For any structurally critical component subject to fatigue, the safety of the structure depends on an accurate prediction of the life under this failure mode. However, in such circumstances it is insufficient to consider only the mean behavior of the material. To ensure structural integrity, a model for the distribution of life to failure is required, which will allow lives to be assessed relative to acceptable safety levels.
In previous work, a methodology for deriving fatigue life estimates for arbitrary specimen and component geometries from plain specimen data has been developed . The methodology is based on a procedure for developing a model for the initiation behavior of the material from the specimen data and for applying this to an arbitrary material geometry or stress field. In the current paper, this method is further developed to allow for the associated distribution of fatigue lives to be calculated. This involves direct consideration of the statistical relationship between crack initiation and crack propagation, so that the distribution of initiation lives can be derived accurately. However, incorporating these considerations directly into the methodology reveals some inconsistencies in the formulation of the original model. These relate to the fact that, at high stresses, the specimens will fail in tension rather than classical fracture, thus altering the interpretation of the data. It is shown that a more robust model can be developed, but only by including the distribution of tensile strength as an additional variable, and by considering the statistical relationship between this and the other fundamental variables.
The methodology which arises from the incorporation of these considerations into the basic calculation scheme is then developed, including a means for estimating the distribution of life to failure at all points on the stress against cyclic life curve.