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.

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 Interaction of Collinear Arrays of Griffith Cracks on Two Radial Lines

1976 ◽  
Vol 98 (3) ◽  
pp. 1086-1091 ◽  
Author(s):  
O. Aksogan
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Mellin Transform ◽  
Singular Integral Equations ◽  
Graphical Form ◽  
Infinite Plane ◽  
Intensity Factors ◽  
Fundamental Function ◽  
Analytical Technique

The elastostatic plane problem of an isotropic homogeneous infinite plane with a number of Griffith cracks lying along two radial lines is considered. The analytical technique consists of the joint use of the Mellin transform and the Green’s function. The system of singular integral equations, thus obtained, is solved numerically taking advantage of the fact that the fundamental function is the weight function of the Chebyshev polynomials. The results for several cases are compared with those of previous authors. Stress intensity factors and probable directions of cleavage, which are important from the viewpoint of fracture mechanics, are studied in detail and illustrative numerical results for selected cases of geometry and loading are presented in graphical form.

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.

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.

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.

Analysis of Multiple Rigid-Line Inclusions for Application to Bio-Materials

2007 ◽  
Author(s):  
Pawan S. Pingle ◽  
Larissa Gorbatikh ◽  
James A. Sherwood
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Building Blocks ◽  
Duality Principle ◽  
Inclusion Problem ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Aspect Ratios ◽  
Rigid Line

Hard biological materials such as nacre and enamel employ strong interactions between building blocks (mineral crystals) to achieve superior mechanical properties. The interactions are especially profound if building blocks have high aspect ratios and their bulk properties differ from properties of the matrix by several orders of magnitude. In the present work, a method is proposed to study interactions between multiple rigid-line inclusions with the goal to predict stress intensity factors. Rigid-line inclusions provide a good approximation of building blocks in hard biomaterials as they possess the above properties. The approach is based on the analytical method of analysis of multiple interacting cracks (Kachanov, 1987) and the duality existing between solutions for cracks and rigid-line inclusions (Ni and Nasser, 1996). Kachanov’s method is an approximate method that focuses on physical effects produced by crack interactions on stress intensity factors and material effective elastic properties. It is based on the superposition technique and the assumption that only average tractions on individual cracks contribute to the interaction effect. The duality principle states that displacement vector field for cracks and stress vector-potential field for anticracks are each other’s dual, in the sense that solution to the crack problem with prescribed tractions provides solution to the corresponding dual inclusion problem with prescribed displacement gradients. The latter allows us to modify the method for multiple cracks (that is based on approximation of tractions) into the method for multiple rigid-line inclusions (that is based on approximation of displacement gradients). This paper presents an analytical derivation of the proposed method and is applied to the special case of two collinear inclusions.

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.

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