Behaviour of a crack in a corner or at a tip of a polygon-like particle

Abstract

Crack propagation in particle composite materials depends on the properties of a matrix and a particle. A changing combination of the materials of a matrix and a particle together with various shape of the particle can result either in an increase or decrease of global fracture properties of the composite. A crack propagating through a particle composite can be found in the following positions: (i) a crack with its tip in the matrix and approaching the particle, (ii) a crack with its tip at the matrix/particle interface, (iii) a crack passing through the particle (iv) a crack lying in the matrix/particle interface, (v) a crack with its tip in a corner or at a tip of a polygon-like particle. The stress state in the second and the last cases differs from the stress field of a crack in a homogeneous material. The last case can be simulated by means of a bi-material notch model. The model can be used for evaluation of toughening mechanisms of silicate based composites with various shapes of aggregates. The stress singularity exponents of the bi-material models are determined and analyzed for typical materials combinations and typical shapes of aggregates. As silicate based composites exhibit quasi-brittle behaviour, the stress field should be described in a larger area ahead of a crack tip. For this reason, the exponents of non-singular stress terms are analysed as well. Stress distribution in the vicinity of a crack tip is analysed and conditions for further crack propagation are estimated.