PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 920–927 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction This work describes a hybrid experimental/numerical approach for Stress Intensity Factor, SIF, calculation for a cracked compact tension (CT) specimen in the presence of a uniaxial tensile fatigue loading. The experimental data was analyzed using a 3D full-filed optical technique, Digital Image Correlation (DIC). The material, geometrical and mechanical characteristics were fully considered. Generally, to study crack growth and evaluate the remaining life of a certain structural component, rigorous numerical/experimental analyses are performed to evaluate SIFs. The ability to tolerate a substantial amount of damage is a demand for contemporary structures, hence it has become increasingly important to enhance methodologies to anticipate failure in fatigue damaged components. The fracture mechanics theory in conjunction with crack growth laws, i.e. Paris’ law, is commonly employed to analyze and predict crack growth and fracture behavior of structural components. To evaluate the SIF, determining the stress data using optical techniques, new numerical techniques were developed in recent years, for DIC method, see e.g. [(McNeill et al. 1987), (Tavares et al. 2015)]; for thermoelastic stress analysis (TSA), see e.g. (B. V. Farahani et al. 2016). Using the experimental data in conjunction with an overdeterministic approach (Pastrama et al. 2008) , the SIF is experimentally determined, and a computational verification was conducted. Sanford et al. (Sanford & Dally 1979) used this overdetermined approach in fracture mechanics to process photoelastic data in experimental SIFs evaluation. When compared with other procedures, the overdeterministic approach has the advantage of using an unlimited number of data points. As a result, errors can be minimized and the accuracy of calculations increased. Numerically, in the early age of the fracture mechanics, two numerical techniques have been applied to the solution of cracked problems consisting of Finite Element Method (FEM) with remeshing and Boundary Element Methods (BEM). Nevertheless, these approaches possessed some significant disadvantages dealing with the cracked structures. For instance, in FEM, it is cumbersome to automatically remesh finite elements. In the same way, remeshing on a large part associated with the finite elements are restricted in BEM analyses (Belytschko, Gu, et al. 1994). Later on, an advanced discretization technique, the Element Free Galerkin (EFG), has been adopted by Belytschko et al. (Belytschko, Lu Y, et al. 1994) and Lu et al. (Lu et al. 1994) to solve elastic problems. The main advantage of this approach is the fact that it requires only a set of nodes to construct the discrete problem domain. An extensive computational study of the cracked structures solved by EFG methods was performed by Belytschko et al. (Belytschko, Gu, et al. 1994). The SIF calculation for intricate crack configurations in finite plates generally presents significant difficulties. Thus, Byskov (Byskov 1970) proposed a comprehensive numerical FEM to resolve such mentioned problems by focusing on specific cracked elements, in which the stiffness matrix is associated with the crack elements. In 1976, Hillerborg et al. (Hillerborg et al. 1976) focused on the crack formation analysis in concrete by fracture mechanics theory combined with FEM. Moreover, a new technique has been proposed by Belytschko et al. (Belytschko & Black 1999) to analyse the 2D cracked problems within FEM, in which a minimal remeshing was required. After that, a recent approach was established by Moës et al. (Moës et al. 1999) where a Haar function was applied to evaluate the crack growth. So, this technique permits the whole crack to be represented independently of the mesh. Likewise, Meshless methods have been a futuristic topic and a trend in the computational field in a variety of science and engineering problems. Comparing with conventional computational methods, such as the FEM and the 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. The 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 study on meshless methods to analyse the linear elastic fractured problem was proposed in 2000 by Rao et al. (Rao & Rahman 2000). It was shown that the crack propagation could be significantly simplified since remeshing is not required, in opposition to the FE analysis. 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 & 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. Then, a coupled numerical method on fracture mechanics was presented by the same authors in