Probabilistic approaches to fatigue with special emphasis on initiation from inclusions

Abstract Existing methods for computing the life of critical components in jet engines, such as discs, are based on determining the design allowable forcing function (e.g. stress, strain). This is done by subtracting six standard deviations from the mean of the property in question. For example, if a stress amplitude-based criterion is used, then the design allowable life is given by: N a design = N a mean - n σ a std dev where: N a design = the safe operating design life at a given nominal stress amplitude, σ a nom . N a mean = the mean life at the nominal stress amplitude. σ a std dev = the experimentally measured standard deviation in life from the mean at the nominal stress amplitude. n = the number of standard deviations or “knock down” from the mean life that will produce an acceptable safe operating life. In the aerospace industry, this value traditionally was 3 but now “6σ” has become common and even the norm. This means that those factors which affect the dispersion of results in the High Cycle Fatigue (HCF) and Very High Cycle Fatigue (VHCF) regimes must be well understood and controlled in order to allow higher operating stresses or, conversely, longer lives at a given operating stress. The fatigue resistance of metallic materials suffers from a number of uncertainties, in particular the dispersion associated with variance in microstructure and a component size effect (i.e. scale effect). At low stresses and longer lives, such dispersions are particularly troublesome since small variations in microstructure, for example, can produce large dispersions or uncertainties in life. An understanding of the life-limiting tail of the defect distribution is crucial for modelling and predicting minimum safe operating fatigue lives. This paper concentrates on the two problems of microstructural variance and on the effect of component or specimen size in introducing uncertainty. In the first part, an attempt is made to summarize the micromechanisms of crack initiation by the formation of intrusions/extrusions along the slip bands in pure metals. This is an attempt to develop microstructural elements which are necessary to model the dispersion in fatigue life. While these features are, for the most part, illustrated by using recent results published on Ni-based and Fe-Ni based superalloys, the procedures are applicable to a wide range of other classes of alloys. In the second part an attempt is made to account for the dispersion associated with specimen or component size in terms of the interaction between the defect distribution and size when fatigue cracks are initiated from inclusions. The case of a Nickel-based alloy, IN 718, in which inclusions are mainly formed by niobium carbides (NbC) is examined in more detail. It is shown how the fatigue resistance of smooth and notched specimens of this material can be simply modelled, knowing the size and the distribution of NbC particles which act as fatigue initiation sites. The approach is further developed to model the fatigue life of notched specimens. The results obtained with this microstructure-sensitive model are compared with those obtained empirically and used in the design of discs in aircraft engines.