PSI - Issue 28

Behzad V. Farahani et al. / Procedia Structural Integrity 28 (2020) 218–225 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2019) 000–000

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with a linear elastic constitutive behavior. Thus, the chief accomplishment of this theory is based on the linearity that makes it feasible to merge and validate theoretical, computational, and experimental analyses of fracture mechanics. The LEFM assumes the crack to propagate, once the strain energy release rate (SERR) at the crack tip reaches a critical value. An important fracture parameter, the Stress Intensity Factor (SIF or K ), describes the level of stress at the crack tip, while the fracture toughness is the critical value of SIF a material will withstand before fracture. The stresses near the crack tip increase in proportion to the SIF. Several researchers have already investigated the crack tip characterization by different methodologies (Di Cocco et al. 2014; Iacoviello et al. 2015; Iacoviello et al. 2013). Computationally, mode I SIFs were evaluated by the Finite Element Method (FEM) for cracked structures including Middle Tension (MT) specimens (He et al. 2018; Branco and Antunes 2008; Starvin, Ganesh, and Pandiyarajan 2017). Erdogan and Sih (Erdogan and Sih 1963) studied the crack extension in large plates submitted to general loading conditions in the plane stress case and in the transverse bending. They proposed an analytical solution to the mode I and mode II SIF on infinite plates containing a slant crack. Later on, Yau et al. (Yau, Wang, and Corten 1980) examined the mixed mode SIF on the two-dimensional (2D) isotropic solids following the conservation elasticity law. Therefore, the proposed reference solution on SIFs was adopted for cracks positioned in the centre, at the edge and emanating from a circular hole, oriented at an angle in respect to the loading direction in infinite plates. The analysis has been formulated using conservation integrals on two independent equilibrium states related to an elastic isotropic solid. Hedayati and Vahedi (Hedayati and Vahedi 2014) examined the SIF evaluation and the crack growth simulation on slant cracked plates made of AA6061-T651 aluminium alloy. Numerically, they implemented FEM and its extended version (XFEM) to characterize the SIF in the uniaxial tensile test condition. A comparison has been drawn between the obtained numerical results and the proposed analytical solution. Ismail et al. (Ismail et al. 2017; Ismail, Kamarudin, and Nor 2017; Ismail, Mohd Ghazali, and Muhd Nor 2017) carried out several research works on the slant-cracked plates to characterize the fracture parameters, SIFs. They numerically analysed a single edge crack oriented at an angle through FEM and the obtained results on the SIFs in terms of the crack length were compared to the experimental and analytical solution. Mahgoub et al. (Mahgoub, Deng, and Sutton 2003) performed the three-dimensional (3D) elastoplastic Finite Element Analysis (FEA) for Arcan 2024-T3 aluminium alloy specimens containing flat and slant cracks submitted to remote Mode I loading conditions. Although there exist several approaches to determine SIFs for distinct fracture models with various material behaviours, this study innovatively intends to propose an alternative analytical solution, which is based on the compliance function. Therefore, a new data reduction scheme is adopted to compute the SIF under mode I loading condition on slanted crack problems. The dead-zone is identified as a region adjacent to the mating surfaces of a central crack in an infinite/finite plate submitted to a uniformly unidirectional tensile stress. Griffith (Griffith 1920) stated this zone can be practically exempted from the stress state. Therefore, this zone, which is associated to a negligible contribution of internal stresses for the global deformation energy, could be discarded from the structural components. It contributes to a structural geometry simplification and thereby an opportunity to adapt simplified analysis on SIFs calculation. Regarding the slant cracked plates, the stress dead-zone notion has been already implemented together with the compliance function based on the SERR criterion and consequently an alternative analytical solution on the Mode I SIF was established in the former work by the authors (Farahani, de Melo, da Silva Tavares, et al. 2020). Due to the significance of the stress dead-zone, the geometrical characterisation of the dead-zone has been also evaluated in the formerly published paper. In addition, the stress dead-zone implication has been already validated for the central horizontal cracked MT specimens through FEM, DIC and meshless methods analysis (Farahani et al. 2019). In the literature, it can be found several studies dealing with the SIF determination using numerical analyses and experimental techniques, c.f. [(Farahani, Tavares, and Moreira 2016; Farahani, Tavares, Belinha, et al. 2017; Mehri Sofiani, V. Farahani, and Belinha 2019; Raposo et al. 2019; Farahani, de Melo, Tavares, et al. 2020)]. In this work, a finite plate (MT) containing a central slant crack with an orientation to the tensile loading direction was studied. The experimental data was captured and analysed by means of an optical contactless deformation measurement tool, the 3D Digital Image Correlation (DIC) (McCormick and Lord 2010). Numerically, the problem was solved using FEM formulation (Ferreira 2009) to acquire comparable results. Owing to the consideration of proposed new analytical formulation on SIF, this work aims at evaluation its robustness and soundness through addressing a practical example. Hence, the physical denotation of dead-zone is assessed in conformity to Griffith’s theory. Thus, � is calculated by experimental DIC, numerical FEM and the