# Diagrams of critical equilibrium for brittle bodies with sharp flaws

• L. L. Libatskii
• V. V. Panasyuk
Article

## Abstract

Certain forms of the stress-intensity factors close to the tips of sharp flaws (plane problem) are used as the basis of a method for plotting critical equilibrium diagrams for brittle bodies with flaws in the form of pointed cavity-cracks [5]. Concrete examples are discussed, mainly in the context of such diagrams, for a brittle body weakened by a circular cavity flaw with a crack leaving the edge of the flaw. Determination of the stress-intensity factors for this problem is based on approximate solution of an integral equation by the method of collocations. Plots of some familiar diagrams are also analyzed.

### Keywords

Mathematical Modeling Mechanical Engineer Brittle Integral Equation Approximate Solution

## Preview

Unable to display preview. Download preview PDF.

### Literature cited

1. 1.
M. L. Williams, “On the stress distribution at the base of a stationary crack,” J. Appl. Mech.,24, No. 1 (1957).Google Scholar
2. 2.
G. R. Irwin, Fracture, Hanbuch Physik, Bd: 6, Springer, Berlin (1958).Google Scholar
3. 3.
G. I. Barenblatt, “Mathematical theory of equilibrium cracks appearing under brittle fracture,” PMTF (J. Appl. Mech. and Tech. Phys.), No. 4 (1961).Google Scholar
4. 4.
G. C. Sih, P. C. Paris, and F. Erdogan, “Crack-tip stress — intensity factors for plane extension and plate bending problems,” Trans. ASME, Ser. E. J. Appl. Mech.,29, No. 2 (1962).Google Scholar
5. 5.
V. V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks [in Russian], Kiev, Naukova Dumka (1968).Google Scholar
6. 6.
V. V. Panasyuk, “On fracture of brittle bodies under plane stress,” Prikl. Mekhan.,1, No. 9 (1965).Google Scholar
7. 7.
V. V. Panasyuk and E. V. Buina, “Critical stress diagrams for brittle bodies with sharp cavitycrack type flaws,” Fiz.-Khim. Mekhanika Materialov,3, No. 5 (1967).Google Scholar
8. 8.
H. F. Bueckner, “Some stress singularities and their computation by means of integral equations,” in: “Boundary Problems in Differential Equations,” Univ. Wisconsin Press (1960), pp. 215–230.Google Scholar
9. 9.
P. M. Vitvitskii and M. Ya. Leonov, “Extension beyond the elastic limit of a plate with a circular hole,” PMTF (J. Appl. Mech. and Tech. Phys.), No. 1 (1962).Google Scholar
10. 10.
L. L. Libatskii, “Application of singular integral equations for determining critical stresses in plates with cracks,” Fiz.-Khim. Mekhanika Materialov,1, No. 4 (1965).Google Scholar
11. 11.
A. G. Kurosh, Course of Higher Algebra [in Russian], Moscow, Gostekhizdat (1955).Google Scholar
12. 12.
N. I. Muskhelishvili, Some Fundamental Problems in Mathematical Theory of Elasticity [in Russian], Moscow, AN SSSR (1954).Google Scholar
13. 13.
L. L. Libatskii, “On plotting strength diagrams for a brittle body containing elliptic flaws,” Fiz.- Khim. Mekhanika Materialov,5, No. 3 (1969).Google Scholar