The effect of thermal-cycling-induced microcracking in fiber-reinforced polymer matrix composites is studied. Specific attention is focused on microcrack density as a function of the number of thermal cycles, and the effect of microcracking on the dimensional stability of composite materials. Changes in laminate coefficient of thermal expansion (CTE) and laminate stiffness are of primary concern. Included in the study are materials containing four different Thornel fiber types: a PAN-based T50 fiber and three pitch-based fibers, P55, P75, and P120. The fiber stiffnesses range from 55 Msi to 120 Msi. The fiber CTE's range from -0.50x10⁻⁶/°F to -0.80x10⁻⁶/°F. Also included are three matrix types: Fiberite's 934 epoxy, Amoco's ERL1962 toughened epoxy, and YLA's RS3 cyanate ester. The lamination sequences of the materials considered include a cross-ply configuration, [0/90]2s, and two quasi-isotropic configurations, [0/+45/-45/90]s and [0/+45/90/-45]s. The layer thickness of the materials range from a nominal 0.001 in. to 0.005 in. In addition to the variety of materials considered, three different thermal cycling temperature ranges are considered. These temperature ranges are ±250°F, ±150°F, and ±50°F. The combination of these material and geometric parameters and temperature ranges, combined with thermal cycling to thousands of cycles, makes this one of the most comprehensive studies of thermal-cycling-induced microcracking to date. Experimental comparisons are presented by examining the effect of layer thickness, fiber type, matrix type, and thermal cycling temperature range on microcracking and its influence on the laminates. Results regarding layer thickness effects indicate that thin-layer laminates microcrack more severely than identical laminates with thick layers. For some specimens in this study, the number of microcracks in thin-layer specimens exceeds that in thick-layer specimens by more than a factor of two. Despite the higher number of microcracks in the thin-layer specimens, small changes in CTE after thousands of cycles indicate that the thin-layer specimens are relatively unaffected by the presence of these cracks compared to the thick-layer specimens. Results regarding fiber type indicate that the number of microcracks and the change in CTE after thousands of cycles in the specimens containing PAN-based fibers are less than in the specimens containing comparable stiffness pitch-based fibers. Results for specimens containing the different pitch-based fibers indicate that after thousands of cycles, the number of microcracks in the specimens does not depend on the modulus or CTE of the fiber. The change in laminate CTE does, however, depend highly on the stiffness and CTE of the fiber. Fibers with higher stiffness and more negative CTE exhibit the lowest change in laminate CTE as a result of thermal cycling. The overall CTE of these specimens is, however, more negative as a result of the more negative CTE of the fiber. Results regarding matrix type based on the ±250°F temperature range indicate that the RS3 cyanate ester resin system exhibits the greatest resistance to microcracking and the least change in CTE, particularly for cycles numbering 3000 and less. Extrapolations to higher numbers of cycles indicate, however, that the margin of increased performance is expected to decrease with additional thermal cycling. Results regarding thermal cycling temperature range depend on the matrix type considered and the layer thickness of the specimens. For the ERL1962 resin system, microcrack saturation is expected to occur in all specimens, regardless of the temperature range to which the specimens are exposed. By contrast, the RS3 resin system demonstrates a threshold effect such that cycled to less severe temperature ranges, microcracking does not occur. For the RS3 specimens with 0.005 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between between ±150°F or ±50°F. For the RS3 specimens with 0.002 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between ±50°F.. Results regarding laminate stiffness indicate negligible change in laminate stiffness due to thermal cycling for the materials and geometries considered in this investigation. The study includes X-ray examination of the specimens, showing that cracks observed at the edge of the specimens penetrate the entire width of the specimen. Glass transition temperatures of the specimens are measured, showing that resin chemistry is not altered as a result of thermal cycling. Results are also presented based on a one-dimensional shear lag analysis developed in the literature. The analysis requires material property information that is difficult to obtain experimentally. Using limited data from the present investigation, material properties associated with the analysis are modified to obtain reasonable agreement with measured microcrack densities. Based on these derived material properties, the analysis generally overpredicts the change in laminate CTE. Predicted changes in laminate stiffness show reasonable correlation with experimentally measured values. / Ph. D.

