On the boundary integral equations for the crack opening displacement of flat cracks

1992 ◽  
Vol 15 (3) ◽  
pp. 427-453 ◽  
Author(s):  
Tuong Ha-Duong
Keyword(s):  
Crack Opening Displacement ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Boundary Integral ◽  
Opening Displacement

A New Boundary Integral Equation Formulation for Elastodynamic and Elastostatic Crack Analysis

1989 ◽  
Vol 56 (2) ◽  
pp. 284-290 ◽  
Author(s):  
Ch. Zhang ◽  
J. D. Achenbach
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Boundary Integral ◽  
Static Case ◽  
Dislocation Densities ◽  
Integral Equation Formulation ◽  
Conventional Manner ◽  
Crack Faces ◽  
Natural Way

An elastodynamic conservation integral, the J˜k integral, is employed to derive boundary integral equations for crack configurations in a direct and natural way. These equations immediately have lower-order singularities than the ones obtained in the conventional manner by the use of the Betti-Rayleigh reciprocity relation. This is an important advantage for the development of numerical procedures for solving the BIE’s, and for an accurate calculation of the strains and stresses at internal points close to the crack faces. For curved cracks of arbitrary shape the BIE’s presented here have simple forms, and they do not require integration by parts, as in the conventional formulation. For the dynamic case the unknown quantities are the crack opening displacements and their derivatives (dislocation densities), while for the static case only the dislocation densities appear in the formulation. For plane cracks the boundary integral equations reduce to the ones obtained by other investigators.

Micromechanical Dynamic Influence of Rigid Disk-Shaped Inclusion on Neighboring Crack in 3D Elastic Matrix

2007 ◽  
Vol 567-568 ◽  
pp. 133-136 ◽  
Author(s):  
Victor V. Mykhas'kiv ◽  
O. Khay ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Chuan Zeng Zhang
Keyword(s):  
Boundary Integral Equations ◽  
Crack Opening ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Elastic Matrix ◽  
Opening Displacement ◽  
Rigid Disk ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Inclusion

A 3D time-harmonic problem for an infinite elastic matrix with an arbitrarily located interacting rigid disk-shaped inclusion and a penny-shaped crack is analyzed by the boundary integral equation method. Perfect bonding between the matrix and the moving inclusion is assumed. The crack faces are subjected to time-harmonic loading. The boundary integral equations (BIEs) obtained are solved numerically by the implementation of regularization and discretization procedures. Numerical calculations are carried out for a crack under tensile loading of constant amplitude, where an interacting inclusion is perpendicular to the crack and has the same radius. Both the normal crack-opening-displacement and the mode-I stress intensity factor are investigated for different wave numbers and distances between the crack and the inclusion.

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.

Scattering by Multiple Crack Configurations

1988 ◽  
Vol 55 (1) ◽  
pp. 104-110 ◽  
Author(s):  
Ch. Zhang ◽  
J. D. Achenbach
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Scattered Field ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Boundary Integral ◽  
Intensity Factors ◽  
Closed Crack ◽  
Scattered Fields

A system of boundary integral equations is presented which governs the crack-opening displacements for two-crack configurations. The integral equations are highly singular and they cannot be solved directly by numerical methods. By the approach of this paper the higher order singularities are, however, reduced to integrable singularities, and the integral equations are subsequently discretized and solved numerically. For several configurations numerical results have been obtained for scattered fields and for elastodynamic stress intensity factors. The scattered-field results are interpreted to apply for a partially closed crack as well as for two separate but neighboring cracks. The stress-intensity factors are intended to apply only to the case of separate cracks. The scattered-field results have relevance to the problem of detection and characterization of cracks in the field of quantitative nondestructive evaluation.

Sign in / Sign up

Export Citation Format

Share Document