A modal analysis for computation of stress intensity factors under dynamic loading conditions at low frequency using eXtended Finite Element Method

In this paper, a modal analysis for computation of stress intensity factors under dynamic loading conditions at low frequency using eXtended Finite Element Method (X-FEM) is conducted. Modal stress intensity factors for a body with a stationary crack are first computed from the displacement fields associated with the deformed mode shapes. The modal approach based on the recombination of the modal stress intensity factors is then employed to compute the dynamic stress intensity factors. A convergence study on the first natural frequency for a plate with an edge crack is conducted to prove the correctness of the model implementation. Then, dynamic stress intensity factors obtained from the modal approach are compared with those obtained from full transient direct dynamic computations in order to validate the X-FEM computational results. The computational results show that the modal approach can be used to obtain accurate stress intensity factors for cracked structure under dynamic loads (at low and moderate frequency ranges) with a significant reduction of the computing time compared to a full transient dynamic computation. Finally, the validated modal analysis is used to investigate the change of the natural frequency due to crack propagation for a cracked turbine blade during operation in a power plant.