The fractal-like finite element method (FFEM) is developed to compute stress intensity factors (SIFs) for isotropic homogeneous and bi-material V-notched plates. The method is semi-analytical, because analytical expressions of the displacement fields are used as global interpolation functions (GIFs) to carry out a transformation of the nodal displacements within a singular region to a small set of generalised coordinates. The concept of the GIFs in reducing the number of unknowns is similar to the concept of the local interpolation functions of a finite element. Therefore, the singularity at a notch-tip is modelled accurately in the FFEM using a few unknowns, leading to reduction of the computational cost.The analytical expressions of displacements and stresses around a notch tip are derived for different cases of notch problems: in-plane (modes I and II) conditions and out-of-plane (mode III) conditions for isotropic and bi-material notches. These expressions, which are eigenfunction series expansions, are then incorporated into the FFEM to carry out the transformation of the displacements of the singular nodes and to compute the notch SIFs directly without the need for post-processing. Different numerical examples of notch problems are presented and results are compared to available published results and solutions obtained by using other numerical methods.A strain energy approach (SEA) is also developed to extract the notch SIFs from finite element (FE) solutions. The approach is based on the strain energy of a control volume around the notch-tip. The strain energy may be computed using commercial FE packages, which are only capable of computing SIFs for crack problems and not for notch problems. Therefore, this approach is a strong tool for enabling analysts to compute notch SIFs using current commercial FE packages. This approach is developed for comparison of the FFEM results for notch problems where available published results are scarce especially for the bi-material notch cases.A very good agreement between the SEA results and the FFEM results is illustrated. In addition, the accuracy of the results of both procedures is shown to be very good compared to the available results in the literature. Therefore, the FFEM as a stand-alone procedure and the SEA as a post-processing technique, developed in this research, are proved to be very accurate and reliable numerical tools for computing the SIFs of a general notch in isotropic homogeneous and bi-material plates.

The thesis deals with the behaviour of a cracked rail wheel. The aim was to perform the strain analysis of intact wheel as well as the fracture analysis of the primary direct cracked wheel. Solution includes an analysis of operating conditions, assessment of the substantiality of articular components of load, stiffness of the wheel, a comprehensive analysis of fracture of the selected railway wheel profile and optimization of the wheel shape depending on the matching fracture properties.

The presented diploma thesis deals with a problem of the determination of the stress intensity factor of the finite length crack in the vicinity of the bi-material interface solved by the distributed dislocation technique. The work is divided into several parts. The first part is theoretical and includes basic concepts of the fracture mechanics, the crack behaviour at the bi-material interface, the formulation of the singular integral equation by virtue of the distributed dislocation technique, the Bueckner's principle, complex potentials and consequently the determination of the stress intensity factor. The second part is the theory application to the specific configuration of the crack of the finite length with respect to the bi-material interface and in the third part, there is carried out the solution of this problem for various configurations of the bi-material solved by the distributed dislocation technique and its comparison with the results obtained from the FE analysis.

A two-parameter fracture criterion (TPFC) is used to correlate and predict failure loads on cracked configurations made of ductile materials. The current study was conducted to validate the use of the fracture criterion on more brittle materials, using elastic-plastic finite-element analyses with the critical crack-tip-opening angle (CTOA) failure criterion. Forman generated fracture data on middle-crack tension, M(T), specimens made of thin-sheet 7075-T6 aluminum alloy, which is a quasi-brittle material. The fracture data included a wide range of specimen widths (2w) ranging from 3 to 24 inches. A two-dimensional (2D) finite-element analysis code (ZIP2D) with a ''plane-strain core" option was used to model the fracture process. Fracture simulations were conducted on M(T), single-edge-crack tension, SE(T), and single-edge-crack bend, SE(B), specimens. The results supported the TPFC equation for net-section stresses less than the material proportional limit. However, some discrepancies were observed among the numerical results of the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens.

This thesis investigates the feasibility and usability of the finite element method approach in the design of crack arresting devices. Current design and manufacturing practices are improving structures' susceptibility to fracture, in particular brittle fracture; however, cracks in structures are still observed within their lifespans due to severe unexpected service conditions, poor designs, or faulty manufacturing. Crack arrester systems can be added during service to prolong the longevity of structures with sub-critical or critical flaws. Fracture properties of different specific structures under specific services can be obtained experimentally, however, experiments are expensive and of high complexity. Alternatively, the finite element method can reduce these factors and provide reliable solutions. Finite element analysis conducted provides insight into the modeling process and the effectiveness of the simulation of fracture problems. Fracture mechanics technology in conjunction with the finite element method allows for the evaluation of the effectiveness of introducing crack arresters to a flawed structure. Additionally, the simulation of recorded crack arrester experiments alongside analytic methods are used to verify the finite element analysis results. The work in this thesis verifies the validity of using the finite element approach in designing crack arrester systems for flawed structures and suggests further investigation be done with variation in crack arrester types.

