13th International Conference on Fracture (ICF13) June 16–21, 2013, Beijing, China (σe) to failure [8]. As mentioned above, in developing a statistical framework for the Kitagawa diagram, the limit state function used for reliability calculation is based on the mathematical formulation developed by El Haddad [8]. The limit state function defines the region in the stress-crack length space where the onset of crack propagation occurs for a nucleated defect, after which a flaw in HCF is expected to rapidly grow to a detectable length. The El-Haddad formulation intrinsically considers the change in ΔKth for cracks shorter than a0, and elegantly describes this change in limiting condition by a simple mathematical formulation: ∆ ߪ ൌ∆ ܭ ௧/ሺܻ ሺܽ ܽ ሻඥ ߨ ሺܽ ܽ ሻ ሻ (1) Although ΔKth is nominally independent of crack length, at small crack sizes this function tends to a limit given by the fatigue endurance stress. A statistical framework was initially developed for the Kitagawa diagram to consider statistical variability of stress and crack lengths; the extended framework allows including variability in any of the parameters (ΔKth, a, Δσ,…), upon consideration of their relative interdependencies [11], as shown in Figure 2. The limit state is defined as the threshold of Kitagawa diagram in combination with El Haddad’s correction which differentiates the nonpropagating from propagating crack. The limit state function for the fatigue framework developed can be written as follows: ݃ ሺܺ ሻி௧௨ ൌΔ ߪ െ ∆ ටగ൫ାబ ಷೌ ೠ൯൫ାబ ಷೌ ೠ൯ (2) The criteria for crack propagation is defined as g(X)<0 with a probability of crack growth: ܲ .. ൌ݂ ሺ௫ሻஸ ሺ ݔ ሻ݀ ݔ (3) and reliability is expressed as R=1-Pc.p. The failure diagram for corrosion is developed along the lines of the modified Kitagawa-Takahashi diagram for fatigue, as described elsewhere [3, 10, 12]. For SCC, by considering that in aggressive environment the material will be exposed to different concentrations of chemicals/ions involved in the corrosion damaging process, a limiting stress condition dependent upon the concentration level can be found. At concentration C, for example, the limiting threshold stress for crack propagation and failure of a smooth specimen, σth, forms a limiting condition in the SCC 10 00 00 01 1 10 100 1000 10000 100000 SCC Pure Fatigue e 1 2 Corrosion Fatigue Th ISCC Th Th_CF e_CF , Stress a, Crack Length Figure 3: developed framework for EAC failure diagram.
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