External Circular Crack Under Normal Load: A Complete Solution

1994 ◽  
Vol 61 (4) ◽  
pp. 809-814 ◽  
Author(s):  
V. I. Fabrikant ◽  
B. S. Rubin ◽  
E. N. Karapetian
Keyword(s):  
Normal Load ◽  
Complete Solution ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Elementary Functions ◽  
Normal Loading ◽  
Method Of Solution ◽  
External Circular Crack ◽  
Concentrated Loading ◽  
Crack Faces

For the first time, a complete solution in terms of elementary functions is given to the problem of a transversely isotropic elastic space weakened by an external circular crack and subjected to arbitrary normal loading applied symmetrically to both crack faces. A complete field of displacements and stresses due to a concentrated loading is given for both transversely isotropic and purely isotropic cases. The method of solution is based on the results published earlier by the first author.

Forced Vibrations of a Transversely Isotropic Composite Containing an External Circular Crack

2001 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Dynamic Stress ◽  
Crack Surface ◽  
Dynamic Stress Intensity Factor ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Force Frequency ◽  
Isotropic Composite ◽  
External Circular Crack

Abstract The problem of a transversely isotropic composite containing an external circular crack is investigated using the method of Hankel transforms. A pair of tensile vibratory forces of equal amplitude are applied normal to the crack surface at infinity. A complete contour integration is employed to simplify the expressions of the results. An exact expression of the dynamic stress-intensity factor is obtained as a function of the force frequency and the anisotropic material constants. The normalized dynamic stress-intensity factor is shown to have different maximum values at different force frequencies for the sample fiber-reinforced and metal matrix composites. The deviation of the dynamic crack surface displacement from the associated static displacement is also shown to be dependent on the force frequency and the anisotropy of the material.

Dynamic Response to Normal Stresses in a Transversely Isotropic Material Containing an External Circular Crack

1992 ◽  
Vol 114 (2) ◽  
pp. 208-212 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Isotropic Material ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
External Circular Crack

The dynamic response of an external circular crack to a harmonic longitudinal wave in a transversely isotropic material is investigated using the techniques of Hankel transform. The wave impinges normally onto the crack surfaces. The inversion integral is evaluated and simplified through a complete contour integration. An exact expression for the dynamic stress intensity factor is obtained in terms of the wave frequency and the anisotropic material constants. The maximum value of the normalized dynamic stress-intensity factor is shown to occur at different wave frequencies for different sample composite and metallic materials. The dynamic effect on the crack surface displacement is also shown to be a function of the wave frequency and the material anisotropy.

A Circular Crack System in an Infinite Elastic Medium Under Arbitrary Normal Loads

1994 ◽  
Vol 61 (3) ◽  
pp. 582-588 ◽  
Author(s):  
Zhou Yong ◽  
M. T. Hanson
Keyword(s):  
Stress Component ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Isotropic Body ◽  
Coefficient Matrix ◽  
Algebraic Equations ◽  
Flat Punch ◽  
Normal Loading ◽  
Crack System ◽  
Penny Shaped Crack

This analysis considers a circular crack system containing a penny-shaped crack and a concentric, coplanar external circular crack under arbitrary normal loading in a transversely isotropic body. The solution is obtained by transforming the governing two-dimensional integral equation to a set of algebraic equations which are easily solved numerically due to the special coefficient matrix. The normal stress component coplanar with the crack system is determined in power series form. The equations are solved and solutions for the stress intensity factors around the crack fronts are given for several different loading conditions. Including the rigid-body displacements at infinity allows the contact problem of an annular flat punch on an elastic half-space to be solved simultaneously.

The Elastic Potentials for Coplanar Interaction Between an Infinitesimal Prismatic Dislocation Loop and a Circular Crack for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S72-S78 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Isotropic Material ◽  
Transverse Isotropy ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Internal Crack ◽  
Elementary Functions ◽  
Elastic Potentials ◽  
Title Problem ◽  
Dislocation Crack ◽  
In The Beginning

This paper gives a closed-form evaluation in terms of elementary functions for the title problem of coplanar dislocation—crack interaction. The two cases of an external and internal crack are considered and the potential for each is found for an isotropic material. The similarity between isotropy and transverse isotropy is discussed in the beginning sections and is used to write the corresponding potential for a transversely isotropic material from the isotropic result.

Torsional Vibration of an External Circular Crack in a Transversely Isotropic Composite

2002 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Dynamic Crack ◽  
Isotropic Composite ◽  
External Circular Crack

The forced torsional vibratory motion of an external circular crack in a transversely isotropic composite is investigated by using the method of Hankel transforms. A pair of vibratory torques of equal amplitude is applied at infinity. The infinite integral involved is evaluated through a contour integration to be discontinuous in nature. An exact expression for the dynamic stress intensity factor is obtained in terms of the frequency factor and the anisotropic material constants. The maximum value of the normalized dynamic stress-intensity factor is shown to occur at different frequency factors for the sample fiber-reinforced and metal matrix composites. The distortion of the dynamic crack surface displacement from the associated static displacement depends also on the forcing frequency and the material anisotropy.

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