures can be traced to the work done by Kennedy and Panecu in the 1940’s (22). The primary difference is the wide array of dedicated hardware and software currently available for the acquisition and analysis of dynamic information. These tools allow complex test programs to be designed and the data to be analyzed much more efficiently. Much of this technology can be directly applied to an NDI testing program. The difference between a modal analysis system and a modal NDI system is an ability to evaluate the relationship between the dynamic characteristics of a structure and its internal damage. In this chapter the aspects of data acquisition and evaluation appropriate to dynamic NDI applications will be examined. In Chapter One the use of high frequency information was proposed as a method for enhancing the sensitivity of dynamic NDI to localized damage. Development of the extended frequency range requires the parameters affecting the performance of a dynamic NDI system be investigated. These parameters include aspects of both data acquisition 12 13 and analysis such as: 1) the need to minimize air damping by maintaining small amplitude vibrations; 2) inherent limitations in the performance characteristics of the transducers used to measure high-frequency small-amplitude vibrations; and 3) the difficulties involved in analytically describing complex mode shapes and their relationships to the system damping. This problem becomes more difficult when the effect of damage must be included in the model. These specific performance considerations are encompassed by three functions that define the operating characteristics of a modal measurement system, namely: (1) system excitation; (2) response measurement; and, (3) data evaluation. For high frequency NDI applications, each of these functions must be optimized by the appropriate selection of experimental components for use in the modal system. In following sections, different approaches to optimizing these modal functions for high frequency measurements will be investigated. Response Measurement Three variables of motion can be utilized for the measurement of a system’s dynamic response, namely displacement, velocity and acceleration. By measuring the time history of any one of these values, a Frequency Response Function (FRF) for the system can be calculated. It is important to note that for linear systems the \ 14 information in an FRF is independent of the variable of motion used. This independence allows the motion transducer to be selected solely on the basis of performance. Three classes of transducers were evaluated for their potential to perform in a high frequency NDI environment. Displacement Measurement The proximity probe is one of the most commonly used vibration transducers for dynamic NDI. These noncontacting devices utilize changes in an eddy current field to indicate relative displacements between the probe and a metallic target. For the measurement of quasi-static displacements it is possible to obtain sensitivities on the order of .001 mm. Additionally, proximity probes generate a linear output over small ranges of motion. When measuring dynamic motions these transducers have two major drawbacks. First, they require small offsets (.1mm) between the target and the probe to obtain maximum sensitivity. This air gap places limitations on the configuration of the test setup by restricting the placement of the probe relative to the target. Secondly, displacement measurements produce an inherently smaller output signal at higher frequencies than either the velocity or acceleration .techniques for comparable excitation levels. This reduced output is a direct consequence of frequency biasing in the measurement of harmonic vibrations (23). The effect of the lower output is to make the position of the probe in 15 relation to the specimen critical. To maximize the high frequency response the probe must be positioned at the point of maximum amplitude of a particular resonant frequency. Locating the points of maximum displacement becomes more difficult as the complexity of the mode shapes increase. Frequency biasing occurs in the differentiation of harmonic functions (sine, cosine). For example if the target displacement is given by x = Asin(wt) then the velocity is v= chos(wt) (a bias of w) and the acceleration is given by a = -Aw=(sinwt) (a bias of wz). A consequence of the bias is that for a given frequency and excitation level the velocity and acceleration components provide an inherently larger signal than the measured displacement. To compensate for the lack of bias at higher frequencies, proximity probes require a larger vibration amplitude to maintain a usable signal to noise ratio. Obtaining the larger displacements requires an increase in the excitation energy, which is not always possible. Even with additional excitation energy, the performance characteristics of the proximity probe are the limiting factor in a displacement-based experimental modal system. Acceleration Piezoelectric accelerometers provide another method for measuring the dynamic response of a system. For many applications these devices offer the best combination of performance and ease of use. There is a wide variety of 16 accelerometers to meet different experimental requirements. For NDI applications miniature accelerometers (< 59) are available that are both rugged and simple to use. The low mass minimizes the effect of transducer inertia on the measurement. Other performance characteristics of the accelerometer are determined by the frequency range to be measured and the interface between the specimen and the transducer. The frequency performance of accelerometers is dependant on the mounting technique used. The highest frequency response requires permanent mounting, ie. stud fixtures. Permanent attachment of the transducer is unacceptable for NDI applications. An alternative is to use adhesive mounting techniques which are easier to apply but limit the high frequency response. In this study, a PCB 306A low mass accelerometer was used to examine the application of accelerometers to high frequency low amplitude vibrations. The specifications for the PCB 306A indicate that frequency can be measured to within five percent of the true value at 10Khz using adhesive mounting techniques (24). In several experiments the effects of accelerometer mass and the adhesive interface on the measured dynamic properties of the system were examined. The results indicated that even the small mass of the transducer creates a significant shift in the measured resonance frequencies. The magnitude of the shift is a function of the l7 accelerometer position, the mode shape being excited and the total mass of the system. This artificial shift is a problem for two reasons. First, for low mass systems the transducer-induced shift is of the same magnitude as could be expected in a damaged specimen. Secondly the addition of mass to the system simulates the effect of damage on the resonant frequencies by decreasing the resonant frequencies. The artificial frequency shift could effectively mask the damage induced changes in the resonance frequencies. Damping measurements obtained using accelerometers are adversely affected by the characteristics of the adhesive interface between the transducer and the specimen. Accelerometer data tends to generate estimates of system damping that are higher then damping measured using noncontacting transducers (25). This transducer-dependent damping mimics the expected change in response due to internal damage and can mask indications of localized damage. Figure 2.1 shows an experimental verification of variations found between contacting and non contacting modal transducers comparison of the measured dynamic properties using an accelerometer and a non-contacting velocity transducer. Finally, accelerometers suffer from a low-signal-to- noise ratio when measuring high frequency low amplitude vibrations. The benefits of a” frequency biasing do not compensate for a decreased sensitivity found in low mass accelerometers. 18 005— O Acclerorneter Data I LDV Data 004T . § 0.03 — 0 O l O 3 I I g 0.02 ~ I 0' .- 000 1 1 L A J 0 2000 4000 6000 8000 10000 Frequency (Hz) Figure 2.1 Comparison of Measured Dynamic Properties Using Accelerometer Data and a Noncontacting Velocity Transducer Velocity Measurement The phenomenon associated with the interference of coherent light has generated a number of specialized techniques for measuring small changes in surface displacement. These techniques include: 1) Moire Interferometry, 2) Shearography, 3) Holography, and 4) Laser Doppler Vibrometry. Of these techniques, Laser Doppler Vibrometry (LDV) allows for the direct measurement of target velocity. LDV relates the instantaneous velocity at a point on a target to the doppler frequency shift in light scattered from that point. The basic relationship that defines LDV is given by: 19 szov (2.1) where Af Doppler Shift Frequency of Light Target Velocity Wavelength of Laser Beam V A A complete derivation and explanation of the principles used in LDV are presented in appendix A. LDV has several unique advantages over the more traditional transducers discussed previously. It is capable of measuring frequencies from 0 Hz to more than 100 Khz. This wide spectrum allows an LDV system to record the dynamic response at the higher frequencies desired in this study. LDV is a true non-invasive technique allowing stand off distances between the target and the LDV unit of up to 10 meters. This remote capability provides a large degree of flexibility in the physical layout of the test system. LDV is sensitive to small vibration amplitudes (< 10E-7 m), minimizing the excitation energy required during the testing. 4 The sensitivity of LDV to high-frequency low-amplitude vibrations is also a limitation to the application of the technique. In LDV measurements it can become difficult to isolate the effect of environmental vibrations unrelated to the excitation signal. The measurement of low frequencies can require an optical bench to provide environmental 20 isolation. The quality of the LDV output is also affected by the method used to excite the system. Best results are obtained by excitation techniques that provide a smooth transfer of energy into the specimen. The comparison of the different response measurement transducers shows the LDV system to be the best suited for high frequency NDI. The capabilities and limitations of LDV were used in the selection of the type of modal excitation. Optimum LDV measurements are obtained when the magnitude of both the in-plane motion and the rotation of the target are small (26). This amplitude restriction and the desire to utilize the non-invasive nature of LDV had a significant impact on the selection of the modal excitation technique. Excitation Methods Standard methods, such as the impulse hammer and massive electromagnetic shakers, do not match the performance capabilities of the LDV method. These excitation techniques lack the remote capabilities, input control, or frequency range to best utilize LDV. Alternative excitation techniques were investigated to generate modal drivers appropriate for use with an LDV-based system. The performance of the potential excitation methods (or drivers) was evaluated using a number of parameters, including the ability to vary the input energy over a wide spectral range and control the frequency characteristics of 21 the input signal, ie. random noise, periodic chirp or burst chirp. Other desired capabilities were minimum intrusion into the dynamics of the system and the ability to predict the frequency and energy characteristics of the input signal. These parameters were used to select four general types of drivers for further examination. (1) Acoustic Pressure (2) Piezoelectric (3) Electromagnetic driver (4) Air jet. Each of these drivers can perform best for particular excitation requirements. The following discussion will show which measurement situations accentuate the positive attributes of each driver. In addition, experimental results will be presented that highlight the performance of selected devices over different frequency ranges. Acoustic Pressure Acoustic pressure waves can be used as a noncontacting method to introduce a dynamic load into a system. Pressure waves are typically the result of acoustic energy radiating from a device such as a loudspeaker. Three characteristics of acoustic drivers tend to limit their application to quantitative NDI studies. The first is the restricted useful frequency range. Acoustic excitation of large 22 structures is most effective at relatively low frequencies. As the frequency is increased it becomes more difficult to introduce sufficient energy into the test object to excite the resonant modes. The usable frequency span is decreased further as the mass or the internal damping of the test object increases. The second characteristic is a complex distribution of the applied acoustic power over the specimen surface. The power distribution is a function of the type of source used to generate the signal, the position of the source relative to the specimen and the excitation frequency. Finally there is the lack of relative phase information between the excitation signal and the system response (27). Not having phase data limits evaluation of the frequency response to the detection of resonant frequencies. Piezoelectric Element The characteristics of bimetal Piezoelectric Elements (PZE) to change volume in response to an applied voltage provides another method of modal excitation. These devices have well-defined dynamic characteristics over frequencies ranging from approximately 1000 hz to 30 Khz. The PZE is self-contained and can be mounted to a specimen using accelerometer adhesives. The obvious