13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Figure 1. Stress distributions in a notched specimen The fatigue notch factor, kf, is determined at a given number of completely reversed cycles (typically 106 or 107) to crack initiation and is given as: unnotched f f notched f k σ σ = (2) Where σf unnotched is the fatigue strength of the unnotched specimen and σf notched is the fatigue strength of the notched specimen. The difference between kt and kf for a given microstructure is typically represented by the notch sensitivity factor, q given as: 1 1 f t k q k − = − (3) At q = 0, there is no notch sensitivity and at q=1 we have full notch sensitivity. i.e. full theoretical elastic concentration effect. Several empirical relations have been developed to estimate the fatigue notch factor of a material and its associated notch sensitivity index. These techniques include: the classical methods (Neubers [6 - 7], Peterson [3, 8] and Heywood [9]), stress field intensity method [10], and probabilistic method based on linear elastic fracture mechanics [11]. Detail review of these methods can be found in [12], each attempt to simplify the complex behavior of fatigue in notched components to a few geometric and characteristic material constants. However, these approaches suffer from some fundamental drawbacks. Among these drawbacks is that the fatigue notch factors are obtained through time consuming and costly experiments. Moreover, the relationship of microstructure to Kf, using these constants has proven difficult to establish. Recently, Owolabi et al. [14] have established a probabilistic framework based on weakest link theory and extreme-value statistics which incorporates information regarding the peak stress and stress gradient relative to microstructure length scales within a well defined fatigue damage process zone around the notch root. This paper combines the developed probabilistic framework with other existing probabilistic formulations that consider the size distribution and different competing damage mechanisms for aero-engine materials. 2. Material Systems The alloy used for this study is a dual-phase titanium alloy, Ti-6Al-4V. Ti-Al alloys offer a range of properties such as high strength and fracture toughness at low temperatures to high strength and creep resistance at elevated temperatures. These wide ranges of properties have led to extensive use of Ti-Al
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