Abstract
The static-equilibrium problem for an elastic orthotropic space with an elliptical crack is solved. The stress state of the space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis’s approach is used. It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material, and Cauchy’s residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied
Similar content being viewed by others
REFERENCES
A. Ya. Aleksandrov and Yu. I. Solov’ev, Three-Dimensional Elastic Problems [in Russian], Nauka, Moscow (1978).
A. E. Andreikiv, Three-Dimensional Problems in the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1982).
A. N. Borodachev, “Plane elliptic crack in an arbitrary field of normal stresses,” Prikl. Mekh., 16, No.12, 118–121 (1980).
N. M. Borodachev, Design of Structural Elements with Cracks [in Russian], Mashinostroenie, Moscow (1992).
G. S. Kit and M. V. Khai, The Method of Potentials in Three-Dimensional Thermoelastic Problems for Cracked Bodies [in Russian], Naukova Dumka, Kiev (1989).
S. G. Lekhnitskii, Theory of Elasticity for Anisotropic Body [in Russian], Nauka, Moscow (1977).
M. P. Savruk, Stress Intensity Factors for Cracked Bodies, Vol. 2 of the four-volume series V. V. Panasyuk (ed.), Fracture Mechanics and Strength of Materials: A Handbook [in Russian], Naukova Dumka, Kiev (1988).
Yu. N. Podil’chuk, Boundary-Value Static Problems for Elastic Bodies, Vol. 1 of the six-volume series Three-Dimensional Problems of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1984).
Yu. N. Podil’chuk, “Exact analytical solutions to three-dimensional boundary-value static problems for a canonical transversely isotropic body (review),” Prikl. Mekh., 33, No.10, 3–30 (1997).
G. Ya. Popov, Concentration of Elastic Stresses near Punches, Notches, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).
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,” Proc. Cambr. Phil. Soc., 44, No.4, 522–533 (1948).
G. V. Galatenko, “Model of plastic deformation at the front of a circular crack under nonaxisymmetric loading,” Int. Appl. Mech., 39, No.1, 105–109 (2003).
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. Sih, Three-Dimensional Crack Problems, Vol. 2 of Mechanics of Fracture, Nordhoff, Leyden (1975).
N. Kinoshita and T. Mura, “Elastic fields of inclusions in anisotropic media,” Phys. Stat. Sol. (a), 5, 759–768 (1971).
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).
P. E. O’Donogue, T. Nishioka, and S. N. Atluri, “Multiple coplanar embedded elliptical crack under arbitrary normal loading,” Int. J. Numer. Math. Eng., 21, 437–449 (1985).
R. C. Shah and A. S. Kobayashi, “Stress intensity factor for elliptical crack under arbitrary normal loading,” Eng. Fract. Mech., 3, No.1, 71–96 (1971).
I. N. Sneddon, “The stress intensity factor for a flat elliptical crack in an elastic solid under uniform tension,” Int. J. Eng. Sci., 17, No.2, 185–191 (1979).
L. J. Willis, “The stress field of an elliptical crack in anisotropic medium,” Int. J. Eng. Sci., 6, No.5, 253–263 (1966).
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. 41, No. 4, pp. 20–29, April 2005.
Rights and permissions
About this article
Cite this article
Kirilyuk, V.S. Stress State of an Elastic Orthotropic Medium with an Elliptic Crack Under Tension and Shear. Int Appl Mech 41, 358–366 (2005). https://doi.org/10.1007/s10778-005-0096-2
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-005-0096-2