Fatigue lifetime prediction is one of significant issues among engineering design and manufacture. Many factors could lead to structure failure such as loading, temperature and imperfect material. The wildly applied S-N curves (Stress-cycles) can be obtained either by numerous experiment on testing machines or running simulations on computers. By the way of experiments, a metal specimen is placed into the testing machine and subjected to thousands of cyclic loading until a crack or failure occurs in the specimen. In general the cycle numbers is up to 10^7 in a high-cycle fatigue testing. This process is expensive and time-consuming because one single test can run for months. Therefore, a fast and accurate numerical method for fatigue lifetime prediction is demanding.

 

The fracture and failure on macro-scale is an acculumative result due to the crack formation on the micro-scale. The damage model should be taken into account to evaluate the damage accumulative under the cyclical loading condition. In order to capture the accurate material response with dynamic loading cycles, both Extended Finite Element(XFEM) method and Wavelet transformation induced multi-time scaling are used for the numerical simulation. Furthermore, a time stepping method is introduced by define the time as fine time scale and coarse time scale. This new time stepping method can accelerate the computational time for high cycles fatigue prediction, and at the same time, track the evolution of local state variables adequately in both elastic region and plastic region.