drawback to PZE's is that, as a contacting method, it has an influence on the natural response of the test object. When selecting the PZE for a particular application it must be determined whether 23 the impact of the additional mass on the system dynamics outweighs the advantages obtained from use of the PZE. An additional consideration is the effect of variations in the applied force over wide frequency spans. The primary advantage of the PZE is its ability to generate a larger excitation energy than the other methods discussed here. Electromagnetic Field An alternative to the PZE is an electromagnetic excitation scheme that has a smaller impact on the dynamics of the system. For this excitation technique, a small permanent magnet was attached to the specimen using an adhesive wax. An induction coil subjected to an alternating current was then brought into close proximity to the magnet. The force that is generated between the magnet and the inductor is proportional to the current in the coil (28). This technique generates a controlled high frequency excitation signal that can be effectively used to drive the target. This method has a minimal impact on the dynamic response of the test specimen but it does not have the available excitation energy of the PZE. Air Jet The last technique investigated utilized the impact of‘ an air jet directed onto a target to excite resonant frequencies. This type of excitation provides a pink noise 24 source with a wide frequency spectrum and a random force distribution (29). Air jets have been used on low mass systems with great success at excitation frequencies of more then 100 khz (30). The difficulties with this technique stem from the random character of the output which make it difficult to predict the frequency and energy characteristics of the input signal. Because the time history of the air jet energy is unavailable, the response is obtained in the form of a spectral power plot. The spectral power does not provide the information on system damping required by this study. While it is feasible to develop air jet excitation into an appropriate NDI technique, it would require a substantial investment in equipment and time. Because the three other techniques provide a good range of capabilities that at least match the air jet, it was not included in the remainder of the comparison. Experimental Evaluation of Excitation Techniques An experimental study was done to compare the frequency response generated in an aluminum cantilever beam by the different excitation sources. The beam dimensions were: Length = 165 mm Width = 50 mm Thickness 3.4 mm The frequency response of the beam was measured using a Dantec LDV system with the output directed to a 25 Hewlett-Packard 3562A Dynamic Signal Analyzer. The details of the experimental apparatus are provided later in this chapter. Three frequency ranges were examined that covered the different parts of the spectrum. The low frequency test was centered on the fundamental bending mode (104 Hz). The frequency peak in the midrange was at approximately 5100 Hz. The high range for this test was a natural frequency centered at approximately 10 Khz. For each excitation technique 10 averages were taken of the response spectrum. The magnitude of the frequency response curve is dependent on positions of the driver and where the LDV laser strikes the target. By adjusting the position of either device the frequency response of different vibration modes can be accentuated. For the purposes of this study the location of the LDV and driver were kept fixed for each frequency range. The frequency responses generated by the different drivers were then compared. The three methods tested, Acoustic, PZE and Electromagnetic, each provided a clear indication of the resonant frequencies as shown in Figures 2.2 - 2.11. The PZE was the weakest in exciting the fundamental bending mode (98 hz), as was expected since it has poor low frequency characteristics. The added mass of the contacting drivers shifted the resonant frequency less then four percent relative to the acoustic method. The measured resonant frequencies are shown in Table 2.1. A more important result is the ability to produce consistent 26 Powgm apnea. aoAvg excavip Una-r . O. O /Dtv Figure 2.2 Beam Response to Low Frequency Acoustic Excitation. _garlgfi .PKCA ADAvg oxavlp Uri-514' 4.o_' /Dtv a. __ $9- _— -°°-° ‘ g 1 L 1 1 n. 1 _L 34—?Efij ——. -a— H; .2 Figure 2.3 Beam Response to Mid-Range Acoustic Excitation. 27 —=81”5T- -P‘ca‘ 1°AV8 O~Ov1|=a Urns? 4. o *— /DA V __ 1— d. _ 233‘ _QC. 0 1 l J 1 _1 i 1 ‘ E"EE"‘ **= ara.ih§91fl=‘ Figure 2.4 Beam Response to High Frequency Acoustic Excitation. -=..‘."ST- .P‘c" laflvu oxavzp Una-r ..¢:_‘ /Da.v _- ru- L_ or 4 )— a. a ,4- .1 1 l ‘3 L, I Figure 2.5 Beam Response to Low Frequency Electromagnetic Excitation. 28 _PEYB$_ OPEC: aaAv. axavap Una-P Ova 4.:3T' /D I. v __ )-— ei- 35" 0—- --80. a -H=71fi#§fififiiL‘ ’ ' .3- ' ‘_4 Lit:=fihi$in$ Figure 2.6 Beam Response to Mid-Range Electromagnetic Excitation. _Psys .P‘cz AOAV- Oxavlp Uni? ‘. a /Dl.v d. v :”3., It —7.. O 7. 7 J 1. 1_ rdL 1 1 1 t=u1 I Figure 2.7 Beam Response to High Frequency Electromagnetic Excitation 29 —ps'ng- .PCCA ADAV. Oxcvlp Una? ..0 o’Dtv __ d. r- 35" F- -1°‘ L'E'EZ—il‘i"? ‘ J J A- 4 ' + “(g—31,1 Figure 2.8 Beam Response to Low Frequency Piezoelectric Excitation. _‘ays; .P‘GA taAv. O~Ov1p UHAF 4.:3" /Dtv __ L. d. _— CHB" 1 —.-. G [:572fifltafiicfi‘ ‘ J 6%.. l ' jfisrarétamififl Figure 2.9 Beam Response to Mid-Range Piezoelectric Excitation. 30 _ngsfi. all-cc: aoAv. axes/1p Univ- 4. D L- /Dtv __ ‘- CH" ‘ -7a.a . J 1 1 1 1 J 1 Q H H- 85. Figure 2.10 Beam Response to High Frequency Piezoelectric Excitation. results by maintaining the relative position of the mass on the test piece. In Table 2.2 the measured values for different loss factors were calculated from the response of the beam to the PZE and electromagnetic drivers. Table 2.1 Tabulation of the Measured Resonance Frequencies Excited using Different Sources. Acoustic Piezoelectric Electromagnetic 99 98.3 98.1 1750 1757 1741 11700 11730 11782 31 Table 2.2 Comparison of the Loss Factors Measured using Different Sources Piezoelectric Electromagnetic 0.0018 0.0022 0.0050 0.0020 0.0260 0.0279 The results showed a general progression in the output quality of the different drivers. The acoustic method provides very good wide spectrum excitation. For low mass and low damping systems it provides an excellent noncontacting method for the determination of the resonance frequencies.- The PZE provides comprehensive data over the mid to high ranges. While the PZE is a contacting method, testing has shown that the effect of the mass on the dynamic response can be kept to a small percentage of the non-contacting response. The electromagnetic driver has a better range than acoustic excitation. It also has less impact on the system dynamics than the PZE. Both the PZE and electromagnetic drivers can provide a good solution to the requirements of modal excitation. Because it is less invasive than the PZE and provides more precise control of the input energy, the electromagnetic driver was selected as the primary excitation method for measurement of the natural frequency and loss factors. .32 Data Analysis The third aspect of the dynamic testing program is the implementation of an appropriate data analysis strategy. The time response history is converted into a Frequency Response Function (FRF) using a Fourier Transform process. The result is a curve that contains information on system damping and stiffness. .A typical FRF for a continuous system is shown in Figure 2.11. In addition to the frequency response function, the utilization of high frequency information requires a detailed measurement of the mode shapes corresponding to the particular resonant frequency. The FRF and mode shape provide complementary information for the determination of any damage within the material. In the following sections an overview of how the each of the different dynamic properties can be used to evaluate damage is presented. Resonant Response The resonant frequencies represent points in the frequency domain where the specimen geometry, boundary conditions and material properties interact with the external excitation to generate peaks in the system response. The detection of the resonant or natural frequencies is a relatively simple measurement using the FFT process. In general the dynamic stiffness decreases with increasing damage. The loss of dynamic stiffness translates to a decrease in the resonant frequencies of the system. 33 Fgeg _RESP 10Avg 07.0v1p um.c 400 /Div Mag p.— D'DLJWI 1 M Y 0 Hz BEAM RESPONSE+ 10k Figure 2.11 Representative Frequency Response Function for Cantilevered Beam. 34 Chapter One outlined some results obtained from investigations that used changes in the natural frequency to detect damage. These studies showed that the low natural frequencies, which tend to be characterized by bending modes, are not sensitive to localized internal damage. The ability of higher mode resonant frequencies to detect internal damage will be analyzed in Chapter 5. Material Damping In Chapter One the enhanced sensitivity of damping to many types of internal damage was discussed. The use of experimental damping data in NDI applications requires a discussion of the theory and practice of material damping. The next chapter will provide an overview of both the analytical and experimental characteristics of system loss mechanisms. Mode Shape The complete description of the dynamic state of a structure requires displacement or mode shape information in addition to the damping and stiffness parameters. As will be shown in Chapter Five, the displacement information is particularly valuable at higher frequencies and as the modal densities increase. There are a limited number of methods available for the experimental measurement of complex mode shapes. 35 One technique that is useful for simple mode shapes is to compare the peak magnitude of the FRF measured at different locations along the beam (31). The peak magnitudes can be used to produce a pointwise map of the modal displacement. Generating the response map becomes more difficult at higher frequencies since the number of measurements required to adequately describe the displacement increases. A qualitative method that has been used relies on the displacement of sand to indicate nodal lines. The specimen is dusted with a thin layer of sand and the system excitation is applied (32). As the beam resonates the sand will tend to move from the areas of maximum displacement to the nodal lines where the displacement is a minimum. An alternative to both the pointwise method and sand is Electronic Speckle Pattern Interferometry (ESPI). ESPI is a differential measurement technique that uses the changes in phase generated by the out-of-plane motion of the target to create a set of interferometric fringes. These fringes indicate lines of constant displacement relative to an initial position (33). ESPI is a noncontacting technique with a sensitivity of approximately 1/2 the wavelength of the coherent light source. As the name implies, ESPI uses image processing technology and software to produce and evaluate the displacement fringes. By eliminating the requirement for photographic processing, the displacement images are produced at video rates (1/30 sec). A detailed 36 explanation of the operating principles of ESPI can be found in Appendix B. ESPI systems can be operated in either a quasi-static or a dynamic mode depending on user requirements. In the dynamic mode the computer generates a set of time average fringes which indicate the nodal lines and the locations of peak displacements in a standing wave. The photographs in Figures 2.12 and 2.13 are computer generated images of a composite beam vibrating at 3.6 and 6.1 Khz respectively. In examining ESPI data, it is important to note that the low intensity fringes are lines of constant average displacement. In this format the fringes do not provide 1' ' e . 0.. :e I . . , l :.',"h¥m . '3 '4 I Odal Zoe s" I" 7'.“ Figure 2.12 ESPI Image of Beam Vibrating at 3642 hz. 37 Figure 2.13 ESPI Image of Beam Vibrating at 6175 Hz. information on the relative phases of the different modal displacement peaks. The lines of zero displacement or nodal lines are indicated by the broad high intensity zones identified in Figures 2.12 and 2.13. The nodal regions act as boundaries to separate the specimen into areas that are in motion. For the remainder of this study, these oscillating regions bounded by nodal zones will be referred to as vibrational cells. The concept of vibrational cells will aid in the discussions of the dynamic behavior of specimens at extended frequency ranges. 38 Experimental Measurement System The details of the system developed in the previous chapters are shown below. Figures 2.14 and 2.15 provide a schematic lay out of the LDV dynamic measurement system and the ESPI measurement system. Photographs of the experimental setup are shown in Figures 2.16 and 2.17. The Dynamic Testing and ESPI systems were composed of the following sub-systems: Dantec Laser Doppler Vibrometer: Dantec 55N20 Doppler Frequency Tracker Dantec 55N10 Frequency Shifter Hewlett Packard 3562A Dynamic Signal Analyzer MB Dynamics amplifier Tectronix 550 oscilloscope Zenith Data systems 286 computer Ealing Electronic Speckle Pattern Interferometer: Queensgate AX100 Phase Controller Data Translation Image Processing Board DT2851 (8 bit) Data Translation Coprocessing Board DT2858 (16 bit) Ohito CCD Camera Hewlett Packard ES-Vectra Computer (80286/87 12.5Mhz) Con Rac Hi Resolution Output Monitor System Excitation A ZOO-winding copper wire induction coil was used to apply the excitation force to the permanent magnet attached to the specimen. A photograph of the driver assembly is 39 4; . Spectrum Analyzer W7 5 i I: Figure 2.14 ‘ 4H .9 . 