Weight function method for three dimensional crack problems—II. Application to surface cracks at a hole in finite thickness plates under stress gradients

1989 ◽  
Vol 34 (3) ◽  
pp. 609-624 ◽  
Author(s):  
W. Zhao ◽  
X.R. Wu ◽  
M.G. Yan
Keyword(s):  
Weight Function ◽  
Function Method ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Surface Cracks ◽  
Weight Function Method ◽  
Stress Gradients ◽  
Crack Problems

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.

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