×

zbMATH — the first resource for mathematics

Analysis of intersonic crack growth in unidirectional fiber-reinforced composites. (English) Zbl 0963.74050
From the summary: For unidirectional fiber-reinforced graphite/epoxy composite materials, we obtain the asymptotic fields near an intersonically propagating crack tip. It is shown that mode-I intersonic crack propagation is impossible because the crack tip energy release rate supplied by the elastic asymptotic field is negative and unbounded, which is physically unacceptable since a propagating crack tip cannot radiate out energy. For mode II, however, we establish that there exists a single crack tip velocity (higher than the shear wave speed) that gives a finite and positive crack tip energy release rate. At all other intersonic crack tip speeds the energy release rate supplied by the elastic asymptotic field is identically zero. This critical crack tip velocity agrees well with the stable crack tip velocity observed in experiments.

MSC:
74R10 Brittle fracture
74E30 Composite and mixture properties
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abraham, F.F., Gao, H., 1999. How fast can cracks propagate? Nature, submitted for publication.
[2] Archuleta, R.J., Analysis of near source static and dynamic measurements from the 1979 imperial valley earthquake., Bulletin of the seismological society of America, 72, 1927-1956, (1982)
[3] Breitenfeld, M.S., Geubelle, P.H., 1999. Numerical analysis of dynamic debonding under 2-D in-plane and 3-D loading. Int. J. Fracture (in press)
[4] Burridge, R., Admissible speeds for plane-strain self-similar shear cracks with friction but lacking cohesion, Geophysical journal of the royal astronormal society, 35, 439-455, (1973) · Zbl 0272.73022
[5] Burridge, R.; Conn, G.; Freund, L.B., The stability of a plane strain shear crack with finite cohesive force running at intersonic speeds, J. of geophysics res., 84, 2210-2222, (1979)
[6] Coker, D., Rosakis, A.J., 1998. Experimental observations of intersonic crack growth in asymmetrically loaded unidirectional composite plates. Caltech SM Report No. 98-16, June
[7] Freund, L.B., The mechanics of dynamic shear crack propagation, J. of geophysics res., 84, 2199-2209, (1979)
[8] Freund, L.B., Dynamic fracture mechanics, (1990), Cambridge University Press Cambridge · Zbl 0712.73072
[9] Gao, H., Surface roughening and branching instabilities in dynamic fracture, J. mech. phys. solids, 41, 457-486, (1993)
[10] Gao, H., A theory of local limiting speed in dynamic fracture, J. mech. phys. solids, 44, 1453-1474, (1996)
[11] Gao, H.; Klein, P., Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds, J. mech. phys. solids, 46, 187-218, (1998) · Zbl 0974.74008
[12] Huang, Y.; Liu, C.; Rosakis, A.J., Transonic crack growth along a bimaterial interface: an investigation of the asymptotic structure of near-tip fields, Int. J. solids struct., 33, 2625-2645, (1996) · Zbl 0924.73184
[13] Huang, Y.; Wang, W.; Liu, C.; Rosakis, A.J., Intersonic crack growth in bimaterial interfaces: an investigation of crack face contact, J. mech. phys. solids, 46, 2233-2259, (1998) · Zbl 1056.74561
[14] Lambros, J.; Rosakis, A.J., Shear dominated transonic crack growth in a bimaterial—I. experimental observations, J. mech. phys. solids, 43, 169-188, (1995) · Zbl 0900.73616
[15] Liu, C.; Huang, Y.; Rosakis, A.J., Shear dominated transonic crack growth in a bimaterial—II. asymptotic fields and favorable velocity regimes, J. mech. phys. solids, 43, 189-206, (1995) · Zbl 0900.73617
[16] Liu, C.; Lambros, J.; Rosakis, A.J., Highly transient elasto-dynamic crack growth in a bimaterial interface: higher order asymptotic analysis and optical experiment, J. mech. phys. solids, 41, 1887-1954, (1993) · Zbl 0803.73058
[17] Liu, C., Rosakis, A.J., Stout, M., Lovato, M., Ellis, R. 1999. On the application of CGS interferometry to the study of mode-I dynamic crack growth in unidirectional composites (in preparation)
[18] Needleman, A., Rosakis, A.J., 1999. The effect of bond strength and loading rate on the attainment of intersonic crack growth in interfaces. J. Mech. Phys. Solids (submitted) · Zbl 0982.74059
[19] Rosakis, A.J., Liu, C., Stout, M., Coker, D. 1999. Can cracks in unidirectional composites propagate intersonically? (in preparation)
[20] Rosakis, A.J.; Samudrala, O.; Singh, R.P.; Shukla, A., Intersonic crack propagation in bimaterial systems, J. mech. phys. solids, 46, 1789-1813, (1998) · Zbl 0945.74511
[21] Rosakis, A.J., Samudrala, O., Coker, D., 1998b. Cracks faster than the shear wave speed. Science, submitted for publication
[22] Simonov, I.V., Behavior of solutions of dynamic problems in the neighborhood of the edge of a cut moving at transonic speed in an elastic medium, Mechanics of solids (mechanika tverdogo tela), 18, 100-106, (1983)
[23] Singh, R.P.; Lambros, J.; Shukla, A.; Rosakis, A.J., Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity, Proc. roy. soc., A453, 2649-2657, (1997)
[24] Singh, R.P.; Shukla, A., Subsonic and intersonic crack growth along a bimaterial interface, J. appl. mech., 63, 919-924, (1996)
[25] Tippur, H.V.; Rosakis, A.J., Quasi-static and dynamic crack growth along bimaterial interfaces: a note on crack-tip field measurement using coherent gradient sensing, Exp. mech., 31, 243-251, (1991)
[26] Xu, X.P.; Needleman, A., Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line, Int. J. fracture, 74, 253-275, (1996)
[27] Yu, H.; Yang, W., Mechanics of transonic debonding of a bimaterial interface: the in-plane case, J. mech. phys. solids, 43, 207-232, (1995) · Zbl 0879.73049
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.