Statistical analysis of the failure stresses of ceramic fibres: Dependence of the Weibull parameters on the gauge length, diameter variation and fluctuation of defect density

The strength distribution of ceramic fibres is commonly described using a two-parameter Weibull distribution function. This study shows that the determination of these parameters from around 30 tensile tests obtained at one single gauge length (L0) does not allow the strength distribution at other gauge lengths to be correctly predicted. The reliability in the Weibull parameter determination is lowered by variations in fibre diameter (D) and the insufficient number of fibres tested. An effective failure stress σE = σ · (π D · L0)1/m is first introduced to take into account fibre diameter variations and to extract the two Weibull parameters from the 180 tests obtained at 6 gauge lengths. It is then shown that the linear size effect, which is expected from the standard Weibull model, is not appropriate to fit correctly this experimental strength distribution. The length dependence follows a power law (L0β) leading to an effective failure stress σE = σ · (π D · L0β)1/m. Diameter variations along the gauge length cannot be responsible for this non linear variation with the length, which is attributed to a large scale fluctuation of the density of defects. The value of β can bring valuable information about fluctuations in the fibre processing conditions.