In this thesis we are interested in the propagation of low-frequency linear elastic waves through composite materials. We use a variety of dynamic homogenization techniques to find the effective elastic properties of some composites. We consider composites with isotropic phases for ease of exposition but the theory could easily be extended to anisotropic inclusions or host.We use a Representative Volume Element approach with the Method of Asymptotic Homogenization to model a random fibre-reinforced composite. The fibres are all aligned in the same direction and are taken to be of infinite extent, so the composite is essentially two-dimensional. For a random composite we have considered the anti-plane case for SH wave propagation and the in-plane case for P and SV elastic wave propagation, extending the previous published work of Parnell and Abrahams (2006), (2008a), in which a periodic fibre-reinforced composite was studied. We also show, for a simple example, that it is possible to extend the Representative Volume Element method to a three-dimensional particulate composite.In this thesis an Integral Equation Method for homogenization is also studied, with application to periodic fibre-reinforced composites. We have extended the work of Parnell and Abrahams (2008b), which considered SH wave propagation only, to the case of P and SV wave propagation.

Advanced composites are playing a rapidly increasing role in all fields of material and structural related engineering practices. Damage tolerance analysis must be a critical integral part of composite structural design. The predictive capabilities of existing models have met with limited success because they typically can not account for multiple damage evolution and their coupling. As a result, current composite design is heavily dependent upon lengthy and costly test programs and empirical design methods. There is an urgent need for efficient numerical tools that are capable of analyzing the progressive failure caused by nonlinearly coupled, multiple damage evolution in composite materials. Such numerical tools are a necessity in achieving virtual testing of composites and other heterogeneous materials. In this thesis, an advanced finite element method named augmented finite element method (A-FEM) has been developed. This method is capable of incorporating nonlinear cohesive damage descriptions for major damage modes observed in composite materials. It also allows for arbitrary nucleation and propagation of such cohesive damages upon satisfactory of prescribed initiation and propagation criterion. Major advantages of the A-FEM include: 1) arbitrary cohesive cracking without the need of remeshing; 2) full compatibility with existing FEM packages; and 3) easy inclusion of intra-element material heterogeneity. The numerical capabilities of the A-FEM have been demonstrated through direct comparisons between prediction results and experimental observations of typical composite tests including 3-point bending of unidirectional laminates, open-hole tension of quasi-isotropic laminates, and double-notched tension of orthogonal laminates. In all these tests, A-FEM can predict not only the qualitative damage patterns but also quantitatively the nonlinear stress-strain curves and other history-dependent results. The excellent numerical capability of A-FEM in accurately accounting for multiple cracking in composites enables the use of A-FEM as a multi-scale numerical platform for virtual testing of composites. This has been demonstrated by a series of representative volume element (RVE) analyses which explicitly considered microscopic matrix cracking and fiber matrix interface debonding. In these cases the A-FEM successfully predicted the cohesive failure descriptions which can be used for macroscopic composite failure analyses. At the sublaminate scale, the problem of a transverse tunneling crack and its induced local delamination has been studied in detail. Two major coupling modes, which depends on the mode-I to mode-II fracture toughness ratio and cohesive strength values, has been revealed and their implications in composite engineering has been fully discussed. Finally, future improvements to the A-FEM so that it can be more powerful in serving as a numerical platform for virtual testing of composites are discussed.

