The presented diploma thesis deals with a problem of a generalized stress intensity factor determination and a consecutive study of stress distribution around the bimaterial notch tip, combining analytical and numerical methods. This task is possible to sectionalize into three parts. The first part is dedicated to the fundamentals of the linear fracture mechanics and the mechanics of composite materials. The second part deals with methods of anisotropic plane elasticity solution. Pursuant to the solution the computational models in the third part are created. The first model makes for determination of a singularity exponent eigenvalue by dint of Lekhnitskii-Eshelby-Stroh formalism. The second model makes for determination of the generalized stress intensity factor using psi-integral method, which is based on the Betti reciprocal theorem. All needed calculation are performed in the software ANSYS 12, Maple 12 and Silverforst FTN95. Results will be compared with the values obtained from a direct method of the generalised stress intensity factor determination.

The master thesis is focused on estimation of crack propagation origin from sharp V-notch. Stress distribution around the tip of the V-notch is described on the base of generalized linear elastic fracture mechanics. The change of the stress singularity exponent caused by geometry of the V-notch and the vertex singularity is taken into account. The first part of the work is devoted to the estimation of the stress singularity exponent of the V-notch either from stress distribution around the tip of the V-notch or by using analytical solution. Formerly derived stability criteria are applied in the second part of the work. The origin of the crack propagation is estimated for several experimental specimens. The aim of this thesis is to compare the available experimentally observed data with results obtained using those criteria based on the application of generalized linear elastic fracture mechanics developer at the Institute of Physics of Materials Academy of Sciences of the Czech Republic. The finite element code Ansys and mathematical software Matlab were used for the necessary calculations.

The presented master’s thesis deals with fatigue crack front shape estimation. The aim of this thesis is to create an iterative process leading to the real fatigue crack front shape. Thesis is solved using finite element method. The work is divided into two logical parts. The first part of the thesis describes the basic concepts of linear elastic fracture mechanic (LEFM), methods used for estimation of stress intensity factor and stress singularity exponent. The first part further describes some phenomenon’s accompanying the mechanism of fatigue crack growth as for example crack tip curving and crack closure. In the second part of the thesis there is studied an affect of the free surface on the fracture parameters, especially the affected distance from the free surface is determined. Based on the assumption of a constant stress intensity factor and stress singularity exponent along the crack front, an iterative process leading to fatigue crack front shape is presented. The accuracy of the result is discussed by comparing of obtained crack front shapes with experimental data at the end of the thesis.

The aim of this master thesis is to explore the influence of frictional forces to the stress and strain on the straight crack tip loaded in shear modes. The first section summarizes the most important things from the field of fracture mechanics. Especially theoretical knowledge about fracture parameters (stress intensity factor, J – integral) and their determination in computational environment ANSYS Workbench. The second part deals with computational modeling. At the beginning, is created the model of material, the model of geometry, the model of loads, etc. Then it is possible to solve the direct problem outlined in the introduction. A result of this thesis is the assessment of how the friction influences the fracture parameters in shear modes II and III.

Disertační práce se věnuje problematice obecných koncentrátorů napětí v anisotropních prostředích. Zejména se jedná o problém trhlin končících na rozhraní dvou různých materiálů, či problém obecného více-materiálového klínu. Cílem práce je vytvořit komplexní nástroj pro posuzování obecných koncetrátorů napětí tj, popis pole napětí v jeho okolí, zahrnutí případného vlivu přemostění trhliny do výsledného pole napětí a definici lomových kritérií pro obecný koncentrátor v anisotropním prostředí. U popisu pole napětí je využit tzv. Lechnického-Strohův formalismus a technika spojitě rozložených dislokací využívající teorii komplexních potenciálů. V práci je rovněž široce uplatněn tzv. dvoustavový "psí"-integrál (pro výpočet různých součinitelů asymptotického rozvoje pro napětí), založený na Bettiho recipročním teorému v kombinaci s metodou konečných prvků. Pro formulaci lomových kritérií je použita teorie tzv. „konečné lomové mechaniky“ a teorie sdružených asymptotických rozvojů. Studován je především vztah mezi ohybem trhliny podél rozhraní a její případnou pentrací do základního materiálu. Veškeré potřebné výpočty jsou prováděny v matematických softwarech MAPLE 10.0, MATLAB 7.1 a konečnoprvkovém systému ANSYS 10.0.

