Publication: Comportamiento mecánico de materiales compuestos de matriz metálica y refuerzo de partículas : un enfoque basado en celdas multipartícula
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2010-06
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2010-06-28
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Abstract
En esta Tesis Doctoral se estudia el comportamiento mecánico de los materiales compuestos de matriz metálica y refuerzo de partículas cerámicas (PMMCs). En su mayor parte, el método empleado consiste en el análisis de celdas multipartícula por el método de los Elementos Finitos, aunque en algunos aspectos, se ha complementado sus resultados mediante el uso de determinados modelos analíticos seleccionados de la literatura. Los aspectos del comportamiento mecánico de PMMCs estudiados en este trabajo fueron, esencialmente tres: (a) la determinación de constantes elásticas efectivas a partir de las propiedades de las fases y de información microestructural, (b) el comportamiento efectivo en régimen elásto-plástico cuando una de las fases del material compuesto posee este tipo de comportamiento y, finalmente, (c) la influencia que los eventos de decohesión entre matriz y partículas tienen sobre la respuesta mecánica efectiva del material. Como herramienta operacional, se ha desarrollado un algoritmo para la generación de distribuciones aleatorias de partículas prismáticas en el espacio tridimensional, permitiendo el control por parte del usuario de parámetros microestructurales como la fracción volumétrica de refuerzo y la esbeltez de las partículas, así como el grado de aleatoriedad de su orientación y de variabilidad de su tamaño. La decisión de considerar partículas de geometría prismática surge del interés de incorporar en los modelos, de algún modo, el efecto de concentración de tensiones asociado a la presencia de aristas en las partículas. Mediante este modelo de celdas multipartícula, usado en conjunto con el método de los Mediante este modelo de celdas multipartícula, usado en conjunto con el método de los Elementos Finitos, se han obtenido valores de las constantes elásticas efectivas de un compuesto formado por una matriz de aleación de aluminio reforzado con partículas cerámicas de carburo de silicio, considerando diferentes escenarios microestructurales. Estos escenarios reflejan diferentes combinaciones de esbeltez de partícula, fracción volumétrica de refuerzo y aleatoriedad de orientación, lo que permitió estudiar tanto materiales isótropos como transversalmente isótropos. Los resultados así obtenidos fueron extendidos mediante la ecuación de Halpin-Tsai, desde los valores puntuales considerados para la fracción volumétrica en los modelos hasta un rango continuo de hasta 30%. Para el parámetro principal que interviene en esta ecuación puede encontrarse en la literatura algunos valores aplicables a un conjunto específico de escenarios microestructurales. Por una parte, en el presente trabajo se ha revisado la validez de los valores utilizados en la literatura. Por otra, se aportan valores nuevos, aplicables a escenarios microestructurales que no tenían descripción previa. En PMMCs, usualmente es la fase matriz la única que, en determinados casos, exhibe un comportamiento no lineal, con deformación plástica y endurecimiento por deformación. Así, en el caso del estudio del comportamiento elasto-plástico de este tipo de materiales, el trabajo se centra en los siguientes aspectos. En primer lugar, se ha descrito el estado tensodeformacional interior del compuesto cuando se impone sobre el material una solicitación mecánica macroscópica de tipo uniaxial. En segundo lugar, se ha buscado establecer una relación fenomenológica entre la curva de endurecimiento de la fase matriz y la curva de endurecimiento del compuesto. En tercer lugar, se ha estudiado, para la misma solicitación de tracción uniaxial, la evolución durante la historia de deformación de determinadas variables energéticas. Esto permitió describir un efecto de confinamiento energético, asociado a la deformación plástica de la fase matriz, que es responsable de la producción de tensiones residuales cuyo origen no es térmico, sino puramente mecánico. Estos estudios se realizaron por medio del análisis numérico de celdas multipartícula. Adicionalmente, ha interesado en esta Tesis, disponer de un método analítico para estimar la respuesta mecánica efectiva (y no lineal) cuando la matriz tiene una respuesta no lineal y las partículas son prismáticas. En la literatura, esto se ha realizado frecuentemente en el contexto de la Elasticidad no lineal, mediante el modelo de homogeneización Secante, ya sea en su versión Clásica o Modificada, para el caso de compuestos reforzados con esferas o elipsoides. Se propone en este trabajo una implementación particular del método Secante aplicable a compuestos con partículas prismáticas y cuyas fases constituyentes tienen una respuesta elástica isótropa. El estudio de la influencia del daño por decohesión entre la matriz y las partículas sobre la respuesta efectiva del material compuesto, se realizó situando en las interfases de los modelos numéricos de celda, elementos finitos cuyo comportamiento constitutivo obedece al modelo de fisura cohesiva, de amplia descripción en la literatura. En este caso, debido al coste computacional y dado que el interés residía en una descripción cualitativa, las simulaciones se realizaron utilizando celdas bidimensionales, tanto en tensión como deformación plana. Además de efectuarse una revisión de algunos elementos conceptuales de la Mecánica del Daño, relacionando la degradación de la rigidez material con el trabajo disipado en un proceso de daño, en este estudio se describió detalladamente el modo en el que la decohesión degrada tanto el límite elástico como el módulo de Young del material compuesto, no sólo a través de la nucleación inicial de poros asociada a la decohesión, sino también por el subsiguiente crecimiento de los mismos. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