No description available.

The AASHTO LRFD design specifications and the AASHTO manual for bridge evaluation are consistently revised using knowledge of previous bridge failures. Although modern steel structures are designed to resist fatigue cracking from service loads, cracks in the tension flanges of steel bridge girders have been observed as a result of stress concentrations, design errors, welding quality control, and vehicular impacts. Cracks can grow in size with time and active cyclic live loads and may result in a member fracture. Fracture is a dangerous limit state which occurs with little to no warning. One method to quantify the stress field in the vicinity of a crack tip is by calculating the Stress Intensity Factor (SIF) around the crack tip. Finding SIFs for a cracked geometry may help an engineer to determine the fracture potential based on crack dimensions found during the inspection. Rolled I-beam and steel plate girders are extensively used as bridge superstructure members to efficiently carry live loads. This research was focused on determining Stress Intensity Factors (SIFs) of partially cracked I-sections using Finite Element Analysis. Two different tension flange crack profiles were studied: edge cracks, and full-width cracks. The SIF solutions were further used to study the fracture behavior and stress redistribution in the partially cracked flexural I-shaped members. / Master of Science / Steel is one of the fundamental materials used in the construction of bridge structures, and steel girder bridges are one of the most common types of bridge structures seen in the United States. Past bridge failures have helped engineers to understand shortcomings in design specifications, and AASHTO codes have been developed and revised over the years to reflect an improved understanding and evolution of engineering behavior. Engineers must make sure that a design is robust enough for functional use of the component during its service life. It is also equally important to understand the potential chances of failure and make the structure strong enough to overcome any failure mechanisms. Fracture is one structural failure mode which occurs with little to no warning and hence is very dangerous. One efficient way to quantify the stress field in the vicinity of a crack tip is by calculating the Stress Intensity Factor (SIF) around a crack tip. Fracture literature is available which describes different methods of determining SIFs for cracked members. However, there are no solutions available to find a SIF of a partially cracked flexural I-shaped members. This research was focused on determining Stress Intensity Factors and studying the fracture behavior of partially cracked I-sections using Finite Element Analysis. The resulting SIF solutions were further used to study the fracture behavior and stress redistribution in partially cracked flexural I-shaped members.

The goal of this research is to investigate the combined effects of glass fibre reinforcement and molecular orientation in polypropylene-short glass fibre composites. Specimens have been fabricated using the injection moulding process and drawn using a small die drawing rig. The effects of die drawing on the fibre composites are complex, with the drawing process orienting both the polymer molecules and the glass fibres. This may be accompanied by the creation of voids in the polymer matrix and their destruction in the compressive stress field thus restoring the interfacial contact area between fibre and matrix. Unfilled and short glass fibre filled polypropylene specimens, with fibre content 7% wt, 13%wt, 27%wt, and 55%wt, were injection moulded prior to the die drawing process. An experimental program of die drawing within an oven at elevated temperature was conducted for polypropylene filled to various levels and at different strain rates. The specimens drew to draw ratios in the range γ=1.41 to γ=5.6. Mechanical characterization of the test materials has been conducted by examining the tensile stress strain and fracture behaviour under uniaxial conditions. The influence of glass fibre content and drawing conditions (draw ratio) on the fracture toughness and crack propagation was investigated using the double edge notched fracture test. The notch lengths ranged from 1.5 to 2.5 mm for 10 mm wide specimens. The critical stress intensity factor increased as the fibre content increased up to a limiting filler level. The fracture toughness of both unfilled and fibre filled polypropylene were found to be highly dependent on draw ratio. The results were analysed to find out the optimal draw ratio and fibre content that yielded the maximum modulus, strength and fracture toughness. Data showed that, at a given draw ratio, modulus, strength and fracture toughness increased with increasing fibre content to a maximum and then decreased. The optimum material was obtained at a draw ratio of 2.5 and filler loading 13wt%.

