Micro-Mechanics of a Segmented Embedded Fibre

Abstract

The isolated elastic fibre embedded in an elastic matrix serves as a useful analogue for the study of micro-mechanics of elastic media reinforced with low concentrations of elongated reinforcing elements. The isolated fibre problem can also be used to model fragmentation tests which are specifically designed to examine the load transfer characteristics at the fibre-matrix interface. This paper examines certain problems related to the behaviour of an isolated cracked fibre embedded in an elastic medium. In the presence of strong or perfect interface adhesion, the segmentation of an isolated fibre results in the initiation of cracks within the matrix region, (Chamis [1], and Busschen and Selvadurai [2].) In this context the paper examines the elastostatic problem related to a penny-shaped crack which exists at a cracked fibre location. It discusses the analytical treatment of the fibre-matrix crack in which there is complete continuity at the fibre-matrix interface. This results in a system of coupled integral equations which are solved in a numerical fashion to generate the stress intensity factor at the crack tip, due to the uniform axial straining of the entire composite region. Stress intensity factors are developed for typical fibre reinforced composite materials. The second aspect of the paper focuses on the study of interface frictional phenomena at the fibre-matrix interface on the behaviour of a penny-shaped fibre-matrix crack. The paper develops an incremental non-linear boundary element modelling of the problem for the specific case where the interface exhibits Coulomb friction effects in the presence of an initial radial stress field. The numerical modelling also accounts for stress singularities at the crack tip, which is located in the matrix region. The results of the numerical modelling can be used to examine the extent to which quasi-static stable matrix crack extension can take place and how such cracking can be influenced by fibre breakage across the penny-shaped crack, fibre-matrix interface friction and interface precompression.KeywordsStress Intensity FactorBoundary ElementMatrix CrackPenny Shaped CrackMatrix RegionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.