Polymer composites are engineered materials widely being used and yet not completely understood for their dynamic response. It is important to fully characterize material properties before using them for applications in critical industries, like that of defense or transport. In this project, the focus is on determining dynamic fracture toughness property of fiber reinforced polymer composites by using a combined numerical- experimental methodology. Impact tests are conducted on Split-Hopkinson pressure bar with required instrumentation to obtain load-history and initiation of crack propagation parameters followed by finite element analysis to determine desired dynamic properties. Single edge notch bend(SENB) type geometry is used for Mode-I fracture testing and similarly end-notched flexure (ENF) type of geometry is proposed to test the samples for Mode-II type of fracture. Two different linear elastic fracture mechanics approaches are used- crack opening displacement and strain energy release rates. Dynamic fracture toughness values of around 50 MPa[square root of m] and 100 MPa[square root of m] in Mode-I, whereas, around 40 MPa[square root of m] and 6 MPa[square root of m] in Mode-II are observed for carbon-epoxy and fiberglass-epoxy composites respectively. To provide a better estimate of material response, Hashin damage model is employed which takes into account non-linear behavior of composites. As observed in previous studies, values estimated using a non-linear response of composite laminates are nearly three times as high, therefore, using a linear elastic material model could underestimate a material's capacity to sustain dynamic loads without failure. It is concluded that fracture initiation toughness property is rate dependent and is higher when subjected to dynamic loads. Microscopic examination of damaged samples and a higher value of dynamic fracture toughness for fiberglass-epoxy laminates as compared to carbon-epoxy laminates suggest that dynamic fracture toughness is also a function of many other variables like mode of fracture, dominant damage criteria, manufacturing process, constituent materials and their ratios.

Este trabalho trata das falhas que podem ocorrer em uniões e juntas de materiais compósitos unidas mecanicamente por parafusos. O compósito de fibra de carbono (tecido) embutido em resina epoxy foi estudado neste trabalho devido ao amplo uso em estruturas de vários segmentos da indústria. O trabalho apresenta vários critérios de falha, demonstrando as vantagens e desvantagens de cada um para materiais compósitos. A fabricação dos corpos de provas e os ensaios necessários para obtenção de parâmetros e validação de estruturas são descritos. A resistência da junta mostrou-se muito menor do que a da estrutura de compósito, demonstrando a importância de estudos assim. Criou-se um modelo numérico utilizando critérios de falhas como o critério de Hashin e o de máxima tensão. Os resultados da simulação de elementos finitos tiveram uma boa relação com os ensaios experimentais e o modelo foi então validado e considerado representativo. / This work shows failures that can occur in composite mechanically fastened joints. The composite carbon fiber embedded in epoxy resin, used in this study, was chosen due to it\'s wide use in structures of any segment of the industry. Many failure criteria, showing the advantages and disadvantages for each, regarding composite structures are presented in this work. Test specimens\' manufacturing is described along with required tests for parameter definition and structures validation. The countersunk fastened joint strength is much lower than the composite structure itself, demonstrating the necessity of studies like this. A numerical model using criteria like Hashin and maximum stress was created. The finite elements\' simulation results had a close response to the experimental results and the model was validated and considered representative.

Este trabalho trata das falhas que podem ocorrer em uniões e juntas de materiais compósitos unidas mecanicamente por parafusos. O compósito de fibra de carbono (tecido) embutido em resina epoxy foi estudado neste trabalho devido ao amplo uso em estruturas de vários segmentos da indústria. O trabalho apresenta vários critérios de falha, demonstrando as vantagens e desvantagens de cada um para materiais compósitos. A fabricação dos corpos de provas e os ensaios necessários para obtenção de parâmetros e validação de estruturas são descritos. A resistência da junta mostrou-se muito menor do que a da estrutura de compósito, demonstrando a importância de estudos assim. Criou-se um modelo numérico utilizando critérios de falhas como o critério de Hashin e o de máxima tensão. Os resultados da simulação de elementos finitos tiveram uma boa relação com os ensaios experimentais e o modelo foi então validado e considerado representativo. / This work shows failures that can occur in composite mechanically fastened joints. The composite carbon fiber embedded in epoxy resin, used in this study, was chosen due to it\'s wide use in structures of any segment of the industry. Many failure criteria, showing the advantages and disadvantages for each, regarding composite structures are presented in this work. Test specimens\' manufacturing is described along with required tests for parameter definition and structures validation. The countersunk fastened joint strength is much lower than the composite structure itself, demonstrating the necessity of studies like this. A numerical model using criteria like Hashin and maximum stress was created. The finite elements\' simulation results had a close response to the experimental results and the model was validated and considered representative.

