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Simulation 3D de la génération et de la réception d'ondes guidées : application à la détection de défauts dans des structures composites

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107 pages
Sous la direction de Michel Castaings
Thèse soutenue le 16 juin 2009: Tongji University, Bordeaux 1
Le Contrôle Non Destructif (CND) de matériaux est en forte expansion dans les domaines de l’aéronautique, de l’aérospatial, des transports et bien d’autres. Les ondes ultrasonores guidées constituent un moyen puissant pour la mise en œuvre du CND, car elles se propagent sur de grandes distances tout en interrogeant les structures à cœur. L’emploi de transducteur à couplage par air, disposés d’un même coté, permet de faire du CND sans contact et sans démontage des pièces testées. Cette thèse a consisté à modéliser, en 3 dimensions et par éléments finis, un système de CND ultrasonore à ondes guidées. Le modèle prend en compte la taille finie des transducteurs, l’ouverture angulaire des faisceaux, la diffraction dans toutes les directions, l’anisotropie, la viscoélasticité et l’hétérogénéité des matériaux. Les prédictions numériques sont systématiquement comparées à des mesures expérimentales. Trois structures ont été étudiées avec succès : une plaque en aluminium avec un trou, une plaque en verre-époxyde avec un dommage causé par impact, un réservoir haute pression ASTRIUM pourvu d’un décollement entre son liner en Titane et son bobinage en carbone-époxyde.
-Ondes guidées ultrasonores
The Non Destructive Testing (NDT) of materials is rapidly expanding in the fields of aeronautics aerospace, transportation, and so on. Guided ultrasonic waves are a powerful means for the implementation o the NDT because they can spread over large distances while interviewing through structures. The use of air coupled transducer allows both non-contact NDT and non-disassembly of tested parts. This thesis is mainly about three-dimensional finite element modelling, and an ultrasonic NDT system based on guided waves. The model takes into account the finite size transducers, the angle of beam diffraction in all directions, anisotropy viscoelasticity and heterogeneity of materials. The numerical predictions are systematically compared with experimental measurements. Three specimens have been studied with success: an aluminium plate with a hole glass-fibre plate with an impact damage, a high pressure tank provided by ASTRIUM with a disbonding defec between the liner titanium layer and wound carbon - fibre.
Source: http://www.theses.fr/2009BOR13805/document
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N° d'ordre : 3805
THÈSE
présentée à
TONGJI UNIVERSITY
et
L'UNIVERSITÉ BORDEAUX I
ÉCOLE DOCTORALE DES SCIENCES PHYSIQUES ET DE L’INGÉNIEUR
par Weina KE
POUR OBTENIR LE GRADE DE
DOCTEUR
SPÉCIALITÉ : Mécanique
________
SIMULATIONS 3D DE LA GENERATION ET DE LA
RECEPTION D’ONDES GUIDEES - APPLICATION A
LA DETECTION DE DEFAUTS DANS DES
STRUCTURES COMPOSITES
________
Soutenue le : 16 juin 2009
Après avis de :
M. H.-H. FENG, Professeur, Chinese Academy of Science, Shanghai Rapporteurs
M. G.-R. LI, Professeur, Chinese Academy
M. W.-X. HU, Professeur, Tongji University
Devant la commission d'examen formée de :
M. C. BACON, Professeur, Université Bordeaux I Président
M. M. CASTAINGS, Professeur, Université Bordeaux I Examinateurs
M. H.-L. ZHANG, Professeur, Chinese Academy of Science, Beijing
M. H.-H. FENG, Professeur, Chinese Academy of Science, Shanghai
M. G.-R. LI, Professeur, Chinese Academy
M. M.-L. QIAN, Professeur, Tongji University
M. W.-X. HU, Professeur, Tongji University -J. XU, Maître de Conférences, Université de Valenciennes
- 2009 - ABSTRACT
ABSTRACT
With rapidly increasing demand of composite materials, the adaptable non-destructive
detection of flaws in materials and evaluation of the structure health is under urgent
requirement to be developed. For this case, guided wave technique accompanied with non-
contact air-coupled transducer is able to provide successfully quick scan through the entire
thickness of plate or plate-like structures for defects. And combined with numerical
simulations, especially three-dimensional modelling exactly according to experimental
conditions, the interaction between guided waves and defects can be fully understood, and
furthermore, the severity of the damages can be quantified by comparing the numerical
predictions together with the experimental data.
