Damage Assessment in Laminated Composite. Structures using Acoustic Methods

Transcription

1 Damage Assessment in Laminated Composite Structures using Acoustic Methods Theoni T. Assimakopoulou Mechanical & Aeronautical Engineer PhD Thesis University of Patras March 29

2 2 Doctoral committee: Theodoros P. Philippidis, Associate Professor Supervisor Vassileios Kostopoulos, Professor Dimosthenis Polyzos, Professor Opponents: Spyridon G. Pantelakis, Professor Theodoros E. Matikas, Professor Dimitrios A. Saravanos, Professor Christos A. Papadopoulos, Associate Professor University of Patras Department of Mechanical Engineering & Aeronautics Section of Applied Mechanics, Applied Mechanics Laboratory P.O. Box 141 Panepistimioupolis, Rio, Patras, GR 2654 Tel.: Fax: tasim@mech.upatras.gr

3 3 To the 3 teachers that lead me to this my supervisor Theodore Philippidis, my English tutor Rannia Mesiskli and my elementary teacher Christos Alexandris To the 2 friends that lead me through this Theodore Phipippidis and Alexandros Antoniou And to the ones that obstructed my work by making me live in the process Thank you!

4 4 Foreword This thesis is based on experimental work performed on an improved Gl/Ep composite, used in the manufacturing of new generation wind turbine rotor blades. The work included thorough material characterization as well as a dedicated experimental series aiming to understand, model and assess the axial, transverse and shear strength degradation of the unidirectional composite. Besides preliminary and benchmark testing, the exhaustive experimental schedule included 713 valid mechanical tests. From these 713 specimens, 222 were tested in tension/compression, 236 were subjected to constant-amplitude fatigue loading and 29 to spectrum loading. Another 217 specimens were used to investigate strength degradation due to constant-amplitude loading and 9 due to variable-amplitude loading. To execute this grand experimental plan, our 4-member team occupied 3 testing machines for 52 months. For the constant-amplitude loading required for material characterization and residual strength testing alone, 186,646,745 fatigue cycles were performed. This translated to about 8,3 machine hours. Conducting the remaining experiments, as well as specimen preparation and mounting, should also be considered in order to complete the description of the work plan. Although scrupulous indeed, the material characterization stage was just a prerequisite for the residual strength experimental task. In common practice, residual strength tests are a combination of a damaging process, e.g. fatigue loading, and a static test to failure. However, the aim of this dissertation was strength degradation assessment using non-destructive techniques. Residual strength tests were thus accompanied with acoustic emission monitoring, stiffness degradation measurements and acousto-ultrasonic scanning. This increased the duration of the experiments at least 4-fold, while rendering the procedure much more complicated. However, a unique database was formed, including data from all discrete steps. This extensive and combined information is a novel contribution in the field of non-destructive inspection. Acoustic emission monitoring and acousto-ultrasonic measurements were herein used to assess material strength degradation due to fatigue-induced matrix cracking. The goal was accomplished with remarkable success and reliable engineering AE and AU-based models were introduced. These validated schemes were based on the largest experimental database so far produced. Moreover, the proposed models were generalized, i.e. applicable in all damage states examined. As obvious this could seem for acousto-ultrasonics, this is not the case regarding acoustic emission measurements. Thus, from the acoustic emission side, this generalization renders an original contribution. AE-based models proved able to assess tensile and also compressive strength degradation. This is another novel achievement. In this thesis, the proposed AE models were superior to the respective descriptor-based AU schemes. However, although performance of the second, using novel descriptors, was more than adequate, wave propagation in the specimen under consideration was also studied. This area failed to produce new descriptors or schemes, however indicated damage-associated qualitative trends in the recorded signals. Several issues related to the acousto-ultrasonic experimental technique were underlined and the complexness of the problem depicted.

5 5 The experiments presented herein were performed in the frame of EC research project "OPTIMAT BLADES: Reliable Optimal Use of Materials for Wind Turbine Rotor Blades", ENK6-CT Partial funding was provided by the Greek Secretariat for Research and Technology, F.K Besides information recorded during acoustic emission and acousto-ultrasonics, all data is free for download in the official OPTIMAT BLADES site ( along with the relevant reports and publications. The rest of the data is available upon request. It is emphasized that no other partner of the OPTIMAT BLADES project, engaged in non-destructive condition assessment, managed to propose successful engineering NDT models.

6 6 Table of contents Foreword... 4 Table of contents... 6 Nomenclature Introduction Damage in composite materials Acoustic non-destructive methods Progress in acoustic emission Progress in acousto-ultrasonics Material characterization Materials Specimens Experimental procedure ISO [±45] S specimens Static tensile tests Constant-amplitude fatigue tests Variable-amplitude fatigue tests OB [9] 7 specimens Static tests Constant-amplitude fatigue tests Residual strength tests Experimental procedure Axial Young modulus measurements Acousto-ultrasonic tests Acoustic emission monitoring Experimental results ISO [±45] S specimens OB [9] 7 specimens Axial Young modulus measurements Acoustic emission ISO [±45] S specimens Model development Model validation Model implementation using alternative descriptors Filtering of AE data Robustness investigation Model implementation on OB [9] 7 specimens Failure modes: discussion Conclusions Acousto-ultrasonics: a phenomenological descriptor approach Acousto-ultrasonic descriptors Time domain... 61

7 Descriptor D 1 : stress wave factor degradation Descriptor D Auto/cross-correlation domain Descriptors D 2 -D Descriptor D Descriptor D Descriptor D Descriptor D Frequency domain Descriptor D Descriptor D Descriptor D Descriptors D 13 -D Empirical acousto-ultrasonic schemes Descriptor D 3 -based model A compound descriptor approach Pattern recognition schemes A supervised PR scheme An unsupervised PR scheme Conclusions Wave propagation considerations General experimental procedure Experimental results: wave propagation in the [±45] S specimen Signature of propagating waves Tone-burst excitation Broadband excitation Dispersion curve determination Basics on plate wave propagation Theoretical dispersion curves vs. experimental (using phase spectra) Theoretical dispersion curves vs. experimental (using TF representation) Influence of damage on dispersion curves: Theoretical estimation Wave propagation in aluminum: simulation and experiment Modeling of wave propagation in 4-mm aluminum plate Model vs. experiment mm aluminum specimen mm aluminum plate Discussion on discrepancies Equipment response Material variation Experimental noise Error in distance measurement Contribution of propagation medium Conclusions References

8 8 Plans and suggestions for future research Appendix A Homogenization of thick laminates (Pagano's long-wave approach) Appendix B Sachse dispersion curve determination (receivers placed at 1 and 12 mm from source) Sachse dispersion curve determination (receivers placed at 2 and 12 mm from source) Appendix C Theoretical group velocity determination Appendix D Validation of Cyberlogic Wave2 Pro v2.2: Bulk wave propagation in aluminum cube Curriculum Vitae

9 9 Nomenclature AE AMP ASTM AU AvF CA CFRP CNP CNT CSM DUR F R FRP E X EN f Gl/Ep G XY h HBM HDT HLT ISO M r MAE NDI NDT n N NNC PAC PDT OB PR PSD R RT S max SPR acoustic emission signal amplitude American Society for Testing and Materials acousto-ultrasonics signal average frequency constant amplitude carbon fibre-reinforced plastics signal counts-to-peak signal counts (or threshold crossings) chopped-strand mat signal duration Felicity ratio fibre-reinforced plastics Young modulus in the x-direction signal energy frequency glass/epoxy shear modulus in the x-y plane thickness Hottinger Baldwin Messtechnik hit definition time hit lock-out time International Organization for Standardization moment of order r modal acoustic emission non-destructive inspection non-destructive testing number of cycles applied number of cycles to failure nearest neighbor classifier Physical Acoustics Corporation peak definition time OPTIMAT BLADES pattern recognition power spectral density stress ratio signal rise time maximum fatigue stress supervised pattern recognition

10 1 STT STC SWF VA C G C P UD UPR UCS UTS WISPER X X R v XY ρ ω static tension static compression stress wave factor variable amplitude group velocity phase velocity unidirectional unsupervised pattern recognition ultimate compressive stress ultimate tensile stress WInd turbine reference SPEctRum ultimate stress residual strength Poisson s ratio in the x-y plane material density angular frequency

11 11 1. Introduction Combining good material properties and low weight, composites have become increasingly popular over the past decades among conventional, well-studied engineering materials. With their anisotropic nature and laminated structure allowing for enhanced design potential compared to metals, the widening use of composites in operating structures has turned the need for reliable inspection and condition assessment into an issue of great importance Damage in composite materials Unlike metals, failing due to a propagating critical crack, the inhomogeneous and anisotropic nature of composites renders a more complicated behavior: composite structures bear the applied design loads during the entire service life, while damage accumulates. High damage tolerance is thus another important advantage over metals. The main source of damage in a composite is mechanical and/or environmental loading. Several failure mechanisms are encountered during service: matrix cracking, debonding of the fibre-matrix interface, delaminations 1 and fibre breakage are common damage modes. Although this is their actual temporal sequence in general, propagation and coalescence of failure mechanisms are often simultaneous and therefore, damage in the composite can be regarded as the superposition of various failure modes. Damage accumulation, either localized or distributed throughout the volume of the composite, leads to degradation of the composite material mechanical properties (Reifsnider [1]). Although activated from external loading, damage mechanisms commence from inherent material imperfections due to manufacturing and handling of fibres and pre-pregs and the fabrication process of the laminates. Common flaws of this kind are "injured" fibres, micro-cracks in the matrix due to residual stresses, undesired inclusions, resin-rich regions and voids, pores or blisters due to gas entrapment. Besides propagating damage modes, extreme environmental conditions also cause material degradation. Thus, large temperature spans, moisture absorption and radiation could be considered as "passive" sources of damage Acoustic non-destructive methods Non-destructive inspection (NDI) of composite materials relishes rapid and broad development. Some common NDI methods are coin-tapping, visual inspection, ultrasonics, radiography, infrared and thermal testing, use of liquid penetrants and acoustic emission. While most NDI methods can delineate the damage, degradation of mechanical properties remains hard or even impossible to assess. 1 In the case of laminated composites

12 12 Acoustic methods, however, are able to reflect the integrated damage state. The scope of this dissertation is NDI assessment of distributed damage in glass/epoxy (Gl/Ep) fibre-reinforced (FRP) composites. For the reason explained above, the particular task was performed using acoustic methods, herein selected to be acoustic emission (AE) and acousto-ultrasonics (AU). The term "acoustic" refers to sound in general and should be discriminated from "audible" (.2 2 khz range). However, since the desired wavelengths in acoustic NDI methods are shorter than the size of defects, higher frequencies (ultrasound) are preferred. Most research on the use of acoustic methods for non-destructive inspection is concentrated on the detection of localized defects, generated either during fabrication or in-service. A considerable amount of publications is also focused on the more complicated, distributed damage, e.g. due to fatigue. Matrix cracking is one of the major damage mechanisms encountered in FRP composites during service. Although seemingly less critical than delaminations and fibre breakage, propagation and coalescence of matrix cracks precede and promote more severe damage modes (Reifsnider [1]). Characteristic consequences of matrix-dominated failure are debondings at the trailing edge or between stiffening components and the skin, in wind turbine rotor blades, and also material degradation due to ingress of fluids, in composite pipes. However, since formation of matrix cracks begins at sub-critical loading stages, appropriate non-destructive tools should contribute to reliable damage assessment throughout service. In most cases, however, acoustic emission and acousto-ultrasonics are not suggested as stand-alone tools, but are rather used to indicate qualitative trends or to complement other methods in the investigation of damage progression. Although a common outcome from this approach is that AE and AU signal parameters are, in general, correlated with damage accumulation, no robust models for remaining life or strength prediction have been proposed. Such NDI tools for the assessment of strength degradation, due to fatigue, in fibre-reinforced composites, exclusively via acoustic non-destructive measurements, are proposed in the present work. Reliable engineering models, based on acoustic emission and acousto-ultrasonic measurements, are established and validated in dedicated chapters. Residual strength prediction in composite specimens, featuring matrix cracking due to fatigue, is thus accomplished Progress in acoustic emission Acoustic emission is a well-established NDI method for structural components. Released from microstructural changes in the material, due to external reasons, AE is used for on-line inspection of components during operation or in maintenance intervals, the second case requiring an appropriate proof-loading (Wevers [2]). Load application is the most common source of acoustic emission, although other causes, e.g. impacts, friction, curing and phase transformation, should also be included. In the acoustic emission technique, transient stress waves resulting from damage progression are recorded using dedicated equipment. With proper sensor spacing, AE monitoring allows signal detection from the entire volume of the structure. However, inspection procedure demands

13 13 experience and methodicalness to ensure reliable results 2, optimum equipment selection and appropriate parameter adjustment. Interpretation of the gathered information, e.g. relating AE events to possible sources, is a nontrivial task. Indeed, the properties of the propagation medium and the sensor/equipment characteristics can mask AE signatures. Thus, universal AE signature determination might not be possible (Godin et al. [3]). During the earliest stages of development and due to constraints in computer resources, AE inspection was performed through the cumulative or frequency distributions of particular signal parameters, e.g. amplitude (AMP), energy (EN), rise time (RT), counts (CNT), duration (DUR), countsto-peak (CNP) (see Pollock [4]). Signal parameters are called "descriptors". Qualitative, descriptorbased assessment of fatigue damage can be found in e.g. [2] and [5]-[14]. To produce schemes of improved performance, pattern recognition (PR) approaches were used for simultaneous processing of groups of AE descriptors in a multi-dimensional space. For coupons subjected to static tension, unsupervised schemes (UPR) were endeavored in e.g. Anastassopoulos et al. [15] and Godin et al. [16]. In the former, a complete clustering procedure was introduced, including hints on descriptor selection, methods to estimate the number of classes, algorithms for data clustering and means for cluster validation. The main problem in the implementation of the proposed method was to distinguish overlapping failure mechanisms, e.g. when various damage modes produced similar AE signals or when the existing classes demonstrated bimodal amplitude distributions. As described in Godin et al. [16], this issue could be investigated through dedicated tests, producing a template class for the AE corresponding to each failure mechanism: tension in single fibres or fibre bundles gave an indicative class for fibre failure, tension in pure resin simulated matrix cracking, tension in 9º specimens matrix cracking and some decohesion and tension in 45º specimens produced a class representing decohesion and some matrix cracking. AE originating from particular plies in composite laminates tested in static tension was identified in Philippidis et al. [17], and classes of similar signals were related to characteristic loading stages. The resulting clustering was used to train a supervised (SPR) scheme and the classifier was validated on a new data set. Damage caused due to tensile loading was also characterized in Philippidis et al. [18], using unsupervised algorithms. An extensive comparison of several SPR algorithms was performed in Anastassopoulos et al. [19] and applied on ultrasonic signals from various kinds of simulated defects. Even use of PR techniques, however, was seldom adequate. In most studies published so far on unsupervised pattern recognition of AE signals, additional use of microscopic examination or other NDI methods was suggested to assist and validate the proposed schemes. The drawback in supervised pattern recognition, on the other hand, was that information on the resulting classes is required in advance. Although use of signal descriptors is practical, an exact description of the acoustic signal, i.e. the integrated imprint of material properties and microstructure, is not provided. To exploit more 2 In acoustic emission testing, results can never be reproducible

14 14 information from the AE waveforms, a succeeding trend, modal acoustic emission (MAE), developed parallel to the conventional acoustic emission technique. On that basis, Johnson et al. [2] suggested probable AE signatures for the waves generated from various micro-cracks, during tensile loading of Gl/Ep specimens. Several laminates, [/9 2 ] S, [9 2 /] S, [±45] S and [ 4 ], were used to separate the various damage mechanisms. In Pappas et al. [21], the MAE approach was used to define the AE signature of continuous organic, ceramic and carbon fibre bundle breaks due to tensile loading. In the recorded acoustic signals, the separate contributions of the data acquisition system, the wave propagation and the damage were depicted. In Giordano et al. [22], the spectral AE signature of fibre breakage was obtained through tension of single-carbon-fibre specimens. In Loutas et al. [23], processing of AE waveforms recorded during tensile loading of center-holed Gl/Pol coupons, using a wavelet-based scheme, related fibre failure to a particular frequency band. Among damage mechanisms, matrix cracking is observed earliest and although considered sub-critical, promotes the formation of delaminations and leads to fibre failure (see Gamstedt et al. [24]). Regarding transverse matrix cracks in particular, Tang et al. [25] and Toyama et al. [26] examined acoustic signals, captured in specimens subjected to tensile static or fatigue loading, in terms of modal characteristics. However, pertinent damage was associated to stiffness rather than strength degradation. A correlation of the Felicity ratio, F R, to the drop in stiffness during progressive tensile loading-unloading-reloading of carbon-carbon specimens is also presented in Gorman [27]. The relation, however, was based on a small number of specimens and suggested for simple loading cases matrix cracking damage. In general, use of F R as an empirical accept/reject criterion for filament-wound FRP pressure vessels is common. Another empirical approach is found in Hill et al. [28], where transverse fibre-resin bonding was evaluated through statistical Weibull parameters extracted during AE monitoring of tensile tests. The Weibull model, used for prediction of the surviving number of fibres in an on-axis loading, was therein customized to receive AE descriptors as input. A similar concept was earlier engaged in Okoroafor et al. [29], where the tensile strength of as-received and degraded Kevlar-49, E-glass and carbon fibres was related to AE parameters. In Unnthorsson et al. [3] and Unnthorsson [31], a successful failure criterion for a CFRP prosthetic foot, subjected to cyclic loading, was presented. The method, intended to provide notice of impending failure rather than perform actual life prediction or damage assessment, relied on a large experimental effort and was validated through comparison with a conventional displacement criterion. Empirical failure criteria based on AE recorded during tensile loading of Gl/Pol [ 3 ] T, [±45 3 ] T and [/±45] S specimens were also proposed in Philippidis et al. [17], aiming to assess the coupon remaining life. Implementation of the criteria relied on previous application of a UPR scheme on the union of the recorded AE data, to depict the most meaningful classes. Then, a supervised classifier was trained and validated on a separate experimental set, comprising [±45/] S specimens. Life prediction schemes of a more quantitative character were developed in Bhat et al. [32]. AE data was recorded throughout tensile fatigue loading, at one particular stress level. A PR algorithm was then used to cluster the data into three classes. These classes were shown to correspond to the three main failure mechanisms, each being dominant at a particular stage of fatigue life. However,

15 15 the class presumed to consist of matrix-crack-induced AE events bore no useful conclusions. Nkrumah et al. [33] used a static proof-loading to estimate remaining life after fatigue. The procedures developed therein relied on limited experimental data and no robust, validated predictive models were proposed. Two sophisticated theoretical models were introduced in Yang et al. [34], to assess tensile strength degradation due to localized erosion damage in [±45//±45/] S specimens. Using Weibull statistics and the AE data recorded during a post-impact tensile test, the curve of cumulative AE vs. stress was predicted. Performance of the second model, using an "erosion damage parameter" and a "stress delay parameter", was not as successful. Few works use AE techniques for actual residual strength prediction of composites after fatigue. An elaborate approach is encountered in Caprino et al. [35], using specimens subjected to constant-amplitude loading at one particular stress level. Except for low-cycle fatigue, a conventional AE parameter (CNT) was well-correlated with residual strength. The same experimental data was processed using a neural networks approach in Leone et al. [36], producing more accurate residual strength predictions. In Philippidis et al. [37], a robust and reliable engineering model predicting degradation of inplane shear strength of a UD composite, due to fatigue, was introduced. The model, presented in two versions, was established and validated on an adequate population of 87 ISO standard 25-mm [±45] S Gl/Ep specimens, undergone CA sinusoidal loading at stress ratio R=.1. To investigate the influence of various loading configurations on damage accumulation, 1 stress level and life fraction combinations were accommodated. The scheme was based on AE monitoring of pre-fatigued specimens during a static proof-loading. Residual strength assessment was performed through a conventional AE descriptor, i.e. CNT, although other AE parameters also proved applicable. The procedure, however heuristic, was reliable in residual strength estimation of composite specimens featuring fatigue damage. As mentioned above, the residual strength predictive model was established on CA fatigue tests. To further validate the method, two additional datasets were used. The validation sets again comprised ISO 25-mm [±45] S Gl/Ep specimens: one consisted of coupons identical to the training set, subjected to tensile spectrum loading, and the second coupons made of another resin matrix, under R=.1 CA loading. The model proved applicable in both cases. Two variations of the same model were introduced. The former scheme, henceforth referred to as "model M 1 ", required a priori information on maximum loading stress. Using this information, a master curve valid for all stress levels and life fractions was obtained. The model was thus suggested for applications where cyclic loading was either fixed or recorded on-line, i.e. when the maximum stress encountered during loading was available. In cases of unknown loading histories a second scheme was recommended, "model M 2 ", demanding no information on previous loading. The methods developed in Philippidis et al. [37] proved capable of predicting the residual static strength of coupons undergone constant or variable-amplitude fatigue, at all stress levels and loading durations. Although applied on tensile loading of the [±45] S coupon, recommended in international standards for shear testing, the work suggested indicative guidelines for implementation in other laminates and loading configurations. Of course, in a generalized laminate

