Preliminary study on the determination of the Weibull modulus of strength distribution in quasi-brittle materials

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 slope of the energy barrier spectrum, which is equivalent to the Weibull modulus. Based on a fracture mechanics model, the fracture energy barrier spectral slope and Weibull modulus can be calculated theoretically. Furthermore, such a model can be extended to take into account the crack interactions and defect-induced degradation. The predicted Weibull modulus is good agreement with that derived from available experimental results.