Tesis sobre el tema "Anisotropic elastic materials"

For an accurate prediction of the low and medium frequency surface vibration and sound radiation behaviour of porous materials, there is a need to improve the means of estimating their elastic and acoustic properties. The underlying reasons for this are many and of varying origin, one prominent being a poor knowledge of the geometric anisotropy of the cell microstructure in the manufactured porous materials. Another one being, the characteristic feature of such materials i.e. that their density, elasticity and dissipative properties are highly dependent upon the manufacturing process techniques and settings used. In the case of free form moulding, the geometry of the cells and the dimensions of the struts are influenced by the rise and injection flow directions and also by the effect of gravity, elongating the cells. In addition the influence of the boundaries of the mould also introduces variations in the properties of the foam block produced. Despite these complications, the need to predict and, in the end, optimise the acoustic performance of these materials, either as isolated components or as part of a multi-layer arrangement, is growing. It is driven by the increasing demands for an acoustic performance in balance with the costs, a focus which serves to increase the need for modelling their behaviour in general and the above mentioned, inherent, anisotropy in particular. The current work is focussing on the experimental part of the characterisation of the material properties which is needed in order to correctly represent the anisotropy in numerical simulation models. Then an hybrid approach based on a combination of experimental deformation, strain field mapping, flow resistivity measurement and physically based porous material acoustic Finite Element (FE) simulation modelling is described. This inverse estimation linked with high quality measurements is crucial for the determination of the anisotropic coefficients of the porous materials is illustrated here for soft foam and fibrous wool materials.
QC 20100729

Electro-active polymers (EAPs) have emerged as a new class of active materials, which produce large deformations in response to an electric stimulus. EAPs have attractive characteristics of being lightweight, inexpensive, stretchable, and flexible. Additionally, EAPs are conformable, and their properties can be tailored to satisfy a broad range of requirements. These advantages have enabled many target applications in actuation and sensing. A general constitutive formulation for isotropic and anisotropic electro-active materials is developed using continuum mechanics framework and invariant theory. Based on the constitutive law, electromechanical stability of the electro-elastic materials is investigated using convexity and polyconvexity conditions. Implementation of the electro-active material model into a commercial finite element software (ABAQUS 6.9.1, PAWTUCKET, RI, USA) is presented. Several boundary and initial value problems are solved to investigate the actuation and sensing response of isotropic and anisotropic dielectric elastomers (DEs) subject to combined mechanical and electrical loads. The numerical response is compared with experimental results to validate the theoretical model. For the constitutive formulation of the electro-elastic materials, invariants for the coupling between two families of electro-active fibers (or particles) and the applied electric field are introduced. The effect of the orientation of the electro-active fibers and the electric field on the electromechanical coupling is investigated under equibiaxial extension. Advantage of the constitutive formulation derived in this research is that the electromechanical coupling can be illustrated easily by choosing invariants for the deformation gradient tensor, the electro-active fibers, and the electric field. For the electromechanical stability, it is shown that the stability can be controlled by tuning the material properties and the orientation of the electro-active fibers. The electromechanical stability condition is useful to build a stable free energy function and prevent the instabilities (wrinkling and electric breakdown) for the electro-elastic materials. The invariant-based constitutive formulation for the electro-elastic materials including the isotropic and anisotropic DEs is implemented into a user subroutine (UMAT in ABAQUS: user defined material) by using multiplicative decomposition of the deformation gradient and the applicability of the UMAT is shown by simulating a complicated electromechanical coupling problem in ABAQUS/CAE. Additionally, the static and dynamic sensing and actuation response of tubular DE transducers (silicone and polyacrylate materials) with respect to combined electrical and mechanical stimuli is obtained experimentally. It is shown that the silicone samples have better dynamic and static sensing characteristics than the polyacrylate. The theoretical modeling accords well with the experimental results.
Ph. D.

Detection of stress corrosion cracks and other types of deterioration in pipes can be performed by producing elastic Lamb waves in the circumferential direction. Availability of Fiber Composite materials that have been utilized to retrofit the pipeline networks necessitates development of new theoretical procedures to analyze the behavior of anisotropic materials including Fiber Composites. The study of propagation of elastic waves in the circumferential direction for anisotropic materials primarily requires the derivation of dispersion curves. To obtain the dispersion curves, governing differential equations must be solved and the boundary conditions must be satisfied. Since differential equations for anisotropic materials are coupled, a general new analytical model is introduced which is capable of solving the coupled differential equations and removes the obstacle of decoupling which might not be always possible. To verify the validity of the new technique the results have been compared with the available data for isotropic materials and have matched satisfactorily. The proposed method can be extended to investigate pipe walls composed of several layers of isotropic and anisotropic materials and for problems with other types of geometry and boundary conditions.

In this study, an analytical procedure to predict the strength and failure of laminated composite structures under monotonically increasing static loads is presented. A degenerated 3-D shell finite element that includes linear elastic and plastic material behavior with full geometric nonlinearity is used to determine stresses at selected points (Gauss quadrature points in each element) of the structure. Material stiffness (constitutive) matrices are evaluated at each Gauss point, in each lamina and in each element, and when the computed stress state violates a user selected failure criterion, the material stiffness matrix at the failed Gauss point is reduced. The reduction procedure involves setting the material stiffnesses to unity. Examples of isotropic, orthotropic, anisotropic and composite laminates are presented to illustrate the validity of the procedure developed and to evaluate various failure theories. Maximum stress, modified Hills (Mathers), Tsai-Wu (F₁₂ = 0), and Hashin's failure criteria are included. The results indicate that for large length-to-thickness ratios, the geometric nonlinear effect should be incorporated for both isotropic and anisotropic structures. The nonlinear material model influences the behavior of isotropic structures with small length-to-thickness ratios, while having nearly no effect at all on laminated anisotropic structures. Of the four failure theories compared, each predicts failure at nearly the same load levels and locations. Hashin's criterion is particularly noteworthy in that the mode is also predicted.
Ph. D.

Les classes de symétrie d'un comportement linéaire définissent les différents types d'anisotropie qui peuvent être modélisés par les tenseurs constitutifs associés. Cependant, les espaces des matériaux linéaires sont très riches et toute une gamme de possibilités intermédiaires peut exister au-delà des classes de symétrie. Les matériaux présentant des propriétés anisotropes non-standard associées à ces possibilités intermédiaires sont appelés matériaux exotiques. Par exemple, le matériau 2D R0-orthotrope est un cas bien connu de matériau exotique.L'objectif principal de cette recherche est de développer des outils géométriques pour caractériser les espaces linéaires des matériaux de manière très fine, ce qui permet de détecter ces possibilités intermédiaires. L'ensemble exotique obtenu est intrinsèquement caractérisé par une relation polynomiale entre les invariants du tenseur d'élasticité. En conséquence, nous prouvons que la R0-orthotropie est le seul type de matériau élastique exotique en 2D. Cependant, lorsque l'on généralise à l'élasticité linéaire 3D, ce nombre s'élève à 163.Le deuxième objectif de cette étude est d'obtenir une mésostructure présentant à grande échelle le comportement exotique décrit précédemment. Un algorithme d'optimisation basé sur la dérivée topologique est implémenté dans Python/FEniCS pour réaliser la design de mésostructure périodiques. Le matériau 2D R0-orthotrope et plusieurs cas de matériaux exotiques 3D sont étudiés. La fonction objective du problème d'optimisation est formulée en termes d'invariants du tenseur d'élasticité effectif cible
The symmetry classes of a linear constitutive law define the different types of anisotropy that can be modelled by the associated constitutive tensors. However, the spaces of linear materials are very rich and a whole range of intermediate possibilities can exist beyond symmetry classes. Materials with non-standard anisotropic properties associated with such intermediate possibilities are called exotic materials. For instance, 2D R0-orthotropic material is a well-known case of exotic material.The primary objective of this research is to develop geometrical tools to characterise the linear material spaces in a very fine way, which allow these intermediate possibilities to be detected. The exotic set obtained is intrinsically characterised by a polynomial relation between elasticity tensor invariants. As a result, we prove that R0-orthotropy is the only type of 2D exotic elastic material. However, when generalised to 3D linear elasticity, this number is up to 163.The second objective of this study is to obtain a mesostructure exhibiting at macroscale the exotic behaviour described previously. A topological derivative-based optimisation algorithm is implemented in Python/FEniCS to realise the design of periodic metamaterials. The 2D R0-orthotropic material and several cases of 3D exotic materials are studied. The objective function of the optimisation problem is formulated in terms of the invariants of the target effective elasticity tensor

