A Method for Assessing the “Local” Accuracy of Weight Functions for Plates With Embedded Cracks

1995 ◽  
Author(s):  
S. W. Ng ◽  
K. J. Lau
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Weight Functions ◽  
Finite Element Analyses ◽  
Intensity Factors ◽  
Local Accuracy ◽  
New Algorithms

Abstract In this paper a procedure is developed to assess the “local” accuracy of weight functions for finding stress intensity factors of centrally cracked finite plates given by Tsai and Ma (1989). It is found that the weight functions can be used to calculate stress intensity factors for practical cases, with “local” accuracy being within 6 %. In addition, weight functions generated from two finite element analyses are found to be accurate and may be used to assess new algorithms for finding weight functions.

Estimation of Stress Intensity Factors due To Welding Residual Stresses for Circumferentially Cracked Pipes

2012 ◽  
Author(s):  
Chang-Young Oh ◽  
Ji-Soo Kim ◽  
Yun-Jae Kim ◽  
Young-Jin Oh ◽  
Kyoungsoo Lee ◽  
...  
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Residual Stresses ◽  
Stress Intensity Factors ◽  
Finite Element Analyses ◽  
Intensity Factors ◽  
Crack Face ◽  
Simple Method ◽  
Weld Geometry ◽  
Nonlinear Stress

This paper proposes a simple method to estimate stress intensity factors due to welding residual stresses. In this study, finite element analyses for circumferentially cracked pipe are performed to calculate stress intensity factors. Four cracked geometries and two types of weld geometry are considered. KI-solutions for the nonlinear stress distribution on the crack face were determined in accordance with codes and standards. The results are compared with KI-solutions from finite element results. It is found that proposed simple method agrees well with FE results.

STRESS INTENSITY FACTORS OF A SEMI-ELLIPTICAL CRACK IN A HOLLOW CYLINDER

2015 ◽  
Vol 39 (3) ◽  
pp. 557-568
Author(s):  
Shiuh-Chuan Her ◽  
Hao-Hi Chang
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Hollow Cylinder ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Depth ◽  
Weight Functions ◽  
Intensity Factors ◽  
Regular Elements ◽  
Wide Range

In this investigation, the weight function method was employed to calculate stress intensity factors for semi-elliptical surface crack in a hollow cylinder. A uniform stress and a linear stress distribution were used as the two references to determine the weight functions. These two factors were obtained by a three-dimensional finite element method which employed singular elements along the crack front and regular elements elsewhere. The weight functions were then applied to a wide range of semi-elliptical surface crack subjected to non-linear loadings. The results were validated against finite element data and compared with other analyses. In the parametric study, the effects of the ratio of the surface crack depth to length ranged from 0.2 to 1.0 and the ratio of the crack depth to the wall thickness ranged from 0.2 to 0.8 on stress intensity factors were investigated.

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%.

Stress Intensity Factors and Weight Functions for Longitudinal Semi-Elliptical Surface Cracks Inside Thick-Walled Cylinders Using Highly-Refined Finite-Element Models

2010 ◽  
Author(s):  
Adam R. Hinkle ◽  
James E. Holliday ◽  
David P. Jones
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Crack Growth ◽  
Stress Intensity Factors ◽  
Weight Functions ◽  
Finite Element Models ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Surface Flaws ◽  
Field Singularity

Fracture mechanics and fatigue crack-growth analysis rely heavily upon accurate values of stress intensity factors. They provide a convenient, single-parameter description to characterize the amplitude of the stress-field singularity at the crack tip, and are used to correlate brittle fracture and crack growth in pressure vessel and piping applications. Mode-I stress intensity factors that have been obtained for longitudinal semi-elliptical surface flaws on the inside of thick-walled cylinders using highly-refined finite element models are investigated. Using these results, weight function solutions are constructed and selected geometries are validated.

Weight Functions and Stress Intensity Factors for Eccentric through Cracks in a 3-D Rectangular Plate Subjected to In-Plane Loading

2016 ◽  
Vol 853 ◽  
pp. 8-14
Author(s):  
Xu Teng Hu ◽  
Xu Jia ◽  
Ying Dong Song
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Rectangular Plate ◽  
Stress Intensity Factors ◽  
Interpolation Method ◽  
Unknown Coefficient ◽  
Weight Functions ◽  
Finite Element Models ◽  
Intensity Factors ◽  
Aspect Ratios

Three unknown coefficient weight functions for eccentric through cracks in a 3-D rectangular plate subjected to in-plane loading are proposed. 3-D finite element models of cracked rectangular plates within the whole range of crack aspect ratios, i.e., 0≤e/W≤0.8, 0.08≤a/(W-e)≤0.9, were established to obtain a reference SIF database for both crack points A and B, rather than 2-D finite element models. To improve the accuracy of the weight function, the coefficients were derived from this database using the Binary Lagrange Interpolation Method instead of Curve-Fitting Expression. Comparisons of stress intensity factors calculated using the present weight functions with finite element data for the high-order power law and residual stress distributions show high accuracy of the present weight functions.

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