The application of lattice structures have become increasingly popular as additive manufacturing (AM) opens up the possibility to manufacture complex configurations. However, modelling such structures can be computationally expensive. The following thesis has been conducted in order for the department of Structural Analysis, at SAAB in Järfälla, to converge with the future use of AM and lattice structures. An approach to model lattice structures using homogenization is presented where three similar methods involving representative volume element (RVE) have been developed and evaluated. The stiffness matrices, of the RVEs, for different sizes of lattice structures, comprising of BCC strut-based units, have been obtained. The stiffness matrices were compared and analysed on a larger solid structure in order to see the deformational predictability of a lattice-based structure of the same size. The results showed that all methods were good approximations with slight differences in terms of boundary conditions (BCs) at the outer edge. The comparative analyses showed that two of the three methods matches the deformational predictability. The BCs in all methods have different influences which makes it pivotal to establish the BCs of the structure before using the approach presented in this thesis. / Ökad implementering av gitterstrukturer i komponenter är ett resultat av utvecklingen inom additiv tillverkning. Metoden öppnar upp för tillverkning av komplexa strukturer med färre delmoment. Dock så uppkommer det svårigheter vid simulering av dessa komplexa strukturer då beräkningar snabbt tyngs ner med ökad komplexitet. Följande examensarbete har utförts hos avdelningen Strukturanalys, på SAAB i Järfälla, för att de ska kunna möta upp det framtida behovet av beräkningar på additivt tillverkade gitterstrukturer. I det här arbetet presenteras ett tillvägagångsätt för modellering av gitterstrukturer med hjälp av represantiva volymselement. Styvhetsmatriser har räknats fram, för en vald gitterkonfiguration, som sedan viktats mot tre snarlika representativa volymselement. En jämförelseanalys mellan de olika styvhetsmatriserna har sedan gjorts på en större och solid modell för att se hur väl metoderna förutsett deformationen av en gitterstruktur i samma storlek. Resultaten har visat att samtliga metoder är bra approximationer med tämligen små skillnader från randeffekterna. Vid jämförelseanalysen simulerades gitterstrukturen bäst med två av de tre metoder. En av slutsatserna är att det är viktigt att förstå inverkan av randvillkoren hos gitterstrukturer innan implementering görs med det tillvägagångssätt som presenterats i det här examensarbetet.

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This dissertation research focuses on micromechanical modeling and simulations of two-phase heterogeneous materials exhibiting anisotropic and non-uniform microstructures with long-range spatial correlations. Completed work involves development of methodologies for realistic micromechanical analyses of materials using a combination of stereological techniques, two- and three-dimensional digital image processing, and finite element based modeling tools. The methodologies are developed via its applications to two technologically important material systems, namely, discontinuously reinforced aluminum composites containing silicon carbide particles as reinforcement, and boron modified titanium alloys containing in situ formed titanium boride whiskers. Microstructural attributes such as the shape, size, volume fraction, and spatial distribution of the reinforcement phase in these materials were incorporated in the models without any simplifying assumptions. Instrumented indentation was used to determine the constitutive properties of individual microstructural phases. Micromechanical analyses were performed using realistic 2D and 3D models and the results were compared with experimental data. Results indicated that 2D models fail to capture the deformation behavior of these materials and 3D analyses are required for realistic simulations. The effect of clustering of silicon carbide particles and associated porosity on the mechanical response of discontinuously reinforced aluminum composites was investigated using 3D models. Parametric studies were carried out using computer simulated microstructures incorporating realistic microstructural attributes. The intrinsic merit of this research is the development and integration of the required enabling techniques and methodologies for representation, modeling, and simulations of complex geometry of microstructures in two- and three-dimensional space facilitating better understanding of the effects of microstructural geometry on the mechanical behavior of materials.