81 'g G “-c - 1 8% a 1, 8 O 0 VJ 2 O m 3 O Block Diagram of the LDV Dynamic Measurement System. IZZZIJ 80286/87 Computer System 40 Minor Lam » Piezoelectric Phase Shifter q 5' Spatial filmfl Spatial filter -——| OCDCamen HP 80286187 Computer System Figure 2.15 Block Diagram of ESPI System. 41 Figure 2.16 Photograph of Dynamic Measurement System. Figure 2.17 Photograph of ESPI System. 42 provided in Figure 2.18. The coil was driven by the signal generated in the HP spectrum analyzer and amplified using an MB signal amplifier. The spectrum analyzer had the capability to produce a variety of signal types (ie. random, chirp, periodic ) providing flexibility in the test procedure. A periodic chirp signal was selected for the Figure 2.18 Photograph of Electromagnetic Coil used to Drive Specimen. test protocol. The periodic chirp has the advantage of providing an efficient energy input into the system while minimizing the leakage errors inherent in digital signal analysis (34). In this chapter the components of a high frequency dynamic NDI system were gathered. The system was built 43 around the performance characteristics of LDV and uses both a PZE and an electromagnetic driver to excite the target specimen. To complement the capabilities of the LDV, an ESPI system was used to visualize the mode shapes that correspond to a particular FRF. In the following chapters this system will be used to examine the dynamic characteristics of advanced composite materials with internal delaminations. CHAPTER THREE DAMPING Introduction Damping is a general term used to describe the complex array of energy loss mechanisms that can dissipate kinetic energy within a system. The damping mechanisms aSsociated with material properties provide the most information in dynamic NDI applications. Material damping includes point relaxation effects as well as heat flow and other relaxational mechanisms (35). Internal flaws tend to enhance these mechanisms, increasing the effective damping of the material. This change in the material damping can then be used as an indication of internal damage. The utilization of damping information in NDI studies requires a careful evaluation of both the analytical and experimental aspects of the damping measurement. In this chapter different analytical and experimental techniques for the evaluation of damping will be discussed. The analytical models used to examine damping will be examined first. 44 45 Analytical Damping Models Viscous Damping Viscous damping is a fundamental damping concept that is based on an assumption that energy loss is velocity dependent (36). The classic differential equation of motion for a damped spring mass system is defined using a viscous damping coefficient (C), Ma 4» Cv + Kx = Fcos(wt) (3-1) The viscous damping quantity can be modeled using a Kelvin Voight element that provides a dissipating force proportional to the velocity of the mass. From the equation of motion with a harmonic deformation given by x = Xsin(wt) then the viscous energy dissipated in 1 vibration cycle is found to be, D = 1(0sz ' (3.2) An important aspect of this formulation is the dependence of the energy dissipation on the frequency of vibration (w) and the square of the maximum displacement amplitude (X5. Viscous damping is often used to represent the lumped value of the different loss mechanisms acting on the system. In this form it is known as an equivalent viscous damping coefficient. In this study, the low amplitude vibrations and the small velocities of the targets minimize the true viscous contribution to the measured 46 damping value. However an equivalent viscous coefficient can still be found using curve fitting techniques (37). Hysteretic Damping Hysteretic Damping or material damping is a model of the energy losses related to the deformation of a material (38). In its simplest form it can be modeled using a spring and dashpot element attached in series. Mathematically, material damping can be described by equation 3.3. _ h F - -kx-(_5)v (3-3) where h is a hysteretic damping constant. For hysteretic damping the energy dissipated in a vibration cycle is given by equation 3.4, D,I = 1th2 (3-4) note that hysteretic damping is independent of frequency. Coulomb Damping Coulomb damping is also known as simple friction and is a function not of velocity but of relative motions. It can be the dominate damping mechanism at joints and fixture interfaces (39). For NDI applications it is important to minimize this particular component of damping by using a rigid test fixture to limit the relative motion between the fixture and the test specimen. 47 Acoustic Damping Acoustic damping (air damping) occurs when the specimen acts as an acoustic radiator and loses energy in the form of emitted sound waves. Acoustic damping is a complex function of specimen geometry and material properties. The complex nature of acoustic damping has resisted the development of exact analytical solutions to the problem. Without an analytical solution, air damping is defined by the lower frequency bound of significant acoustic energy losses (coincident frequency). Below this frequency air damping is insignificant, and above this frequency it is an additional component to the overall damping. The general equation for the coincident frequency fi:of a plate is given by equation 3.5. f = ‘EEJJV (1'22” (3.5) ‘ u E where Co is the velocity of sound, h is the thickness of the plate, and E,», and-n are Stiffness,density and poissons ratio for the material. There is little that can be done to reduce air damping without resorting to drastic measures such as measuring the loss factors in a vacuum chamber. Fortunately, acoustic damping tends to be a more important loss mechanism for lightly damped metallic structures. 48 Complex Modulus For linear viscoelastic materials a complex modulus approach is often used to estimate the material properties. Using this model, material properties E°,G',v', . . are determined from the following equations where E',G',v' are the various material storage modula and iniis the appropriate loss factor; .E':E’(1+inE) (3-5) G‘=G’(i+in6) (3.7) r'=v’(l+inJ (3.8) The behavior of the complex modulus model can provide additional insights into the damping characteristics of fiber reinforced plastic materials. Sun et al,(50) showed that by treating the fiber and matrix as linear viscoelastic materials and using Classical Lamination Theory (CLT) the global expressions of: A = Complex Extensional Stiffness B' = Complex Coupled Stiffness If = Complex Flexural Stiffness can be found as, 49 A',=A,(1+in,) (3.9) B',=B,(1+1n,) (3.10) D',=D,(1+in,) (3.11) where nfi.are the directional components of the material damping. The complex modulus model predicts the material damping to be inversely related to stiffness. Energy Formulation Another model based on the CLT description of thin composite plates was derived by Lin et al (51). They examined the material damping in a fiber reinforced composite using strain energy (U) defined in terms of the constitutive relations; U=%[67[D]edv (3.12) where [D] is the mean elasticity matrix. To solve for the strain energy contained in each mode shape an assumption of small displacements is made and the strain variation in the beam is described using the following relations: a, = x,z (3-13) 8, a x22 7”? “1(1 ‘ 4Z’lh’) 7.: "5(1 - WW) 70‘ Kg: 50 n are the curvatures of the plate and are independent of 2. Through use of these equations in combination with the finite element technique, the strain energy for the individual modes can be found. Using this formulation, Lin separated the energy dissipation for each element 6(AU) into 5 components, the principle directions (AUUAUZ) , shear dissipation (AUG) ,the transverse shear (AU,) and rotary inertia (AU,) effects in the plate. The combined damping in each mode was then represented by equation 3.14, 6 (AU) =6 (A0,) +6 (AUz) +6 (A0,) +6 (A05) +6 (AU6) (3 . 14) A specific damping capacity ¢ was defined by equation 3.15. ¢=_ (3.15) The specific damping capacity is related to the loss factor by equation 3.16, n=i¢ (3.16) The individual components of the specific damping capacity were represented using the specific damping coefficient in equation 3.17, 6 (A0,) =% (¢,e,o,) 6z (3 . 17) where i = 1,2,4,5,6. This equation shows the measured loss factor to be directly related to the mode shape. For pure bending modes at, and x6, are zero. This can be seen in the ESPI image shown in 51 Figure 3.1. This photograph of a beam vibrating at 4000 hz shows deflections only in the x-z plane. Based on this model the material damping contribution would be the sum of loss factors corresponding to, AU = AU, +AU, + AU, (3.1:) When the curvature of the mode becomes more complex, as shown in Figure 3.2, the number of components of material damping that contribute to the measured system loss factor increases. The damping models presented above provide some background into the types of mechanisms that impact the evaluation of damping measurements in NDI applications. Figure 3.1 Beam Vibrating in x-z Plane 52 Figure 3.2 Beam Vibrating in x-z and y-z planes. Experimental Measurement of Damping In general, the experimentally determined values of damping are combinations of different physical mechanisms. The measured damping value can be represented as a sum of individual loss mechanisms (52), 77mm: 2’71 = 71mm.) + flfim “Im- The specific damping mechanisms can be functions of frequency, temperature,and loading. As a result it is difficult to quantify the contribution of any particular loss mechanism to the overall damping value. The sum of the individual loss mechanisms are evaluated as equivalent viscous loss factors. The loss factor is a standard measure of damping that is defined to be the energy loss per radian (D/2n) divided by the peak potential or strain energy (U), 53 D g— 3.1, 17 21m ‘ ’ Except for a limited number of special cases the measured damping is not a specific material property (53). The distinction between measured damping and material damping must be made if the experimental loss factors are to be used appropriately. The convention is to use the term structural damping to indicate an equivalent damping factor. Except where noted the loss factors used in this study are structural damping values. The experimental determination of the structural damping in composite materials presents a number of technical difficulties that must be examined to insure accurate NDI procedures. Typical experimental difficulties include: 1) Damping values are inferred from the dynamic characteristics of a specimen ie. resonant response; 2) The relative contributions of different loss mechanisms are difficult to determine uniquely, 3) Careful control of the test fixture is required to minimize the effect of external factors on the measured loss factors, and 4) Reinforced composite materials have complex material properties. These difficulties will be examined in the following sections. The majority of the techniques used to measure loss factors are based on the dynamic response of the specimen under test. In a dynamic test the response of a specimen is monitored while it is excited over a frequency range that 54 includes a resonance frequency. The time response is then transformed using a Fast Fourier technique into the frequency domain resulting in the classic frequency response plot. In the neighborhood of the natural frequency the shape of the response function is determined by the amount of damping within the system. A system loss factor n can then be calculated using the characteristics of the response curve. The use of resonant techniques has ramifications on the potential sensitivity of the dynamic method to damage. The loss factors obtained using this technique provide damping information for a particular resonant frequency, which is determined by the inter-relationships between material stiffness, mode shape and boundary conditions. An important aspect of this study was to examine these relationships and their impact on the sensitivity of the dynamic NDI method. The use of the resonance method is restricted by the modal density over a given frequency range. For systems that have closely spaced natural frequencies, the individual contribution of each peak to the overall response curve must be determined using curve fitting routines to extract the poles and zeros of the response (54). The following sections will examine specific techniques for utilizing the resonant information to obtain the loss factors. 55 Bandwidth of Half-Power Points This technique is also referred to as the peak-amplitude method. It is related to the original Kennedy-Pancu (55) method and is the most commonly used method for evaluating structural damping. The loss factor is defined to be, ._AI ”-7; (3.20) where Af is the bandwidth at 3 dB below the resonant peak, and fo is defined to be the frequency at the maximum response amplitude as shown in Figure 3.3. This definition for loss factor works well for simple structures where the modes are well spaced; however, it is susceptible to errors as the frequency spacing between resonant peaks become smaller. Problems are also encountered with composite materials at higher frequencies where the response curve varies significantly from the ideal Single Degree of Freedom (SDoF) oscillator. Quality Factor A Quality Factor can be defined using the real components of the mobility response to be, 56 FREE! _BESP 10Avg 0Z0vlp UniF 0v2 18.0 2. 0" (fl —f2) _ (fl f2) /Div 1] " f 0 3db dB __ r- f0 2'91! 111 111.th 3. 68633k Hz BEAM RESPONSE 3. 84258k Figure 3.3 Bandwidth Method for the Determination of Loss Factors. 57 8 0= 1,: 2 1 (3.21) [7.]