Analytic methods of elastic wave scattering in fiber-reinforced composite materials are investigated in this study to calculate the effective static stiffness (axial shear modulus, m) and wave properties (axially shear wave speed, B and attenuation, Y) in composites. For simplicity only out-of-plane shear waves are modeled propagating in a plane transverse to the fiber axis. Statistical averaging of a spatially random distribution of fibers is performed and a simultaneous system of linear equations are obtained from which the effective global wave numbers are numerically calculated. The wave numbers, K=Re(K)+iIm(K), are complex numbers where the real parts are used to compute the effective axial shear static stiffness and wave speed; the imaginary parts are used to compute the effective axial shear wave attenuation in composites. Three major parts of this study are presented. The first part is the discussion of multiple scattering phenomena in a successive-events scattering approach. The successive-events scattering approach is proven to be mathematically exact by comparing the results obtained by the many-bodies-single-event approach. Scattering cross-section is computed and comparison of the first five scattering orders is made. Furthermore, the ubiquitous quasi-crystalline approximation theorem is given a justifiable foundation in the fiber-matrix composite context. The second part is to calculate m, B and Y for fiber-reinforced composites with interfacial layers between fibers and matrix. The material properties of the layers are assumed to be either linearly or exponentially distributed between the fibers and matrix. A concise formula is obtained where parameters can be computed using a computationally easy-to-program determinant of a square matrix. The numerical computations show, among other things, that the smoother (more divisional layers), or thinner, the interfacial region the less damped are the composite materials. Additionally composites with exponential order distribution of the interfacial region are more damped than the linear distribution ones. The third part is to calculate m, B and Y for fiber-reinforced composites with interfacial cracks. The procedures and computational techniques are similar to those in the second part except that the singularity near the crack tip needs the Chebychev function as a series expansion to be adopted in the computation. Both the interfacial layers and interfacial crack cases are analyzed in the low frequency range. The analytic results show that waves in both cases are attenuated and non-dispersive in the low frequency range. The composites with interfacial layers are transversely isotropic, while composites with interfacial cracks are generally transversely anisotropic. / Ph. D.

Orientador: Paulo Sollero / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-10T03:16:07Z (GMT). No. of bitstreams: 1 Paiva_SeilaVastiFariade_M.pdf: 1387945 bytes, checksum: 04ad3c76f01698f24ef5fd7ebfb49264 (MD5) Previous issue date: 2006 / Resumo: Nesta dissertação é apresentada uma análise de problemas da mecânica da fratura elástica linear em estruturas bimateriais anisotrópicas. Utilizando o método dos elementos de contorno é possível calcular os fatores de intensidade de tensão em problemas planos (2D) devido à presença de trincas interfaciais entre as lâminas que compõem o material. A estrutura pode estar submetida à carregamento em modo I ou modo misto. O problema é modelado usando-se a técnica de sub-regiões para descrever cada um dos diferentes subdomínios, representado por cada material. Na interface das sub-regiões, em que o domínio é dividido, são impostas condições de equilíbrio de forças e continuidade de deslocamentos, exceto na região que corresponde à trinca. O comportamento singular apresentado pelo campo de tensões próximo à ponta da trinca é modelado com elementos de ponto a um quarto com singularidade de forças de superfície. São apresentados exemplos numéricos de problemas com carregamentos no plano. Foi também apresentada a análise de convergência de malhas, mostrando uma pequena dependência da discretização mesmo quando malhas pouco refinadas foram usadas. Alguns dos exemplos têm correspondentes na literatura, os quais foram utilizados para comparação com os resultados obtidos. Observou-se uma boa concordância na comparação dos resultados / Abstract: This thesis presents an analysis of problems of linear elastic fracture mechanics in anisotropic bimaterial structures. Using the boundary element method, it is possible to evaluate stress intensity factors in plane problems (2D) due to the presence of interfacial cracks between the laminae that constitute the material, when the structure is submitted to a mode I or in mixed mode loading. The problem is modeled using the subregion technique to describe each one of the different subdomains, represented by each material. On the interface of subregions, which the domain is divided, conditions of tractions equilibrium and displacements continuity are imposed, except in the corresponding crack region. The singular behavior presented by the stress field near the crack tip is modeled by traction singular quarter point element. Numerical examples of problems with in-plane loading are presented. Mesh convergence analyses are also presented, showing little dependence on the discretization even when coarse meshes were used. Some of these examples have correspondents in literature, that were used for comparisons with the obtained results. A good agreement in the comparisons of results was observed. / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

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