<p>Aluminum alloys have broad applications in aerospace, automotive, and defense industries as structural material due to the low density, high-specific strength, good castability and formability. However, aluminum alloys commonly suffer from problems such as low yield strength, low stiffness, and poor wear and tear resistance, and therefore are restricted to certain advanced industrial applications. To overcome the problems, one promising method is the fabrication of aluminum matrix composites (AMCs) by introducing ceramic reinforcements (fibers, whiskers or particles) in the metal matrix. AMCs typically possess advanced properties than the matrix alloys such as high specific modulus, strength, wear resistance, thermal stability, while remain the low density. Among the AMCs, particulate reinforced aluminum matrix composites (PRAMCs) are advantageous for their isotropic properties, ease of fabrication, and low costs. Particularly, the PRAMCs with in-situ particulate reinforcements have received great interest recent years. The in-situ fabricated particles are synthesized in an aluminum matrix via chemical reactions. They are more stable and finer in size, and have a more uniform distribution in the aluminum matrix and stronger interface bonding with aluminum matrix, compared to the ex-situ particulate reinforcements. As a consequence, the in-situ PRAMCs have superior strength and mechanical properties as advanced engineering materials for a broad range of industrial applications.</p> <p>This dissertation focuses on the investigation of high strength aluminum matrix composites reinforced with in-situ particulates. The first chapter provides a brief introduction for the studied materials in the dissertation, including the background, the scope, the significance and the research questions of the study. The second chapter presents the literature review on the basic knowledge, the fabrication methods, the mechanical properties of in-situ PRAMCs. The strengthening mechanisms and strategies of in-situ PRAMCs are summarized. Besides, the micromechanical simulation is introduced as a complementary methodology for the investigation of the microstructure-properties relationship of the in-situ PRAMCs. The third chapter shows the framework and methodology of this dissertation, including material preparation and material characterization methods, phase diagram method and finite element modelling. </p> <p>In Chapter 4, the microstructures and mechanical properties of in-situ Al₃Ti particulate reinforced A356 composites are investigated. The microstructure and mechanical properties of in-situ 5 vol. % Al₃Ti/A356 composites are studied either taking account of the effects of T6 heat treatment and strontium (Sr) addition or not. Chapter 5 studies the evolution of intermetallic phases in the Al-Si-Ti alloy during solution treatment, based on the work of Chapter 4. The as-cast Al-Si-Ti alloy is solution treated at 540 °C for different periods between 0 to 72 h to understand the evolution of intermetallic phases. In Chapter 6, a three-dimensional (3D) micromechanical simulation is conducted to study the effects of particle size, fraction and distribution on the mechanical behavior of the in-situ Al₃Ti/A356 composite. The mechanical behavior of the in-situ Al₃Ti/A356 composite is studied by three-dimensional (3D) micromechanical simulation with microstructure-based Representative Volume Element (RVE) models. The effects of hot rolling and heat treatment on the microstructure and mechanical properties of an in-situ TiB₂/Al2618 composite with minor Sc addition are investigated in Chapter 7. TiB₂/Al2618 composites ingots were fabricated <i>in-situ</i> via salt-melt reactions and subjected to hot rolling. The microstructure and mechanical properties of the TiB₂/Al2618 composite are investigated by considering the effects of particle volume fraction, hot rolling thickness reduction, and heat treatment. </p>

Les matériaux cellulaires poreux de type mousse présentent un grand intérêt pour de nombreuses applications. Leurs propriétés thermiques, mécaniques, acoustiques dépendent fortement de leur microstructure complexe. Afin de mieux comprendre la relation microstructure/propriétés mécaniques de ces matériaux, une modélisation micromécanique basée sur une méthode d’homogénéisation périodique et le lemme de Hill est proposée pour prédire les propriétés élastiques effectives de ces matériaux. Une approche basée sur le diagramme de Voronoï est utilisée pour générer des structures de mousse périodiques réalistes plus ou moins irrégulières, couvrant une large gamme de matériaux . Différents types de mousses à forte porosité sont générés, non seulement des matériaux cellulaires à pores ouverts mais aussi des matériaux cellulaires à pores fermés. Des comparaisons avec des résultats issus de tomographie X d’architectures réelles 3D de mousses valident ces approches de Voronoï. Les simulations numériques permettent d’étudier l’influence des paramètres morphologiques des mousses sur les propriétés élastiques effectives. De nouvelles lois analytiques génériques de propriétés effectives sont déduites pour des mousses à cellules ouvertes de type Kelvin. Une attention particulière est portée sur la détermination de l’élément de volume représentatif (VER). Des méthodes statistiques spécifiques sont proposées pour déterminer le VER approprié aux modèles de mousse. Dans le cas des mousses polymères isolantes à cellules fermées irrégulières anisotropes, la confrontation avec des résultats d’essais mécaniques