Statistical distributions of toughness and fracture stress for homogeneous and inhomogeneous materials

Abstract The first part of this paper deals with the fracture behaviour of material that is sensibly homogeneous. The statistical distributions of toughness and fracture stress for this case are determined, and the accuracies of the methods used of measuring toughness and fracture stress are assessed. Subsequently, the second part deals with the fracture of microstructurally inhomogeneous (two-phase) materials. The statistical distributions obtained for fracture stress, fracture toughness and critical crack opening displacement are assessed, and the relationships between them for inhomogeneous materials are discussed. A model is developed which explains the shapes of the distributions obtained in terms of a sampling argument. In Part III the model is applied to data for metallurgically inhomogeneous material. This is material which has a homogeneous microstructure but has chemical inhomogeneity due to segregation of alloy elements. These data are from the transition region and the lower shelf and the model predicts accurately the effect of specimen size. The model is also faithful to the change of distribution shape with proximity to the sharp transition in toughness and this too is explainable by the sampling argument.