Elastodynamic Analysis of a Periodic Array of Mode III Cracks in Transversely Isotropic Solids

1992 ◽  
Vol 59 (2) ◽  
pp. 366-371 ◽  
Author(s):  
Ch. Zhang
Keyword(s):  
Integral Equation ◽  
Crack Opening Displacement ◽  
Boundary Integral Equation ◽  
Crack Opening ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Crack Spacing ◽  
Periodic Array ◽  
Mode Iii ◽  
Opening Displacement

Time-harmonic elastodynamic analysis is presented for a periodic array of collinear mode III cracks in an infinite transversely isotropic solid. The scattering problem by a single antiplane crack is first formulated, and the scattered displacement field is expressed as Fourier integrals containing the crack opening displacement. By using this representation formula and by considering the periodicity conditions in the crack spacing, a boundary integral equation is obtained for the crack opening displacement of a reference crack. The boundary integral equation is solved numerically by expanding the crack opening displacement into a series of Chebyshev polynomials. Numerical results are given to show the effects of the crack spacing, the wave frequency, the angle of incidence, and the anisotropy parameter on the elastodynamic stress intensity factors.

Three-dimensional analysis of cracks in layered transversely isotropic media

1989 ◽  
Vol 424 (1867) ◽  
pp. 307-322 ◽  
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Crack Opening ◽  
Mathematical Formulation ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Opening Displacement ◽  
Transversely Isotropic Media ◽  
Isotropic Media

A general mathematical formulation to analyse cracks in layered transversely isotropic media is developed in this paper. By constructing the Green’s functions, an integral equation is obtained to determine crack opening displacements when an applied crack face traction is specified. For the infinite body, the Green’s functions have solutions in a closed form. For layered media, a flexibility matrix in the integral transformed domain is formed that establishes the relation between the traction and the displacement for a single layer; the global matrix is formed by assembling all of the flexibility matrices constructed for each layer. The Green’s functions in the spatial domain are obtained by inversion of the Hankel transform. Finally, the crack opening displacement and the crack-tip opening displacement for a vertical planar crack in a layered transversely isotropic medium are obtained numerically by the boundary integral equation method.

Dynamic crack-opening displacement of a mode III edge crack in a semi-infinite piezoceramic strip under electric excitation

2007 ◽  
Vol 221 (9) ◽  
pp. 1009-1017
Author(s):  
X-F Li ◽  
Kang Yong Lee
Keyword(s):  
Crack Opening Displacement ◽  
Edge Crack ◽  
Crack Opening ◽  
Transversely Isotropic ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Opening Displacement ◽  
Electric Excitation

The transient response of a semi-infinite transversely isotropic piezoceramic strip containing an edge crack is analysed for the case where electric excitation is suddenly exerted at the material end surface. The crack is assumed to be impermeable to electric field. Ahypersingular integral equation for crack-opening displacement (COD) is derived via solving the associated mixed initial-boundary-value problem and solved numerically based on a collocation technique. By performing a numerical inversion of Laplace transform, dynamic CODs are determined and illustrated graphically.

scholarly journals Periodic Array of Cracks in a Half-Plane Subjected to Arbitrary Loading

1987 ◽  
Vol 54 (3) ◽  
pp. 642-648 ◽  
Author(s):  
H. F. Nied
Keyword(s):  
Integral Equation ◽  
Half Plane ◽  
Crack Surface ◽  
Mixed Boundary ◽  
Crack Opening ◽  
Periodic Array ◽  
Hypersingular Integral Equation ◽  
Opening Displacement ◽  
Surface Displacements ◽  
Displacement Based

The plane elastic problem for a periodic array of cracks in a half-plane subjected to equal, but otherwise arbitrary normal crack surface tractions is examined. The mixed boundary value problem, which is formulated directly in terms of the crack surface displacements, results in a hypersingular integral equation in which the unknown function is the crack opening displacement. Based on the theory of finite part integrals, a least squares numerical algorithm is employed to efficiently solve the singular integral equation. Numerical results include crack opening displacements, stress intensity factors, and Green’s functions for the entire range of possible periodic crack spacing.

Square Cracks in Three-Dimensional Transversely Isotropic Solids

2012 ◽  
Vol 487 ◽  
pp. 617-621
Author(s):  
Ya Dong Bian ◽  
Yu Zhou Sun
Keyword(s):  
Crack Opening ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Least Square ◽  
Weight Functions ◽  
Opening Displacement ◽  
Moving Least Square ◽  
Moving Least Square Approximation ◽  
Fracture Damage

This paper presents a study for the square crack in a three-dimensional infinite transversely isotropic medium, which can model the fracture damage of rock that displays transversely isotropic behavior. The study is based on a newly derived boundary integral equation. To carry out the numerical simulation, the crack opening displacement is first expressed as the product of the weight functions and the characteristic terms, and the unknown weight is approximated with the moving least-square approximation. A boundary type numerical scheme is established, and the effect of the orientation of the principle axis on the stress intensity factor is studied. The interaction between two coplanar square cracks are also modeled and discussed.

Diffraction of Antiplane Shear Waves by an Edge Crack

1980 ◽  
Vol 47 (2) ◽  
pp. 359-362 ◽  
Author(s):  
S. F. Stone ◽  
M. L. Ghosh ◽  
A. K. Mal
Keyword(s):  
Integral Equation ◽  
Crack Opening Displacement ◽  
Edge Crack ◽  
Incident Angle ◽  
Crack Opening ◽  
Shear Waves ◽  
Antiplane Shear ◽  
Opening Displacement ◽  
Low Frequencies ◽  
High Frequencies

The diffraction of time harmonic antiplane shear waves by an edge crack normal to the free surface of a homogeneous half space is considered. The problem is formulated in terms of a singular integral equation with the unknown crack opening displacement as the density function. A numerical scheme is utilized to solve the integral equation at any given finite frequency. Asymptotic solutions valid at low and high frequencies are obtained. The accuracy of the numerical solution at high frequencies and of the high frequency asymptotic solution at intermediate frequencies are examined. Graphical results are presented for the crack opening displacement and the stress intensity factor as functions of frequency and the incident angle, Expressions for the far-field displacements at high and low frequencies are also presented.

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