confirme la validité des modèles développés. / Thanks to the excellent combination of physical, mechanical and thermal properties, foam materials bring new possibilities to extend the range of the properties for engineering, which is limited by fully dense solids. In this study, a micromechanical modeling based on Hill's lemma (Hill's lemma periodic computational homogenization approach) is proposed for predicting the effective elastic properties of foam materials. An approach based on Voronoi diagram is used to generate realistic periodic foam structures, including regular and irregular open-cell structures, and irregular closed-cell structures. First, the influences of morphological parameters of open-cell foams on the effective elastic properties are studied. The generated structures allow representing the details of the microstructure and cover a large range of foam materials for engineering purposes. With the assessments, new generic analytical laws are proposed for Kelvin open-cell foams by considering their morphological parameters. Second, the tomography images are analysed to obtain the morphological description of the real irregular open-cell structure. With these morphological parameters, numerous numerical realistic structures are generated. Specific statistic methods are proposed to determine the Representative Volume Element (RVE) for foam models. Third, the anisotropic irregular closed-cell foam is studied. The numerical structures are generated with the morphological description of the reconstructed tomography structure and the effective elastic properties of the closed-cell foam models are estimated. The numerical results show the satisfying agreement with the experimental results.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-08-30T13:26:19Z No. of bitstreams: 2 Dissertação - Paula Viana Queiroz Andrade - 2017.pdf: 2686282 bytes, checksum: d828cc8979cf594c108b844e7b806230 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-15T13:36:35Z (GMT) No. of bitstreams: 2 Dissertação - Paula Viana Queiroz Andrade - 2017.pdf: 2686282 bytes, checksum: d828cc8979cf594c108b844e7b806230 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-09-15T13:36:35Z (GMT). No. of bitstreams: 2 Dissertação - Paula Viana Queiroz Andrade - 2017.pdf: 2686282 bytes, checksum: d828cc8979cf594c108b844e7b806230 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-07-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work deals with analysis of the microstructures composed of metal matrix composites (MMC) and its application in Structural Engineering. The main goal of this essay is considered the potentialities and limitations when using the modeling activity suggested. For this, it is intended to consider the dissipative processes of plastification, occurring in the matrix, and phase debonding, that occurs in the matrix/inclusion interface region, where the influence of such processes on the macroscopic response of the material will be investigated. Initially, the applicability of this material in the various Engineering areas is described. For the numerical simulations of the MMC structural behavior, the von Mises model is used in the modeling of the matrix and a cohesive fracture model is used in the simulation of the phase debonding process. Inclusion is considered elastic with great rigidity. However, the dissipative processes that occur in the microstructure and that affect the macro mechanical behavior of the material are analyzed through a microscale modeling using a homogenization process based on the concept of Representative Volume Element (RVE) and the Finite Element Method (FEM). The strain and deformation are volumetric means of the respective microscopic fields on the EVR. The general objective is to verify through numerical analysis the potentialities and limitations of the use of the proposed modeling for future applications of metallic matrix composites in engineering, which shows a good representativeness of the mechanical behavior of the CMM. / Este trabalho trata de uma contribuição sobre a análise da microestrutura de materiais compósitos com matriz metálica (CMM) e sua aplicação na Engenharia Estrutural. O objetivo geral é verificar as potencialidades e limitações do emprego da modelagem proposta. Para isso, consideram-se os processos dissipativos de plastificação, que ocorre na matriz, e de descolamento, que ocorre na região de interface matriz/inclusão, onde a influência de tais processos na resposta macroscópica do material será investigada. Inicialmente, a aplicabilidade deste material nas diversas áreas de Engenharia é descrita. Para as simulações numéricas do comportamento estrutural de CMM, o modelo de von Mises é utilizado na modelagem da matriz assim como um modelo de fratura coesiva na simulação do processo de descolamento na interface. A inclusão é considerada elástica com grande rigidez. Contudo, os processos dissipativos que ocorrem na microestrutura e que repercutem no comportamento macromecânico do material são analisados através de uma modelagem na microescala utilizando um processo de homogeneização baseada no conceito de Elemento de Volume Representativo (EVR) e no Método dos Elementos Finitos (MEF). A tensão e deformação são médias volumétricas dos respectivos campos microscópicos sobre o EVR. Por fim, as análises numéricas apresentadas com o emprego da modelagem proposta evidenciam sua boa representatividade do comportamento mecânico do CMM contribuindo para futuras aplicações de compósitos de matriz metálica na engenharia.

