La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits.El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen.Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents.Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals. / This thesis proposes a methodology for the probabilistic simulation of the transverse failure of Carbon Fibre Reinforced Polymers (CFRP) by analyzing the random distribution of the fibres within the composite. First chapters are devoted to the State-of-the-art review on the modelization of random materials, the computation of effective properties and the transverse failure of fibre reinforced polymers.The first step in the proposed methodology is the definition of a Statistical Representative Volume Element (SRVE). This SRVE has to satisfy criteria based on the analysis of the volume fraction, the effective properties, the Hill Condition, the statistics of the stress and strain components, the probability density function of the stress and strain components and the inter-fibre distance statistical distributions. Once this SRVE has been achieved, a comparison between a periodic model and a random model is performed to quantitatively analyze the differences between the results they provide.Also a methodology for the statistical analysis of the distribution of the fibre within the composite from digital images of the transverse section. This analysis is performed for four different materials.Finally, a two-scale computational method for the transverse failure of unidirectional laminae is proposed. This method is able to provide probability density functions of the mechanical variables in the composite. Some applications and possibilities of the method are given and the simulation results are compared with experimental tests.

Les HEMT AlGaN/GaN sont en passe de devenir incontournables dans le monde de l'amplification de puissance radiofréquence, grâce à leurs performances exceptionnelles. Cependant,en raison de la relative jeunesse de cette technologie, des études de fiabilité dans plusieurs modes de fonctionnement sont toujours nécessaires pour comprendre les mécanismes de défaillance propres à ces composants et responsables de leur vieillissement. Cette étude porte sur l'analyse des défaillances dans les transistors HEMT AlGaN/GaN de puissance,en régime de fonctionnement de type RADAR (pulsé et saturé). Elle s'appuie sur la conception d'amplificateurs de test, leur caractérisation et leur épreuve sur bancs de vieillissement. La mise en place d'une méthodologie visant à discriminer les mécanismes de dégradation prépondérants, conjointement à une analyse micro-structurale des composants vieillis, permet d'établir le lien entre l'évolution des performances électriques et l'origine physique de ces défauts. / AlGaN/GaN HEMTs are on the way to lead the radiofrequency power amplificationfield according to their outstanding performances. However, due to the relative youth of this technology, reliability studies in several types of operating conditions are still necessaryto understand failure mechanisms peculiar to these devices and responsible for their wearingout. This study deals with the failure analysis of power AlGaN/GaN HEMTs in RADARoperating mode (pulsed and saturated). This is based on the design of test amplifiers, theircharacterization and their stress on ageing benches. The setting up of a methodology aimingat discriminating predominant degradation modes, jointly with a micro-structural analysisof aged devices, permits to link the evolution of electrical performances with the physicalroots of these defects.

The present dissertation reports the findings of a study of cracking behavior of a newly developed superalloy, Allvac 718Plus during high power beam welding and post-weld heat treatment. Microstructures of the base alloy, heat affected zone (HAZ) and fusion zone (FZ) of welded and post-weld heat treated (PWHT) coupons were examined by the use of standard metallographic techniques involving optical microscopy, analytical scanning electron microscopy (SEM) and analytical transmission electron microscopy. Moreover, grain boundary segregation behavior of boron atoms during pre-weld heat treatments was evaluated using secondary ion mass spectroscopic system. In the first phase of the research, 718Plus was welded using a low and high heat input CO2 laser to assess its weld cracking response. Detailed examination of the welds by analytical electron microscopic technique revealed the occurrence of cracking in the HAZ of low heat input welds, while their FZ was crack free. However, both the FZ and HAZ of high heat input welds were crack-free. Resolidified constituents were observed along the cracked grain boundaries of the lower heat input welds, which indicated that HAZ cracking in this newly developed superalloy was associated with grain boundary liquation. However, despite a more extensive liquation of grain boundaries and grain interior in the HAZ of high heat input welds, no cracking occurred. This was attributed to the combination of lower welding stresses generated during cooling, and relaxation of these stresses by thick intergranular liquid. Although HAZ cracking was prevented by welding with a high heat input laser, it resulted in a significant damage to the parent microstructure through its extensive liquation. Thus, the use of low heat input welding is desirable. However, this resulted in HAZ cracking which needs to be minimized or eliminated. Therefore, during the second phase of this research, the effects of pre-weld thermal processing on the cracking response of 718Plus were investigated. Results from the quantification of the cracking of the alloy showed that HAZ cracking may be significantly reduced or eliminated through an adequate selection of pre-weld thermal cycle. In the third stage of this research, crack-free welds of 718Plus were post-weld heat treated using standard thermal schedules. A significant solid state cracking of the alloy occurred during the PWHT. The cracking was attributed to the presence of embrittling phases on HAZ grain boundaries, coupled with aging contraction stresses that are generated by a considerable precipitation of gamma prime phase during aging.