[pt] A Mecânica da Fratura é uma área da mecânica clássica que estuda os processos que podem resultar no surgimento e propagação de fraturas e trincas nos materiais. Seus conceitos podem ser empregados em diversas áreas, como, por exemplo, no desenvolvimento de novos materiais, na área industrial (auxiliando na definição dos parâmetros de criticidade de defeitos) e em projetos estruturais, onde a presença de descontinuidades pode resultar na diminuição da resistência do material, levando-o ao colapso estrutural. As fraturas podem surgir como defeitos básicos nos materiais constituintes dos elementos, podem ser induzidas nos processos de construção ou, ainda, podem ser desenvolvidas durante a vida útil da estrutura. O estudo do comportamento de uma fratura é fundamental para a verificação coerente de tensões e deformações nos projetos estruturais. Alguns autores apresentaram diferentes metodologias para o cálculo de parâmetros importantes associados à propagação de fraturas. Tais parâmetros podem variar de acordo com o comportamento do material, características geométricas, carregamentos, condições de contorno e configuração das trincas. Essas análises também podem ser validadas através de metodologias numéricas. O presente projeto tem por objetivo avaliar o Fator de Intensidade de Tensões a partir de análises numéricas de três casos de fratura com base nos conceitos da Mecânica da Fratura Linear Elástica (MFLE). Para tal, aplicaram-se duas técnicas de modelagem em Elementos Finitos: elementos quarter-point 2D e 3D e o Método dos Elementos Finitos Estendidos (XFEM) 3D. Por fim, os resultados obtidos são comparados com os resultados publicados na literatura. Apesar das vantagens associadas ao uso do XFEM para modelagem de fraturas, o cálculo pela integral de domínio para esta técnica apresenta oscilações nos valores fornecidos para as diferentes solicitações de contornos. A técnica de modelagem com Elementos Quarter-Points 2D e 3D apresenta resultados mais estáveis e próximos das soluções analíticas. / [en] Fracture Mechanics is an area of classical mechanics that studies processes that can result in the creation and propagation of fractures and cracks in materials. Its concepts can be utilized in many areas, such as, for example, the development of new materials, in the industrial area (to assist in the definition of defect criticality parameters) and in structural projects, where the presence of discontinuities can result in decreased material resistance, leading to its structural collapse. The fractures can emerge as basic defects in materials that constitute the structural elements, can be inducted in construction processes or could even be developed during the lifespan of the structure. Studying the behavior of a fracture is fundamental to verifying coherently stress and deformations on structural projects. Some authors presented different methodologies to calculate important parameters associated to the propagation of cracks. These parameters could vary according to the material behavior, geometrical characteristics, loads, boundary conditions and cracking patterns. Those analyses can also be validated through numerical methodologies. This present project aims at evaluating the Stress Intensity Factor from numerical analyses of three cracks cases based on the concepts of Linear Elastic Fracture Mechanics (LEFM). Two techniques of Finite Element modeling were considered: quarter-point elements 2D and 3D and Extended Finite Element Method (XFEM) 3D. In the end, the results obtained are compared with results already published in the available literature. Despite the advantages associated with the use of XFEM for fracture modeling, the calculation of the stress intensity factor by the domain integral for this technique presents oscillations in the values provided for the different contour requests. The modeling technique with 2D and 3D quarter-points elements presents results that are more stable and closer to the analytical solutions.

