Simulation Of Plane And Bending Crack Problem With Extended Finite Element Method

There were a lot of numerical methods which were used to simulate discontinues problems, but it's not satisfactory, especially on computational efficiency and simplification of method. XFEM (eXtended Finite Element Method) was presented formally on 1999. With basing on the framework of CFEM (convention Finite Element Method), XFEM separated the mesh from discontinuities by introducing enriched nodes and functions. So XFEM was used on discontinues problems widely.Firstly, the concepts and theory of LEFM (linear elastic fracture mechanics) were introduced, especially the compute method of SIF (stress intensity factors) and crack propagation criterion. The theory of XFEM and displacement model were expounded detailedly, meanwhile an effective numerical integral scheme was given. After proposing the flow of implementing XFEM, the XFEM program was developed basing on above theory and methods.Secondly, the plane crack problems were simulating by using the developed program. The factors of effecting result were discussed, including J-integral radius and mesh. The SIF were evaluated with varied crack relative length, ratio of plate's length-width and crack angle. And then the quasi-static crack propagation was simulated, using the maximum tangential stress criterion, under pure modeⅠ, pure modeⅡand mixed modeⅠ-Ⅱload.Finally, the XFEM program of bending crack was developed based on Reissner plate theory. The effect of J- integral radius and mesh were studied. The changes of SIF were presented with varied crack relative length, ratio of plate's length-width, plate thick and crack angle. The difference of simply supported and free boundary conditions was analyzed. The quasi-static crack propagation was simulated, using the maximum tangential stress criterion, under bending, torsion and combined bending and torsion. The compute result of SIF provided the reference for crack problems in engineering.In addition, the program and method of simulating crack propagation was significance for researching the plate and shell crack propagation under impacting load.