The present dissertation reports the findings of a study of cracking behavior of a newly developed superalloy, Allvac 718Plus during high power beam welding and post-weld heat treatment. Microstructures of the base alloy, heat affected zone (HAZ) and fusion zone (FZ) of welded and post-weld heat treated (PWHT) coupons were examined by the use of standard metallographic techniques involving optical microscopy, analytical scanning electron microscopy (SEM) and analytical transmission electron microscopy. Moreover, grain boundary segregation behavior of boron atoms during pre-weld heat treatments was evaluated using secondary ion mass spectroscopic system. In the first phase of the research, 718Plus was welded using a low and high heat input CO2 laser to assess its weld cracking response. Detailed examination of the welds by analytical electron microscopic technique revealed the occurrence of cracking in the HAZ of low heat input welds, while their FZ was crack free. However, both the FZ and HAZ of high heat input welds were crack-free. Resolidified constituents were observed along the cracked grain boundaries of the lower heat input welds, which indicated that HAZ cracking in this newly developed superalloy was associated with grain boundary liquation. However, despite a more extensive liquation of grain boundaries and grain interior in the HAZ of high heat input welds, no cracking occurred. This was attributed to the combination of lower welding stresses generated during cooling, and relaxation of these stresses by thick intergranular liquid. Although HAZ cracking was prevented by welding with a high heat input laser, it resulted in a significant damage to the parent microstructure through its extensive liquation. Thus, the use of low heat input welding is desirable. However, this resulted in HAZ cracking which needs to be minimized or eliminated. Therefore, during the second phase of this research, the effects of pre-weld thermal processing on the cracking response of 718Plus were investigated. Results from the quantification of the cracking of the alloy showed that HAZ cracking may be significantly reduced or eliminated through an adequate selection of pre-weld thermal cycle. In the third stage of this research, crack-free welds of 718Plus were post-weld heat treated using standard thermal schedules. A significant solid state cracking of the alloy occurred during the PWHT. The cracking was attributed to the presence of embrittling phases on HAZ grain boundaries, coupled with aging contraction stresses that are generated by a considerable precipitation of gamma prime phase during aging.

