Stress-strain state of a cracked elastic wedge under anti-plane deformation with mixed boundary conditions on its faces
Source abstract
Abstract
A problem about the stress-strain state of an elastic wedge with an arbitrary angel of opening, when on its bisector there is a system of a finite number collinear cracks, is studied by the means of the theory of elasticity. The anti-symmetric mixed boundary conditions given on both wedge-faces, together with the forces applied to the cracks' surfaces are provoking the anti-plane deformation of the wedge. The displacement components are given for the same group of nonintersecting intervals on each wedge-face and the stress components are given on the rest of the faces. The problem is formulated as a known mixed boundary problem of the theory of harmonic functions for a half-wedge because of the wedge symmetry relative to its bisector. The solution of this mixed boundary problem is derived in the closed form by using the Mellin integral transformation in combination with the methods of singular integral equations. Based on this the density of displacements' dislocations on the cracks' surfaces, the stress intensity factors, the stresses on those intervals on the wedge-faces, where the displacements are given, and other characteristics of the investigating problem are determined by explicit analytical formulas. Particular cases are discussed as well.
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Research context
OpenAlex topics: Structural mechanics and materials · Elasticity and Wave Propagation · Material Properties and Applications
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References (20)
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1. Abramowitz, and Stegun, I.A. (1972). Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, INC., New York.
2. Bateman, and Erdelyi, A. (1953). Higher Transcendental Functions. V.1, McGraw-Hill Book Company, INC., New York, Toronto, London.
3. Bateman, and Erdelyi, A. et al. (1969). Tables of Integral Transformations. V.1, Nauka, Moscow.
4. Bilby, (1980). Tewksbury lecture: Putting fracture to work. Journal of Material Science. V. (3)15, 535-556.10.1007/BF00551716 ↗
5. Cherepanov, (1974). Mechanics of Brittle Fracture. Nauka, Moscow.
6. Gakhov, (1977). Boundary Value Problems. Nauka, Moscow.
7. Gradshteyn, and Ryzhik, I.M. (1965). Tables of Integrals, Series and Products. Academic Press, New York and London.
8. Lavrente, and Sabat, B.V. (1973). Methods of the Theory of Functions from the Complex Variables. Nauka, Moscow.
9. Mkhitaryan, (1993). On two mixed problems regarding the questions of the interaction between different kinds of stress concentrators and massive bodies in the case of the ant-plane deformation. In Mechanics of Deformable Solid Bodies. Publishing House of Armenian Academy of Sciences, Yerevan, 129-143.
10. Murakami, (1987). Stress Intensity Factors Handbook. Pergamon Press, Oxford.
11. Muskhelishvili, (1953). Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen.
12. Muskhelishvili, (1968). Singular Integral Equations. Nauka, Moscow.
13. Nosati, (1987). Longitudinal fault of bodies with cracks under point forces. Journal on Physical and Chemical Mechanics of the Materials 23(1), 78-82.
14. Panasuk, Savruk, M.P. and Datzhishin, A.P. (1976). Stress Distribution near the Cracks in Plates and Shells. Naukova Dumka, Kiev.
15. Popov, (1982). Elastic Stress Concentration near Punches, Cuts, Fine Inclusions and Reinforcements. Nauka, Moscow.
16. Savruk, (1988). Stress Intensity Factors for the Bodies with Cracks. Handbook in 4 volumes. V.2, Nauka Dumka, Kiev.
17. Shtaerman, (1949). Contact Problems of the Theory of Elasticity. Gostexizdat, Moscow-Leningrad.
18. Sih, (1965). External cracks under longitudinal shear. Journal of the Franklin Institute, V. 280(2), 139-149.10.1016/0016-0032(65)90399-6 ↗
19. Ufland, (1968). Integral Transformations in Problems of the Theory of Elasticity. Nauka, Leningrad.
20. Yatomi, (1981). Note on the energy-release rate for a crack starting from the apex of a wedge. Translation ASME. Journal of Applied Mechanics 48(1), 194-195.10.1115/1.3157568 ↗