Rapid Mode III Interface Flaw Extension: Dissimilar Anisotropic Solids with Largely Arbitrary Orientations of their Principal Material Axes

Abstract

Two half-spaces are rigidly bonded along a semi-infinite portion of their interface, but separated by a vanishingly-thin flaw along its remainder. They consist of dissimilar elastic solids with single planes of material symmetry. The symmetry planes coincide, but principal material axes of the two solids in the common plane are of arbitrary orientation with respect to each other, and to the interface. Anti-plane shear forces moving on the flaw surfaces are assumed to create steady-state interface flaw extension; flaw and forces move at the same constant speed. Exact solutions for any constant speed show that the interface shear wave speed in each solid is sensitive to material properties and principal axis orientation. The subsonic case is studied in more detail, and the energy dissipation rate is extracted. Calculations when one solid is isotropic show its sensitivity to non-orthotropy and to ratios of the shear moduli and mass densities.

Keywords

Anisotropic mode III dynamic fracture debonding principal material axes non-orthotropy

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References

[1] Yu, H. and Wang, W. : Mechanics of transonic debonding of a bimaterial interface: the anti-plane shear case. J. Mech. Phys. Solids, 42, 1789-1802 (1994).

[2] Huang, Y. , Liu, C. and 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).

[3] Rosakis, A. J. , Samudrala, O. and Coker, D. : Cracks faster than the shear wave speed. Science, 284, 1337-1340 (1999).

[4] Brock, L. M. : Interface crack extension at any constant speed in orthotropic or transversely isotropic bimaterials-I. General exact solutions. Int. J. Solids Struct., 39, 1165-1182 (2002).

[5] Brock, L. M. and Hanson, M. T. : Interface crack extension at any constant speed in orthotropic or transversely isotropic bimaterials-II. Two important examples. Int. J. Solids Struct., 39, 1183-1198 (2002).

[6] Brock, L. M. : Transient study of mode III fracture in an elastic solid with a single plane of material symmetry. ASME J. Appl. Mech., at press (2002).

[7] Freund, L. B. : Dynamic Fracture Mechanics. Cambridge University Press, 1993.

[8] Sokolnikoff, I. S. : Mathematical Theory of Elasticity. Krieger, Malabar, FL, 1983.

[9] Nye, J. F. : Physical Properties of Crystals, Their Representation by Tensors and Matrices. Clarendon Press, Oxford, 1957.

10.

[10] Theocaris, P. S. and Sokolis, D. P. : Invariant elastic constants and eigentensors of orthorhombic, tetragonal, hexagonal and cubic crystalline media. Acta Crystallogr., A 56, 316-331 (2000).

11.

[11] Kraut, E. A. : Advances in the theory of anisotropic wave propagation. Rev. Geophys., 1, 401-488 (1963).

12.

[12] Payton, R. G. : Elastic Wave Propagation in Transversely Isotropic Media. Martinus Nijhoff, The Hague, 1983.

13.

[13] Achenbach, J. D. : Elastic Wave Propagation in Elastic Solids. North-Holland, Amsterdam, 1973.

14.

[14] Eshelby, J. D. , Read, W. T. and Shockley, W. : Anisotropic elasticity with applications to dislocation theory. Acta Metall., 1, 251-259 (1953).

15.

[15] Van der Pol, B. and Bremmer, H. : Operational Calculus based on the Two-Sided Laplace Integral. Cambridge University Press, 1950.

16.

[16] Carrier, G. F. and Pearson, C. E. : Partial Differential Equations. Academic Press, New York, 1988.

17.

[17] Carrier, G. F. , Krook, M. and Pearson, C. E. : Functions of a Complex Variable. McGraw-Hill, New York, 1966.

18.

[18] Brock, L. M. : Sliding contact with friction at arbitrary constant speeds in a pre-stressed highly-elastic half-space. J. Elasticity, 57, 85-103 (1999).

19.

[19] Brock, L. M. and Georgiadis, H. G. : Sliding contact with friction on a thermoelastic solid at subsonic, transonic and supersonic speeds. J. Thermal Stresses, 23, 629-656 (2000).

20.

[20] Ewalds, H. L. and Wanhill, R. J. H. : Fracture Mechanics, Edward Arnold, London, 1985.

21.

[21] Brock, L. M. and Achenbach, J. D. : Extension of an interface flaw under the influence of transient waves. Int. J. Solids Struct., 9, 53-68 (1973).

22.

[22] Brock, L. M. : Interface flaw extension under in-plane loadings. Int. J. Eng. Sci., 14, 191-199 (1976).

23.

[23] Freund, L. B. : The mechanics of dynamic shear crack propagation. J. Geophys. Res., 84, 2199-2209 (1979).

24.

[24] Broberg, K. B. : Intersonic crack propagation in an orthotropic material. Int. J. Fract., 99, 1-11 (1999).

25.

[25] Lekhnitskii, S. A. : Theory of Elasticity of an Anisotropic Body. Holden-Day, San Francisco, 1963.

26.

[26] Ting, T. C. T. : Anisotropic Elasticity. Oxford Science Publishers, New York, 1996.

27.

[27] Peirce, B. O. and Foster, R. M. : A Short Table of Integrals. Blaisdell, Waltham, MA, 1956.