Le but de ce travail est d'étudier l'influence de la microstructure de roches poreuses hétérogènes sur le comportement à l'échelle macroscopique. Ainsi, nous avons caractérisé la microstructure et les propriétés micromécaniques (grâce à des tests de nano-indentation) de deux roches oolithiques poreuses (calcaire de Lavoux et minerai de fer) pour calculer leurs propriétés mécaniques et thermiques effectives. Les roches oolithiques sont constituées d'un assemblage de grains poreux (oolithes), de pores et de cristaux intergranulaires. La microscopie électronique à balayage et la tomographie 3D aux rayons X ont été utilisées pour identifier les différents composants de ces roches. Une attention particulière a été accordée à la tomographie aux rayons X car cette méthode analytique permet de caractériser le réseau poreux (taille, distribution spatiale et fraction volumique), ainsi que la forme des oolithes et des cristaux inter-oolithiques. La nouveauté de ce travail réside dans la prise en compte de la forme 3D réelle des pores. Par conséquent, nous avons approximé les oolites poreuses par des sphères et les pores de forme irrégulière par des ellipsoïdes. Cette approximation a été réalisée grâce à l'analyse en composantes principales (ACP), qui fournit les propriétés géométriques telles que la longueur des demi-axes et l'orientation des ellipsoïdes résultants. La sphéricité des oolites approximées a été calculée et les valeurs proches de 1 nous ont permis de considérer les oolithes comme des sphères. Pour vérifier l'approximation dans le cas des pores, nous avons évalué la contribution de ces pores tridimensionnels de forme irrégulière aux propriétés élastiques et thermiques effectives. Ainsi, les tenseurs de contribution de souplesse pour les pores irréguliers 3D et leurs approximations ellipsoïdales ont été calculés en utilisant la méthode des éléments finis (FEM). Ces tenseurs ont été comparés et une erreur relative a été estimée pour évaluer la précision de l'approximation. Cette erreur produit une distance maximale de 4,5% entre les deux solutions pour les pores et les ellipsoïdes, ce qui vérifie la procédure d'approximation proposée basée sur ACP. La méthode numérique FEM a été vérifiée en comparant la solution numérique des tenseurs de contribution des ellipsoïdes à la solution analytique basée sur la théorie d'Eshelby. La différence entre ces deux solutions ne dépasse pas 3%. La même méthode numérique a été utilisée pour calculer les tenseurs de contribution de résistivité thermique. Les tenseurs de souplesse et de résistivité calculés ont été utilisés pour évaluer les propriétés élastiques effectives (module élastique et coefficient de cisaillement) et la conductivité thermique effective en considérant le schéma d'homogénéisation de Maxwell en deux étapes. Les résultats ont montré une influence importante de la porosité sur les propriétés effectives. Enfin, les résultats obtenus pour les pores irréguliers ont été comparés à ceux des ellipsoïdes et ils ont montré un bon accord avec un écart maximal de 4% ce qui vérifie l'approximation des pores de forme irrégulière par des ellipsoïdes triaxiaux / The aim of this work is to study the influence of the microstructure of heterogeneous porous rocks on the behavior at the macroscopic scale. Thus, we characterized the microstructure and micromechanical properties (thanks to nano-indentation tests) of two porous oolitic rocks (Lavoux limestone and iron ore) to calculate their effective mechanical and thermal properties. Oolitic rocks are constituted by an assemblage of porous grains (oolites), pores and inter-granular crystals. Scanning electron microscopy and X-ray 3D Computed Tomography were used to identify the different components of these rocks. Particular attention was given to X-Ray computed tomography since this analytical method allows the characterization of the porous network (size, spatial distribution, and volume fraction), and the shapes of oolites and inter-oolitic crystals. The novelty of this work lies in taking into account the 3D real shape of pores. Hence, we approximated porous oolites by spheres and irregularly shaped pores by ellipsoids. This approximation was performed thanks to the principal component analysis (PCA), which provides the geometrical properties such as length of semi-axes and orientation of resulting ellipsoids. The sphericity of the approximated oolites was calculated and the values close to 1 allowed us to consider oolites as spheres. To verify the approximation in the case of pores, we evaluated the contribution of these irregularly shaped three-dimensional pores to the overall elastic properties. Thus, compliance contribution tensors for 3D irregular pores and their ellipsoidal approximations were calculated using the finite element method (FEM). These tensors were compared and a relative error was estimated to evaluate the accuracy of the approximation. This error produces a maximum discrepancy of 4.5% between the two solutions for pores and ellipsoids which verifies the proposed approximation procedure based on PCA. The FEM numerical method was verified by comparing the numerical solution for compliance contribution tensors of ellipsoids to the analytical solution based on Eshelby’s theory. The difference between these two solutions does not exceed 3%. The same numerical method was used to calculate thermal resistivity contribution tensors. Calculated compliance and resistivity contribution tensors were used to evaluate effective elastic properties (bulk modulus and shear coefficient) and effective thermal conductivity by considering the two-step Maxwell homogenization scheme. The results showed an important influence of the porosity on effective properties. Finally, the results obtained for irregular pores were compared to those for ellipsoidal ones and they showed a good agreement with a maximum deviation of 4% which verifies once again the approximation of irregularly shaped pores by tri-axial ellipsoids