Modeling the Mechanical Response of Fibrous Monolith Composites
Creators: name: Lu, Liwei
Publisher: name: Maryland Shared Open Access Repository
Year: 2009
Subjects: Composites
Fibrous Monolith
Mechanical Response
Modeling

description: Fibrous Monolith Composites (FMCs) have emerged as an exciting new class of structural ceramics in recent years primarily due to their advantageous characteristics, such as enhanced damage tolerance, high fracture energy, high toughness and R-curve behavior, improved thermal and chemical stability, while fabricated at relatively low cost. FMC material systems have been used in wear and high temperature applications and most recently in energetic reactive structures. Understanding the mechanical characteristics of FMCs is critical for their safe and reliable use. However, critical tools for stress and failure analysis for FMC based structures have not yet been developed. Therefore, the objective of the present research is to establish effective tools for the analysis of this new generation of FMC material systems. In this study, we develop suitable numerical and analytical tools to characterize the performance of FMC material systems, including their linear elastic and non-linear mechanical response, their proportional limit, their fracture characteristics through near-tip stress field studies and macroscopic mechanical response through modeling of tensile experiments. The elastic response of FMCs is investigated using the finite element method (FEM). In this study, we assume material, geometric and loading uniformity in the z direction which allows us to reduce the problem to a two-dimensional (2-D) problem. A representative unit-cell is extracted from micro-structure of FMCs for FEM studies. Robust 2-D FEM meshes are developed capable of modeling a wide range of FMC micro-structures. Three in-plane Boundary Value Problems (BVPs) are established for estimating the in-plane effective properties of FMCs. Parametric studies are employed on predicting elastic properties for a broad range of FMC micro-structures. Out of plane properties are obtained through complementary 3-D finite element studies. A failure model is utilized for predicting the initiation of cracking in FMCs subjected to general in-plane loading. The non-linear response of FMCs is investigated by employing a discrete microcracking model as part of an incremental and iterative modeling scheme. The model is represented by a microcracking law which relates the current state of stress to the current state of microcracking damage. It is expected that the FMC material systems behave non-linearity due to the degradation of micro-constituent stiffness. Non-linear stress-strain curves are also obtained through parametric studies. Degradation of the in-plane effective properties of FMC unit-cell and evolution of damage within FMC unit-cell are monitored throughout the simulations. Also in this study a computationally efficient semi-analytical method is developed for calculating the elastic micro-stress fields of FMCs. Analytical displacement estimates are derived using the Rayleigh-Ritz method for a FMC composite plate, the approximation solutions are derived with the aid of Kirchhoff-Love deformation hypothesis. The elastic micro-fields under remote in-plane loading are obtained by solving requisite BVPs. The semi-analytical results are compared with respective finite element results. It is evident that the finite element approximations are in an overall sense in good agreement with the semi-analytical model predictions. A specialized finite element is developed utilizing an asymptotic displacement expansion comprised of the homogenized displacements and the local micro-displacements which are based on Rayleigh-Ritz method. The element performance is demonstrated via near-tip studies for a crack under mode-I and mode-II fracture conditions. As the final task of this research, the tensile stress-strain response of fiber reinforced FMCs is analyzed using a crack propagation model. The crack growth in the composite specimens is evaluated using a stress intensity approach. The influences of the fibers that bridge the matrix cracking are represented by closure tractions at the crack surface. The calculated stress-strain curves are compared with experiments which are used for the mechanical characterization of a special class of reactive FMC systems. Importantly, the latter systems contain a polymer binder phase used in forming the fabrication slurry and left in the system for their safe production.  Useful insights are gained regarding the effects of the composite microstructure and processing conditions on the mechanical response of the composite system. The models developed in this research aim at assisting the material design community in developing novel composite micro-structures associated with superior macro-mechanical performance.