Cieľom predkladanej diplomovej práce je skúmať a analyzovať možnosti prispôsobovania koeficientu tepelnej rozťažnosti nástrekov z kompozitných materiálov deponovaných na substráty pomocou technológie cold spray. Kompozitné materiály sú v tomto prípade reprezentované zmiešanými práškami, ktoré sú pripravené pridávaním fázy s negatívnou tepelnou rozťažnosťou do základného materiálu s kladným koeficientom tepelnej rozťažnosti. Takto pripravené nástreky môžu byť užitočné pri opravovaní a renovácii strojárenských súčiastok. V prvej časti je priblížená samotná technológia cold spray spolu s jej využitím pri opravách a renováciách v strojárenskom priemysle. Ďalej sa práca zaoberá tepelnou rozťažnosťou materiálov, kde je predstavený jav negatívnej tepelnej rozťažnosti. V experimentálnej časti práce je vyhodnotený potenciálny efekt negatívnej tepelnej rozťažnosti pri deponovaní nástrekov pomocou technológie cold spray.

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L'objectif de ce travail concerne l'étude de l'amorphisation sous pression (PIA) dans des aluminophosphates, qui présentent des coefficients de expansion thermiques négatif (NTE). La synthèse de ces aluminophosphates, leur stabilité en température (dilatation) ainsi que leur comportement sous pression (amorphisationant) été étudiés. Les aluminophosphates choisis pour réaliser cette étude sont AlPO4-54, premier tamis moléculaire uniforme ayant des pores (unidimensionnelles parallèles à l'axe c) de diamètre supérieur à 1 nm, et AlPO4-17, qui présente une porosité tridimensionnelle et le plus fort coefficient de dilatation thermique négatif connu dans les matériaux oxydes. Chaque matériau déshydrataté a été étudié par diffraction des rayons-X sous pression en cellule à enclume de diamants (CED). AlPO4-54 subit une transformation de phase vers AlPO4-8 sous pression avant l'amorphisation. Au contraire, AlPO4-17 qui s'amorphise à basses pressions, est extrêmement compressible et présente une instabilité élastique, avec valeur négative pour B0'. Des valeurs anormales (négatives) pour B0' sont rares et ont déjà été observées pour des cyanures et des MOF (metal organic framework). Cette instabilité semble être caractéristique des matériaux présentant une forte NTE, montrant le lien entre la NTE et la compressibilité anormale. L'influence de la basse température sur l'eau confinée dans les pores de la structure d'AlPO4-54•xH2O a été étudié par diffraction des rayons X et par spectroscopie Raman sur monocristal. Les résultats ont été comparés à des simulations Monte Carlo sur le matériau. Les résultats ont montré que les molécules d'eau en contact avec la surface de la structure du pore unidimensionnel sont plus ordonnées vers 173 K, alors que l'eau du centre du pore est restée dans un état de type verre (liquide) à toutes les autres températures étudiées. L'amorphisation d'AlPO4-54•xH2O a été suivie par diffraction des rayons X et par spectroscopie Raman in-situ sous pression dans une CED en utilisant huile de silicone et l'eau comme milieux transmetteurs de pression. Des analyses ex-situ des échantillons de la forme amorphe d'AlPO4-54•xH2O ont été réalisées par résonance magnétique nucléaire et spectroscopie d'absorption de rayons x au synchrotron Soleil (ligne LUCIA). L'analyse de la structure locale a révélé qu'un changement de coordinence est responsable pour la déstabilisation de la structure : deux molécules d'eau ont été contraintes à entrer dans la sphère de coordination de l'Al tétraédrique, devenant ainsi un site octaédrique. / The aim of this study is to investigate pressure-induced amorphisation (PIA) in negative thermal expansion (NTE) aluminophosphates. The aluminophosphates AlPO4-17 and AlPO4-54 are of particular importance, the first exhibits the highest known degree of negative thermal expansion for an oxide and the second exhibits the largest pores known for zeolites with a diameter of 12 Å. These materials exhibit unusual behavior upon compression due to the softening of a large number of low frequency modes leading to pressure-induced amorphisation. The pressure-induced amorphisation in the exceptional NTE material AlPO4-17 was studied by in situ X-ray powder diffraction. AlPO4-17 shows anomalous behavior under pressure with elastic instability and negative value of B0'. Anomalous compressibility behavior may be observed in other materials that exhibit strong NTE, indicating a link between these two physical properties due by low-energy lattice vibrations. The pressure-induced phase transition of the AlPO4-54 to AlPO4-8 and the consequent amorphisation of the final structure, was studied by X-ray diffraction in situ at high pressures. The freezing of nanoconfined water in the AlPO4-54•xH2O was studied by Single Crystal X-ray Diffraction and Raman spectroscopy experiments and were compared to Monte Carlo and Molecular Dynamics simulations. Results shows that, at the pore surface, the adsorbed layer of water molecules had a crystal-like orientational order, in contrast, a cylindrical core of glassy water in the pore center is present due to the frustration arising from the curvature. The effect of H2O on the (PIA) of AlPO4-54•xH2O was studied by in situ X-ray powder diffraction and Raman spectroscopy under high pressures. Ex situ analysis were used to investigate the local structure of pressure-amorphized microporous AlPO4-54•xH2O by nuclear resonance magnetic and by X-ray absorption spectroscopy at the synchrotron Soleil (beamline LUCIA) which shows that, upon increasing the pressure, two water molecules enters in the coordination sphere of IVAl, changing the coordination from 4- to 6-fold, which destabilizes the structure.

