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

2020 ◽  
Author(s):  
Huimin Zhou ◽  
Shuiting Ding ◽  
Guo Li
Keyword(s):  
Weight Function ◽  
Flat Plate ◽  
Function Method ◽  
Damage Tolerance ◽  
Negative Relationship ◽  
Local Stress ◽  
Surface Damage ◽  
Weight Functions ◽  
Flat Plates ◽  
Weight Function Method

Abstract 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.

scholarly journals Calculation of Stress Intensity Factors for Elliptical Cracks in Finite Bodies by Using the Boundary Weight Function Method

1999 ◽  
Vol 121 (2) ◽  
pp. 181-187 ◽  
Author(s):  
C.-C. Ma ◽  
I-K. Shen
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Function Method ◽  
Weight Functions ◽  
Mode I ◽  
Intensity Factors ◽  
Weight Function Method ◽  
Arbitrary Loading

In this study, mode I stress intensity factors for a three-dimensional finite cracked body with arbitrary shape and subjected to arbitrary loading is presented by using the boundary weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. A numerical finite element method for the determination of weight function relevant to cracked bodies with finite dimensions is used. Explicit boundary weight functions are successfully demonstrated by using the least-squares fitting procedure for elliptical quarter-corner crack and embedded elliptical crack in parallelepipedic finite bodies. If the stress distribution of a cut-out parallelepipedic cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple surface integration. Comparison of the calculated results with some available solutions in the published literature confirms the efficiency and accuracy of the proposed boundary weight function method.

Weight functions for T-stress for semi-elliptical surface cracks in finite-thickness plates

2005 ◽  
Vol 40 (5) ◽  
pp. 403-418 ◽  
Author(s):  
Xiao Yu ◽  
Xin Wang
Keyword(s):  
Weight Function ◽  
Function Method ◽  
Finite Thickness ◽  
Weight Functions ◽  
General Point ◽  
Surface Cracks ◽  
Weight Function Method ◽  
Aspect Ratios ◽  
Crack Problems ◽  
T Stress

This paper presents the application of the weight function method for the calculation of elastic T-stress for semi-elliptical surface cracks. First, the weight function method for the calculation of T-stress previously developed for two-dimensional crack problems was extended for the T-stress calculation for three-dimensional crack problems. Then, the T-stress weight functions for the deepest point (corresponding to the parametric angle ϕ = 90°) and for any general point (5° ≤ ϕ < 90°) along the crack front of semi-elliptical surface cracks in finite-thickness plates for wide ranges of crack aspect ratios a/c and relative depths a/t were derived. The resulting weight functions were validated using available finite element results for non-linear stress fields and remote tension and bending cases, and very good agreement was achieved. The weight functions are suitable for the calculation of the T-stress under complex loading conditions for any general point (5° ≤ ϕ ≤ 90°) of surface cracks with wide ranges of aspect ratios, 0 ≤ a/c ≤ 1, and relative depths, 0 ≤ a/t ≤ 0.8.

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

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3155
Author(s):  
Kun-Pang Kou ◽  
Jin-Long Cao ◽  
Yang Yang ◽  
Chi-Chiu Lam
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Function Method ◽  
Functionally Graded ◽  
Weight Functions ◽  
Surface Cracks ◽  
Functionally Graded Plates ◽  
Intensity Factors ◽  
Weight Function Method

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.

Stress Intensity Factors and Weight Function for Internal Surface Faults in Cylindrical Vessels

2013 ◽  
Vol 705 ◽  
pp. 209-215
Author(s):  
Yan Ling Ni ◽  
Shang Tong Yang ◽  
Chun Qing Li
Keyword(s):  
Stress Intensity ◽  
Aspect Ratio ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Function Method ◽  
Stress Singularity ◽  
Weight Functions ◽  
Intensity Factors ◽  
Weight Function Method ◽  
Aspect Ratios

Failure of cylindrical vessels can be caused by stress singularity at pitting corrosion induced cracks. Literature suggests that most of research focuses on how to determine stress intensity factors for surface cracks with low aspect ratios, i.e.,a/c1.0. Situation may well arise where the aspect ratio of cracks is larger than one. This paper attempts to propose a weight function method to determine stress intensity factors for high aspect ratio semi-elliptical cracks in cylindrical vessels. The weight functions are derived based on three dimensional finite element analysis. The proposed weight function method is verified numerically. It is found that the higher the aspect ratio of cracks the larger the stress intensity factors, and that the aspect ratio of cracks may alter the failure mode of cylindrical vessels.

scholarly journals Analysis of Axial Cracks in Hollow Cylinders Subjected to Thermal Shock by Using the Thermal Weight Function Method

1996 ◽  
Vol 118 (2) ◽  
pp. 146-153 ◽  
Author(s):  
C.-C. Ma ◽  
M.-H. Liao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Thermal Shock ◽  
Function Method ◽  
Thermal Loading ◽  
Weight Functions ◽  
Weight Function Method ◽  
Hollow Cylinders

In this study, stress intensity factors for axial cracks in hollow cylinders subjected to thermal shock are determined by using the thermal weight function method. The thermal weight function is a universal function for a given cracked body and can be obtained from any arbitrary mechanical loading system. The thermal weight function may be thought of as Green’s function for the stress intensity factor of cracked bodies subject to thermal loadings. Once the thermal weight function for a cracked body is determined, the stress intensity factor for any arbitrary distributed thermal loading can be simply and efficiently evaluated through the integration of the product of the temperature and the correspondent thermal weight function. A numerical boundary element method for the determination of thermal weight functions for axial cracks in hollow cylinders is used in this study to evaluate the transient stress intensity factor. As a demonstration, some examples of axial cracks in hollow cylinders subjected to thermal shock are solved by using the thermal weight function method, and the results are compared with available results in the published literature.

A weight function method for multiaxial low-cycle fatigue life prediction under variable amplitude loading

2018 ◽  
Vol 53 (4) ◽  
pp. 197-209 ◽  
Author(s):  
Xiao-Wei Wang ◽  
De-Guang Shang ◽  
Yu-Juan Sun
Keyword(s):  
Fatigue Life ◽  
Weight Function ◽  
Life Prediction ◽  
Function Method ◽  
Low Cycle Fatigue ◽  
Fatigue Life Prediction ◽  
Cycle Fatigue ◽  
Critical Plane ◽  
Variable Amplitude ◽  
Weight Function Method

A weight function method based on strain parameters is proposed to determine the critical plane in low-cycle fatigue region under both constant and variable amplitude tension–torsion loadings. The critical plane is defined by the weighted mean maximum absolute shear strain plane. Combined with the critical plane determined by the proposed method, strain-based fatigue life prediction models and Wang-Brown’s multiaxial cycle counting method are employed to predict the fatigue life. The experimental critical plane orientation and fatigue life data under constant and variable amplitude tension–torsion loadings are used to verify the proposed method. The results show that the proposed method is appropriate to determine the critical plane under both constant and variable amplitude loadings.

Sign in / Sign up

Export Citation Format

Share Document