Abstract
The static-equilibrium problem for an elastic orthotropic space with a circular (penny-shaped) crack is solved. The stress state of an elastic medium is represented as a superposition of the principal and perturbed states. To solve the problem, Willis’ approach is used, which is based on the triple Fourier transform in spatial variables, the Fourier-transformed Green’s function for an anisotropic material, and Cauchy’s residue theorem. The contour integrals obtained are evaluated using Gauss quadrature formulas. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. E. Andreikiv, Spatial Problems in Crack Theory [in Russian], Naukova Dumka, Kiev (1982).
N. M. Borodachev, Design of Structural Members with Cracks [in Russian], Mashinostroenie, Moscow (1992).
G. S. Kit and M. V. Khai, The Method of Potentials in Three-Dimensional Problems of Thermoelasticity for Cracked Bodies [in Russian], Naukova Dumka, Kiev (1989).
S. G. Lekhnitskii, The Theory of Elasticity of Anisotropic Body [in Russian], Nauka, Moscow (1977).
M. P. Savruk, Stress Intensity Factors in Cracked Bodies [in Russian], Vol. 2 of the four-volume series Fracture Mechanics and Strength of Materials: A Handbook, Naukova Dumka, Kiev (1988).
Yu. N. Podil’chuk, “Mechanical and thermal strain states of transversely isotropic bodies with elliptic and parabolic cracks,” Int. Appl. Mech., 29, No.10, 784–793 (1993).
Yu. N. Podil’chuk, “Exact analytical solutions of spatial boundary static problems for a transversely isotropic body of canonical form (review),” Prikl. Mekh., 33, No.10, 3–30 (1997).
Y. Murakami (ed.), Stress Intensity Factors Handbook, Vol. 2, Ch. 9, Pergamon Press (1986).
J. D. Eshelby, “The continuum theory of lattice defects,” in: F. Seitz and D. Turnbull (eds.), Progress in Solid State Physics, Vol. 3, Acad. Press, New York (1956), pp. 79–303.
A. H. Elliott, “Three-dimensional stress distributions in hexagonal aelotropic crystals,” in: Proc. Cambr. Phil. Soc., 44, No.4, 522–533 (1948).
G. V. Galatenko, “The stress intensity factor for an elliptical crack under a piecewise-constant load,” Int. Appl. Mech., 38, No.7, 854–860 (2002).
A. Hoenig, “The behavior of a flat elliptical crack in an anisotropic elastic body,” Int. J. Solids Struct., 14, 925–934 (1978).
M. K. Kassir and G. C. Sih, Three-Dimensional Crack Problems, Vol. 2 of the series Mechanics of Fracture, Nordhoff, Leyden (1975).
V. S. Kirilyuk, “Interaction of an ellipsoidal inclusion with an elliptic crack in an elastic material under triaxial tension,” Int. Appl. Mech., 39, No.6, 704–712 (2003).
V. S. Kirilyuk, “The stress state of an elastic medium with an elliptic crack and two ellipsoidal cavities,” Int. Appl. Mech., 39, No.7, 829–839 (2003).
T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff, Boston-London (1987).
L. J. Willis, “The stress field of an elliptical crack in anisotropic medium,” Int. J. Eng. Sci., 6, No.5, 253–263 (1968).
Wu Kuang-Chong, “The stress field of an elliptical crack in anisotropic medium,” Int. J. Solids Struct., 37, 4841–4857 (2000).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 76–83, December 2004.
Rights and permissions
About this article
Cite this article
Kirilyuk, V.S. The stress state of an elastic orthotropic medium with a penny-shaped crack. Int Appl Mech 40, 1371–1377 (2004). https://doi.org/10.1007/s10778-005-0042-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-005-0042-3