Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Penny-shaped crack bridged by fibres

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.

References [Enhancements On Off] (What's this?)

  • [1] D. B. Marshall and B. N. Cox, Tensile fracture of brittle matrix composites: Influence of fibre strength, Acta Metall. 35, 2607-2619 (1987)
  • [2] L. N. McCartney, Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites, Proc. Royal Soc. London A409, 329-350 (1987)
  • [3] J. R. Willis and S. Nemat-Nasser, Singular perturbation solution of a class of singular integral equations, Quart. Appl. Math. 48, 741-753 (1990) MR 1079917
  • [4] 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, 331-350 (1993) MR 1232635
  • [5] J. T. Guidera and R. W. Lardner, Penny-shaped cracks, Journal of Elasticity 5, 59-73 (1975)
  • [6] J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover, New York, 1952 MR 0051411
  • [7] J. R. Willis, Asymptotic analysis of crack bridging by ductile fibres, Composites 24, 93-97 (1993)
  • [8] A. B. Movchan and J. R. Willis, An asymptotic procedure and numerical study for the analysis of an elastic body with a thin subsurface crack, Euro. J. Appl. Math. 6, 1-23 (1995) MR 1317871
  • [9] M. D. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York, 1964 MR 0176702
  • [10] W. E. Olmstead and A. K. Gautesen, Asymptotic solution of some singularly perturbed Fredholm equations, Z. Angew. Math. Phys. 40, 230-244 (1989) MR 990629

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DOI: https://doi.org/10.1090/qam/1622503
Article copyright: © Copyright 1998 American Mathematical Society

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