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-equil ibrating stress fields. As the crack becomes a mesocrack it will deviate it s path to meet the regions with higher possible local tension. The necessar y statistical properties of the microcrack-generated random stress field ca n be calculated using the dipole asymptotics to approximate the stresses ge nerated by each microcrack. The microcracks are assumed to be noninteractin g and surrounded by nonintersecting excluded volumes. For the case of spher ical excluded volumes the correlation radius is found to be less than the m icrocrack radius, which suggests that the stresses acting on each microcrac k 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 m aterials under uniaxial compression wing cracks are developed which, in rea l 3-D situations, cannot grow extensively and therefore cannot themselves c ause failure. Instead, they induce stress fluctuations which generate mesoc racks 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 tens ion 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 increas e 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 ra tes and resulted strengths.