A Crack in an Anisotropic Layered Material Under the Action of Impact Loading

1988 ◽  
Vol 55 (1) ◽  
pp. 120-125 ◽  
Author(s):  
W. T. Ang
Keyword(s):  
Stress Intensity ◽  
Laplace Transform ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Impact Loading ◽  
Layered Material ◽  
Fredholm Integral Equations ◽  
Transform Domain ◽  
Intensity Factors ◽  
The Laplace Transform

The problem of a plane crack in an anisotropic layered material under the action of impact loading is considered in this paper. The problem is reduced in the Laplace transform domain to a set of simultaneous Fredholm integral equations of the second kind. Once these integral equations are solved, the crack tip stress intensity factors in the Laplace transform domain may be readily calculated. The dynamic stress intensity factors can then be obtained through the use of a numerical technique for inverting Laplace transforms. Numerical results are given for specific examples involving particular transversely isotropic materials.

Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method

1999 ◽  
Vol 67 (3) ◽  
pp. 606-615 ◽  
Author(s):  
W.-H. Chen ◽  
C.-L. Chang ◽  
C.-H. Tsai
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Laplace Transform ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Alternating Method ◽  
The Laplace Transform

The Laplace finite element alternating method, which combines the Laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. By the Laplace transform technique, the complicated elastodynamic fracture problem is first transformed into an equivalent static fracture problem in the Laplace transform domain and then solved by the finite element alternating method developed. To do this, an analytical solution by Tsai and Ma for an infinite plate with a semi-infinite crack subjected to exponentially distributed loadings on crack surfaces in the Laplace transform domain is adopted. Finally, the real-time response can be computed by a numerical Laplace inversion algorithm. The technique established is applicable to the calculation of dynamic stress intensity factors of a finite plate with arbitrarily distributed edge cracks or symmetrically distributed central cracks. Only a simple finite element mesh with very limited number of regular elements is necessary. Since the solutions are independent of the size of time increment taken, the dynamic stress intensity factors at any specific instant can even be computed by a single time-step instead of step-by-step computations. The interaction among the cracks and finite geometrical boundaries on the dynamic stress intensity factors is also discussed in detail. [S0021-8936(00)02103-6]

Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

scholarly journals Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

1997 ◽  
Vol 64 (1) ◽  
pp. 66-72 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Stress Intensity ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Layered Medium ◽  
Transform Domain ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.

Eccentric annular crack under general nonuniform internal pressure

2016 ◽  
Vol 25 (3-4) ◽  
pp. 69-76 ◽  
Author(s):  
S. Moeini-Ardakani ◽  
M.T. Kamali ◽  
H.M. Shodja
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Analytical Approach ◽  
Fredholm Integral Equations ◽  
Crack Model ◽  
Intensity Factors ◽  
Rigorous Solution ◽  
Annular Crack ◽  
Uniform Tension

AbstractFor a better approximation of ring-shaped and toroidal cracks, a new eccentric annular crack model is proposed and an analytical approach for determination of the corresponding stress intensity factors is given. The crack is subjected to arbitrary mode I loading. A rigorous solution is provided by mapping the eccentric annular crack to a concentric annular crack. The analysis leads to two decoupled Fredholm integral equations of the second kind. For the sake of verification, the problem of a conventional annular crack is examined. Furthermore, for various crack configurations of an eccentric annular crack under uniform tension, the stress intensity factors pertaining to the inner and outer crack edges are delineated in dimensionless plots.

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 2: Fully Anisotropic Materials

1984 ◽  
Vol 51 (4) ◽  
pp. 780-786 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Mathematical Problem ◽  
Stress Singularity ◽  
Interfacial Crack ◽  
Singular Integral Equations ◽  
Intensity Factors

Dynamic stress intensity factors for an interfacial crack between two dissimilar elastic, fully anisotropic media are studied. The mathematical problem is reduced to three coupled singular integral equations. Using Jacobi polynomials, solutions to the singular integral equations are obtained numerically. The orders of stress singularity and stress intensity factors of an interfacial crack in a (θ(1)/θ(2)) composite solid agree well with the finite element solutions.

