Análise do coeficiente geométrico de intensidade de tensões utilizando o método dos elementos finitos
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Data
2016-05-16
Autores
Giovanetti, Lucas [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
O coeficiente geométrico de intensidade de tensões é utilizado em análises de propagação de trincas, ou seja, em análises de estruturas tolerantes a dano, como é o caso da maioria das estruturas aeronáuticas primárias. Para estruturas com geometrias simples, estes coeficientes podem ser obtidos através de equações presentes na literatura, normas e manuais. Nos casos onde as geometrias são complexas, os coeficientes geométricos de intensidade de tensões ou fatores de correção geométrica podem ser obtidos através do método dos elementos finitos. Este trabalho tem como objetivo determinar os coeficientes geométricos de intensidade de tensões utilizando o método dos elementos finitos. Para isto, três tipos de estruturas são analisadas. A primeira estrutura analisada é uma placa plana finita com uma trinca central, submetida à tensão normal de tração (Caso 1). A segunda estrutura analisada neste trabalho é uma placa plana finita com uma trinca lateral na borda esquerda, submetida à tensão normal de tração (Caso 2). E a terceira estrutura analisada neste trabalho é uma placa plana finita com duas trincas laterais nas bordas, submetida à tensão normal de tração (Caso 3). Estas configurações foram escolhidas propositalmente porque são geometrias simples que possuem soluções analíticas para o coeficiente geométrico. Os modelos de elementos finitos foram construídos considerando trincas, que variavam de 1,5 a 25,5 mm. Para cada tamanho de trinca, o coeficiente geométrico foi calculado numérica e analiticamente, para os três tipos de configurações. Os resultados foram obtidos e comparados. O erro médio obtido para todos os tamanhos de trincas foi de 2,56%, considerando o Caso 1. Para o Caso 2, a diferença média entre os cálculos numéricos e analíticos considerando todos os tamanhos de trincas foi de 3,552%. E, para o Caso 3, o erro médio obtido foi de 2,655%. Conclui-se que de uma maneira geral, o método de obtenção do fator de correção geométrica apresentado neste trabalho possui uma boa segurança e erros relativamente pequenos.
Geometric coefficient of stress intensity is used in analyzes of crack propagation, or damage tolerant structures analyzes, as is the case of most primary aeronautics structures. For structures with simple geometries, these coefficients can be obtained by equations present in the literature, standards and manuals. In cases where the geometry is complex, the geometric coefficients of stresses intensity or factors of geometric correction can be obtained through the finite element method. Objective of this dissertation is to determine the geometric coefficients of intensity of stresses using finite element method. For this purpose, three types of structures are analyzed. The first structure analyzed is a finite flat plate with a central crack, subjected to normal tensile stress (Case 1). Second structure analyzed in this study is a finite flat plate with a lateral crack at the left edge, subjected to a normal tensile stress (Case 2). The third structure analyzed in this work is a finite flat plate with two lateral cracks on the edges, subjected to normal tensile stress (Case 3). These configurations were selected because they are simple geometries that have exact analytical solutions for the geometric coefficient of stresses intensity. Finite element models were built considering cracks ranging from 1.5 to 25.5 mm. For each crack size, the geometrical factor was calculated numerically and analytically for the three types of configurations. Results were obtained and compared. Average error obtained for all cracks sizes was 2.56% for Case 1. In Case 2, the average difference between the numerical and analytical calculations of all cracks sizes was 3,552%. And, for Case 3, the average error obtained was 2.655%. It is concluded that in general, the method of obtaining the geometric correction factor has a good safety and it presented small errors.
Geometric coefficient of stress intensity is used in analyzes of crack propagation, or damage tolerant structures analyzes, as is the case of most primary aeronautics structures. For structures with simple geometries, these coefficients can be obtained by equations present in the literature, standards and manuals. In cases where the geometry is complex, the geometric coefficients of stresses intensity or factors of geometric correction can be obtained through the finite element method. Objective of this dissertation is to determine the geometric coefficients of intensity of stresses using finite element method. For this purpose, three types of structures are analyzed. The first structure analyzed is a finite flat plate with a central crack, subjected to normal tensile stress (Case 1). Second structure analyzed in this study is a finite flat plate with a lateral crack at the left edge, subjected to a normal tensile stress (Case 2). The third structure analyzed in this work is a finite flat plate with two lateral cracks on the edges, subjected to normal tensile stress (Case 3). These configurations were selected because they are simple geometries that have exact analytical solutions for the geometric coefficient of stresses intensity. Finite element models were built considering cracks ranging from 1.5 to 25.5 mm. For each crack size, the geometrical factor was calculated numerically and analytically for the three types of configurations. Results were obtained and compared. Average error obtained for all cracks sizes was 2.56% for Case 1. In Case 2, the average difference between the numerical and analytical calculations of all cracks sizes was 3,552%. And, for Case 3, the average error obtained was 2.655%. It is concluded that in general, the method of obtaining the geometric correction factor has a good safety and it presented small errors.
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Palavras-chave
Fator de correção geométrica, Propagação de trincas, Método dos elementos finitos, Fator de intensidade de tensões, Geometric correction factor, Crack propagation, Finite Element Method, Stress intensity factor