Micro-Mechanical Simulation of Composite Materials Using the Serial/Parallel Mixing Theory
Xavier Martínez Advisor: S. Oller ~ PhD Thesis ~
`cnica de Catalunya Universitat Polite ` Escola Tecnica Superior d’Enginyers de Camins, Canals i Ports `ncia de Materials Departament de Resiste i Estructures a l’Enginyeria
Micro Mechanical Simulation of Composite Materials Using the Serial/Parallel Mixing Theory
Doctoral Thesis Xavier Mart´ınez
Advisor: Dr. Sergio Oller
Barcelona, June 2008
´ DE LA TESI DOCTORAL ACTA DE QUALIFICACIO Reunit el tribunal integrat pels sota signants per jutjar la tesi doctoral: T´ıtol de la tesi: Micro-Mechanical Study of Composites Materials Using the Serial/Parallel Mixing Theory Autor de la tesi:Xavier Mart´ınez Acorda atorgar la qualificaci´o de: No apte Aprovat Notable Excel·lent Excel·lent Cum Laude
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Acknowledgments
I would like to express my grateful acknowledgment to my supervisor, Sergio Oller, who gave me the opportunity and the trust to start this project. Without his help and knowledge on the topics discussed in this document, and on many others, this work would never have been possible. I also want to give thanks to CIMNE, specially to Eugenio O˜ nate, for its financial support and for giving me the opportunity to collaborate in some of the research projects that have helped to create this document1 . My most sincere gratitude to all the people of CIMNE, the RMEE department of the UPC, and the MAE department of WVU, among them Alex Barbat and Ever Barbero, for their interaction during the development of this project. No research is possible without interacting with other people; thanks for your ideas, comments, suggestions and knowledge. Thanks to all my friends, for all the conversations in which the finite elements and the composite materials where not the main topic. Thanks to my family, specially my parents, for the education received, for teaching me how to enjoy learning. And thanks Iria. This work is as much mine as yours.
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Most of the developments included in this work are consequence of several research projects. The institutions and companies responsible of these projects are gratefully acknowledged. These are, CEE–FP6 (LESSLOSS project, ref. FP6-50544(GOCE)); the Spanish Goverment through the Ministerio de Ciencia y Tecnolog´ıa (RECOMP project, ref. BIA2005-06952 and DECOMAR project, ref. MAT2003-08700-C03-02) and the Ministerio de Fomento (project “Retrofitting and reinforcement of reinforced concrete structures with composite materials. Numerical and experimental developments applied to joint of bars and composites anchorage proposal”); AIRBUS through the project FEMCOM and ACCIONA Infraestructuras through the project SPHERA
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Abstract In last decades, advanced composites have become a revolution in structural engineering. Their high strength/weight and stiffness/weight ratios, together with the possibility to tailor made the material for the specific loading environment in which it is used, make these new materials optimal for many structural applications, specially in the aeronautical and nautical fields. However, despite all existing information and actual knowledge about these materials, their complex behavior, highly non-linear, anisotropic and with different failure causes not found in traditional materials, requires a greater effort in their study in order to improve their performance and take advantage of all possibilities offered by them. Among all possible numerical procedures and formulation available to predict the mechanical performance of fiber reinforced composites, this work uses the serial/parallel mixing theory. This theory obtains the mechanical performance of the composite by coupling the constitutive performance of its constituents, fiber and matrix. This is done taking into account the directional behavior of fibers, which contribution to the strength and stiffness of the composite is found, mainly, in their longitudinal direction. However, although it is necessary to consider material non-linearities for a correct characterization of fiber reinforced composites, it is not sufficient. The most common failure modes of advance composites, like delamination or fiber buckling, are produced by the interaction between the composite components, and not as a result of a material failure. Therefore, an accurate simulation of composites must take into account the micro-mechanical interaction between its components, in order to be able to characterize their failure modes. This work studies and proposes different formulations and numerical procedures to simulate the micro-mechanical phenomenons that take place in composites, using the serial/parallel mixing theory. Two different failure modes are discussed: delamination and compression failure due to fiber buckling. Delamination consists in the lost of adherence between the different layers of the composite, which leads to a reduction of the section strength and stiffness, that can finish in a structural failure. This failure mode is simulated straightforward with the serial/parallel mixing theory, if the appropriate constitutive equations are chosen to predict the mechanical performance of the composite constituents. The compression strength of composite materials is defined by the fiber micro-buckling phenomenon. This failure mode depends as much on fiber material (stiffness and initial misalignments), as it depends on the confinement made by matrix over fibers. To predict this failure mode a new methodology has been developed, consisting in the introduction of the micro-structural interaction between fibers and matrix into the serial/parallel mixing theory. This is done using an homogenization procedure, that modifies the constitutive performance of fiber and matrix, taking into account their micro-mechanical interaction. The methodology proposed not only solves the fiber buckling problem, but it can also be used to characterize other micro-structural effects, such as the interaction between fibers in woven composites. All formulations and procedures included in this work provide a new numerical approach to characterize composite materials, capable of considering both, the material non-linearities and the micro-mechanical phenomenons that take place in them. Simulations performed with this new formulation can contribute to increase the actual knowledge of advanced composites, improving their reliability and opening new application fields.
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