Publication: Aplicación del método de elementos finitos extendido a la propagación de fisuras en vigas cilíndricas
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2015-07
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2015-07-07
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Abstract
Las estructuras que se construyen en la actualidad son cada vez más complejas y exigentes. La seguridad de las mismas es un requisito fundamental, es por ello que el campo de la Mecánica de Fractura ha adquirido un papel fundamental en las últimas décadas a la hora del diseño. Las estructuras pueden estar sometidas a cargas estáticas o dinámicas y la capacidad de predecir el crecimiento de las fisuras en elementos como las vigas es fundamental para asegurar la seguridad durante la vida útil y para alargar esta última
Con la llegada de los métodos numéricos y su posterior desarrollo se han conseguido realizar grandes avances en este campo. Paulatinamente se han ido introduciendo nuevos métodos que permitieran realizar estudios cada vez más precisos de los mecanismos de fractura. Uno de los más útiles y que ha sido desarrollado recientemente es el conocido como Método de Elementos Finitos eXtendido o XFEM.
La principal ventaja que ofrece el XFEM es la posibilidad de estudiar el crecimiento de fisuras de un modo mucho más libre que el que permitía el Método de Elementos Finitos tradicional (MEF). Sin embargo, el XFEM también presenta desventajas, la más destacable es la complejidad tanto para alcanzar la convergencia en algunas ocasiones como por la necesidad de un conocimiento extenso de los mecanismos de fractura por parte del usuario.
En este Trabajo Fin de Grado se ha desarrollado un modelo numérico tridimensional mediante el XFEM y cuyo principal objetivo es cuantificar la dispersión en los resultados al utilizar diferentes tipos de mallado en condiciones cuasiestáticas. Es muy importante conocer la importancia relativa del mallado en los resultados para poder realizar análisis fiables que garanticen la seguridad adecuada de cualquier estructura. Con cada tipo de mallado se ha estudiado la propagación de fisuras en vigas cilíndricas en función del tamaño inicial de las mismas. Asimismo se proporciona un manual en el que se explican perfectamente las dos alternativas que ofrece el código Abaqus para este tipo de problemas: la de los modelos cohesivos CZM (que es la que se ha utilizado) y la que se basa en la Mecánica de Fractura Elástico-Lineal MFEL. Por último se han comparado los resultados obteniendo varias conclusiones esclarecedoras, sobre todo, en lo respectivo a la influencia del mallado.
The structures which are built nowadays are more complicated and tough each time. The safety of them is an essential requirement, for this reason the field of the fracture mechanisms has got a vital role in the last decades, especially concerning in design aspects. The structures can be subdued to static or dynamic forces and the capacity of prediction about the growth of cracks in elements like beams is absolutely necessary to assure the security during the useful life as well as to extend this life. Many progresses have been done in this area with the arrival of the numeric methods and their following development. Progressively new methods, which allow to do more accurate analysis of the fracture mechanisms, have been introduced. One of the most useful and which has been developed recently is the eXtended Method of Finite Element as known as XFEM. The main advantage which XFEM offers is the possibility of studying the growth of cracks in a freer mode than the traditional Finite Element Method (FEM) allows. However, the XFEM presents disadvantages too, the most important of them is the complexity to reach the convergence in the equations occasionally enough to have a vast knowledge of the fracture mechanisms by the user. Within this Project a 3D XFEM numeric model has been developed, the main objective is quantify the dispersion of the results when different kind of meshes are used in quasistatic conditions. The mesh shape and dimensions are important for the reliability of the analysis which must guarantee the suitable safety of any structure. With each kind of mesh the cracks propagation in beams has been studied in function of the initial depth of each crack. In addition, a manual in the Abaqus code is provided in which the two alternatives offered by Abaqus for this kind of problems are fully explained: the first one based on the Cohesive Zone Model (which is the used one) and the second one based on the Linear Elastic Fracture Mechanics. Finally, the obtained results have been discussed, leading to some clarifying conclusions, above everything, in the influence of the mesh.
The structures which are built nowadays are more complicated and tough each time. The safety of them is an essential requirement, for this reason the field of the fracture mechanisms has got a vital role in the last decades, especially concerning in design aspects. The structures can be subdued to static or dynamic forces and the capacity of prediction about the growth of cracks in elements like beams is absolutely necessary to assure the security during the useful life as well as to extend this life. Many progresses have been done in this area with the arrival of the numeric methods and their following development. Progressively new methods, which allow to do more accurate analysis of the fracture mechanisms, have been introduced. One of the most useful and which has been developed recently is the eXtended Method of Finite Element as known as XFEM. The main advantage which XFEM offers is the possibility of studying the growth of cracks in a freer mode than the traditional Finite Element Method (FEM) allows. However, the XFEM presents disadvantages too, the most important of them is the complexity to reach the convergence in the equations occasionally enough to have a vast knowledge of the fracture mechanisms by the user. Within this Project a 3D XFEM numeric model has been developed, the main objective is quantify the dispersion of the results when different kind of meshes are used in quasistatic conditions. The mesh shape and dimensions are important for the reliability of the analysis which must guarantee the suitable safety of any structure. With each kind of mesh the cracks propagation in beams has been studied in function of the initial depth of each crack. In addition, a manual in the Abaqus code is provided in which the two alternatives offered by Abaqus for this kind of problems are fully explained: the first one based on the Cohesive Zone Model (which is the used one) and the second one based on the Linear Elastic Fracture Mechanics. Finally, the obtained results have been discussed, leading to some clarifying conclusions, above everything, in the influence of the mesh.
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Mecánica de fractura, Fisuras, Vigas cilíndricas, Método de elementos finitos