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:Nickel base superalloy Non-metallic inclusions Probabilistic framework Fatigue notch factor Crystal plasticity a b s t r a c t Nickel base superalloys are used in hot sections of gas turbine engines due to its high strength and good creep, fatigue, and corrosion resistance at high temperature. In this paper, a new probabilistic approach based on weakest-link theory that accounts for the effects of the microstructure, notch size and notch acuity is described and applied to nickel base superalloy to determine the fatigue notch factor, notch sensitivity index and the probability of forming microstructurally small crack from the notch root. The simulation results obtained from this framework are compared with experimental results and results obtained using existing classical methods for notched polycrystalline nickel base superalloys for the different notch root radii and acuities considered.

Titanium alloy is used for airframe components and compressor blades application because of its high strength and fracture toughness at low temperatures and high strength and creep resistance at elevated temperature. This paper extends a recently developed probabilistic mesomechaniccs based model to notched titanium alloy components using simulation strategies that capture both the essence of notch root stress gradient and the complexity of realistic microstructures. The notch size effects and notch root and inelastic behavior are combined with probability distributions of microscale stress 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 method for determining the fatigue notch factor than the existing classical methods. The fatigue notch factors predicted using the new probabilistic mesomechanics based model are in good agreements with experimental for notched titanium alloy specimens subjected to cyclic loads with various stress ratios.

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