Stress Intensity Factors of Corner Cracks in Three Dimensional Finite Plates Based on Universal Weight Function Method

The probabilistic damage tolerance method for life limited parts is important to evaluate the risk of fractures. Generally, the stress intensity factor (SIF) as the core parameter during fracture analysis is difficult to calculate efficiently because of the varied geometries and complex stress fields induced by thermal and centrifugal stress. The universal weight function method (WFM) is believed an efficient way to obtain SIFs of cracks subjected to arbitrary stress distributions along crack depth. However, although the WFM has been successful applied like in corner cracks of plates with limited side along crack depth, the available weight functions are inapplicable for some components such as rotor disks with both finite sides along and perpendicular to crack depth. To overcome the complications mentioned above, this paper derives the weight functions of 1/4 circle corner cracks in three dimensional finite rectangular plates. The reference SIFs under uniform and linear stress distribution are obtained by finite element analysis with J integral method. Then, the relationship between SIFs and geometries are built based on response surface method, and a database is established by the derived weight functions. Results show that, the SIFs of cracks under complex stress distribution can be quickly and accurately obtained by numerical integration process. The mean errors between the WFM results and the finite element results are less than 1.35% and the mean absolute errors are less than 0.512 MPa√m under uniform and linear stress distribution. Additionally, the errors under high order stress distributions are less than 6.49% with monotonic stress on the crack surface, and the mean absolute errors are less than 1.078 MPa√m. The mean errors with non-monotonic stress are less than 43.39% while the absolute errors are less than 1.709 MPa√m. Therefore, the proposed method and the established weight function database can help to improve the efficiency and accuracy of the probabilistic surface damage tolerance evaluation.