On the role of stress fluctuations in brittle fracture

Cracks in random stress fields are assumed to be originated in regions with high local tension. As a legacy of this special location, additional local tractions opening the crack in its centre are developed even in self-equilibrating stress fields. As the crack becomes a mesocrack it will deviate its path to meet the regions with higher possible local tension. The necessary statistical properties of the microcrack-generated random stress field can be calculated using the dipole asymptotics to approximate the stresses generated by each microcrack. The microcracks are assumed to be noninteracting and surrounded by nonintersecting excluded volumes. For the case of spherical excluded volumes the correlation radius is found to be less than the microcrack radius, which suggests that the stresses acting on each microcrack can be assumed to be statistically independent. In brittle fracture under uniaxial tension the effect of the stress fluctuations is shown to be able to significantly reduce the macroscopic strength. In fracture of brittle materials under uniaxial compression wing cracks are developed which, in real 3-D situations, cannot grow extensively and therefore cannot themselves cause failure. Instead, they induce stress fluctuations which generate mesocracks growing towards compression in such a way as to avoid the wing cracks. Hence, only stresses outside excluded volumes around the wing cracks will affect the mesocrack growth. These stresses have positive mean even if the full stress field is self-equilibrating. This results in a background tension acting perpendicular to the compression axis, amplifying the mesocrack growth and eventually causing failure. The growth and opening of mesocracks results in a specific dependence between dilatancy, i.e. inelastic increase of the sample volume, and the applied compressive stress. This dependence has a universal nature independent of the particular model of wing cracks. It corresponds well to the data of uniaxial compressive tests on 4 samples of Oshima granite (Sano et al. 1981) despite markedly different loading rates and resulted strengths.