Volume 17, Issue 1 (January 1989)
A Model to Predict the Sources and Magnitude of Scatter in Toughness Data in the Transition Region
Scatter in cleavage fracture toughness data is analyzed with a statistical model. This model indicates that when a material fails by weakest-link cleavage under J-controlled conditions, the corresponding fracture toughness data will follow a two-parameter Weibull distribution with a characteristic slope. This slope is 2.0 for critical J-integral and crack tip opening displacement (CTOD) data, and 4.0 for critical stress intensity values. Published experimental data for a wide range of materials verify these slopes.
The discovery of an invariant Weibull slope that is the same for all materials has important practical implications. For example, it is now possible to predict the relative magnitude of toughness scatter prior to testing. It is also possible to extract useful information from small data sets. The authors demonstrate these applications with sample calculations. A number of additional analyses are presented, including evaluations of the effects of thickness and local brittle zones on toughness. Also, a methodology is presented which allows one to predict fracture toughness distributions when specimens belonging to multiple populations are tested. This latter analysis can be used to assess the effect of experimental error.
The analyses in this article are not valid when cleavage fracture is preceded by large-scale plasticity or stable crack growth. In such cases, the crack tip stresses are lower than predicted by J-integral theory. This causes the Weibull slope to decrease from its theoretical value. Current research is aimed at predicting fracture toughness distributions for large-scale yielding conditions.