- where f. corresponds to the frequency with a maximum response amplitude at a frequency greater than the resonant frequency, and f,, is the frequency that corresponds to the minimum response amplitude at frequencies below the resonant frequency (56) as shown in Figure 3.4. The quality factor is related to the loss factor by, Q = lln (3.22) If the phase information is available to generate the real and imaginary responses, then equation 3.21 offers better precision than the simple 3dB bandwidth method (equation 3.20). Logarithmic Decay The measurement of vibration decay is one of the few ways that damping can be measured directly. The reduction in vibration amplitude can be directly related to material damping (57). Unfortunately the measurement of amplitude decay is typically limited to low frequency vibrations and simple bending mode shapes. Curve Fitting The dynamic characteristics of a system can also be determined from the Laplace transform that best describes 58 F SE8 jESP 10Avg 0X0v1 p Un i F .. f 2 2.0 f_€l +1_ fb fa /Div 17 _ - —— - Q f 2 a 1 r— f— '- b Real __ r- -8.CJ I J I I L I l i L I 1.25313k Hz BEAM RESPONSE 1.35313k Figure 3.4 Use of Real Response to Calculate the Quality Factor. 59 the response curve. A least squares routine in combination with the coherence function provides a consistent procedure for determining loss factors. An SDoF response curve can be described by the classic equation of motion in the form Ma+Cv+Mx = F(t) (3.22) The Laplace transform of this equation is given by $[Ma+Cv+Kx] = EB{F(t)} (3.23) or, M{s=X(s)—sx(0)-v(0)}+C{sX(s)-x(0)}+K{X(s)} (3.24) where (s) is the Laplace== $912333: l:‘B(y8)forcing the initial velocity v(0) and displacement x(0) to be identically zero the equation 3.24 reduces to, [11 X(s) = T! (3.25) F(S) 2 C K [5 +892] where, sz+§s+§ (3.26) is the characteristic equation of the system. The roots of this equation are given by equation 3.27 =.. C + C 2-x (3.27) Sm '2Tr’h'2‘1'r) T1. The roots of equation 3.27 can be reduced to estimates of system characteristics by using the definition of critical damping Cc and the damping ratio t given in equations 3.28 and 3.29 respectively. 60 (3.28) N 3.9 II ‘—-—1 anal ==C' I E: (3.29) The roots of the characteristic equation can now be written as, saws/@710. «a-w for an underdamped systems. When I <1, the characteristic equation of the underdamped system can be further simplified to, s=-('w':F.iwd (3.31) At the roots of equation 3.31 the loss factor can be written as, n = 2f/w, (3.32) where ( is the viscous damping ratio and.au is the damped resonant frequency. In this study the equivalent viscous damping coefficient for each specimen was calculated using a curve fitting routine contained within the Hewlett-Packard spectrum analyzer. These values were then evaluated using ideas contained in both the complex modulus and energy method predictions for damping behavior in composite materials. The basic functions required for a high frequency modal NDI system have now been determined. In Chapters Four and 61 Five this approach was used to examine delaminations in glass/epoxy composite specimens. CHAPTER FOUR EXPERIMENTAL PROCEDURE Introduction In the previous chapters, different aspects of dynamic testing were combined into a system optimized for the detection of high-frequency low-amplitude vibrations. In this chapter a test protocol appropriate for the optimized measurement system is developed. The protocol includes: 1) the evaluation of appropriate test fixtures, 2) the initial adjustment of system instrumentation, and 3) the experimental procedure used for data acquisition. Selection of Test Fixture Four test fixtures were evaluated for their effects on the performance of the optimized dynamic measurement system. These fixtures were defined by the constraints they imposed on the free edges of the specimen. The boundary conditions investigated include: 1) 1 clamped edge - 3 free edges (1C-3F); 2) 2 clamped edges - 2 free edges (2C-2F); 3) 2 edges simply supported - 2 edges free (ZSS-ZF); and, 4) 4 pseudo free edges (4F). In evaluating the different fixtures, three characteristics were compared: 1) the influence of the 62 63 fixture on the measured damping, 2) fixture contribution to variance in the damping values, and 3) fixture compatibility with interferometric techniques. The (1C-3F) condition (cantilevered) has become a standard experimental fixture. To generate the cantilever one edge of the specimen was mounted into a vice (Figure 4.1) using a clamping force of approximately 20 Newtons. The (2C-2F) condition was generated using a fixture that clamps the opposing ends of the specimen between steel blocks (Figure 4.2). In both the cantilever and 2C-2F loading frames the clamping force was kept at a constant value. The application of a constant clamping force reduces the experimental variation in damping measurements between different test sequences (59). A characteristic of the 2C-2F boundary condition is the shifting of resonant modes to higher frequencies when compared with the cantilevered beam. The frequency shifting impacts the dynamic analysis by requiring an increase in the excitation energy for comparable mode shapes. The 2SS-2F was generated by resting the test specimen on a pair of knife edges mounted to an adjustable fixture (Figure 4.3). With this fixture the relative positions of the knife edges and the specimen could be easily changed. The interface between the specimen and the ZSS-ZF fixture was much less constrained than in either the cantilever or the 2C-2F. The use of simple supports increased the array of mode shapes that were excited at the lower frequencies. 64 Figure 4.1 Photograph of 1C-3F Test Fixture. Figure 4.2 Photograph of 2C-2F Test Fixture. 65 Figure 4.3 Photograph of 2SS-2F Test Fixture. A limitation to the ZSS-ZF condition was the use of gravity to maintain specimen contact with the supports. The orientation of the specimen was restricted to planes perpendicular to the gravitational field, limiting the use of the ESPI system for recording the mode shapes of interest. An additional limitation to the application of the 28S-2F condition was the dependence of the measured damping response on the position of the supports. The damping associated with the ZSS-ZF fixture is a minimum when the supports and the resonant nodal lines coincide. The damping value will be a maximum when the supports are positioned at the antinodes. The variation in the fixture damping is difficult to predict for mixed mode vibrations 66 where the supports and the vibrating specimen interact in a complex manner. Pseudo 4F conditions were created by the suspension of the specimen from thin threads located along the specimen nodal lines (60) as shown in Figure 4.4. An important advantage to this technique is that the fixture contribution to the loss factor is minimized. The 4F fixture does require locating the support threads on the predicted nodal lines. Like the ZSS-ZF fixture, the excitation of mixed modes can generate variations in the measured damping. The general use of the 4F fixture was limited by the unrestricted rigid body motions of the specimen. These motions were a consequence of both air currents, the initial Figure 4.4 Photograph of 4F Test Fixture. 67 positioning of the specimen, and the non-contacting drivers. The rigid body motion interfered with the ability of both the LDV and ESPI systems to maintain correlation between the object and reference beams. The 4F fixture has specific uses in an interferometric system but is not appropriate for normal testing procedures. The other three were tested to examine their impact on the measured dynamic characteristics of composite beams. Experimental Evaluation of Boundary Conditions Using information from these experiments, a test fixture was identified that provided for a diversity of mode shapes at lower frequencies and minimized the variation in the measurement of loss factors and resonant frequencies. A glass-epoxy beam 25 mm wide and 3.4 mm thick was used for a test specimen. The active length of the beam was determined by the specific test fixture under study. Active Length of Beam (mm) (lC-3F) I (2C-2F) I (235-211?) 1 162.5 I 130.0 I 200.0 I For each fixture the resonant response method was used to measure the dynamic information over a frequency span of 16 kHz. Between tests the specimen was removed and then repositioned in the fixture to determine the variability in the applied boundary conditions. Data consisting of the mean frequencies and loss factors associated with particular resonant modes and test fixtures were calculated. These 68 values were plotted against frequency in Figure 4.5. The standard deviation in the values were also calculated and appear as error bars on the plot. The relative standard deviations at points within three frequency ranges-Low (0- 1000) mid-range (1kHz -5 kHz) and High (> 5 kHz) are summarized in Table 4.1. Table 4.1 and Figure 4.5 combine O 1C-3F 0.04 r A 2C—2F V 2SS-2F 0.03 — I T . T O ‘9 1 u— 002-— l (n U) 3 % l 0.01 ~ J. 0 T 09 000 l i l 1 l l l l l l 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Frequency Figure 4.5 Comparison of the Loss Factors for the Different Test Fixtures. to show the impact of the different boundary conditions on the measured dynamic properties of the composite beam. A striking aspect of these results is that the deviations in the measured resonant frequency are small when compared with the experimental deviation in the loss factor. 69 Table 4.1 Relative Standard Deviation (%) Frequency (1C-3F) (2C-2F) (ZSS-ZF) _Ra_nge (Hz) 8.0, S-D. 8.0, 8.0,, 3.1), 8.0, 100 1.3 12.2 2.0 23. 2.2 19.9 2000 1.0 5.8 0.5 10. 1.6 2.7 10000 0.1 17.7 2.5 35. 2.3 37 This difference in the measurement variance was common to each of the fixtures. The standard deviation in the measurement has a major impact on the actual sensitivity of the dynamic technique. In evaluating the data the small uncertainty in the frequency measurements can be used to provide additional information in the detection of internal damage. A comparison of the results shows the ZSS-ZF condition to have the largest overall uncertainty in both the measured loss factor and the resonant frequency. The uncertainty was particularly high for the torsional modes since these displacement fields produce a complex interaction between the vibrating test specimen and the supports. The use of clamping-type fixtures removes additional degrees of freedom from the test apparatus and provides a fixed reference point for repositioning the specimen. Each of these factors tends to decrease the variance in the experimental measurement. The fixed boundary conditions also apply a consistent constraint for both flexural vibrations and mixed mode conditions. The comparison of the 2C-2F and 1C-3F boundary conditions showed 70 the double cantilever to produce higher loss factor values over the entire frequency range.. This increased magnitude in the measured damping is not necessarily associated with material properties and could mask the small damping increases. The cantilever beam provides consistent experimental values for both the frequency and damping measurements. Based on these results the 1C-3F cantilever fixture was chosen for the bulk of the testing. An interesting aspect of Figure 4.5 is the convergence of the measured loss factors to an upper bound as the frequency is increased, independent of the boundary conditions. This characteristic of the measured loss factors has an impact on the evaluation of the experimental data and will be discussed in detail in Chapter five. Specimen Preparation The material used for the experiments was a glass epoxy with a (05/905/05) layup. With only two interfaces, the location of the damage in the z direction was localized in two distinct regions. The test specimens were cut from 130 mm X 130 mm glass epoxy plates. After cutting, the specimen was mounted into the fixture using a micrometer to insure accurate positioning. The goal was to consistently locate the specimen in the fixture. The magnet for the electromagnetic driver was then mounted to the specimen using a thin layer of wax. In linear modal analysis theory the frequency 71 response function (FRF) is independent of the excitation location (61). However, the output response can be increased by the intelligent selection of both the excitation and LDV imaging point. For some fixtures there were locations on the specimen that coincided with a minimum number of nodal points over the testing frequency range. For example, locating the magnet at the free end of the cantilever beam minimized the number of modes where the excitation coincided with a nodal point. For other boundary conditions some experimentation was required to obtain the best results over the frequency range of interest. Initial Adjustment of LDV system After the specimen was mounted into the selected test fixture, the LDV system was adjusted to maximize the output signal. Initially the object beam emitted from the Vibrometer was focused onto the surface of the target using a 100 mm Fujita f/1.8 lens. For some light absorbing materials it might be necessary to enhance the back scattering of the laser illumination by attaching foil or retroreflecting tape to the beam. For this study, in which opaque glass/epoxy materials were used, scattering enhancement techniques were not required. After focusing the beam onto the target, the Vibrometer was tuned to obtain the best signal-to-noise ratio. Tuning was accomplished by making incremental changes in the orientation of the LDV unit relative to the target. Adjustment screws mounted to 72 the instrument base were provided for this adjustment. While making these changes the Vibrometer output was monitored using an oscilloscope (see Figure 2.14). When the system was properly tuned