Analysis Of Crack Growth Based On XFEM

The extended finite element method (XFEM)uses enrichment function with characteristicsof discontinuous to represent the non-smooth features,the discontinuous field can be completelyindependent of the grid boundary, so the XFEM is convenient to simulate crack,holes,kinks,andother non-smooth features. In addition, the XFEM can use known analytical solutions toconstruct the shape function matrix, thus you can get more accurate solutions in the coarse grid,which improves the work efficiency. Based on these advantages,this article simulates the crackpropagation with the XFEM and describes the crack with a hybrid explicit-implicit method.The main contents are showed as follows:(1) The XFEM and a method for a hybrid explicit and implicit crack descriptions areintroduced. the relevant linear elastic fracture mechanics and fracture dynamics mechanicstheory are summarized.how to construct the enrichment function and how to choose the set ofenrichment nodes are also introduced in this paper.(2) The static numerical simulation of common cracks and the crack propagation numericalsimulation of the strong and weak jumps are implemented by the XFEM and the reliability ofthis method is verified.(3) The fatigue crack propagation numerical simulation ofⅠ-crack, Ⅱ-crack, andⅠ-Ⅱcomplex crack are analyzed and the fatigue crack numerical simulation with the residual stressfield ofⅠ-crack,Ⅱ-crack and Ⅰ-Ⅱcrack are implemented.In addition,the influence of theresidual stress field are studied by the comparison.(4) The stress analysis of gear is carried by the traditional finite element method, thelocation of the enrichment element is confirmed. On the other hand, the crack propagation ofgear root are implemented and the influence of torque, rotation angle are analyzed.(5) The dynamic crack propagation simulation analysis is realized and the reliability of thecrack is also verified.