Dispersion et polarisation des ondes de surface dans des structures anisotropes lateralement homogenes. L'equation des ondes elastiques dans des structures planes isotropes est perturbee par l'introduction de coefficients elastiques anisotropes. On en deduit l'anomalie de vitesse de phase et l'anomalie de polarisation decomposee sur les modes propres de la structure isotrope de reference. Ces resultats sont illustres par le calcul d'anomalies de vitesse et de polarisation dans des modeles oceaniques ou l'anisotropie est cree par orientation de fissures dans la croute ou de cristaux d'olivine dans le manteau

Poro-viscoelastic materials are well modelled with Biot-Allard equations. This model needs a number of geometrical parameters in order to describe the macroscopic geometry of the material and elastic parameters in order to describe the elastic properties of the material skeleton. Several characterisation methods of viscoelastic parameters of porous materials are studied in this thesis. Firstly, quasistatic and resonant characterization methods are described and analyzed. Secondly, a new inverse dynamic characterization of the same modulus is developed. The latter involves a two layers metal-porous beam, which is excited at the center. The input mobility is measured. The set-up is simplified compared to previous methods. The parameters are obtained via an inversion procedure based on the minimisation of the cost function comparing the measured and calculated frequency response functions (FRF). The calculation is done with a general laminate model. A parametric study identifies the optimal beam dimensions for maximum sensitivity of the inversion model. The advantage of using a code which is not taking into account fluid-structure interactions is the low computation time. For most materials, the effect of this interaction on the elastic properties is negligible. Several materials are tested to demonstrate the performance of the method compared to the classical quasi-static approaches, and set its limitations and range of validity. Finally, conclusions about their utilisation are given.

Ce travail de thèse a pour objectif de caractériser le comportement anisotrope des mousses acoustiques. Ces matériaux, couramment employés pour lutter contre les nuisances sonores et vibratoireset sont modélisés à l'aide du modèle de Biot. Celui-ci est basé sur le formalisme de lamécanique des milieux continus à deux champs couplés, l'un associé au solide et l'autre au fluidesaturant. Nous nous intéresserons plus particulièrement dans ce travail aux paramètres du solideet aux matériaux présentant une anisotropie (c'est-à-dire des propriétés qui varient suivant lesdirections) du squelette solide. Ici, deux types d'anisotropie sont distingués, l'anisotropie naturelledu matériau et celle induite par une action extérieure, cette dernière ayant pour principale cause lacompression statique des échantillons. Par ailleurs, trois types de symétries naturelles sont considérés : isotropie, isotropie transverse avec et sans rotation de direction principale. Celles-ci sont leplus couramment rencontrées.L'analyse expérimentale du type de symétrie des mousses se fait au moyen d'un dispositif, appelé rigidimètre, qui permet de déterminer la raideur mécanique d'échantillons cubiques de moussesous hypothèse quasi-statique. Celui-ci est couplé à une mesure au vibromètre laser à balayage, permettantde mesurer le déplacement normal des faces des cubes. Des lignes de niveaux des champsde déplacements normaux surfaciques sont ainsi obtenues. Il est alors possible de classer les différentstypes d'anisotropie en analysant ces courbes de niveaux. Ainsi, avec ces a-priori, une méthodea été élaborée pour déterminer les coefficients de Poisson à l'aide de techniques de minimisationà partir des autres constantes élastiques préalablement déterminées. Ce problème est construit àpartir d'indicateurs expérimentaux et d'indicateurs provenant d'un modèle éléments finis.L'influence de la compression statique sur les modules élastiques est ensuite étudiée. Toutd'abord, la variation du module d'Young en fonction du taux de compression est caractérisée àpartir de mesures au rigidimètre. Ensuite, la variation du module de cisaillement en fonction de lacompression statique est caractérisée par une méthode d'ondes guidées (en collaboration avec laKULeuven). Il a été montré que les variations de modules élastiques pouvaient être importantespuisqu'elles peuvent atteindre 50 %. A partir de ces déterminations expérimentales, quatre zones decomportement de la mousse ont été mises en évidence. Ces quatre zones correspondent respectivementà des effets de compression, de flambement, de densification et de réarrangement des cellules.Un modèle éléments-finis microstructural, dans lequel la cellule élémentaire est modélisée par untétrakaidécaèdre de Kelvin, est enfin proposé. Celui-ci permet de modéliser les trois premièreszones, qui correspondent aux compressions statiques usuelles dans les applications acoustiques.

