Stress Intensity Factors for Penny-Shaped Cracks: Part 1—Infinite Solid

1967 ◽  
Vol 34 (4) ◽  
pp. 947-952 ◽  
Author(s):  
F. W. Smith ◽  
A. S. Kobayashi ◽  
A. F. Emery
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Elastic Solid ◽  
Pure Bending ◽  
Normal Loading ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Symmetric Loading ◽  
Embedded Crack

An expression is developed for the stress intensity factor of a penny-shaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. The stress intensity factor can then be determined for penny-shaped cracks in infinite or finite solids subjected to symmetric loading about the plane containing the crack. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. Results are also presented for two problems: A penny-shaped crack subjected to two symmetrically located concentrated forces and a penny-shaped crack in a large beam subjected to pure bending.

The Matrix-Fiber Crack in an Elastic Solid

1996 ◽  
Vol 63 (3) ◽  
pp. 639-649 ◽  
Author(s):  
A. P. S. Selvadurai ◽  
B. M. Singh ◽  
M. C. Au
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Elastic Solid ◽  
Numerical Results ◽  
Fiber Reinforced ◽  
Matrix Cracks ◽  
Penny Shaped Crack ◽  
The Matrix ◽  
Shaped Crack

In the presence of strong interface adhesion, the fracture of an embedded fiber can also result in the cracking of the surrounding matrix. While the orientation of such matrix cracks can be varied, the flat penny-shaped crack represents a critical crack orientation which is of particular interest to the study of the micromechanics of fracture processes in fiber-reinforced solids. This paper considers the axisymmetric problem of the uniform straining of a composite elastic solid which contains a penny-shaped crack occupying both the fiber and matrix regions. The isolated cracked fiber-matrix crack interaction is formulated as a mixed boundary value problem related to a two-domain half-space region. The resulting integral equations are solved in a numerical fashion to evaluate the stress intensity factor at the boundary of the penny-shaped crack. The numerical results presented, in the paper illustrate the influence of the elasticity mismatch between the fiber and the matrix on the stress intensity factor at the crack-tip located in the matrix. The numerical results are presented for typical fiber-reinforced composites consisting of epoxy and ceramic matrices reinforced with silicon, glass, and kevlar fibers.

Indentation of a Penny-Shaped Crack by an Oblate Spheroidal Rigid Inclusion in a Transversely Isotropic Medium

1984 ◽  
Vol 51 (4) ◽  
pp. 811-815 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Penny Shaped Crack ◽  
Shaped Crack

The stress distribution produced by the identation of a penny-shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of Hankel transforms. This three-part mixed boundary value problem is solved using the techniques of triple integral equations. The normal contact stress between the crack surface and the indenter is written as the product of the associated half-space contact stress and a nondimensional crack-effect correction function. An exact expression for the stress-intensity is obtained as the product of a dimensional quantity and a nondimensional function. The curves for these nondimensional functions are presented and used to determine the values of the normalized stress-intensity factor and the normalized maximum contact stress. The stress-intensity factor is shown to be dependent on the material constants and increasing with increasing indentation. The stress-intensity factor also increases if the radius of curvature of the indenter surface increases.

A note on the problem of the penny-shaped crack

1965 ◽  
Vol 61 (2) ◽  
pp. 609-611 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Constant Pressure ◽  
Cylindrical Coordinates ◽  
Lower Face ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Image Position ◽  
Distribution Of Stress

1. The problem of determining the distribution of stress in the neighbourhood of a penny-shaped crack defined in terms of cylindrical coordinates (ρ, φ, z) by 0 ≤ ρ ≤ α, z = 0, has been considered by Sneddon ((2)) and Sack ((1)). In the latter paper the solution is derived only in the case in which the stress field is due to the application of constant pressure to the faces of the crack. In the former paper the analysis given applies to an axisymmetric distribution of pressure p(ρ) applied to both the upper and lower face of the penny-shaped cavity, but the calculation of the stress intensity factorand of the energy W required to open up the crack is a complicated matter even in the case in which p(ρ) is a constant.

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