A MULTILEVEL MULTIPOLE METHOD FOR MODELINGELASTIC-WAVE MULTIPLE SCATTERING IN FIBER-REINFORCED COMPOSITES

Arnaud Lange1, Anthony Harker2 and Nader Saffari1

Department of Mechanical Engineering, University College London, LondonWC1E7JE,UK

Department of Physics & Astronomy, University College London, LondonWC1E6BT,UK

ABSTRACT. A Multilevel Multipole method is presented for modeling elastic wave multiplescattering in fiber-reinforced composites. Results are given for the case of an incident SH waveimpinging on a bounded Ti/SiC composite region, the plane of propagation being orthogonal to thefibers' axis. The scattering effects of a square and hexagonal arrangement for the fibers are compared.

INTRODUCTION

Elastic-wave multiple scattering effects are significant in the NDE of fiber-reinforced composites (FRCs). Indeed specific attenuation and dispersion effects are due tomultiple scattering, which in turn are related to the composite properties. These include theelastic parameters, distribution, concentration and nature of the fiber reinforcements.Varadan et al. [1] demonstrated the effects of multiple scattering on the coherent wave, inparticular the dependence on concentration at wavelengths comparable to scatterer size. Atvery low concentrations (< 1% by volume) multiple scattering can be neglected and eachscatterer can be treated as independent [2], In many practical situations however, theconcentration can range from 1% to 40% where multiple scattering effects are important.Considerable effort is being directed towards development of numerical models that can beused as analysis tools for optimizing NDE techniques for these composites.

In general, available results for multiple scattering in FRCs are limited to theRayleigh scattering regime. The large number of fibers usually prevents the solution ofsuch large-scale scattering problems via standard numerical methods. Thus variousapproximate theories have been developed to model the average field. Bose & Mal [3] andMal & Chatterjee [4] have used a statistical approach to study the multiple scattering ofelastic waves. This approach generally results in a hierarchy of equations for the averagefields with increasing order correlation functions. Various assumptions are proposed tobreak this hierarchy [5]. In mixture theories [6] [7] [8], the composite constituents aresuperimposed in space and may undergo individual deformations. In theory models ofarbitrary orders of accuracy may then be determined. The complexity of this approachhowever, constrained the authors to applications with a first order theory. Because theseapproaches are concerned with the average field, it is difficult to evaluate the sensitivity of

CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00

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the actual field to local perturbations of the composite structure, which is of major interestin practice.

To consider local perturbations, several deterministic multiple scatteringformulations have been considered. Twersky [9] introduced the concept of "orderedscattering" for acoustic wave problems, where the overall multiple scattering problem isdecomposed into several single scattering problems in the frequency domain. Using thisapproach, the solution is computed recursively. Cheng [10] extended this concept to thecase of elastic waves. Varadan, Varadan & Pao [11] derived an implicit form of themultiple scattering solution. Although these formulations lead to the multiple scatteringsolution, none of them can efficiently compute the solution for a large number of scatterers.The convergence of the recursive forms of the solution is too slow, and the other forms arelimited by the computer memory.

Recent advances in multi-bodies problems however have allowed the numericalcost to be reduced considerably by using multipole methods. Rokhlin & Greengard [12]originally developed the Multilevel Multipole method for the rapid evaluation of thepotential field in systems involving a large number of particles whose interactions areCoulombic or gravitational in nature. This approach was latter extended to acoustic [13]and electromagnetic [14] scattering problems. Indeed, considering a 2D multiple scatteringproblem with TV scatterers, using a multilevel technique may reduce the algorithmcomplexity from O(N2) to O(N). It is proposed here to apply this approach to elastic-wavescattering problems.

In this study Titanium composites reinforced with Silicon Carbide fibers are ofparticular interest. The problem considered is that of an incident SH wave field propagatingin the cross-section plane and scattered by a bounded Titanium composite region. TheTitanium matrix and the various materials involved in the scatterers are taken to behomogeneous and isotropic.

THEORY

Wave Fields Representations

Considering an incident SH wave, no mode conversion occurs during scattering,and the out-of-plane displacement w can be expressed in the form:

w(r ,0 = 0(r)e-ia"9 where V 20 + k 2(j) = 0 (1)

is the scalar Helmholtz equation, ris the position vector, t is time, co is the angularfrequency, is the displacement amplitude, k=co/ft is the shear wavenumber and ft the shearvelocity. For cylindrical scatterers only, the displacement amplitudes of the various fieldscan be expanded in terms of the cylindrical solutions of the Helmholtz equation i.e. theBessel functions. For a single-scatterer problem, the incident wave amplitude (fnc isexpanded in terms of regular Bessel functions of the first kind :

* ={A}T{J(r,0», (2)

and the scattered wave amplitude 0s in terms of singular Hankel functions of the first kind :

= BnH?(kr)eine ={B}T{H(r,0)}, (3)

where (r,9) are the polar coordinates of the observation point in the scatterer's localcoordinate system, whose origin lies within the scatterer.

