Penny-shaped crack bridged by fibres

Movchan, N. V.; Willis, J. R.

doi:10.1090/qam/1622503

Authors: N. V. Movchan and J. R. Willis
Journal: Quart. Appl. Math. 56 (1998), 327-340
MSC: Primary 73M25; Secondary 73B50
DOI: https://doi.org/10.1090/qam/1622503
MathSciNet review: MR1622503
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Abstract: An axi-symmetric problem for a penny-shaped crack bridged by fibres is considered. The study is reduced to the analysis of a hypersingular integral equation with respect to the relative crack-face separation over a circular domain occupied by the crack. The special case of a large crack subjected to Mode-I loading is examined. A matched asymptotic expansions technique is used in order to estimate the stress intensity factor at the crack edge and to evaluate the magnitude of the applied load which provides the critical opening for failure of fibres at the centre of the crack.

D. B. Marshall and B. N. Cox, Tensile fracture of brittle matrix composites: Influence of fibre strength, Acta Metall. 35, 2607–2619 (1987)

L. N. McCartney, Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites, Proc. Royal Soc. London A409, 329–350 (1987)

J. R. Willis and S. Nemat-Nasser, Singular perturbation solution of a class of singular integral equations, Quart. Appl. Math. 48 (1990), no. 4, 741–753. MR 1079917, DOI https://doi.org/10.1090/qam/1079917
A. B. Movchan and J. R. Willis, Asymptotic analysis of the reinforcement of a brittle crack by bridging fibres, Quart. J. Mech. Appl. Math. 46 (1993), no. 2, 331–350. MR 1232635, DOI https://doi.org/10.1093/qjmam/46.2.331

J. T. Guidera and R. W. Lardner, Penny-shaped cracks, Journal of Elasticity 5, 59–73 (1975)

Jacques Hadamard, Lectures on Cauchy’s problem in linear partial differential equations, Dover Publications, New York, 1953. MR 0051411

J. R. Willis, Asymptotic analysis of crack bridging by ductile fibres, Composites 24, 93–97 (1993)

A. B. Movchan and J. R. Willis, An asymptotic procedure and numerical study for the analysis of an elastic body with a thin sub-surface crack, European J. Appl. Math. 6 (1995), no. 1, 1–23. MR 1317871, DOI https://doi.org/10.1017/S0956792500001649
Milton Van Dyke, Perturbation methods in fluid mechanics, Applied Mathematics and Mechanics, Vol. 8, Academic Press, New York-London, 1964. MR 0176702
W. E. Olmstead and A. K. Gautesen, Asymptotic solution of some singularly perturbed Fredholm integral equations, Z. Angew. Math. Phys. 40 (1989), no. 2, 230–244. MR 990629, DOI https://doi.org/10.1007/BF00945000