[pt] Alguns óxidos cerâmicos apresentam Coeficiente de Expansão Térmica Negativa (ETN). Estes materiais usados como compósitos podem controlar a expansão térmica em valores determinados, inclusive zero. Este trabalho tem como objetivo propor novos óxidos da família A2M3O12 com coeficiente de expansão próximo a zero. Foi usada a Análise de Componentes Principais (PCA) para se verificar estatisticamente a causa de ETN em 45 óxidos conhecidos desta família e a partir daí foi usada uma Rede Neural para simulação de novos óxidos. / [en] Some ceramic oxides exhibit negative coefficient of thermal expansion. These material generally used as compounds can control the thermal expansion in determined values, including zero. The aim of this work is to propose new oxides of the family type A2M3O12 with coefficient of thermal expansion close to zero. The Principal Component Analysis (PCA) is used to statistically verify the reason for negative thermal expansion in 45 known oxides of this family and then, the neural network approach is used for simulation of new oxides.

[pt] Materiais que apresentam expansão térmica baixa ou negativa possuem grande potencial de emprego em diversas aplicações que requerem resistência ao choque térmico, assim como para aplicações odontológicas, em placas de circuitos eletrônicos, em componentes ópticos e para produzir compósitos em que compensam a expansão térmica positiva de outros materiais. Por este motivo, o estudo e a produção de materiais com expansão térmica controlada têm crescido nos últimos anos. No presente trabalho, foram estudadas algumas famílias de óxidos com estruturas que apresentam este tipo de comportamento. Foi avaliada a expansão térmica em três sistemas da família A2M3O12 com o intuito de produzir materiais com expansão térmica controlada pela substituição química do cátion A pelos cátions Al, Cr e Fe. Os sistemas produzidos foram: Cr2xFe2-2xMo3O12 (molibdato de cromo - ferro), Al2xCr2- 2xMo3O12 (molibdato de alumínio - cromo) e Al2xFe2-2xMo3O12 (molibdato de alumínio - ferro). Além destes, o composto HfMgMo3O12 foi também sintetizado para testar a viabilidade de substituição dos cátions A trivalentes por um cátion divalente e um tetravalente. Foi possível obter soluções sólidas monofásicas e seus parâmetros de rede variam linearmente com o aumento no conteúdo do cátion de maior tamanho, conforme a lei de Vegard. Análise térmica realizada por DSC permitiu determinar a temperatura de transição de fase da estrutura monoclínica (P21a) à ortorrômbica (Pbcn). Os valores encontrados foram: para o Al2Mo3O12, 200oC, para o Cr2Mo3O12 , 403oC e para o Fe2Mo3O12, 512oC. Coeficientes de expansão térmica intrínsecos foram determinados por difração de raios-X utilizando luz síncrotron, encontrando-se valores bem reduzidos para todos os sistemas estudados, a saber: para o Al2Mo3O12, (alfa)l = 2,32 x 10- 6/oC, para o Cr2Mo3O12 , (alfa)l = 0,65 x 10-6/oC e para o Fe2Mo3O12, (alfa)l = 1,72 x 10-6/oC. / [en] Negative and low thermal expansion materials have important potential applications as resistance to thermal shock, as well as, for odontological applications, printed circuit boards, optical components and to produce composites to compensate the positive thermal expansion of materials. For this reason, the study and production of materials with controlled thermal expansion have increased in the recent years. In the present work, some oxide families with structures that present this type of behavior were investigated. The thermal expansion in three systems of A2M3O12 family was evaluated in order to produce materials with controlled thermal expansion through the chemical substitution of cation A with Al, Cr and Fe. The produced systems were: Cr2xFe2-2xMo3O12 (chromium - iron molybdate), Al2xCr2-2xMo3O12 (chromium - aluminum molybdate) and Al2xFe2-2xMo3O12 (aluminum - iron molybdate). Besides that, HfMgMo3O12 was synthesized to test the viability of substitution of trivalent cations for one divalent plus one tetravalent. It was possible to obtain single- phase solid solutions and their lattice parameters increased linearly with the increase of the largest cation content, following the Vegard`s law. Thermal analysis carried out by DSC allowed the determination of the phase transition temperature from monoclinic (P21a) to orthorhombic (Pbcn) structure. The values were 200oC for Al2Mo3O12, , 403oC for Cr2Mo3O12 , and 512oC for Fe2Mo3O12. Intrinsic thermal expansion coefficients were determined by X-rays diffraction using syncrotron radiation, and low values were found for all studied systems: (alfa)1 = 2,32 x 10- 6/oC for Al2Mo3O12, (alfa)1 = 0,65 x 10-6/oC for Cr2Mo3O12 , and (alfa)1 = 1,72 x 10-6/oC for Fe2Mo3O12.

