Effect of Contact Interaction on the Stress Intensity Factors for a Crack under Harmonic Loading

2006 ◽  
Vol 5-6 ◽  
pp. 173-180 ◽  
Author(s):  
O.V. Menshykov ◽  
I.A. Guz
Keyword(s):  
Contact Interaction ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Harmonic Loading ◽  
Dynamic Problems ◽  
Intensity Factors ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Cracked Solids ◽  
Crack Faces

This paper concerns fracture dynamic problems for elastic cracked solids with allowance for crack faces contact interaction. The contact problem for a penny-shaped crack with an initial opening under normally incident tension-compression wave is solved by the method of boundary integral equations. The solution is compared with those obtained without allowance for crack faces contact interaction for various values of the initial opening.

Boundary integral equations in elastodynamics of interface cracks

2008 ◽  
Vol 366 (1871) ◽  
pp. 1835-1839 ◽  
Author(s):  
O.V Menshykov ◽  
I.A Guz ◽  
V.A Menshykov
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Harmonic Loading ◽  
Interface Cracks ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Cracked Solids

The paper concerns the validation of a method for solving elastodynamics problems for cracked solids. The proposed method is based on the application of boundary integral equations. The problem of an interface penny-shaped crack between two dissimilar elastic half-spaces under harmonic loading is considered as an example.

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

scholarly journals Boundary Integral Equations for an Anisotropic Bimaterial with Thermally Imperfect Interface and Internal Inhomogeneities

2016 ◽  
Vol 10 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Heorhiy Sulym ◽  
Iaroslav Pasternak ◽  
Mykhailo Tomashivskyy
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Bimaterial Interface ◽  
Intensity Factors ◽  
New Approach ◽  
Adhesive Layers ◽  
Type Integral ◽  
Anisotropic Bimaterial

Abstract This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant inter-facial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.

scholarly journals Doubly Periodic Cracks in the Anisotropic Medium with the Account of Contact of Their Faces

2014 ◽  
Vol 8 (3) ◽  
pp. 160-164 ◽  
Author(s):  
Olesya Maksymovych ◽  
Iaroslav Pasternak ◽  
Heorhiy Sulym ◽  
Serhiy Kutsyk
Keyword(s):  
Complex Variable ◽  
Boundary Integral Equations ◽  
Solution Procedure ◽  
Boundary Integral ◽  
Singular Boundary ◽  
Anisotropic Elastic Medium ◽  
Periodic Cracks ◽  
Anisotropic Elastic ◽  
Crack Faces ◽  
Integral Formulae

Abstract The paper presents complex variable integral formulae and singular boundary integral equations for doubly periodic cracks in anisotropic elastic medium. It utilizes the numerical solution procedure, which accounts for the contact of crack faces and produce accurate results for SIF evaluation. It is shown that the account of contact effects significantly influence the SIF of doubly periodic curvilinear cracks both for isotropic and anisotropic materials.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

2017 ◽  
Vol 29 (6) ◽  
pp. 1255-1271 ◽  
Author(s):  
MingHao Zhao ◽  
Yuan Li ◽  
CuiYing Fan
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Green Functions ◽  
Intensity Factors

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

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 New Boundary Integral Equation Method for Cracked Piezoelectric Bodies

2006 ◽  
Vol 306-308 ◽  
pp. 465-470 ◽  
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Present Method ◽  
Boundary Integral Equations ◽  
Integral Formula ◽  
Electric Displacement ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Equation Method ◽  
Intensity Factors

A novel integral equation method is developed in this paper for the analysis of two-dimensional general piezoelectric cracked bodies. In contrast to the conventional boundary integral methods based on reciprocal work theorem, the present method is derived from Stroh’s formalism for anisotropic elasticity in conjunction with Cauchy’s integral formula. The proposed boundary integral equations contain generalized boundary displacement (displacements and electric potential) gradients and generalized tractions (tractions and electric displacement) on the non-crack boundary, and the generalized dislocations on the crack lines. The boundary integral equations can be solved using Gaussian-type integration formulas without dividing the boundary into discrete elements. The crack-tip singularity is explicitly incorporated and the generalized intensity factors can be computed directly. Numerical examples of generalized stress intensity factors are given to illustrate the effectiveness and accuracy of the present method.

scholarly journals Boundary integral equations for an interface linear crack under harmonic loading

2010 ◽  
Vol 234 (7) ◽  
pp. 2279-2286 ◽  
Author(s):  
I.I. Mykhailova ◽  
O.V. Menshykov ◽  
M.V. Menshykova ◽  
I.A. Guz
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Harmonic Loading

Axisymmetric Problem of Energetically Consistent Interacting Annular and Penny-Shaped Cracks in Piezoelectric Materials

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
H. M. Shodja ◽  
S. S. Moeini-Ardakani ◽  
M. Eskandari
Keyword(s):  
Axisymmetric Problem ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Intensity Factors ◽  
Annular Crack ◽  
Penny Shaped Crack ◽  
Contour Plots ◽  
Shaped Crack ◽  
Electromechanical Loading

The axisymmetric problem of a concentric set of energetically consistent annular and penny-shaped cracks in an infinite piezoelectric body subjected to uniform far-field electromechanical loading is addressed. With the aid of a robust innovated technique, the pertinent four-part mixed boundary value problem (MBVP) is reduced to a decoupled Fredholm integral equation of the second kind. The results of two limiting cases of a single penny-shaped crack and a single annular crack are recovered. The contour plots of dimensionless intensity factors (IFs) at each crack front provide the stress and electric displacement intensity factors (SIFs and EDIFs, respectively) for all combination of crack sizes. The impermeable, permeable, and semipermeable models are also examined as limiting cases.

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