Universal Weight Function Method on the Probabilistic Surface Damage Tolerance Assessment of Aeroengine Rotors

The methodology referred as probabilistic surface damage tolerance for aeroengine rotors is used to evaluate the risk of fractures induced by low-cycle failure problems, and fracture mechanical models are usually used to carry out the analysis, in which stress intensity factors (SIFs) need to be calculated. Weight function method (WFM) can help improve the probabilistic surface damage tolerance methodology. The WFM offers remarkable computational efficiency in calculating SIFs for cracks in aeroengine rotors with complex stress gradients that are mainly induced by a local stress concentration or multiple loads, including centrifugal, thermal, and residual stresses. In this case, the universal weight functions (mode I) for surface cracks in three-dimensional finite plates, including flat plates and plates with holes, are presented. The critical step of WFM is to obtain certain coefficients in the universal weight function. Response surface method (RSM) can effectively derive the coefficients determined by multiple geometric parameters, including the length and thickness of a flat plate and the length, thickness, radius of a plate with a hole. Errors between the WFM results and the finite element results are less than 5MPam within the application scope. Furthermore, a surface damage tolerance analysis of the hole features in the aeroengine rotors based on the abovementioned two types of WFM is conducted. The selection of the weight function influences the SIF results, and the probability of failure (POF) calculated by the applied weight function of the plate with a hole is 2.02% higher than that of the flat plate. The relevant difference, which is determined by the fracture threshold crack size, has a negative relationship with the magnitude of stress distributed on the crack surface.

Weight Function Method for Stress Intensity Factors of Semi-Elliptical Surface Cracks on Functionally Graded Plates Subjected to Non-Uniform Stresses

In this paper, a weight function method based on the first four terms of a Taylor’s series expansion is proposed to determine the stress intensity factors of functionally graded plates with semi-elliptical surface cracks. Cracked surfaces that are subjected to constant, linear, parabolic and cubic stress fields are considered. The weight functions for the surface, deepest and general points on the crack faces of long and deep cracked functionally graded plates are derived, which has never been done before in the literature. The accuracy of the method in this study is then validated by comparing the results with those of finite element modeling. The numerical results indicate that the derived weight functions are highly accurate and robust enough to predict the stress intensity factors for cracked functionally graded plates subjected to non-uniform stress distributions. The weight function method is therefore a time-saving technique and suitable for handling non-uniform stress fields.