摘要
Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.
Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.
