Preliminary study on the determination of the Weibull modulus of strength distribution in quasi-brittle materials
Chengzhi Qi, Chunsheng Lu, А. И. Чанышев, Xiaozhao Li, Xiaolei Qu
Abstract
In this paper, how to determine the Weibull modulus of a fracture strength distribution is discussed with its physical implications for quasi-brittle materials. Based on the Markov chain assumption, it is shown that the lifetime (i.e., the time taken for formation of a critical defect) in a quasi-brittle material can be described by a gamma probabilistic distribution function. Prior to macroscopic failure, the effective number of energy barriers to be overcome is determined by the energy barrier spectrum decline slope that is equivalent to the Weibull modulus. Based on a fracture mechanics model, the fracture energy barrier spectrum decline slope and Weibull modulus can be theoretically calculated. Furthermore, such a model can be extended and taken into account the crack interaction and defect-induced degradation. The predicted Weibull's modulus is well consistent with that derived from available experimental results.