| In engineering field, damage accidents often originate from the fracture or end in the crack propagation. Study on the fracture failure process of structure is of significance for improving the standard of engineering design. It is not necessary to remesh when the extended finite element method (XFEM) simulates crack propagation. But the complex enrichment functions based on a priori knowledge of the asymptotic expansions of the displacements in the crack-tip are required. Besides, the special numerical integration techniques are always inevitable. The scale boundary finite element method (SBFEM) has a great advantage in solving the infinite domain and singularity problems. Due to both methods are linked up through finite element theory, a numerical coupling model with the combination of advantages can be established.Above all, based on the principle of virtual work, a new fracture numerical method called the extended SBFEM (X-SBFEM) is proposed by taking advantage of displacement coordination and force balance on the boundary. In this method, the Heaviside enrichment is used to represent the jump across the discontinuity surface in split element while the nonsmooth behavior around the crack tip is described by the semi-analytical SBFEM. Moreover, the solution procedure of the displacement fields and the stress intensity factors in orthotropic material and biomaterial interface crack including the effect of surface tractions are derived in detail based on X-SBFEM. Subsequently, the X-SBFEM is combined with the level set method so that it can be applied to solve the complicated problems of crack propagation. At last, the X-SBFEM is applied to a practical structure, the crack propagation process and the displacement response of Koyna dam with a preset notch due to reservoir overflow loading is obtained.During its numerical evaluation, the mixed mode crack, the edge-cracked semi-infinite plate with distributing surface tractions, the three-point bending specimen, the four-point shear specimen and Koyna dam with a preset notch is modelled by a complete MATLAB code. Through the numerical examples, several important features of X-SBFEM can be obtained. This method:1) does not require a priori knowledge of the asymptotic fields; 2) does not require special numerical integration technique so that the stiffness of the region containing the crack tip is computed directly; 3) the generalized stress intensity factors of many kinds of singularities could be calculated directly from definition by the consistent formula and 4) does not need to add new node or element and the reconstruction workload of super element is minimal when simulating crack propagation.To enhance the engineering applicability of the algorithm, some significant conclusions are acquired based on the sensitivity analysis of parameters. First of all, the computational accuracy is affected by the number of layers for super-element. As the number of nodes on the boundary is increased, the error could decrease within the acceptable range quickly. Next, the mesh dependence is low especially when the grid size is less than the propagation length. Finally, the crack propagation process could be influenced by the crack propagation length obviously. The oversize propagation length would lead to sawtooth crack growth path and instability of numerical calculation. In order to obtain the stable and convergent solution, crack propagation length should be taken for 1/10 to 1/25 of the width of the component near crack. |
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