In the present work, the mechanical behavior of Particle Reinforced Metal Matrix Composites is studied. Mainly, the method employed is based on the numerical analysis of multiparticle cell models through the Finite Element Method. Specifically, three aspects of the mechanical behavior were studied: (a) calculation of the effective elastic constants from the elastic properties of the constituents and information about the composite microstructure, (b) study of the non linear effective behavior when the matrix deforms plastically, with strain hardening and, finally, (c) study of the influence of particlematrix decohesión events on the composite’s mechanical response. As a tool for the above mentioned studies, an algorithm for the generation of random spatial distributions of prismatic particles in the tridimensional space has been developed, that allows control of microstructural factors such as reinforcement volume fraction, particle aspect ratio and degree of randomness in particle orientation. The use of particles with prismatic geometry arises from the desire to include in some way in the modeling the effect of stress and strain concentration due to the presence of sharp edges on particles. By means of a Finite Element discretization of these multiparticle cells, values of the effective elastic constants were obtained for an Al alloy based composite reinforced with silicon carbide particles, considering different microstructural scenarios. These scenarios reflect different combinations of particle aspect ratio, volume fraction of reinforcement and randomness of orientation, which allowed the study of both, isotropic and transversely isotropic materials. Using the well-known Halpin-Tsai equation, the results are extended from the specific values used for particle volume fraction in the cell models to a continuous range up to 30%. New values for the ‘s’ parameter of the HT equation for microstructural scenarios not covered in the literature, and improved values for some of the scenarios covered by some authors, are presented. It is also shown that results can be extended to other systems such as steel reinforced with SiC particles using the new ‘s’ values. In PMMCs, the matrix phase is usually the one that in some cases, exhibits a nonlinear behavior, with plastic deformation and strain hardening. Thus, for the study of elastic-plastic behavior of these materials, the work focuses on the following aspects. First, the stress-strain state inside the composite is described, when uniaxial macroscopic loading is externally applied. Secondly, a phenomenological relationship between the hardening curve of the matrix phase and the hardening curve of the composite has been investigated. Finally, for the same uniaxial loading, the evolution during the strain history of certain energy variables has been studied. This allowed the description of an energy confinement effect associated with plastic straining of the matrix phase, which is responsible for the production of residual stresses whose origin is not thermal, but purely mechanical. All of these studied were made by numerical analysis of multiparticle cells. Additionally, the author of this Thesis considered of interest to have at hand an analytical method to estimate the effective (and nonlinear) mechanical response when the matrix phase has a nonlinear response and the particles are prismatic. In literature, this has been done frequently in the context of Nonlinear Elasticity, by means of the Secant homogenization method, whether in its Classical or Modified version, in the case of composites reinforced with spheres or ellipsoids. A particular implementation of the Secant method is proposed in this work. It is applicable to composites reinforced with prismatic particles, when its constituent phases have an isotropic elastic response. The study of the influence of particle-matrix decohesion damage on the composite’s effective response was performed by placing at the interfaces of numerical cell models, finite elements whose constitutive behavior follows the Cohesive Crack model, which is widely described in the literature. In this case, due to computational cost and since the interest lay in a qualitative description, the simulations were performed using two-dimensional cells, both in plane stress and plane strain. Besides carrying out a review of some conceptual elements of Damage Mechanics (relating the material stiffness degradation with the work dissipated in a process of damage), in this study is described in detail the mechanism by which particle-matrix decohesion degrades both the yield strength and Young's modulus of the composite material, not only through the nucleation of pores due to the decohesion, but also for their subsequent growth.
