Numerical modelling of particulate and fibre reinforced composites
This thesis presents research into the micromechanical modelling of composite materials using numerical techniques. Composite materials are generally examined from two points of view: macromechanics and micromechanics, owing to their inherent heterogeneous nature. In this research, the material behaviour is examined on a microscopic scale, as the properties of interest, i.e. strength and toughness, are dependent on local phenomena. In general, the strength and toughness of composite materials are not as well understood as the simpler elastic properties, because in many cases the modes of failure under a given system of external load are not predictable in advance. Previous research in this field has typically involved specially designed experiments, theoretical/statistical studies, or the use of numerical models. In this study, advanced implementations of numerical methods in continuum mechanics, i.e. the boundary element and the finite element methods are employed to gain a greater understanding of composite behaviour. The advantage of using numerical methods, as opposed to experimental studies, is that the geometric and material characteristics can be investigated parametrically, in addition to the reduced time and expense involved. However, to model the complete behaviour of real composites is still not possible, due to the degree of complexity and uncertainty involved in modelling the various mechanisms of damage and failure, etc. and also due to the immense computational cost. Therefore, simplified models must be employed which are limited by their assumptions. For the preliminary studies within this thesis, geometrically simplified models are presented to provide an understanding of the influence of embedding second phase inclusions on the local stress fields, and also to validate the numerical techniques with readily available analytical solutions. These models are then extended to accommodate additional phenomena, such as inclusion interaction, spatial inclusion arrangement, material formulation, i.e. consisting of two- and three-phases of various material properties. The influence of such factors on the local stress concentrations, which play an important role in determining the strength of the composite, is analysed through a series of parametric studies. The localised toughening of composites is also considered through novel investigations into the interaction between a propagating crack with inclusions and microcracks. Through the development of the numerical models a more realistic representation of composite behaviour is achieved, which in tum, provides an improved knowledge of the factors that control strength and toughness. Such information is invaluable to composite material designers, who presently rely heavily on experimental studies to develop composite materials.