The Hashin failure criteria and damage evolution model for laminated fiber reinforced polymers are explored. A series of tensile coupon finite element analyses are run to characterize the variables in the physical model as well as modeling techniques for using an explicit dynamic solver for a quasi-static problem. An attempt to validate the model on an axial tube crush is presented. It was found that fiber buckling was not occurring at the impactor-tube interface. Results and speculation as to why the failure initiation is incorrect are discussed. Lessons learned from the tube crush are applied successfully to the quasi-static Formula SAE nosecone crush test. The model is validated by experimental data and the impact metrics between the test and model are within 5%. Future work and possible optimization techniques are discussed.

Depuis le début du vingtième siècle, l'usage des matériaux sous la forme de plaques et de poutres s'est considérablement développé jusqu'à nos jours que ce soit dans l'industrie automobile, la construction, et plus récemment en aéronautique. Pourtant une des difficultés dans l’étude du comportement de ces structures réside essentiellement dans leur caractère hétérogène. L'utilisation de méthodes numériques classiques pour estimer les constantes élastiques globales des structures multicouches et hétérogènes est coûteuse en temps de calcul C'est pourquoi de nombreuses méthodes simplifiées ont vu le jour, notamment quand la taille de l'hétérogénéité est petite devant les dimensions caractéristiques de la structure. Dans ce cas cette dernière peut être perçue comme un milieu continu homogène et des méthodes d'homogénéisation peuvent donc très utilisées. En revanche, il existe des structures hétérogènes pour lesquelles la taille de l'hétérogénéité est du même ordre que l'épaisseur. Dans ce cas l'utilisation des méthodes d'homogénéisation n'est plus appropriée. Dans le cadre de cette thèse, nous étudions quelques nouvelles méthodes pour l'estimation des propriétés effectives des plaques hétérogènes. Nous proposons dans la première partie un modèle de plaque basé sur la théorie de déformation en cisaillement de premier ordre pour les matériaux fonctionnellement gradués où les coefficients de correction de cisaillement sont identifiés. Dans la deuxième partie, nous proposons une nouvelle méthode numérique pour calculer des propriétés élastiques effectives des plaques hétérogènes périodiques. La méthode est basée sur un nouvel opérateur de Green pour les milieux périodiques avec des conditions aux limites de bord libre, un procédé itératif et la Transformée de Fourier Rapide. Une étude de l’effet d’échelle des plaques hétérogènes est également effectuée. Le résultat obtenu montre que cet effet est faible / From the beginning of the twentieth century, the use of materials in the form of plates and beams has grown until today, especially in the automobile industry, construction, and more recently in aeronautics. However one of the difficulties of studying the mechanical behavior of these structures consists of its heterogeneous nature. Using conventional numerical methods for estimating the global elastic constants of heterogeneous and multi-layered structures is costly in time of computation. That is why many simplified methods have been presented, particularly when the size of the heterogeneity is much smaller than the characteristic dimensions of the structure. In this case, the latter may be perceived as a continuous homogeneous medium and homogenization methods can be therefore widely used. On the other hand, there are heterogeneous structures for which the size of the heterogeneity is the same order as the thickness. In this case, the use of homogenization methods is not appropriate anymore. In the context of this thesis, we study some new methods for estimating the effective properties of heterogeneous plates. We propose in the first part a plate model based on the first-order shear deformation theory for functionally graded materials where shear correction coefficients are identified. In the second part, we propose a new numerical method for computing the effective elastic properties of periodic heterogeneous plates. The method is based on a new Green’s operator for periodic media with traction-free boundary conditions, an iterative method and the Fast Fourier Transform. A study of scale effect is also performed. The obtained result shows that this effect is small