Les métamatériaux mécaniques microstructurés attirent de plus en plus l'attention de la communauté scientifique et technique. Nous choisissons une approche qui évoque la théorie classique de l'élasticité : celle de la mécanique des milieux continus enrichie. Le but de cette thèse est d'utiliser le nouveau modèle de continuité enrichie appelé modèle micromorphique relaxé détendu afin d'étudier la propagation des ondes et les phénomènes de diffusion aux interfaces entre matériaux et métamatériaux. Lorsqu'il s'agît d'étudier les propriétés de diffusion de structures de taille finie, il devient difficile de traiter les conditions limites correctes. Nous montrons comment les problèmes aux valeurs limites de domaines finis peuvent être mis en place dans le cadre du modèle micromorphique relaxé. Nous mettons en place la solution d'onde plane complète de la diffusion à partir d'une interface séparant un milieu de Cauchy d'un milieu micromorphique relaxé. Les conditions aux limites macroscopiques généralisées sont présentées. Ils permettent de bien décrire les propriétés de diffusion. Le flux d'énergie généralisé associé est introduit. On considère deux cas différents dans lesquels le milieu homogène gauche est soit plus rigide soit plus flexible que le métamatériau droit et le coefficient de transmission est obtenu en fonction de la fréquence et de la direction de propagation. Le contraste des raideurs macroscopiques des deux milieux, influencent l'apparition des ondes Stoneley. On considère par la suite un problème de propagation des ondes de volume et on démontre que les formes d'ondes transitoires résultant de plusieurs impulsions localisées dans un matériau microstructuré peuvent être reproduite. Nous comparons la réponse dynamique d'un matériau microstructuré et lié à celle d'un milieu lié avec des propriétés cinématiques particulières. On démontre que, bien que la théorie de Cauchy soit capable de décrire le comportement global de la métastructure à de basses fréquences, le modèle micromorphique détendu va bien au-delà en donnant une description correcte de la propagation de l'impulsion dans la bande de fréquence et à des fréquences qui croisent les branches optiques. Enfin, on présente le cas d'une dalle de métamatériau de largeur finie. Ses propriétés de diffusion sont étudiées en utilisant une solution semi-analytique du modèle micromorphique relaxé et comparées à des simulations. Le coefficient de réflexion obtenu par les deux méthodes est présenté en fonction de la fréquence et la direction de propagation de l'onde incidente. On trouve un excellent accord pour une large gamme de fréquences, allant de la limite des ondes longues aux fréquences au-delà de la première limite de la bande, et pour des angles d'incidence allant d'une incidence normale à une incidence presque parallèle. Le cas d’un métamatériau semi-infinie est également présenté et est considéré comme une mesure fiable du comportement moyen de la métastructure finie
Mechanical microstructured metamaterials are increasingly gaining attention from the scientific and engineering community. The question of modeling the behavior of metamaterials is of extreme importance. Some choose an approach, which is reminiscent of the classical theory of elasticity: enriched continuum mechanics. We employ the enriched continuum model named relaxed micromorphic model in order to study wave propagation and scattering at interfaces between materials and metamaterials. Dealing with the correct boundary conditions at the macroscopic scale becomes challenging. We show how finite-domain boundary value problems can be set-up in the framework of the relaxed micromorphic model. We set up the full plane wave solution of the scattering from an interface separating a Cauchy medium from a relaxed micromorphic one. Both media are isotropic and semi-infinite. Generalized macroscopic boundary conditions are presented, which allow the effective description of the scattering properties of an interface between a homogeneous solid and a mechanical metamaterial. The associated generalized energy flux is introduced. We show that the contrast of the macroscopic stiffnesses of the two media, together with the type of boundary conditions strongly influence the onset of Stoneley waves at the interface. This allows to tailor the scattering properties of the interface at both low and high frequencies, ranging from zones of complete transmission to zones of zero transmission well beyond the band-gap. We then consider a bulk wave propagation problem and show that the transient waveforms arising from several localised pulses in a micro-structured material can be reproduced. We compare the dynamic response of a bounded micro-structured material to that of bounded continua with special kinematic properties. We show that, while the Cauchy theory is able to describe the overall behavior of the metastructure only at low frequencies, the relaxed micromorphic model goes far beyond by giving a correct description of the pulse propagation in the frequency bandgap and at frequencies intersecting the optical branches. Finally, we present the case of a metamaterial slab of finite width. Its scattering properties are studied via a semi-analytical solution of the relaxed micromorphic model and compared to numerical simulations encoding all details of the selected microstructure. The reflection coefficient obtained via the two methods is presented as a function of the frequency and the direction of propagation of the incident wave. We find excellent agreement for a large range of frequencies. The case of a semi-infinite metamaterial is also presented and is seen to be a reliable measure of the average behavior of the finite metastructure

Afin de modéliser le comportement des géométariaux sous des charges complexes, plusieurs études et travaux expérimentaux ont été réalisées afin d’établir des modèles constitutifs relatifs. Une caractéristique importante des matériaux granulaires est que la relation entre la contrainte et la déformation et ce même dans le domaine élastique n’est pas linéaire, contrairement aux réponses du métal. Il a également été constaté que la réponse contrainte-déformation des matériaux granulaires montre les caractéristiques de l’anisotropie induite, ainsi que les non-linéarités. En outre, l’anisotropie induite par la contrainte se produit pendant le processus de chargement sur les sols, par exemple, les charges ou les déplacements. Dans ce travail, un nouveau modèle qui est une combinaison de modèle hyperélastique Houlsby et modèle élastoplastique Plasol a été proposé. Ce nouveau modèle a pris en compte la réponse non linéaire de la contrainte dans le domaine élastique et plastique, et l’élasticité anisotrope a également été bien considérée. En outre, les problèmes de l’écoulement de la déformation plastique a été calibré par un algorithme d’intégration approprié. Plus tard, le nouveau modèle a été vérifié en utilisant la méthode numérique et comparé aux expériences de laboratoire dans des conditions triaxiales axisymmétriques. Les résultats de comparaison ont montré un bon effet de simulation du nouveau modèle qui a juste utilisé un seul ensemble de paramètres pour un sol spécifique dans différentes situations de contraintes. Ensuite, l’analyse de la nouvelle variable interne du modèle, c’est-à-dire l’exposant de pression, a montré que la valeur de l’exposant de pression qui correspond au degré d’anisotropie a eu un effet évident sur la réponse contrainte-déformation. De plus, ce type d’effet est également affecté par la densité et l’état de drainage des échantillons. En s’appuyant sur un nouveau modèle, un facteur de sécurité qui fait référence au critère de travail de deuxième ordre a été adopté et testé dans un modèle axisymétrique et un modèle de pente réel. Il a montré que la valeur négative ou la diminution spectaculaire du travail global normalisé de second ordre se produit lors d’une défaillance locale ou globale avec apparition d’énergie cinétique. Cette caractéristique du travail du second ordre peut également être affectée par l’exposant à pression variable. Enfin, un nouveau modèle a également été comparé à un modèle élastoplastique qui considère à la fois l’anisotropie élastique et la dilatation anisotrope, c’est-à-dire le modèle SANISAND modifié. Les avantages et les inconvénients ont été illustrés dans les résultats de comparaison
In order to model the behavior of geometarials under complex loadings, several researches have done numerous experimental works and established relative constitutive models for decades. An important feature of granular materials is that the relationship between stress and strain especially in elastic domain is not linear, unlike the responses of typical metal or rubber. It has been also found that the stress-strain response of granular materials shows the characteristics of cross-anisotropy, as well as the non-linearities. Besides, the stress-induced anisotropy occurs expectedly during the process of disturbance on soils, for example, the loads or displacements. In this work, a new model which is a combination of Houlsby hyperelastic model and elastoplastic Plasol model was proposed. This new model took into account the non-linear response of stress and strain in both elastic and plastic domain, and the anisotropic elasticity was also well considered. Moreover, the overflow problem of plastic strain in plastic part was calibrated by a proper integration algorithm. Later, new model was verified by using numerical method and compared with laboratory experiments in axisymmetric triaxial conditions. The comparison results showed a good simulation effect of new model which just used one single set of parameters for a specific soil in different confining pressure situations. Then the analysis of new model internal variable, i.e., pressure exponent, illustrated that the value of pressure exponent which corresponds to the degree of anisotropy had an obvious effect on the stress-strain response. Moreover, this kind of effect is also affected by the density and drainage condition of samples. Basing on new model, a safety factor which refers to the second-order work criterion was adopted and tested in axisymmetric model and actual slope model. It showed that the negative value or dramatic decreasing of global normalized second-order work occurs accompanying with a local or global failure with a burst of kinetic energy. This feature of second-order work can also be affected by the variable pressure exponent. At last, new model was also compared with an elastoplastic model which considers both anisotropic elastic and anisotropic dilatancy, i.e., modified SANISAND model. Both advantages and disadvantages were illustrated in the comparison results

In this research, the homogenization relations for elastic properties in isotropic and anisotropic materials are studied by applying two-point statistical functions to composite and polycrystalline materials. The validity of the results is investigated by direct comparison with experimental results. In todays technology, where advanced processing methods can provide materials with a variety of morphologies and features in different scales, a methodology to link property to microstructure is necessary to develop a framework for material design. Statistical distribution functions are commonly used for the representation of microstructures and also for homogenization of materials properties. The use of two-point statistics allows the materials designer to consider morphology and distribution in addition to properties of individual phases and components in the design space. This work is focused on studying the effect of anisotropy on the homogenization technique based on two-point statistics. The contribution of one-point and two-point statistics in the calculation of elastic properties of isotropic and anisotropic composites and textured polycrystalline materials will be investigated. For this purpose, an isotropic and anisotropic composite is simulated and an empirical form of the two-point probability functions are used which allows the construction of a composite Hull. The homogenization technique is also applied to two samples of Al-SiC composite that were fabricated through extrusion with two different particle size ratios (PSR). To validate the applied methodology, the elastic properties of the composites are measured by Ultrasonic methods. This methodology is then extended to completely random and textured polycrystalline materials with hexagonal crystal symmetry and the effect of cold rolling on the annealing texture of near- Titanium alloy are presented.

