http://hdl.handle.net/123456789/15 Subcomunidade do DEMA 2026-05-05T12:25:59Z http://hdl.handle.net/123456789/916 Modelagem e simulação do campo contínuo com irregularidades: aplicações em mecânica da fratura com rugosidade Alves, Lucas Máximo Desenvolveu-se a fundamentação matemática básica para uma Mecânica de Meios Irregulares (MMI), definindo-se um tensor de rugosidade e uma fração volumétrica irregular efetivamente deformada, de onde se obteve uma equação de movimento generalizada. O problema de irregularidades em meio contínuo foi abordado fazendo-se uma contextualização teórica da Mecânica da Fratura Fractal (MFF) dentro dessa nova MMI. A modelagem e a simulação do campo de tensão/deformação elástico para uma trinca com e sem rugosidade foi realizada para compreender o efeito dessa irregularidade sobre o campo de tensões no processo de fratura. Usando-se a Teoria Fractal foi feita uma revisão dos conceitos matemáticos da Mecânica da Fratura Clássica (MFC) os quais foram historicamente estabelecidos usando-se a geometria Euclidiana. Uma superfície de fratura generalizada foi modelada para uma dimensão de rugosidade fractal local e global, considerando-se essa superfície fraturada (ou um perfil de trinca) como sendo um fractal auto-afim, com dimensão média de rugosidade H(expoente de Hurst). Análise fractais das superfícies de fratura foram realizadas. As relações matemáticas entre as áreas fraturadas, reais e projetadas, foram obtidas e incluídas, explicitamente, na MFC junto com a rugosidade da superfície de fratura, tornando sua descrição matemática mais realista e autêntica. O campo de tensão na ponta de uma trinca rugosa fractal para os três modos de carregamento foi calculado. Além disso, um completo modelamento do crescimento estável e instável de trincas em materiais frágeis e dúcteis foi realizado, utilizando conceitos extraídos da teoria fractal. As relações matemáticas obtidas apareceram, explicitamente, incluídas dentro de um Mecânica da Fratura Fractal (MFF) junto com as relações de tenacidade à fratura e da rugosidade da superfície de fratura, as quais foram comparadas com resultados experimentais. Foi deduzido um critério de fratura generalizado e as expressões matemáticas fractais para as curvas G – R e J – R para materiais elásticos lineares e materiais elásto-plásticos, que dependem do tamanho do entalhe e do tamanho crítico do Griffith. Relações matemáticas entre a MFC e a MFF foram estabelecidas. Ensaios experimentais de curva G-R e J-R de acordo com a norma ASTM 1737-96 foram realizados e os resultados experimentais para a fratura em metais e polímeros foram obtidos e comparados com o modelo e também com o resultados de outros autores. Uma curva J-R fractal generalizada que depende das propriedades geométricas e energéticas, válida para todos os tipos de materiais,foi obtida. Portanto, uma reformulações matemáticas da MFC, utilizando a teoria fractal com suas respectivas validações experimentais, foram realizadas. Concluiu-se que uma modificação da Mecânica da Fratura Clássica, além de necessária, foi comprovada experimentalmente.; A basic mathematical foundation for a Irregular Medium Mechanics (IMM) was developed, where one defined a roughness tensor and a volume fraction irregular effectively deformed, where a general equation of motion was obtained. The problem of irregularities on continuum medium was approached making a theoretical contextualization of Fractal Fracture Mechanics (FFM) inside of this new IMM. A modeling and simulation of the elastic stress/strain field for a crack with and without roughness was carried out to understand the effect of irregularities on the stress field in the fracture process. Using Fractal Theory was done a mathematical revision of the concepts of Classical Fracture Mechanics (CFM) which were historically established using Euclidean geometry. A generalized fracture surface was modeled for a dimension of local and global fractal roughness considering the fractured surface (or a crack profile) as a self-affine fractal with roughness average dimension H (Hurst exponent). Fractal analyses of fracture surfaces were performed. The mathematical relationships between the fractured areas, true and projected, were obtained and inserted, explicitly, in CFM to taken into account the roughness of fracture surface, making its mathematical description more realistic and authentic. The stress field at the fractal rough crack tip for the three kinds of loading modes was calculated. In addition, a complete modeling of the stable and unstable crack growth in brittle and ductile materials were accomplished, using concepts extracted from fractal theory. The mathematical relationships obtained appeared, explicitly, included into a Fractal Fracture Mechanics (FFM) along with the relationships of fracture toughness and fracture surface roughness, which were compared with experimental results. A generalized fracture criterion and mathematical fractal expressions for G-R and J-R curves, for linear elastic and non-linear elastic-plastic materials, which depends on the notch size and the Griffith critical, were obtained. Mathematical relationships between the FFM and CFM were established. Experimental standard tests of G-R and J-R curve according to ASTM 1737-96 method were performed and the experimental results for the fracture in metals and polymers were obtained and compared with the proposed model and also with the results of other authors. A generalized fractal J-R curve that depends on the geometric and energetic properties, valid for all kinds of materials, was obtained. Therefore, mathematical reformulations of the CFM using the fractal theory with their respective experimental validations were accomplished. It was concluded that a modification of Classical Fracture Mechanics turning it into a Fractal Fracture Mechanics, besides of necessary, has been proven experimentally. 2011-01-01T00:00:00Z http://hdl.handle.net/123456789/883 Influence of reprocessing in the formation of functional groups during low density polyethylene aging Selonke, Maurício M; Moreira, Tiago F; Schafranski, Lincon L; Bassani, Adriane; Carvalho, Benjamim de M; Pinheiro, Luís A; Prestes, Rosilene A.; Almeida, Denise M In recent years, the interest in polymer recycling has increased. However, in every reprocessing step the material undergoes shear stress and is affected by temperature and oxygen. The aim of this paper is to investigate the influence of multiple extrusion in the generation of functional groups, namely hydroperoxide, carbonyl, and transvinylene. Low density polyethylene was reprocessed three times in a single screw extruder. In each recycling step hot pressed films were prepared. These films were submitted to a heat treatment in an oven with air circulation and renovation to proceed with aging tests at different times and temperatures. The results obtained showed that all functional groups had their concentration increased with the increase in number of reprocessing, the aging time and temperature of the heat treatment. The factorial design was applied to verify the influence of these parameters. All the parameters had significant effects, since their regression coefficients had the same order of magnitude, with the most influential parameter being the aging temperature, followed by the aging time and number of extrusions. Most of the interactions were influential, indicating that the formation of functional groups depends upon their interaction, and not only on their isolated effects. 2012-01-01T00:00:00Z http://hdl.handle.net/123456789/855 Fractal fracture mechanics applied to materials engineering Alves, Lucas Máximo; Lacerda, Luiz Alkimin de The theory presented in this chapter introduces fractal geometry (to describe ruggedness) in the formalism of classical EPFM. The resulting model is consistent with the experimental results, showing that fractal geometry has much to contribute to the advance of this particular science. 2012-01-01T00:00:00Z http://hdl.handle.net/123456789/854 Foundations of measurement fractal theory for the fracture mechanics Alves, Lucas Máximo 2012-01-01T00:00:00Z