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Fracture analysis of functionally graded materials based on extended finite element method

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Fracture Analysis of Functionally Graded Materials Based on Extended Finite Element Method by Linlin SUN Thesis Supervisor: Associate Professor Kou Kun Pang Structural and Geotechnical Engineering ABSTRACT As a kind of typical non-homogeneous composite materials, functionally graded materials (FGMs( are designed to meet the harsh requirements of many important industrial fields. Since there are many conditional limitations and expensive cost for experimental method, numerical methods have become an effective way to explore the fracture behaviors for diversified conditions. The present article uses a new numerical calculation method, namely the extended finite element method, to investigate the fracture behavior of FG plates. The extended finite element method (XFEM) is based on the concept of partition of unity method and within standard finite element framework. The enrichment functions typically consist of the near-tip asymptotic functions which represent the jump in displacement across the crack surfaces. So, the crack surface can be presented and it is not associated with finite element model and that is why XFEM can simulate crack propagation conveniently. In this thesis, both homogenous plate and functionally graded plate are modeled and II analyzed. The main studied fracture parameter is the stress intensity factor. The propagation paths are explored as well. All cases of models are subjected to uniform tension loadings on the top and bottom surface. For homogenous plates, the stress intensity factors are analyzed by considering the following main parameters: the integral domain factor (R/d) varying from 1.0 to 5.0, the initial crack length (a) varying from 0.1 to 0.5, and the crack initial angle varying from 0° to 75°. The relationships between stress intensity factors and the crack characteristics such as initial crack length and the initial angle have been established based on XFEM. The precision of XFEM is verified by comparing the analytical solutions at the same time. For functionally graded plate, the stress intensity factors are analyzed by considering the material gradient ratio (E2/E1) varying from 0.2 to 10.0 and initial inclined angle varying from 120° to 165°. The relationships between them are also established by using XFEM. Besides the static analysis, the quasi-static crack propagation paths are analyzed with XFEM as well. The connection between the propagation direction and crack initial angle is defined in the case of homogenous plate, following which, the relevancies between the propagation initiation angle and configuration parameters such as the material gradient ratio and initial crack angle based on the maximum energy release rate criterion are also proposed in the case of functionally graded plate. The analysis results and all the problems which were overcome during the research procedure have a certain reference value to the actual project and subsequent researches.

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Sun, Lin Lin


Faculty of Science and Technology


Department of Civil and Environmental Engineering




Functionally gradient materials

Composite materials


Kou, Kun Pang

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