PSI - Issue 21

Mehmet F. Yaren et al. / Procedia Structural Integrity 21 (2019) 31–37 Yaren M. F. et al / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Fatigue crack growth life estimation is a very important aspect of fracture mechanics. Different equations have been proposed in the literature for estimation of crack propagation life; Paris and Erdogan (1963), Walker (1970), Forman (1972). Crack growth rate is identified as a function of stress intensity factor and material constants (C-n) by Paris and Erdogan (1963). The necessity of adding the stress ratio to Paris-Erdogan equation is discussed in literature and new equations are proposed by Forman (1972) and Walker (1970). These equations are used for life calculation under constant amplitude loading. Operating conditions for many engineering structures generally involve variable amplitude loads. Because of the load interaction effect, crack growth life calculation under variable amplitude loading is more complex. Because of plasticity at the crack tip, load sequence effects are important. During crack propagation, if an overload is applied, higher level of yielding and plastic zone size occurs at the crack tip. Due to the higher compressive residual stress at the crack tip following the overload, crack opening and growth rate decrease during the subsequent load cycles unti l this region is passed by the crack tip. This is called the retardation effect. It’s clear that plastic zone size determines the number of cycles to retardation. Wheeler (1972), added a retardation parameter to Paris-Erdogan equation. Wheeler model includes a shaping factor which is determined empirically. Another accepted crack retardation model is proposed by Willenborg (1971), which is based on Forman crack growth model. Crack retardation is a function of stress intensity factor and plastic zone size is related to the overload stress intensity factor. Therefore, an empirical factor is not necessary for Willenborg model. Modifications and details of these models are explained in Section 2. Crack growth under variable amplitude loading is classified in terms of three different loading types. The most basic one is the single overload, on which most retardation models are based. The second type of variable amplitude loading is named block loading, in which multiple cycles of loads are contained in different loading blocks. High-low high or the combination of these block loads are studied in the literature and load sequence effect is investigated. Many models are proposed to calculate crack growth rate under block loading, Gallegher (1974), Sheu et al. (1995), Yuen and Taheri (2006), Huang X. et al. (2008). Although it is the most common type of loading under practical service conditions, random spectrum loading is the most complex for modeling (third type). Cycle by cycle analyses or rain flow counting methods are widely used in literature to calculate crack growth life. In this paper, single overload and its retardation effect are studied experimentally. Crack growth retardation models are used to calculate crack growth rate. 7075-T6 Aluminum alloy is used in fatigue crack growth tests under mode-I loading. Crack growth rate for single overload is calculated by seven different models, which include Wheeler, Willenborg and their various modifications. 2. Background Theory In this section, overload and retardation mechanisms at the crack tip are discussed briefly. Widely used models, Wheeler and Willenborg are explained detail. Wheeler proposed the most basic model to calculate crack growth retardation due to overload. This model includes a retardation parameter which is related to plastic zone size around crack tip. Wheeler model compares the plastic zone size and decides whether crack growth is retarded. Larger plastic zone size is related to the overload level. After the overload, the crack is subjected to previous load levels and their plastic zone sizes will be smaller than the plastic zone size created by the overload. Therefore, due to the compressive residual stress in the larger plastic zone, crack growth will be retarded until this region is passed by the crack tip. The definition of plastic zone is given in Fig.1. Dark black region in Fig. 1 is plastic zone at cycles except overload cycle and its size is R y . The gray colored region is plastic zone in the overload cycle. 2.1. Wheeler Model