A Surface Crack in a Graded Medium Under General Loading Conditions

2002 ◽  
Vol 69 (5) ◽  
pp. 580-588 ◽  
Author(s):  
S. Dag ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Half Plane ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Surface ◽  
Local Perturbation ◽  
Local Problem ◽  
Loading Conditions ◽  
Intensity Factors ◽  
Perturbation Problem

In this study the problem of a surface crack in a semi-infinite elastic graded medium under general loading conditions is considered. It is assumed that first by solving the problem in the absence of a crack it is reduced to a local perturbation problem with arbitrary self-equilibrating crack surface tractions. The local problem is then solved by approximating the normal and shear tractions on the crack surfaces by polynomials and the normalized modes I and II stress intensity factors are given. As an example the results for a graded half-plane loaded by a sliding rigid circular stamp are presented.

Analysis of Surface Flaw in Pressure Vessels by a New 3-Dimensional Alternating Method

1982 ◽  
Vol 104 (4) ◽  
pp. 299-307 ◽  
Author(s):  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Surface ◽  
Pressure Vessels ◽  
Pressure Loading ◽  
Intensity Factors ◽  
Alternating Method ◽  
Magnification Factors

An alternating method, in conjunction with the finite element method and a newly developed analytical solution for an elliptical crack in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. The problems considered in the present paper are: (i) an outer semi-elliptical surface crack in a thick cylinder, and (ii) inner semi-elliptical surface cracks in a thin cylinder which were recommended for analysis by the ASME Boiler and Pressure Vessel Code (Section III, App. G, 1977). For each crack geometry of an inner surface crack, seven independent loadings, such as internal pressure loading on the cylinder surface and polynomial pressure loadings from constant to fifth order on the crack surface, are considered. From the analyses of these loadings, the magnification factors for the internal pressure loading and the polynomial influence functions for the polynomial crack surface loadings are determined. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived by using the polynomial influence functions to check the internal consistency of the present analysis. These values agree excellently with the magnification factors obtained directly. The present results are also compared with the results available in literature.

A Surface Crack in Shells Under Mixed-Mode Loading Conditions

1988 ◽  
Vol 55 (4) ◽  
pp. 795-804 ◽  
Author(s):  
P. F. Joseph ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Mixed Mode ◽  
Shallow Shell ◽  
Crack Problem ◽  
Three Dimensional ◽  
Loading Conditions ◽  
Intensity Factors ◽  
Crack Problems

The problem of a shallow shell containing a surface crack and subjected to general loading conditions is considered. It is shown that, as in the three-dimensional elasticity formulation, the mode I state can be separated whereas modes II and III remain coupled. A line spring model is developed to formulate the part-through crack problem under mixed-mode conditions. A shallow shell of arbitrary curvature having a part-through crack located on the outer or the inner surface of the shell is then considered. Reissner’s transverse shear theory is used to formulate the problem by assuming that the shell is subjected to all five moment and stress resultants. The uncoupled antisymmetric problem is solved for cylindrical and toroidal shells having a surface crack in various orientations and the primary and the secondary stress intensity factors are given. The results show that, unlike the through crack problems, in surface cracks the effect of shell curvature on the stress intensity factors is relatively insignificant.

Stress intensity factors in novel specimens for crack propagation under loading conditions II+III in polymers

2020 ◽  
Author(s):  
Ondrej Slávik ◽  
Pavel Hutař ◽  
Michael Berer ◽  
Anja Gosch ◽  
Tomáš Vojtek ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Loading Conditions ◽  
Intensity Factors

Dynamic Behavior of an Orthotropic Material Containing a Central Crack

1989 ◽  
Vol 111 (2) ◽  
pp. 172-176 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Orthotropic Material ◽  
Crack Surface ◽  
Frequency Factor ◽  
Wave Frequency ◽  
Intensity Factors ◽  
Central Crack ◽  
Material Constants ◽  
Principal Axes

The dynamic response of a central crack in an orthotropic material is investigated. The crack is situated along one of the principal axes of the material. The load is harmonic in time and normally applied to the crack surface. The Fourier transform is used to solve the dynamic fracture problem, and the results are simplified through a complete contour integration. The dynamic stress intensity factor is obtained in an exact expression in terms of the frequency factor and the material constants. The frequency factor is defined as the product of the wave frequency and the half-crack length, divided by the shear wave speed. Glass/epoxy and graphite/epoxy composite materials are used as example materials in calculating the numerical values of the stress intensity factors. The maximum values of the stress intensity factors are shown to be dependent on the value of the nondimensional frequency factor and the material anisotropy. The motion of the crack surface is also investigated. The crack surface distortion from the associated static crack shape also depends on the wave frequency and the orthotropic material constants.

Mixed Mode Interface Cracks in a Bi-Material Half Plane and a Bi-Material Strip

1999 ◽  
Author(s):  
Haiying Huang ◽  
George A. Kadomateas ◽  
Valeria La Saponara
Keyword(s):  
Stress Intensity ◽  
Free Boundary ◽  
Half Plane ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Infinite Strip ◽  
Infinite Plane ◽  
Intensity Factors ◽  
Interface Cracks ◽  
Mode Stress

Abstract This paper presents a method for determining the dislocation solution in a bi-material half plane and a bi-material infinite strip, which is subsequently used to obtain the mixed-mode stress intensity factors for a corresponding bi-material interface crack. First, the dislocation solution in a bi-material infinite plane is summarized. An array of surface dislocations is then distributed along the free boundary of the half plane and the infinite strip. The dislocation densities of the aforementioned surface dislocations are determined by satisfying the traction-free boundary conditions. After the dislocation solution in the finite domain is achieved, the mixed-mode stress intensity factors for interface cracks are calculated based on the continuous dislocation technique. Results are compared with analytical solution for homogeneous anisotropic media.

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 a surface crack in a tubular T-joint

2001 ◽  
Vol 78 (10) ◽  
pp. 677-685 ◽  
Author(s):  
S.P. Chiew ◽  
S.T. Lie ◽  
C.K. Lee ◽  
Z.W. Huang
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Intensity Factors
Sign in / Sign up

Export Citation Format

Share Document