In-Plane Bending Fracture of a Large Beam Containing a Circular-Arc Crack

2002 ◽  
Vol 18 (3) ◽  
pp. 145-151
Author(s):  
Y. C. Shiah ◽  
Jiunn Fang ◽  
Chin-Yi Wei ◽  
Y.C. Liang
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Stress ◽  
Bending Moments ◽  
Intensity Factors ◽  
Boundary Equation ◽  
Circular Arc ◽  
Stress Functions ◽  
Arc Crack ◽  
Circular Arc Crack

AbstractIn this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

Weight Functions for an External Longitudinal Semi-Elliptical Surface Crack in a Thick-Walled Cylinder

1997 ◽  
Vol 119 (1) ◽  
pp. 74-82 ◽  
Author(s):  
A. Kiciak ◽  
G. Glinka ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Reference Stress ◽  
Pressurized Cylinder ◽  
Walled Cylinder

Mode I weight functions were derived for the deepest and surface points of an external radial-longitudinal semi-elliptical surface crack in a thick-walled cylinder with the ratio of the internal radius to wall thickness, Ri/t = 1.0. Coefficients of a general weight function were found using the method of two reference stress intensity factors for two independent stress distributions, and from properties of weight functions. Stress intensity factors calculated using the weight functions were compared to the finite element data for several different stress distributions and to the boundary element method results for the Lame´ hoop stress in an internally pressurized cylinder. A comparison to the ASME Pressure Vessel Code method for deriving stress intensity factors was also made. The derived weight functions enable simple calculations of stress intensity factors for complex stress distributions.

Stress Intensity Factors for Circular-Arc Cracks in Plates

2018 ◽  
Author(s):  
D. J. Shim ◽  
S. Tang ◽  
T. J. Kim ◽  
N. S. Huh
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Crack Model ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Element Analysis ◽  
Crack Face ◽  
Circular Arc

Stress intensity factor solutions are readily available for flaws found in pipe to pipe welds or shell to shell welds (i.e., circumferential/axial crack in cylinder). In some situations, flaws can be detected in locations where an appropriate crack model is not readily available. For instance, there are no practical stress intensity factor solutions for circular-arc cracks which can form in circular welds (e.g., nozzle to vessel shell welds and storage cask closure welds). In this paper, stress intensity factors for circular-arc cracks in finite plates were calculated using finite element analysis. As a first step, stress intensity factors for circular-arc through-wall crack under uniform tension and crack face pressure were calculated. These results were compared with the analytical solutions which showed reasonable agreement. Then, stress intensity factors were calculated for circular-arc semi-elliptical surface cracks under the lateral and crack face pressure loading conditions. Lastly, to investigate the applicability of straight crack solutions for circular-arc cracks, stress intensity factors for circular-arc and straight cracks (both through-wall and surface cracks) were compared.

Interface Crack in a Three-Phase Composite Constitutive Model

1991 ◽  
Vol 58 (2) ◽  
pp. 428-434 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
Material Model ◽  
Complex Stress ◽  
Intensity Factors ◽  
Reinforced Composite ◽  
Three Phase ◽  
Shaped Crack

An arc-shaped crack in fiber-reinforced composite material is the subject of this paper. A three-phase composite cylinder is taken as the material model to take into account the effect of surrounding fibers. Using Muskhelishvili’s complex variable method, an exact elastic solution is derived based on the conventional crack opening assumption. The complex stress intensity factors for the interface crack, in the sense defined by Hutchinson, Mear, and Rice, are determined. Some numerical examples are given. It is shown that, as the volume concentration of the fiber is increased, the magnitude of the complex stress intensity factors varies considerably.

scholarly journals Crack Paralleling an Interface Between Dissimilar Materials

1987 ◽  
Vol 54 (4) ◽  
pp. 828-832 ◽  
Author(s):  
J. W. Hutchinson ◽  
M. E. Mear ◽  
J. R. Rice
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Dissimilar Materials ◽  
Complex Stress ◽  
External Loading ◽  
Universal Relation ◽  
Intensity Factors ◽  
Elastic Solids ◽  
Complex Stress Intensity Factor

A crack paralleling a bonded plane interface between two dissimilar isotropic elastic solids is considered. When the distance of the crack from the interface is small compared to the crack length itself and to other length scales characterizing the geometry, a simple universal relation exists between the Mode I and Mode II stress intensity factors and the complex stress intensity factor associated with the corresponding problem for the crack lying on the interface. In other words, if the influence of external loading and geometry on the interface crack is known, then this information can immediately be used to generate the stress intensity factors for the sub-interface crack. Conditions for cracks to propagate near and parallel to, but not along, an interface are derived.

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