Dans le domaine de l'ameublement, garantir la sécurité des structures conformément aux normes européennes représente un enjeu important pour les fabricants de meubles. Avant leur commercialisation, les meubles sont soumis à des tests de validation normalisés, qui ne permettent de connaître leur comportement mécanique qu'a posteriori. Cette thèse vise à développer des outils de modélisation et de simulation numérique pour prédire la rupture par fissuration au niveau des connexions entre les éléments de meuble. Pour atteindre cet objectif, l'approche méthodologique combine la modélisation et la simulation numérique avec des essais expérimentaux. Elle utilise la méthode des éléments finis couplée à des modèles de rupture/endommagement par champ de phase pour simuler la fissuration dans des matériaux élastiques linéaires isotropes et anisotropes, dans un cadre déterministe et probabiliste. Une campagne d'essais expérimentaux est menée sur des échantillons d'épicéa troués soumis en compression uniaxiale, afin de reproduire les mécanismes de fissuration observés dans des structures réelles, notamment dans les connexions de lits en hauteur. Une procédure d'identification est développée et mise en place pour caractériser les propriétés élastiques et d'endommagement de l'épicéa, en exploitant notamment des mesures expérimentales de champs de déplacement obtenues par corrélation d'images numériques. Une méthode d'accélération des simulations d'endommagement par champ de phase est proposée pour réduire leur coût élevé en temps de calcul. Cette approche permet de prédire, indépendamment du type de connexions, le déplacement ou la force critique précédant l'amorçage de la fissuration. Les résultats numériques indiquent que, sous réserve d'appliquer des conditions aux limites réalistes et d'avoir correctement identifié les propriétés du matériau, le critère d'amorçage de fissure s'avère utile pour prédire l'emplacement des zones potentiellement endommagées/fissurées et fournir un ordre de grandeur cohérent pour l'effort ou le déplacement nécessaire à l'initiation de la fissuration. Ce critère requiert seulement une unique simulation dans le domaine élastique linéaire, suivi d'un post-traitement avec un modèle d'endommagement par champ de phase, afin de faciliter son utilisation dans un contexte industriel, en particulier le secteur de l'ameublement. Les outils numériques développés, accessibles en open source, pourraient aider les industriels de l'ameublement à prédire la rupture fragile dans le bois et à optimiser la conception des meubles, tout en garantissant la conformité aux normes de sécurité
In the furniture industry, ensuring the safety of structures in accordance with European standards presents a significant challenge for furniture manufacturers. Before commercialization, furniture are subjected to standardized validation tests, which only allow for a retrospective understanding of its mechanical behavior. This thesis aims to develop modeling and numerical simulation tools to predict the cracking failure mechanism at the connections between furniture elements. To achieve this objective, the methodological approach combines modeling and numerical simulation with experimental testing. It employs the finite element method coupled with phase-field fracture/damage models to simulate cracking in linear elastic isotropic and anisotropic materials within a deterministic and probabilistic framework. An experimental testing campaign is conducted on perforated spruce wood samples subjected to uniaxial compression to reproduce the cracking mechanisms observed in real structures, particularly in the connections of high loft beds. An identification procedure is developed and implemented to characterize the elastic and damage properties of spruce wood, in particular by exploiting experimental displacement field measurements obtained through digital image correlation. A method for accelerating phase-field damage simulations is proposed to reduce their high computational cost. This approach allows for the prediction, independently of the type of connections, of the displacement or critical force preceding crack initiation. The numerical results indicate that, provided realistic boundary conditions are applied and the material properties are correctly identified, the crack initiation criterion is useful for predicting the location of potentially damaged/cracked areas and providing a consistent order of magnitude of the force or displacement required to initiate cracking. This criterion only requires a single linear elastic simulation, followed by a post-processing with a phase-field damage model, to facilitate its use in an industrial context, in particular the furniture sector. The numerical tools developed, available in open source, could help furniture manufacturers to predict brittle fracture in wood and optimize furniture design, while guaranteeing compliance with safety standards

High-entropy alloys (HEAs) represent a special group of solid solutions containing five or more principal elements. The new design strategy has attracted extensive attention from the materials science community. The design and development of HEAs with desired properties have become an important subject in materials science and technology. For understanding the basic properties of HEAs, here we investigate the magnetic properties, Curie temperatures, electronic structures, phase stabilities, and elastic properties of paramagnetic (PM) body-centered cubic (bcc) and face-centered cubic (fcc) AlxCrMnFeCoNi (0 ≤ x ≤ 5, in molar fraction) HEAs using the first-principles exact muffin-tin orbitals (EMTO) method in combination with the coherent potential approximation (CPA) for dealing with the chemical and magnetic disorder. Whenever possible, we compare the theoretical predictions to the available experimental data in order to verify our methodology. In addition, we make use of the previous theoretical investigations carried out on AlxCrFeCoNi HEAs to reveal and understand the role of Mn in the present HEAs. The theoretical lattice constants are found to increase with increasing x, which is in good agreement with the available experimental data. The magnetic transition temperature for the bcc structure strongly decreases with x, whereas that for the fcc structure shows a weak composition dependence. Within their own stability fields, both structures are predicted to be PM at ambient conditions. Upon Al addition, the crystal structure changes from fcc to bcc with a broad two-phase field region, in line with the observations. Bain path calculations suggest that within the duplex region both phases are dynamically stable. Comparison with available experimental data demonstrates that the employed approach describes accurately the elastic moduli of the present HEAs. The elastic parameters exhibit complex composition dependences, although the predicted lattice constants increase monotonously with Al addition. The elastic anisotropy is unusually high for both phases. The brittle/ductile transitions formulated in terms of Cauchy pressure and Pugh ratio become consistent only when the strong elastic anisotropy is accounted for. The negative Cauchy pressure of CrMnFeCoNi is found to be due to the relatively low bulk modulus and C12 elastic constant, which in turn are consistent with the relatively low cohesive energy. Our findings in combination with the experimental data suggest anomalous metallic character for the present HEAs system. The work and results presented in this thesis give a good background to go further and study the plasticity of AlxCrMnFeCoNi type of HEAs as a function of chemistry and temperature. This is a very challenging task and only a very careful pre-study concerning the phase stability, magnetism and elasticity can provide enough information to turn my plan regarding ab initio description of the thermo-plastic deformation mechanisms in AlxCrMnFeCoNi HEAs into a successful research.

