×
Nagar, A. K.; Fu, L. S.; Mendelsohn, D. A.

On quadruple integral equations related to a certain crack problem. (English) Zbl 0585.73162

J. Elasticity 16, 163-177 (1986).
Summary: An exact solution of a four part mixed boundary value problem representing a three colinear crack system connected with specified crack opening displacements between the cracks is obtained. The three cracks thus become one with pressure and/or opening displacement prescribed on the crack face. From considerations of dual symmetry and a formulation based on Papkovich-Neuber harmonic functions, the boundary value problem is reduced to solving a quadruple set of integral equations. An exact solution of these equations is derived using a modified finite Hilbert transform technique. The closed form results for the stress distributions and the crack-tip stress intensity factors are presented. Limiting cases of the solution yield results which agree with well known solutions.

Cited in 3 Documents

MSC:

74R05 Brittle damage
74G70 Stress concentrations, singularities in solid mechanics
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
45F10 Dual, triple, etc., integral and series equations

Keywords:

exact solution; four part mixed boundary value problem; three colinear crack system; specified crack opening displacements; dual symmetry; Papkovich-Neuber harmonic functions; quadruple set of integral equations; modified finite Hilbert transform technique; closed form results; stress distributions; crack-tip stress intensity factors; Limiting cases

Citations:

Zbl 0377.73102
Cite Review PDF
Full Text: DOI

References:

[1] K.N. Srivastava, and M. Lowengreb, Finite Hilbert Transform Technique for Triple Integral Equations with Trigonometric Kernels,Proceedings of the Royal Society of Edinburgh, Vol. LXVIII, part IV, No. 20 (1970) 309-321. · Zbl 0189.11301
[2] M. Lowengreb, and K.N. Srivastava, Two Coplanar Griffith Cracks in an Infinitely Long Elastic Strip,International Journal of Engineering Science 6 (1968) 425-434. · Zbl 0193.54007 · doi:10.1016/0020-7225(68)90048-7
[3] Y. Konishi, On the Coplanar Cracks in an Infinite Transversely Isotropic Medium,International Journal of Engineering Science,10 (1972) 917-923. · Zbl 0251.73071 · doi:10.1016/0020-7225(72)90001-8
[4] J. Tweed, The Determination of the Stress Intensity Factors of a Pair of Coplanar Griffith Cracks Whose Surfaces are Loaded Asymmetrically,Engineering Fracture Mechanics,3 (1971) 381-402. · doi:10.1016/0013-7944(71)90054-3
[5] B.M. Singh, and R.S. Dhaliwal, Three Coplanar Griffith Cracks in an Infinite Elastic Strip,Journal of Elasticity,12 (1982) 127-141. · Zbl 0483.73079 · doi:10.1007/BF00043708
[6] G.K. Dhawan, and R.S. Dhaliwal, On Three Coplanar Cracks in an Infinite Transversely Isotropic Medium,Internal Journal of Engineering Science 16 (1978) 253-262. · Zbl 0377.73102 · doi:10.1016/0020-7225(78)90091-5
[7] Y. Nakai, K. Tanaka, and M. Yamashita, Analysis of Closure Behavior of Small Fatigue Cracks,Journal of Materials (Japanese),32 (1983) 19-32.
[8] A.K. Nagar, The Fracture Mechanics of a Slit Crack with Crack-Tip Dual Zones, PH.D. Dissertation, The Ohio State University, June 1984.
[9] A.K. Nagar, and L.S. Fu, Analysis of a Crack-Tip Dual Zones Model,International Journal of Fracture, 28 (1985) 245-259.
[10] I.N. Sneddon, and M. Lowengreb,Crack Problems in the Theory of Elasticity, John Wiley (1969). · Zbl 0175.22202
[11] I.S. Sokolnikoff,Mathematical Theory of Elasticity, McGraw-Hill (1946). · Zbl 0070.41104
[12] I.S. Gradshtegn, and I.M. Ryzhik,Tables of Integrals, Series and Products, Academic Press (1965).
[13] P.F. Byrd, and M.D. Friedman,Handbook of Elliptic Integrals for Engineers and Scientists, Springer-Verlag (1971). · Zbl 0213.16602
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.