By definition, the transition matrix [7] of the scatterer relates the wave expansioncoefficients of the incident and scattered waves as:

{B} = [T]{A}. (4)

Multilevel Multipole Method

The method may be implemented in five steps: partition of the structure,aggregation of scatterers, transfer-regularization, de-aggregation of fields and transition tothe next scattering order. Twersky's approach of orders of scattering is used [9].

Structure Partition

Considering a set of TV scatterers, the first step of the multilevel technique is topartition this set in subsets, at different scales. This partition is usually done in quadraturefor convenience. Different scales or levels of partition are considered: a coarse levelcorresponds to a partition in a small number of large cells, whereas a fine level partitionsthe structure in a large number of small cells.

The procedure to build the partition is as follows: a cell that encompasses the wholeset of scatterers is defined first. This level is called Level 0. Then, following a 2D partitionin quadrature, the cell is partitioned in four identical cells. These correspond to the Level 1of partition. The partition in quadrature is performed for each cell at level 1, thus definingthe Level 2 of partition, and this procedure is repeated until each cell contains a smallnumber of scatterers (Cf. Fig.l). A cell at level / is said to be the parent of the cells itgenerates at level /+ 1 i.e. its offspring.

Aggregation of Scatterers

Once a partition has been defined, the first scattering order fields of the scatterers ineach cell are aggregated [12] at the finest level L:

with: = J-kdei^ (6)where Ns is small since the partition is chosen so that, at the finest level, each cell containsa small number of scatterers. The aggregated fields of the cells at level l+l are thenthemselves aggregated to define an approximation of the first scattering order field for theparent cell at level /, for l=L-l,...,l (Cf. Fig.2) :

87

Offspring of Cell

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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

ooo p/6 oooo o o|*o ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

0000o o o oo o o oo o o o00000000o o o oo o o o0000o o o oO O O 0o o o oo o o o0000o o o o

000000000000o o o oo o o oo o o oo o o oo o o oo o o oo o o o0 O O Oo o o oo o o oo o o oo o o o

o o d/o00f/°o oq oo o o oo o J> oo ô oo o o oo o o oo o o oo o o oo o o oo o o oo o o oo o o oo o o o

p\o o o«Hf O O6000o o o o

1. Aggregation atscatterer's level

2. Aggregated Cells atlevel L

oe/oe/3. Aggregation at

level L

FIGURE 2. Aggregation from offspring to parents' level.

cell c at level Lc+l via Graf series :

:i)lr nlistyZs=l

with : offspr(i} \nm = Jn-m (kds offspr(i} ) e

^soffsprd) _]\J Voffspr(i}' Uoffspr(i)

i(n-m)6soffspr(i}

(9)

(10)

The interaction list of each offspring at level Lc+l is then taken into account via the sameprocedure as in the previous section. Both steps Transfer-Regularization and De-aggregation are repeated until the finest level L is reached. Scatterers whose contributionshave not been taken into account are transferred at the scatterers' level.

Transition to next Scattering Order

At this stage, for each scatterer s, all the contributions from the other scatterers havebeen transferred to the local coordinate system associated with scatterer s. The T-matrix ofscatterer s is then applied to compute the next scattering order field:

^'(2) ={C™}T{H(r.,e.)}, where: {cf>] = [r,]{C

List of Cell IiittractMifiList of Cell

Level /

FIGURE 3. Interaction list at different levels (white cells).

Level l+l

NUMERICAL RESULTS

In the following applications, an incident harmonic SH plane wave is propagatingalong the horizontal x-axis in the positive direction in the cross-sectional plane. The waveis scattered by a bounded composite region. The displacement amplitude of the total field0totis computed in the neighborhood of the composite region. A composite structurecontaining 1024 fibers is considered, and results are compared for two typical fiberarrangements, square and hexagonal, respectively. The fiber diameter is 140um. Each fiberhas a carbon core of 30um diameter, and a thin carbon layer of lum at the fiber/matrixinterface is also taken into account in the models.

The displacement amplitude of the total field in the near-field region of thecomposite structure is plotted on Fig.4 at frequency of 1 MHz. This corresponds to awavelength of about 23 times the fiber diameter. Major differences may be seen in thefields for the different fiber arrangements. For a square fiber arrangement, little reflectionand attenuation occur along the x-axis in the backscattered and transmitted regions,respectively. Higher reflection and transmission exist however for a hexagonal fiberarrangement. The symmetry of the composite structure is apparent from the field obtainedfor a square fiber arrangement, as opposed to the hexagonal one. In both cases, an effectfrom the structure corners is visible at about the 40° direction. The far-field displacementamplitude is plotted in Fig.5. Differences between both composite structures in reflectionand attenuation along the axis of propagation are still present. A slight effect due to thestructure corners is also visible.

