PSI - Issue 13

Danilo D’ Angela et al. / Procedia Structural Integrity 13 (2018) 939–946 Danilo D’Angela and Marianna Ercolino / Structural Integrity Procedia 00 ( 2018) 000 – 000

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and Fuchs, 2001); such type of failure is often brittle and unexpected. Therefore, the risk related to the failure of metal structures under fatigue is significant (Reed et al., 1983). Efficient fatigue design can significantly reduce the risk of fatigue failure. Fatigue fracture behavior can be assessed by both experimental testing and numerical analysis. Several experimental testing campaigns investigated the fatigue performance of structural components supplying a deep understanding of the problem (Schijve, 2003). However, fatigue behavior should be still investigated (Stephens and Fuchs, 2001). In order to generalize the results of fatigue tests, too extensive experimental campaigns would be needed, which can be often time-consuming and economically expensive. Therefore, numerical studies have been developed by means of FE analysis in recent years (Lee et al., 2012). The recent development of both analytical approaches and software products allowed to simulate some complex phenomena such as the fatigue fracture in metal components (Belytschko and Black, 1999; Lee et al., 2012; Shi et al., 2010). However, the numerical simulation is still extremely challenging. Several parameters (e.g., temperature and mean stress) affect fatigue behavior (Li, 1999; Stephens and Fuchs, 2001), and advanced models often undergo convergence problems as well as they demand high computational time. The modelling is often based on user developed commercial software or expert programming (Khelil et al., 2013; Kim et al., 2015; Ural et al., 2009; Zhan et al., 2017). Moreover, the literature models are usually validated by only considering specific applications (Kim et al., 2015; Zhan et al., 2017) or by comparing the numerical results to theoretical/analytical solutions (Hedayati and Vahedi, 2014; London et al., 2015). In the present study, a simplified approach is proposed to simulate the fatigue fracture in plates by means of FE analysis. The adopted fatigue model and analysis methods are exhaustively described to facilitate the understanding of the model implementation as well as the outcomes. Direct cyclic analysis using Low-Cycle Fatigue (LCF) approach (Simulia, 2016) is performed in order to predict the fatigue crack growth of 7% Nickel steel compact tension (CT) specimens with an existing pre-crack surface. The cracking process is implemented by using the eXtended Finite Element Method (XFEM) (Belytschko and Black, 1999; Simulia, 2016). The Paris law (Paris and Erdogan, 1963) is adopted for the fatigue response of the material. The numerical results are compared to the analytical solution as well as they are validated by past experimental results (Kim et al., 2015). 1.1. Background: fracture and fatigue Fatigue is the phenomenon of localized structural damage within a material caused by fluctuating stress/strain, which can lead to the complete failure (ASTM International, 2013). Fatigue processes usually consist of three consecutive phases: Stage I or crack initiation, Stage II or crack propagation and Stage III or unstable fracture leading to failure (Baxter, 2007; Makkonen, 2009). There are three elementary crack opening modes (Fig. 1): Mode I is the crack opening mode; it involves the plane of maximum tension. Mode II is the sliding mode; it involves in-plane shearing. Mode III is a tearing mode; it involves anti-plane shear. Mode II and III usually occur along with Mode I , which controls the fracture.

Fig. 1. Fracture modes.

Griffith (1921) demonstrated that the product between the applied tensile stress and the square root of half crack length is constant in a tensile testing of brittle material pre-cracked plates. This allowed to define the strain energy r elease, called Griffith’s strain energy ( G ). Eq. 1 shows the theoretical formulation of G , where: σ is the externally applied stress, c is the half crack length and E’ is defined as a function of E and ν , i.e., the Young modulus and Poisson’s ratio, respec tively.