Presented is an overview of a semi-analytical solution which was developed to study the response of internally pressurized elliptical composite cylinders with clamped boundaries. Using a geometrically linear analysis and the solution scheme, the response of a quasi-isotropic elliptical cylinder is compared with the response of a quasi-isotropic circular cylinder in order to study the effects of elliptical geometry. The distinguishing features of the response of an elliptical cylinder are the inward normal displacement of the cross section at the ends of the major diameter that occur despite the outward force of the internal pressure, the presence of circumferential displacements, and the presence of inplane shear strains. These effects lead to spatial variations, including sign reversals, of a number of displacement, strain, and curvature responses. The responses of a quasi-isotropic elliptical cylinder evaluated using a geometrically linear analysis are then compared to the responses evaluated using a geometrically nonlinear analysis. It is shown that geometric nonlinearities tend to flatten certain responses at the ends of the minor diameter, and reduce the magnitude of certain responses in the boundary region. To study the influence of material orthotropy, the responses of axially-stiff and circumferentially-stiff elliptical cylinders evaluated using geometrically nonlinear analyses are examined. It is shown that in some instances material orthotropy can be used to mitigate the influence of the elliptical geometry and make particular responses look like those of a circular cylinder. An evaluation of failure using the maximum stress and Hashin failure criteria and geometrically linear and nonlinear analyses is presented for elliptical cylinders. These failure criteria involve interlaminar shear stresses which are computed by integrating the equilibrium equations of elasticity through the thickness of the cylinder wall. The failure criteria are used to assess the mode of failure (e.g., tensile or compressive fiber or matrix modes), the location of failure, and the pressure at failure. Both criteria predict first failure to occur at the clamped boundaries because of matrix cracking. The predicted failure pressures and circumferential locations are very similar for the two criteria, and the nonlinear analyses predict slightly higher pressures at somewhat different circumferential locations. First fiber failure is also considered. For this failure the two criteria predict similar failure scenarios for the linear analyses, but they differ in their predictions for the nonlinear analyses. Specifically, using the maximum stress criterion, the circumferentially-stiff elliptical cylinder is predicted to fail due to fiber compression, but the Hashin criterion predicts failure to be due to fiber tension, and at a different circumferential location. Also, first fiber failure pressures are at least a factor of two greater than the first matrix failure pressure. / Master of Science

Depuis le début du vingtième siècle, l'usage des matériaux sous la forme de plaques et de poutres s'est considérablement développé jusqu'à nos jours que ce soit dans l'industrie automobile, la construction, et plus récemment en aéronautique. Pourtant une des difficultés dans l'étude du comportement de ces structures réside essentiellement dans leur caractère hétérogène. L'utilisation de méthodes numériques classiques pour estimer les constantes élastiques globales des structures multicouches et hétérogènes est coûteuse en temps de calcul C'est pourquoi de nombreuses méthodes simplifiées ont vu le jour, notamment quand la taille de l'hétérogénéité est petite devant les dimensions caractéristiques de la structure. Dans ce cas cette dernière peut être perçue comme un milieu continu homogène et des méthodes d'homogénéisation peuvent donc très utilisées. En revanche, il existe des structures hétérogènes pour lesquelles la taille de l'hétérogénéité est du même ordre que l'épaisseur. Dans ce cas l'utilisation des méthodes d'homogénéisation n'est plus appropriée. Dans le cadre de cette thèse, nous étudions quelques nouvelles méthodes pour l'estimation des propriétés effectives des plaques hétérogènes. Nous proposons dans la première partie un modèle de plaque basé sur la théorie de déformation en cisaillement de premier ordre pour les matériaux fonctionnellement gradués où les coefficients de correction de cisaillement sont identifiés. Dans la deuxième partie, nous proposons une nouvelle méthode numérique pour calculer des propriétés élastiques effectives des plaques hétérogènes périodiques. La méthode est basée sur un nouvel opérateur de Green pour les milieux périodiques avec des conditions aux limites de bord libre, un procédé itératif et la Transformée de Fourier Rapide. Une étude de l'effet d'échelle des plaques hétérogènes est également effectuée. Le résultat obtenu montre que cet effet est faible