CONCLUSIONS

The Multilevel Multipole method allows full-scale simulations of elastic wavemultiple scattering in fiber-reinforced composites. Deterministic models can thus bedeveloped to investigate the effects of various composite configurations on the totalscattered wave field. Major differences at low frequency have been detected in the near-field as well as in the far-field between a square and a hexagonal fiber arrangement.

90

30 150

0 180

330 210

(a) (b)FIGURE 4. Near total displacement field for a composite structure with 1024 fibers: (a) square fiberarrangement; (b) hexagonal fiber arrangement.

30 150

o iao

330 210

(a) (b)FIGURE 5. Far total displacement field for a composite structure with 1024 fibers: (a) square fiberarrangement; (b) hexagonal fiber arrangement.

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Higher frequency solutions are currently being studied. Although the method andthe results have been presented in the frequency domain for SH waves only, time-domainsolutions may be obtained using an inverse Fourier-Laplace transform. Moreover, theextension to P/SV waves is straightforward [15]. The various materials involved in themodel have been taken to be homogeneous and isotropic, however a weak anisotropy forthe Titanium matrix can be taken into account by modifying the bases functions [16].Cylindrical scatterers of various cross-sections may be implemented via a multiplemultipole method [17]. The results will be validated experimentally.

ACKNOWLEDGEMENTS

This work is supported by the Engineering and Physical Sciences Research Councilof the United Kingdom, grant no. GR/M83049.

REFERENCES

1. V.K. Varadan, T. Ma and V.V. Varadan, A Multiple Scattering Theory for Elastic WavePropagation in Discrete Random Media, J. Acoust. Soc. Am. 77, pp. 375-385 (1985).

2. A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic, NewYork (1978).

3. Bose S. K., Mal A. K., Int. J. Solids & Struct. 9, pp. 1075-1085 (1973).4. A.K. Mal and A.K. Chatterjee, J. Appl. Mech. 44, p. 61 (1977).5. M. Lax, Multiple Scattering of Waves, Revs. Modern Phys. 23, pp. 287-310 (1951).6. B. Lempriere, On the Practicability of Analyzing Waves in Composites by the Theory of

Mixtures, Lockheed Palo Alto Research Laboratory, Report No. LMSC-6-78-69-21(1969).

7. A. Bedford and M. Stern, Toward a Diffusing Continuum Theory of CompositeMaterials, J. Appl. Mech. 38, 8 (1971).

8. G.A. Hegemier, G.A. Gurtman and A.H. Nayfeh, A Continuum Mixture Theory ofWave Propagation in Laminated and Fiber Reinforced Composites, Int. J. SolidsStructures 9, pp. 395-414 (1973).

9. Twersky V., /. Acoust. Soc. Am. 24, pp. 42-46 (1952).10. Cheng S. L., /. Appl. Mech. 36, pp. 523-527 (1969).11. Varadan V. K., Varadan V. V. & Pao Y.-H., /. Acoust. Soc. Am. 63, pp. 1310-1319

(1978).12. L. Greengard and V. Rokhlin, A Fast Algorithm for Particle Simulations, J. Comp.

Phys. 73(2), pp.325-348 (1987).13. C.C. Lu and W.C. Chew, A Multilevel Algorithm for Solving a Boundary Integral

Equation of Wave Scattering, Micro. Opt. Tech. Lett. 7, pp. 466-470 (1994).14. L. Greengard and V. Rokhlin, A New Version of the Fast Multipole Method for the

Laplace Equation in Three Dimensions, Acta Numerica 6, pp. 226-269 (1997).15. L.-W. Cai, Multiple Scattering of Elastic Waves in Fiber Reinforced Composites, Sc.D.

Thesis, pp. 162-163, MIT, Cambridge, MA, June 199816. Hafner C., Post-modern Electromagnetics : Using Intelligent Maxwell Solvers, John

Wiley, New York, 1999.17. Lange A., Marker A. and Saffari N., A Coupled Semi-Analytical/Boundary Method for

Modeling Ultrasound Scattering in Titanium Metal-Matrix Composites, Rev. ofProgress in QNDE 20, AIP Conference Proceedings, New York, pp. 43-50 (2001).

