Probability density functions: From porosities to fatigue lifetime

• We propose a novel method to establish a probabilistic fatigue lifetime prediction.
• The method is based on an observed statistical distribution of defects and a growth law.
• We discuss real defect observations and lifetime data for aluminum alloys and automotive applications.
• The method provides similar match quality with observations as standard fatigue criteria.
• The resulting probability distribution is an input for reliability methods such as the stress–strength interference method.

This paper proposes a novel method to establish and identify a probability density function characterizing the fatigue lifetime. The method is initiated with a quantitative analysis of the microstructure of the material, which provides the initial probability distribution of defects. After identifying a given probability density function of defects, one can transport it into a lifetime probability density function using a growth law involving a measure of the loading over a cycle. Several parameters of the growth law are finally estimated from a given set of fatigue experiments on specimens and several techniques are discussed. The method is applied on real defect observations and lifetime data. The estimated lifetimes using the novel technique is of similar quality with standard estimation providing the probability density function of lifetime as an additional output. This output can be used directly as an input in a stress–strength interference method.