16 16 where damage is not matrix-dominated, as in the [±45] S specimen, all possible failure mechanisms should also be considered. Again, a dedicated database might be required for each application. As argued in Philippidis et al. [37], implementation of the proposed AE models for residual strength assessment after fatigue is restricted to cases where matrix cracking is the dominant damage mode, at least up to the proof-loading magnitude. Adopting this outcome in Philippidis et al. [38], the models were applied on an additional coupon configuration, 145-mm long [9] 7 specimens, made of the same material as the original model dataset. Results from R=.1, R=-1 and R=1 CA loading were presented, suggesting the AE model to be applicable in tensile, reversed and compressive fatigue, although e.g. R=-1 is shown to be more detrimental than R=.1 (see for example Gamstedt et al. [24] and El Kadi et al. [39]). Thus, in contrast to the concluding remark in Maier et al. [6], experiments at different R-ratios could indeed be compared 3. Another major accomplishment of that work (Philippidis et al. [38]) was using the same model for compressive residual strength estimation. Indeed, for R=-1, both tensile and compressive residual strength tests were available. Failure, both in tension and compression, was matrixdominated and although the respective failure modes are distinguished as "mode A" and "mode C" in current damage-mode-based failure criteria (e.g. Puck et al. [4]), model response seemed to follow a universal trend. Later than the models proposed in Philippidis et al. [37]-[38], use of AE data in tensile residual strength assessment was also suggested in Minak et al. [41]. Therein, damage was induced via transverse loading. Two important drawbacks were, however, involved: implementation of the methodologies was much more complicated and both strain and AE data was required as input information, strain being the one imposed during transverse loading Progress in acousto-ultrasonics Acousto-ultrasonics, introduced by A. Vary in the late 9's, is a contraction of "acoustic emission monitoring and ultrasonic characterization" or "acoustic emission simulation with ultrasonic sources". The original idea, however, was conceived by D. M. Egle (see for example Egle et al. [42]) long before Vary, under the term "simulated emission". As in ultrasonics, loading is not needed in the acousto-ultrasonic technique: stress waves are produced by an external source of excitation. The propagating waveforms are captured at certain distances from the source, using receiving transducers. Thus, the acousto-ultrasonic method is actually ultrasonic testing in nature. The main difference of acousto-ultrasonics with the traditional ultrasonic method lies in defect scale and wavepath characteristics. In ultrasonic flaw detection, ideal for the inspection of metal structures, defect size is comparable to the beam wavelength. In addition, wave propagation paths 3 To be fair, however, one should mention that the work of Maier et al. was conducted on [ 2 /±45/ 2 /±45/9] S carbon fibre-reinforced polyimide specimens. Furthermore, from the fatigue tests at R=.1 and R=-1 presented, R=-1 specimens failed in compression due to buckling, in contrast to Philippidis et al. where the corresponding failure mode was tensile

17 17 are well-defined. Ultrasonic waveforms are examined for additional echoes (pulse-echo mode) or reductions in magnitude (through-transmission mode). Empirical models for assessment of damage due to fatigue loading of carbon-fibre [45//- 45/9] 2S composites, using C-scan ultrasonic readings, were introduced in e.g. Pantelakis et al. [43]- [44]. Therein, a non-destructive damage parameter reflecting the integrated damage state in the volume of the specimen was used to estimate axial stiffness and strength degradation. As fibre breakage is improbable to delineate using the C-scan technique, model implementation was suggested for low stress levels where delaminations are considered as the major damage mode. Nevertheless, the methods proved applicable for various durations and stress levels of reversed constant or variable-amplitude loading. In acousto-ultrasonic measurements, on the other hand, the signal is a result of multiple interactions with the material microstructure as well as a number of existing (sub)critical flaws: a long, "random walk" wavepath is thus desirable (pitch-catch mode). With much more information than the simple presence (or absence) of a defect contained in the recorded signal, acoustoultrasonics is a most advantageous NDT method for the inspection of large composite structures. However, AU signals are much harder to interpret. An AU approach, introducing the famous "stress wave factor" to estimate tensile and shear strength variations associated with fibre-resin bonding, void content or fibre volume fraction, was endeavored in Vary et al. [45]. The stress wave factor was an NDT parameter defined as e=grn: "g" was the automatic reset time of a timer, "r" the pulse repeat rate and "n" the number of oscillations exceeding a fixed threshold. Gr/Ep [ 8 ], [1 8 ], [9 8 ], [/±45/] S and [±45] S specimens were used, none containing intentional defects. With the stress wave factor serving as a measure of stress wave energy transmission, weak areas along the gauge length were located with great success. Nondestructive predictions were validated with results from tensile tests to failure. A simpler version of the stress wave factor, and the most popular one, however, is the one proposed in Williams et al. [46], i.e. the number of oscillations exceeding a pre-determined threshold. In Williams et al. [46], this parameter is named "SWF" and is used to assess tensile strength degradation due to impact damage, in Gr/Pol [ 1 ] specimens. However, as stated in Egle et al. [42], parameters computed from the recorded AU (or AE) signals should not be considered usable unless the length of the wavepath remains constant throughout the entire experimental procedure: distortion due to geometric dispersion and damping due to material attenuation 4 otherwise render such time-domain parameters incomparable. Considering that dispersion does not affect the span of the signal spectra, data processing in the frequency domain thus flourished. Govada et al. [47] investigated several spectral AU parameters and correlated them to fatigue-induced damage development in Gr/Ep laminates, expressed through stiffness degradation. In Talreja [48], a respective set of AU parameters was also used in quality control during fabrication of Gr/Ep composite components as well as in delamination detection. A major finding was the dependence of a certain AU descriptor (area of power spectrum) 4 Assuming no reflections, the causes of attenuation are diffraction, scattering and absorption

18 18 on fibre orientation of UD composites: the observed trend followed the corresponding stiffness behavior. However, resorting to spectral methods and/or constant-length wavepaths is often impractical or undesirable. On the other hand, issues such as flaw location in e.g. large dispersive media are impossible to resolve using threshold-defined conventional descriptors. Thus, while acoustoultrasonics were conceived and developed through scalar parameters extracted from the recorded signals, as in acoustic emission, the succeeding trend in AU data processing was again waveformbased. Thus, wave propagation also had to be studied. Besides the inherent issue of attenuation, investigation of dispersion was required. Dispersion is the frequency dependence of phase velocity, i.e. the propagation speed of each frequency component. Possible causes of this elusive phenomenon (Sachse et al. [49]) are the presence of structure boundaries (geometric dispersion), scattering (in inhomogeneous materials), irreversible absorption or dissipation of wave energy (dissipative dispersion), frequency dependence of material constants (material dispersion), and dependence of propagation speed on signal amplitude (non-linear dispersion). In linear causal systems, dispersion and attenuation are linked through the Kramers-Kronig relations (see O' Donnell et al. [5]). Bulk wave propagation in unbounded free space can thus be dispersive, provided that material attenuation is frequency-dependent (Droin et al. [51], Wear [52]). In a similar manner, propagation in waveguides is dispersive even for non-dispersive materials. Since the laminated nature of composite materials promoted their use on plate and shell-like structures, composite plates and shells are used in a vast range of high-performance applications, including aerospace components, pipes, pressure vessels and wind turbine rotor blades. Substantial research was thus conducted on Lamb and plate wave propagation (e.g. Gorman [53], Alleyne et al. [54], Prosser et al. [55]). Practical tools for in-situ inspection were also developed. For instance, the F-scan TM presented in Huang et al. [56] was shown to perform stiffness measurements in composite plates and sandwich structures, as well as detection of delamination, impact damage and debonding. The method was based on the propagation characteristics of the A mode. In subsequent studies, a fusion of AU parameters from several domains was performed. Evaluation of stress level and fatigue damage in PVC specimens under tensile loading was performed in Haddad et al. [57], using a large number of AU parameters and an SPR scheme. Therein, the influence of the coupling agent was also studied. In this thesis, the acousto-ultrasonic technique was investigated in whole. Various approaches were adopted to process the acousto-ultrasonic measurements: from the simplest, using individual AU descriptors, to more complex ones engaging groups of descriptors. Wave propagation in the particular [±45] S Gl/Ep specimens was also studied, aiming to relate AU measurements to strength degradation due to matrix cracking. A large database of AU measurements was produced, on the 87 [±45] S Gl/Ep specimens described in the previous section. Damage was introduced to the specimens via constant-amplitude fatigue loading. Two acousto-ultrasonic experiments were performed on each specimen: one in the virgin and one in the damaged state.

19 19 Several AU descriptors from various domains, found in the literature or introduced herein, were thus compared and evaluated in terms of their potential to reflect matrix damage in [±45] S Gl/Ep specimens. However, correlation of individual AU parameters with residual strength was found to be mediocre. In an attempt to produce more effective AU schemes, a custom technique using a "compound descriptor", determined as a linear combination of selected NDT parameters, was introduced. Performance of the resulting scheme in residual strength estimation was ameliorated and although improvement was far from spectacular, its simple and costless implementation rendered the proposed method quite appealing. In general, performance of the compound descriptor proved superior to conventional SPR algorithms. Even more so, since the compound descriptor approach provides an engineering model correlating descriptor values to residual strength, rather than separating the data into a desired number of classes. Regarding this generalized problem of data clustering, an example of a UPR scheme was also given. The unsupervised classifier created classes of rational geometrical structure, although the particular results could not be evaluated in a strict sense. To complement the investigation on the potential of the acousto-ultrasonic method, recorded waveforms were also processed as to reveal the modal characteristics of the propagating waves. Plate wave symmetric and antisymmetric modes were detected, corresponding dispersion curves were calculated and experimental signals were simulated using numerical modeling. However, although the problem was studied in a considerable level, association of modal characteristics to matrix damage remained qualitative.

20 2 2. Material characterization A comprehensive experimental program was performed in order to characterize the composites under consideration in terms of static mechanical properties and fatigue behavior. This stage, however scrupulous, was a prerequisite for subsequent residual strength testing Materials The main experimental series was performed on specimens of the same Gl/Ep material, i.e. same glass reinforcement and resin matrix. This material, named "OB" or "reference" material (see Jacobsen et al. [58]), was the composite investigated during the OPTIMAT BLADES (OB) project. The reinforcement of the OB material was an 115 g/m 2 non-woven unidirectional glass roving, stitched together with a chopped-strand-mat (CSM) layer of 5 g/m 2 with 5 g/m 2 of off-axis PES yarn stitches. Total weight was 1258 g/m 2 and glass fibre density 259 kg/m 3. The resin used was Prime 2 from SP Systems, mixed with slow hardener. The cured resin had a density of 1145 kg/m 3. Laminates were post-cured at 8 C for 4 hours, resulting in a fibre content of 73±3% by weight and 55±3% by volume. The nominal average thickness of each layer was.88 mm. A peel-ply was used during fabrication, producing a somewhat rough resin-rich surface finish to promote stable placement of extensometers. A smaller number of tests was conducted on an "alternative" material. The matrix of the alternative material was from a resin batch other than that of the main set, leading to variations in material behavior Specimens Damage in FRP components, due to fatigue, was herein simulated on 2 coupon configurations: 25x25 [±45] S and 145x25 [9] 7 specimens, dimensions given in mm. Specimens were produced and provided by LM Glasfiber. The manufacturing method was vacuum infusion. All coupons were made of the reference (OB) material except for a small number of [±45] S specimens, made of the alternative material. Being 25 mm long, [±45] S specimens were intended for tensile loading (see Figure 2.1a). The particular laminate and loading configuration is recommended in ISO 14129:1997(E) standard [59] for the investigation of the in-plane shear properties of the unidirectional material. This method prevailed amongst others in the relevant review of Lee et al. [6] and is the one used in Yang et al. [61] and Philippidis et al. [62], on shear strength degradation due to CA loading. To the knowledge of the author, no other works besides [61] and [62] are published so far on the subject. One of the aims of the OB project was to design a specimen suitable for universal testing, i.e. to be used both in tension and compression, static or fatigue loading, on-axis or off-axis direction. The short 145-mm [9] 7 specimen, illustrated in Figure 2.1b, was the outcome of this investigation for the transverse loading direction. Mechanical properties derived using this coupon were in perfect

21 21 agreement with the respective ISO ones, as discussed in Philippidis [63]. Thus, albeit failure planes were near the tab area, the experimental results were considered valid and the failure modes acceptable. Figure 2.1. Experimental specimens. (a) [±45] S ISO 14129:1997(E), (b) OB [9] Experimental procedure ISO [±45] S specimens Static tensile tests Ultimate tensile stress, UTS or X, tensile Young modulus in the axial direction, E x, and Poisson s ratio, v xy, of the reference material were determined through 26 static tensile tests (STT), to derive a reliable statistical static shear strength distribution of the stochastic behavior of the Gl/Ep composite. Experiments, outlined in Philippidis et al. [64], were performed in displacement control mode, at a cross-head speed of 2 mm/min, in accordance to ISO 14129:1997(E) [59] specifications. The 25 kn set-up of a 25 kn hydraulic MTS test machine was used. Each coupon was equipped with a 6-mm strain gauge rosette on one side and a single 6-mm strain gauge on the opposite. All strain gauges were HBM, with a nominal electrical resistance of 35 Ohms. Strains and loaddisplacement readings from the test machine were recorded via an HBM Spider8 data acquisition device. The mechanical properties of the alternative material were also determined, through 5 similar tensile static tests (Philippidis et al. [65]). The average tensile strength of the alternative material was found to be about 85% of the one of the reference material. Mechanical properties of both composites are listed in Table 1. The UTS of the reference material could be modelled using a bi-parameteric Weibull distribution, as shown in Figure 2.2. UTS results from the static tensile tests are illustrated in Figure 2.3. Table 1. Mechanical properties, [±45] S specimen Material E x (GPa) v xy G 12 UTS (GPa) (MPa) Reference Alternative

22 STT Weibull a= b= CDF UTS (MPa) Figure 2.2. Tensile static strength and respective bi-parametric Weibull distribution, [±45] S specimen Constant-amplitude fatigue tests A set of 17 reference material coupons was tested in CA fatigue, at stress ratio R=.1 5, in load control mode and until specimen separation. The determined S-N curve, presented in Figure 2.3, is given through: S max = N (MPa) (1) "S max " is used to denote maximum fatigue stress and "N" the corresponding number of cycles to failure. Fatigue behavior of the alternative material, inferior to that of reference material, was also investigated through 14 similar CA tests at R=.1. Results are demonstrated in Figure 2.3. The corresponding S-N curve equation was: S max( alter) = N (MPa) (2) Fatigue data was treated according to the statistical method introduced in Whitney [66], to provide reliability bounds for the determined S-N curves. The probabilistic formulation was expressed as: S max 1 1 = kf S [ ] afk ln PS (N) f N (3) 5 Stress ratio R is equal to S min over S max

23 23 Eq. (3) describes the S-N curve at a desired probability of survival, P S (N). Constants a f, k f and S were found equal to 4.43, and 1.873, for the reference material and 5.826, and for the alternative material. The stress level definitions produced during CA fatigue tests, for subsequent use in residual strength testing, are listed in Table 2. Test frequencies, f, varied depending on stress level, so as to keep constant dissipated energy (Krause [67]). Indeed, temperature on the coupon surface during all fatigue tests was maintained below 35 C. Lab air-conditioning and the use of a cooling fan were thus required. Temperature measurements were performed using Pt1 thermo-resistances, placed on the side of the lower-grip tab area with thermo-conducting glue S max (MPa) STT (reference) STT (alternative) CA R=.1 (reference) CA R=.1 (alternative) S-N (reference) S-N (alternative) N Figure 2.3. Tensile static and fatigue tests and S-N curves at R=.1 for the reference and the alternative material, [±45] S specimen Table 2. Stress level definitions for the reference and the alternative material, [±45] S specimen Stress N level (cycles) index S max (MPa) f Reference material Alternative material (Hz)

24 Variable-amplitude fatigue tests A set of 1 variable-amplitude fatigue tests were also performed on the reference material, see Figure 2.4a. Experiments are described in Philippidis et al. [68]. Specimens were subjected to the "new WISPER" spectrum, introduced in Soker et al. [69]. Two maximum stress levels were investigated. New WISPER was based on the WISPER spectrum. WISPER, WInd turbine reference SPEctRum, was established on measurements conducted on 9 wind turbines, with diameters ranging from 11.7 to 1 m. Rotor blades were made of steel, GRP or wood. The sequence comprised load cycles, representing two months of operation. New WISPER, on the other hand, was based on measurements performed on 7 wind turbines, with diameters ranging from 37 to 8 m. Rotor blades were made of GFRP or CFRP. The series consisted of load cycles and represented two months of operation (Soker et al. [69]). The new WISPER spectrum is demonstrated in Figure 2.4b. This is the general form, expressed in bins valued from 5 to 59. Level 59 corresponds to the "normalized" S max value. S max (MPa) S max = passes -1/12.37 (MPa) VA data S-N curve Passes (a) Bins 6 55 New WISPER spectrum (1 pass) (b) Time samples x 1 4 Figure 2.4. (a) Variable-amplitude fatigue tests, reference material, [±45] S specimen, (b) new WISPER spectrum, used in variable-amplitude fatigue loading OB [9] 7 specimens Static tests Ultimate tensile and compressive stress (UTS, UCS) and elastic properties of the UD material, in the transverse direction, were determined through 25 tensile (STT) and 26 compressive (STC) static tests, conducted in displacement control mode on a 1 kn servo-hydraulic Dennison-Mayes DH 1S test rig, equipped with a 47 MTS controller. Tensile experiments were performed at ISO-recommended strain rate (see EN ISO 527-5:1997(E) [7]), resulting in a crosshead speed of.25 mm/min. For better resolution in load application, a configuration calibrated for a maximum load of 25 kn was used. Each coupon was

25 25 instrumented with a 6-mm strain gauge rosette on one side and a single 6-mm strain gauge on the opposite. UTS was thus found equal to MPa, tensile Young modulus in the axial direction (i.e. transverse to the fibres), E 2T, was GPa and minor Poisson s ratio, v 21,.95. Compressive tests were conducted at 1 mm/min crosshead speed, in accordance to ISO 14126:1999(E) [71]). Specimens were equipped with a 6-mm single strain gauge on each side. UCS was MPa and compressive Young modulus, E 2C, was GPa. Again, strains and load-displacement readings from the test machine were recorded using an HBM Spider8 data acquisition device. All static experiments are outlined in Philippidis et al. [72] Constant-amplitude fatigue tests Fatigue tests were performed on the 25 kn set-up of a 25 kn MTS test machine, in load control and until specimen separation. A set of 15 coupons was tested at stress ratio R=.1, 32 experiments were performed at R=-1 and 24 at R=1. Fatigue response is reported in Philippidis et al. [73]. Stress level definitions, produced during CA fatigue tests for subsequent use in residual strength testing, are listed in Table 3. Experimental results are summarized in Figure 2.5 and Figure 2.6 along with the respective, S-N curves given through: S max 1 k = S N (MPa) (4) For R=.1, S and k are equal to MPa and while for R=-1 the respective values are MPa and For R=1, S max represents the absolute S min value and S, k are equal to MPa and For the sake of illustration, static tests in Figure 2.5 and Figure 2.6 are shown to correspond to a fatigue life of N=1 instead of N=1. Table 3. Stress level definitions for the CA R=.1, R=-1 and R=1, OB [9] 7 specimen Stress N level (cycles) index S max (MPa) (Hz) R=.1 R=-1 R=1 R=.1 R=-1 R=1 1A f

26 26 S max (MPa) STT CA R=.1 CA R=-1 S-N R=.1 S-N R= N Figure 2.5. Static tensile tests, fatigue data and S-N curves at R=.1 and R=-1, OB [9] 7 specimen STC CA R=1 S-N R=1 abs(s min ) (MPa) N Figure 2.6. Static compressive tests, fatigue data and S-N curve at R=1, OB [9] 7 specimen

27 27 3. Residual strength tests The research presented herein was on an improved Gl/Ep composite, for use in new generation wind turbine rotor blades. This included thorough material characterization (see Chapter 2) as well as a dedicated experimental series aiming to investigate strength degradation. In the case a behavior other than "sudden death" were to be observed, residual strength as a function of induced damage would be modeled and predicted. The plan of the experimental program can be found in Philippidis et al. [74]. The aim of this dissertation was strength degradation assessment using non-destructive techniques. Residual strength experiments were thus performed, accompanied with acoustic emission monitoring, stiffness degradation measurements and acousto-ultrasonic scanning. An overview of the experimental program is given in the corresponding OB deliverable report, Philippidis et al. [75]. The source of damage was selected to be sinusoidal loading, both for [±45] S and [9] 7 coupons, except for a small number of [±45] S specimens where a variable-amplitude spectrum was applied. The experimental database comprised specimens subjected to several stress level and life fraction combinations, to investigate the influence of various loading configurations on damage accumulation. Designed for tension, [±45] S specimens were subjected to R=.1 constant-amplitude or tensile variable-amplitude loading, and then tested in tension until failure. On the other hand, [9] 7 coupons were pre-fatigued at R=.1, R=-1 or R=1 stress ratio and residual strength tests either in tension or compression were performed. Acousto-ultrasonic inspection and measurements of axial Young modulus degradation were performed both on the virgin and the damaged material. This means that coupons had to be removed from the test machine and remounted at least once, whereas acoustic emission was recorded during residual strength test to failure. Although residual strength testing became extremely time-consuming, a unique, most interesting experimental database was produced, including results from all three separate measuring procedures along with the actual strength degradation findings Experimental procedure Axial Young modulus measurements Prior to fatigue, coupons were loaded up to their corresponding constant-amplitude cyclic S max. Via these tests, performed in displacement control at the crosshead speed of the corresponding static tests, Young modulus of the virgin material, E A, was calculated (EN ISO [7]). Two HBM clip gauges in tandem were used for the measurement, see Figure 3.1, the gauge length being 25 mm. Test was performed on the 25 kn set-up of a 1 kn servo-hydraulic Dennison Mayes DH 1S test rig, equipped with a 47 MTS controller. Data acquisition, i.e. strains from the clip gauges and load