The single-sided ultrasonic scan technique used here take one air-coupled transducer
to launch the incident mode, while another one is moved together with that transmitter, over
the surface of the sample, to detect the Lamb waves propagating in the plate, or if possible the
ones scattered by the defect. The zero-order anti-symmetric Lamb mode A is chosen as the 0
incident mode for the high level of normal displacements that it produces at solid-air
interfaces, thus making easy its generation/detection using air-coupled elements. Changes in
the amplitudes of the mode are monitored and plotted versus positions along the scanning axis,
as an indicator of the damage. In the experiments, the amplitudes are picked-up at a given
frequency in the frequency spectrum of each measured temporal waveform.
Correspondingly, three-dimensional simulations are performed with a commercially
available code based on the finite element method. For fast and accurate numerical
predictions, the equations of dynamic equilibrium are solved in the frequency domain. Both
anisotropy and viscoelasticity of the materials are considered in our model when required.
The air-coupled transmitter is modelled by the normal stress that it locally applies on the
sample surface, and the air-coupled receiver by integrating normal displacements over
corresponding areas selected on the plate surface according to its positions. In this case, the
air-coupled, Lamb, NDT system is fully simulated, considering the finite size of both
transducers and of the defect, as well as the beam angular aperture of the incident and
scattered wave modes.
i ABSTRACT
Different techniques are used to reduce the number of degrees of freedom, which usually
are huge in 3D models. One is an improved definition of absorbing regions (AR), such
regions being known to suppress unwanted reflections coming from the edges of the meshed
domain. Another consists in simply applying standard symmetrical or anti-symmetrical
boundary conditions when possible.
Two simple cases are firstly investigated: the diffraction by a through-thickness hole
in an Aluminium plate, and that by an impact damage in a Glass-Polyester composite plate.
The frequency of the excitation producing the incident mode is chosen equal to 250 kHz,
which is roughly the centre frequency of the air-coupled transducers used in the experiments.
This frequency is below the cut-off frequency of the A mode for the Aluminium plate, and 1
above it for the composite sample. Then, the case of a high-pressure composite tank supplied
by EADS-ASTRIUM, having a Teflon insert for a disbond-like defect between its Titanium
liner and Carbon-Epoxy winding, is investigated. In this case, the frequency is 100 kHz and
the incident wave is not precisely an A mode because the structure is not symmetric with 0
respect to its median plane. However, both the mode shape and the high-coupling level to the
surrounding air clearly indicate similarity with A modes existing in single plates. Three-0
dimensional Finite Element (3D FE) predictions of changes in the amplitude delivered by the
receiver are systematically compared to experiments performed either on laboratory samples
or on the tank.
Good agreements have been attained between numerical predictions and experiments.
Such a numerical tool may be used in the future for optimizing the parameters of the NDT
system, thus representing a strong benefit for low-cost improving and preparing of
experiments before they are set and run, e.g. optimizing the size of the transducers, their
orientation with respect to the tested sample, the distance one from each other, and eventually
their focalization or the frequency. This may also be helpful for defining the limits of a given
system, e.g. minimum sizes or possible localisations of detectable defects.

ii
ACKNOWLEDGMENTS
I would like to express my gratitude to all those who gave me the possibility to complete this
thesis.
I would like to thank my director, Prof. Menglu QIAN, for the patient guidance,
encouragement and advice he has provided throughout my time as his student. I have been
extremely lucky to have a supervisor who cared so much about my career and created me the
opportunity to study abroad.
I wish to thank my director, Prof. Michel CASTAINGS for his invaluable guidance and
assistance in making this research possible. I am greatly indebted to him for helping me to
overcome obstacles in the process of conducting the research.
I would like to thank Prof. Bernard HOSTEN, Prof. Christophe BACON, and Prof. Dmitrii
ZAKHAROV for their professional advices. I would also like to thank all my colleagues who
helped me and always very kind to me, Bénédicte, Mahmoud, Mihai, Stanislav, Slah,
Ludovic, Hugues, Christine, Olivier, Sacha, Christophe. In particular I would like to thank
Béatrice and Sandrine for all those gentle helps. Thanks also to Prof. Marc DESCHAMPS for
his support to corporation and communication between the two labs.