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WelcomeContentsMINISYMPOSIUM: IMPORTANT TECHNOLOGY ADVANCES FOR NDEAdvances in Information TechnologyNDE of Material Degradation by Embrittlement and FatiguePractical Long Range Guided Wave Inspection Managing Complexity

ELASTIC WAVES AND ULTRASONIC TECHNIQUESSection A. Ultrasonic ModelingA Coupling Method of Boundary Element Method and Generalized Ray Theory for Elastic Wave Scattering in a Thick PlateAn Extension of the Spring Model to Nonlinear InterfacesDiffraction of an Elastic Wave by a Rough Crack EdgeScattering of Elastic Waves by a Rectangular Crack in a Thick Walled Anisotropic SolidHybrid Modeling of Elastic Wave Scattering in a Welded CylinderA Formal Approach to Include Multiple Scattering in the Estimation of Ultrasonic Backscattered SignalsA Multilevel Multipole Method for Modeling Elastic-Wave Multiple Scattering in Fiber-Reinforced CompositesA Multilevel Multipole Method for Modeling Elastic-Wave Multiple Scattering in Fiber-Reinforced CompositesModelling of the Ultrasonic Response of Inclusions in SteelsUltrasonic Attenuation as Influenced by Elongated GrainsComputational Study of Grain Scattering Effects in Ultrasonic MeasurementsAdvances in Modeling Ultrasonic Noise Induced by Machining Advances in Modeling Ultrasonic Noise Induced by Machining Roughness: Development and ValidUltrasonic Detection of Damage in Heterogeneous MediaWaves in Anisotropic Elastic Media

Section B. Guided WavesScattering of the SHO Mode from Geometrical Discontinuities in PlatesRemote Monitoring of Plate-Like Structures Using Guided Wave ArraysSimulations of Laser-Generated Guided Waves in Two-Layer Bonded Plate with a Weak InterfaceCrack Detection for Aircraft Holes with Limited Accessibility Containing Fasteners and SealantModels for Crack Detection in a Cylindrical Hole Containing an Elastic Layer and a Fluid-Filled Cylindrical HoleOn the Detectability of Fatigue Crack Growth at Fastener Holes Using Guided WavesReflection of the S0 Lamb Mode from a Part-Depth Circular Defect in a Plate, When the Incident Wave is Created by a Small SourceHigh Frequency Guided Wave Virtual Array S A F TFast Techniques for Calculating Dispersion Relations of Circumferential Waves in Annular StructuresThe Scattering of Ultrasonic Guided Waves in Partly Embedded Cylindrical StructuresDetection of Scale Inside of Water Supply Pipes Using Guided WavesLong Range Inspection of Rail Using Guided WavesNon-Axisymmetric Wave Focusing in Pipe InspectionSemianalytical Finite Element Analysis for Ultrasonic Focusing in a PipeThe Application of Finite Element Modelling to Guided Wave Testing Systems

Section C. Laser UltrasonicsLaser Ultrasonic System for On-Line Steel Tube GaugingDoppler Frequency-Shift Compensated Photorefractive Interferometer for Ultrasound Detection on Objects in MotionA Theoretical Model for the Ultrasonic Detection of Surface-Breaking Cracks with the Scanning Laser Source TechniqueCalculation of Ultrasound Excited by a Pulsed Thermal Source Distributed Along the Depth DirectionThe Optimization of Lamb and Rayleigh Wave Generation Using Wideband-Low-Frequency EMATsLaser Generation of Focused Ultrasonic WaveAn Effective Generation of Lamb Waves in a Thin Plate Using Laser Line Array Illumination and Their Propagation CharacteristicsHigh Frequency Ultrasound Generation Using a Femtosecond LaserA New Thermoelastic Source Model for Non-MetalsLamb Wave Dispersion Characterization Using Multiplexed Two-Wave Mixing InterferometryUsing Computer Vision to Map Laser Ultrasound onto CAD Geometries

ELECTROMAGNETIC, THERMAL, AND X-RAY TECHNIQUESSection A. Eddy Current Modeling, Probes, and ArraysCoupled Transient Thermal and Pulsed EC Modeling for NDT of Materials Subjected to Laser Based Heat TreatmentSimulation of Eddy-Current Corrosion Detection Using a Sensor ArraySimulation of Ultrasonic and Electromagnetic Nondestructive Evaluation of CorrosionElectric Potential in Eddy Current TestingAdvances in Modeling Eddy-Current NDE of Ferromagnetic BodiesPulsed Eddy-Current NDE at Iowa State University Recent Progress and ResultsDevelopment of Eddy Current Probe for Thick-Walled Plates and Quantitative Evaluation of CracksAn RFECT Probe with a Superconducting ShieldA New Eddy Current Surface Probe for Short Flaws with Minimal Lift-Off NoiseGMR Magnetic Sensor Arrays for NDE Eddy-Current TestingEddy Current Testing of Thick Aluminum Plates with Hidden CracksExperimental Verification of Model-Based ECT Signal Interpretation for Quantitative Flaw Characterization in Steam Generator Tubes

