PSI - Issue 52

J.C. Wen et al. / Procedia Structural Integrity 52 (2024) 625–646 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Developing new materials with the goal of improving structural performance has been a challenge faced by researchers over the past few decades. Functionally graded materials, as a special type of composite materials first proposed in the 1980s, have the advantage of combining two or more materials with different properties without being affected by different material properties compared with traditional composite materials. Its properties can not only continuously change, but also eliminate the influence of the interface on the material. Due to the complexity of the preparation process and the particularity of the usage environment, cracks often produce during the processing in FGMs, which increases the possibility of material damage. The fracture analysis for FGMs has always been the focus of many researchers (Wang, 2016; Wen, 2014; Wen et al., 2014; Dolbow, 2002; Kim, 2002). Erdogan (1995) introduced the concept of fracture mechanics in inhomogeneous materials and based on energy balance theory, using FGM to reduce crack driving force. Lal (2019) combines the Extended Finite Element Method (XFEM) and the Second Order Perturbation Technique (SOPT), and uses the interaction integral to calculate the mixed mode Stress intensity factor through partition of unity method. Noda (2008) established a piecewise exponential model method, and used this method to study the fracture problem of FGMs with arbitrary properties. The real properties of FGMs are somewhat arbitrary. It is generally difficult to obtain the analytical expression of the temperature and stress fields in materials, and the material properties can only be assumed to be in a specific functional form. A challenging issue with the failure of these materials is the failure caused by fracture. However, the singular stress field at the crack tip region favors the driving force to initiate fracture. It has been recognized that the stress intensity factor at the crack tip is an important parameter that determines the safety of cracked components. The main task of linear fracture mechanics is to determine the SIFs of the continuous singular field near the crack tip, and various methods have been proposed to obtain the SIFs in FGM components under static or dynamic loads. There are two approaches to obtain SIFs, one is through the singularity of the stress at the crack tip (Aliabadi, 1991), but this method has limitations in some specific cases. Another one is to evaluate the SIFs by the entire stress field of the crack tip, rather than the stress field adjacent to the crack tip, such as the J-integral method (Walters, 2004; Wen, 2017) and variational method (Wen, 2019), both of these methods use contour integration. For functionally graded materials, contour integration also considers domain integration, which does not require precise capture of the details of singular fields in vicinity of the crack tip. Specifically, this method eliminates fine grids near the crack tip and singular elements incident at the crack tip. Rooke (1976) and Cartwright collected several hundred analytical and numerical solutions in A Compendium of Stress Intensity Factors in 1976 first time, which has been considered as the most popular handbook and database in the application of fracture mechanics. As the analytical solutions of the stress intensity factor are very rear in literature and publications, advanced numerical methods are necessary. Nowadays, several numerical methods have been well developed in analyzing fracture mechanics, which include the finite element method (FEM) (Zienkiewicz, 1971), the boundary element method (BEM) (Aliabadi, 2002). Although the FEM has made some achievements in the research field of crack problems in functionally graded materials (Wang et al., 2006; Paulino, 2006), the characterization of the stress singularity at the crack tip is still a difficult point because of the inhomogeneity of the material. The FEM obtains the stress intensity factor that meets the accuracy requirements by refining the mesh. The BEM requires fundamental solutions and is not applicable to fracture problems with continuously non homogenous media. Ayhan (2007) used the 3D enriched finite element method to calculate the stress intensity factors of Mode I for 3-D edge cracks in a FGM strip and surface cracks in a finite thickness FGM plates. The meshless method has attracted much attention in recent years, as it can avoid the influence of mesh division on the analysis of crack problems, and has certain advantages in the static and dynamic crack analysis of functionally graded materials. Sladek (2010) combined the local integral equation method and the moving least squares method to propose a local Petrov-Galerkin method to solve the functional gradient piezoelectric material. Zhang (2011) used the meshless boundary element method and radial integration method to solve the elastic static analysis of FGM for 3-D cracks. Wen (2020, 2021, 2021) and his collaborators proposed a hybrid meshless/displacement discontinuity method (MDDM) for solving problems in fracture mechanics of FGMs, which made the BEM successfully applied to fracture problems of non-homogenous materials. Tanaka (2023) proposed the extended wavelet Galerkin method (XWGM), which studied the SIF of the mixed mode of the FGM cracked plate under static and dynamic loads. Recently, the Finite Block Method (FBM) proposed by Wen et al (2014, 2014, 2015, 2016) has been applied to fracture mechanics,