In the present work, the mechanical behavior of Particle Reinforced Metal Matrix Composites is studied. Mainly, the method employed is based on the numerical analysis of multiparticle cell models through the Finite Element Method. Specifically, three aspects of the mechanical behavior were studied: (a) calculation of the effective elastic constants from the elastic properties of the constituents and information about the composite microstructure, (b) study of the non linear effective behavior when the matrix deforms plastically, with strain hardening and, finally, (c) study of the influence of particlematrix decohesión events on the composite’s mechanical response. As a tool for the above mentioned studies, an algorithm for the generation of random spatial distributions of prismatic particles in the tridimensional space has been developed, that allows control of microstructural factors such as reinforcement volume fraction, particle aspect ratio and degree of randomness in particle orientation. The use of particles with prismatic geometry arises from the desire to include in some way in the modeling the effect of stress and strain concentration due to the presence of sharp edges on particles. By means of a Finite Element discretization of these multiparticle cells, values of the effective elastic constants were obtained for an Al alloy based composite reinforced with silicon carbide particles, considering different microstructural scenarios. These scenarios reflect different combinations of particle aspect ratio, volume fraction of reinforcement and randomness of orientation, which allowed the study of both, isotropic and transversely isotropic materials. Using the well-known Halpin-Tsai equation, the results are extended from the specific values used for particle volume fraction in the cell models to a continuous range up to 30%. New values for the ‘s’ parameter of the HT equation for microstructural scenarios not covered in the literature, and improved values for some of the scenarios covered by some authors, are presented. It is also shown that results can be extended to other systems such as steel reinforced with SiC particles using the new ‘s’ values. In PMMCs, the matrix phase is usually the one that in some cases, exhibits a nonlinear behavior, with plastic deformation and strain hardening. Thus, for the study of elastic-plastic behavior of these materials, the work focuses on the following aspects. First, the stress-strain state inside the composite is described, when uniaxial macroscopic loading is externally applied. Secondly, a phenomenological relationship between the hardening curve of the matrix phase and the hardening curve of the composite has been investigated. Finally, for the same uniaxial loading, the evolution during the strain history of certain energy variables has been studied. This allowed the description of an energy confinement effect associated with plastic straining of the matrix phase, which is responsible for the production of residual stresses whose origin is not thermal, but purely mechanical. All of these studied were made by numerical analysis of multiparticle cells. Additionally, the author of this Thesis considered of interest to have at hand an analytical method to estimate the effective (and nonlinear) mechanical response when the matrix phase has a nonlinear response and the particles are prismatic. In literature, this has been done frequently in the context of Nonlinear Elasticity, by means of the Secant homogenization method, whether in its Classical or Modified version, in the case of composites reinforced with spheres or ellipsoids. A particular implementation of the Secant method is proposed in this work. It is applicable to composites reinforced with prismatic particles, when its constituent phases have an isotropic elastic response. The study of the influence of particle-matrix decohesion damage on the composite’s effective response was performed by placing at the interfaces of numerical cell models, finite elements whose constitutive behavior follows the Cohesive Crack model, which is widely described in the literature. In this case, due to computational cost and since the interest lay in a qualitative description, the simulations were performed using two-dimensional cells, both in plane stress and plane strain. Besides carrying out a review of some conceptual elements of Damage Mechanics (relating the material stiffness degradation with the work dissipated in a process of damage), in this study is described in detail the mechanism by which particle-matrix decohesion degrades both the yield strength and Young's modulus of the composite material, not only through the nucleation of pores due to the decohesion, but also for their subsequent growth.
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Keywords
Materiales compuestos de matriz metálica y refuerzo de partículas cerámicas, PMMCs, Comportamiento de materiales, Celdas multipartícula, Método de elementos finitos