Research On Crack Growth Simulation Algorithm Based On XFEM And Dynamic Self-adapting Mesh

The presence of cracks can significantly reduce the strength and service life of the structure.Studying the propagation law of cracks in structures under external loads and quantifying crack propagation life is critical to structural safety assessment.Numerical simulation in the research of crack propagation problem has always been a research hotspot in this field.In recent decades,with the development of computer technology,various computational mechanics methods have emerged,especially the extended finite element method(XFEM),which has become one of the most effective methods to solve the complex crack propagation problem.However,the traditional XFEM mostly uses a uniform mesh,and local mesh refinement is difficult to achieve due to crack propagation.For the largescale and complex three-dimensional crack propagation problem,it is difficult to solve the contradiction between computational accuracy and efficiency with the traditional XFEM.To overcome the shortcomings of the traditional XFEM,under its basic framework,a simple and efficient dynamic adaptive mesh refinement method is proposed in this study by introducing the shape function of the virtual node polygonal element method(VPM).Based on this method,an improved XFEM for crack propagation problem is formulated and a corresponding computational program is developed.The biggest advantage of this algorithm is that it realizes the dynamic multi-level refinement only for the meshes near the discontinuities,and the refinement region automatically updates with the growth of the crack,which can make a balance between the computational accuracy and efficiency.A simple and efficient dynamic adaptive mesh refinement method is proposed in this study.Throughout the whole crack propagation process,dynamically changing high quality meshes can be provided considering the information of discontinuities in different sub-steps.For the commonly used two-dimensional quadrilateral elements and three-dimensional tetrahedral elements,a quadtree(octree)structure is used to achieve the mesh refinement.The construction method of the VPM shape function is extended from two dimensions to three dimensions to deal with the hanging nodes generated in the mesh refinement process.Two sets of meshes are introduced to ensure that the refinement area is automatically updated as the crack tip moves,thereby realizing the automatic refinement and coarsening of the mesh.Combined with the above-mentioned mesh refinement method,an improved crack propagation numerical simulation algorithm(VP-XFEM,virtual node polygonal extended finite element method)is proposed and the corresponding computational program is developed.Under the framework of linear elastic fracture theory,the discrete format of VPXFEM is derived,and its calculation process and integration scheme are given.To obtain accurate fracture parameters,the calculation formulas of two-dimensional and threedimensional stress intensity factors are derived,and detailed calculation methods and processes are provided.Based on the commonly used crack propagation model,the update method of crack propagation model is given,which provides the precondition for the complete automation of crack propagation simulation.The computational accuracy,convergence and efficiency of VP-XFEM are verified by multiple cracking examples.The results show that VP-XFEM can achieve the same convergence rate as traditional XFEM,and VP-XFEM can save about 70% of the calculation time by selecting the appropriate mesh refinement parameters under the same calculation accuracy.Based on the proposed VP-XFEM,the crack propagation problem in heterogeneous materials is studied.At the macroscopic and microscopic levels,the crack propagation problems with different types of discontinuities(inclusions,holes,cracks)were simulated,and the influence of micro-defects near the macro-crack on the stress intensity factors and the propagation path is analyzed.The analysis of several numerical examples shows that VP-XFEM can obtain accurate fracture parameters and crack propagation paths at both scales,and also ensures high computational accuracy.At the same time,the study of microdefects near macro-crack shows that the nearest micro-defects have an absolutely dominant effect on the macro-crack,and the amplification or shielding effect of the micro-defects varies with their locations and sizes as well as other relevant parameters.Finally,the self-developed VP-XFEM computational program is used to simulate the crack propagation problem in two practical projects.For the crack propagation problem of a highspeed railway hollow axle under fatigue load,the finite element method with remeshing technique as well as the VP-XFEM are used to simulate this problem.The accuracy and efficiency of VP-XFEM in calculating the crack tip stress intensity factors and predicting the crack propagation path are verified.For the hot cracking problem of roll castings in the casting process,a method to simulate the initiation and propagation of hot cracks is proposed.The most likely location of thermal crack initiation is determined by the existing thermal cracking criterions and a prefabricated initial crack is inserted here,then the propagation process is simulated by sub-model technique and VP-XFEM.The crack propagation path obtained by the simulation is basically consistent with the actual observation results,which verifies the feasibility of the above method.