Par synthese de fourier, expression des ondes acoustiques sous forme d'integrale, evaluee dans le champ lointain par la methode de la plus grande pente dans le domaine complexe du nombre d'onde. Determination des ondes de surface et des ondes de volume rampantes d'apres les singularites de l'integrant et des ondes de volume rayonnees qui se propagent dans une direction commandable par la frequence d'excitation, a l'approximation geometrique du rayon. Calcul de leur diagramme de rayonnement pour un grand nombre de configurations du quartz et de linbo::(3). Proposition de nouveaux dispositifs electroacoustiques utilisant ces ondes de volume

In this dissertation we study free boundary problems that model the evolution of interfaces in the presence of elasticity, such as thin film profiles and material void boundaries. These problems are characterized by the competition between the elastic bulk energy and the anisotropic surface energy. First, we consider the evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate. The film is strained due to the mismatch between the crystalline lattices of the two materials and anisotropy is taken into account. We present the results contained in [62] where the author establishes short time existence, uniqueness and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2 -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity. Second, we consider the relaxed energy introduced in [20] that depends on admissible pairs (E, u) of sets E and functions u defined only outside of E. For dimension three this energy appears in the study of the material voids in solids, where the pairs (E, u) are interpreted as the admissible configurations that consist of void regions E in the space and of displacements u of the atoms of the crystal. We provide the precise mathematical framework that guarantees the existence of minimal energy pairs (E, u). Then, we establish that for every minimal configuration (E, u), the function u is C 1,γ loc -regular outside an essentially closed subset of E. No hypothesis of starshapedness is assumed on the voids and all the results that are contained in [18] hold true for every dimension d ≥ 2.

En sciences et dans l'industrie pour limiter le nombre de maquettes expérimentales dans les projets R&D afin de mieux comprendre et de bien interpréter les phénomènes ultrasonores complexes observés sur site, des simulations de contrôles ultrasonores sont effectuées. Ces simulations sont d'autant plus réalistes que la description des structures à contrôler est précise, en particulier au niveau des constantes d'élasticité et d'atténuation intrinsèque. Les objectifs de cette étude sont d'améliorer d'une part les connaissances sur l'influence des caractéristiques métallurgiques des matériaux anisotropes et hétérogènes sur la propagation ultrasonore et d'autre part les performances des codes de calcul (logiciel ATHENA d'EDF) qui nécessitent de disposer des données d'entrée pertinentes, notamment en ce qui concerne les constantes d'élasticité et l'atténuation ultrasonore. Cette étude est dédiée à la caractérisation des matériaux à gros grains, comme les aciers austéno-ferritiques moulés par centrifugation et les soudures en acier inoxydable austénitique ou en alliages à base nickel. Un système expérimental unique permettant de mesurer les constantes d'élasticité et l'atténuation en incidence oblique à été mis au point. Le point fort de ce dispositif est qu'il permet de travailler au-delà de l'angle critique longitudinal et donc de mesurer les propriétés d'atténuation des ondes transversales. Les constantes d'élasticité sont déduites des vitesses ultrasonores à partir d'un processus d'optimisation basé sur la résolution de problème inverse. Nous avons montré les potentialités d'algorithmes d'optimisation globaux tels que les algorithmes génétiques moins susceptibles de converger vers des minima locaux de la fonction à minimiser. Les résultats obtenus à partir des mesures expérimentales sont en accord avec la littérature. Des résultats de l'atténuation des ondes longitudinales et transversales par décomposition du faisceau en spectre d'ondes planes sont présentés.

Traitement numérique des milieux infinis de la géomécanique: méthodes d'équations intégrales régulières et singulières pour les structures géotechniques en conditions dynamiques; méthode de couplage itérative éléments finis/équations intégrales (applications au demi-espace et demi-plan); vibration d'un pieu fiché dans le demi espace stratifié. Comportement frottant des milieux granulaires: algorithmes locaux d'intégration numérique pour matériaux élastoplastiques type Drucker-Prager; partie élastique déformation des sols; influence de la contrainte moyenne. Problèmes liés à l'anisotropie en grandes transformations (rotations plastiques). Etude de deux types de bifurcation sur les sables; conséquences macroscopiques de la structure granulaire des sables; non-linéarité incrémentale et localisation des déformations.

Приведен обзор случаев использования изделий, изготовленных по аддитивной технологии для имплантации. Проанализирован международный стандарт на испытания пористых материалов, изготовленных по аддитивной технологии. Выявлены проблемы и предположительные пути их решения при использовании изделий, изготовленных аддитивным методом из сплавов на основе титана. решена краевая задача определения напряженно-деформированного состояния ячеистого имплантат методом конечных элементов в программном модуле ABAQUS. Рассмотрен вопрос влияния геометрии ячеек испытываемого материала на механические свойства конечного изделия для трех различных форм ячеек. Рассмотрен вопрос влияния трения между испытываемой заготовкой и бойками испытательной машины на свойства конечного изделия при различных уровнях трения.
An overview of the cases of using products made using additive technology for implantation is given. The international standard for testing porous materials manufactured by additive technology is analyzed. The problems and possible ways of their solution are revealed when using products manufactured by the additive method from titanium-based alloys. the boundary value problem of determining the stress-strain state of a cellular implant by the finite element method in the ABAQUS software module has been solved. The question of the influence of the geometry of the cells of the test material on the mechanical properties of the final product for three different cell shapes is considered. The question of the influence of friction between the tested workpiece and the strikers of the testing machine on the properties of the final product at various levels of friction is considered.

Le développement de nouveaux matériaux pose le problème de la connaissance de leurs constantes élastiques. Les méthodes de mesure des constantes élastiques sont nombreuses, mais ne permettent que très rarement de déterminer simultanément et de façon non destructive un grand nombre des composantes du tenseur des rigidités élastiques. Grâce l'essor des outils de calcul numérique et de traitement du signal, une nouvelle méthode est développée, basée sur l'analyse du comportement dynamique d'une plaque rectangulaire complètement libre à orthotropie spéciale. Deux modèles théoriques sont décrits selon que la plaque est mince ou épaisse conduisant aux équations aux dérivées partielles du mouvement et à l'expression des conditions aux limites. La résolution en terme de fréquences propres et modes propres de ces équations n'est pas simple, et par souci d'économie de temps calcul, une méthode semi-analytique originale est développée: il s'agit de la méthode dite de superposition qui permet de décomposer un problème qui n'admet pas de solution analytique, en deux sous problèmes dont la solution peut être décrite grâce à des développements en séries trigonométriques. Par ailleurs, un dispositif expérimental est mis au point, permettant, grâce à une bonne simulation des conditions aux limites complètement libres et à l'utilisation d'une métrologie sans contact, de déterminer avec précision les fréquences propres et modes propres d'une plaque. Sachant calculer théoriquement et mesurer expérimentalement les fréquences propres de la plaque, un algorithme est développé afin de déterminer les quatre ou six constantes élastiques (selon qu'elle est mince ou épaisse) régissant au mieux au sens des moindres carrés son comportement dynamique. Finalement, des résultats expérimentaux valident la méthodologie proposée et montrent sa précision et sa sensibilité

碩士
國立成功大學
航空太空工程學系
105
Based upon the special feature that Stroh formalism for two-dimensional anisotropic elasticity can be extended to the piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension, an adaptable adjustment technique is proposed to deal with the problems with simultaneous existence of anisotropic, piezoelectric and magneto-electro-elastic materials. With this technique, the analytical solutions, boundary element methods and boundary-based finite element method developed previously for the problems of anisotropic elastic inclusion can now be employed to most of the related inclusion problems with simultaneous existence of these three different kinds of materials. This technique also be applied to AEPH, the structure engineering analysis software of our group. To verify the correctness of the proposed method, three typical examples: (1) one anisotropic/piezoelectric inclusion in piezomagnetic matrix, (2) one anisotropic/piezoelectric inclusion and one crack in piezomagnetic matrix, (3) two anisotropic/piezoelectric inclusions in piezomagnetic/magneto-electro-elastic matrix, are presented and compared with the other existing solutions. This technique also can be applied to analysis of other multi-material problems and some practical applications.

