13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Three dimensional finite element study of crack in functionally graded material under thermal loading Parya Aghasafari1*, Vahid Arabzadeh1,Ali Daraei1 ,Mahmoud Salimi2 1 Department of Mechanical Engineering, IUT University, 8415683111, Iran 1 International Petro-Structure Co, 8015673611, Iran 1 Department of Physics, UI University, 8174673441, Iran 2 Faculty of mech.Eng dept, Institute of IUT, 8415683111, Iran * Corresponding author: p.aghasafari@me.iut.ac.ir Abstract This article focused on three-dimensional analyses of a functionally graded material plate which contains a semi-elliptical surface crack and subjected to transient thermal loading. Strain singularity around the crack front is simulated using collapsed 20 – node quarter – point brick elements. Three –dimensional displacement correlation technique is utilized to extract the mixed mode stress intensity factors around the crack front for different inclination angles of the semi-elliptic surface crack. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the applied three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs. Keywords: FGM, semi–elliptical inclined surface crack, displacement correlation technique, mixed modes stress intensity factors, finite element method 1. Introduction Numerical simulations of crack initiation, propagation and branching are a computationally intensive process. Traditional finite element packages simulate the crack propagation problem either by using singularity elements or by using line spring elements with built-in fracture criteria. Recently, a popular method to do this task is the cohesive surface modeling of the fracture zone. Following the work of Baren blatt[2], Dugdale [3] ,and Willis [4], many researchers have addressed the issue to this approach. Nee-dleman[5] provided a framework for these parathion process starting from initial de-bonding in the cohesive zone. Larsson [6] used this approach to simulate crack growth in brittle materials, while Xia and Shih[7] simulated fracture inductile material sunder static loading. Camacho and Ortiz[8] have used cohesive surface modeling to study material fragmentation, while Xu and Needleman[9] used it to study dynamic crack tip in stabilities by allowing cracks to formal on element boundaries. The method by Xu and Needleman involves introducing special boundary elements between regular elements, where the boundary Elements obey a cohesive law. Three factors influence the cohesive law behavior, namely the cohesive Strength, the critical separation at cohesive strength and the fracture energy in the separation process. These Models obviate the need for a separate external fracture criterion in fracture simulations. The effects of Plasticity inside volumetric elements have been investigated using the embedded-process-zone cohesive Fracture model by Tvergaard and Hucthinson[10,11]. Gullerud and Dodds [12] have used 3-D cohesive Elements for modeling ductile crack growth. More recently Foulketal.[13] presented a procedure for Implementing the cohesive zone modeling a 3-D finite
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