13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Application of Weakest Link Probabilistic Framework for Fatigue Notch Factor to Turbine Engine Materials Oluwamayowa A. Okeyoyin1,*, Gbadebo M. Owolabi1 1 Department of Mechanical Engineering, Howard University, Washington DC 20059, USA * Corresponding author: oluwamayowa.okeyoy@bison.howard.edu Abstract This paper is concerned with the extension of a recently developed probabilistic framework based on Weibull’s weakest link and extreme-value statistics to aero-engine materials like titanium alloy and nickel-base super alloys using simulation strategies that capture both the essence of notch root stress gradient and the complexity of realistic microstructures. In this paper, notch size effects and notch root inelastic behavior are combined with probability distributions of microscale stress-strain gradient and small crack initiation to inform minimum life design methods. A new approach which can be applied using crystal plasticity finite element or closed-form solution is also proposed as a more robust approach for determining fatigue notch factor than the existing classical methods. The fatigue notch factors predicted using the new framework are in good agreements with experimental results obtained from literature for notched titanium alloy specimens subjected to uniaxial cyclic loads with various stress ratio. Keywords: probabilistic mesomechanics, weakest link, microstructure-sensitive, fatigue notch factor, fatigue indicator parameters. 1. Introduction Titanium alloy is widely used in aero engine components. The fatigue resistance of aero-engine components made from this material can be drastically reduced by the presence of small notches on the components formed from the ingestion of foreign objects causing foreign object damage (FOD) [1 - 2]. To account for the effects of FOD on the fatigue strength of these materials, the damage are usually modeled as notches with a certain depth and notch root radius [1- 2]. The severity of these notches in materials is characterized by the elastic stress concentration factor, kt which is the ratio of peak (maximum) local stress at the notch root to the remotely applied stress, S as shown in Figure 1. σ = peak tk S (1) kt is dimensionless and a compilation of its values for different notch geometries and loading modes can be found in Peterson’s book [3]. However, kt under-estimate fatigue life and several arguments have been attributed to this observation. The fatigue life of notched component is not only dependent on the peak stress as predicted by kt, but also on the average stress that acts over a finite damage process zone. Consequently, fatigue life prediction methods based on kt typically do not consider stress gradients which have been shown to influence the fatigue life of complex notched components [4 - 5]. Thus, the actual reduction factor on long fatigue lives is typically represented by the concept of fatigue notch factor, otherwise known as the fatigue strength reduction factor, kf.
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