The goal of this work is to develop and demonstrate a comprehensive analysis of single and multi-body composite strip-beam systems using an asymptotically-correct geometrically nonlinear theory. The comprehensiveness refers to the two distinguishing features of this work, namely the unified framework for the analysis and the inclusion of the usually ignored cross-sectional nonlinearities in thin-beam and multi-beam analyses. The first part of this work stitches together an approach to analyse generally anisotropic composite beams. Based on geometrically exact nonlinear elasticity theory, the nonlinear 3-D beam problem splits into either a linear (conventionally considered) or nonlinear (considered in this work) 2-D analysis of the beam cross-section and a nonlinear 1-D analysis along the beam reference curve. The two sub-tasks of this work (viz. nonlinear analysis of the beam cross-section and nonlinear beam analysis) are accomplished on a single platform using an object-oriented framework. First, two established nonlinear cross-sectional analyses (numerical and analytical), both based on the Variational-Asymptotic Method (VAM), are invoked. The numerical analysis is capable of treating cross-sections of arbitrary geometry and material distributions and can capture certain nonlinear effects such as the trapeze effect. The closed-form analytical analysis is restricted to thin rectangular cross-sections for generally anisotropic composites but captures ALL cross-sectional nonlinearities, and not just the well-known Brazier and trapeze effects. Second, the well-established geometrically-exact nonlinear 1-D governing equations along the beam reference curve, after being generalized to utilize the expressions for nonlinear stiffness matrix, are solved using the mixed variational finite element method. Finally, local 3-D stress, strain and displacement fields for representative sections in the beam are recovered, based on the stress resultants from the 1-D global beam analysis. This part of the work is then validated by applying it to an initially twisted cantilevered laminated composite strip under axial force. The second part is concerned with the dynamic analysis of nonlinear multi-body systems involving elastic strip-like beams made of laminated, anisotropic composite materials using an object-oriented framework. In this work, unconditionally stable time-integration schemes presenting high-frequency numerical dissipation are used to solve the ensuing governing equations. The codes developed based on such time-integration schemes are first validated with the literature for two standard test cases: non-linear spring mass oscillator and pendulum. In order to apply the comprehensive analysis code thus developed to a multi-body system, the four-bar mechanism is chosen as an example. All component bars of the mechanism have thin rectangular cross-sections and are made of fiber reinforced laminates of various types of layups. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. Each component of the mechanism is modeled as a beam based on the first part of this work. Results from this analysis are compared with those available in the literature, both theoretical and experimental. The margins between the linear and non-linear results are evaluated specifically due to the cross-sectional nonlinearities and shown to vary with stacking sequences. This work thus demonstrates the importance of geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. To enable graphical visualization, the behavior of the four-bar mechanism is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). Finally, the component-laminate load-carrying capacity is estimated using the Tsai-Wu-Hahn failure criterion for various layups and the same criterion is used to predict the first-ply-failure and the mechanism as a whole.

The goal of this work is to develop and demonstrate a comprehensive analysis of single and multi-body composite strip-beam systems using an asymptotically-correct geometrically nonlinear theory. The comprehensiveness refers to the two distinguishing features of this work, namely the unified framework for the analysis and the inclusion of the usually ignored cross-sectional nonlinearities in thin-beam and multi-beam analyses. The first part of this work stitches together an approach to analyse generally anisotropic composite beams. Based on geometrically exact nonlinear elasticity theory, the nonlinear 3-D beam problem splits into either a linear (conventionally considered) or nonlinear (considered in this work) 2-D analysis of the beam cross-section and a nonlinear 1-D analysis along the beam reference curve. The two sub-tasks of this work (viz. nonlinear analysis of the beam cross-section and nonlinear beam analysis) are accomplished on a single platform using an object-oriented framework. First, two established nonlinear cross-sectional analyses (numerical and analytical), both based on the Variational-Asymptotic Method (VAM), are invoked. The numerical analysis is capable of treating cross-sections of arbitrary geometry and material distributions and can capture certain nonlinear effects such as the trapeze effect. The closed-form analytical analysis is restricted to thin rectangular cross-sections for generally anisotropic composites but captures ALL cross-sectional nonlinearities, and not just the well-known Brazier and trapeze effects. Second, the well-established geometrically-exact nonlinear 1-D governing equations along the beam reference curve, after being generalized to utilize the expressions for nonlinear stiffness matrix, are solved using the mixed variational finite element method. Finally, local 3-D stress, strain and displacement fields for representative sections in the beam are recovered, based on the stress resultants from the 1-D global beam analysis. This part of the work is then validated by applying it to an initially twisted cantilevered laminated composite strip under axial force. The second part is concerned with the dynamic analysis of nonlinear multi-body systems involving elastic strip-like beams made of laminated, anisotropic composite materials using an object-oriented framework. In this work, unconditionally stable time-integration schemes presenting high-frequency numerical dissipation are used to solve the ensuing governing equations. The codes developed based on such time-integration schemes are first validated with the literature for two standard test cases: non-linear spring mass oscillator and pendulum. In order to apply the comprehensive analysis code thus developed to a multi-body system, the four-bar mechanism is chosen as an example. All component bars of the mechanism have thin rectangular cross-sections and are made of fiber reinforced laminates of various types of layups. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. Each component of the mechanism is modeled as a beam based on the first part of this work. Results from this analysis are compared with those available in the literature, both theoretical and experimental. The margins between the linear and non-linear results are evaluated specifically due to the cross-sectional nonlinearities and shown to vary with stacking sequences. This work thus demonstrates the importance of geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. To enable graphical visualization, the behavior of the four-bar mechanism is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). Finally, the component-laminate load-carrying capacity is estimated using the Tsai-Wu-Hahn failure criterion for various layups and the same criterion is used to predict the first-ply-failure and the mechanism as a whole.

碩士
國立臺灣大學
土木工程學研究所
100
This paper is to study the effect of anisotropic property of steel for seismic capacity of steel frame. Due to anisotropic property of steel plate, the yielding stress and ultimate strain is much lower in the through-thickness direction than in rolling direction of steel plate. However, there is an impact on the column faces of beam-column connections for the application of anisotropic steel members in the steel frame. Because beam members of beam-column connection by the effect of moment produce tension and pressure on column faces of beam-column connections, column faces of beam-column connections under tension are prone to a result of lamellar tearing in the through-thickness direction of column with anisotropic property. The tensile strength, shear capacity, moment resisting capacity, and ductility of column members and beam members will significantly go down and even induce serious damage of steel frame if column faces produce lamellar tearing. The paper is to make use of reducing yielding stress of steel beams and columns for simulating the steel anisotropic mechanical behavior on the effect of stress for assessing seismic capacity of steel frame. Therefore, there are different reduction ratios of yielding stress to simulate differences of anisotropic property of steel member on the effect of seismic capacity of steel moment-resisting frames. Adopting methods of assessing seismic capacity of this research include Pseudo-elastic approach method and pushover analysis to obtain the structure nonlinear behavior as the analysis and comparison of seismic capacity. There is an assumption that structure behavior is linear firmly for the theory of Pseudo-elastic approach method. Firstly, it is essential to carry out members forces of structure under design earthquake by static analysis or dynamic analysis. Then, gradually enlarge the design earthquake, and thus members forces of structure will be amplified by the same scale. The structure behavior will not become inelastic until the first plastic hinge of the structure appears. According to the energy conservation principle, exceeding the elastic strain energy range of the total energy can be converted into the corresponding plastic energy by using Pseudo-elastic approach method with assumption of linear structure to figure out structure nonlinear behavior in the relationship of base shear and roof lateral displacement. Finally, the yielding lateral force, ultimate lateral force, ductility ratio, and collapsed ground acceleration of the structure can be worked out as the seismic capacity assessment index of the structure. Due to Pseudo-elastic analysis method with the advantages of rapidity, simplicity and convenience on assessing the seismic capacity of structures, this study will make use of the Pseudo-elastic analysis method and pushover analysis of ETABS software to assess the impact of seismic capacity of multi-storey steel moment-resisting frames with differences of anisotropic property of steel member. According to analysis result, do with the comparison and evaluation in order to understand the differences of steel properties between isotropic and anisotropic for impact of seismic capacity of steel frames.

