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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returns to its pre-overload levels. This is called retardation of the fatigue crack growth. Wheeler (1972) and Willenborg et al. (1971) are the most common models in the literature to calculate crack growth rate under variable amplitude loading. While calculating the crack propagation rate with the Wheeler model, the Paris and Erdogan (1963) equation is used with an additional retardation parameter. The Wheeler exponent required for the calculation of the Wheeler retardation parameter is found empirically. Sheu et. al. (2001) proposed a modification on the plastic zone to calculate the Wheeler retardation parameter as an effective plastic zone created by overload. Therefore, the retardation effect in their model lasts longer compared to the Wheeler model. Other modifications of Wheeler model used in this study aims to model interaction effects between multiple overloads. Xiaoping H. et al. (2008) calculated the retardation effect as a piecewise function of stress ratio and also they identified it as a parameter of interaction effect. Yuen and Taheri (2006) added a new term to the Wheeler model to calculate the effects of consecutive overloads. The Willenborg model substitutes equivalent stress intensity factor in the Forman (1972) crack propagation equation. Thus, there is no need for any empirical exponents. In addition, the stress ratio is also taken into account by using the Forman crack propagation equation. Details of the mentioned fatigue crack growth models can be seen in previous study (Yaren et al. 2019) and in (Yaren 2021). Block loading and the interaction of blocks are also studied in the literature for variable amplitude loading. Porter (1972) experimentally investigated several variable amplitude load cases for a two-dimensional crack in a thin plate made of 7075 aluminum alloy. One of these examined cases is the effect of the number of block overload cycles on the crack propagation life. It was shown in this specified case that, the crack propagation life may increase or decrease depending on the effect of block overload size. In this study, the effect of block overload size for two-dimensional crack propagation under plane strain conditions was experimentally investigated. Life prediction studies were also performed using models of Wheeler, Willenborg and their modifications under the same block loading conditions applied in the experiments. Details of the experimental and computational part of the study will be explained in the following sections. 2. Numerical Study The models of Wheeler (1972), Willenborg (1971) and their modifications were used in this study. In this section, these models as they exist in the literature will be explained briefly. 2.1. Wheeler Model and its modifications It is one of the most common models in the literature for crack propagation under variable amplitude loading conditions. Crack propagation under a single overload load was the focus of Wheeler ’s (1972) study. This model determines the crack propagation behavior by comparing the size of the plastic zone at the crack tip generated by load cycles. When an overload is applied, a larger plastic region is generated at the crack tip than the plastic zone size generated by previous load cycles. As long as the plastic zone formed by the load cycles after the overload does not exceed the plastic zone created by the overload, the retardation effect is observed. As seen in Eq. 1, Wheeler added a retardation parameter to Paris and Erdogan (1963) crack propagation equation to determine the retardation effect. In Eq. 1, C and n are Paris-Erdogan constants. Ø R is the retardation parameter related to plastic zone size. Eq. 2 determines the crack retardation parameter. The summation of current crack size ( ɑ ) and diameter of the current plastic zone (R y ) are compared with crack size at overload ( ɑ p ). The term y in Eq.2 is Wheeler exponent, which depends on the material and is determined empirically. = ∅ ( ∆ ) ü (1) ∅ = { ( − ) ; ( + ) < 1 ( + ) ≥ (2)