PSI - Issue 35

M. Faruk Yaren et al. / Procedia Structural Integrity 35 (2022) 98–105 Yaren M. F. et al / Structural Integrity Procedia 00 (2021) 000 – 000

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In the Wheeler model, if the crack tip plastic zone reaches the limits of the plastic region created by the overload, the crack retardation effect is terminated. Sheu et al. (2001) proposed a model, in which the crack growth retardation effect lasts longer compared to the Wheeler model. They proposed that the retardation effect is active while the active plastic zone goes out of the plastic zone generated by overload, and they calculated the Wheeler retardation parameter with the effective plastic zone created by overload. Since the Wheeler model is based on the equation of Paris-Erdogan, the stress ratio is not taken into account in the crack propagation life calculation. Xiaoping H. et al. (2008) used the equivalent SIF to include the stress ratio in their calculations as a modification to Wheeler ’s model. ΔK eq0 in Eq. () is the SIF for zero stress ratio. Crack growth curves obtained under different stress ratios are converted to R = 0 by using Equations (4) and (5). The term β is empirical, and by changing its value, the crack growth curves obtained under different stress ratios are gathered in da/dN vs. (MR. ΔK ) graph. M P identifies the interaction effect between load profiles, and with the help of M P, this model realizes the determination of the second overload effect where the plastic zone of the first overload is still active. = [(∆ 0 ) − (∆ ℎ0 ) ] (3) ∆ 0 = ∆ (4) = { (1 − ) − 1 − 5 ≤ < 0 (1 − ) − 0 ≤ < 0.5 (1.05 − 1.4 + 0.6 2 ) − 0.5 ≤ < 1 (5) Yuen and Taheri (2006) proposed another modification to Wheeler ’s model, by taking into account the acceleration of the crack growth rate right after the overload, the retardation, the interaction between the loading profiles and the yielding in the critical cross-section. In addition to the Wheeler parameter, this model contains three different parameters as seen in Eq. 6. Ø D is the delay parameter for crack growth and Ø I is the interaction parameter related to the loading profiles. Details of this model and the calculation of the terms in the Eq. 6 can be seen in previous studies Yuen and Taheri (2006) and in (Yaren 2021). = ∅ ∅ ∅ [ (∆ ) ] (6) 2.2. Willenborg Model and Generalized Willenborg Model The Willenborg model is another widespread cycle by cycle yield zone model in the literature. The crack propagation calculation is based on the Forman equation, in which the stress ratio is included. Since the retardation of the crack growth rate is defined as a function of the SIF, Wheeler exponent-like paramater is not required in this model. K r , the residual SIF is the main parameter to determine the crack retardation. While the plastic zone size at the current cycle is smaller than the plastic zone size at the overload cycles K r is calculated using Eq. 10, otherwise, it is equal to zero. If K r is greater than K min,max the effective stress intensity factor K min,max,eff becomes zero. (K max ) OL is the SIF at the overload cycle . Δa is the crack growth distance under the retardation effect. In this model, if the overload ratio is smaller than or equals 2.0. = (∆ ) (1 − ) − ∆ (7)