Section B. Microwave and SQUID NDENear-Field Microwave and Embedded Modulated Scattering Technique (MST) for Dielectric Characterization of MaterialsNano Spatial Resolution with 60 GHz Near-Field Scanning Millimeter-Wave MicroscopeNear-Field Scanning Microwave Microscope Using a Dielectric ResonatorNear-Field Microwave Detection of Corrosion Precursor Pitting under Thin Dielectric Coatings in Metallic SubstrateInfluence of Cyclical Soaking in Chloride Bath and Drying of Mortar on its Microwave Dielectric Properties: The Forward ModelMicrowave Radar Detection of Gas Pipeline LeaksDetecting Incipient Fatigue Damage with Scanning SQUID Microscopy

Section C. Thermosonics and Thermal Wave ApplicationsLaser Vibrometry and Strain Gage Measurements of Thermosonic ActivationRecent Developments in Sonic IR ImagingOptimizing the Thermosonics SignalSonic IR Imaging and Vibration Pattern Studies of Cracks in an Engine DiskAcousto-Thermal Microstructure CharacterizationModeling of Effects of Excitation Velocities on the Thermal Image Obtained for Thermosonic N D EUltrasound Burst Phase Thermography (UBP) for Applications in the Automotive Industry

Section D. X-Ray Techniques and ApplicationsSpecial Features in Radiography Accessed by 3D Monte Carlo ModelA Monte Carlo Analysis of the Lead Screen Impact on Film Radiography Image FormationNew Developments in Virtual X-Ray Imaging: Fast Simulation Using a Deterministic ApproachIssues with the High Energy Radiography SimulationsAutomated Identification of Intergranular Corrosion in X-Ray CT Images

SIGNAL AND IMAGE PROCESSING, SIZING, INVERSION, AND RECONSTRUCTIONSection A. Signal and Image ProcessingData Fusion Method for the Optimal Mixing of Multi-Frequency Eddy Current SignalsDesign of an NDE Integrated Data Acquisition System (NIDAS)Time-of-Flight Measurements from Eddy Current TestsWavelet for Ultrasonic Flaw Enhancement and Image CompressionNeural Network Analysis for Evaluating Welding ProcessNew Modular Ultrasonic Signal Processing Building Blocks for Real-Time Data Acquisition and Post ProcessingSwept Frequency Multiplication (SFM) Techniques for Improved Air-Coupled Ultrasonic NDEModel-Based Enhancement of the TIFD for Flaw Signal Identification in Ultrasonic Testing of Welded JointsMechanical and Electrical Noise in the PVLAS ExperimentStatistical Characterization of Multi-Phase Flow by Dynamic TomographyApplication of Taguchi Methodology for Optimizing Test Parameters in Magneto-Optic ImagingUltrasonic Array Approach for the Evaluation of Electrofusion Joints of Polyethylene Gas PipingUltrasonic Tomographic Imaging of Air Flow in Pipes Using an Electrostatic Transducer ArrayIdentification of Thermal and Optical Effects for the Detection of Open-Crack in Photothermal Nondestructive TestingA New Approach to Thermal TomographyAutomatic Evaluation of Welded Joints Using Image Processing on Radiographs3D Modeling of a Magneto-Optic Imager by a Dyadic Green's Functions Approach

Section B. Sizing, Inversion, and ReconstructionQuantitative Approaches to Flaw Sizing Based-On Ultrasonic Testing ModelsGroove Sizing Using a Robust Neural Network ApproachEstimation of Defect's Geometric Parameters with a Thermal MethodApplication of Linearized Inverse Scattering Methods to the Material with Flat Measurement SurfaceThree Dimensional Born and Kirchhoff Inversions for Shape Reconstruction of DefectsApplication of Optimization Methods to Crack Profile Inversion Using Eddy CurrentsReconstruction of 3D Flaws in Eddy Current Quantitative Nondestructive Evaluation

ULTRASONIC ARRAYS, TRANSDUCERS, SENSORS, TECHNIQUES, AND DEVICESSection A. Ultrasonic ArraysGuided Wave Beam Steering from Omni-Directional Transducer ArraysComparative Evaluation between Ultrasonic Phased Array and Synthetic Aperture Focusing TechniquesUltrasonic NDT Simulation Tools for Phased Array TechniquesDevelopment and Optimization of a Rotating Phased Array Inspection SystemPhased Arrays Techniques and Split Spectrum Processing for Inspection of Thick Titanium Casting ComponentsGroundwork for Rail Flaw Detection Using Ultrasonic Phased Array InspectionCorrosion Monitoring of Airframe Structures Using Ultrasonic Arrays and Guided WavesAn EMAT Array for the Rapid Inspection of Large Structures Using Guided Waves

