Weight Functions of Radial Cracks in Hollow Disks

1986 ◽  
Vol 108 (2) ◽  
pp. 403-413 ◽  
Author(s):  
George T. Sha ◽  
Chien-Tung Yang
Keyword(s):  
Stress Intensity ◽  
Stress Field ◽  
Stress Intensity Factors ◽  
Weight Functions ◽  
Mode I ◽  
Loading Conditions ◽  
Intensity Factors ◽  
Crack Face ◽  
Disk Radius ◽  
Radial Cracks

Explicit nodal weight functions for both bore and rim radial cracks in a hollow disk are presented with special emphasis on the load independent characteristics of the weight functions that can eliminate the repeated finite element computations of the Mode I stress intensity factors (KI) for a given crack geometry under different loading conditions. An analytical expression, which relates the explicit crack-face weight functions to the radial distance (rs) from the crack tip along the crack face, is also provided for wide range ratios of crack length (a) to the difference between outer disk radius (Ro) and inner disk radius (Ri) [0.01 ≤ a/(Ro − Ri) ≤ 0.8]. The accurate explicit weight functions of any crack length can be obtained easily with a cubic spline interpolation technique from an adequate set of explicit crack-face weight functions of discrete crack lengths. With the availability of the explicit crack-face weight functions for both the bore and rim cracks, the Mode I stress intensity factors under any complex loading conditions can be calculated accurately and inexpensively by a sum of worklike products between the equivalent “un-cracked” stress field and the interpolated crack-face weight functions. This equivalent uncracked stress field could include the body force loading of a rotating disk, thermal loading, complex residual stresses, the applied tractions at the crack face and other locations, and any combinations of these loading conditions.

scholarly journals Stiffness Derivative Finite Element Technique to Determine Nodal Weight Functions With Singularity Elements

1983 ◽  
Author(s):  
George T. Sha
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Weight Functions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Crack Face ◽  
Crack Geometry ◽  
Crack Problems

The use of the stiffness derivative technique coupled with “quarter-point” singular crack-tip elements permits very efficient finite element determination of both stress intensity factors and nodal weight functions. Two-dimensional results are presented in this paper to demonstrate that accurate stress intensity factors and nodal weight functions can be obtained from relatively coarse mesh models by coupling the stiffness derivative technique with singular elements. The principle of linear superposition implies that the calculation of stress intensity factors and nodal weight functions with crack-face loading, σ(rs), is equivalent to loading the cracked body with remote loads, which produces σ(rs) on the prospective crack face in the absence of crack. The verification of this equivalency is made numerically, using the virtual crack extension technique. Load independent nodal weight functions for two-dimensional crack geometry is demonstrated on various remote and crack-face loading conditions. The efficient calculation of stress intensity factors with the use of the “uncracked” stress field and the crack-face nodal weight functions is also illustrated. In order to facilitate the utilization of the discretized crack-face nodal weight functions, an approach was developed for two-dimensional crack problems. Approximations of the crack-face nodal weight functions as a function of distance, (rs), from crack-tip has been successfully demonstrated by the following equation: h a , r s = A a √ r s + B a + C a √ r s + D a r s Coefficients A(a), B(a), C(a) and D(a), which are functions of crack length (a), can be obtained by least-squares fitting procedures. The crack-face nodal weight functions for a new crack geometry can be approximated using cubic spline interpolation of the coefficients A, B, C and D of varying crack lengths. This approach, demonstrated on the calculation of stress intensity factors for single edge crack geometry, resulted in a total loss of accuracy of less than 1%.

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.

Sign in / Sign up

Export Citation Format

Share Document