the oscilloscope displayed a sine wave. This indicated that a well defined speckle pair had been imaged onto the internal Vibrometer photodetecter. The amplitude of the sine wave was adjusted using a gain control. The gain was properly set when the displayed sine wave was at its maximum amplitude without being clipped. After tuning the Vibrometer, the relative frequency offset between the reference and object beam was set using a Bragg cell. Frequency shifting allows the direction of the velocity to be uniquely determined (appendix A). The Bragg cell used in the Dantec LDV system has an initial frequency shift of 40 Mhz. This offset can be moved an additional amount (0 t0' 110 Mhz) using the supplied hardware. The appropriate shift depends on the expected velocity of the target, with a larger shift being required for higher velocities. The imposed frequency shift is a trade-off between improved sensitivity (small shift) and high velocities (large shift). Figure 4.6 shows the instrument operating envelope defined by the relationships between the variables of motion and the different offset frequencies. If the preshifting of the reference beam is inadequate to separate positive and negative velocities, the LDV signal will be lost. The loss of signal can be monitored at the tuning oscilloscope. ‘0. .025 m (1.0 w.) - - S -2 S (a M (M) > " 32210-0321. i {\/ (1. no In») ‘0‘ § '° 1 10 n’ 10’ 10‘ 10’ WW“ Figure 4.6 Operating Envelope for Dantec LDV Unit As the shifting is increased, there is a point where there will be no loss in the output signal. That point is the optimum shift for that particular combination of test parameters. It should be noted that as long as the LDV signal is maintained, any frequency shift will generate an accurate indication of the target velocity. The cost of having an unnecessarily high shift is a decrease in the sensitivity to low amplitude vibrations. Initial Adjustment of ESPI System An Ealing Electronic Speckle Pattern Interferometer (ESPI) was used to record the mode shapes of interest. Three adjustments to the ESPI system were made prior to evaluating the ESPI image. First, the intensity balance 74 between the reference beam and the object beam was adjusted using a gimbaled mirror and an adjustable aperture. Balance was complete when the displayed speckles had the greatest contrast. The target was then focused onto the photodiode array using an adjustable focus compound lens. The third adjustment was made after exciting the standing wave of interest. The fringe contrast was adjusted to maximize the visibility of the fringes. The resulting fringe map at each natural frequency was then captured using either video tape or photographs of the fringes displayed on the output monitor. »Data Acquisition With the Vibrometer adjusted for maximum output, the velocity information was acquired for further processing and analysis. The velocity output from the Vibrometer was measured using a Hewlett Packard 3562A Dynamic Signal Analyzer. This device transformed the response time history into the frequency domain using a fast Fourier algorithm. The signal analyzer was configured with the following operating parameters; 1) No Windowing Function, (equal weight given to each part of the signal); 2) Ensemble averaging, (provided a significant reduction in the noise); and 3) Periodic Chirp Output Signal, (High input efficiency, Low signal leakage). The signal analyzer was controlled using a Zenith 80286/87 computer. A compiled basic program controlled the 75 different aspects of data acquisition and disk storage of the recorded FRF's. Response Evaluation As discussed previously, the third component of modal analysis is response evaluation. This function encompasses a number of important aspects including data acquisition and response verification. From the response function the damping was calculated using a curve fitting routine internal to the HP signal analyzer. The calculated loss factor and resonant frequencies were then correlated to the mode shape using the ESPI system. These three dynamic parameters were then recorded for further post-test evaluation. Damage of the Test Specimen: There are several different ways to artificially damage composite materials. One is to actually build-in the damage by introducing a foreign material to restrict the interlamina bonding. The creation of artificial delaminations and disbonds during the layup process has the advantage of producing a well defined disbond position and geometry. However these flaws do not present a valid representation of the behavior of load induced delaminations. In this study the delaminations were created using an impact tester shown in Figure 4.7. 76 Figure 4.7 Impact Tester This device uses the kinetic energy contained in a dropped weight (4.54 Kg) to produce the internal delaminations. To generate the damage the test specimen is mounted to a rigid fixture and the impacter is dropped onto the specimen. The impact force and the associated damage area can be varied by changing the drop height. Validation of Dynamic System An additional aspect of the experimental methodology to be examined in this chapter is the validation of both the .overall dynamic system and the test protocol. The system validation will be performed by the comparison of results from different researchers measuring the damping loss factor of aluminum beams. 77 Aluminum beams were used for the validation testing for three reasons: 1) the material properties of aluminum are well documented, 2) there is a large data base of damping information available, and 3) aluminum can be modeled as elastically isotropic for small displacements. The material damping of elastically isotropic materials can be estimated directly from flexural vibrations (62). The comparisons were made using test fixtures that approximate the free-free response. Table 4.2 contains loss factors measured by 4 different researchers, each using a different aluminum alloy. Table 4.2 Comparison of Loss Factors Measured in Different Studies. Bending Lee (20) Gibson (44) Whaley (69) Nokes Mode 1 0.0014 0.0010 0.0018 0.00023 2 0.0003 0.0005 ---- 0.0006 3 0.0002 0.0003 ---- 0.00024 4 ---- 0.0005 ---- 0.00027 An examination of the different values shows that there is‘a wide variation in the reported values of damping. The variation underscores the need for consistent testing procedures if the results are to be compared. The comparison also indicates the LDV based NDI system to be consistent with accepted data from different research groups. 78 On the following pages is a chronological summary of the experimental procedure used in this study. Summary of Experimental Procedure - Mount specimen into desired test fixture Focus LDV laser onto target Tune LDV support electronics - Adjust signal analyzer No windowing Periodic Chirp 10 ensemble averages - Set the frequency span to 500 hz - Set appropriate excitation Level monitor LDV output watch for signal clipping - Trigger data acquisition in signal analyzer - Examine mobility function - Center the measured frequency range around the point of maximum mobility. Use the zoom capability of the HP signal analyzer to obtain the minimum frequency span that encloses a 3db drop from the peak mobility amplitude. - Adjust the excitation level - Repeat procedure for new bandwidth - Examine coherence function to ensure a good measurement - Apply curve fitting routine to the response function - Use the computer controller to record the different components of the mobility response function to disk. 79 - Record the loss factor,and natural frequency calculated from the curve fit. - Place test fixture in ESPI system. - Adjust ESPI optics. - Use the measured resonant frequencies to drive specimen. - Photograph resulting mode shape. - Delaminate specimen using drop impacter. - Repeat the dynamic characterization for the damaged beam. The first four chapters of this study have established the groundwork for the application of a high frequency dynamic measurement system to the NDI of composite materials. In the next chapter the results obtained from the examination of delaminations will be discussed. CHAPTER FIVE RESULTS/DISCUSSION In the previous chapters the effects of different experimental parameters on the dynamic response of a system were presented. Optimizing these parameters for NDI applications led to a modal system based on the operating characteristics of LDV and ESPI. The excellent high- frequency, low-amplitude characteristics of these devices provides a potential for the detection of localized damage with greater damage sensitivity than other available modal NDI systems. In this chapter experimental results documenting the enhanced sensitivity of the optical NDI system are presented. Evaluation of Data Three different methods for analyzing the dynamic information were compared for sensitivity to internal delaminations. In the first technique, the loss factors measured from a specimen of known condition were compared with the loss factors obtained from a suspect specimen. The percentage change in the loss factor at each resonant frequency was used to measure the amount of internal damage. The second technique examined changes in the resonant 80 81 frequencies between a known and a suspect specimen. The magnitude of the frequency shift calculated at each resonant mode provides an indication of the extent of internal damage. The third method utilized the relationship between the dynamic stiffness, loss factor, and mode shape to determine the magnitude of the internal damage. The details of the third technique will be developed in the following section. Modified Method of Data Analysis The evaluation of changes in either the loss factor or the resonant frequencies have been used by other researchers to determine damage as was discussed in Chapter one. Evaluating the change in individual dynamic parameters over a large frequency span has two major problems. The first is a requirement that similar mode shapes be compared when calculating the changes in dynamic properties. As the mode shape grows more complex and the size of the damaged area increases, matching resonant modes between the initial and the damaged condition becomes difficult. The second problem is the experimental variation found in damping measurements. When evaluating changes in individual resonant frequencies, the measurement variability can mask the effect of damage in the loss factor. To address the difficulties associated with the loss factor and the resonant frequency techniques, a modified approach to the data evaluation was investigated. m— 82 In the modified analysis method, a loss factor/frequency curve was defined using the data measured over the extended dynamic testing frequencies. The curve contains both the loss factor and resonant frequency signatures of the system. For typical material behavior the resonant frequencies can be expected to decrease and the loss factor to increase in response to internal damage. The complementary response of the dynamic properties to damage would be expected to generate a shift in the dynamic property curve. The curve offset could then be used as a measure of internal damage. The offset of the damage curve 'is modified by the fact that the dynamic properties do not tend to change uniformly with increasing frequency. The literature has shown the low frequency bending modes to be less sensitive to localized damage then are higher bending modes. The proportional response to damage will tend to shift and rotate the curve about the origin as shown in Figure 5.1, producing a change in the curve’s slope. After evaluating the experimental data a more precise analysis of the response of the loss factor curve to damage can be provided. The appropriate utilization of the changes in the loss factor curve required an examination of the relationships between damping, stiffness, mode shape and damage. To begin development of the modified loss factor analysis, data from undamaged beams was evaluated. Typical loss factor data measured over an extended 83 Initial Response ______ Damaged Response . .9 /’/ U /// O / Lt. /// (I) // U) ’x O /’ _J // Frequency Figure 5.1 Expected Shift in Loss Factor Curve in Response to Localized Damage. frequency range consisted of scattered data points with an upward trend as shown in Figure 5.2. If viscous energy dissipation is assumed then the loss factor curve can be modeled as linear with frequency. An initial attempt to show the system damping to be linear with frequency was made using a best fit line through the loss factor data as shown in Figure 5.3. Examination of the fit indicates that a simple linear relation could not adequately account for the measured scatter in the dynamic response. To generate a more accurate representation of the visco-elastic slope the digital nature of the damping measurement must be considered. The different resonant techniques available for measuring the dynamic characteristics of a system were 84 um~ e e xm~ e . e S‘zmar O O 3 . § 15)- 0 g 0 L1. (n m 3 1m>s o 50. o e O 1 1 1 1 1 1 1 1 L J 0 10 20 30 40 so 60 70 80 90 100 Normalized Frequency Figure 5.2 Measured Loss Factor Data for Glass-Epoxy Beam. discussed in Chapter Three. These methods use the modal information measured at a particular resonant frequency to indicate two of the three dynamic properties (loss factor, stiffness) associated with the resonant mode. These techniques do not provide a measure of the third dynamic property, specifically mode shape. It is the mode shape that provides the digital character to the measurement, each mode shape is distinct from the adjacent resonant modes. As a result, bending modes can be followed by either another bending mode or a torsional mode and vice versa. If the effect of the mode shape is neglected, there will be apparent discontinuities in the loss factor/frequency plots. The scatter in the data pairs can be reduced by examining the influence of the mode shape on its corresponding loss 85 300 — rm ‘6 am 0 O 3 § 60 U S (n (n 3 um 50 0 1 1 l l 1 l 1 1 1 J o 10 20 30 40 so so 70 80 90 100 Normalized Frequency Figure 5.3 Linear Curve Fit of Damping and Frequency Data factor resonant frequency data point. Using the energy formulation of damping discussed in Chapter Three, the measured loss factor was shown to be a strong function of the dynamic displacement field. Equation 3.17 describes the relationship between the strain field in the vibrating specimen and the individual energy dissipation components. a (40,) =_: (0,3,0) 62 (3. 