Os silicetos de metais de transição têm sido investigados para possíveis aplicações em altas temperaturas. A expansão térmica é uma das principais propriedades a serem consideradas nas aplicações. Este trabalho teve como objetivos a determinação dos coeficientes de expansão térmica das fases αTa5Si3 e Cr5Si3 e a investigação da formação da fase (Hf, Ti)5Si3. As ligas de Ta-Si e Cr-Si foram produzidas por fusão a arco. As ligas de Ta-Si foram tratadas termicamente a 1900 °C por 3 h em argônio, enquanto que as ligas de Cr-Si foram tratadas a 1200 °C por 24 h em argônio. As ligas foram caracterizadas por difratometria de raios X e microscopia eletrônica de varredura. As medidas de difratometria de raios X de alta resolução com fonte de luz síncrotron foram realizadas nas amostras contendo as fases de interesse, αTa5Si3 e Cr5Si3 num intervalo de temperatura entre ambiente e 800 °C. A fase αTa5Si3, de estrutura tetragonal (T2), apresentou expansão térmica de αa = 5,9(3).10-6 K-1 e αc = 9,2(4).10-6 K-1 na liga Ta62,5Si37,5 e αa = 6,2(3).10-6 K-1 e αc = 9,5(4).10-6 K-1 na liga Ta62Si38, resultando em uma anisotropia de αc/αa de 1,5 para ambas as amostras. A fase Cr5Si3 de estrutura hexagonal (D88) apresentou expansão térmica de αa = 17,1(3).10-6 K-1 e αc = 11,1(4).10-6 K-1 na liga Cr62,5Si37,5 e αa = 17,2(3).10-6 K-1 e αc = 10,7(4).10-6 K-1 na liga Ta62Si38, com anisotropia αc/αa de 1,5 e 1,6, respectivamente. Na segunda parte deste trabalho, as ligas de composições Hf(62,5-x)TixSi37,5 (0 ≤ x ≤ 62,5) com diferentes proporções de Hf e Ti foram preparadas por fusão a arco e tratadas termicamente a 1200 °C por 24 h em atmosfera de argônio. A formação da fase (Hf,Ti)5Si3 foi observada em todas as amostras preparadas. As amostras de composições Hf38,9Ti23,6Si37,5 e Hf22,5Ti40Si37,5 a Ti62,5Si37,5, apresentaram-se monofásicas. A variação nos parâmetros de rede a e c da fase hexagonal (Hf,Ti)5Si3 contendo diferentes teores de Hf e Ti mostrou que a fase constitui uma solução sólida em toda a extensão entre Hf5Si3 e Ti5Si3, com substituição parcial dos átomos de Hf por Ti. / The transition metal silicides have been investigated aiming high temperature applications. The thermal expansion is one of main properties for applications. The aim of this work was the evaluation of the thermal expansion coefficients for αTa5Si3 and Cr5Si3 phases and the investigation of (Hf, Ti)5Si3 phase formation. The Ta-Si and Cr-Si alloys were prepared by arc-melting. The Ta-Si alloys were heat-treated at 1900 °C for 3 h in argon atmosphere. The Cr-Si alloys were treated at 1200 °C for 24 h in argon. The alloys were characterized by X-ray diffractometry and scanning electron microscopy. The αTa5Si3 and Cr5Si3 phases were analyzed in high temperatures up to 800 °C using high-resolution X-ray diffraction with synchrotron radiation source. The thermal expansion coefficients for the αTa5Si3 tetragonal phase (T2) was found to be 5.9(3).10-6 K-1 and αc = 9.2(4).10-6 K-1 in Ta62.5Si37.5 composition alloy and αa = 6.2(3).10-6 K-1 and αc = 9.5(4).10-6 K-1 in Ta62Si38 composition alloy. The anisotropy αc/αa was determined to be 1.5 for both samples. The thermal expansion coefficients for Cr5Si3 hexagonal phase was found to be αa = 17.1(3).10-6 K-1 and αc = 11.1(4).10-6 K-1 for Cr62.5Si37.5 composition alloy and αa = 17.2(3).10-6 K-1 and αc = 10.7(4).10-6 K-1 for Ta62Si38 composition alloy. The values of the anisotropy αc/αa were respectively, 1.5 and 1.6. In the second part of this work, the alloys of Hf(62.5-x)TixSi37.5 (0 ≤ x ≤ 62.5) compositions with different proportion of Hf and Ti were prepared by arc-melting and heat-treated at 1200 °C for 24 h in argon atmosphere. The formation of (Hf,Ti)5Si3 phase was observed for all prepared alloys. The alloys of Hf38.9Ti23.6Si37.5 and Hf22.5Ti40Si37.5 to Ti62.5Si37.5 compositions were found to be single-phase. The variation in the lattice parameters a and c for the hexagonal (Hf,Ti)5Si3 phase with different proportion of Hf and Ti shown the formation of solid solution in all range between Hf5Si3 and Ti5Si3 with partial substitution of Hf by Ti.