Section B. Transducers, Sensors, and ProbesNew Piezocomposite Transducers for Improvement of Ultrasonic InspectionsA Modular Multi-Gaussian Beam Model for Isotropic and Anisotropic MediaSimilarity of Gaussian and Piston Transducer VoltagesApplication of a Giant Magnetoresistive (GMR) Sensor for Characterization of Corrosion in a Laboratory SpecimenLow-Coherence Optical Probe for Non-Contact Detection of Photothermal and Photoacoustic Phenomena in BiomaterialsDesign of a Fiber Bragg Based Measurement System for Strain and Temperature Monitoring

Section C. Techniques and DevicesModulation Enhanced Detectability of Cracks Using Surface Acoustic WavesAcoustic Interferometer for Localized Rayleigh Wave Velocity MeasurementsDevelopment of a Manual Air-Coupled Ultrasonic Inspection Instrument for Use on Aeronautical Structures Under In-Service ConditionsDevelopment of a High Performance Acousto-Ultrasonic Scan SystemAcquisition of Time of Flight Diffraction Data by Mobile RobotsSequential Evaluation of QNDE Devices for Underground Storage TanksDevelopment of Modeling and Simulation for Magnetic Particle Inspection Using Finite ElementsThree-Channel Non-Force Magnetic MicroscopeDevelopment of a Magnetic NDE Imaging System Using Magnetoresistive DevicesQuantitative Evaluation of a Crack Inside of Pressure Pipeline by Shearography and ESPIDevelopment and Testing of Prototype Giant Magnetoresistive (GMR) Rotating Probe System

ENGINEERED MATERIALS AND COMPONENTSSection A. Composites and ComponentsPrediction of Ultrasonic Fields into Composite Multi-Layered Structures: Homogenization Approach for the Direct Field and Statistical Approach for theOptical Absorption of Epoxy Resin and its Role in the Laser Ultrasonic Generation Mechanism in Composite MaterialsNon-Contact Inspection of Composites Using Air-Coupled UltrasoundThermographic Depth Profiling of Delaminations in CompositesImaging of Fatigue Damage in CFRP Composite Laminates Using Nonlinear Harmonic GenerationAn Experimental Study on the Impact Collapse Characteristics of CF/Epoxy Circular TubesInfrared Scanning of FRP Composite MembersNondestructive Evaluation of Ceramic Matrix Composite Combustor ComponentsDevelopment of Nondestructive Inspection Methods for Composite Repair

Section B. NDE for Bonds, Interfaces, and CoatingsModeling of Transmitted Ultrasonic Signals Through Bonded Aluminum SkinA Comparison of the Detectability of Dry Contact Kissing Bonds in Adhesive Joints Using Longitudinal, Shear and High Power Ultrasonic TechniquesNonlinear Angle Beam Ultrasonic Evaluation of Adhesive BondsThe Development of Shear and Compression Elastic Moduli in Curing Epoxy Adhesives Measured Using Non-Contact Ultrasonic TransducersRoughness-Caused Dispersion of High Frequency Surface Acoustic Waves on Crystal MaterialsThe Interaction of Lamb Waves with Solid-Solid InterfacesThe Use of Ultrasound to Measure Contact Stiffness and Pressure in Large Contacting InterfacesDetection of Weak Interface Signals for Same Material Bond/Weld InspectionTransmission and Reflection of AO Mode Lamb Wave in a Plate OverlapA Comparison of Ultrasonic Wave Reflection/Transmission Models from Isotropic Multi-Layered Structures by Transfer-Matrix and Stiffness-Matrix RecursiApplication of Fast Multipole Boundary Element Method to Scattering Analysis of SH Waves by a Lap JointCharacterization of Weathering Degradation in Aircraft Polymeric Coatings Using NDE Imaging Techniques

Section C. Infrastructure Materials, Components, and SystemsUltrasonic Methodology to Characterize the State of CureCrack Depth Measurement in Concrete Using Surface Wave TransmissionMicrowave Reflection and Dielectric Properties of Mortar Exposed Periodically to 2% Chloride Salt Solution and Compression ForceInspection of Steel Tendons in Concrete Using Guided WavesRadar Detection of Rebars Including Use of Neural Networks and Horn AntennasCalculation and Measurement of Ultrasonic Attenuation for Distributed Cracks in a SolidNondestructive Evaluation of Double Bevel T-Joint by Tandem Array Ultrasonic TransducerNDE of FRP Wrapped Timber Bridge Components Using Infrared ThermographyNDE of FRP Bridge Beams and DecksImproving the Accuracy of Impact-Echo in Testing Post-Tensioning DuctsThree-Dimensional Steady-State Green's Function for a Layered Isotropic PlateAxisymmetric Modes that Propagate in Buried Iron Water PipesDesigning and Building to "Impossible" Tolerances for Vibration Sensitive Equipment