[pt] O surgimento de trincas em projetos estruturais tem sido um problema para engenharia por algumas décadas, e uma das áreas onde este tópico é amplamente estudado é em aeronaves comerciais. Vários acidentes ocorreram nas últimas décadas devido ao aparecimento de uma trinca em aeronaves comerciais, e por essa razão o estudo da mecânica da fratura é tão importante para este campo da engenharia. Um componente estrutural é tolerante a danos se puder sustentar com segurança o comprimento crítico a trincas até que seja reparado ou sua vida econômica expire. Enrijecedores ou reforçadores têm a função principal de melhorar a resistência e estabilidade dessas estruturas e fornecer um meio de desacelerar ou parar a propagação de trincas em contenções nucleares, reatores, viadutos, edifícios altos, aeronaves, cascos de navios, pontes e estruturas offshore. Analisando o fator de intensidade de tensão e como o comportamento de uma folha com e sem reforços é diferente são alguns dos problemas estudados neste trabalho. O fator de intensidade de tensão (FIT), é um parâmetro que descreve a intensidade do campo de tensão singular, foi usado com sucesso para estimar a resistência à fratura e taxas de propagação de trinca por fadiga em situações em que as suposições de elasticidade são válidas. Neste trabalho, o FIT foi obtido para placas com reforços colados e rebitados, com base no método dos elementos finitos (MEF) utilizando elementos quarter point por meio de simulações realizadas no software ABAQUS. Forças no rebite foram calculadas para uma trinca com rebites e longarinas espaçadas uniformemente. Os resultados apresentados são comparados com os valores encontrados na literatura por meio de gráficos e mostram que o FIT é significativamente menor do que para uma folha não enrijecida para os casos de reforço estudados. / [en] The emergence of fractures in structural designs has been a problem for engineering for some decades, and one of the areas where this topic is widely studied is in commercial aircraft. Several accidents have occurred in the last decades due to the appearance of a fracture in commercial aircraft, and for this reason the study of fracture mechanics is so important for this field of engineering. A structural component is tolerant of damage if it can safely sustain critical length fractures until it is repaired or its economic life has expired. Reinforcers or stiffeners have the main function of improving the resistance and stability of these structures and providing a means of decelerating or stopping the propagation of fractures in nuclear containments, reactors, viaducts, tall buildings, aircraft, ship hulls, bridges and offshore structures. Analyzing the stress intensity factor and how the behavior of a sheet with and without stiffeners is different are some of the issues studied in this work. The stress-intensity factor (SIF), a parameter that describes the intensity of the singular stress field, has been used successfully to estimate fracture strength and fatigue crack growth rates in situations where the assumptions of linear elasticity are valid. In this work, the SIF was obtained for plates with adhesive and riveted reinforcements, based on the finite element method (FEM) using quarterpoint elements through simulations carried out in the ABAQUS software. Forces in the rivet were calculated for a crack with riveted and evenly spaced stringers. The complete results presented are compared with values found in the literature through graphs. The results show that the stress intensity factor for the hardened sheet is significantly lower than for an un-hardened sheet for both studied stiffener cases.

Due to the increasing use of cyclically loaded cast aluminum components in automotive and aerospace applications, fatigue and fatigue crack growth characteristics of aluminum castings are of great interest. Despite the extensive research efforts dedicated to this topic, a fundamental, mechanistic understanding of these alloys' behavior when subjected to dynamic loading is still lacking. This fundamental research investigated the mechanisms active at the microstructure level during dynamic loading and failure of conventionally cast and SSM Al-Si-Mg alloys. Five model alloys were cast to isolate the individual contribution of constituent phases on fatigue resistance. The major constituent phases, alpha-Al dendrites, Al/Si eutectic phase, and Mg-Si strengthening precipitates were mechanistically investigated to relate microstructure to near-threshold crack growth (Delta Kth) and crack propagation regimes (Regions II and III) for alloys of different Si composition/morphology, grain size, secondary dendrite arm spacing, heat treatment. A procedure to evaluate the actual fracture toughness from fatigue crack growth data was successfully developed based on a complex Elastic-Plastic-Fracture-Mechanics (EPFM/J-integral) approach. Residual stress-microstructure interactions, commonly overlooked by researches in the field, were also comprehensively defined and accounted for both experimentally and mathematically, and future revisions of ASTM E647 are expected.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.