Weight functions for curved crack fronts using bem

1993 ◽  
Vol 28 (2) ◽  
pp. 67-78 ◽  
Author(s):  
R Bains ◽  
M H Aliabadi ◽  
D P Rooke
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Three Dimensional ◽  
Function Technique ◽  
Weight Functions ◽  
Intensity Factors ◽  
Penny Shaped Crack ◽  
Curved Crack ◽  
Shaped Crack

This paper presents an efficient numerical weight function technique, based on the boundary element method, for the determination of stress intensity factors of curved crack fronts in three-dimensional finite bodies. The weight functions are based on the notion of fundamental fields, which are defined from point loads acting at the crack front. A regularization procedure that incorporates the fundamental fields of the penny-shaped crack in an infinite elastic body is used to obtain weight functions for a penny-shaped edge crack in a cylindrical bar. Stress intensity factors for elliptical crack fronts can be generated by employing the properties of the fundamental fields at the load points on the crack front. Stress intensity factor variations along the crack-fronts are presented when these finite cracked geometries are subjected to various loads that produce mode I deformation of the crack faces. Wherever possible, solutions are compared with values published in the literature and are found to be in good agreement.

Stress Analysis of a Penny-Shaped Crack Located Between Two Spherical Cavities in an Infinite Solid

1980 ◽  
Vol 47 (4) ◽  
pp. 806-810 ◽  
Author(s):  
H. Hirai ◽  
M. Satake
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Stress Intensity Factors ◽  
Harmonic Functions ◽  
Linear Equations ◽  
Intensity Factors ◽  
Cylindrical Coordinates ◽  
Spherical Cavities ◽  
Penny Shaped Crack ◽  
Shaped Crack

The problem of a penny-shaped crack located between two spherical cavities in an infinite solid subjected to uniaxial loads is considered. Using transformations between harmonic functions in cylindrical coordinates and those in spherical ones, the problem is reduced to nonhomogeneous linear equations. The obtained equations are solved numerically and the influence of the two spherical cavities upon the stress-intensity factors at the penny-shaped crack tip is shown graphically.

A General Numerical Procedure for Extracting Mixed-Mode Stress Intensity Factors Along the Fronts of Three-Dimensional Nonplanar Cracks

2002 ◽  
Author(s):  
M. Gosz ◽  
R. Cammino
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Intensity Factors ◽  
Hydrostatic Tension ◽  
Energy Integrals ◽  
Shaped Crack ◽  
Mode Stress

A numerical procedure is described for extracting mixed-mode stress intensity factors along the fronts of three-dimensional, nonplanar cracks embedded in solids. The mixed-mode stress intensity factors at points along the crack front are obtained by evaluating interaction energy integrals for three-dimensional, non-planar cracks. To assess the validity of the numerical procedure, two numerical examples are considered. First, we consider the problem of a non-planar, lens-shaped crack in an infinite solid subjected to hydrostatic tension. The numerical results are shown to be in excellent agreement with available analytical results. We then consider the case of a non-planar, warped elliptical crack surface, where to our knowledge no analytical solution exists, and the results are discussed.

scholarly journals Shear Stress Intensity Factors for a Planar Crack With Slightly Curved Front

1986 ◽  
Vol 53 (4) ◽  
pp. 774-778 ◽  
Author(s):  
Huajian Gao ◽  
James R. Rice
Keyword(s):  
Shear Stress ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Line Tension ◽  
Elastic Displacement ◽  
Intensity Factors ◽  
Order Accuracy ◽  
First Order ◽  
Curved Crack

Recent work (Rice, 1985a) has presented the calculations of the first order variation in an elastic displacement field associated with arbitrary incremental planar advance of the location of the front of a half-plane crack in a loaded elastic full space. That work also indicated the relation of such calculations to a three-dimensional weight function theory for crack analysis and derived an expression for the distribution of the tensile mode stress intensity factor along a slightly curved crack front, to first order accuracy in the deviation of the crack front location from a reference straight line. Here we extend the results on stress intensity factors to the shear modes, solving to similar first order accuracy for the in-plane (Mode 2) and antiplane (Mode 3) shear stress intensity factors along a slightly curved crack front. Implications of results for the configurational stability of a straight crack front are discussed. It is also shown that the concept of line tension, while qualitatively useful in characterizing the crack extension force (energy release rate) distribution exerted on a tough heterogeneity along a fracture path as the crack front begins to curve around it, does not agree with the exact first order effect that is derived here.

Calculation of Stress Intensity Factors and Crack Opening Displacements for Cracks Subjected to Complex Stress Fields

2003 ◽  
Vol 125 (3) ◽  
pp. 260-266 ◽  
Author(s):  
A. Kiciak ◽  
G. Glinka ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Fatigue Cracks ◽  
Crack Opening ◽  
Complex Stress ◽  
Pressure Vessels ◽  
Stress Fields ◽  
Function Technique ◽  
Weight Functions ◽  
Intensity Factors

Fatigue cracks in shot peened and case hardened notched machine components and high-pressure vessels are subjected to the stress fields induced by the external load and the residual stress resulting from the surface treatment or autofrettage. Both stress fields are usually nonuniform and available handbook stress intensity factor solutions are in most cases unavailable for such configurations, especially in the case of two-dimensional surface breaking cracks such as semi-elliptical and quarter-elliptical cracks at notches. The method presented in the paper makes it possible to calculate stress intensity factors for such cracks and complex stress fields by using the generalized weight function technique. It is also shown that the generalized weight functions make it possible to calculate the crack opening displacement field often used in the determination of the critical load or the critical crack size.

Sign in / Sign up

Export Citation Format

Share Document