Modelling of ceramic matrix composite microstructure using a two-dimensional fractal spatial particle distribution

Particulate composite reinforcements are good candidates for the fracture toughness of ceramics. In order to predict mechanical response of ceramic matrix composites, an efficient method capable of modelling their complex microstructure is needed. The purpose of this research is the development of such a model using fractal spatial particle distribution.; A review of different toughness mechanisms for particulate composites and associated models for deriving their constitutive relationships is presented in chapter 2.; These different toughening mechanisms as well constitutive properties depend on particle shape, size and spatial distribution, which lend themselves to a self-similar fractal based modelling approach. A self-similar distribution of particles linked to the fractal geometry is proposed. Fractal geometry provides an ideal tool for describing the randomness and disorder of the system. Its foundations are reviewed in chapter three with emphasis on iterated function systems that are subsequently used to obtain the particle configurations in the proposed model. For the sake of completeness, a review of fractal structure in science is given to illustrate possible applications. Derivation of the volume fraction associated with self similar distributions is provided in chapter 4.; This is followed by a description of the numerical model and the boundary conditions. A Finite Element simulation is performed for different volume fractions, generators and number of particles for different displacements (two uniaxial and biaxial cases) and 2-D stress state cases. From these simulations the inverse distribution of the maximum principal stress is computed. Then the self similar models are compared with the model obtained by the Yang Teriari Gokhale (Y.T.G.) method and model obtained by only one iteration. Fractal dimension for real microstructure are computed and microstructure based on the fractal dimension and number of particle is simulated. It can be derived that the fractal dimension can be related to the average radius of circular particle in special cases. General conclusion and recommendation for future work brings this investigation to a close.