I also would like to express special thanks to my parents, all my friends, especially Qian
CHENG and Qi LI for the great help.
Regarding the study of the high-pressure composite tank, the authors are grateful to EADS-
ASTRIUM, France, for its financial and technical support and also to the Conseil Regional
d’Aquitaine, France, for its support. Finally, I would like to thank Chinese Scholar
Council, not only for providing the funding which allowed me to undertake this research, but
also for giving me the opportunity to meet so many interesting people. Table des matières
Table des matières
 CHAPTER I.INTRODUCTI ON ........................................................................................1
   1 GUIDED WAVE TECHNIQUE...........................2
   2 FINITE ELEMENT SIMULA TION.....................5
   3 OUTLINE OF THE THESIS...............................6
 CHAPTER II.ELASTIC WAVES IN PLA TES .................................................................7
   1 TWO­DIMENSIONAL GUIDED W AVES PROPAGATING IN  SINGLE PLATE......................8
   1.1 ISOTROPIC SINGLE PLAT E............9
   1.1.1 Lamb waves............................................................9
   1.1.2SH waves...............................................................13
   1.1.3 Mode shape normalzation.............................15
   1.2 ANISOTROPIC SINGLE PL ATE....................................16
   1.3 W AVES IN MULTI ‐LAYER PLATE..............................19
 2 THREE­DIMENSIONAL ACOUSTIC AL FIELD OF GUIDED W AVES IN ISOTROPIC PL ATE UNDER CYLINDRICA L 
 SYSTEM................................................................23
   3 SUMMARIES................................................27
 CHAPTER III. FINITE ELEMENT SIMULATION OF GUIDED WAVES IN ANISOTROPIC PLA TE 29
   1 2D  FINITE ELEMENT SIMULATIONS OF GUIDED WA VES IN ANISOTROPY SI NGLE­LAYER ........................30
   1.1 PDE  AND  COMSOL  FORMALISM............................30
   1.2 SOURCES OF EXCITATION  AND BOUNDARY CONDIT IONS....................................................35
   1.3 ABSORBING  REGION ..................................................37
   1.3.1 Viscoelastic Absorbing Region37
   1.3.2Perfectly Matched Layer................................38
   1.3.3 Improved Viscoelastic Absorbing Region...............................39
   1.4 MODELLING OF DEFECTS..........41
   2 3D  FINITE ELEMENT SIMULATION OF GUIDED WAV ES IN ANISOTROPY SIN GLE­LAYER PLATES ............42
   2.1 3D  SETTINGS OF  PDE  AND  B OUNDARY  CONDITIONS........................................................42
   2.2SIMPLIFICATIONS IN MODELS ..................................44
   2.2.1Absorbing Region..............44
   2.2.2Symmetrical and Anti‐symmetrical Boundary conditions..............................46
   2.3 MESHES .......................................47
I Table des matières
   3 SUMMARY ...................................................................................48
 CHAPTER IV.EXPERIMENTAL SYSTEM AND  METHODS...................................50
   1 EXPERIMENTAL PRINCIPL ES AND SETUP..51
   1.1 GENERATION AND RECEPT ION OF GUI DED WAVES..............................51
   1.2 SAMPLING AND  FOURIER TRANSFORM..................53
   1.2.1Sampling................................53
   1.2.2Post processing of data...................................54
   1.2.32D Fourier Transform.....55
   1.3 AIR‐COUPLED TRANSDUCER A ND SCAN SYSTEM..55
   1.3.1 Air‐coupled transducer..55
   1.3.2Scan system.........................................................57
   2 TECHNIQUES AND APPLIC ATIONS.............................................58
   2.1 SINGLE‐SIDED SCAN TECHNIQUE.............................58
   2.2MEASURE FOR DISPERSIO N CURVES.......................59
   3 SUMMARY...................62
 CHAPTER V. EXPERIMENTAL AND 3D SIMULATION RESULTS......................................................63
   1 3D  NUMERICAL SIMULATIO N OF THE EXPERIMENTA L SYSTEM...............................64
   1.1 E XCITATION MODELLING ..........................................64
   1.2 RECEIVER  MODELLING.............66
   1.3 MODELLING OF THE SCAN  PROCESS.......................................................67
   2 EXPERIMENTAL AND SIMU LATION RESULTS.............................68
   2.1 ALUMINIUM PLATE WITH  A THROUGH THICKNESS  HOLE...................68
   2.2COMPOSITE PLATE.....................74
   2.3 COMPOSITE S TRUCTURE TANK ................................................................80
   3 SUMMARY87
 CHAPTER VI.CONCLUSIONS AND PERSPECTIVES..............................................88
   1 CONCLUSIONS .............................................88
   2 PERSPECTIVES............90
REFERENCES..................93 

II


Chapter I.