17) where i = 1,2,4,5,6 In the modified data evaluation technique the mode shapes were identified and labeled according to a displacement pattern defined by the vibrational cells. The displacment pattern could then be related back to equation 3.17 and to 86 specific combinations of dissipation components. In this study three basic mode patterns were identified, bending, torsion (mixed), and transitional. Bending modes could be distinguished by displacements constrained to the x-z plane as shown in Figure 5.4. Torsion modes characterized by well-developed vibrational cells exhibiting displacements in both the x-z and y-z planes are illustrated in Figure 5.5. The transitional modes had the characteristics of both bending and torsion displacement fields. Typically the transitional modes did not have the well defined vibration cells associated with either the bending or torsional modes as shown in Figure 5.6. The torsional mode vibrations could be further Figure 5.4 Bending Mode Pattern. 87 a.i§$é..:2 C 4J9EI€25 It" .3..- 'O' . Figure 5.5 Torsional Mode Pattern. subdivided according to the number of vibrational cells formed across the width of the specimen. Figure 5.7 shows a mixed mode vibration that can be identified by two cells across the width while Figure 5.8 shows the same beam vibrating in a mode characterized by three cells across the width. An illustration of typical relative magnitudes for the loss factors associated with different mode types can be seen in Figure 5.9. These curves are a compilation of results from different test sequences and using a variety of materials. To apply the modified analysis method to the data, the loss factor/resonant frequency pairs were grouped into bending and torsional mode families using ESPI images. 88 Figure 5.6 Transitional Mode Pattern. Figure 5.7 Two Cell Torsional Mode. 89 Three Cell Torsional Mode. Figure 5.8 --—~ Bending ------ Transition ------- Torsion -,,.—""’ 5 ,- rrrrrrrrr , IIII - —— r 15 ”.x- ”””” , c , ’ , 1 u. ”””” w ,1 (I) O __1 Frequency Figure 5.9 Relative Magnitude of the Loss Factors Associated with the Different Mode Shapes. 90 For each mode family a best fit line of the form n = mf,-+ b was calculated. In this equation m is the slope of the curve, b represents the offset and:fi,are the normalized resonant frequencies. Normalization of the natural frequencies provided consistency between different specimen geometries. The fundamental bending frequency was used to normalize the all of the frequencies in each test sequence. The slopes of the calculated lines were related to the particular mode family (bending, transitional or torsion) and changes in the damping mechanisms affected by frequency (viscous effects). An advantage to using a graphical representation for evaluating the dynamic data was the inherent normalization of the loss factor magnitudes. The normalization process removed many of the external contributions to the loss factor, such as fixture effects. The normalized data provided more consistent loss factor values between the different test sequences and specimens. In this study the relative offset b of the curve was not evaluated. In practice the offset is an indication of the frequency invariant aspects of the measurement such as fixture effects. The data presented in Figure 5.3 was re-evaluated using the concept of normal, transitional and mixed mode vibrations. The resulting curves are shown in Figure 5.10. The data analysed using the modified analysis approach clearly indicates that both the bending and torsional modes can be closely approximated using the linear model. 91 O Bending Modes 300 r V Transitioanl Mode V Torsional Made 250 r— ' v 3 200 — o o § 1331 V U 0 LL rn (n 3 100 - 50 ~ . (e O 1 l 1 1 1 l 1 1 1 1 0 10 20 30 4O 50 60 70 80 90 100 Normalized Frequency Figure 5.10 Results of Combined Data Evaluation Technique. Additional materials were tested to determine some rules for separating the mode shapes into independent curves. A sheet molding compound (SMC) consisting of short glass fibers was examined initially. As a first order approximation the fibers could be considered to be randomly oriented in the plane of the sheet. The dynamic response of the material is shown in Figure 5.11. SMC does not show the distinct separation of dynamic properties. This finding is not surprising since the material is quasi-isotropic in the x-y plane. The energy dissipation due to bending strains will not vary much with the direction of curvature. A unidirectional carbon-epoxy material was also evaluated. Figure 5.12 presents the data acquired from samples with the fibers oriented along the major axis of the beam. The large 92 250 — 200 - 8 . o o . z 5.. l 5 5. 0 8 100-— Q U) 1. U) o .J 50 _ SMC Cantilver Beam Loss Factor Data . 10/09/91 0 b 1 l 1 1 1 l 1 1 1 l 1 1 i 1 1 1 l 0 2000 4000 6000 8000 10000 Frequency (Hz) Figure 5.11 SMC Dynamic Characterization. 300 _ [3 Bending Modes A Torsion 1 - V Torsion 2 250 _ I Transition I ’8‘ . o 200 5 150 :3 .. 0 L D- 3 100 O .. _J 50 O P l 1 1 1 l 1 1 1 A 1 1 1 l 1 1 1 l 1 1 1 L 1 11 J 0 1O 20 30 40 5O 60 70 Normalized Frequency Figure 5.12 Carbon/Epoxy Dynamic Characterization (90 degree ply orientation). 93 stiffness mismatch between fibers and the matrix allows a very diverse group of mode shapes to be easily generated. In Figure 5.12 there are two distinct torsion families as well as the bending and the transitional mode shapes. Each of the different modal families follows the predicted linear behavior. In a second sequence of experiments the carbon fibers were oriented transverse to the long axis of the beam. This orientation had a significantly different characteristic loss factor curve. The high transverse stiffness prevented the torsional modes from developing in the lower frequency ranges. Figure 5.13 shows the beam behavior to be dominated by the bending modes. The trend for the bending mode loss factor data can be approximated AS4/EPON 12 ply Composite Beam Fiber Orientation 3’50 f C] Bending Mode » A Torsion Made 300 C. I Transition r C] ; 90 6‘250» 1 o _ O . J; 200 i D ———————>-0 .5. : LL l- m C I / U) ‘3 100l5 .A l. L- 50 r- *- 0*.11111111111114111111111111111111 25 50 75 100 125 150 175 200 0 Normalized Frequency Figure 5.13 Carbon/Epoxy Dynamic Characterization (0 degree ply orientation). 94 with a straight line. However, the curve appears to be taking on characteristics of a power law curve. The observed curvature is consistent with the behavior of composite beams over a wide frequency range. As presented in Chapter Four, the loss factor magnitudes tend to converge to an upper bound that is independent of the boundary condition. In order to converge, the slope of the loss factor data cannot be a constant. For the limited number of data points available for each modal family, however, a linear damping model has been shown to provide an excellent fit to the experimental data obtained for a number of types of orthotopic composites. In the discussion that follows, the sensitivity to damage of the two established data analysis techniques, change in loss factors and change in resonant frequencies, will be compared to changes in the slope of the different modal family curves. Test Results In order to identify and catalog the experimental data, the following labeling convention was used for each test sequence. @_bbbb.xx where the first character (6) indicates the damage state of the beam I = no damage, D = damaged. The characters (b) are used to identify the specimen, and the trailing two digits (.XX) represents the width to length ratio. For example a data set labeled I_1CP3.72 would contain the data collected 95 during test sequence one, representing the initial response of the CP3 beam in the test group with a w/l of 0.72. In the initial sensitivity experiments, glass epoxy cross ply beams with a width to length (w/l) ratio of 0.22 were used. This specimen geometry produced response data with widely spaced resonant frequencies and readily identifiable mixed mode vibrations. The simple dynamic behavior provided an opportunity for close examination of the experimental procedures and further evaluation of the different facets of data analysis. The beams were tested over a frequency span of 10 Khz. The plot of damping vs frequency for the initial beam conditions are found in Figure 5.14. In beams with a small w/1 there are a limited 350— . I_cp1.22 v I_cp2.22 v 300 " e I_cp3.22 A I_cp4.22 8 250 h / O 9 ‘ ////’5 .3 200— . 3 I E 150— ' 3 I ’////’V/. 3 100 — ' /’/ 50 / O l J 1 1 I o 20 4o 60 80 100 Normalized Frequency Figure 5.14 Plot of Initial Loss Factor and Resonant Frequency Data for the Glass - Epoxy Beam (l/w =0.22). 96 number of mixed mode data points over the frequency range examined. The small number of mixed mode data points tend hto produce an exaggerated variation in the torsional slope calculated for these beams. The bending data consisted of the first four bending modes while the torsional slope was calculated from three mixed modes. The plot of the cross ply material shows the overlap of the different modal families. The dynamic response of the different beams compared well except for beam I_cp3.22. The dynamic response of this specimen deviated from the other three beams in the measured resonant frequencies and loss factors. To investigate the source of the dynamic property variation, the geometry of each beam was examined. The inspection of beam I_cp3.22 detected a significant variation in the beam thickness. The reason for the variation was that I_cp3.22 was cut from the edge section of the master plate, which did not have a uniform cross-section. The thickness of the beam varied 18 percent over the face of the specimen, from a maximum thickness of 3.18 mm to a minimum of 2.6 mm. The variation in cross-section was not uniform over the beam, resulting in a loss factor curve different from that of the other beams cut from the same plate. The deviation in the slope of the loss factor curve is an indication of the sensitivity of the damping to aspects of the beam geometry. After measuring the initial condition, the beams were damaged in the manner discussed in Chapter four. The 97 projected area of the delamination was measured to provide an indication of the internal damage. The dynamic measurement procedure was then repeated for the damaged beams. The calculated bending and mixed slopes were compared for the different projected damage areas of 10%, 15%, 25% and 50%. The measured response for both the initial and damaged conditions are plotted in Figures 5.15- 5.18. The changes in the modal slopes are summarized in Tables 5.1 and 5.2. The comparison of the initial and damaged slopes showed that over the extended frequency range the bending mode slope was not a particularly sensitive measure of the internal damage. This finding supports the results found in the literature. An important aspect of the 350 — D I_cpl.22 O D_cpl.22 300 - 10% Delamination D O ’0‘ 250 — o o c, 200 ~ 00 E 8 150 ~ L (I) (I) 3 100 50 O l l l l l 0 20 4O 60 80 100 Normalized Frequency Figure 5.15 Comparison of I_CP1.22 and D_CP1.22 (10% Delamination) 98 350 — Cl I_cp4.22 D I D_cp4.22 300 ~ 15% Delamination 8 250 o O 3.5 200 5‘3 8 150 LL (D (I) 3 100 50 O r 1 1 1 1 1 1 1 1 4 J O 10 20 3O 4O 50 5O 7O 80 90 100 Normalized Frequency Figure 5.16 Comparison of I_CP4.22 and D_CP4.22 (15% Delamination) 400 r :1 I_cp2.22 I D_cp2.22 350 c 25% Delaminatior 300 250 200 150 Loss Factor (#1000) 100 50 0 1 1 1 1 1 O 20 4O 60 80 100 Normalized Frequency Figure 5.17 Comparison of I_CP2.22 and D_CP2.22 (25% Delamination) 99 400— I 350 r- e 300 e 250 — . 200 ~ D 150 Loss Factor (#1000) D I_cp3.22 I D_cp3.22 50% Delamination 100 50 O 1 l 1 1 l 1 J 1 1 4 0 10 20 30 40 50 60 70 80 90 100 Normalized Frequency Figure 5.18 Comparison of I_CP3.22 and D_CP3.22 (50% Delamination) bending mode data was the consistency in the initial slopes when beam I_cp3.22 is neglected. Recall that I_cp3.22 had a non-uniform cross-section. As expected, evaluation of the bending slopes was simplified by the dynamic behavior of the beams at low frequencies. Table 5.1 Comparison of Bending node Slopes. % Damage Initial Damaged Area Slope Slope % Diff CP1.22 10% 1.45 1.60 10 CP2.22 25% 1.39 2.41 73 CP3 . 22 50% 2 . 13 9 . 69 LARGE CP4.22 15% 1.45 1.63 12 100 Table 5.2 Comparison of Mixed node Slopes. % Exaggge Insiltolpf‘el Dasmlaéeed 3 Diff CP1.22 10% 2.97 2.2 -35 CP2.22 25% 3.67 4.68 27 CP3.22 50% 2.18 2.83 29 CP4.22 15% 3.38 2.75 -23 The insensitivity of the dynamic properties to damage at the lower modes provided a convenient anchor for the loss factor curve. With the base of the curve fixed, the reaction of the damping and frequency response to damage at higher frequencies forced the expected increase in the slope. The positive change in the slope agrees with the expected visco-elastic behavior of these materials. In addition, the magnitudes of the percent difference in the slope are consistent with the projected damage area. The ability to measure the torsional loss factors provided excellent sensitivity to the different damage conditions. However, the interpretation of the torsion data was complicated by apparently inconsistent changes in the torsion mode slope. Specifically, at the smaller damage levels, the torsional mode slope decreased relative to the initial torsional slope. The ambiguity in the slope change for small damage areas is an indication of a limitation in the dynamic method for detecting localized damage. The effect of flaw size, and position in the beam will be discussed below. 