Probabilistic aspects of strength of unidirectional fibre-reinforced composites with matrix failure

In the previous paper 1], the stress distribution and the expected number of successive fibre breakages around broken fibres were calculated. It showed the following results. The fracture process that the crack originates from one isolated broken fibre and propagates due to the stress redistribution following the fibre breakage is unlikely to occur in the real unidirectional fibre-reinforced composite material. The matrix-failure is considered to play an important role in the fracture process of real composite materials. In the present paper, the stress (or strain) distribution and the expected number of successive fibre breakages around broken fibres are calculated when the matrix-damaged regions exist. The stress (or strain) distribution is obtained based on the three-dimensional hexagonalarray shear-lag model. Uniform shear force is assumed to occur in the matrix-damaged region. The expected number of the successive fibre breakages is calculated on the assumption that the flaws in the fibre follow a Poisson process.