28 28 and displacement from the test machine, was performed via an HBM Spider8 device. Test was repeated in all specimens after fatigue. Figure 3.1. Axial Young modulus measurement, [±45] S and [9] 7 specimen Acousto-ultrasonic tests An AU measurement, illustrated in Figure 3.2, Figure 3.3 and Figure 3.4 for a [±45] S specimen, was conducted on the undamaged material. Two broadband, 2-75 khz, miniature PAC transducers (5.8 mm in diameter), model "Pico", one serving as pulser and the other as receiver, were placed on opposite sides of the test specimen and quite near to the tabs, on marked spots: the wavepath ran along the specimen diagonal. The face-to-face response of the sensors in a broadband negative spike excitation is demonstrated in Figure 3.5a, Figure 3.5b and Figure 3.5c. Grease for roller bearings served as couplant. Sensors were mounted on the [±45] S specimens using metal jigs (see Figure 3.3a) and on the [9] 7 ones using elastic straps (Figure 3.3b). Several lead breaks (Hsu pencil source excitation, see ASTM E [76]) ensured good sensor coupling. This procedure, conducted before each AU measurement, also ascertained that the performance of the transducers remained stable throughout the entire testing period. Indeed, variations in the sensors response due to possible damage or aging were not observed. The Hsu source was a mechanical pencil with.5-mm diameter, 3-mm length HB lead. Although no Nielsen shoe was used, effort was made to keep a 3 o angle between lead tip and coupon surface. The instrumentation included a PAC wave generator, used to provide a.3 msec sine-sweep excitation of 1-2 khz (Figure 3.5d). Coupons were supported on foam material in the tab areas, to attenuate reflected waves. Captured signals were amplified using a PAC model 122A preamplifier, with a 4 db gain and no filters. Each waveform contained 512 samples. Sampling rate was 1 MHz, pre-trigger time -3x1-6 sec and threshold was fixed at 4 db. A 2-channel PAC MI-TRA

29 29 custom board (1-2 khz) was used for data acquisition. The same AU measurement was also performed on the damaged coupons. Figure 3.2. Acousto-ultrasonic experimental set-up Figure 3.3. Sensor arrangement in acousto-ultrasonic measurements, [±45] S and [9] 7 specimen

30 3 Figure 3.4. Schematic of the experimental set-up used for acousto-ultrasonic testing (a) 4 (b) Signal amplitude (Volts) PSD (db) Volts Time (μsec) (c) Volts f (khz) (d).4 2 f (MHz).3.2 f (MHz) Time (μsec) Time (μsec) Figure 3.5. Face-to-face response of the sensors in (a) pulser excitation, time domain, (b) pulser excitation, frequency domain, (c) pulser excitation, time-frequency representation and (d) sinesweep excitation, time-frequency representation

31 Acoustic emission monitoring Acoustic emission was monitored during the static residual strength tests to failure, see Figure 3.6. Experiments were performed in displacement control, at the crosshead speed of the corresponding static tests. A 1 kn servo-hydraulic Dennison Mayes DH 1S test rig, equipped with a 47 MTS controller was used for the purpose. A PAC 2-channel MISTRAS 21 custom board (1-2 khz) was used to extract and record conventional AE descriptors from the transient stress waves. One Pico sensor, placed in the middle of the gauge length, and same pre-amplifier as in the AU tests were used. The transducer was mounted on the coupons using a metal jig (see Figure 3.7) and grease as coupling agent. Residual strength was recorded via both an HBM Spider8 device and the AE board. System timing parameters PDT (peak definition time), HDT (hit definition time), HLT (hit lock-out time) were set to 5, 15 and 3 μsec respectively. Threshold was 4 db, fixed, since receiver was broadband and specimen dimensions small. For instance, use of floating amplitude threshold is suggested in Godin et al. [16], claiming to thus reduce the influence of sensor resonance on the AE data. Figure 3.6. AE monitoring during residual strength test to failure, [±45] S and [9] 7 specimen Figure 3.7. Sensor mounted on specimen for AE monitoring, [±45] S specimen

32 Experimental results ISO [±45] S specimens Specimens were subjected to tensile constant (R=.1) or variable-amplitude fatigue loading. The main experimental program comprised a set of 87 reference material coupons. For each coupon, one out of 4 specific fatigue stress levels was used, corresponding to 43%, 5%, 57% and 7% of the nominal reference material ultimate stress, equal to MPa. Respective expected fatigue lives, N, i.e. corresponding to P S (N)=5%, were 1 6, , and cycles. Duration of the CA loading reached up to 2, 5 or 8% of the estimated life. Two independent experimental sets were used to validate the proposed schemes. One was a small set of 9 reference material coupons, subjected to variable-amplitude loading. VA specimens were fatigued using the new WISPER spectrum until half of the expected passes to failure (5% life fraction). The other set consisted of 16 alternative material coupons, subjected to CA fatigue at three respective stress levels and for 2, 5 or 8% life fraction. The number of tests corresponding to each configuration is listed in Table 4. Table 4. Number of [±45] S coupons for each loading configuration Stress level index S max N n/n (MPa) (cycles) 2% 5% 8% VA passes 5 VA passes Material Reference Alternative Residual strength experiments were performed at a constant crosshead speed of 2 mm/min. Experimental results, reported in Philippidis et al. [77], are presented in Figure 3.8 for the reference and in Figure 3.9 for the alternative material. At each stress level, there is clear strength degradation of up to 4% of the UTS, as fatigue cycles increase. This is in accordance to e.g. Pantelakis et al. [43]-[44] where a 3% drop in the residual strength of pre-fatigued carbon-fibre composites was observed. Horizontal reference lines in Figure 3.8 and Figure 3.9 are used to indicate the mean value (solid lines) and scatter band (dashed lines) of the UTS, determined in the respective static tests for material characterization. Note that while N is used to denote cycles to failure, n represents the

33 33 number of cycles that a specimen is subjected to, at life fraction n/n. Residual strength is denoted as "X R " nominal UTS 1 9 X R (MPa) S-N curve 78.3 MPa 63.6 MPa 55.6 MPa 48.5 MPa n Figure 3.8. Tensile residual strength test results and S-N curve at R=.1, [±45] S reference material nominal UTS 9 X R (MPa) S-N curve 7. MPa 58.1 MPa 45.6 MPa n Figure 3.9. Tensile residual strength test results and S-N curve at R=.1, [±45] S alternative material OB [9] 7 specimens For the [9] 7 specimens, residual strength tests were performed at a crosshead speed of.25 mm/min in tension and 1 mm/min in compression. For better resolution in tensile load application, a test machine configuration calibrated for a maximum load of 25 kn was used. Experiments are reported in detail in Philippidis et al. [78].

34 34 Static tests to failure were performed on specimens pre-fatigued at three stress ratios, R=.1, R=-1 and R=1. For each coupon, one out of 5 specific fatigue stress levels was used, corresponding to expected fatigue lives, N, of 1 6, 2 1 5, 5 1 4, or 1 3 cycles. Duration of the CA loading reached up to 2, 35, 5 or 8% of the estimated life. The respective stress levels, for each stress ratio, are given in Table 5. For R=1, S max corresponds to the absolute S min value. The number of tests corresponding to each loading configuration is also listed in Table 5. At R=.1, a total of 17 [9] 7 coupons was used whereas 19 [9] 7 coupons were tested at R=1. Residual strength tests of the respective specimens were tensile. However, at R=-1, a total of 31 experiments was performed, with 2 coupons tested in tension and 11 in compression. Stress levels for residual strength testing at R=-1 do not match the respective S-N curve, given in Table 3, as at the time CA experiments for R=-1 S-N curve determination were not concluded. Residual strength test results are presented in Figure 3.1 to Figure Horizontal reference lines denote the mean UTS or UCS value (solid lines) and corresponding experimental scatter band (dashed lines). As mentioned above, UTS was found equal to MPa and UCS to MPa. Although tensile strength degradation was considerable, all measured values of compressive residual strength fell in the static UCS scatter band. Table 5. Number of [9] 7 coupons for each loading configuration Stress ratio S max (MPa) N (cycles) n/n (tensile RS) n/n (compressive RS) 2% 35% 5% 8% 2% 5% R=.1 R=-1 R=

35 nominal UTS 5 X R (MPa) S-N R= MPa 31.9 MPa 22.5 MPa n Figure 3.1. Tensile residual strength test results and S-N curve at R=.1, OB [9] 7 specimen nominal UTS 5 X R (MPa) S-N R= MPa 25.1 MPa 17.6 MPa n Figure Tensile residual strength test results and S-N curve at R=-1, OB [9] 7 specimen

36 nominal UTS 5 X R (MPa) MPa MPa MPa MPa n Figure Tensile residual strength test results after CA R=1 fatigue loading, OB [9] 7 specimen MPa 25.1 MPa 17.6 MPa X R (MPa) nominal UCS n Figure Compressive residual strength test results after CA R=-1 fatigue loading, OB [9] 7 specimen

37 37 4. Axial Young modulus measurements As expected, axial Young modulus of both [±45] S and [9] 7 virgin materials, E A, was uncorrelated to residual strength. However, for damaged [±45] S specimens and although correlation between strength and stiffness was moderate, there was an obvious trend (see Figure 4.1). A smaller stiffness drop of about 1% was also reported in Pantelakis et al. [43]-[44], in carbon-fibre-reinforced composites Virgin Damaged 15 X R (MPa) (GPa) E x Figure 4.1. Tensile residual strength vs. E x, virgin and damaged [±45] S specimens, reference material For the damaged [9] 7 specimens, on the other hand, modulus variations could not be correlated with residual strength. This is also documented in El Kadi et al. [39]. A possible explanation lies in the failure mechanisms: [±45] S specimens demonstrated distributed matrix cracking, due to tensile loading. In tension, [9] 7 specimens failed due to a single crack propagating along the tab, perpendicular to the loading axis. However, the crack was not contained in the measurement length of the clip-gauges. Thus, in practice, E 2 -measurements on the [9] 7 specimens took place on undamaged material. Since no compressive strength degradation was observed on the [9] 7 specimens, no drop in the Young modulus of the damaged material, E B, was expected. As results from the [9] 7 specimens were poor, respective measurements on the R=1 coupons were skipped. Data from the tensile residual strength R=.1 and R=-1 specimens are presented in Figure 4.2a whereas results from R=-1 coupons tested in compression are demonstrated in Figure 4.2b. Virgin and damaged specimens cannot be discerned, as in Figure 4.1.

38 R=.1 virgin R=.1 damaged R=-1 virgin R=-1 damaged (a) R=-1 virgin R=-1 damaged (b) X R (MPa) 45 X R (MPa) E 2 (GPa) E 2C (GPa) Figure 4.2. (a) Tensile residual strength vs. E 2, virgin and damaged OB [9] 7 specimens at R=.1 and R=-1, (b) compressive residual strength vs. E 2, virgin and damaged OB [9] 7 specimens, R=-1 E x degradation for the [±45] S specimens is illustrated in Figure 4.3. Measurements from 8 out of the 9 variable-amplitude specimens 6 and the 16 alternative material coupons are also presented. Axial Young modulus degradation, E d, was defined as: E d E A E = E A B 1% (5) CA reference VA reference CA alternative X R (MPa) R 2 = E d (%) Figure 4.3. Tensile residual strength vs. axial Young modulus degradation, [±45] S specimens 6 The 9 th measurement was invalid

39 39 In Figure 4.3, all negative E d -values correspond to coupons fatigued at the 2% life fraction, except for one belonging to the 5% set. Increase of the E x in some low-damage cases could be attributed to the alignment of the ±45 o oriented fibres parallel to the loading axis (see also Kim et al. [79]). A linear strength degradation model could be thus established, based on the measurements performed on the constant-amplitude fatigue specimens. The model, henceforth denoted as "model E", is given through: X =.9684E d (6) R + Correlation of acoustic measurements with stiffness was the main topic of Tang et al. [25], Toyama et al. [26] and Gorman [27]. However, Govada et al. [47] demonstrated that stiffness degradation is a less sensitive damage indicator compared to particular spectral parameters derived from acousto-ultrasonic measurements.

40 4 5. Acoustic emission Acoustic emission measurements proved sensitive to damage accumulation, although the proofloading values used in this work were low enough to avoid entering critical damage stages, e.g. the formation of delaminations in the case of [±45] S specimens. Indeed, delaminations were not observed until failure. In addition, since there was no bridging of the 45 o oriented fibres from one coupon end to the other, fibre breakage was not expected. Acoustic emission was thus attributed to matrix cracking. This is also supported in Godin et al. [3], where the chronological order of damaging events in [±35] and [±55] Gl/Ep specimens is determined. Moreover, matrix cracking was the exclusive failure mode for the [9] 7 specimens, in all loading configurations. In the presence of other damage modes, however, the recorded AE signals should be assigned to particular mechanisms, as in e.g. Godin et al. [3], Anastassopoulos et al. [15], Godin et al. [16] and Bhat et al. [32], prior to model implementation. Then, data corresponding to matrix cracking could be treated as proposed herein while other schemes would have to be developed for the rest ISO [±45] S specimens Model development As shown in Philippidis et al. [62], conventional non-linear residual strength models, e.g. the one introduced in Reifsnider et al. [8] and Schaff et al. [81], proved capable of modeling the residual strength data, reported in Philippidis et al. [77]. Residual strength, X R, could thus be modeled using a generic equation of the form: X n = X (X S )( (7) N k R max ) In Eq. (7), n is the number of cycles to which the coupon is subjected at maximum stress S max and N the number of cycles to failure, corresponding to S max. Parameter k can assume either constant values or functions of loading variables, such as the stress level or life fraction (Philippidis et al. [62]). The particular residual strength model was adapted to accommodate AE data from the main CA dataset. The modified model was: X n AE m R = X (X Smax )( ) N AE (8) In Eq. (8), cumulative CNT recorded up to a particular stress value (proof load) was denoted as "n AE ". The unknown parameters of the model, henceforth denoted as "model RS mod ", were N AE and m.

41 41 To define the n AE -parameter, an appropriate proof-loading magnitude was required. According to common practices in pressure vessels as well as previous works performed on acoustic emission proof-testing of wind turbine rotor blades (AEGIS [82]), the empirical stress value of 11%S max was selected. Thus, although coupons were tested in tension until failure and AE monitoring was continuous, n AE was extracted from signals recorded up to a proof load 1% higher than S max. Using this proof load, n AE was defined as the cumulative AE counts up to 11%S max. Since the particular proof-loading value could produce a considerable amount of acoustic emission without causing severe damage to the specimens, a fair descriptor was produced. Correlation of the specific AE descriptor to residual strength is shown in Figure 5.1. Unknown parameters N AE and m were calculated via the commercial MATLAB function lsqcurvefit, used to solve non-linear data-fitting problems in the least-squares sense. Appropriate initial values N and m were required to ensure convergence of the algorithm, for each specific stress level. Herein, N was taken equal to the average n AE -value from all coupons of that stress level while m =1. Calculated values for N AE and m, for each stress level, are given in Table 6. For completeness purposes, it should be stated that the linear version of modified model RS mod (i.e. for constant k=m=1), proposed in Broutman et al. [83], exhibited bad performance X R (MPa) MPa 63.6 MPa 55.6 MPa 48.5 MPa log 1 (n AE ) Figure 5.1. Tensile residual strength vs. log 1 (n AE ), [±45] S reference material. Unknown parameters: N AE, m Table 6. Calculated values for RS mod model parameters N AE and m, for each stress level Stress level index S max (MPa) N AE m

42 It becomes clear that CNT is a function of both fatigue cycles, n, and S max. Assuming that CNT is correlated to the general term "damage", then damage could be quantified (n) and qualified (S max ). For example, two coupons presenting the same residual strength would produce different AE if not fatigued at the same stress level: each stress level follows a distinct trend. Life fraction does not seem to influence the slope of the trend of the data points, but rather their position on the alleged curve. Thus, besides being correlated with AE descriptors (e.g. CNT), fatigue damage should also relate to S max. This is also stressed in Kim et al. [79], where the evolution of matrix crack density is shown to depend on S max. In accordance to Eq. (8), damage "D" could be expressed as: X S D = X max n ( N AE AE ) m (9) Residual strength is plotted vs. calculated damage, defined through Eq. (9), in Figure 5.2. AE data from coupons fatigued at various stress levels seem to converge into the same scatter band MPa 63.6 MPa 55.6 MPa 48.5 MPa X R (MPa) R 2 = D Figure 5.2. Tensile residual strength vs. calculated damage, [±45] S reference material (model RS mod ) However, the master curve derived from model RS mod cannot be generalized for a new stress level, unless enough data is available to estimate parameters m and N AE corresponding to the new S max. A practical solution to the problem of residual strength correlation to acoustic emission descriptors is not therefore provided.

43 43 As observed in Figure 5.1, each stress level follows a distinct trend. Thus, the slope of model RS mod could be a function of S max. In a logarithmic scale, this slope is equal to the m-parameter. With m given e.g. through: S m = max (1) X An interesting new damage parameter was obtained, henceforth denoted as "descriptor AE 1 ": m AE1 = log1(n ) (11) Parameter m is given through Eq. (1). The resulting correlation of descriptor AE 1 to the ratio of S max over residual strength is presented in Figure m=s max /X.9 S max /X R R 2 = MPa 63.6 MPa 55.6 MPa 48.5 MPa AE 1 Figure 5.3. S max over residual strength vs. descriptor AE 1 for CA tests, [±45] S reference material A linear model, henceforth denoted as "model M 1 " could thus be introduced: Smax =.1449AE X R (12) Since numerous structures are subjected to a particular constant-amplitude loading, a priori information on fatigue S max, combined with the conventional CNT descriptor, could therefore lead to reliable residual strength prediction. To investigate whether the master curve of Figure 5.3 could be considered universal, the same procedure was also implemented on the VA and alternative material datasets. For the alternative material data, the respective UTS value was used.