Du fait leur conductivité thermique élevée, les matériaux composites à matrice métallique et renfort carbone possèdent un fort potentiel d’application pour la gestion thermique en électronique. Ces travaux présentent le développement d’un nouveau procédé pour la synthèse de matériaux composites Ag/rGO (argent / « reduced Graphene Oxide ») et Ag/GF (argent / « Graphite Flakes ») par métallurgie des poudres. Ce procédé, inspiré des méthodes de « molecular level mixing », permet d’obtenir des poudres composites Ag/rGO dans lesquelles les nano-renforts sont individualisés jusqu’à une concentration volumique de 1 %. Lorsqu’il est appliqué à la synthèse de matériaux composites Ag/GF, ce dernier permet l’élaboration de matériaux composites denses avec une concentration volumique en graphite jusqu’à 70 % et une conductivité thermique jusqu’à 675 W.m-1.K-1 (426 W.m-1.K-1 pour l’argent pur). En outre, il a été montré que le procédé d’élaboration des poudres composites Ag/GF a une forte influence sur l’anisotropie structurale des matériaux massifs ainsi que sur la résistance thermique d’interface extrinsèque Ag-graphite. Le procédé d’élaboration développé dans ces travaux permet ainsi d’obtenir des matériaux ayant une conductivité thermique jusqu’à 19 % supérieure à celle des matériaux obtenus par un procédé de mélange conventionnel. Néanmoins, comme la plupart des matériaux composites métal/GF (à matrice Cu, Al, Mg et Fe), la dilatation thermique des matériaux composites Ag/GF présente des « anomalies ». En effet, l’anisotropie de leur coefficient d’expansion thermique (CTE) est opposée à leur anisotropie structurale, leur CTE a une dépendance anormalement élevée vis-à-vis de la température et ces matériaux présentent une instabilité dimensionnelle en cyclage thermique. S’il est communément admis dans la littérature que ces anomalies sont la conséquence des contraintes internes générées lors de l’élaboration des matériaux (du fait de la différence de CTE entre matrice et renfort), ce phénomène reste mal compris et difficile à maitriser. Une part importante de ces travaux est consacrée à l’étude de ces « anomalies » et en particulier à l’étude de l’influence des propriétés mécaniques de la matrice d’argent sur la dilation thermique des matériaux composites. Grâce à la combinaison des caractérisations d’EBSD, de DRX, de microdureté instrumentée et de microscopie, des phénomènes clés responsables des propriétés thermomécaniques des matériaux composites Ag/GF ont pu être identifiés. En particulier, il a été montré qu’une part importante des contraintes internes est relaxée via la déformation plastique de la matrice d’argent et la déformation pseudo plastique du graphite lors du refroidissement post-densification des matériaux composites. Ainsi, le contrôle des propriétés mécaniques de la matrice métallique (en particulier de sa limite d’élasticité) permet d’atténuer les anomalies en CTE et confère une meilleure stabilité dimensionnelle aux matériaux composites Ag/GF lors d’un cycle thermique. L’addition de rGO dans la matrice d’argent des matériaux composites Ag/GF a également permis de réduire l’instabilité dimensionnel des matériaux jusqu’à 50 % grâce aux propriétés d’amortissement du rGO. / Due to their high thermal conductivity, metal matrix composite materials reinforced with carbon allotropes exhibit a high potential application for thermal management in electronics. This work deals with the elaboration of new synthesis process to produce Ag/rGO (silver/reduced Graphene Oxide) and Ag/GF (silver/Graphite Flakes) composite materials. This process, based on “molecular level mixing” methods, makes it possible to obtain Ag/rGO composite powders with individualized nano-reinforcements up to a concentration of 1 % in volume. Applied to the synthesis of Ag/GF composite materials, it allows to synthesize dense composite materials with a graphite concentration