Introduction
Since the 1960s, composite materials are widely investigated and developed according to
the requirements of aeronautical applications, as their properties allow the significant
improvements in the performances of aircrafts. In addition, composite materials are also
replacing materials like wood, metals or alloys in the industry of transport, such as for cars,
ships and so on. Nowadays, the advanced production technique also supports significant
increase in the use of composite materials in civil engineering applications, including for
bridge structure components, decks, buildings, pressure vessels, chemical plant components
or pipelines [1].
Composite materials, generally composed of matrix and fibre reinforcement, can be
formed directly into requested complicated shapes with specific manufacture techniques and
economic consuming of materials. Different from natural materials, composite materials can
be designed using different reinforcements with different orientations, embedded in a matrix
according to the requirements of mechanical properties, like strength, stiffness, durability,
damage tolerance, energy absorption and so on. For example, with the same strength,
composite material can be one-third weight lighter than aluminium alloy; besides, it also has
advantages for vibration and impact resistance, as well as resistances to fatigue, corrosion and
thermal damage. All these advantages are contributed to the structure of composite materials.
Since the matrix, which can be either metal, such as aluminium, copper, magnesium, alloy
and so on, or non metal, such as resin, ceramics, rubber and so on, and reinforcement, which
is generally glass-fibre, carbon-fibre, metal fibre or hard particle, are supplementary in
material properties, the global quality and performance of composite materials are thus
superior to the original materials according to the requirements.
The final composite structure will present some inhomogeneity and anisotropy, and also
sometimes some common defect types [2, 3]. The volatile components in matrix, such as low
molecular weight impurities, solvents, and Hydrone, may result in defects at the interfaces
and interior of material such as porous cavities, cracks, disbonding and delamination during
1

Introduction
manufacturing process, while the instabilities introduced by artificial influence factors and
process quality during matrix production, placement and solidification processes may lead to
randomness in the quality of composite components.
In spite of these defects introduced during manufacturing process, the mechanical
effects, fatigue and thermal factors encountered in actual application environments may also
cause damages in the composite material. And the generation, expansion and accumulation of
defects will strengthen the environmental stress-corrosion cracking, seriously decrease
hydrothermal aging resistance and accelerate aging, lead to significant loss in strength and
stiffness, greatly reduce the service life of structures, and may finally lead to disastrous results
as composite materials are widely used in transportation.
Associated with advanced manufacturing process, available techniques for monitoring
the production and in-service health of composite materials provide assurance for
improvement in product quality and security, based on the researches on detection and
characterization of defects in composite materials [ 4-11]. Among non-destructive testing
techniques adoptable for detecting general defects in advanced composite materials [12-18],
ultrasonic C scan imaging, infrared thermography technique and X-ray real time image
technique are widely used. Generally speaking, each has its own advantages and
drawbacks, and thus is limited in some application ranges. Therefore, for optimum selection
of the NDT process to be used, different parameters should be simultaneously considered, like
for instance taking into account the characteristics of the tested material structure (anisotropy,
heterogeneity, temperature, ...), defining the type of defect that is likely to exist (cracks,
porosity, delamination,...), and considering various constraints like limited access (in space
and/or in time) to the structure to be tested, cost and so on.
1 Guided wave technique
Ultrasonic techniques are the most commonly used effective NDT techniques with the widest
applicable range [19-28]. Traditional ultrasonic NDT generally consists in detecting defects
using longitudinal or transverse waves, in a point-by-point scanning mode. For instance,
ultrasonic C-scan images [25] of delaminations in composites can be produced. However,
point-by-point techniques are very time consuming, especially for large structures. Besides,
anisotropy and non uniform distribution in mechanical properties of composite materials, as
well as various types of defects (porosity, cracks, …), may cause very high acoustic
attenuation that will lead to very low signal-to-noise ratio for the measured signals, thus
2

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