44 44 Two methods were used to derive the appropriate cumulative CNT amounts, in the VA data case. One engaged the 11% of an equivalent S max, calculated as proposed in Bronsted et al. [84], and the other the maximum stress 7 of the load spectrum. Perhaps due to the inherent handicap in the assessment of a representative equivalent S max, performance of the former method was mediocre. On the other hand, and since being closer to the concept of proof-loading, the second method performed well. Residual strength of the alternative material specimens was also predicted with considerable precision. Results are illustrated in Figure m=s max /X.9 S max /X R R 2 = CA reference CA alternative VA VA (Bronsted) AE 1 Figure 5.4. S max over residual strength vs. descriptor AE 1 for CA tests, [±45] S specimens. For VA specimens, either a proof load of S max (instead of 11%S max ) or 11% of an equivalent S max (Bronsted method) was used Exclusive use of the acoustic emission data, no information on fatigue S max being required, was a less precise, although more robust, option. The load at which AE was released, henceforth referred to as S onset, was thus used instead of S max. As a convention, S onset was defined as the stress above which at least 1 consecutive hits were emitted at smaller than 2-MPa intervals. In practice, this approached the actual acoustic emission onset. A characteristic example from a specimen subjected to S max =48.55 MPa, n/n=5%, is illustrated in Figure 5.5. S onset depends both on S max, see Figure 5.6, and fatigue life fraction n/n, as shown in Figure The reason S max was used, instead of 11%S max, was that it was considered excessive for a proof loading purpose

45 AE hits Stress (MPa) S onset =46.3 MPa S max =48.5 MPa n/n=5% Time (sec) Figure 5.5. Acoustic emission from a characteristic specimen. Definition of S onset X R (MPa) MPa 63.6 MPa 55.6 MPa 48.5 MPa S onset (MPa) Figure 5.6. Residual strength vs. onset of acoustic emission

46 MPa 63.6 MPa 55.6 MPa 48.5 MPa S onset (MPa) n/n (%) Figure 5.7. Onset of acoustic emission vs. fatigue life fraction With S onset being smaller than S max in general, Felicity ratio (F R ) could be used to describe experimental AE behavior, as proposed in e.g. Gorman [27]. F R is a macroscopic parameter indicating damage in composites, defined in this case as the ratio of S onset over S max. F R values are in the 1 range, "" representing a state of absolute damage and "1" the undamaged condition. Although use of F R is common, e.g. as an empirical accept/reject criterion for filament-wound FRP pressure vessels, a more appropriate scheme was proposed herein. The relevant damage parameter, AE 2, was: m AE = onset 2 log1(nonset ) (13) In Eq. (13), S onset was thus used to substitute S max in the calculation of the m-parameter of Eq. (11), resulting in the master curve of Figure 5.8. Cumulative CNT recorded up to 11% of the S onset was used, named n onset. Selection of a proof-loading magnitude of 11%S onset was made according to the practice followed in the previous models and since S onset was close to S max, see Figure 5.5. In Figure 5.8, VA and alternative material data is also illustrated. Due to an error in data acquisition, 2 out of the 87 AE recordings were not available. Thus, experimental results presented in Figure 5.8 are of 85 specimens. The master curve, shown as solid line, is again a linear regression model named "model M 2 ": Sonset =.1793AE X R (14)

47 CA reference CA alternative VA reference S onset /X R R 2 = AE 2 Figure 5.8. S onset over residual strength vs. descriptor AE 2, [±45] S specimens As in the case of model M 1, the scheme becomes more reliable with increase of the proof-loading value, see Table 7. In some cases, however, high proof loads lead to an increasing number of specimen failures, as e.g. for 12%S max. Indeed, although no rupture was observed during proofloading at S max, there were 5 specimens failing below 12%S max in the respective case. Model performance for 12%S max, estimated using all specimens 8, thus seemed inferior to the one corresponding to the 11%S max proof-loading. To unmask the proof-loading value effect, the particular 5 specimens were excluded from all levels, i.e. S max, 11%S max, and 12%S max. The trend is presented in Table 7. Table 7. Correlation of proof-loading magnitude with model scatter Model M 1 M 2 Proof load R 2 (all coupons) R 2 (excluding failures below 12%S max ) S max %S max %S max S onset %S onset %S onset When rupture occurred below the proof-loading magnitude, cumulative counts at failure were used 9 5 specimens failed below 12%S max

48 48 A compromise between model performance and preservation of the non-destructive nature of the method is nonetheless required. Using 11%S max in model M 1 was indeed a safe practice. Nevertheless, a proof load of 11%S onset implies an important advantage: the material self-dictates an appropriate magnitude for safe proof-loading, i.e. S onset. Thus, information on S max is no longer needed. Of course, model remains insensitive to previous load history, and is therefore expected to perform well on specimens subjected to stochastic loading sequences Model validation To validate models M 1 and M 2 for the set of 87 CA residual strength tests on the [±45] S reference material specimens, modeling the experimental data with a regression line was repeated k=87 times 1, each time using (k-1) points to fit the model (leave-one-out method). Performance was interrogated with residual strength prediction of the remaining k th coupon, not used in model implementation. Errors in residual strength estimation are given in Figure M 1 M 2 Error in X R estimation (%) Coupon number Figure 5.9. Error in residual strength prediction of [±45] S reference material CA coupons, using acoustic emission models M 1 and M 2 (leave-one-out method) For model M 1, average error for the set of 87 coupons is listed in Table 8. The corresponding cumulative probability distribution (CDF) of the error in residual strength prediction was described through a bi-parametric Weibull distribution, see Figure 5.1. It is seen that the bulk of the data points corresponds to a prediction error of less than 6.24%, while it can be estimated that at reliability level of 95% the error does not exceed 1.2%. In the case of model M 2, the respective CDF of the error in residual strength prediction was again described by a Weibull distribution, as seen in Figure 5.1. The bulk of the data points 1 Due to an error in AE data acquisition, 85 of 87 data points were available for M 2 implementation

49 49 corresponds to a prediction error of less than 7.15%. At a reliability level of 95%, the error did not exceed 11.8%. Table 8. Performance of acoustic emission models, reference material (leave-one-out method) Weibull distribution Model Error mean Error min Error max parameters (%) (%) Shape Scale M M CDF M 1 M 2 Weibull Error in X R estimation (%) Figure 5.1. Probability distribution of error in residual strength prediction using models M 1 and M 2, [±45] S reference material specimens To investigate whether the models could be applied in other loading configurations as well as similar materials, residual strength of the VA and the alternative material dataset was predicted. In the VA data case, as stated before, the maximum stress encountered in the loading spectrum was considered as proof-loading value for the determination of cumulative CNT. Model predictions are presented in Figure 5.4 for model M 1 and in Figure 5.8 for M 2. Error in residual strength prediction is demonstrated in Figure 5.11 for VA data and in Figure 5.12 for the alternative material. Some error statistics are given in Table Predictions are excellent. 11 Error values for the alternative material are herein computed using the UTS of the particular material in model implementation. In the respective journal publication, however, UTS of the reference material is used

50 5 Error in X R estimation (%) (VA data) M 1 M Coupon number Figure Error in residual strength prediction of VA tests, using acoustic emission models M 1 and M 2 Error in X R estimation (%) (alternative material) M 1 M Coupon number Figure Error in residual strength prediction of alternative material CA tests, using acoustic emission models M 1 and M 2 Table 9. Performance of AE models on VA and alternative material validation sets Validation Error mean Error min Error max Model set (%) (%) M VA M M 1 Alternative

51 51 M Model implementation using alternative descriptors As presented in the above, models M 1 and M 2 are based on the cumulative number of AE counts. However, alternative AE parameters were also examined in Assimakopoulou et al. [85] and proved as applicable. Predictions generated using various descriptors were then averaged to minimize error in overall residual strength assessment. The "new" descriptors were signal amplitude, counts-to-peak, duration, energy and rise time. Of course, in each case, the constants in Eq. (12) are varied. In the case of RT, for instance, the respective model is given through: Smax =.1485AE X R (15) Values of the squared correlation coefficient, R 2, are demonstrated in Table 1. For comparison, performance of the number of recorded AE events is also listed. Table 1. Ranked performance of various AE descriptors AE descriptor RT DUR AMP CNP CNT EN AE events R As demonstrated, all the above AE descriptors could be used for reliable residual strength assessment of FRP composites, featuring fatigue damage. The remarkable performance of all descriptors lies in their cumulative nature. Indeed, since AE hits can provide a decent input for model implementation, cumulative waveform parameters are bound to prove at least as adequate. Residual strength predictions for the main reference material CA dataset, using all AE descriptors, are illustrated in Figure 5.13 along with measured residual strength values. Data is sorted for ascending actual residual strength. Considerable agreement is observed. An interesting indication is the increasing error in residual strength assessment, as damage decreases. Indeed, prediction seems more reliable in the case of "weaker" specimens. The explanation for this convenient observation is simple: in "strong" coupon cases, recorded AE is poor, thus degenerating the statistics of cumulative parameters. Average error in model performance, using CNT, was evaluated to be 3.62%, with maximum value equal to 12.93%. Using RT instead, mean error is 3.52% and maximum error 11.89%. For the VA dataset, corresponding mean-max errors for the CNT implementation were 2.39 and 4.31%. Using RT, errors were reduced to 1.96 and 4.11%. However, mean error for the alternative material deteriorated from 5.62 to 6.12%, although maximum error decreased from to 13.1%.

52 52 Although rise time seems to be the optimal choice, this cannot be also guaranteed for other applications without substantial experimentation. In cases where performance of AE descriptors cannot be a priori evaluated, and since all seem to provide a good estimation for strength degradation, individual predictions could be all averaged in an attempt to optimize model performance. For example, using predictions from all descriptors, average error reduces to 3.53% and maximum error to 12.38%. Although improvement is fair, it can be achieved without additional cost, using all available descriptor data. 13 X R estimation (MPa) RS actual CNT EN DUR RT CNP AMP AE events Coupon number Figure Residual strength assessment using several AE descriptors During the material characterization stage, UTS was found equal to MPa. This average was extracted from 25 static tensile tests. Minimum and maximum values, encountered in the 25-coupon population, were 18.8 and MPa. Censoring residual strength predictions that exceed this maximum UTS value, i.e. forcing them equal to MPa, average error is further reduced to 3.46% Filtering of AE data All AE data presented herein was filtered before use, to eliminate outliers and false recordings, perhaps due to electromagnetic interference (EMI) (Philippidis et al. [17]). Records with average frequency 12 (AvF) greater than 5 khz, zero signal energy, counts-to-peak greater than counts and rise time greater than duration were rejected 13. Major reduction of more than 5% of the available 12 Average frequency is defined as the ratio of AU counts over duration 13 A negligible amount of records with CNT<CNP were encountered. There were no hits with DUR<RT

53 53 acoustic emission data was thus performed before processing. Peculiar enough, this procedure seems to have a minor influence on model performance, see Figure This observation can be explained while considering the nature of the rejected data. Some indicative statistics (mean descriptor values) for a "strong" and a "weak" specimen, up to 11%S max, are presented in Table 11. Indeed, rejected data originated from quite weak signals, not expected to contribute in damage assessment. As seen in Table 11, the average CNT number of the rejected signals is much lower than the respective CNT of the accepted ones. Thus, the cumulative number of AE counts, used in model implementation, is barely influenced. Although this is expected to hold for other descriptors as well, this is not the case for the number of AE events. This is depicted in Figure CA reference CA reference (unfiltered).9.8 S max /X R AE 1 Figure S max over residual strength vs. descriptor AE 1 for CA tests, [±45] S reference material: standard model M 1 implementation vs. implementation using unfiltered data Table 11. Indicative statistics (mean values) of the accepted and the rejected (filtered-out) AE data RT CNP CNT EN DUR AMP Strong Rejected Weak Strong Accepted Weak

54 CA reference CA reference (unfiltered).9.8 S max /X R AE 1 (events) Figure S max over residual strength vs. descriptor AE 1, formulated using AE events instead of CNT: standard model M 1 implementation vs. implementation using unfiltered data Robustness investigation The main experimental database, used to determine the residual strength predictive models, comprised 87 specimens. However, reliable predictions could be accomplished using a smaller database, e.g. 1/3. This corresponds to a number of 29 experiments. To evaluate the performance of this "reduced" model, these 29 entries must be selected. Selection can be either random or conform to a certain rationale. Random selection of e.g. 29 out of 87 entries leads to possible combinations and is thus impractical to run. However, a feeling of model robustness can be acquired using less, e.g. 1 5, random combinations. This is illustrated in Figure Depending on input selection, model performance is thus varied. The worse scenario is expected when data spreading is inadequate. With smart selection of experimental data, however, such a case could be avoided. Even a single stress level should be enough, provided that fatigue loading for the available specimens is interrupted at several, perhaps equally spaced, fractions of the expected life.

55 R No. of random combinations x 1 4 Figure Correlation coefficient vs. number of random combinations 5.2. Model implementation on OB [9] 7 specimens As expressed in the above, implementation of the proposed acoustic emission models for residual strength assessment after fatigue is restricted to cases where matrix cracking is the dominant damage mode. To validate this statement, the developed M 1 and M 2 methodologies were applied on the OB [9] 7 specimens, also expected to fail due to matrix cracking. Again, an extensive experimental program was conducted in order to characterize the particular specimen configuration. Residual strength tests were performed at three stress ratios, i.e. R=.1, R=-1 and R=1. Specimens pre-fatigued at R=.1 and R=1 were tested for tensile residual strength whereas from the coupons subjected to R=-1 loading both tensile and compressive tests to failure were performed. Implementation of M 1 (Eq. (12)) on the [9] 7 R=.1 and R=-1 AE data, both failing in tension, is presented in Figure Of course, the UTS value of the [9] 7 specimen was used in descriptor AE 1 estimation. Proof-loading values, albeit 1% higher than S max, were in most cases quite lower than residual strength. In some R=.1 cases, however, specimens failed below the proof-loading value (see x-marks in Figure 5.17). Observing the experimental results, several coupon tests are encountered where almost no acoustic emission was recorded during proof-loading. Indeed, for R=.1 specimens, cumulative AE counts ranged from 51 to 148,28 while the respective range for R=-1 was to 17,913. Although this could be attributed to data acquisition parameters, e.g. threshold, limited acoustic emission is expected in cases where a low proof-loading value is used and/or specimens retain most of their strength.

56 R=.1 Failed below 11%S max R=-1 M 1 S max /X R m=s max /UTS AE 1 Figure S max over tensile residual strength vs. descriptor AE 1, OB [9] 7 specimens at R=.1 and R=-1 Although M 1 performs well in the R=.1 and R=-1 tensile residual strength case, there are certain considerations/limitations to be discussed. In M 1 implementation, knowledge of S max is required. Therefore, in pure tensile loading, e.g. R=.1, a proof-loading of 11%S max value could be used for tensile residual strength prediction. Likewise, for R=1, a negative proof load of 11%S min would serve for compressive residual strength assessment. As obvious, however, meaningful proof-loading values for compressive residual strength prediction after tensile fatigue or for tensile strength prediction after compressive fatigue cannot be defined. Model M 1 could thus be used either for tensile of for compressive residual strength assessment, depending on the sign of preceding fatigue loading. In an ideal case of R=-1, provided that UTS= UCS, M 1 could perhaps be implemented for both directions at the same time. However, even for R=-1, when UCS is greater than UTS, as for the [9] 7 specimen, and with the proof-loading value being 11%S max for tension and -11%S max for compression, compressive residual strength prediction might not be feasible. Indeed, for [9] 7 specimens, no AE events were recorded at compressive proof loads of -11%S max. Model M 2, on the other hand, uses an alternative stress value, S onset, to substitute S max. Stress S onset was defined as the stress above which at least 1 consecutive AE hits were recorded at smaller than 2-MPa intervals. Using M 2, information on S max is no longer needed and the model becomes insensitive to previous loading. Moreover, performing a tensile and then a compressive proof-loading on the same specimen, both tensile and compressive residual strength could be predicted. This is illustrated in Figure Model M 2 (Eq. (14)) performance for each stress ratio, [9] 7 specimen, is presented in Table 12.

57 S onset /X R R=.1 R=-1 (T) R=1 R=-1 (C) Failed below 11%S onset M AE 2 Figure S onset over residual strength vs. descriptor AE 2, OB [9] 7 specimens at R=.1, R=-1 and R=1, tensile and compressive tests to failure Table 12. Model performance in tensile or compressive residual strength estimation, OB [9] 7 specimen M 1 M 2 Stress RST Error ratio mean Error min Error max Error mean Error min Error max (%) (%) (%) (%) R= R=-1 Tensile R= R=-1 Compressive In addition, using M 2 requires a proof load of S onset, which in general is lower than S max. Thus, in Figure 5.18 there is one coupon failing below 11%S onset, instead of 5 in the M 1 case (Figure 5.17). Note that while M 1 failures were in the R=.1 stress ratio, the M 2 failure was pre-fatigued under R=- 1. There are 5 data points diverging from the general trend of model M 2 (see lower left end of Figure 5.18). Acoustic emission in these cases began at low loads, i.e. below 1 MPa. Residual strength of these specimens cannot be well-predicted using M 2, however the model provides a safe estimate of the actual residual strength Failure modes: discussion As shown in Figure 5.17 and discussed in Philippidis et al. [37]-[38], tensile residual strength data from R=.1 and R=-1 stress ratios, all stress levels and life fractions, can be described using model

58 58 M 1, both for the [±45] S and the [9] 7 specimen. Two materials were examined, both performing well under the same regime. In addition to CA loading, specimens subjected to a variable-amplitude spectrum were also investigated. All these cases bear the same failure mode, classed in Puck et al. [4] as "mode A" and referring to matrix cracks due to shear stresses and/or transverse tensile loading. The discriminating characteristic of mode A is the crack plane being perpendicular to the plies and running parallel to the fibre direction. This work indicates that although M 1 was established on [±45] S specimens, failing mostly due to shear stresses, it could also be applied on the [9] 7 coupons, failing due to tension transverse to the fibres. As mentioned earlier, both cases are characterized as failure mode A. On the other hand, all mode A cases including tension after R=1 fatigue, complied with a single model, M 2, see Figure In addition, compressive residual strength after R=-1 loading could also be predicted using M 2 although the corresponding damage mode, distinguished as "mode C" in Puck et al. [4], is a matrix failure mode due to shear stresses and perhaps also transverse compressive loading. The difference in failure modes A and C is depicted in Figure Mode C crack plane, still parallel to the fibres, forms an oblique angle with the normal-to-the-plies plane. Figure Characteristic failure modes for the OB [9] 7 specimen. (a) mode A (tensile), (b) mode C (compressive) Therefore, model M 2 is applicable independent of the failure mode and loading conditions such as stress ratio, R. An obvious explanation for the former is that AE behavior from matrix failure in general, including e.g. transverse cracking and fibre-matrix debonding, is similar for impeding A and C failure modes since AE data used in model implementation are acquired well before coupon rupture. Nevertheless, although the universal trend is supported, more research on the particular issue is required Conclusions An extensive experimental program was performed to investigate strength degradation of a [±45] S and a [9] 7 Gl/Ep composite, due to constant or variable-amplitude fatigue. Strength degradation, a function of stress ratio, maximum stress and life fraction spent under cyclic loading, was matrixdominated. Correlation of tensile and compressive strength degradation with characteristic parameters, measured via acoustic emission, was accomplished.

59 59 In the case of the [±45] S specimen, all loading was tensile. Coupons were subjected to CA R=.1 or tensile stochastic loading, resulting in considerable tensile strength degradation of up to 4%. Specimens made of an alternative material were also tested, after CA R=.1 sinusoidal loading. [9] 7 specimens, on the other hand, were subjected to constant-amplitude loading of either R=.1, R=.1 or R=.1 stress ratio. Static tests to failure indicated tensile strength degradation of up to 41%, although there was no considerable degradation in compression. The drop in tensile strength, in particular, was more intense under R=.1 and R=-1, while almost non-existent for R=1. Simple and reliable engineering models, suitable for design considerations, provided excellent residual strength predictions. Two of the proposed AE descriptors, AE 1 and AE 2, prevailed in residual strength assessment of composite specimens, featuring fatigue damage. The corresponding models, M 1 and M 2, were validated with remarkable success. Model M 1 was more accurate, however required a known fatigue maximum load. Using this information, a master curve valid for all stress levels and life fractions was obtained. M 1 could thus be implemented in applications where cyclic loading is either fixed or recorded on-line. Model M 2, on the other hand, presented adequate performance with no implementation requirements. In both cases, the proofloading was low enough to cause further material damage, e.g. delaminations. The proposed models were established on CA fatigue tests on the [±45] S reference material. Two independent validation sets were also used to test the schemes: one contained data from [±45] S reference material VA (spectrum) tests and the other from [±45] S specimens of an alternative resin matrix, subjected to CA loading. Again, performance of both models was remarkable. An interesting observation is that alternative cumulative AE descriptors proved as adequate in model implementation. Their performance was similar to the CNT-based model, as all parameters originated from the number of recorded AE events. The various predictions could thus be combined to produce more accurate overall residual strength assessment. The schemes provided excellent residual strength predictions for the [9] 7 stacking sequence, for R=.1, R=-1 and R=1 CA loading, both in tension and compression. Although [9] 7 specimens present disparate failure behavior in tension and compression, distinguished as mode A and mode C respectively, all cases were well-described using the same model. It could therefore be presumed that the model is valid for all similar materials, stress ratios, life fractions, stress levels, constant or variable-amplitude loading, tensile or compressive residual strength test. However, further research on more materials, specimens and loading configurations would still be interesting, as well as an evaluation of the effectiveness of the model using alternative equipment and software settings. The procedures established using the proposed AE descriptors, however heuristic, proved capable of predicting the residual static strength of coupons undergone constant or variableamplitude fatigue. Provided that prior application to an adequate number of samples is performed, to establish a robust database, the introduced methodologies are expected to perform well in residual strength estimation of new members of the population. This work accomplished to correlate strength degradation with characteristic parameters measured via acoustic emission, a method suited for health monitoring of operating structures.

60 6 However, being insofar validated on small test specimens, the method is still in need of development. For example, since damage in a generalized laminate is not matrix-dominated, as in the [±45] S and [9] 7 cases, it is imperative to consider all possible failure mechanisms as well. For structures where failure is fibre-dominated, enhancement accounting for all expected damage mechanisms, e.g. fibre breakage and delaminations is required. Assigning the recorded data to particular damage modes, e.g. using a pattern recognition algorithm, perhaps respective, similar models could be introduced. Again, a dedicated database should be established for each particular application. In large structures, however, signal attenuation should be considered. Furthermore, in waveguides such as plate and shell structures, e.g. wind turbine rotor blades, geometrical dispersion should also be accounted for. To compensate for the alteration of wave propagation characteristics due to such phenomena, all emitted signals should be recorded and studied. Then, developed schemes should be re-evaluated through full-scale testing. An alternative approach is using a zonal location technique. Thus, scale issues could be overcome. For instance, using a more refined sensor mesh on areas more susceptible to damage and with the neighborhood of each sensor being of similar size as the test specimens, localized condition assessment could indeed be accomplished. The shear webs of the spar beam and the trailing edge sandwich panels of a wind turbine rotor blade are such locations. Most interesting, the particular areas lack axial fibre-reinforcement, rendering the proposed model directly applicable. The technique could be further developed so that periodical measurements of appropriate AE descriptors during service, e.g. using embedded sensors, provide information on the damage state of the component. The goal is to establish smart maintenance schedules to replace conservative prevention-aimed repair routines. Monitoring of wind turbine rotor blades, using own weight as loading, is a promising possible application.

