Resonance Effects for a Crack Near a Free Surface

1984 ◽  
Vol 51 (1) ◽  
pp. 65-70 ◽  
Author(s):  
L. M. Keer ◽  
W. Lin ◽  
J. D. Achenbach
Keyword(s):  
Free Surface ◽  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Wave Equations ◽  
Plate Theory ◽  
Resonance Effect ◽  
Harmonic Excitation ◽  
Intensity Factors ◽  
Resonance Effects

Stress intensity factors are computed for a horizontal subsurface crack that is subjected to 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. At specific values of the frequency, a resonance effect is observed and a correlation with the natural frequencies calculated by a Timoshenko plate theory for the layer between the crack and the free surface is noted.

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 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.

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.

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.

scholarly journals Thermoelastic Analysis for Two Collinear Cracks in an Orthotropic Solid Disturbed by Antisymmetrical Linear Heat Flow

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Bing Wu ◽  
Jun-gao Zhu ◽  
Daren Peng ◽  
Rhys Jones ◽  
Shi-hu Gao ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Heat Flow ◽  
Intensity Factor ◽  
Thermal Resistance ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Mode Ii ◽  
Intensity Factors ◽  
Collinear Cracks

The problem of two collinear cracks in an orthotropic solid under antisymmetrical linear heat flow is investigated. It is assumed that there exists thermal resistance to heat conduction through the crack region. Applying the Fourier transform, the thermal coupling partial differential equations are transformed to dual integral equations and then to singular integral equations. The crack-tip thermoelastic fields including the jumps of temperature and elastic displacements on the cracks and the mode II stress intensity factors are obtained explicitly. Numerical results show the effects of the geometries of the cracks and the dimensionless thermal resistance on the temperature change and the mode II stress intensity factors. Also, FEM solutions for the stress intensity factor K are used to compare with the solutions obtained using the method. It is revealed that the friction in closed crack surface region should be considered in analyzing the stress intensity factor K.

Stress Intensity Factor Interaction for Subsurface to Surface Flaw Transformations Under Stress Concentration Fields

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Pierre Dulieu ◽  
Valéry Lacroix ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity Factor ◽  
Free Surface ◽  
Stress Intensity ◽  
Stress Concentration ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Concentration Field ◽  
Surface Flaw ◽  
Intensity Factors ◽  
Surface Proximity

If a single subsurface flaw is detected that is close to a component's free surface, a flaw-to-surface proximity rule is used to determine whether the flaw should be treated as a subsurface flaw, or transformed to a surface flaw. The transformation from subsurface to surface flaw is adopted as flaw-to-surface proximity rules in all fitness-for-service (FFS) codes. These proximity rules are applicable when the component's free surface is without a stress concentration. On the other hand, subsurface flaws have been found under notches, such as roots of bolts, toes in welded joints, or geometrical discontinuities of components. The stress intensity factors of the subsurface flaws are affected by the stress concentrations caused by the notches. The stress intensity factor of the subsurface flaw increases with increasing stress concentration factor of the notch and decreasing ligament distance between tip of the subsurface flaws and the notch, for a given notch width. Such subsurface flaws are transformed to surface flaws at a distance from the notch tip for conservative evaluations. This paper shows the interactions of stress intensity factors of subsurface flaws under stress concentration fields. Based on the interaction, a flaw-to-surface proximity criterion is proposed for a circular flaw under the stress concentration field induced by a notch.

Collinear Internal Cracks and Edge Crack in a Semi-Infinite Sheet Subjected to Arbitrary Tractions

1995 ◽  
Vol 117 (3) ◽  
pp. 256-259 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Numerical Analysis ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Edge Crack ◽  
Mutual Interaction ◽  
Internal Crack ◽  
Intensity Factors ◽  
Plate Edge

The stress intensity factors are calculated for collinear internal cracks and an edge crack in a semi-infinite sheet subjected to arbitrary tractions. Analysis is conducted by formulating the integral equations of tractions along the plate edge and crack surfaces. The accuracy is checked with known results in the literature. Then, the numerical analysis is used to establish the stress intensity factors for various sizes of the edge crack and internal cracks in tension. Also, the stress intensity factors are calculated for the edge crack and internal crack subjected to typical distributed loadings, and the effects of mutual interaction between the cracks are presented.

Sign in / Sign up

Export Citation Format

Share Document