13th International Conference on Fracture (ICF13) June 16–21, 2013, Beijing, China predominantly subjected to HCF during the component lifetime and with limited or no possibilities of secondary load paths. The difficulty in characterizing the long life fatigue region interferes with the calculation of component retirement time, and the difficulties in crack growth predictions highly impacts the inspection intervals spacing [5]. The Kitagawa diagram, as modified by El Haddad to address crack growth threshold for short cracks (Figure 1), has been shown to be a powerful framework for the rationalization of initiation vs propagation of subcritical defects in metals and structural materials [7-10]. El Haddad introduced the correction factor a0 into the Kitagawa diagram formulation, which can be interpreted as a subcritical defect size above which the long crack growth threshold holds. By dividing the stress-crack length space into two main areas, one where subcritical defects or crack are not expected to grow, and one where both fatigue and LEFM methodologies predict defects or cracks to grow in fatigue, the Kitagawa diagram can be used as a framework for the investigation of defect growth in HCF from the subcritical level to a detectable size level [3]. A statistical framework for the Kitagawa-Takahashi diagram in fatigue is here developed, with the goal of determining the likelihood that a nucleated defect propagates when subjected to a stress at a specific structure or component location, given a material behavior defined in terms of fatigue endurance, σe, and crack growth stress intensity threshold, ΔKth. Additionally, a failure diagram in the form of a modified Kitagawa diagram for EAC is also developed by considering the corrosion fatigue (CF) and stress corrosion cracking (SCC) behavior of the material. The goal of this framework is to address whether a nucleated defect is likely to grow by CF by considering the concomitant SCC damage phenomena. The two frameworks are described in Section 2. Probabilistic methods such as first order reliability method (FORM), second order reliability method (SORM) and the Monte Carlo simulation (MCS) can be employed in conjunction with fatigue and fracture mechanics to estimate the probability of the growth of a critical/propagating defect [11]. The reliability methods as used in the developed frameworks are described in Section 3. The developed framework for fatigue is validated with available experimental data and finally an application example to HCF subcritical crack propagation is described. 2. Developed Framework in Fatigue and Environmentally Assisted Cracking The Kitagawa diagram was introduced by Kitagawa and Takahashi [7] showing the transition as crack-size decreases from LEFM controlled growth (K), to stress controlled behavior as the fatigue limit () is approached. The Kitagawa diagram conveys two different thresholds: the minimum threshold stress intensity range for crack growth (ΔKth) for a fracture mechanics specimen, and the endurance limit of a smooth specimen, that characterizes the minimum stress amplitude Figure 2: developed stochastic framework for the KitagawaTakahashi diagram.
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