61 61 6. Acousto-ultrasonics: a phenomenological descriptor approach Although of inferior performance compared to AE monitoring, acousto-ultrasonic measurements also proved able to reflect damage accumulation. Several AU descriptors were extracted from the recorded signals and investigated, in terms of their discrimination potential regarding residual strength. Introduced and implemented in numerous studies, candidate descriptors originated from the time, frequency, cross and auto-correlation domains. Herein, the most prominent AU parameters are presented and evaluated on the [±45] S specimens. Experiments were also performed on the [9] 7 coupons, however, as in the case of axial Young modulus measurements, no useful results were obtained. The reason was that the major crack, leading to rupture, was located outside the wavepath. The same [±45] S database as in Chapter 5 is used, containing 87 reference material specimens undergone CA R=.1 sinusoidal loading, 8 reference material specimens subjected to tensile stochastic (spectrum) loading and 16 alternative material specimens under CA R=.1 sinusoidal fatigue. For easier indexing in this chapter, descriptors are named "D i ", while respective normalized values are denoted as "d i ". Descriptors extracted from signals recorded on the virgin material (A-signals) are denoted as "D ia ", while the ones corresponding to the damaged specimens (B-signals) as "D ib " Acousto-ultrasonic descriptors Time domain Descriptor D 1 : stress wave factor degradation The most famous AU descriptor, leading the acousto-ultrasonics breakthrough, is perhaps the stress wave factor (SWF). In accordance with the most popular definition (Williams et al. [46]), SWF is the conventional AU counts parameter. In Williams et al. [46], SWF proved sensitive to tensile strength degradation due to impact damage. As a measure of stress wave energy transmission, SWF could also be a good material damage indicator. Except in Vary et al. [45], where introduced, SWF was used in several studies. A characteristic waveform, recorded on a damaged [±45] S specimens, is illustrated in Figure 6.1. SWF is defined as the number of threshold 14 crossings. Signal amplitude, duration and rise time are also shown. Based on SWF, descriptor D 1 was formulated as: SWFA SWFB D1 = 1% SWF A (16) 14 In all calculations, threshold value was 1.5 mv

62 62 Correlation of D 1 with residual strength is presented in Figure 6.2. Variable-amplitude and alternative material data is also demonstrated Risetime Amplitude Signal amplitude (Volts) Duration Time samples Figure 6.1. Characteristic waveform recorded on a damaged, reference material, [±45] S specimen X R (MPa) CA reference 6 VA reference CA alternative D 1 Figure 6.2. Residual strength vs. descriptor D 1 Correlation coefficient, R 2, of D 1 with residual strength was low,.28. However, performance of individual descriptors SWF B and SWF 15 A were even lower,.1543 and.18. Indicative performance of other descriptors, on damaged material, is.1115 for AMP B,.868 for EN B and.7 for CNP B. 15 In an ideal virgin material, R 2 of all descriptors is expected to be zero. Thus, measurements on the virgin material are used to normalize descriptor values on the damaged specimens and indicate possible pre-existing flaws

63 Descriptor D 11 Descriptor D 11 is the average value of absolute (A-B). Small D 11 values thus correspond to almost identical A and B-signals, in the time domain. Correlation of descriptor D 11 with residual strength is presented in Figure 6.3. Performance of D 11, in terms of R 2, is.2583 whereas e.g. maximum of the absolute (A-B) value is still lower, X R (MPa) CA reference VA reference CA alternative D 11 x 1-3 Figure 6.3. Residual strength vs. descriptor D Auto/cross-correlation domain For simpler reasoning, the cross-correlation function is henceforth referred to as xcorr, in accordance to the corresponding MATLAB function. In signal processing, cross-correlation xcorr AB is a function of the relative time delay between signals A and B, sometimes called the "sliding innerproduct". Auto-correlation of a signal A, xcorr AA, is a symmetric function maximized for zero-lag. Herein, A-signals were taken on the virgin material and B-signals on the damaged specimens. Where required, the element-by-element product of an A and a B-signal is denoted as "A.B" Descriptors D 2 -D 4 The cross-correlation value of the signals taken on the damaged and the virgin material, xcorr AB, for zero lag, was called D 2. D 3 was then defined as the abscissa (time delay) of maximum crosscorrelation, i.e. xcorr AB (D 3 )=max(xcorr AB ), (see Hull et al. [86] and ASTM C [87]). D 4 was the maximum cross-correlation value, i.e. D 4 =max(xcorr AB ). After some experimentation, it was decided to extract descriptors D 2, D 3 and D 4 from the part of the 512-point waveform containing samples 91 to 13. This practice excluded most reflections, as well as the initial dead part of the signal. A characteristic example depicting the effectiveness of descriptors D 2, D 3 and D 4 is given in Figure 6.4,

64 64 where distinction between a weak and a strong coupon becomes evident. Dependence of D 2 on residual strength is demonstrated in Figure X R =74%UTS Weak specimen (a).8.6 X R =98%UTS Strong specimen (b) Signal amplitude (Volts) Signal amplitude (Volts) Virgin Damaged Virgin Damaged Time samples Time samples.7.7 Cross-correlation of A and B-signal (Volts 2 ) Weak specimen (D 3,D 4 ) (zero lag,d 2 ) Time samples 2 x 1-3 (c) Cross-correlation of A and B-signal (Volts 2 ) Strong specimen Time samples 2 x 1-3 (d) 15 Weak specimen (e) 15 Strong specimen (f) A.B (Volts 2 ) 1 5 A.B (Volts 2 ) Time samples Time samples Figure 6.4. (a) Characteristic waveforms from a coupon with low and (b) high residual strength, (c) cross-correlation from the part of the signals in (a), (d) cross-correlation from the part of the signals in (b), (e) product of the full-length signals of (a), (f) product of the full-length signals of (b)

65 X R (MPa) CA reference VA reference CA alternative D 2 (Volts 2 ) Figure 6.5. Residual strength vs. descriptor D 2 While R 2 of D 2 was.5221, xcorr BB and xcorr AA for samples 91-13, calculated at zero lag, resulted in respective R 2 -values of.1545 and.292. Performance of AU descriptors D 3 and D 4 is presented in Figure 6.6 and Figure 6.7. For D 4, R 2 is.273 whereas for max(xcorr BB ) and max(xcorr AA ), samples 91-13, respective R 2 -values are.1691 and X R (MPa) 9 8 CA reference 7 D outlier 3 VA reference 6 CA alternative Without outlier (R 2 =.6538) With outlier (R 2 =.496) D 3 (Samples) Figure 6.6. Residual strength vs. descriptor D 3

66 X R (MPa) CA reference D 3 outlier VA reference CA alternative D 4 (Volts 2 ) Figure 6.7. Residual strength vs. descriptor D 4 Although D 3 is a powerful descriptor, especially for cases of low signal-to-noise ratios (see Hull et al. [86]), automated extraction should be treated with caution. Indeed, in cases where two or more peaks are of similar magnitude, see Figure 6.4c and Figure 6.4d, it is probable that the global maximum does not correspond to the "correct peak", thus leading to outliers. This was observed in one of the specimens of the main 87 coupon set, and the maximum was manually assigned to a neighboring peak, to be in accordance with the rest of the data. This was also the case in three of the alternative material tests, as seen in Figure 6.6, where there was no human intervention in the computation of descriptor D 3. D 3 also affects the corresponding D 4 value. In the D 4 case, however, as shown in Figure 6.7, the phenomenon is not so dramatic Descriptor D 5 AU descriptor D 5, presented in Figure 6.8, was extracted as described in Philippidis et al. [88]. D 5 was defined as the ratio of positive A.B area over total A.B area 16, A.B being the element-by-element product of the AU signals, taken in the virgin and the damaged material. The phenomenon behind descriptor D 5 is the decrease of the propagation velocity of an ultrasonic signal in the presence of damage. In the case of no damage, the product of the almost identical signals should be positive for most time samples. In a damaged specimen, on the other hand, the product of the two waveforms is expected to have a negative sign in more time instants. Therefore, for the stronger specimens, the positive area occupies the largest portion of the total area amount. The opposite observation can be made for the weaker coupons, as seen in Figure 6.4e and Figure 6.4f. The full-length waveforms were used in the calculation of D In the original version, descriptor D 5 was called "R PN " and was the positive to negative area ratio. Herein, however, using the total area in the denominator resulted in an improved R 2 of.5382, compared to the negative area performance (R 2 =.228)

67 CA reference VA reference CA alternative X R (MPa) D 5 Figure 6.8. Residual strength vs. descriptor D Descriptor D 9 Descriptor D 9 was the average value of the A.B product (full-length waveforms used). Correlation of D 9 with residual strength is shown in Figure X R (MPa) CA reference VA reference CA alternative D 9 x 1-4 Figure 6.9. Residual strength vs. descriptor D Descriptor D 1 Descriptor D 1 was the correlation coefficient of the A and B signals (full-length waveforms used), also suggested in Philippidis et al. [88]. Correlation of D 1 with residual strength is shown in Figure 6.1.

68 X R (MPa) CA reference VA reference CA alternative D 1 Figure 6.1. Residual strength vs. descriptor D Descriptor D 6 D 6 was the skewness of product A.B. Skewness is a measure of asymmetry of a distribution around the sample mean. Again, the full-length waveforms were used. The correlation of D 6 with residual strength is shown in Figure Corresponding R 2 is.4151, while e.g. R 2 of the skewness of the A.A and B.B products is.27 and.39 respectively. Kurtosis of A.B was also of bad performance, corresponding R 2 being equal to.38. Kurtosis is a measure of the "peakedness" of a distribution or else of how outlier-prone a distribution is CA reference VA reference CA alternative X R (MPa) D 6 Figure Residual strength vs. descriptor D 6

69 Frequency domain Descriptor D 7 Descriptor D 7 was the average coherence value, in the to khz range (see Philippidis et al. [88]). Coherence is a function of frequency, with values 1, indicating the correlation of input A to output B at each frequency. Herein, input was the signal taken on the virgin material and output was the corresponding waveform after fatigue. Coherence was computed using standard MATLAB function cohere, with default settings (Hanning window, zero-padding at 256 points), 5% overlap. Coherence function for the representative cases of a strong and a weak coupon, same as in Figure 6.4, is given in Figure Since the operation bandwidth of the transducers was 2 to 75 khz, D 7 was extracted from the to khz range. Performance of D 7 is shown in Figure (a).9.8 Weak specimen Strong specimen (b).7.7 Coherence (-) Coherence (-) D 7 (strong) D 7 (weak) f (khz) f (khz) Figure Coherence functions for a weak and a strong specimen. (a) Total bandwidth, (b) detail of (a), demonstrating the sensor operation bandwidth X R (MPa) Zero-padding length: 256 5% overlap CA reference VA reference CA alternative D 7 Figure Residual strength vs. descriptor D 7

70 Descriptor D 8 Considering fatigue damage as a system, transforming input signal A to output signal B, the respective transfer function is expected to contain relevant information. Descriptor D 8 was the average value of the transfer function estimate, in the to khz range. The transfer function estimate was computed using standard MATLAB function tfe, with default settings (Hanning window and zero-padding at 256 points) and 5% overlap. The transfer function estimate for the representative cases of a strong and a weak specimen, same as in Figure 6.4, is given in Figure Performance of D 8 is illustrated in Figure (a) 1 Weak specimen Strong specimen (b) Transfer function estimate (-) Transfer function estimate (-) D 8 (strong) D 8 (weak) f (khz) f (khz) Figure Transfer function estimates for a weak and a strong specimen. (a) Total bandwidth, (b) detail of (a), demonstrating the sensor operation bandwidth X R (MPa) Zero-padding length: 256 5% overlap CA reference VA reference CA alternative D 8 Figure Residual strength vs. descriptor D 8

71 Descriptor D 12 The power spectral density (PSD) estimates of signals A and B were computed using standard MATLAB function psd, with default settings (Hanning window and zero-padding at 256 points) and 5% overlap. As observed in Govada et al. [47] and Talreja [48], the second harmonic of the PSDspectrum is reduced in the presence of damage. This trend can also be demonstrated herein. PSD estimates for representative cases of a strong and a weak specimen, same as in Figure 6.4, are shown in Figure (a).12 (b) -6.1 PSD (db) PSD Virgin Damaged Weak specimen f (khz) f (khz) -4 (c).12 (d) -6.1 PSD (db) PSD Virgin Damaged Strong specimen f (khz) f (khz) Figure PSD estimates for (a) a weak and (c) a strong specimen, (b) detail of (a), (d) detail of (c) Several parameters could be extracted from the PSD spectra. A simple descriptor, named D 12, is the maximum value of the PSD estimate of the B-signals, in the to khz range. Correlation of D 12 with residual strength is shown in Figure Performance of D 12 is poor,.2134, however higher than the global maximum of the PSD estimate of the B-signals, equal to R 2 =.152. Correlation of the maximum value of the PSD estimate of the A-signals, in the to khz range was.61.

72 Zero-padding length: 256 5% overlap 1 X R (MPa) CA reference VA reference CA alternative D x 1-3 Figure Residual strength vs. descriptor D Descriptors D 13 -D 18 A set of descriptors, derived from the PSD-spectra, was proposed and used in Govada et al. [47] and Talreja [48]. Introduced in a previous work (Talreja [89]), the particular parameters were suggested to be convenient representatives of a power spectrum. Thus, considering a power spectrum as a plane figure, the various moments of the figure about a certain axis, the area of the figure and the location of its centroid are the constructing elements of descriptors D 13 to D 18. A generic equation for the computation of moments of various orders, r, of a function S(f) is: f = 2 r M r S(f)f df f (17) 1 In Eq. (17), S(f) is the power spectral density and f is the frequency. Recalling the nomenclature used in Talreja [48], where descriptors are named "SWF i ", 1=1,,5, descriptors are given through: D 13 = SWF1 = M (18) M D 14 = SWF2 = M D = = SWF3 ( ) M D = 1 M M = SWF4 ( ) M2 (19) (2) (21) 2 SWF3 M = ( ) SWF4 MM4 D = (22)

73 73 MM D 18 = SWF5 = M M (23) Descriptors D 13 to D 16 were used in Govada et al. [47] for damage assessment of Gr/Ep [/9 2 ] S, [/±45] S and [/9/±45] S laminates, under tension or after a number of R=.1 fatigue cycles. All AU measurements were performed under load. With increasing fatigue damage, behaviour of descriptor (D 13 ).5 was similar to the laminate stiffness degradation, measured via an extensometer. However, (D 13 ).5 proved more appropriate. In Talreja [48], descriptors (D 13 ).5, D 17 and D 18 were shown to be sensitive to fibre orientation in a UD [] 8 Gl/Ep composite. For the (D 13 ).5 case in particular, the resulting trend was similar to the corresponding in-plane Young modulus variation. This correlation was also validated on a [] 8 Gr/Ep composite, using a different transducer. Descriptor (D 13 ).5 was also used to control the manufacturing procedure of filament-wound ring-shaped specimens. Indeed, transverse to the fibre direction, specimens containing voids and chopped pieces of Teflon in the resin matrix were both distinguished from the flawless specimens and also from one-another. In addition, (D 13 ).5 was effective in delamination detection in a multi-laminated 5-mm Gr/Ep plate. Descriptors D 16 to D 18 were also good delamination indicators. Performance of (D 13 ).5 on the data available herein along with axial Young modulus measured on the damaged specimens are illustrated in Figure Drop of (D 13 ).5, in the presence of damage, is indeed more intense than measured stiffness degradation, although there appears to be more scatter. However, the geometrical structure of the descriptor rather promotes clustering, in e.g. a weak and strong-coupon class, than provides reliable estimation of actual strength degradation. Performance of all descriptors is presented in Figure 6.19 to Figure D 13 E B (D 13 ).5 or E B (normalized) X R (MPa) Figure Descriptor D 13 and axial Young modulus on the damaged specimens vs. residual strength (D 13 and E B are normalized in the 1 range)

74 X R (MPa) CA reference VA reference CA alternative (D 13 ).5 Figure Residual strength vs. descriptor (D 13 ) X R (MPa) CA reference VA reference CA alternative D 14 Figure 6.2. Residual strength vs. descriptor D X R (MPa) CA reference VA reference CA alternative D 15 Figure Residual strength vs. descriptor D 15

75 X R (MPa) CA reference VA reference CA alternative D x 1-3 Figure Residual strength vs. descriptor D CA reference VA reference CA alternative X R (MPa) D 17 Figure Residual strength vs. descriptor D X R (MPa) CA reference VA reference CA alternative D 18 Figure Residual strength vs. descriptor D 18

76 Empirical acousto-ultrasonic schemes Correlation of the presented AU descriptors with residual strength is given in Table 13. D 2, D 3, D 5 and D 9 are evaluated as the best strength degradation indicators and are the ones used in the proposed acousto-ultrasonic schemes. Table 13. Correlation of AU descriptors with residual strength AU descriptor R 2 AU descriptor R 2 D 1.28 D D D D D D 3(uncorrected).496 D D D D D D D D D D D D Descriptor D 3 -based model The AU model predicting residual strength in Figure 6.6, named "model D 3 ", is expressed through: X R 3 = 1.123D (24) It should be reminded that model D 3 uses the corrected value of the outlier D 3 datum. If the correction is not performed, prediction is given through the dashed line of Figure 6.6. To validate model D 3 for the set of 87 CA residual strength tests on the [±45] S reference material specimens, the leave-one-out method was again used. Error in residual strength estimation is given in Figure Predictions produced using model E (derived from axial Young modulus measurements), i.e. Eq. (6), are also presented for comparison purposes. Average errors for the set of 87 coupons are given in Table 14 and respective CDFs of the error in residual strength prediction in Figure For model D 3, the bulk of the data points corresponds to a prediction error of less than 8.32%, while it can be estimated that at reliability level of 95% the error does not exceed 12.3%. For model E, the bulk of the data points corresponds to an error of less than 8.7%, while at 95% the error does not exceed 15.98%.

