Summary
The effect of a viscoelastic substrate on an anisotropic elastic cracked body under in-plane concentrated loading is studied in this paper. Based on the correspondence principle, the viscoelastic solution is directly obtained from the corresponding elastic one. The fundamental elastic solution is solved as three complex potentials via the property of analytical continuation to satisfy the continuity condition along the interface between dissimilar media. A singular integral technique in association with the dual coordinate transformation is applied to obtain the stress intensity factors for various crack orientations. Using the standard solid model to formulate the viscoelastic constitutive equation, some numerical examples are considered to demonstrate the use of the present approach.
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References
Miller, G. R.: Analysis of cracks near interfaces between dissimilar anisotropic materials. Int. J. Engng. Sci.27, 667–678 (1989).
Lekhnitskii, S. G.: Theory of elasticity of an anisotropic elastic body. San Francisco: Holden-Day 1963.
Suo, Z.: Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. Roy. Soc. London, Ser. A,427, 331–358 (1990).
Eshelby, J. D., Read, W. T., Shockley, W.: Anisotropic elasticity with applications to dislocation theory. Acta Metallurg1, 251–259 (1953).
Stroh, A. N.: Dislocation and cracks in anisotropic elasticity. Philos. Magazine7, 625–646 (1958).
Atkinson, C., Bourne, J. P.: Stress singularities in viscoelastic media. Quart. J. Mech. Appl. Math.42, 385–412 (1989).
Ryvkin, M., Banks-Sills, L.: Steady-state mode III propagation of an interface crack in an inhomogeneous viscoelastic strip. Int. J. Solids Struct.30, 483–498 (1993).
Ryvkin, M., Banks-Sills, L.: Mode III delamination of a viscoelastic strip from a dissimilar viscoelastic half-plane. Int. J. Solids Struct.31, 551–566 (1994).
Atkinson, C., Chen, C. Y.: The influence of layer thicknes on the stress intensity factor of a crack lying in an elastic (vicoelastic) layer embedded in a different elastic (viscoelastic) medium (mode III analysis). Int. J. Eng. Sci.34, 639–658 (1996).
Muskhelishvili, N. I.: Some basic problems of mathematical theory of elasticity. Groningen: Noordoff 1953.
Ting, T. C. T.: Explicit solution and invariance of the singularities at an interface crack in anisotropic composites. Int. J. Solids Struct.22, 956–983 (1986).
Irwin, G. R.: Analysis of stresses and strains near the end of a crack transversing a plate. J. Appl. Mech.24, 109–114 (1957).
Christensen, R. M.: Theory of Viscoelasticity. An introduction, 2nd ed., New York: Academic Press 1982.
Schapery, R. A.: Correspondence priciples and a generalized J integral for large deformation and fracture analysis of viscoelastic media. Int. J. Fracture25, 195–223 (1984).
Schapery, R. A.: Approximate method of transform inversion for viscoelastic stress analysis, Proc. 4th U.S. National Congress of Applied Mechanics, pp. 1075–1086 (1962).
Sih, G. C., Paris, P. C., Erdogan, F.: Crack tip, stress-intensity factor for plane extension and plane bending problem. J. Appl. Mech.29, 306–312 (1962).
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Chang, R.C., Wang, S.C. & Chao, C.K. Effects of a viscoelastic substrate on a cracked body under in-plane concentrated loading. Acta Mechanica 148, 215–229 (2001). https://doi.org/10.1007/BF01183679
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DOI: https://doi.org/10.1007/BF01183679