Dynamic Stress Intensity Factors for an Inclined Subsurface Crack

1984 ◽  
Vol 51 (4) ◽  
pp. 773-779 ◽  
Author(s):  
W. Lin ◽  
L. M. Keer ◽  
J. D. Achenbach
Keyword(s):  
Free Surface ◽  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Wave Equations ◽  
Harmonic Excitation ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Time Harmonic

Stress intensity factors are computed for an inclined subsurface crack in a half space, whose surface is subjected to uniform time-harmonic excitation. The problem is analyzed by determining displacement potentials that satisfy reduced wave equations and specified boundary conditions. The formulation of the problem leads to a system of coupled integral equations for the dislocation densities. The numerical solution of the integral equations leads directly to the stress intensity factors. Curves are presented for the ratios of the elastodynamic and the corresponding elastostatic Mode-I and Mode-II stress intensity factors for various frequencies and various inclinations of the crack with the free surface. For small angles of inclination with the free surface and large crack length-to-depth ratios, strong resonance vibrations of the layer between the crack and the free surface may arise.

Stress Analysis for a Double Lap Joint

1975 ◽  
Vol 42 (2) ◽  
pp. 353-357 ◽  
Author(s):  
L. M. Keer ◽  
K. Chantaramungkorn
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Lap Joint ◽  
Intensity Factors

The problem of a double lap joint is analyzed and solved by using integral transform techniques. Singular integral equations are deduced from integral transform solutions using boundary and continuity conditions appropriate to the problem. Numerical results are obtained for the case of identical materials for the cover and central layers. Stress-intensity factors are calculated and presented in the form of a table and contact stresses are shown in the form of curves for various values of geometrical parameters.

Transient Analysis of a Propagating In-Plane Crack in a Finite Geometry Body Subjected to Static Loadings

1997 ◽  
Vol 64 (3) ◽  
pp. 620-628 ◽  
Author(s):  
Chwan-Huei Tsai ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Transform Domain ◽  
Free Boundaries ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Reflected Waves ◽  
The Laplace Transform

In this study, a cracked body with finite boundaries subjected to static loading and the crack propagating with a constant speed are analyzed. The interaction of the propagating crack with reflected waves generated from traction-free boundaries is investigated in detail. The methodology for constructing the scattered field by superimposing the fundamental solution in the Laplace transform domain is proposed. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or a crack. The dynamic stress intensity factors of a propagating crack induced from the interaction with the first few reflected waves generated from the traction-free boundary are obtained in an explicit closed form. The analytical solutions of dynamic stress intensity factors are compared with available numerical and experimental results and the agreement is quite good. We find one thing very interesting: the dynamic stress intensity factor for a long time period is a universal function of the instantaneous extending rate of a crack tip times the static stress intensity factor for an equivalent stationary crack for the finite strip problem. It was also found that the reflected waves generated from free boundaries always increase the stress intensity factor, and the influence from reflected waves generated from the boundary, which is perpendicular to the crack, are weaker than those generated from the boundary, which is parallel to the crack.

Contact Analysis for Collinear Multiple Cracks in Residual Stress Field

1994 ◽  
Vol 116 (2) ◽  
pp. 169-174 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Infinite Plate ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Residual Stress Field ◽  
Crack Face

A method is proposed for analyzing stress intensity factors and crack profiles for collinear multiple cracks perpendicular to welded joints in an infinite plate. Using the basic solution of a single crack and taking unknown density of fictitious tractions, Fredholm integral equations and algebraic equations are formulated based upon traction-free conditions and crack face displacements, respectively. These equations are solved simultaneously, considering the contact effect of crack surfaces. Using the derived density of fictitious tractions, the stress intensity factors and displacements of multiple cracks are determined. Some numerical examples are analyzed.

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