101 Sensitivity Limitations for High Frequency Data For small vibration amplitudes, the strain field is related to the curvature of the beam (65). To maximize the damage-induced changes in the loss factor two conditions must be met. First the damage should be centered in an area of high curvature ( ie. high strain energy). This condition follows from the definition of the loss factor measurement. Second, the distance between amplitude peaks in the standing wave should be smaller than the physical extent of the damage to be detected. An illustration of the sensitivity conditions is provided in Figure 5.19. When the peak-to- peak distance is larger then the damage zone, the contribution of the flaw to the damping associated with that vibration cell is decreased. A further consideration when evaluating the sensitivity of the dynamic method is the fact that the strain energy associated with different vibration cells in the same resonance frequency varies. In meeting these conditions, limits are imposed on the useful frequency range for NDI applications. The limit is another artifact of the resonant techniques for measuring the system damping. The measured loss factor is an average of the damping associated with each vibrational cell. As the number of vibration cells increases, the effect of any single cell on the overall damping value is reduced. This implies that as the peak-to-peak distance in a standing wave gets smaller, the impact of a damage zone on any single vibrational cell is averaged out of the overall loss factor 102 Modal Activity Zone / ~ NodalZancs DamageZone Condinon 1. DamageZoneShouldbeIncanodinRegionoflfighModaledvity Conditional MEMtofdeDemgeZoneshonldbeSnnlladmanismBMModdAodvity Regims. Figure 5.19 Description of Sensitivity Conditions for the Detection of Localized Damage Areas. 103 value. For bending modes which have limited sensitivity at the lower modes, the expected response of the loss factor curve presented in Figure 5.1 can be modified as shown in Figure 5.20. To support the modifications, the percent change in the system loss factors were plotted in Figure 5.21. Figure 5.21 shows the change in the loss factors to be closely related to both the damage size and the frequency. For large damage areas almost any mode generates a large indication of damage; however, for the smaller damage zones there is a maximum indication of damage that occurs in the mid range of the testing frequency range. These data support the behavior indicated in Figure 5.20, with the maximum change in the damping occurring at the ___________ Damaged Response Undamaged Response Loss Factor Frequency Figure 5.20 Expected Loss Factor Response for Small Localized Damage Zones. 104 80 .- A 10% Damage Area 0 15% Damage Area C] 257. Damage Area 50 _ V 50% Damage Area V a Cl 0 6 LE 40— m (I) 3 -E 20*. v A 1, 71 >6 D 0‘ _i g 0 D D ‘_ g/ A 1 ‘ 8 J ‘5 (>2 Q//1 0 2o 30 40 so so 39 \, _20 3 Normalized Frequency .—40— Figure 5.21 Percent Change in Bending Mode Loss Factors (1/w = 0.22). third bending mode. The third mode provides the closest match between the sensitivity constraints and the size of the localized damage zone. The data also show that as the damage zone increases the dynamic response can no longer be correlated between the damaged and initial conditions. In effect, the initial and damaged beams are no longer related. For torsional modes the response can be visualized by the trend indicated in Figure 5.22. To support this assertion, the percentage change in the torsional loss factors are plotted in Figure 5.23. The results indicate that the maximum sensitivity to damage will occur at the mode shape that has the minimum number of vibrational cells that satisfy the two conditions on flaw size and position. The sensitivity constraints also 105 —————————— Damaged Response Undamaged Response , £52 ,,,, ,1, o ,,,, 0 Li. (D U) 0 _J Frequency Figure 5.22 Expected Behavior of Torsional Loss Factors with Localized Damage. 200 — A 10% Damage Area V O 15% Damage Area Cl 25% Damage Area 1 150 r V 5096 Damage Area 0 ‘6 0 LL. 3 100 >- O _J E 81 50 — v S 5 g\ D MD 39 0 1 1 1 1 1 8 \ 1 1 1 C) 10 20 30 4o 50 so MN 100 Normalized Frequency I -50 a Figure 5.23 Percent Change in Torsional Mode Loss Factors (l/w = 0.22). 106 indicate why the change in the torsional mode slope is negative for small damage zones. Since the lower frequency torsional modes can produce a larger change in the measured loss factor, the slope will decrease as indicated in the data. Comparison of Different Data Analysis Techniques Examination of the simple frequency shifting data to indicate damage confirmed the lack of sensitivity to small localized flaws. The data shown in figure 5.24 showed the shift to be less then 10 percent at each resonance mode for damage less then 25 percent. The value of evaluating the frequency shift for the detection of small scale damage is Normalized Frequency O 20 4O 60 80 100 O r V 1 l I l _5 I I\ r. ’ v 0’ <1) 1 -1. _ : E v _15 ,— Q) 0‘ C O {3 -20 P a? O 107. Damage Area -25 _ V 15% Damage Area I 257. Damage Area A 507. Damage Area -301. Figure 5.24 Percent Change in Resonant Frequencies for (l/w =0.22) 107 the small standard deviation of the measurement. The use of loss factors to detect the damage was more sensitive than using the frequency shift for small damage zones. The difficult aspect of using the individual dynamic properties to detect the damage is determining the appropriate resonance mode to evaluate, since each can have a different sensitivity to a particular damage zone. The comparison of individual mode shapes has the potential to give the strongest indication of a specific damage zone. The primary advantage in using the loss factor slope is a significant decrease in the standard deviation of the measurement. Additional testing was done using a glass/epoxy cross ply specimen with a w/l ratio of 0.32. The increase in the w/l ratio created a number of additional torsion modes over the test range. For the w/l = 0.32 beams the projected damage area was close to 10 percent. To provide information on the effect of position on the measured output, the damage position was varied. The initial loss factor data for these beams is shown in figure 5.25. The plots comparing the damaged response to the initial response are shown in figures 5.26 to 5.29,and the comparison of the initial and damaged condition for the different beams are listed in tables 5.3 and 5.4. The results from the wider beam further support the relationship between damping, damage and mode shape discussed with the previous test sequence. An additional observation for the wider test specimens was an apparent Loss Factor (#1000) Figure 5.25 350 300 250 200 150 100 50 Loss Factor (#1000) Figure 108 F V I_cp1.32 - _ Cl I_cp2.32 A I_cp3.32 l l l 1 1 1 1 J 1 l 0 10 20 30 40 50 60 70 80 90 100 Normalized Frequency Initial Loss Factor and Resonance Frequency Data for a Glass-Epoxy Beam (l/w =0.32). V I_cp1.32 v I_cp1.32 (Transition) EJ D_cpl.32 300 I D_cp1.32 (Transition) 250 V v 200 D I 150 ' 100 50 O 1 1 1 1 1 1 1 1 1 1 10 20 30 4o 50 60 7o 80 90 100 Normalized Frequency 5.26 Comparison of I CP1.32 to D_CP1.32 (15% Delamination) 109 350 A I_cp2.32 F A I_cp2.32 (Transition) [:1 D_cp2.32 A 300 _ I D_cp2.32 (Transition) 3 250 ~ 0 S A 3, 200 E 8 150 Li. (D (D 3 100 50 O 1 1 1 1 1 l 1 1 l J 0 10 20 30 40 50 60 70 80 90 100 Normalized Frequency Figure 5.27 Comparison of I_CP2.33 to D_CP2.22 (10% Delamination) A I_cp3.32 400 F A I_cp3.32 (Transition) Cl D_cp3a.32 350 b I D_cp3a.32 (Transition) A ,1 300— O o S 250 — .3, D D :2 200 U E .1 150 U) 3 100 50 O 1 ‘ 11 1 l I l 1 1 1 1] 0 10 20 30 40 50 60 70 80 90 100 Normalized Frequency Figure 5.20 Comparison of I CP3.33 to D_CP3a.33 (10% Delamination) 110 A I_cp3.32 400 l— A I_cp3.32 (Transition) D D_cp3b.32 350 1- I D_cp3b.32 (Transition) A A 300 — o o 5 200 U E g 150 3 100 50 O l J_ 1 1 1 1 1 L 1 1 0 10 20 3O 40 50 50 70 80 90 100 Normalized Frequency Figure 5.29 Comparison of I_CP3.33 to D_CP3b.33 (10% Delamination) decrease in the loss factor magnitude for damaged beams at higher frequencies. If the mode shape remains consistent Table 5.3 Comparison of Bending Loss Factor Slope (w/l = 0.32) % Damage Initial Damaged Area Slope Slope % Diff CP1.32 15% 1.43 2.03 42 CP2.32 13% 1.31 1.73 32 CP3a.32 10% 1.73 1.54 - 11 CP3b.32 10% 1.73 1.75 1 111 Table 5.4 comparison of nixed Loss Factor Slopes (w/l = 0.32) % Damage Initial Damaged Area Slope Slope % Diff CP1.32 15% 1.30 -0.69 -43 CP2.32 13% 1.61 0.56 -65 CP3a.32 10% 2.18 0.64 -71 CP3b.32 10% 2.18 1.46 -33 between the initial and damage conditions, a decrease in the loss factor is inconsistent with the linear visco-elastic models used to evaluate the loss factor slope. The decreases in loss factor were limited to torsional modes and found primarily in the beams with smaller damage zones. To investigate this phenomenon the capabilities of the ESPI system were utilized. A comparison of images before and after the damage indicates a significant change in the mode shapes. In general the torsional mode shapes of the damaged specimens did not develop vibration cells that were as well defined as the initial condition. Instead, the mode shapes had more characteristics of the transitional modes shapes. In effect, the decrease in loss factor is an indication of a significant change in the mode shape. Figure 5.30 is an example of this blurring effect. The photograph in Figure 5.30 is an excellent example of the blurring for a carbon- epoxy plate vibrating at 8560 hz. The modifications in the mode shape are more apparent at the high frequency extremes of the test range. Figure 5.30 ESPI Image of Mode Shape Before and After Damage (8560 hz) 113 To quantify the variation in the modal displacement field will require significant modifications to the ESPI system software to allow additional processing of the displacement images. The decreasing of the damping magnitudes does not adversely effect the NDI capability of the modal system. The negative slopes actually create a more distinctive indication of internal damage. It is important to remember the primary NDI potential for the dynamic testing methods are as screening methods that attempt to either pass or fail a particular specimen. The data from the wider beams emphasised the relationship between the sensitivity of the dynamic method, the location of the damage zone and the mode shape under investigation. One consequence of the more complex dynamic signatures in the wider beams was a blurring of the distinction between the different families of mode shapes. The blurring is inherent to the dynamic test method which relies on the resonant characteristics of the system. Photographs of selected mode shapes are included in Figures 5.31 to 5.34 to aid in the visualization of the displacement fields. In comparing the results of the different methods for analyzing the dynamic data, the slope technique was found to have several advantages over the direct comparison of dynamic properties at individual resonant frequencies. These advantages include: 1) variations in individual data 114 Figure 5.31 2nd Bending Made (700 Hz) Figure 5.32 Torsion Mode (3000 hz). 115 Figure 5.33 6th Bending Mode (8000 hz). Figure 5.34 Torsion Mode (9000 hz) 116 individual points tend to be smoothed out; 2) the slope technique does not require the direct comparison of properties at resonant frequencies; and, 3) the method tends to be less sensitive to the position of the damage. The disadvantages of the modified data analysis technique include a reduction in the absolute sensitivity of the dynamic method. The reduction occurs since the mode shape with a maximum change in dynamic properties is blended into an overall characterization of the material. The other characteristic of the slope technique is that the slope measured is not a material property; it is dependant on the specimen geometry and boundary conditions. Even with the high frequency information, there are limits on the available sensitivity of the dynamic method to localized damage. The experimental results suggest that limits of the sensitivity can be circumvented by adjusting the effective geometry of the problem such that the critical damage size is larger relative to the testing area. By making the damage relatively larger, the mode shape can be excited that more completely meets the dynamic test criteria for maximum sensitivity. In the next chapter the conclusions that were drawn from the development and experimental testing of the optical dynamic NDI system will be presented. CHAPTER 81! CONCLUSIONS AND RBCONNENDATIONB As discussed in Chapter one, the focus of the majority of the quantitative research into dynamic methods of NDI has revolved around either fatigue type damage or matrix cracking. Dynamic testing techniques provide a sensitive indication of these damage types which are characterized by a wide dispersion of the damage. A more difficult problem is increasing the sensitivity of the dynamic technique to localized defects such as delaminations. In this thesis an integrated experimental and analytical approach to increasing the available sensitivity has been described. The approach to increasing the sensitivity was to develop both the measurement procedure and analytical tools capable of evaluating dynamic information from an extended