Abstract
A model is suggested for a partially bridged penny-shaped crack (axisymmetric problem) in a brittle aligned material like for a composite ceramic. Two different fracture criteria for its components (matrix and fiber) are accepted. On the basis of an analytical solution for a homogeneous anisotropic body, a force-separation law, and Novozhilov’s brittle fracture criterion, the variation intervals of a diameter of an equilibrium crack and the width of a bridged crack part are estimated. It is shown that, like a fracture toughness, the critical width of the bridged crack part can be accepted as a constant parameter for a composite material reinforced by fibers. The value of this parameter for a penny-shaped crack is the same as for a crack under plane deformation. For two types of ceramics the variation intervals of a bridged part of a critical crack are found, and a dependence of an ultimate load upon the size of the crack in 2-D and axisymmetric problems is presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Grekov, M.A. and Morozov, N.F. (2000) Disk-shaped equilibrium cracks, Prikl. Mat. Mekh., 64, No. 1, pp. 172–175 (in Russian). J. Appl. Math. Mech, 64, No. 1, pp. 169-172 (English translation).
Novozhilov, V.V. (1969a) On the necessary and sufficient criterion for brittle strength, Prikl. Mat. Mekh., 33, No. 2, pp. 212–222 (in Russian). J. Appl. Math. Mech., 33, No. 2, pp. 201-210 (English translation).
Novozhilov, V.V. (1969b) On the foundation of a theory of equilibrium cracks in elastic solids, Prikl. Mat. Mekh., 33, No.5, pp. 797–812 (in Russian). J. Appl. Math. Mech, 33, No. 5, pp. 777-790 (English translation).
Thomson, R.and Hsieh C. and Rana, V. (1971) Lattice trapping of fracture cracks, J. Appl. Phys., 42, No 8, pp. 3154–3160.
Morozov, N.F. and Paukshto M.V. (1988) On ‘lattice’ trapping, Dokl. AN SSSR., 299, No. 2, pp. 323–325 (in Russian). Sov. Phys.-Dokl., 33, No. 3, pp. 235-236. (English translation).
Morozov, N. and Paukshto, M. (1991) On the crack simulation and solutions in the lattice, Trans. ASME J. Appl. Mech, 58. No 3, pp. 290–292.
Morozov, N. and Paukshto, M. and Ponikarov, N. (1997) On the problem of equilibrium length of bridged crack, Trans. ASME. J. Appl. Mech, 64, No. 2, pp. 427–430.
Nemat-Nasser, S. and Hori, M. (1987) Toughening by partial or full bridging of crack in ceramics and fiber reinforced composites, Mechanics of Materials, 6, pp. 245–269.
Movchan, N.V. and Willis, J.R. (1998) Penny-shaped crack bridged by fibers, Quarterly of Applied Mathematics., 56, No. 2, pp. 327–340.
Budiansky, B. and Evans, A.G. and Hutchinson, J.W. (1995) Fiber-matrix debonding effects on cracking in aligned fiber ceramic composites, Int. Journal of Solids and Structures, 32, No. 3/4, pp. 315–328.
Morozov, N.F. (1984) Mathematical Problems of Cracks Theory, Nauka, Moskva (in Russian).
Panasyuk, V.V. (1968) The Limit Equilibrium of Brittle Bodies with Cracks, Naukova Dumka, Kiev (in Russian).
Fabrikant, V.I. (1990) Complete solution to some mixed boundary value problems in elasticity, Advances in Applied Mechanics. Eds. J. Hutchinson and T.Wu. Boston. Acad. Press, 27, pp. 153–223.
Christensen, R.M. (1979) Mechanics of composite materials, John Wiley & Sons Inc.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Kluwer Academic Publishers
About this paper
Cite this paper
Grekov, M.A., Morozov, N.F., Ponikarov, N.V. (2003). Penny-Shaped Equilibrium Cracks in Aligned Composites. In: Ståhle, P., Sundin, K.G. (eds) IUTAM Symposium on Field Analyses for Determination of Material Parameters — Experimental and Numerical Aspects. Solid Mechanics and its Applications, vol 109. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0109-0_18
Download citation
DOI: https://doi.org/10.1007/978-94-010-0109-0_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-1283-9
Online ISBN: 978-94-010-0109-0
eBook Packages: Springer Book Archive