77 77 3 Error in X R estimation (%) Model D 3 Model E D 3 uncorrected Coupon number Figure Error in residual strength prediction of [±45] S reference material CA coupons, acoustoultrasonic model D 3 and axial Young modulus degradation model E (leave-one-out method) Although use of descriptor D 3 is susceptible to outliers and would be safer to avoid in practice, model D 3 was presented as an indicative example of the exploitation of the AU data. Model D 3, as shown in Figure 6.6, also depicts possible dangers in using automated procedures to extract NDT parameters. For this purpose, error in residual strength estimation using uncorrected descriptor D 3 is also presented in Figure 6.25: the outlier induces a peak error of 61.3%. Table 14. Performance of acousto-ultrasonic and axial Young modulus degradation models, reference material (leave-one-out method) Weibull distribution Model Error mean Error min Error max (%) (%) parameters Shape Scale D E D 3(uncorrected)

78 CDF D 3 E Weibull Error in X R estimation (%) Figure Probability distribution of error in residual strength prediction using models D 3 and E, [±45] S reference material specimens A compound descriptor approach For the problem discussed herein, a successful supervised pattern recognition approach would be limited to separating the data in a pre-defined number of classes, e.g. groups of coupons with low and high residual strength. Thus, the challenge of this work, i.e. actual residual strength prediction, would not be accomplished. As indicated in the above, AE descriptors produced reliable strength degradation models. On the other hand, individual AU descriptors had moderate correlation to residual strength. To compete with the acoustic emission schemes, a linear combination of selected AU parameters was used to form a more effective "compound AU descriptor". Through this compound descriptor, C AU, the intrinsic measurement inaccuracies of individual parameters are probable to cancel out and the potential of non-destructive evaluation can thus be enhanced. In accordance to the practice followed so far, the compound AU descriptor was established and tested on the 87 [±45] S reference material specimens subjected to constant-amplitude fatigue loading. To further validate the proposed method, the additional variable-amplitude and alternative material datasets were then used. Acousto-ultrasonic measurements thus provided the components of an appropriate compound AU descriptor, capable of sorting a number of fatigued coupons according to their residual strength. C AU was defined as the sum of a group of normalized AU parameters of the same monotonic trend. An immense number of possible combinations could be evaluated. An example of an AU-based compound descriptor is given in Assimakopoulou et al. [9]. Another combination, using the 4 best-performance descriptors D 2, D 3 (uncorrected), D 5 and D 9 is calculated through:

79 79 1 = (d 2 + d 3(uncorrected) + d 5 d ) (25) 4 C AU + 9 The particular D i descriptors and, of course, d i also, are all increasingly monotonic with respect to residual strength and can thus be added up without transformation. The equation of the model, named "model D 2359 ", is: X = 38.89C AU (26) R + The correlation of C AU with residual strength, illustrated in Figure 6.27, is improved compared to each of the individual components. The uncorrected version of D 3 is being used on purpose, to demonstrate how possible inaccuracies in the descriptor values can be moderated. Indeed, the influence of the outlier of descriptor D 3 (see Figure 6.6) on the total model response (Figure 6.27) is "compensated". In Figure 6.27, VA and alternative material data is also shown CA reference VA reference CA alternative X R (MPa) 9 8 R 2 = D 2359 Figure Residual strength vs. compound descriptor C AU (contributing AU descriptors: D 2, D 3 (uncorrected), D 5 and D 9 ) Pattern recognition schemes Since the correlation of acousto-ultrasonic signal parameters to the tensile residual strength of [±45] S Gl/Ep specimens, featuring various levels of fatigue damage, had moderate performance in general, other approaches were also engaged. Indeed, in some practical applications, the problem is to assess whether the residual strength of a structural component falls lower than a certain threshold, e.g. 9% of the nominal UTS of the virgin material, rather than to approximate the actual residual strength value. This could be treated

80 8 using pattern recognition (PR) schemes to separate the data into an appropriate number of classes, in a multi-dimensional space. In Tou et al. [91], the term "pattern" is used to denote the description of an object. The patterns are thus groups of measurements or observations, determining points in the corresponding multidimensional space. According to Tou et al. [91], "pattern recognition is the categorization of input data into identifiable classes via the extraction of significant features or attributes of the data from a background of irrelevant detail". Pattern recognition is thus a method used for data, or pattern, classification. It is based either on a priori knowledge (supervised pattern recognition) or on information extracted from the patterns themselves (unsupervised pattern recognition). A supervised classification scheme (SPR) requires a set of pre-classified patterns, termed "training set". In unsupervised learning (UPR), the classification scheme is not given a priori labeling of the data, instead it establishes the desired or inherent number of classes based on the statistical or structural regularities of the patterns. In general, the classification schemes use either a statistical or a structural approach. Statistical pattern recognition is based on statistical characterization of the data, assuming that the generation mechanism of the patterns is probabilistic. On the other hand, structural pattern recognition, implemented herein, is based on the structural interrelationships of the features. A wide range of algorithms can be applied for pattern recognition, from simple classifiers to complicated neural networks. A complete pattern recognition procedure requires a sensor that gathers the observations, a feature extraction mechanism that computes information, or descriptors, from the observations and a classification scheme. In this work, the observations were the acousto-ultrasonic descriptors. AU descriptors were used as input to several classifiers A supervised PR scheme A simple SPR algorithm was implemented on the data, to compare with the compound descriptor performance. To implement the SPR method, the data of the training set was a priori assigned to the desired classes. Since the discrimination criterion was residual strength, each class of the training set contained patterns of a specific "residual strength range". The training set was thus separated into two classes: one containing the data with residual strength less than e.g. 9% of the UTS and the other consisting of the rest. The most appropriate scheme to validate the method, using no residual strength information whatsoever, was to use the leave-one-out method, i.e. (k-1) patterns of a k-point union as training set and the k th as testing set. Before use, the 87 CA descriptor-vectors were normalized so as to range from to 1. Euclidean distance was used as measure of similarity between patterns. The algorithm used was "1-NNC" (Tou et al. [91]). n-nnc, i.e. Nearest Neighbour Classifier, is a non-iterative procedure that assigns an unknown point to the class containing the most of its n nearest patterns. The n patterns are taken from the entire set, n being odd to avoid ties in the case of the 2-class problem. 3-NNC and 5-NNC

81 81 were also implemented and their behavior was similar to 1-NNC. Higher n-values were not used, as the dataset contains no more than 87 descriptor vectors. The descriptors used were again D 2, D 3 (uncorrected), D 5 and D 9 so as to compare the performance of the classifier to the compound approach scheme. Although the compound descriptor model is designed to provide direct residual strength predictions rather than a "yes" or "no" in the question of membership in a particular class, the scheme can be simplified to serve the purpose. Therefore, to calculate the compound descriptor performance in terms of "membership" or "no membership", the leave-one-out method was again applied. If both the model prediction and the actual residual strength were over a specific level, e.g. 9% of the UTS, then classification for the particular pattern and for the 9%UTS level was correct. Classification was also correct if both values were below 9%UTS. Results, in terms of success in classification for remaining strength equal to 8 99% of the UTS, are presented in Figure 6.28a. Performance of AE model M 1 is also shown, for comparison. Here in an example explaining Figure 6.28a: consider that specimens are separated into a class containing those whose residual strength is below e.g. 9% of the UTS and one including the rest. The 1-NNC algorithm, using the leave-one-out method, assigns 6 out of the 87 specimens in the correct class (see also Figure 6.28b, showing the misclassified data). Classification success score is thus equal to 69%. Performance of 1-NNC for the particular group of descriptors is the worse, especially for specimens retaining about 88 9% of their nominal tensile strength. Classification success score (%) C AU 7 Model M 1 1-NNC Separation level: Residual strength (% of UTS) (a) X R (MPa) UTS 9%UTS D 2 (b) Strong Weak Misclassified Figure (a) Performance of the 1-NNC classifier vs. compound descriptor C AU (contributing AU descriptors: D 2, D 3 (uncorrected), D 5 and D 9 ) and AE model M 1. (b) 1-NNC clustering into a class corresponding to residual strength below 9%UTS and the complement class corresponding to residual strength above 9%UTS For further validation of the supervised classifier, the variable-amplitude data was also used. The 87-vector CA set was thus used to train the 1-NNC algorithm, while VA patterns formed the validation set. The performance of the 1-NNC classifier is demonstrated in Figure 6.29a, for various levels of residual strength. Again, performance of the respective compound descriptor model as well as AE model M 1 is also presented. There is a characteristic drop in the performance of all

82 82 methods around 9% of the UTS. However, since the residual strength of the VA data varies between and 93.5%UTS, see designated area in Figure 6.29a, classification for similar levels of strength degradation is bound to be an almost unmanageable problem: optimum performance cannot be expected when the classifier is interrogated whether the strength degradation of specimen, with a residual strength of e.g. 89%UTS, exceeds or falls below 1% of the UTS (see Figure 6.29b. Classification success score (%) C AU Model M 1 1-NNC VA data Separation level: Residual strength (% of UTS) (a) X R (MPa) UTS 9%UTS 8 Strong Weak 75 Misclassified D 2 (b) Figure (a) Performance of the 1-NNC classifier on the VA data vs. compound descriptor C AU (contributing AU descriptors: D 2, D 3 (uncorrected), D 5 and D 9 ) and AE model M 1. (b) 1-NNC clustering of the VA data into a class corresponding to residual strength below 9%UTS and the complement class corresponding to residual strength above 9%UTS An unsupervised PR scheme The potential of the selected descriptor set was also interrogated using an unsupervised pattern recognition scheme. Conventional algorithm K-means (Tou et al. [91]) was engaged for the purpose. K-means is an iterative process using K points from the data set as initial cluster centers. The number of classes, K, is user-defined. The remaining patterns are assigned to the K classes using nearest neighbor classification. In each iteration, cluster centers are updated as the mean of the resulting classes. Procedure stops when none of the patterns change class membership. The farthest points in the data set were used as initial cluster centers. A number of 1 iterations were performed in the implementation. Computational time required for each run was negligible and descriptor normalization was the same as in the supervised 1-NNC case. The UPR procedure resulted in the clusters of Figure 6.3. Classes were well-defined and the data was separated in a «strong» and «weak» group. The particular clustering was used to train the 1-NNC algorithm, while the VA set served as validation set. The corresponding classification of the VA data is also presented in Figure 6.3. All specimens were assigned to the strongest class. Since their residual strength values are high enough, this is a rational outcome.

83 83 It should be stated that unsupervised clustering cannot be validated, in a strict sense, as there is no reference for comparison. However, both the resulting classes themselves and the classification of the VA data indicate a good discrimination potential for the descriptor set, regarding residual strength assessment X R (MPa) D 2 Strong Weak VA (1-NNC) Figure 6.3. Unsupervised clustering (K-means) of 87 constant-amplitude data, 2-class problem. Supervised classification of VA data (1-NNC) Conclusions Selected descriptors from acousto-ultrasonics measurements were used to assess residual strength of composite Gl/Ep [±45] S specimens featuring various levels of fatigue damage. The correlation of individual descriptors with residual strength was mediocre. To improve this correlation, a compound descriptor approach was introduced and pattern recognition schemes were implemented. An example of an AU-model based on a compound descriptor was given. The compound descriptor used herein was defined as a linear combination of the 4 best-performance AU parameters. The aim of the scheme, i.e. to cancel out possible measurement inaccuracies and other discrepancies from a statistical view and thus produce a new model demonstrating improved overall performance, was accomplished. The compound descriptor was established on AU measurements from specimens subjected to constant-amplitude fatigue loading and validated with considerable success. Two independent data sets were also used to validate the scheme: one contained data from variable-amplitude tests and the other from specimens of an alternative resin matrix. Good results were obtained. Performance of the compound descriptor was thus more than encouraging. Comparison with respective classification results from a conventional supervised pattern recognition algorithm was in favor of the compound descriptor scheme. Additional features, such as the cost-free and simple implementation, render it advantageous compared to more complicated SPR techniques.

84 84 Unsupervised clustering, using the same descriptor set, seemed quite sensible and resulted in well-separated classes regarding residual strength. Using the resulting clustering for classification of the VA data also seemed rational. However, unlike SPR and the compound descriptor schemes, there is no means to evaluate the performance of UPR algorithms. Although somewhat less reliable than the respective acoustic emission models presented in the previous chapter, stand-alone NDT tools for strength degradation assessment in fatigued [±45] S composite specimens were thus established. As AE-model M 2, the AU method developed herein is universal, i.e. able to assess the residual strength of coupons undergone any kind of fatigue loading.

85 85 7. Wave propagation considerations As presented in Chapter 6, using heuristic acousto-ultrasonic descriptors for the assessment of strength degradation in pre-fatigued [±45] S specimens indeed demonstrated a clear trend. Several empirical schemes were thus implemented. However, compared to the outstanding results from AE monitoring, AU performance in actual residual strength prediction seemed moderate. Since wave propagation characteristics depend on the material elastic properties, axial Young modulus measurements, described in the above and available both for the virgin and the damaged material, could perhaps be of use. For instance, as axial Young modulus is proved to reduce with damage accumulation, mode propagation could provide a useful descriptor regarding shear strength degradation. In order to ameliorate AU assessment and also improve understanding of the respective mechanics, wave propagation in the [±45] S laminate was studied. Several pulser-receiver combinations and wavepath lengths were used. In addition, besides the 1-2 khz sine-sweep described in the baseline AU experimental procedure, broadband Dirac-like spikes and tone-burst excitations were also applied. Experimental results indicated the presence of symmetric and antisymmetric plate wave modes. Comparison of the respective experimental dispersion curves with theoretical predictions revealed the fundamental S and A modes. Changes in the dispersion behavior, due to damage accumulation, are herein presented and studied. However, although a qualitative correlation was indeed observed between damage and modal characteristics, no appropriate descriptors could be defined. To investigate this phenomenon and also validate the experimental findings, wave propagation was then simulated using CyberLogic "Wave2 Plus", a commercial package for computational ultrasonics in orthotropic media [92]. The rather bad agreement between real and simulated transient behavior indicated that wave propagation in anisotropic materials is perhaps too complicated. To address a simpler problem, an isotropic material was then studied. Aluminum specimens of similar dimensions as the [±45] S ones as well as a thinner aluminum plate were used. In this case, simulation of wave propagation was performed via CyberLogic "Wave2 Pro", used for isotropic media. Before use, the package response was validated for bulk wave propagation in an aluminum cube and guided wave propagation in a steel plate. Experimental and model response were compared, suggesting possible limitations of the acousto-ultrasonic technique in as simple as isotropic materials General experimental procedure As described in the above, a certain kind of acousto-ultrasonic measurement was performed on all [±45] S specimens, both reference and alternative material (see Figure 3.2 and Figure 3.4). Two broadband, 2-75 khz, PAC Pico transducers, one serving as pulser and the other as receiver, were placed on opposite sides of the specimen and along the specimen diagonal, using metal jigs (see Figure 3.3). Coupons were supported on foam material in the tab areas, to attenuate reflected

86 86 waves, and grease for roller bearings served as acoustic couplant. Excitation was a.3 msec sinesweep of 1-2 khz (see Figure 3.5d). This series of AU experiments was conducted on the virgin and then on the damaged material. Besides these experiments, some additional AU configurations were implemented on the [±45] S alternative-material specimens. These comprised Dirac-like spike and tone-burst excitations, more sensor combinations and propagation lengths and, most important, capturing of the same signal at different locations (see e.g. Figure 7.1). Measurements from sensors placed back-to-back on opposite specimen surfaces were also conducted. During these experimental series, transducers were strapped on the coupons using elastic tapes instead of metal jigs, in order to reduce/prevent possible extinguishing of flexural modes. Since experimental procedure varied depending on the individual purpose of each test, relevant details shall be provided in the following, where appropriate. Figure 7.1. Experimental set-up for dispersion curve determination. Receivers placed 1 and 12 mm from the pulser, [±45] S specimen 7.2. Experimental results: wave propagation in the [±45] S specimen Signature of propagating waves To gain some insight on wave propagation on the [±45] S specimen, a couple of identical receiving sensors were placed on opposites sides of a virgin coupon, see Figure 7.2. Receivers were PAC Pico sensors while a Panametrics V133-RM 2.25 MHz transducer (videoscan with right-angle microdot connector) served as pulser. Captured signals were amplified using a couple of identical PAC in-

87 87 line pre-amplifiers, with a gain of 4 db and khz band-pass filters. Two excitations were applied: sine-enveloped 5-cycle tone-bursts of various central frequencies and maximum amplitude of 1 Volts (Figure 7.3a) and a Dirac-like spike (broadband excitation), see Figure 7.3b. Respective PSD estimates are also presented, in Figure 7.3c and Figure 7.3d. Tone-bursts were produced using a PAC WaveGen board and Dirac excitation using a model PAC C-11-HV pulse generator. Two propagation distances were examined in the experiments where Dirac excitation was used, in order to investigate dispersion and attenuation issues. Figure 7.2. Experimental set-up used to determine the signature of propagating waves. Receivers R 1 and R 2 placed on opposite sides of the [±45] S specimen (a).3.2 (b) Amplitude (Volts) Amplitude (Volts) Time (msec) Time (μsec) (c) -6 (d) PSD (db) PSD (db) f (khz) f (khz) Figure 7.3. The excitations used in the experiments. (a) 1-kHz 5-cycle sine-enveloped tone-burst excitation, (b) Dirac-like broadband excitation, (c) power spectral density estimate of (a), (d) power spectral density estimate of (b)

88 Tone-burst excitation Tone-burst excitation was a sine-enveloped 5-cycle sine wave, at central frequencies of 5, 1, 15 or 2 khz. Use of the envelope ensured actual narrow-band excitation (no side-lobes in the spectrum) and the small number of cycles confined the duration of the propagating wavetrain (thus helping to resolve echoes), see Alleyne et al. [54]. Maximum excitation amplitude was 1 Volts. Propagation path ran again along the specimen diagonal, however, receivers were placed at 1 mm from the pulser. Signals recorded on the upper and the bottom side of the specimens, at these particular central frequencies, are presented in Figure 7.4. Note that peak amplitude was maximized at 1 khz. Signal amplitude (Volts) Top Bottom Signal amplitude (Volts) Top Bottom -.6 (a) Tone burst: 5 khz Samples (b) Tone burst: 1 khz Samples.3.3 Top Bottom.2 Top Bottom Signal amplitude (Volts) (c) Tone burst: 15 khz Samples Signal amplitude (Volts) (d) Tone burst: 2 khz Samples Figure 7.4. Signals recorded on opposite sides of a virgin alternative-material [±45] S specimen, along the diagonal and at 1 mm from the source. Tone-burst excitation. Central frequencies (a) 5 khz, (b) 1 khz, (c) 15 khz, (d) 2 khz As seen in Figure 7.4, indeed both symmetric and antisymmetric modes were generated. Symmetric or "S" modes can be discerned in the beginning of each signal, where transverse surface displacement with respect to the mid-plane is the same for both receivers (see also Figure 7.5a). On the other hand, opposite surface displacements are characteristic of antisymmetric or "A" modes

89 89 (see Figure 7.5b). Antisymmetric modes arrive later than symmetric ones, thus travel slower. For lower frequencies, however, symmetric modes were hard to distinguish. This was also observed in antisymmetric modes for higher central frequencies. Figure 7.5. Schematic of the transverse surface displacement in plate wave propagation. (a) Symmetric mode, (b) antisymmetric mode Broadband excitation Using a monochromatic tone-burst excitation, modes of propagation were indeed revealed. To obtain a more general view, however, a more realistic source had to be investigated. A broadband Dirac-like excitation was thus used. This experiment was conducted along the coupon axis. Pico sensors were again placed on opposite sides of the specimen, as seen in Figure 7.2, at a 4-mm and then a 12-mm distance from the V133 source. Test results are shown in Figure 7.6. Signal amplitude (Volts) mm from pulser -2 Top Bottom Samples (a) Signal amplitude (Volts) mm from pulser -.6 Top Bottom Samples (b) Figure 7.6. Signals recorded on opposite sides of a virgin alternative-material [±45] S specimen, Dirac broadband excitation. On-axis propagation. Receiver at (a) 4 mm, (b) 12 mm from the source At the 4-mm distance, modes are overlapping. At the larger distance of 12 mm, however, due to dispersion, there is clear separation of an S and an A-mode: the particular S-mode travels faster and thus still occupies the earliest portion of the signal whereas the A-mode is encountered at subsequent arrival times. As a consequence of dispersion, there is apparent signal distortion: as

90 9 stressed in Wilcox et al. [93], waveforms demonstrated in Figure 7.6a are much more "condensed" compared to Figure 7.6b (note the difference in the time scale). Therefore, a longer path of propagation lead to clearer separation between the modes. On the other hand, damping in composites is quite intense (see e.g. Gorman [53] and Prosser et al. [94], comparing signals recorded in aluminum and composite plates). As demonstrated in Figure 7.6, a difference from 4 to 12 mm in the wavepath length caused a signal amplitude reduction of more than threefold. This poses limitations in the "allowed" propagation length, i.e. the topology of the sensors Dispersion curve determination The presence of symmetric and antisymmetric propagating plate modes was thus confirmed. To reveal possible correlations between propagation characteristics and degradation of elastic properties due to fatigue, the order of these modes had to be determined. Some theoretical considerations on plate wave propagation are thus required Basics on plate wave propagation The boundaries of a solid medium govern, or "guide", wave propagation. Plate-like structures are a common waveguide. For propagation of plane waves in a free, boundless, homogeneous and isotropic plate, propagating waves are known as "Lamb" waves. Lamb waves are generated in a distance of 5 1 specimen thicknesses from the excitation source, from the superposition of multiple reflections of longitudinal and transverse waves in the plate upper and bottom boundaries. Lamb waves are the solution to the homogeneous equation of H. Lamb (Lamb [96], Graff [97], Rose [98]) derived from the equation of motion for a propagating disturbance, assuming plane harmonic wave propagation 17 and using boundary conditions corresponding to zero stress on the upper and lower plate surfaces. Since an equivalent equation was also given by Rayleigh, the formulation is known as "Rayleigh-Lamb" equation: c 2 tan(bh/ 2) 4abk + = tan(ah/ 2) (27) (k b ) In Eq. (27), a 2 =(ω/c L ) 2 -k 2, b 2 =(ω/c T ) 2 -k 2. Plate thickness is denoted as "h", angular frequency as "ω", wavenumber as "k", longitudinal wave velocity as "C L " and transverse wave velocity as "C T ". Parameter "c" is equal to +1 for symmetric and -1 for antisymmetric mode of propagation. 17 Plane waves are propagating disturbances in two or three dimensions, where the motion of all particles in the plane perpendicular to the direction of propagation is the same, or else, the wavefront lies in a plane

91 91 Symmetric modes are also called "extensional" or "dilatational" while antisymmetric modes can be found as "flexural". As illustrated in Figure 7.5, modes are distinguished in terms of the plate transverse surface displacement with respect to the mid-plane. Due to Poisson's effect, both modes also feature "in-plane" components. However, since acoustic measurements are performed on the surface of the specimen rather than the edge, the transverse or "out-of-plane" components are the ones usually detected (Gorman [53]). Eq. (27) is a complex expression of frequency and wavenumber, also called the "dispersion" relation. Dispersion is the dependence of wavenumber, or propagation speed, on frequency. A brief description of the phenomenon is given in Section In a non-dispersive medium, the dispersion relation is: C = ω (28) k where "C" is the propagation speed, constant throughout the frequency spectrum (see slope of curve in Figure 7.7a). As argued above, propagation velocity in a dispersive medium is frequencydependent (see slope variation in Figure 7.7b). The propagation velocity corresponding to a monochromatic component is called "phase velocity" and is again given through Eq. (28). In the presence of multiple modes of propagation, the dispersion relation renders multiple solutions, each corresponding to a particular mode. Therefore, more than one mode can be encountered for a particular frequency. An unlimited number of S and A modes can thus propagate in a plate. Zero-order modes S and A emerge at zero frequency and can be encountered over the entire spectrum. Higher-order modes are generated at the plate resonant frequencies and therefore sustain cut-off bounds for the frequency thickness product. Thus, when ultrasound excitation frequency is too low or the plate is too thin, fundamentals A and S are the only Lamb modes "allowed" to propagate in the plate. (a) (b) C G ω ω C P k k Figure 7.7. Example illustrating the shape of the dispersion relation in a (a) non-dispersive, (b) dispersive medium