Magnetostrictive materials belong to an important class of smart magnetic materials which have potential applications as ultrasonic transducers, sensors, actuators, delay lines, energy harvesting devices etc. Although, magnetostrictive property is exhibited by almost all ferro and ferrimagnetic materials, the R-Fe type (R represents rare earth elements) intermetallic compounds display maximum promise owing to the large magnetostriction exhibited by them at ambient temperature. Among the several R-Fe type compounds, Tb-Fe and Sm-Fe alloys are found to exhibit maximum room temperature positive and negative magnetostriction respectively. Recently, Fe-Ga based alloys have gained significant interest as newly emerging magnetostrictive material due to a good combination of magnetic and mechanical properties. These magnetostrictive materials in thin film form are of interests for several researchers both from fundamental and applied perspectives. Currently, many researchers are exploring the possibility of using magnetostrictive thin films in micro- and nano-electromechanical systems (MEMS and NEMS). Three material systems viz. Fe-Ga, Tb-Fe and Sm-Fe in thin film form have been chosen for our investigations. DC magnetron sputtering and e-beam evaporation techniques were used for deposition of these thin films on Si (100) substrates. Several aspects such as evolution of microstructure, film surface morphology, structure and change in film composition with different processing conditions were investigated in detail, as the existing literature could not provide a clear insight. Further, detailed magnetic characterizations of these films were carried out and established a process-structure-property correlation. The thesis is divided into seven chapters. The first chapter presents a brief introduction of magnetostrictive phenomena and the physics behind its origin. A brief history of evolution of magnetostrictive materials with superior properties is also brought out. Introduction to the material systems considered for the present study has also been presented. Discussions on various aspects like crystal structures, magnetic properties, and phase diagrams of these material systems are also included in this chapter. Magnetostriction in thin films and its importance in current technological applications are discussed in short. Further, a summary of existing literature on thin films of these materials has been narrated to highlight the perspective of the work done in subsequent chapters. In addition to this, a clear picture of the grey area for further investigations has been provided. Formulation of detailed scope of work for this study is also provided in this chapter. Details of different experimental techniques used in this study for deposition and characterization of these films are given in chapter 2. In the third chapter of the thesis a detailed study on the structural, microstructural and magnetic properties of Fe-Ga films deposited using dc magnetron sputtering technique are presented. The effect of sputtering parameters such as (i) Ar pressure, (ii) sputtering power, (iii) substrate temperature and (iv) deposition time/film thickness on the magnetic properties of the films are discussed in detail. All the films are found to be polycrystalline in nature with A2 type structure as evidenced from grazing incidence X-ray diffraction (GIXRD) and transmission electron microscope (TEM) studies. Surface morphology of the films are found to be affected with processing conditions considerably. Thermomagnetic behaviour of the films studied using a Superconducting Quantum Interference Device (SQUID) magnetometer under zero field cooled (ZFC) and field cooled (FC) conditions are also presented. The sputtering parameters are also found to influence the magnetic properties of the films through modifications in microstructure, surface morphology and film compositions. Irrespective of the sputtering parameters, room temperature (RT) deposited Fe-Ga films are found to exhibit large magnetic coercively and large saturation magnetic field as compared to the bulk alloy of similar compositions which are not desirable for micromagnetic device applications. A significant improvement in the magnetic properties of the films was obtained in the films deposited at higher substrate temperatures and is correlated with modifications in grain size and film surface roughness. These films are also found to exhibit better magnetostriction than the RT deposited films. Further, the magnetic properties of Fe-Ga films as a function of film thickness in the range 2 – 480 nm are also presented. The nature of variation of coercively with film thickness was correlated with grain size effect and explained successfully with the help of random anisotropy model. In the fourth chapter, studies on the microstructural and magnetic properties of Tb-Fe films were presented. It was reported earlier that TbxFe100-x films exhibit in-plane magnetic anisotropy for the films with x > 42 at.% of Tb and out-of-plane anisotropy for the composition 28 < x < 42. Presence of these anisotropies is technologically important for different applications. We have studied the magnetic properties of Tb-Fe films in these two composition range. TbxFe100-x films with 54  x  59 were prepared using dc magnetron sputtering technique under varying Ar pressure and sputtering power and the details about microstructural and magnetic properties are presented in this chapter. All the films are found to be amorphous in nature. While the composition of the film is found to remain constant with sputtering power, the Fe concentration in the film is found to be depleted with increase in Ar pressure. Magnetic properties are found to change from superparamagnetic to ferromagnetic behaviour with increase in sputtering power. Curie temperature of the films are found to be low (below RT) and is explained based on sperimagnetic ordering of magnetic sub-lattices. The perpendicular magnetic anisotropy (PMA) or out-of-plane anisotropy behaviour of Tb-Fe films were not studied in detail as a function of film thickness. We have successfully prepared TbxFe100-x films with 29  x  40 using e-beam evaporation technique using alloy target composition of TbFe in order to study the PMA behaviour as a function of film thickness. The thickness of the films was varied from 50 to 800 nm. All the films are found to be amorphous and columnar growth structure with fine channels of voids are observed from the TEM studies. Detailed magnetization and thermomagnetic measurements were carried out using SQUID magnetometer at different temperatures. The out-of-plane magnetic coercivity of the films was found to increase with film thickness and then decreases with further increase in thickness. Maximum coercivity of ~ 20 kOe has been obtained for the 400 nm thick film. Magnetic domain patterns were studied using magnetic force microscopy (MFM) technique and the observed magnetic properties are correlated with domain pattern and microstructures. Although there are several reports on device applications of Sm-Fe thin films which exhibit negative magnetostriction, a comprehensive study on the effect of different process parameters on the magnetic properties and its correlation with structure and microstructure is still elusive. Hence, Sm-Fe films were deposited on Si (100) substrate using dc magnetron sputtering technique under varying Ar pressure and sputtering power. Effect of these parameters on the microstructural and magnetic properties of the films was studied in detail and is presented in chapter 5. The curie temperature of the films was found to increase with increase in sputtering power and Ar pressure. This was attributed to increase in film thickness and size of islands (atomic clusters). Coercivity as low as 30 Oe has been achieved in the film deposited at 15 mTorr Ar pressure. The Curie temperature for the films deposited at higher Ar pressure (10 and 15 mTorr) are found to be above RT. Maximum saturation magnetostriction of ~ - 390 -strains has been achieved in the film deposited at 15 mTorr Ar pressure. Rapid thermal processing (RTP) experiments were also carried out to increase the magnetic ordering in the films deposited at low Ar pressure (5 mTorr) by imparting structural ordering. Large improvement in magnetization and Curie temperature of the film was observed after RTA. However, this could be attributed to the formation of nano-crystalline Fe phase as evidenced from the TEM studies and thermomagnetic measurements. An overall summary of the experimental results has been presented in chapter 6. The scope of work for further study in future has also been highlighted in chapter 7.

