Study and Application of the Extended Finite Element Method to Crack Propagation of Porous Bioceramic

Abstract: In the preparation process of porous bio-ceramics, defect such as crack is easy to be introduced. If such a cracking material is loaded during the application process, stress concentration often appears in the crack tip, causing damage and failure of the material, and leading to a number of security issues. Therefore, studying the crack propagation of porous bioceramic has great significance on further improving the performance of porous ceramics, and ensuring the structural safety, and expanding applications.Extended finite element method (XFEM) is a new numerical method developed in recent years, under the conventional finite element framework, to solve the discontinuous problems particularly crack propagation. The principle is that using crack tip asymptotic displacement field function and jump function to strengthen the traditional finite element basis functions on the element nodes that are impacted by the crack area, so to consider the displacement discontinuities caused by the existence of crack. It inherits all the advantages of standard finite element, however, the mesh in extended finite element method is independent of the internal geometry and physical interfaces, such that the trouble of high density meshing and re-meshing in the discontinuous field can be overcome. This greatly simplifies the analysis of the crack propagation process.In this paper, the displacement field of the homogeneous body containing crack has been studied based on XFEM idea, and the chief contents are as follows:①Discussed in detail the establishment method of discontinuous displacement field; Research on how to describe and determine the location of crack by the level set method; Elements cut by crack will be divided into a number of sub-elements in order to ensure the integration accuracy; The specific methods and formulas to calculate the stress intensity factor using the displacement extrapolation method in XFEM is derived and given out in detail; Crack growth distance and direction is studied, and the maximum circumferential tensile stress theory is selected to establish the mixed-mode crack propagation criteria;②The paper focus on the crack location, propagation and tracking problems; Improved the level set method to determine the location of the oblique crack and a local search method is proposed to accurately determine the crack-tip element; The process of continuous expansion of crack is discreted into a number of incremental extension in one-way along the straight-line form, and the expression of its level set function is derived to accurately track the crack growth;③XFEM procedure is developed using FORTRAN language to calculate stress intensity factor of plane problem, achieving a good match with analytical solution; The crack propagation behavior is simulated under three-point bending load and eccentric tensile load; Finally, XFEM is used to study the impact of porosity on the fracture mechanical properties of porous bio-ceramic materials and to simulate the pore edge crack propagation behavior of porous ceramic. The results show that XFEM have broad prospects in the porous bio-ceramic applications, demonstrating powerful advantage of XFEM in solving the strong discontinuity problems…
Key words: porous ceramic; discontinuous displacement field; XFEM; crack propagation; stress intensity factor

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