PSI - Issue 28

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Behzad V. Farahani et al. / Procedia Structural Integrity 28 (2020) 226–233 Behzad V. Farahani et al / Structural Integrity Procedia 00 (2020) 000–000

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In the literature, it is feasible to find more works focusing on the fatigue and fracture characterization, including SIF determination, through stress field analysis at the crack tip, c.f. Mode I fatigue testing and then development to the mixed mode case by Tomlinson et al. (Tomlinson and Olden 1999); Dulieu-Barton (Dulieu-Barton 1999) formulated essential mathematical equations to evaluate the SIF range related to the temperature change for isotropic homogenous materials under plane stress state; Fatigue damage assessment (Emery and Dulieu-Barton 2010); SIF calculation for orthotropic composites by (He and Rowlands 2004); CCD analysis of crack propagation in aluminium friction stir welded joints conducted by (Cavaliere et al. 2009). 4. Computational Methods In the early age of the fracture mechanics, two numerical techniques have been applied to the solution of cracked problems consisting of FEM and Boundary Element Methods (BEM). Nevertheless, these methods show some substantial disadvantages dealing with the cracked structures. Jia et al. (Jia, Shippy, and Rizzo 1988) conducted a research on the 2D SIF determination with the BEM for several cracked components. They considered infinite plates with singular, mid-point, traction shape functions at crack tips to assess the SIF under mode I and II loading states. Afterward, Dong et al. (Dong, Wang, and Wang 1997) investigated on the SIF calculation of the interfacial cracks relying on the quarter-point BEM and thus essential formulae associated with the displacement and traction nodal values were established. Furthermore, Moreira et al. (Moreira, Pastrama, and de Castro 2009) conducted a research on a stiffened cracked plate to acquire the 3D SIF. Ayatollahi et al. (Ayatollahi, Razavi, and Yahya 2015) numerically studied the mixed mode fatigue crack initiation and growth in an AA6061-T651 CT specimen repaired by stop hole technique. Meshless methods (Farahani, Belinha, et al. 2018; Farahani, Belinha, et al. 2019) have been an innovative topic and a trend in the computational field in a variety of solid and fracture problems. Compared with conventional computational approaches, such as the FEM and BEM, meshless methods follow a local approximation combined with a flexible domain discretization. In these advanced discretization techniques, the nodes do not form a mesh, since there is no previous relation between them. Therefore, meshless method possesses some benefits to solve demanding problems in fracture and damage mechanics particularly where the computational efforts are considered. As an illustration, a comprehensive meshless methods study to analyze the LEFM problem was proposed by (Rao and Rahman 2000). It was shown that the crack propagation could be significantly simplified since remeshing is not required unlike the FE study. Considering the mixed mode loading conditions, the meshless method results agreed well with the FE and experimental solution showing the great success of the forgoing approach. Later on, the foregoing authors extended their methodology, based on the Galerkin meshless method, to evaluate the stress intensity factor rate on several linear structures in the presence of a single crack (Rao and Rahman 2002). In addition, they have succeeded to reproduce the first-order derivative of the stress intensity factor in terms of the crack size for mode I and II loading conditions. Good agreements were accomplished for the meshless method results compared to the FE and finite difference method. In the literature, there exist more works dealing with the numerical analysis of fracture mechanics c.f. BEM: (Aliabadi and Wen 2010); referring to Fig. 1, Meshless Methods: [(Farahani, Tavares, et al. 2018; Farahani, Tavares, Moreira, et al. 2017; Mehri Sofiani, V. Farahani, and Belinha 2019; Raposo et al. 2019)]; Coupled numerical method on fracture mechanics to determine mode I and mode II SIFs (Rao and Rahman 2001). 5. Novel Analytical Solution based on the Stress Dead-zone Concept Although there are several exact and analytical solutions on SIF which can be found in the literature, there is a methodology that links the classic mechanic to the contemporary fracture mechanics based on the compliance function. Following this, the authors are dealing with the SIF determination through the compliance function implemented on the stress dead-zone notation. In this regards, Farahani et al. (Farahani, de Melo, da Silva Tavares, et al. 2020) proposed a novel analytical solution on mode I SIF for finite plates including slant notches respecting an orientation to the loading direction defined as . A set of equations was constituted relying on the compliance function together with the stress dead-zone concept and the LEFM theory. According to the stress dead-zone hypothesis, the