Les matériaux architecturés font émerger de nouvelles possibilités en termes de propriétés structurales et fonctionnelles, repoussant ainsi les limites des cartes d'Ashby. Le terme "matériaux architecturés" inclus toute microstructure conçue de façon astucieuse, de sorte que certaines de ses propriétés soient optimisées. Les exemples sont nombreux : composites fibreux et particulaires, matériaux cellulaires, structures sandwiches, matériaux tissés, structures treillis, etc. Un enjeu de taille pour l'emploi de tels matériaux est la prédiction de leurs propriétés effectives. Dans ce travail, deux types de microstructures sont considérées : des structures auxétiques périodiques et des milieux fibreux aléatoires. Les auxétiques sont des matériaux apparus au milieu des années 1980, présentant un coefficient de Poisson négatif. On attend des auxétiques qu'ils présentent des propriétés mécaniques améliorées, comme le module de cisaillement ou la résistance à l'indentation. Les milieux fibreux aléatoires considérés dans ce travail sont constitués de fibres 3D infinies interpénétrantes aléatoirement distribuées et orientées. Ce type de structure aléatoire est très défavorable à la détermination d'une taille de volume élémentaire statistiquement représentatif. Pour les deux types de matériaux, l'homogénéisation numérique à l'aide de la méthode des éléments finis est implémentée dans le but d'estimer les propriétés thermiques et mécaniques effectives. / Architectured materials bring new possibilities in terms of structural and functional properties, filling gaps and pushing the boundaries of Ashby's materials maps. The term "architectured materials" encompasses any microstructure designed in a thoughtful fashion, so that some of its materials properties have been improved. There are many examples: particulate and fibrous composites, foams, sandwich structures, woven materials, lattice structures, etc. One engineering challenge is to predict the effective properties of such materials. In this work, two types of microstructures are considered: periodic auxetic lattices and stochastic fibrous networks. Auxetics are materials with negative Poisson's ratio that have been engineered since the mid-1980s. Such materials have been expected to present enhanced mechanical properties such as shear modulus or indentation resistance. The stochastic fibrous networks considered in this work is made of 3D infinite interpenetrating fibres that are randomly distributed and oriented. This case of random structure is challenging regarding the determination of a volume element size that is statistically representative. For both materials, computational homogenization using finite element analysis is implemented in order to estimate the effective thermal and mechanical properties.

Composite materials show heterogeneity at different length scales. hence concurrent multiscale analysis is the only reliable method to analyze them. But unfortunately there is no concurrent multi-scale strategy that is efficient, and accurate while addressing all kinds of problems. This lack of reliability is partly because there is no micro-mechanical model which inherently keeps all relevent global information with it. This thesis tries to fill this gap. The presented micro-mechanical model not only homogenizes the micro-structure but also keeps the global information with it. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis which results in loss of information and accuracy. In the present approach also, the RVE has been extracted from the continuum but with the major difference that all the macro/meso-scopic parameters are accounted for. Five macro/meso-scopic one dimensional parameters have been defined which completely define the effect of continuum. 11 for one dimensional stretch, _1 for torsion, __ (_ = 2, 3) for bending and _33 for uniform pressurization due to the presence of the continuum. Further, the above macro/meso-scopic parameters are proven, by the asymptotic, theory to be constant at a cross section but vary, in general, over the length of the fiber. Hence, the analysis is valid for any location and is not restricted to any local domain. Three major problems have been addressed: • Homogenization and analysis of RVE without any defects • Homogenization and analysis of RVE with fiber-matrix de-bonding • Homogenization and analysis of RVE with radial matrix cracking. Variational Asymptotic Method (VAM) has been used to solve the above mentioned problems analytically. The results have been compared against standard results in the literature and against 3D FEA. At the end, results for “Radial deformation due to torsion” problem will be presented which was solved “accidentally.”