MATERIALS CHARACTERIZATIONSection A. Materials Properties, Microstructure, and DegradationPrincipal Surface Wave Velocities in the Point Focus Acoustic Materials Signature V(z) of an Anisotropic SolidErrors in the Measurement of Ultrasonic Phase Velocity in the Context of Materials EvaluationA Guided Wave Technique for the Characterization of Highly Attenuative Viscoelastic MaterialsParabolic Mirror and Air-Coupled Transducer for Multimodal Plate Wave DetectionCharacterization of Solution Annealing Behaviour in Titanium Alloys by Ultrasonic Velocity MeasurementsIdentification of Sintered Irons with Ultrasonic NonlinearityUltrasonic Backscattering Profiles on Periodically Rough InterfaceMaterials Characterization Using Reconstructed Thermographic DataInvestigation of Velocity Surface of Bulk Acoustic Waves for Proton-Exchanged LiNbO3 CrystalCalculation of the Saw Velocity Change of Proton-Exchanged LiNb03CrystalInvestigation of Thermal Diffusivity of Nano-Structured TiO2FilmsA Study on Point Defects of ZnSe/Ga Sa Epilayer Obtained from Photoluminescience MeasurementA Study on Properties of Infrared Detector for a HGCDTE Epilayers Using Photocurrent MeasurementElectrostatic Detection of Density Variations in Green-State Powder Metallurgy CompactsA Study of Drying and Cleaning Methods Used in Preparation for Fluorescent Penetrant Inspection-Part IA Study of Drying and Cleaning Methods Used in Preparation for Fluorescent Penetrant Inspection-Part IIModeling Ultrasonic Grain Noise within Ti-6Al-4V ForgingsSimultaneous Measurement of Grain Size and Shape from Ultrasonic Backscattering Measurements Made from a Single SurfaceCorrelation between Local Ultrasonic Properties and Grain Size within Jet-Engine Nickel Alloy BilletsEffect of Surface Curvature on Backscattered Ultrasonic Grain Noise in Titanium ForgingsLocalization of Dwell Fatigue Cracks in Ti-6242 Alloy SamplesA Lamb Wave Study on Thermal Damage in a Degraded PlateDependence of the Perpendicular Residual Leakage Magnetic Flux Density on Fatigue Damage in an Austenitic Stainless SteelMonitoring Fatigue Damage Accumulation with Rayleigh Wave Harmonic Generation MeasurementsEstimation of Degradation of Strength Properties of a Material of Structures Intended for a Long Service Life Using a Combination of Mathematical ModeComparison of Ultrasound with Tensile Testing of Thermally Damaged Polyimide Insulated Wiring (MIL-W-81381)Non-Baseline Damage Detection from Changes in Strain Energy Mode Shapes. Experiments on Armored Vehicle Launched Bridge

Section B. Applications of Acoustic Emission for Materials CharacterizationMultifrequency Acoustic Emissions (AE) for Monitoring the Time Evolution of Microprocesses within SolidsRelation between Amplitude and Duration of Acoustic Emission SignalsAcoustic Emission Technique for Characterizing Deformation and Fatigue Crack Growth in Austenitic Stainless SteelsAcoustic Emission Performance for Damage Monitoring of Impacted FRP Composite LaminatesDetection and Identification of Concrete Cracking in Reinforced Concrete by Acoustic Emission

Section C. Applications of Laser Ultrasonics for Materials CharacterizationLaser Ultrasound: An Inspection Tool of Soft Porous Low-Dielectric Constant Films for Microelectronic InterconnectLaser Ultrasonic Inspection of Compositionally Graded Mullite CoatingsNonlinear Laser Ultrasonic Measurements of Localized Fatigue DamageLaser Ultrasonic Study of Crack Tip DiffractionVisualization of Surface-Breaking Tight Cracks by Laser-Ultrasonic F-SAFTLaser Ultrasonic Characterization of Residual Stresses in Thin FilmsRepeatability of an Ablation Source Using a Time-Frequency Representation

