On the effect of sampling volume on the microscopic cleavage fracture stress

Reported observations of an experimental variation in the microscopic fracture stress for transgranular cleavage (σ∗ f) with specimen geometry and size are quantitatively examined in terms of a weakest-link statistical model for brittle fracture, wherein failure coincides with the critical propagation of a particle microcrack into the matrix. By analysing the onset of fracture in the ‘sharp-crack’ (KIc ) specimen, the ‘rounded-notch’ (Charpy) specimen, and the uniaxial tensile specimen, it is shown that values of σ∗ f are reduced progressively in the ‘sharp-crack’, notched and unnotched geometries and with increasing specimen size, consistent with an increase in statistical sampling volume. Quantitative predictions for the magnitude of this variation are given for a low strength steel.