92 92 In order to obtain useful data from guided wave inspection, excitation and detection of a single and preferably non-dispersive mode is important (Alleyne et al. [54], Wilcox et al. [93], Castaings et al. [95]). To excite a particular mode, longitudinal transducers should be fixed at a given angle and frequency. If longitudinal wave velocity of the medium between the sender and the tested plate is C L and the phase velocity of the desired mode is C P, the incidence angle, a P, required for the excitation of the particular mode is calculated through the Snell-Descartes law: a P = sin 1 C ( C L P ) (29) A basic concept in the investigation of wave propagation, besides phase velocity, is group velocity. Group velocity, C G, is associated with the propagation speed of a group of waves of similar frequencies. C G could thus be regarded as the velocity of energy transportation. C G is equal to the slope of the dispersion relation (see Figure 7.7b), i.e.: C G = ω k (3) As seen in Figure 7.7, in a dispersive medium C P C G. Both phase and group velocity should be distinguished from pulse velocity, i.e. the speed of the signal front. Lamb theory describes wave propagation in homogeneous isotropic plate-like structures, i.e. where thickness, h, is much smaller than the other dimensions. To accommodate anisotropic media, e.g. composites, a much more complicated approach is required. This approach uses the "exact elasticity" theory, a generalization of Lamb wave theory for anisotropic media. Dispersion relations for plate wave propagation in homogeneous anisotropic media can be found in e.g. Rose [98] and Nayfeh et al. [99]. On-axis wave propagation in orthotropic plates is a popular sub-case of general plate wave propagation in anisotropic media. Unlike anisotropic materials, demonstrating no elastic symmetry, in orthotropic media there are three perpendicular planes of elastic symmetry. This means that directions symmetrical to each plane of symmetry are elastically equivalent. The term "on-axis" is used to denote coincidence with the principal 3-axis coordinate system of the medium, i.e. the one defined by the intersection of the planes of-symmetry. The contracted elastic material properties matrix C pq (p,q=1,2,,6) of an on-axis orthotropic medium is given through: C11 C12 C13 C21 C22 C23 C 31 C32 C33 C = (31) C44 C 55 C66

93 93 Thus, due to the elastic symmetry, the number of 21 independent elastic constants required to describe an anisotropic medium is reduced to 9 in the case of an orthotropic material. The elements of the tensor, as functions of the engineering constants of the orthotropic medium, are: C C C C C C C = 1 v 23v 32 = E Δ 2E3 v 21 + v 31v 23 v12 + v 32v = = E Δ Δ 2E3 E1E3 v 31 + v 21v 32 v13 + v12v = = E Δ Δ 2E3 E1E2 1 v13v 31 = E Δ 1E3 v 32 + v12v 31 v 23 + v 21v = = E Δ Δ 1E3 E1E2 1 v12v 21 = E E 44 G 23 C = 55 G Δ C 66 = G 12 1 v12v 21 v 23v 32 v13v 31 2v Δ = E E E v 32 v 13 (32) (33) (34) (35) (36) (37) (38) (39) (4) (41) In the above equations, "E m " is Young modulus in the m-direction, "v mn " is the Poisson's ratio for transverse contraction in the n-direction due to axial tensile loading in m-direction and "G mn " is the shear modulus in the (m-n) plane. Due to the symmetry of the C-tensor, the following relation holds: v E mn m = v E nm n (42) Dispersion relations for on-axis propagation in a homogeneous orthotropic lamina of thickness h, material density ρ and stiffness tensor C pq are given in the literature (e.g. Nayfeh et al. [99]): D11 D23 cot( δ a1) D13D21 cot( δa 3) = for symmetric modes (43) D11 D23 tan( δ a1) D13D21 tan( δa3) = for antisymmetric modes (44) where: D 11 C13 + C33a1W1 D 13 C13 + C33a3W3 D21 = C55(a1 + W 1) D23 = C55(a3 + W 3) = (45) = (46) (47) (48)

94 94 2 P C C11 C55a W1 = ρ (C + C )a 2 P C C11 C55a W3 = ρ (C + C )a B + a = a 1 3 B = B 4AC 2A 2 B 4AC 2A 2 3 A = C 33 C 55 (53) 2 2 B = (C ρ C )C (C ρc P )C (C + C 2 (54) 11 P ) ρcp )(C55 ρcp ) C = (C (55) ωh δ = 2C P (56) (49) (5) (51) (52) It is worth mentioning that when the propagation wavelength, λ, is much larger than plate thickness, a simpler set of governing equations can be used to describe the wave motion (Gorman [53], Graff [97]). This approach, ignoring shear and rotary inertia effects 18, is addressed to as "classical plate theory" and although proving adequate in low frequencies, produces incorrect predictions at higher ranges. Velocities of lowest A and S plate wave modes (exact solutions) tend to reach the solutions derived from classical plate theory, as plate thickness reduces to zero Theoretical dispersion curves vs. experimental (using phase spectra) Measuring group and phase velocity in the time domain is a questionable practice: for group velocity estimation, a good reference point is the centroid of the pulse (see Wear [52]), whereas for phase velocity measurements an appropriate "phase point" should be selected. This could be e.g. the n th peak of the waveform or the n th zero-crossing. However, this method is susceptible to errors, as argued in e.g. Ragozzino [1]. Such problems could result in e.g. erroneous flaw location (see Gorman [53]). Therefore, spectral techniques are considered more appropriate for accurate phase and group velocity assessment. Herein, the method proposed in Sachse et al. [49] was used to extract experimental dispersion curves. Two measurements, performed at different distances from the source, are required to implement the method. The experimental set-up is demonstrated in Figure 7.1. With receiver separation denoted as L and the phase spectra of the recorded signals as φ 1 and φ 2, C P is obtained as: 18 Transverse shear moduli are considered large enough and transverse shear deformation is thus neglected (plane sections of the plate remain plane and perpendicular to the midplane). Plane stress state is assumed to ignore rotary inertia. Shear and rotary inertia effects are accounted for in higher-order (Mindlin) plate theory

95 95 C P ωl = φ φ 2 1 (57) Calculation of the phase spectra as well as "phase unwrapping" were performed using MATLAB standard functions. Unwrapping is required in order for the phase spectrum to be a continuous function of frequency, as the direct result of a Fast Fourier Transform (FFT) is bounded in the [,2π) interval. Using the method of Sachse et al. [49], the generated dispersion curves extend over the entire frequency spectrum. However, unless ideal broadband signals are used, this result is deceiving. As argued in Schumacher et al. [11], the calculated dispersion curves should be considered as valid in the bandwidths of the signal used. Thus, to produce the data required for experimental dispersion curve generation, a wide band of frequencies was introduced into the [±45] S specimen, through a broadband excitation resembling a Dirac signal (see Figure 7.3b). For the same purpose, a custom 1-2 khz MI-TRA board was used. Another requirement is that propagating modes are well-separated, so that the phase velocities of each mode can be derived from appropriate portions of the available signal. The earlier part of the waveforms should correspond to an S-mode whereas A-modes are expected to arrive later and be of greater amplitude than S-modes (see Figure 7.6b). However, several considerations were raised. An important issue was the recommended wavepath length. Sensors placed far from the source were destined to receive attenuated signals. The "weaker" S-mode, in particular, might thus no longer be usable or even detectable. On the other hand, long distances from the excitation source lead to clearer mode separation: placing the receivers too close to the source would result in overlapping of the various modes, as shown in Figure 7.6a, and then the method of Sachse et al. [49] could not be applied. Distance between receivers also posed some more restrictions. A long distance would cover a larger area, promoting faster inspection. However, the signal reaching the remote sensor could have undergone severe attenuation. There was thus a risk that the signal portions used in the extraction of the experimental dispersion curves might not belong to the same mode. All these factors were investigated and a couple of "optimum" configurations were selected. Experiments were conducted along the coupon axis and all sensors were placed on the same side of the specimen. In both cases, distance between pulser (V133 Panametrics transducer, 2.25 MHz central frequency, 4 MHz bandwidth) and remote receiver (miniature PAC Pico sensor, 2-75 khz bandwidth) was 12 mm. The receiving sensor in-between (PAC Pico sensor) was placed at either 1 or 2 mm from the source, rendering corresponding receiver distances of 2 or 1 mm. Again, AU tests were performed both on the virgin and the damaged specimens. The experimental set-up for receivers taped 1 and 12 mm from the source (2-mm separation) is shown in Figure 7.1. During the experiments, specimens were placed on foam material. The pre-amplifiers used were PAC 32-1 khz, 4 db gain. Grease for roller bearings served as acoustic couplant. Before proceeding to the calculation of experimental dispersion curves and in order to obtain a reference basis for comparison and validation, theoretical dispersion curves were determined. Calculation of theoretical dispersion curves was numerical, based on Lee [13]. Implementation

96 96 was performed using an in-house-developed FORTRAN code to solve the exact theory problem for a homogeneous orthotropic material (see Antoniou et al. [12]), i.e. Eqs. (43) and (44). The [±45] S laminate is indeed an orthotropic material consisting of unidirectional, and thus transversely isotropic, laminas. Transversely isotropic media are of higher degree of symmetry compared to orthotropic material, requiring 5 independent elastic constants to be described. A transversely isotropic medium assumes an axis, all perpendicular directions to which are elastically equivalent. Due to this symmetry, Eq. (31) becomes simpler: C 12 = C 13 (58) C 22 = C 33 (59) 1 C 44 = (C 22 C23) 2 (6) C 55 = C 66 (61) In terms of engineering constants, the above translate to: E 3 = E 2 (62) G 13 = G 12 (63) v 13 = v 12 (64) E2 G23 = 2(1 + v ) (65) 23 Since the basic elastic properties of the reference-material unidirectional lamina were derived during the material characterization stage, as seen in Table 15, all information required to compute the corresponding matrix components was available except for v 23. A theoretical estimation of v 23 was thus performed as proposed in Philippidis et al. [14]: v 23 = v 12 1 v 1 v (66) Table 15. Engineering constants of the unidirectional reference material E 1 E 2 (GPa) (GPa) v 12 G 12 (GPa) Thus, the elastic behavior of the lamina was determined. The last problem was "homogenization" of the resulting [±45] S laminate. This was performed as suggested in Pagano [15] and Sun et al. [16] using the elastic properties of the basic unidirectional º and 9º laminas. This approach, based on the "long-wave" concept, is presented in Appendix A. The resulting matrix, corresponding to the homogenized [±45] S laminate, is:

97 C = GPa (67) Using these properties and a material density value of 195 kgr/m 3 in the developed FORTRAN code, theoretical dispersion curves for on-axis plate wave propagation in the "homogenized" [±45] S (orthotropic) laminate were thus computed. Results are illustrated in Figure A 1 S 1 3 S C P (m/sec) A f. d (khz. mm) Figure 7.8. Theoretical dispersion curves for a virgin reference-material [±45] S laminate, on-axis propagation As argued above, there are cut-off bounds for higher order modes at low frequencies. For e.g. a 4- mm laminate thickness, same as the specimens examined in this work, and in the 3 khz band, no other modes can propagate except fundamentals S and A. Indicative wavelengths for this laminate, for e.g. 2 khz, are 15.6 mm for the S mode and 6.6 for A. Experimental dispersion curves were in good agreement with theoretical predictions. Comparison demonstrated that the S and A-modes, detected above, were indeed the fundamentals S and A. An example is given in Figure 7.9. AU measurements were taken on a particular alternative-material coupon, virgin and damaged state. Receivers were placed 1 and 12 mm from the source, in order for the modes to be well-separated. Receiver distance was thus equal to 2 mm. Experimental dispersion curves for the S-modes have herein been extracted using the 1 st oscillation of each waveform. For A-modes, the 1 st "large amplitude" cycle was used. An indicative case is demonstrated in Figure 7.9e. However, although well-defined for the S-mode (Figure 7.9a),

98 98 this practice in the A-mode case (Figure 7.9b) is vague and thus unreliable. Therefore, experimental phase velocities for the antisymmetric modes are indicative and should be regarded with skepticism A1 S 1 (a) 35 (b) 3 S 3 C P (m/sec) A C P (m/sec) Theoretical 5 Virgin Damaged f. d (khz. mm) Theoretical Virgin Damaged f. d (khz. mm) 1.9 (c).9 (d) Normalized PSD S mode Normalized PSD A mode.2 Virgin.1 Damaged f. d (khz. mm).4 Remote receiver (12 mm).3 Virgin material.2.1 Virgin Damaged f. d (khz. mm) (e).2 Signal amplitude S -.3 A Total waveform Used portions Samples Figure 7.9. Theoretical and experimental dispersion curves for an alternative-material [±45] S specimen, before and after fatigue. Receivers placed at 1 and 12 mm from the source. (a) Mode

99 99 S, (b) mode A. (c) PSD of the 1 st oscillation, (d) PSD of the 1 st large-amplitude oscillation. (e) Signal portions used for extraction of experimental dispersion curves Vertical reference lines in Figure 7.9a-d indicate the bandwidths wherein the method is considered reliable, as suggested in Schumacher et al. [11]. Therein, the same spectral method is applied on waveforms recorded on a steel plate. Modes S, A and A 1 are isolated in the time domain and the frequency spectra of each portion are computed. Then, the "peak neighborhood" of each spectrum is used to define cut-off frequencies, wherein the results of the method are considered valid. In the present work, the peak neighborhood was defined as the area above 5% of the normalized PSD spectrum. The frequencies enclosing this area were the cut-off bounds. This practice is illustrated in Figure 7.9c and Figure 7.9d. Two PSD curves are shown for each "virgin" and "damaged" case: these correspond to the pair of signals used to implement the method of Sachse et al. [49]. In the selection of the cut-off bounds, the most conservative (narrower-band) choice is demonstrated. Figure 7.1, on the other hand, illustrates some more AU measurements, on the same specimen, for receiver separation equal to 1 mm (receivers placed 2 and 12 mm from the source). Since modes are not distinguished for the propagation distance of 2 mm, the dispersion curve of the A mode could not be extracted. Vertical reference lines for the damaged specimen coincided with those of the virgin one C P (m/sec) Theoretical Virgin Damaged f. d (khz. mm) Figure 7.1. Theoretical and experimental dispersion curves for an alternative-material [±45] S specimen, before and after fatigue. Receivers placed at 2 and 12 mm from the source. Mode S From both Figure 7.9 and Figure 7.1, C P seems to reduce with damage accumulation. However, in the total of 16 alternative material specimens, no consistent trend could be observed (see Appendix B). In some cases, C P of the damaged material was even higher than in the virgin state. Thus, even qualitative conclusions were hard to deduce.

100 Theoretical dispersion curves vs. experimental (using TF representation) In the above, on-axis wave propagation in the [±45] S laminate was discussed. Nature of the propagating modes was determined and theoretical dispersion curves were produced and compared to the experimental ones, calculated using the method of Sachse et al. [49]. The aim was to observe the alteration of wave propagation characteristics due to matrix cracking and perhaps introduce appropriate descriptors, expressing this phenomenon. However, no solid conclusion on damage assessment was derived. Another approach to visualize the propagating modes and also their reflections is using a timefrequency representation (TFR), i.e. temporal localization of the signal spectral components 19. This is described in e.g. Prosser et al. [18], indicating some important advantages of this processing technique over Fourier-related methods. For instance, combining TFR processing and a broadband excitation, even a single AU measurement could be adequate. Moreover, the technique requires no phase-unwrapping. Hlawatsch et al. [19] and Auger et al. [11] are indicative tutorials reviewing some basic linear (e.g. the short-time Fourier transform and the wavelet transform) and quadratic TFRs (e.g. the Wigner distribution, the spectrogram and the scalogram). Linear TFRs conform to the superposition principle, i.e. the TFR of the linear combination of a number of signal components is the same linear combination of the TFRs of each component alone. However, linear TFRs are subject to an inherent resolution trade-off: improvement of temporal resolution results in reduced spectral resolution and vice-versa. When considering TFRs as energy distributions and, since energy is a quadratic signal parameter, using bilinear (quadratic) representations seems more appropriate. Quadratic TFRs, however, are liable to "interference" cross-terms: as a general rule, for each signal component there corresponds an auto-component, i.e. the signal term. Moreover, for each pair of signal components, there corresponds a meaningless cross-component, the interference term. Thus, the TFR of an N- component signal should comprise N signal components and N(N-1)/2 interference terms. Among quadratic TFRs and although the adequate sampling rate to avoid aliasing is estimated to be almost double the one required in a respective Fourier transform, Wigner distribution presents excellent temporal-spectral resolution. However, quadratic interference terms are substantial even when signal components do not overlap. Cross-terms, sometimes assuming negative signs, "oscillate" in both axes according to component separation in each domain. This oscillation is characteristic in Wigner distributions. In "smoothed 2 " versions of the Wigner distribution, however, these cross-terms reduce in strength. Smoothing is performed when a Gaussian window function is convolved with the distribution. Nonetheless, as in linear TFRs, smoothing causes a loss in the combined temporal-spectral resolution. This handicap is removed in the smoothed pseudo Wigner distribution, where smoothing in the time domain is decoupled from smoothing in the frequency domain. Moreover, using the 19 Using the FFT transform, a signal can be studied either in the time or frequency domain: a combination of these domains is not feasible 2 In essence, smoothing is low-pass filtering

101 11 analytic signal, sampling requirements become the same as in a Fourier transform. This is the Wigner-Ville distribution. To render a Wigner distribution more readable, "reassignment" can also be performed (see Auger et al. [11]). Reassignment is used to "condense" the representation around the gravitational center rather than the geometrical center, in each neighborhood. The reassigned smoothed pseudo Wigner-Ville representation (RSPWV), as implemented in MATLAB function tfrrspwv (N F =16, logarithmic scale, threshold=.5%) was used herein. Processing was applied on the discrete-time analytic signal, Y=Y RE +i Y IM, such that Y IM was the Hilbert transform of real vector Y RE. To improve comprehension of the processed signals and establish a reference baseline, the AU experiment was simulated using CyberLogic "Wave2 Plus v3. R3" 21, supporting orthotropic materials. The material properties used were the ones given in Eq. (67). Simulated experimental setup is illustrated in Figure Receivers were placed at 1 and 12 mm from the source and model thickness was 4 mm. Figure Model set-up used to simulate plate wave propagation in orthotropic media Simulated excitation was a 1/3-μsec Dirac-like triangular spike. Mass density, ρ, was 195 kgr/m 3 and viscous damping terms "eta" and "phi" were.278 and.1 Pa sec 22. Boundary conditions applied on the specimen edges restricted longitudinal and shear movement on the left and shear movement on the right side, covering all thickness. Measured response in the virtual-receiver locations was in displacement units. Simulation time was 12 microseconds and model resolution was 1 pixels/mm. Comparison of the orthotropic model response and a representative [±45] S alternativematerial specimen is demonstrated in Figure Each sub-plot is generated from the companion signal on top. For simulated signals, the top plot illustrates the displacement response of both sides of the plate. Thus, S and A-modes can be discerned. 21 Wave2 solves the two-dimensional (2D) acoustic (elastic) wave equation using a method of finite differences. Wave2 allows the user to compute the full acoustic wave solution in an arbitrary 2D object, subjected to user-defined acoustic sources. Although corresponding to 2D ultrasound problems, computed solutions can be also considered applicable for three-dimensional (3D) objects which are "quite long" in the dimension perpendicular to the object plane. To generate losses, a "viscosity tensor" is incorporated into the lossless acoustic equation. With the introduced loss being proportional to the temporal derivative of the strain, material attenuation and velocities thus become frequency-dependent 22 The combination of viscous damping parameters eta (1 st or shear viscosity) and phi (2 nd or bulk viscosity) assigns a certain amount of attenuation to the material

102 12 An important comment regarding TFR processing should be made before proceeding: TFR images are 3D graphs in essence, the color scale representing the third axis. One edge of the color scale thus corresponds to zero spectral magnitude while the other edge to the magnitude of the dominant frequency component. Thus, z-axis is normalized, meaning that e.g. high-amplitude modes would obscure lower-amplitude ones (see Prosser et al. [18]). This can be seen in Figure 7.12a and Figure 7.12b, where the S -mode is rather invisible. However, S -modes are revealed in Figure 7.12c and Figure 7.12d, where the low-amplitude earliest component of the signal is considered. Volts.1 (a) Volts.5 (b) f (MHz).6.4 f (MHz) Volts Time (μsec).2 (c) Volts Time (μsec).5 (d) f (MHz).3.2 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of simulated and experimental response of a [±45] S composite specimen in a Dirac spike, 1-mm wavepath. (a) Model response, (b) experimental signal, V133 pulser, Pico receiver, (c) model response, detailed view, (d) experimental signal, detailed view Simulated signals (Figure 7.12a and Figure 7.12c) are in considerable agreement with theoretical predictions for the group velocity. Herein, group velocity curves for S and A were computed from the phase velocity dispersion curves, as described in Appendix C. However, other methods can also be found in the literature, e.g. in Wang et al. [111] for symmetric laminates. Theoretical group velocity curves are shown as white lines, solid for the S -mode and dashed for A. Higher-order modes are also present (Figure 7.12a). In the experimental waveforms, however, conclusions are hard to derive. Fundamentals S and A seem to be encountered, although A is not clear.

