Micromechanical models and the statistical analysis of fracture and fracture toughness

The paper addresses ways in which distributions of defects in engineering alloys lead to a distribution or 'scatter' in measures of resistance to plastic flow or brittle fracture. The argument is that the statistical treatment and interpretation of any such distribution should be based on inferences drawn from micromechanical modelling of flow and fracture processes, rather than from empirical analysis. Examples cover distributions of ultimate tensile strength in aluminium alloy castings, the cleavage fracture stress in notched bars of ferritic weld-metal and fracture toughness values in 'quasihomogeneous' quenched-and-tempered steels. Visual inspection of distributions are used to assess changes produced by heat treatment or processing variables. Attention is paid to the fracture toughness distributions obtained for 'heterogeneous' materials and to the extrapolation of fracture toughness values to very low failure probabilities.