A statistical theory of the brittle fracture of steel

A statistical model for the brittle fracture of steel is formulated and analyzed. Fracture is assumed to occur by coalescence of a number of arrested cracks initiated at different points. The upper tail of the distribution of maximum stress is shown, to be given by the formula 1-(x/(σ_o)^θ, where σ_o and θ are functions of the microstructural constants of the material. It is further shown that the size effect in this model is much less marked than in the case of weakest-link models. Finally, some experimental results from a pilot program are presented and suggestions for further experimental work given.