103 13 Another issue should be reminded: although experimental results were from alternativematerial specimens, theoretical dispersion curves correspond to the reference material. This should be considered in the comparison of experimental and theoretical dispersion curves. As stated in the above, one of the main advantages of TF processing is that no more than one signal is required. Therefore, as a subsequent step, the basic acousto-ultrasonic experimental series was also studied. In this series, a broadband sine-sweep excitation was applied as described in Section Tests were performed both on the reference and the alternative material. Two representative reference-material [±45] S specimens are herein considered. The weaker one retained 74% of the nominal UTS whereas residual strength of the "strong" coupon was 98%UTS. Results for the "weak" and the "strong" specimen are presented in Figure 7.13 and Figure In the top sub-plots, signals corresponding to the virgin state are shown in blue and waveforms recorded on the damaged material in red. Although the example is indicative, there is greater variation in the morphological characteristics of the weaker specimen, from virgin to damaged state, than in the case of the stronger coupon. A second observation is that signals from the virgin material seem to contain higher-order modes, which are absent in the damaged specimens. Theoretical dispersion curves for the A and S -modes, for on-axis propagation 23, are also shown. The curves correspond to the modal group velocities, the horizontal axis being computed using a wavepath length 24 of mm. A comment should be made: the receiver channel was activated using the excitation signal, i.e. once one of the channels was triggered, the other one also started recording. Therefore, there was a small amount of time elapsing from actual triggering to the trigger signal reaching the pre-defined threshold. This was corrected while "placing" the theoretical dispersion curves along the abscissa of the RSPWV diagrams. Volts.1 (a) Volts.1 (b) f (MHz).3.2 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of AU signals taken on a "weak" specimen, (a) virgin, (b) damaged state 23 On-axis propagation is presented instead of the direction along the specimen diagonal 24 Wavepath length is equal to the distance between pulser and receiver centres along the specimen diagonal

104 14 Volts.2 (a) Volts.2 (b) f (MHz).3.2 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of AU signals taken on a "strong" specimen, (a) virgin, (b) damaged state As illustrated in Figure 7.13 and Figure 7.14, theoretical and experimental dispersion curves are in bad agreement. Moreover, large-amplitude signal portions (e.g. A-modes) obscure earlier-arriving lower-amplitude modes (see Prosser et al. [18]). Thus, although visible in the time domain, loweramplitude portions are not discerned in the RSPWV diagrams. To overcome this drawback, lowamplitude segments were isolated and the RSPWV process was again applied. Results for both the "weak" and the "strong" coupon are presented in Figure 7.15 and Figure 7.16, where detailed views are presented. Volts.2 (a) Volts.2 (b) f (MHz).3.2 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of AU signals taken from a "weak" specimen, (a) virgin, (b) damaged state, earliest arrivals

105 15 Volts.1 (a) Volts.1 (b) f (MHz).3.2 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of AU signals taken from a "strong" specimen, (a) virgin, (b) damaged state, earliest arrivals Due to apparent contamination of the respective signal, Figure 7.16a is not commented upon. However, Figure 7.15a and Figure 7.16b seem to demonstrate that signals from undamaged and "low-damaged" specimens follow the theoretical dispersion curves (S -mode), at least for a particular segment of the time-frequency response. This is also emphasized in the work of Protopappas et al. [112], on Lamb mode propagation in healing bones. Behavior of a damaged specimen is presented in Figure 7.15b. Indeed, experimental results seem to deviate from the theoretical trend Influence of damage on dispersion curves: Theoretical estimation In the experimental results presented above, the S mode was recognized. An interesting trend was also observed: experimental dispersion curves deviated from the theoretical ones as damage increased. This phenomenon can be explained. In Figure 7.17, theoretical dispersion curves (group velocity) for the S mode are presented both for virgin material and a simulation of "degraded" material. The degraded material simulation is herein based on matrix cracking being the dominant failure mechanism in the [±45] S specimen under tensile loading and prior to failure (see Philippidis et al. [37]). Elastic properties of the unidirectional component of the laminate that matrix cracking can influence are e.g. E 2, the Young modulus transverse to the fibres, and G 12, shear modulus (Reifsnider [1]). The degraded material of Figure 7.17 features a 5%E 2 reduction, whose influence is obvious.

106 S (virgin) S (5%E 2 reduction) f (MHz) Time (μsec) Figure Theoretical dispersion curves (group velocities) of the S mode, virgin and simulated damaged state To assess the expected behavior of the damaged composite, theoretical dispersion curves for the lower modes were again computed. The new input data contained a 25%E 2 or 25%G 12 reduction in the respective properties of the unidirectional component. In Figure 7.18, theoretical dispersion curves for the "undamaged" reference material laminate (on-axis propagation) are presented in blue solid lines. The effect of the 25%E 2 or 25%G 12 reduction is also illustrated, in red dashed lines. The drop in E 2 is of greater influence on the dispersion curves, especially for (f d) products above 8 khz mm (a) 35 (b) 3 3 C P (m/sec) C P (m/sec) Virgin material 25%E 2 reduction 5 Virgin material 25%G 12 reduction f. d (khz. mm) f. d (khz. mm) Figure Influence of (a) E 2 and (b) G 12 variation on the theoretical dispersion curves of the reference-material [±45] S laminate, on-axis propagation

107 Wave propagation in aluminum: simulation and experiment Although TF processing of the AU signals in the composite [±45] S specimen revealed some of the S mode, theoretical dispersion curves for the A -mode were in bad agreement with experimental results. This could perhaps be due to discrepancies in the actual material properties and the ones used for dispersion curve extraction. Another possible reason could be waveguiding through the ±45º-oriented fibres, leading to faster wave propagation. To resolve the poor agreement between theoretical and experimental dispersion curves in the orthotropic laminate, wave propagation in a 4-mm isotropic aluminum plate was simulated. CyberLogic "Wave2 Pro v2.2" was used for modeling, where plane strain state is considered. Simulated excitation was a 1-Volt Dirac-like triangular spike. Two spike durations were used: 2 and 1/3 μsec. Receiver output was displacement. Default values were used in all fields, unless otherwise stated. Then, model response and experimental results were compared in a 2.9-mm specimen and a.7-mm plate Modeling of wave propagation in 4-mm aluminum plate The simulated problem is illustrated in Figure Model was 25-mm long and 4-mm thick and receivers were placed 1 and 12 mm from the source. Source and receivers respective diameters were 5 and 3 mm. Simulation time was 6 microseconds. No boundary conditions were assumed, i.e. there was no restriction in longitudinal and transverse displacement. For the Dirac-spike durations used, i.e. 2 and 1/3 μsec, and for the wavepath of 12 mm, model predictions are demonstrated in Figure Waveforms both from the upper and bottom side of the specimen are presented, indicating fast a S -mode and slower A -mode. In the case of the narrower excitation, however, a higher-order symmetric mode can be discerned between S and A (see Figure 7.19b). Signal amplitude Top Bottom Samples (a) Signal amplitude Top Bottom Samples (b) Figure Model predictions for wave propagation in 4-mm aluminum plate, 12-mm wavepath. Duration of driving spike (a) 2 μsec, (b) 1/3 μsec

108 18 To implement the method of Sachse et al. [49] for the S -mode, the 1 st oscillation following a positive threshold crossing was again used. Theoretical dispersion curves (phase velocity) were extracted using PACshare Dispersion Curves v1. for the following material properties: longitudinal wave velocity C L = m/sec, transverse wave velocity C T = m/sec, surface (Rayleigh) wave velocity C R =295. m/sec, mass density ρ=27 kgr/m 3 and characteristic acoustic impedance 25 z =ρ C L = kgr/m 2 sec. Comparison between theoretical and numerical (Sachse et al. [49]) dispersion curves, for the S and A -modes, is shown in Figure 7.2. Good agreement is observed. The indicated frequency thickness (f d) bands (vertical reference lines) are used to highlight the maximum of the PSD estimates of the considered waveform portions (see Schumacher et al. [11]). 6 6 (a) (b) C P (m/sec) 3 C P (m/sec) Theoretical A mode (numerical) S mode (numerical) 1 Theoretical A mode (numerical) S mode (numerical) f. d (khz. mm) f. d (khz. mm) Figure 7.2. Theoretical and computed dispersion curves for wave propagation in a 4-mm aluminum plate. Receivers placed 1 and 12 mm from the source. Duration of driving spike (a) 2 μsec, (b) 1/3 μsec Corresponding RSPWV representations are presented in Figure Theoretical group velocity was also calculated using PACshare Dispersion Curves v1.. S-modes are demonstrated as white solid lines whereas A-modes as white dashed lines. In both cases, considerable agreement is observed, although larger-amplitude A -mode obscures the S -mode. As expected, the narrower excitation introduced a wider band of frequencies and the higher-order S-mode observed in Figure 7.19b is now clear and recognized as mode S 2 (Figure 7.21b). 25 Acoustic impedance of a material is a measure of the particles opposing to sound-induced displacement

109 19 Volts (a) Volts (b) f (MHz).5 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of the simulated signals and theoretical dispersion curves for wave propagation in 4-mm aluminum plate. Receivers placed 12 mm from the source. Duration of driving spike (a) 2 μsec, (b) 1/3 μsec Model vs. experiment Dispersion curves computed from simulated AU signals in a 4-mm aluminum plate demonstrated considerable agreement with theoretical dispersion curves in aluminum. In this section, real experimental signals are studied mm aluminum specimen A 2.9-mm aluminum plate model response in a 1/3 μsec spike excitation was compared to an experiment on a 26x25x2.9 (dimensions in mm) specimen. Model configuration was the same as in the 4-mm case described in the above except for thickness, reduced to 2.9 mm. Receivers were again placed at 1 and 12 mm from the source. Boundary conditions applied on the specimen edges restricted longitudinal and shear movement on the left and shear movement on the right side, covering all thickness. Model resolution was 15 pixels/mm instead of the default value of 1 pixels/mm. During the experiment, the aluminum specimen was placed on foam material. Pulser excitation (medium energy) was used. The source was a V133 Panametrics transducer (2.25 MHz central frequency, 4 MHz bandwidth), while 2 miniature PAC Pico sensors (2-75 khz bandwidth), serving as receivers, were placed at 1 and 12 mm from the source. Sensors were taped on the aluminum specimen, using grease as acoustic couplant. Pre-amplifiers were PAC 32-1 khz, 4 db gain. Respective TFRs are shown in Figure S-modes are demonstrated as white solid lines whereas A-modes as white dashed lines. The effect of taping the transducers onto the specimen as well as possible interference of the front sensor on the back receiver response is also investigated in Figure 7.22, where the TFRs from the front (1 mm) and the back (12 mm) receiver are compared.

110 11 Indeed, the signal recorded using the front sensor (Figure 7.22c) is closer to the theoretical dispersion curves whereas the back waveform (Figure 7.22b) seems contaminated. Volts (a) Volts 5-5 (b) f (MHz).4 f (MHz) Volts Time (μsec) (c) Volts Time (μsec) 1 (d) f (MHz).4 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of the (a) simulated and (b) experimental signal, receivers placed 12 mm from the source. (c) Simulated and (d) experimental signal, receiver placed 1 mm from the source. Thickness of aluminum medium: 2.9 mm Observing the front receiver signals, i.e. Figure 7.22c and Figure 7.22d, an obvious comment is that TF processing of experimental signals results in a far more complicated representation compared to the numerical simulation. S of the experimental signal is the mode resembling the most to the simulated waveform. To reveal the S -mode, the earliest portion of the simulated and experimental signals, captured at 1 mm from the source, are presented in Figure Response is almost identical. However, small differences could be due to discrepancies in the actual material properties of the specimen and the ones used for modeling and extraction of theoretical dispersion curves. To investigate the influence of transducers on the experimental results, the standard set-up of a V133 Panametrics source with a couple of PAC Pico receivers, was «inverted» to a new set-up of a Pico source with a couple of V133 receivers. The response of the front sensor (1 mm) is presented in Figure 7.24a. Although V133 is a broadband sensor with 2.25-MHz central frequency and flat response over a 4-MHz bandwidth, the A -mode at frequencies below 2 khz could still not be

111 111 captured. The lack of frequency content above 8 khz, even using the V133 sensor as receiver, could be attributed to the relatively large specimen thickness as well as to the propagation medium. To capture frequencies below 2 khz, a PAC R6 general-purpose sensor (35-1 khz operational bandwidth) was used as receiver. The R6 transducer was placed at a 12-mm distance from a V133 source. No R6 receiver was placed at 1 mm, as R6 sensors are quite large (19.5 mm in diameter) rendering the particular set-up impractical. Results for the 12-mm distance are shown in Figure 7.24b: comparison to Figure 7.24a is still possible, despite the difference in propagation distance. However, coincidence of experimental results with the theoretical dispersion curves in Figure 7.24b is hard to evaluate: while the A -mode seems to be recognized, S cannot be discerned. R6 signals are thus inconclusive. Volts (a) Volts 5-5 (b) f (MHz).4 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation, earliest arrival, of the (a) simulated and (b) experimental signal, receivers placed 1 mm from the source. Thickness of aluminum specimen: 2.9 mm Volts 5 (a) Volts 5 (b) -5.8 Time (μsec) f (MHz).4 f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation of AU experiments on a 2.9-mm aluminum specimen and theoretical group velocity. (a) Pico pulser, V133 receiver, 1-mm distance and (b) V133 pulser, R6 receiver, 12-mm distance

112 mm aluminum plate To exclude reflections from the specimen boundaries in the recorded signal, a.7-mm aluminum plate model response to a 1/3 μsec spike excitation was also compared to a respective experiment on a 298x187x.7 plate (dimensions in mm). Model was the same as in the previous, except for thickness, reduced to.7 mm. Receivers were again placed at 1 and 12 mm from the source. Boundary conditions were applied on the specimen edges, covering all thickness and restricting longitudinal and shear movement on the left and shear movement on the right side. Model resolution was 15 pixels/mm. Model response for a 1-mm wavepath is shown in Figure 7.25a. Experiment was performed on the.7-mm aluminum plate, placed on foam material. Pulser excitation (medium energy) was used. The source was a V133 transducer, while a couple of PAC Pico receivers were placed at 1 and 12 mm from the source. Results for a 1-mm wavepath are shown in Figure 7.25b. Respective detailed views of the S -mode, model and experiment, are presented in Figure 7.25c and Figure 7.25d. Volts (a) Volts (b) f (MHz) f (MHz) Volts Time (μsec).5 (c) Volts Time (μsec) (d) f (MHz) f (MHz) Time (μsec) Time (μsec) Figure RSPWV representation for wave propagation on a.7-mm aluminum plate, 1-mm wavepath, and theoretical group velocity curves. (a) Model response in 1/3 μsec Dirac-like spike, (b) experimental signal (V133 pulser, Pico receiver), (c) model response, detailed view, (d) experimental signal (V133 pulser, Pico receiver), detailed view

113 113 The experimental results indicated that while the A -mode was predicted, (Figure 7.25b), S was in fair agreement with theoretical dispersion curves (Figure 7.25d). Again, this could be due to discrepancies in the actual material properties of the specimen and the ones used for extraction of theoretical dispersion curves. However, although reflections are excluded from the signal, experimental TF representations continue to be more complex than the ones corresponding to numerical simulations Discussion on discrepancies In the above, plate wave propagation in a [±45] S composite laminate was studied. In particular, appropriate acousto-ultrasonic experiments were performed and the propagating modes were depicted in the recorded signals. Two techniques were used to determine experimental dispersion curves: the one proposed in Sachse et al. [49], using phase spectra, and processing in the timefrequency domain. Using the former method, experimental dispersion curves for the S -mode were in good agreement with the theoretical ones. However, no solid descriptors of damage accumulation could be extracted. An interesting remark is the large scatter of about 5 m/sec in the calculated S dispersion curves for the virgin material (see Appendix B): such a variation in theoretically identical specimens suggests a problematic procedure. The TFR technique also revealed some of the S -mode. In most cases, S demonstrated a predictable behavior in the presence of material degradation, although no more than a qualitative trend was observed. Specialized processing techniques, e.g. image processing, could perhaps be used to determine appropriate descriptors from the TF representations. Thus, AU experiments rather failed to reach the desired purpose, indicating the complexness of the problem. Some additional work on plate wave propagation in aluminum confirmed this argument: experimental dispersion curve determination in as simple as isotropic materials was also quite puzzling. Besides the complex nature of the problem and the inherent implications related to inhomogeneous and anisotropic media, possible handicaps in the generation and interpretation of the results are discussed below. These concern equipment-related issues, material variations, noise in the experimental signals, errors in the measurement of the propagation wavepath and the contribution of the propagation medium in the recorded signals Equipment response Some considerations on the response of the AU set-up should be expressed. All recorded signals undergo electronic and hardware filtering, due to software parameters and the transfer function of the equipment. The narrowest of these filters, in the particular configuration, is the transfer function of the Pico sensor. Thus, Pico receivers define the actual limit of the total set-up response. The face-to-face response of the Pico transducers in a broadband negative spike (Dirac) excitation was demonstrated in Figure 3.5. Sensor actual operation bandwidth was seen to range

114 114 between about 2 5 khz, peaking at about 3 and 4 khz (see Figure 3.5c). Therefore, for a coupon thickness of about 4 mm, the expected operational range is 8 2 khz mm. For composite materials in particular, where higher frequency components are more attenuated, the upper bound is even more conservative. Thus, using the particular equipment and experimental setup, higher-order modes as well as frequencies below e.g. 1 khz cannot be captured. This also became obvious in the TF representations Material variation An interesting remark could be made through comparison of the computed dispersion curves for S, from the simulated and experimental waveforms (Figure 7.26). Indeed, in Figure 7.26a, dispersion curves extracted from the simulated signal (blue dashed line) and the theoretical one (black solid line) were in considerable agreement, at least below 1 khz mm. However, processing of the respective experimental signals from a representative alternative-material specimen (Figure 7.26b) resulted in higher-than-expected phase velocity for the S -mode: even more so, since theoretical predictions corresponded to the stronger reference (OB) material instead of the weaker alternative one (a) 4 35 (b) 3 3 C P (m/sec) C P (m/sec) Theoretical Numerical 5 Theoretical Experimental f. d (khz. mm) f. d (khz. mm) Figure Theoretical and computed dispersion curves from (a) numerical simulation, (b) experimental signal from a representative alternative-material specimen. Receivers were placed 1 and 12 mm from the source Experimental noise Except the difference in material properties, another source for discrepancies between modelled and experimental results is noise. As argued in Hull et al. [86], extraction of dispersion curves using the method of Sachse et al. [49] is susceptible to noise. To demonstrate the influence of noise, a particular time series was superimposed to the model waveforms. This time series was the noise recorded using the same equipment and set-up parameters as in the experiments. The signal-to-

115 115 noise ratio (SNR) that was investigated was equal to 5 (see Figure 7.27). In low f d ranges, a small drop in C P was indeed observed. Reversing the sign of the added noise, the respective influence on C P was inverted. This, however, is a rather exaggerated example: the noise level in the actual experiments was much lower, e.g. for the case of Figure 7.26b SNR exceeded 16. Thus, noise in this case can be considered as a negligible cause of discrepancies C P (m/sec) Theoretical Numerical Numerical+noise (SNR=5) f. d (khz. mm) Figure Influence of superimposed noise on dispersion curves computed from numerically simulated signals. Receivers were placed 1 and 12 mm from the source Error in distance measurement Using the method of Sachse et al. [49] for dispersion curve computation requires a known distance between receivers. This length measurement is susceptible to errors (see Prosser et al. [18]). For e.g. a 2-mm receiver distance, a 2.5% (.5 mm) measurement error leads to important uncertainties in the calculated results. An example is given in Figure Receiver distance in the simulation is equal to L A =2. mm. Using an «erroneous» distance of L error =L±.5, in mm, computed dispersion curves for the S -mode are altered as demonstrated in Figure Thus, although skipped in the experiments presented herein, use of a micrometrical contraption for precise sensor placement is suggested. To further minimize error in length measurement, a larger receiver distance could also be used.

116 C P (m/sec) Theoretical Numerical Numerical (distance error=-2.5%) Numerical (distance error=+2.5%) f. d (khz. mm) Figure Influence of error in receiver distance measurement on dispersion curve calculation for the S mode Contribution of propagation medium As argued in Section , a longer wavepath leads to clearer separation between the propagating modes. On the other hand, damping in composites is quite intense, in particular for higher-frequency components. This is demonstrated in Figure 7.29 where the TF representations of the signals of Figure 7.6 (broadband Dirac-like source, receivers placed in a 4 and a 12-mm distance from the pulser, on both specimen surfaces) are presented. Volts mm wavepath (a) Volts mm wavepath (b) f (MHz).4 f (MHz) Time (μsec) Time (μsec) Figure TF representations of signals recorded on opposite sides of a virgin alternative-material [±45] S specimen, Dirac broadband excitation. On-axis propagation. Receivers at (a) 4 mm, (b) 12 mm from the source