Neste trabalho apresenta-se a formulação do problema de múltiplas fissuras baseada numa abordagem de superposição utilizada pelo Método da Partição (Splitting Method). Um dos objetivos principais deste trabalho refere-se à aferição da capacidade deste método na obtenção de fatores de intensidade de tensão, tendo em vista o seu desenvolvimento recente e a ausência de outras fontes de pesquisa além daquelas oriundas dos seus próprios autores. Segundo a abordagem do Método da Partição, os fatores de intensidade de tensão finais de uma estrutura podem ser encontrados a partir da sobreposição de três subproblemas. Deste modo, o problema é resolvido mediante imposição de que nas faces das fissuras as tensões que resultam da sobreposição sejam nulas. Sendo assim, apresenta-se a formulação do Método da Partição para uma ou mais fissuras e diversas análises numéricas que contemplam interação entre fissuras submetidas aos modos I e II de abertura. Outra etapa do trabalho refere-se à aplicação do Método dos Elementos Finitos Generalizados (MEFG) num dos subproblemas, dito local, ao invés do emprego do Método dos Elementos Finitos (MEF), que em sua forma convencional pode requerer um refinamento excessivo da malha, particularmente junto à ponta da fissura, aumentando o custo computacional da análise. Exemplos de simulação numérica são apresentados no sentido de comprovar que a utilização do MEFG viabiliza a obtenção de resultados com boa aproximação mesmo com malhas pouco refinadas, reduzindo significativamente o custo computacional de toda a análise. Além disto, é apresentada a formulação do Método da Partição para casos que contemplam também fissuras internas, uma vez que a formulação atual admite somente fissuras de borda. / This work presents the formulation of the problem of multiple cracks based on an superposition approach used by the Splitting Method. The main goal of this work concerns the verification of the ability of this method of obtaining stress intensity factors, in view of its recent development and the absence of other research sources beyond those derived from their own authors. According to the approach of Splitting Method, the final stress intensity factors of a structure can be found from the superposition of three subproblems. Thus, the problem is solved by superposition and then imposing the nullity of the stresses on the faces of cracks. Thus, the formulation of the Splitting Method is presented to one or more cracks and also several numerical simulations that consider the interaction between cracks subjected to opening mode I and II. Another part of this work concerns the application of the Generalized Finite Element Method (GFEM) in the local subproblem instead of the use of Finite Element Method (FEM), which in its conventional form may require an excessive mesh refinement, particularly near the tip the crack, increasing the computational cost of analysis. Examples of numerical simulation are presented in order to show that the use of GFEM enables to obtain results with good approximation even with little refined meshes, thus significantly reducing the computational cost of the entire analysis. Moreover, the formulation of the Splitting Method is presented for cases which also have internal cracks due to the current formulation admits only boundary cracks.

Neste trabalho, apresenta-se a formulação do método dos elementos de contorno dual (MECD) aplicada a análise de problemas da Mecânica da Fratura Elástica Linear (MFEL). O objetivo da pesquisa consiste em avaliar o fator de intensidade de tensão (FIT) de sólidos bidimensionais fraturados, por meio de três técnicas distintas, quais são: a técnica da correlação dos deslocamentos, a técnica com base no estado de tensão na extremidade da fratura e a técnica da integral. As análises são realizadas utilizando o código computacional desenvolvido durante a pesquisa, que incorpora as formulações diretas em deslocamento e em força de superfície, do método dos elementos de contorno (MEC), com destaque para a utilização dos elementos de contorno curvos de ordem qualquer. No MECD as equações integrais singulares do tipo O(\'R POT.-1\') e O(\'R POT.-2\') são avaliadas satisfatoriamente com o Método da Subtração de Singularidade (MSS). Dessas integrais resultam termos analíticos, os quais são avaliados por meio do Valor Principal de Cauchy (VPC) e da Parte Finita de Hadamard (PFH). Compara-se o código desenvolvido com as soluções analíticas encontradas na literatura inclusive na análise de sólidos com fraturas predefinidas e para a avaliação do FIT, que produziram bons resultados. / This work presents the dual boundary element formulation applied to linear crack problem. The goal of this research is the evaluation of stress intensity factor for two-dimensional crack problem using three different techniques, which are: the technique of correlation of displacements, the technique based on the state of tension at the crack tip and J integral. The analysis is performed using the computational code developed during the research, which incorporates the direct formulations related to displacement and traction boundary element equation. A greater emphasis is given to the use of curved boundary element of any order. In the dual boundary element method the singular integral equations with singular others O(\'R POT.-1\') and O(\'R POT.-2\') are assessed satisfactorily with the application of the singularity subtraction method. The results of these singular integrals are evaluated by the Cauchy Principal Value and the Hadamard Finite Part. The code developed is compared with the analytical solutions found in the literature including the analysis of solids with fractures default and evaluation of stress intensity factor, which produced good results.