Magnetostrictive materials belong to an important class of smart magnetic materials which have potential applications as ultrasonic transducers, sensors, actuators, delay lines, energy harvesting devices etc. Although, magnetostrictive property is exhibited by almost all ferro and ferrimagnetic materials, the R-Fe type (R represents rare earth elements) intermetallic compounds display maximum promise owing to the large magnetostriction exhibited by them at ambient temperature. Among the several R-Fe type compounds, Tb-Fe and Sm-Fe alloys are found to exhibit maximum room temperature positive and negative magnetostriction respectively. Recently, Fe-Ga based alloys have gained significant interest as newly emerging magnetostrictive material due to a good combination of magnetic and mechanical properties. These magnetostrictive materials in thin film form are of interests for several researchers both from fundamental and applied perspectives. Currently, many researchers are exploring the possibility of using magnetostrictive thin films in micro- and nano-electromechanical systems (MEMS and NEMS). Three material systems viz. Fe-Ga, Tb-Fe and Sm-Fe in thin film form have been chosen for our investigations. DC magnetron sputtering and e-beam evaporation techniques were used for deposition of these thin films on Si (100) substrates. Several aspects such as evolution of microstructure, film surface morphology, structure and change in film composition with different processing conditions were investigated in detail, as the existing literature could not provide a clear insight. Further, detailed magnetic characterizations of these films were carried out and established a process-structure-property correlation. The thesis is divided into seven chapters. The first chapter presents a brief introduction of magnetostrictive phenomena and the physics behind its origin. A brief history of evolution of magnetostrictive materials with superior properties is also brought out. Introduction to the material systems considered for the present study has also been presented. Discussions on various aspects like crystal structures, magnetic properties, and phase diagrams of these material systems are also included in this chapter. Magnetostriction in thin films and its importance in current technological applications are discussed in short. Further, a summary of existing literature on thin films of these materials has been narrated to highlight the perspective of the work done in subsequent chapters. In addition to this, a clear picture of the grey area for further investigations has been provided. Formulation of detailed scope of work for this study is also provided in this chapter. Details of different experimental techniques used in this study for deposition and characterization of these films are given in chapter 2. In the third chapter of the thesis a detailed study on the structural, microstructural and magnetic properties of Fe-Ga films deposited using dc magnetron sputtering technique are presented. The effect of sputtering parameters such as (i) Ar pressure, (ii) sputtering power, (iii) substrate temperature and (iv) deposition time/film thickness on the magnetic properties of the films are discussed in detail. All the films are found to be polycrystalline in nature with A2 type structure as evidenced from grazing incidence X-ray diffraction (GIXRD) and transmission electron microscope (TEM) studies. Surface morphology of the films are found to be affected with processing conditions considerably. Thermomagnetic behaviour of the films studied using a Superconducting Quantum Interference Device (SQUID) magnetometer under zero field cooled (ZFC) and field cooled (FC) conditions are also presented. The sputtering parameters are also found to influence the magnetic properties of the films through modifications in microstructure, surface morphology and film compositions. Irrespective of the sputtering parameters, room temperature (RT) deposited Fe-Ga films are found to exhibit large magnetic coercively and large saturation magnetic field as compared to the bulk alloy of similar compositions which are not desirable for micromagnetic device applications. A significant improvement in the magnetic properties of the films was obtained in the films deposited at higher substrate temperatures and is correlated with modifications in grain size and film surface roughness. These films are also found to exhibit better magnetostriction than the RT deposited films. Further, the magnetic properties of Fe-Ga films as a function of film thickness in the range 2 – 480 nm are also presented. The nature of variation of coercively with film thickness was correlated with grain size effect and explained successfully with the help of random anisotropy model. In the fourth chapter, studies on the microstructural and magnetic properties of Tb-Fe films were presented. It was reported earlier that TbxFe100-x films exhibit in-plane magnetic anisotropy for the films with x > 42 at.% of Tb and out-of-plane anisotropy for the composition 28 < x < 42. Presence of these anisotropies is technologically important for different applications. We have studied the magnetic properties of Tb-Fe films in these two composition range. TbxFe100-x films with 54  x  59 were prepared using dc magnetron sputtering technique under varying Ar pressure and sputtering power and the details about microstructural and magnetic properties are presented in this chapter. All the films are found to be amorphous in nature. While the composition of the film is found to remain constant with sputtering power, the Fe concentration in the film is found to be depleted with increase in Ar pressure. Magnetic properties are found to change from superparamagnetic to ferromagnetic behaviour with increase in sputtering power. Curie temperature of the films are found to be low (below RT) and is explained based on sperimagnetic ordering of magnetic sub-lattices. The perpendicular magnetic anisotropy (PMA) or out-of-plane anisotropy behaviour of Tb-Fe films were not studied in detail as a function of film thickness. We have successfully prepared TbxFe100-x films with 29  x  40 using e-beam evaporation technique using alloy target composition of TbFe in order to study the PMA behaviour as a function of film thickness. The thickness of the films was varied from 50 to 800 nm. All the films are found to be amorphous and columnar growth structure with fine channels of voids are observed from the TEM studies. Detailed magnetization and thermomagnetic measurements were carried out using SQUID magnetometer at different temperatures. The out-of-plane magnetic coercivity of the films was found to increase with film thickness and then decreases with further increase in thickness. Maximum coercivity of ~ 20 kOe has been obtained for the 400 nm thick film. Magnetic domain patterns were studied using magnetic force microscopy (MFM) technique and the observed magnetic properties are correlated with domain pattern and microstructures. Although there are several reports on device applications of Sm-Fe thin films which exhibit negative magnetostriction, a comprehensive study on the effect of different process parameters on the magnetic properties and its correlation with structure and microstructure is still elusive. Hence, Sm-Fe films were deposited on Si (100) substrate using dc magnetron sputtering technique under varying Ar pressure and sputtering power. Effect of these parameters on the microstructural and magnetic properties of the films was studied in detail and is presented in chapter 5. The curie temperature of the films was found to increase with increase in sputtering power and Ar pressure. This was attributed to increase in film thickness and size of islands (atomic clusters). Coercivity as low as 30 Oe has been achieved in the film deposited at 15 mTorr Ar pressure. The Curie temperature for the films deposited at higher Ar pressure (10 and 15 mTorr) are found to be above RT. Maximum saturation magnetostriction of ~ - 390 -strains has been achieved in the film deposited at 15 mTorr Ar pressure. Rapid thermal processing (RTP) experiments were also carried out to increase the magnetic ordering in the films deposited at low Ar pressure (5 mTorr) by imparting structural ordering. Large improvement in magnetization and Curie temperature of the film was observed after RTA. However, this could be attributed to the formation of nano-crystalline Fe phase as evidenced from the TEM studies and thermomagnetic measurements. An overall summary of the experimental results has been presented in chapter 6. The scope of work for further study in future has also been highlighted in chapter 7.