Fracture of brittle materials: effects of test method and threshold stress on the Weibull modulus

The cumulative probability of failure of a brittle material during loading can be related to the mean number of flaws in the body that are critical, i.e. satisfy some fracture criterion. Here, this approach is related to the more conventional Weibull statistics via Wilshawʹs concept of a searched area. A power-law function for the flaw distribution is assumed and also the existence of a maximum crack size, and hence a threshold stress. The Weibull modulus, m, is regarded as a quantity that may vary with stress. It is shown that m(σ)=[σN(σ)][dN(σ)dσ] where σ is the stress and N(σ) is the appropriate number of critical flaws. Quantitative expressions for m(σ) are derived for tension tests, three-point bend tests, four-point bend tests and Hertzian indentation. It is shown that these test methods may all give different values for the Weibull modulus even though the flaw distribution remains the same.