Section D. Stress and TextureCharacterization of Plastically Deformed Steel Utilizing EMAT Ultrasonic Velocity MeasurementsMonitoring of the Level of Residual Stress in Surface-Treated Specimens by a Noncontacting Thermoelectric TechniqueResidual Stress Relaxation Due to Fretting Fatigue in Shot Peened Surfaces of Ti-6Al-4VA New Model Equation for Interpreting the Magnetomechanical Effect Using a Generalization of the Rayleigh LawStress Evaluation by Chaotic Characteristic of Barkhausen NoiseThe Effect of Plastic Deformation and Residual Stress on Magnetic Barkhausen Noise Signals in Mild SteelExperimental Observation of Linear and Non-linear Guided Wave Propagation in Rolled Aluminum SheetsTheoretical Aspects of Linear and Non-linear Guided Wave Propagation in Rolled Aluminum Sheets

NDE APPLICATIONSSection A. "Smart" Systems for Structural Health MonitoringA Hybrid Approach to Structural Health Monitoring Using Nondestructive Evaluation (NDE) and Active Damage InterrogationSensor Technology for Integrated Vehicle Health Management of Aerospace VehiclesLasernet Fines Wear Debris Analysis Technology: Application to Mechanical Fault DetectionFatigue and Stress Monitoring Using Scanning and Permanently Mounted MWM-ArraysConcepts for an Integrated Vehicle Health Monitoring SystemPlate-Wave Diffraction Tomography for Structural Health MonitoringEmbedded Ultrasonic Transducer Design and Wireless Communications for Intelligent Monitoring of StructuresDevelopment of an Intelligent Electromagnetic Sensor to Detect Ferrous Corrosion Products Under Structural Coatings

Section B. NDE for Process Characterization and ControlUsing Ultrasonic Diffraction Grating Spectroscopy to Characterize Fluids and SlurriesCharacterization of Solid Liquid Suspensions Utilizing Ultrasonic MeasurementsArtificial Neural Network Based Algorithm for Acoustic Impact Based Nondestructive Process Monitoring of Composite ProductsThe Consistency of Phenomenological Models of Ultrasonic Wave Propagation in a Curing ThermosetA Laboratory Laser-Ultrasonic Instrument for Measuring the Mechanical Properties of Paper WebsAn Ultrasonic Meter to Characterize Degree of Fouling and Cleaning in Reverse Osmosis FiltersLaser-Ultrasonic Characterization of the Annealing Process of Low-Carbon SteelWide Bandwidth Air-Coupled Ultrasonic Testing of Food Containers in AirDepth Profiling of Machined Surfaces Using Cross Correlation of Barkhausen Noise Butterfly CurvesLocating LCD Glass for Robotic HandlingOptical Low-Coherence Reflectometry for Nondestructive Process MeasurementsDefect Signal Enhancement in Inspection Lines by Magnetic Flux LeakageOn-Line NDE for Advanced Reactor Designs

Section C. NDE for Bio MaterialsNeural and Decision Theoretic Approaches for the Automated Segmentation of Radiodense Tissue in Digitized MammogramsCT Based Radiography Simulations for Both Industrial and Medical RadiographyNoninvasive Imaging for Tissue Characterization and Hyperthermia ThermometryAttenuation Coefficient Estimation Using Equivalent Diffraction Points with Multiple Interface Reflections

BENCHMARK COMPARISONS, RELIABILITY, AND EDUCATIONSection A. Benchmark Problems2002 Ultrasonic Benchmark Problem: Overview and Discussion of ResultsModeling Ultrasonic Problems for the 2002 Benchmark SessionPrediction of Insonifying Velocity Fields and Flaw Signals of the 2002 Ultrasonic Benchmark ProblemsPrediction of Transient Flaw Signals of the Ultrasonic Benchmark ProblemUltrasonic Benchmark Problem: Application of a Paraxial Model to Side-Drilled Holes and Oblique IncidenceEvaluation of Standard Configurations for Nondestructive Eddy-Current TestingSimulation of the World Federation's Second Eddy Current Benchmark ProblemMFL Benchmark Problem 2: Laboratory MeasurementsNumerical Predication of Signal for Magnetic Flux Leakage Benchmark Task

Section B. Reliability — POD Jack Lincoln Memorial SessionStatistical Analysis of Probability of Detection Hit/Miss Data for Small Data SetsRecent Studies on the POD Analysis of "a vs. a" NDI DataReliability Assessment of Ultrasonic Nondestructive Inspection Data Using Monte Carlo SimulationThe Application of Case-Based Reasoning to Ultrasonic Data for Use in Inspection QualificationEvaluation of Multizone Inspection Variability at the Supply Base for 8 Inch-Diameter Ti-6Al-4V: A Round-Robin StudyAutomated Error Interpretation in Flaw Response Models for Ultrasonic NDTInteractive Software Tools for Inspection QualificationFluorescent Penetrant Inspection Probability of Detection Demonstrations Performed for Space Propulsion

Section C. NDE EducationCollaboration for Nondestructive Testing EducationŠExtending the Reach

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