up to 70 % in volume and with a thermal conductivity up to 675 Wm-1.K-1 (426 Wm-1.K-1 for pure silver). Moreover, it has been shown that Ag/GF powders elaboration process has a strong influence on the structural anisotropy of bulk materials as well as on the extrinsic thermal boundary resistance Ag-graphite. The process developed in this work allows Ag/GF composite materials to reach thermal conductivity up to 19 % higher than the same materials synthesized by conventional mixing powder process. However, like most metal/GF composite materials (with Cu, Al, Mg and Fe matrix), thermal expansion of Ag/GF composite materials shows “anomalies”. Indeed, the anisotropy of their coefficient of thermal expansion (CTE) is opposed to their structural anisotropy, their CTE has an abnormally high dependence on temperature and these materials exhibit dimensional instability during thermal cycling. While it is commonly admit in literature that these “anomalies” are the consequence of internal stresses generated during materials densification (because of CTE mismatch between matrix and reinforcement), this phenomenon remains poorly understood and difficult to control. A significant part of this work is devoted to the study of these anomalies and especially to the study of the influence of matrix mechanical properties on composite materials thermal expansion. Thanks to EBSD, XRD, instrumented microhardness and microscopy analysis, key phenomena responsible of thermomechanical behavior of Ag/GF composite materials have been identified. Especially, it has been shown that a large part of the internal stresses is relaxed by plastic deformation of silver matrix and pseudo-plastic deformation of graphite during the post-densification cooling step of the materials. Thus, the control of mechanical properties of metallic matrix (especially of its elastic limit) makes it possible to attenuate the anomalies in CTE and confers a better dimensional stability to Ag / GF composite materials during thermal cycling. Finally, the addition of rGO in silver matrix of Ag/GF composites materials has also reduced material dimensional instability by up to 50 % thanks to the damping properties of rGO.

The properties of composite materials in which spherical inclusions are embedded in a matrix of some kind, have been studied for many decades and many analytical models have been developed which measure these properties. There has been a steady progression in the complexity of models over the years, providing greater insight into the nature of these materials and improving the accuracy in the measurement of their properties. Some of the properties with which this thesis is concerned are, the elastic, thermal and electrical properties of such composites. The size of the spherical inclusion which acts as the reinforcing phase, has a major effect on the overall properties of composite materials. Once an inclusion is embedded into a matrix, a third region of different properties between the inclusion and matrix is known to develop which is called the interphase. It is well known in the composite community that the smaller the inclusion is, the larger the interphase region which develops around it. Therefore, with the introduction of nanoparticles as the preferred reinforcing phase for some composites, the interphase has a major effect on its properties. It is the aim of this thesis to consider the role of the interphase on the properties of composites by modeling it as an inhomogeneous region. There is much scientific evidence to support the fact that the interphase has an inhomogeneous nature and many papers throughout the thesis are cited which highlight this. By modeling the inhomogeneous properties by arbitrary mathematical functions, results are obtained for the various properties in terms of these general functions. Some specific profiles for the inhomogeneous region are considered for each property in order to demonstrate and test the models against some established results.