PSI - Issue 16

Roman Chepil et al. / Procedia Structural Integrity 16 (2019) 211–217 Roman Chepil, Olena Stankevych, Orest Ostash, Bohdan Klym / Structural Integrity Procedia 00 (2019) 000 – 000

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nominal stress. Local stresses are determined by fatigue stress concentration factor K f , which can be estimated by experiment or known analytical dependencies ( Socie et al. (1979)) . Coefficient K f depends on geometry of a specimen and a notch, mode of loading, structure, and strength of the material ( Schijve (2009)) , loading stress range ( Socie et al. (1979)) . Therefore, the computational methods for K f factor determination are developed. The well-known models of Neuber, Peterson, Pluvinage and others ( Yu et al. (1991), DuQuesnay et al. (1998), Qylafku et al. (1999) ) are among them, but they often give the results which differ from the experimentally established ( Yu et al. (1991) ). The question is how the data of the smooth specimen endurance are a reference point for notched specimens. Significant variation in the test results of smooth specimens especially at high-cycle fatigue is known. Thus, for reliable fatigue life prediction of structural elements with stress concentrators the base materials characteristics established by means of notched and cracked specimens should be used. This deficiency is absent in fracture mechanics approach ( Socie et al. (1979), Vazquez et al. (2010)) where periods N i and N p are calculated separately, and durability N f = N i + N p for the given conditions is predicted. But a problem of initial macrocrack criteria exists (length of a 0 , a i , l 0 , l i , etc.) when the linear fracture mechanics approaches can be used and the transition from macrocrack initiation to propagation stage can be defined. It is shown experimentally (Ostash et al. (1999)) that the size of the initial fatigue macrocrack is significantly larger than the structural parameter of the material but smaller than the plastic zone size in the vicinity of the stress concentrator. Therefore, the concept of "fatigue process zone" (FPZ) was introduced within which the initial damages of material due to intensive reverse microplastic strain are localized and the initial macrocrack is formed Qylafku et al. (1998), (Ostash et al. (1999), Ostash and Panasyuk (2001), Kryzak et al. (2017)). Taking into account this special feature, the structural parameter а 0 , proposed by El Haddad et al. (1979) at the macrocrack initiation stage and the elementary block size  * (Noroozi et al. (2005)) at the macrocrack growth stage are used ( Socie et al. (1979), Vazquez et al. (2010)). However, these parameters do not provide any physical content and are calculated on the basis of the materials mechanical characteristics. There are other models for predicting fatigue lifetime of the notched components based on Theory of Critical Distances ( Taylor et al. (1999, 2000), Susmel (2008) ), also known as Point Method and Line Method. The main empirical parameter here is the critical distance L determined as L = a 0 from El Haddad equation (El Haddad et al. (1979)). It is shown (Ostash et al. (2010)) that some problem exists when notched specimens fatigue life at high ( R = 0.5) stress ratio is estimated by such an approach. Its modification does not significantly improve prediction of fatigue life of samples with stress concentrators, and the difference between the predicted and experimental values of N f differs also by almost 5 times ( Hu et al. (2019) ). The prediction accuracy of approaches based on the results of smooth specimen is satisfactory for specimens with blunt notches, but insufficient for specimens with sharp notches when the estimated values of N f versus experimentally established may differ in 3-6 times (Vazquez et al. (2010), Kryzak et. al. (2017)). 2. A unified model of fatigue fracture The model of fatigue fracture, which considers the entire process as the fatigue macrocrack initiation and growth from a unified position (Ostash et al. (1999, 2003, 2006)), is promising for prediction the lifetime N f of notched structural components. A crack is modeled as a sharp notch and its propagation is the repeated acts of re-initiation. This model is based on the material parameter d * , which is determined by a linear dimension of FPZ in the vicinity of a notch (Fig. 1) or a macrocrack tip, due to the yield strength anomaly of below-surface layers, strain hardening coefficient and microstructure of a material (Ostash et al. (1999, 2003)). As a result, the fatigue (effective) stress concentration factor K f is determined by the parameter d * (Ostash and Panasyuk (2001)) via   * * 1 ( 1) 1 / f t K K d d      , (1)

* y  near the notch tip (Ostash et al. (1999, 2006)) may be written as

and maximum local stress range