The approximate analytical solution for both surface and embedded cracks in cylinder with finite size
✍ Scribed by Yuan-Xun Fan; Tian-You Fan; Da-Jun Fan
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 784 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0013-7944
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✦ Synopsis
The exact solution for a penny-shaped crack in an infinite elastic body under the action of an arbitrary normal load and the trigonometric series solution for a cylinder with finite size under an arbitrary lateral surface load are taken as basic solutions. From the alternate action of the basic solutions, we have obtained the approximate analytical expressions of K, for both the surface and embedded cracks in cylinder with finite size. The first approximate expressions of K, for a cylinder under tensile load and pure bending respectively and some numerical results of K, are given as an example of practical calculation. NOTATION radius of penny-shaped crack or partial penny-shaped crack, radius of cylinder. half length of the cylinder cylindrical coordinates with origin in the center 0 of the crack components of stress tensor in cylindrical coordinates cylindrical coordinates with origin in the center 0' of the cylinder components of stress tensor in cylindrical coordinates with origin at 0 geometric parameters half open angle of partial penny-shaped crack with respect to circle 0 the nth Bessel function of the first kind modified nth Bessel function of the first kind elastic constants functions of displacements pressure parameter stress intensity factor