×

zbMATH — the first resource for mathematics

A detailed analysis of cracks bridged by fibers. I: Limiting cases of short and long cracks. II: Cracks of intermediate size. (English) Zbl 0807.73055
Summary: Two axisymmetric bridged crack problems that correspond to the limiting cases of short and long cracks are studied. The objective is to understand such details of crack bridging as the tensile stress distribution in bridging fibers, the effect of bridging on crack propagation and the load transfer from bridging fibers to the matrix. The solution method, which accounts for interfacial slip explicitly, involves the use of continuous distributions of dislocation loops to represent the opening of the crack and the slip at the fiber-matrix interfaces. This yields a set of coupled singular integral equations, which are solved numerically. In Part II, cracks of intermediate size will be studied. The results will be used to determine the effect of initial flaw size on the proportional limit and to assess the range of validity of a commonly used model of crack bridging in which bridging fibers are represented by distributed springs.

MSC:
74R99 Fracture and damage
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aveston, J.; Cooper, G.A.; Kelly, A., The properties of fibre composites, ()
[2] Budianksy, B.; Hutchinson, J.W.; Evans, A.G., Matrix fracture in fiber-reinforced ceramics, J. mech. phys. solids, 34, 167-189, (1986) · Zbl 0575.73106
[3] Choi, I.; Shield, R.T., A note on a flat toroidal crack in an elastic isotropic body, Int. J. solids struct., 18, 479-486, (1982) · Zbl 0482.73083
[4] Cooper, G.A.; Sillwood, J.M., Multiple fracture in a steel reinforced epoxy resin composite, J. mater. sci., 7, 325-333, (1972)
[5] Dollar, A.; Steif, P.S., A tension crack impinging upon frictional interfaces, J. appl. mech., 56, 291-298, (1989) · Zbl 0709.73064
[6] Dollar, A.; Steif, P.S., Stresses in fibers spanning an infinite matrix crack, Int. J. solids struct., 27, 1011-1024, (1991)
[7] Dundurs, J.; Comninou, M., Some consequences of the inequality conditions in contact and crack problems, J. elasticity, 9, 71-82, (1979) · Zbl 0393.73117
[8] Eason, G.; Noble, B.; Sneddon, I.N., On certain integrals of lipsehitz-Hankel type involving products of Bessel functions, Phil. trans. R. soc. lond., A247, 529-551, (1955) · Zbl 0064.06503
[9] Evans, A.G.; Marshall, D.B., The mechanical behavior of ceramic matrix composites, Acta metall., 37, 2567-2583, (1989)
[10] He, M.; Hutchinson, J.W., Crack deflection at an interface between dissimilar elastic materials, Int. J. solids struct., 25, 1053-1067, (1989)
[11] Kelly, A.; McCartney, L.N., Matrix cracking in fibre-reinforced and laminated composites, (), 210-222
[12] Kroupa, F., Circular edge dislocation loop, Czech. J. phys., B10, 284-292, (1960)
[13] Luk, V.K.; Keer, L.M., Stress analysis for an elastic half space containing an axially-loaded rigid cylindrical rod, Int. J. solids struct., 15, 805-827, (1979) · Zbl 0409.73007
[14] Marshall, D.B., An indentation method lor measuring matrix-fiber frictional stresses in ceramic composites, J. am. ceram. soc., 67, C259-C260, (1984)
[15] Marshall, D.B.; Cox, B.N.; Evans, A.G., The mechanics of matrix cracking in brittle-matrix fiber composites, Acta metall., 33, 2013-2021, (1985)
[16] McCartney, L.N., Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites, (), 329-350
[17] McCartney, L.N., New theoretical model of stress transfer between fibre and matrix in a uniaxially fibre-reinforced composite, (), 215-244
[18] Meda, G.; Hoysan, S.F.; Steif, P.S., The effect of fiber Poisson expansion in microindentation tests, J. appl. mech., 60, 986-991, (1993) · Zbl 0800.73385
[19] Meda, G.; Steif, P.S., Analysis of a crack bridged by a single fiber, J. appl. mech., 59, 524-529, (1992) · Zbl 0775.73209
[20] Mori, T.; Saito, K.; Mura, T., An inclusion model for crack arrest in a composite reinforced by sliding fibers, Mech. mater., 7, 49-58, (1988)
[21] Rice, J.R., Mathematical analysis in the mechanics of fracture, () · Zbl 0214.51802
[22] Schwietert, H.R.; Steif, P.S., Analysis of a broken fiber in a weakly bonded composite, Int. J. solids struct., 28, 283-297, (1991) · Zbl 0825.73421
[23] Shetty, D.K., Shear-lag analysis of fiber push-out (indentation) tests for estimating interfacial friction stress in ceramic-matrix composites, J. am. ceram. soc., 71, C107-C109, (1988)
[24] Singh, R.N., Influence of interfacial shear stress on first-matrix cracking stress in ceramic-matrix composites, J. am. ceram. soc., 73, 2930-2937, (1990)
[25] Tada, H.; Paris, P.C.; Irwin, G.R., The stress analysis of cracks handbook, ()
[26] Takaku, A.; Arridge, R.G.C., The effect of interfacial radial and shear stress on fibre pull-out in composite materials, J. phys. D: appl. phys., 6, 2038-2047, (1973)
[27] Wijeyewickrema, A.C.; Keer, L.M.; Hirashima, K.; Mura, T., The annular crack surrounding an elastic fiber in a tension field, Int. J. solids struct., 27, 315-328, (1991)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.