The Axisymmetric Crack Problem in a Nonhomogeneous Medium

1993 ◽  
Vol 60 (2) ◽  
pp. 406-413 ◽  
Author(s):  
M. Ozturk ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Shear Modulus ◽  
Mixed Mode ◽  
Crack Opening ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Nonhomogeneous Medium ◽  
Intensity Factors ◽  
Simple Simulation ◽  
Graded Properties

In this paper, the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by μ = μ0eαz. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formualated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter a for various loading conditions. Also given are some sample results showing the crack opening displacements.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Stress Intensity Factors for Fully Interacting Cracks in a Multicrack Solid

1994 ◽  
Vol 116 (2) ◽  
pp. 56-63 ◽  
Author(s):  
W. K. Binienda
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Damage Growth ◽  
Intensity Factors ◽  
Rigorous Solution ◽  
Damage State ◽  
Perturbation Problem ◽  
Solution Formulation

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF). Here, a methodology and rigorous solution formulation for SIF of a multicracked plate, with fully interacting cracks, subjected to a far-field arbitrary stress state is presented. The fundamental perturbation problem is derived, and the steps needed to formulate the system of singular integral equations whose solution gives rise to the evaluation of the SIF are identified. This analytical derivation and numerical solution are obtained by using intelligent application of symbolic computations and automatic FORTRAN generation capabilities in form of symbolic/FORTRAN package, named SYMFRAC, that is capable of providing accurate SIF at each crack tip. The accuracy of the results has been validated for the two parallel interacting crack problem. Limits and sensitivity of the results for the problem of a horizontal notch interacting with ten microcracks have been analyzed.

The Surface Crack Problem for a Plate With Functionally Graded Properties

1997 ◽  
Vol 64 (3) ◽  
pp. 449-456 ◽  
Author(s):  
F. Erdogan ◽  
B. H. Wu
Keyword(s):  
Crack Opening ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Opening Displacement ◽  
Nonhomogeneous Layer ◽  
Edge Cracks ◽  
Graded Properties ◽  
Plane Elasticity Problem

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.

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.

Size Effect of a Crack in a Micropolar Piezoelectric Medium

2009 ◽  
Vol 417-418 ◽  
pp. 525-528
Author(s):  
Gan Yun Huang ◽  
Shou Wen Yu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Constitutive Relations ◽  
Electric Displacement ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Piezoelectric Medium ◽  
Intensity Factors

A crack problem in a micropolar piezoelectric solid is considered. By using simplified constitutive relations, the problem can be reduced to the solution of a set of Cauchy singular integral equations with the help of Fourier integral transform technique. Numerical results for stress intensity factors, couple stress intensity factors and electric displacement intensity factors show that micropolar theory can be expected to explain certain size effects in piezoelectric solids.

scholarly journals The Problem of Internal and Edge Cracks in an Orthotropic Strip

1977 ◽  
Vol 44 (2) ◽  
pp. 237-242 ◽  
Author(s):  
F. Delale ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Elastic Constants ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Infinite Plane ◽  
Intensity Factors ◽  
Orthotropic Strip ◽  
Edge Cracks ◽  
Elastostatic Problem

The plane elastostatic problem of internal and edge cracks in an infinite orthotropic strip is considered. The problems for the material types I and II are formulated in terms of singular integral equations. For the symmetric case the stress-intensity factors are calculated and are compared with the isotropic results. The results show that because of the dependence of the Fredholm kernels on the elastic constants in the strip (unlike the crack problem for an infinite plane) the stress-intensity factors are dependent on the elastic constants and are generally different from the corresponding isotropic results.

Three-Dimensional Analysis of Cracking Through the Boundary of a Two-Phase Material

1989 ◽  
Vol 56 (4) ◽  
pp. 850-857 ◽  
Author(s):  
M. T. Hanson ◽  
W. Lin ◽  
L. M. Keer
Keyword(s):  
Stress Intensity ◽  
Phase Boundary ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
Three Dimensional ◽  
Singular Integral Equations ◽  
The Body ◽  
Intensity Factors ◽  
Two Phase ◽  
Penny Shaped Crack

The penetration through a two-phase boundary by a biplanar (kinked) crack of arbitrary shape is considered in this paper. The two-phase boundary is modeled as the interface between two perfectly-bonded elastic, isotropic, homogeneous half spaces with different elastic constants. The planar crack on either side of the interface may be arbitrarily orientated with respect to the interface boundary. The body-force method is used to derive a set of coupled two-dimensional singular integral equations which are solved numerically. The solution yields the three crack opening displacements as well as the three modes of stress intensity factors along the crack contour. Numerical results are given for a penny-shaped crack symmetrically oriented with respect to the interface. Mode I stress intensity factors are given for the biplanar crack that experiences a kink when passing through the interface.

Crack Problem for a Semi-Infinite Solid With Heated Bounding Surface

1977 ◽  
Vol 44 (4) ◽  
pp. 637-642 ◽  
Author(s):  
H. Sekine
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Thermal Stresses ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
Bounding Surface ◽  
Edge Dislocations

On the basis of the stationary two-dimensional theory of thermoelasticity, the thermal stresses near the tips of a thermally insulated line crack situated in a semi-infinite solid which is heated on a part of the bounding surface is considered. The crack is replaced by continuous distributions of temperature dislocations and edge dislocations. Then the integral equations are obtained as a system of singular integral equations with Cauchy kernels. By means of this method, the singular behavior of the thermal stresses around the crack tips is easily examined and the stress-intensity factors can be readily evaluated. Numerical results for the stress-intensity factors are plotted in terms of the geometrical parameters.

The Mixed Mode Crack Problem in a FGM Layer

2003 ◽  
Author(s):  
X. Long ◽  
F. Delale
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Crack Problem ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Multiphase Composites ◽  
Fgm Layer ◽  
First Time

Functionally graded materials (FGMs) are multiphase composites whose composition, microstructure and properties vary gradually. They can be tailored to meet the requirements encountered in practice through the design of their constituents. In this paper, analytical expressions for stress intensity factors off mixed-mode cracks in a FGM strip have been derived for the first time. A parametric study, by varying both the geometric and material parameters, is conducted to determine their effects on the stress intensity factors.

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