Abstract
By using the basic displacements and stresses caused by a single elastic inclusion and a single crack on infinite plane, the interaction problem between a crack and an elastic inclusion is reduced to solve a set of Cauchy-type singular integral equation. Based on this result, the singular behaviour of the solution for the inclusion-branching crack is analysed theoretically and the oscillating singular interface stress field is obtained. For the separating inclusion-crack problem, the stress intensity factors at the tips and the interface stress of the inclusion are calculated and the results of which are satisfactory.
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References
Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen, Holland (1953).
Chen, Y. Z. and H. Norio, An alternative Fredholm integral equation approach for multiple crack problem and multiple rigid line problem in plane elasticity,Engng. Frac. Mech., 2 (1992), 257–268.
Liu Xue-hui and F. Erdogan, The crack-inclusion interaction problem,Engng. Frac. Mech., 5 (1986), 821–832.
Atkinson, C., Some ribbon-like inclusion problems,Internal. J. Engrg. Sci.,11(1973), 243–266.
Dundurs, J., Elastic interaction of dislocations with inhomogeneities, inMathematical Theory of Dislocations, Ed. by T. Mura, New York (1969).
Erdogan, F., G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations, inMechanics of Fracture 1, Ed. by G. C. Sih, Noordhoff (1973), 368–425.
Wo Gou-wei, Qin Tai-yan and Tang Ren-ji, A new engineering model for a linear inclusion and its applications,Acta Mechanica Solida Sinica (submitted for publication).
Muskhelishvili, N. I.,Singular Integral Equations, Noorhoff (1953).
Tang Ren-ji and Li Yu-lan, Torsion of the cylinders with a rectangular hole and with a crack,Acta Mech. Sinica,8 (1992), 165–172.
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Project supported by the National Natural Science Foundation and National P. H. D. Foundation of China
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Ming-huan, Z., Ren-ji, T. Interaction between crack and elastic inclusion. Appl Math Mech 16, 307–318 (1995). https://doi.org/10.1007/BF02456943
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DOI: https://doi.org/10.1007/BF02456943