frequency range. To obtain the response information at higher frequencies a modal analysis system was developed which incorporated both a Laser Doppler Vibrometer (LDV) and an Electronic Speckle Pattern Interferometer (ESPI). The LDV system was used to measure the dynamic characteristics of composite beams over a frequency range extending to approximately 12Khz. ESPI provided a technique for 117 118 acquiring whole field displacement maps of the various mode shapes. The evaluation of this system and the experimental results supported the conclusions mentioned below. Analysis of the extended frequency data presented two major difficulties. One was the need to match made shapes between the damaged and initial beams before comparing the results. Secondly, there was a large variance in the measured loss factors. To minimize these difficulties, a modified data analysis approach was developed that combined the information contained in all three dynamic parameters (loss factor, dynamic stiffness, and mode shape). The modified analysis approach used the dynamic parameters to form a linear relationship between loss factor and frequency. The slope of this line was found to be related to the particular specimen geometry and material. By recording changes in the slope of this line, a sensitive indication of the internal damage could be made. To improve the correlation between the modified analysis approach and the experimental data, the relationship between energy dissipation and mode shape was investigated. It was found that mode shapes could be divided into specific groups according to the form of the displacement field. For this study, the mode shapes were grouped into three families, bending modes, transition modes and torsional modes. Where bending modes where restricted to vibrations in the y-z plane, torsional vibrations had well developed motions in both the x-z and y-z directions, and 119 the transitional modes were poorly defined mode shapes that did not fit well into the other two configurations. For more complex systems, the mode shapes could be divided into additional families. By analyzing the dynamic response of each modal family separately, an excellent agreement with linear visco-elastic energy theories was obtained. Each family of mode shapes was represented by a linear relation of the form n = mfnd-tn The slope m was evaluated for potential as an indicator of the internal damage. The advantages of using the modified data analysis method over traditional dynamic NDI evaluation techniques are: 1) variations in individual data points tend to be smoothed out; 2) The slope technique does not require the direct comparison of properties at individual resonant frequencies; and, 3) The method tends to be less sensitive to the position of the damage. The disadvantage of the slope technique is a reduction in the absolute sensitivity of the dynamic method, since the mode shape with a maximum change in dynamic properties is blended into an overall characterization of the material. A recommendation for future work is to investigate the loss factors associated with the specific mode shapes. It may be possible to determine the specific components of the material damping for use in the analytical models of damping. A comparison of the initial dynamic properties with the damaged conditions provided an indication of some inherent 120 limitations in the dynamic testing method. Investigating these limitations provided insights into the experimental requirements to obtain the maximum sensitivity. Namely; 1) The damage location should be centered in a location of high curvature; 2) the distance between maximum amplitudes in the standing wave should be close to the size of the minimum damage zone to be detected; and 3) The number of vibration cells excited in a test should be minimized. The density of the vibration cells on the specimen must be minimized because the measured loss factor is an average of the damping associated with each vibration cell. As the number of cells increases the impact of damage to a any single cell will be averaged away. For testing large parts, the sensitivity requirements can be meet by changing the geometry of the test conditions. In future work different types of test fixtures will be examined, for example, a specimen could be mounted into a fixture consisting of multiple frames. Each frame would isolate the material within its boundaries. By artificially decreasing the vibrating area the sensitivity conditions could be meet for smaller critical flaw sizes. In spite of the restrictions on the ultimate sensitivity, the use of extended frequency information creates a significant improvement in flaw detectibility over the results currently reported in the literature. The pure bending modes were the least sensitive to localized damage. This finding supports the results of Lee (20) and the other 121 researchers discussed in Chapter One. The torsional modes provided significantly more sensitivity to the localized damage, in part because the torsional modal cells could more closely meet the sensitivity criteria. Beyond the research tangents indicated above and throughout the thesis, subsequent work needs to expand the NDI data base to include more complex systems, utilizing the background obtained from the beam studies. Other research directions would be to further integrate the processing of the ESPI system such that the complete dynamic description of a system would be available in real time. Other work that should be done is to develop a method for measuring loss factors without relying on resonance techniques. The inherent characteristics of the resonant methods for damping measurement are the principle limitation in using the dynamic properties for NDI. Dynamic NDI techniques are better suited to indicating the presence of damage than for describing its extent. In this thesis the optical techniques of LDV and ESPI were shown to be a fast reliable method for indicating the presence of delaminations in cross ply composites. APPENDIX A. Laser Doppler Vibrometry Laser Doppler Vibrometry (LDV) is a noncontacting interferometric technique for measuring surface velocities. The surface velocities are calculated from the measured Doppler frequency shifting in waves reflected from the vibrating targets. The velocity information available from the Doppler frequency shift is extracted using a modified _ Optical Detector ii Direction Beam of Motion Splitter Object Beam H Laser 7 1 E :3 Target Reference Beam L Mirror Figure A.1 Michelson Interferometer 122 123 Mishelson interferometer as shown in Figure A.1. In the Michelson arrangement the object beam is scattered from the vibrating target, collected, and combined with a reference beam. The resulting interference between the Doppler shifted light and the reference beam creates a beat frequency equal to the difference between the frequency of the Doppler shifted object beam and the reference beam. The derivation of the beat frequency can be generated using a wave formulation to describe the interference of the object and reference beam. With this model the addition of two coherent beams is described by; E;=E;+E; (A.1) where E; is the electric vector for the light scattered from the target (the object beam) and similarly'ig represents the reference beam. Because:i% and.ig have the same polarization the vector designation can be dropped resulting in equations (A.2) and (A.3). Eo(t) Acos(vot + (110) (A.2)‘ ERUI) Bcos(vot + 4’3) (1)-3) where A and B are the amplitudes of each electromagnetic wave respectively, «no and (pk are the phases, and 1:0 is the frequency of the laser. When the frequency of the object beam E0 is shifted an amount Av, the sum of equations (A.2) and (A.3) is given by (A.4). The response characteristics of optical detection devices 124 E,(t) = Acos( (vo+Ay)t+¢o) + Bcos(vot+¢k) . (3-4) transform the measurement of Edt) into a measure of RMS intensity, so the combined intensity (IC) of the object and reference beam is recorded as shown in equation (A.5), Ic =(E0+ER)2 (3.5) or expanding; Ic = [Acos((vo+Av)t+¢o) )2 + [Bcos(vot+¢k) ]2 (A.6) +2AB(cos((vo+Av)+¢0)-cos(vot+¢k)) Equation A.6 can be reduced further using trigonometric identities and neglecting terms that are beyond the performance capabilities of optical detectors. In general, optical detection elements are insensitive to frequency terms on the order of ya ( 10“ Hz) or phase information. With these limitations the output from the detector is a frequency modulated signal with a beat frequency of vR - VD. IC = AB[cos(uR-vD)t] (A.7) where on is the frequency of the Doppler shifted beam. The magnitude of the Doppler shift is given by, Au = ¥- 81110;), (A.8) where V is the signed velocity of the target, A is the wavelength of the laser, and a is the scattering angle of the object beam. For applications where the object beam is normal to the target surface, ie. awn, then the sin(a/2) term can be approximated by 1. The Doppler shifted 125 frequency VD is then given by: ”D = ”R +T’ (A99) R v, and A1 are the frequency and wavelength of the reference beam. For simple LDV systems wk is identical to the initial laser frequency v0. The frequency difference between the reference beam and object beam is then centered about we, with a magnitude of, 20V :_x;. (A.10) depending on the sign of the target velocity. The sign of the frequency difference cannot be detected using the simple Michelson configuration. The result of the sign ambiguity is a frequency modulated signal proportional to the absolute magnitude of the velocity term. To uniquely identify the sign of the velocity a modification to the LDV system must be made. The strategy for determining the direction of the velocity is to offset the frequency of the reference beam from the initial frequency of the laser. A common device for shifting the reference beam frequency is a Bragg cell. The Bragg cell is an acousto-optic device that utilizes diffraction effects to shift optical frequencies. When a Bragg cell is inserted into the LDV system, the equation for the Dappler shift becomes, 126 IC =.AB[COS(VS-(Vo-VD))t] (A.11) ‘where vs== v0 + ”no is the frequency of the shifted reference beam emitted from the Bragg Cell and ”ac is the frequency of the Bragg cell modulator. With the frequency of the reference beam adjusted, the difference between Doppler shift and the reference frequency is no longer symmetrical about the frequency of the laser, and the sign of the target velocity can be determined as shown in Figure A.2. The above discussion provides some details into the background of the heterodyne LDV technique. There are variations to the LDV technique that are appropriate for 1) +1) “ BC? [) ”BC—DD <1 4.- UO-UD “0 00-1-00 ‘05 = D0+UBC Figure A.2 The Effect of Pre-shifting the Reference Beam on Direction Discrimination. 127 solving particular measurement requirements. An excellent discussion of particular LDV systems can be found in reference 28. APPENDIX 3. Electronic Speckle Pattern Interferometry (ESPI) ESPI is a differential technique that interferometrically compares phase changes in the coherent speckle pattern of an object before and after deformation. The comparison of the different phase maps generates fringes that are related to the out-of—plane displacement of the target surface. To generate the phase map of the target, a laser beam is split into an object beam and a reference beam as suggested in Figure 8.1. The object beam is scattered from the target surface creating a characteristic speckle pattern. The phase and intensity characteristics of the speckle pattern are unique to the spatial relationship between the target and the interferometer. Changes in the out-of-plane displacement of the target can be evaluated by examination of the phase changes in the speckle pattern. To extract the phase information, the speckle pattern is interferometrically combined with the reference beam. The resulting interferogram transforms the phase information contained in the object beam to intensity data. Transforming the phase information allows the interferograms 128 129 “Splitter sumac __..|c:cr>c..an [] Iii [:]d\\‘\\\\\\\\\\‘L 0115'”:I L.. lemma! mil Canine-:5,“ _> W"' Figure B.1 ESPI System to be analyzed using standard optical detectors. The creation of the displacement fringes is a two step process. An initial interferogram is acquired and stored in computer memory. The specimen is deformed and a second interferogram is recorded. The subtraction of the initial interference pattern from the interferogram representing the deformed object produces a set of interferometric correlation fringes with an intensity given by equation B.1. I=Io[1+7o-cos(A¢)] (B.1) where I0 is the D.C. intensity of the image, 7b is the fringe modulation and Ad is the change in the wavefront phase. The correlation fringes contain both phase and 130 intensity information. For ESPI, a phase modulation technique (PMT) is used to remove the intensity components from the phase calculation thereby producing fringes with less noise. A moving mirror is used to precisely shift the path length of the reference beam. A minimum of three different interferograms with a known phase relationship are used to solve equation B.1 for ¢(x,y). The phase relationship is generated by using a piezoelectric mirror as shown in Figure B.1 to shift the reference beam a pre-determined fraction of a wavelength for each of the recorded images. For each image it is assumed that the intensity Io and fringe modulation 70 are approximately constant. Then given the three images, with a relative phases of 0°, 90°, and 270°, the phase map can be calculated using equation 8.2, -1 [13(xIY) -IZ(XIY) (3.2) [11(xIY) -IZ(XIY) ¢(xIY) = tan The phase values can be easily converted into displacements using the equation, z