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.

scholarly journals Interaction of a finite crack with shear waves in an infinite magnetoelastic medium

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Sourav Kumar Panja ◽  
Subhas Chandra Mandal
Keyword(s):  
Integral Equation ◽  
Integral Transformation ◽  
Crack Opening ◽  
Shear Waves ◽  
Fourier Integral ◽  
Opening Displacement ◽  
Field Interaction ◽  
Low Frequencies ◽  
Finite Crack ◽  
Magnetoelastic Medium

The aim of this paper is to investigate the interaction of a finite crack with shear waves in an infinite magnetoelastic medium. Fourier integral transformation is applied to convert the boundary value problem for a homogeneous, isotropic elastic material to the Fredholm integral equation of second kind. The integral equation is solved by the perturbation method and the effect of magnetic field interaction on the crack is discussed. The stress intensity factor at the crack tip is determined numerically and plotted for low frequencies. Moreover, shear stress outside the crack, crack opening displacement, and crack energy are evaluated and shown by means of graphs.

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.

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 From an Elliptic Crack by an Integral Equation Method: Normal Loading

2002 ◽  
Vol 69 (6) ◽  
pp. 775-784
Author(s):  
T. K. Saha ◽  
A. Roy
Keyword(s):  
Integral Equation ◽  
Crack Opening Displacement ◽  
Cross Section ◽  
Infinite System ◽  
Crack Opening ◽  
Scattering Cross Section ◽  
Elliptic Crack ◽  
Opening Displacement ◽  
Normal Loading ◽  
Scattering Cross

The scattering of normally incident elastic waves by an embedded elliptic crack in an infinite isotropic elastic medium has been solved using an analytical numerical method. The representation integral expressing the scattered displacement field has been reduced to an integral equation for the unknown crack-opening displacement. This integral equation has been further reduced to an infinite system of Fredholm integral equation of the second kind and the Fourier displacement potentials are expanded in terms of Jacobi’s orthogonal polynomials. Finally, proper use of orthogonality property of Jacobi’s polynomials produces an infinite system of algebraic equations connecting the expansion coefficients to the prescribed dynamic loading. The matrix elements contains singular integrals which are reduced to regular integrals through contour integration. The first term of the first equation of the system yields the low-frequency asymptotic expression for scattering cross section analytically which agrees completely with previous results. In the intermediate and high-frequency scattering regime the system has been truncated properly and solved numerically. Results of quantities of physical interest, such as the dynamic stress intensity factor, crack-opening displacement scattering cross section, and back-scattered displacement amplitude have been given and compared with earlier results.

Axisymmetric Singular Stresses in a Thick-Walled Spherical Shell With an Internal Edge Crack

1983 ◽  
Vol 50 (1) ◽  
pp. 37-42 ◽  
Author(s):  
A. Atsumi ◽  
Y. Shindo
Keyword(s):  
Integral Equation ◽  
Spherical Shell ◽  
Edge Crack ◽  
Integral Transform ◽  
Crack Opening ◽  
Cauchy Kernel ◽  
Opening Displacement ◽  
Inner Surface ◽  
Dominant Part ◽  
Integral Transform Technique

The paper considers the elastostatic axisymmetric problem for a thick-walled spherical shell containing a circumferential edge crack on the inner surface. The ring-shaped edge crack and the inner surface of the spherical shell are subjected to internal pressure. Using an integral transform technique we obtain a singular integral equation of the first kind which has a generalized Cauchy kernel as the dominant part. The integral equation is solved numerically, and the influence of the geometrical configuration on the stress-intensity factor and the crack-opening displacement is shown graphically in detail.

Fatigue Crack Growth Tests on Glass Fibre Reinforced Polymer Matrix Composite

2005 ◽  
Vol 473-474 ◽  
pp. 189-194
Author(s):  
Zilia Csomós ◽  
János Lukács
Keyword(s):  
Cyclic Loading ◽  
Crack Opening Displacement ◽  
Matrix Composite ◽  
Glass Fibre ◽  
Crack Opening ◽  
Loading Conditions ◽  
Opening Displacement ◽  
Interfacial Cracks ◽  
Glass Fibre Reinforced ◽  
Number Of Cycles

E-glass fibre reinforced polyester matrix composite was investigated, which was made by pullwinding process. Round three point bending (RTPB) specimens were tested under quasi-static and mode I cyclic loading conditions. Load vs. displacement (F-f), load vs. crack opening displacement (F-v) and crack opening displacement range vs. number of cycles (ΔCOD-N) curves were registered and analysed. Interfacial cracks were caused the final longitudinal fracture of the specimens under quasi-static and cyclic loading conditions.

Uncertainty Characterization of the CrCOD Circumferential Crack Opening Displacement Module for xLPR

2015 ◽  
Author(s):  
Richard Olson ◽  
Paul Scott
Keyword(s):  
Crack Opening Displacement ◽  
Crack Opening ◽  
Opening Displacement ◽  
Crack Face ◽  
Pipe Surface ◽  
Circumferential Crack ◽  
The Us ◽  
Experimental Values ◽  
Metal Weld

The US NRC/EPRI xLPR (eXtremely Low Probability of Rupture) probabilistic pipe fracture analysis program uses deterministic modules as the foundation for the calculation of the probability of pipe leak or rupture as a consequence of active degradation mechanisms, vibration or seismic loading. The circumferential crack opening displacement module, CrCOD, estimates crack opening displacement (COD) at the inside pipe surface, at the mid-wall thickness location, and at the outside pipe surface using a combined tension/crack face pressure/bending GE/EPRI-like solution. Each module has an uncertainty beyond the uncertainty of the xLPR data inputs. This paper documents the uncertainty for CrCOD. Using 36 pipe fracture experiments, including: base metal, similar metal weld, and dissimilar metal weld experiments; bend only and pressure and bend loading; static and dynamic load histories; cracks that range from short to long, the uncertainty of the CrCOD methodology is characterized. Module uncertainty is presented in terms mean fit and standard deviation between prediction and experimental values.

Sign in / Sign up

Export Citation Format

Share Document