Abstract
We analyze the problem of the stress distribution in an elastic orthotropic medium with an arbitrarily oriented elliptical crack. To construct the problem solution, the Willis approach is used which is based on the triple Fourier transformation of spatial variables and Fourier-image of Green’s function for an infinite anisotropic space. The investigation results in special cases are compared with the data of other authors. The effect of the elliptical crack orientation in an orthotropic space on the distribution of the stress intensity factors along its contour 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, Three-Dimensional Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1982).
A. N. Borodachev, “A flat elliptical crack in an arbitrary field of normal stresses,” Prikl. Mekh., 16, No. 12, 118–121 (1980).
S. Atluri (Ed.), Computational Methods in the Fracture Mechanics [Russian translation], Mir, Moscow (1990).
V. V. Panasyuk (Ed.), Fracture Mechanics and Strength of Materials. Handbook [in Russian], in 4 volumes, Vol. 2: M. P. Savruk, Stress Intensity Factors in Bodies with Cracks, Naukova Dumka, Kiev (1990).
I. V. Orynyak and A. Yu. Gienko, “Mode-I elliptical crack in an infinite elastic body. Part 1. Crack-face displacement for the polynomial law of loading,” Strength Mater., 34, No. 1, 12–26 (2002).
I. V. Orynyak, A. Yu. Gienko, and A. V. Kamenchuk, “Mode-I elliptical crack in an infinite elastic body. Part 2. Contact of the crack faces,” Strength Mater., 34, No. 2, 135–143 (2002).
Yu. N. Podil’chuk, “Boundary problems of the statics of elastic bodies,” in: A. N. Guz’ (Ed.), Three-Dimensional Problems of the Theory of Elasticity and Plasticity [in Russian], in 6 volumes, Naukova Dumka, Kiev (1984).
Y. Murakami (Ed.), Stress Intensity Factors Handbook [Russian translation], in 2 volumes, Mir, Moscow (1990).
M. K. Kassir and G. Sih, Three-Dimensional Crack Problems, Noordhoff Int. Publ., Leyden (1975).
R. C. Shan and A. S. Kobayashi, “Stress intensity factors for an elliptical crack under arbitrary normal loading,” Eng. Fract. Mech., 3, No. 1, 71–96 (1971).
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, No. 4, 437–449 (1985).
P. Livieri, F. Segala and O. Ascenzi, “Analytic evaluation of the difference between Oore-Burns and Irwin stress intensity factors for elliptical cracks,” Acta Mech., 176, No. 1, 95–105 (2005).
Yu. N. Podil’chuk, “Accurate analytical solutions of three-dimensional boundary-value problems on the statics of transversely isotropic bodies of a canonical form (review),” Prikl. Mekh., 33, No. 10, 3–30 (1997).
C.-R. Chiang, “Some crack problems in transversely isotropic solids,” Acta Mech., 170, No. 1, 1–9 (2004).
V. I. Fabrikant, “Elliptic crack in a transversely isotropic body, revision: New symbolism,” Acta Mech., 172, No. 3–4, 181–193 (2004).
Kuang-Chang Wu, “On an elliptic crack embedded in an anisotropic material,” Int. J. Solids Structure, 37, No. 35, 4841–4857 (2000).
A. Hoenig, “The behavior of a flat elliptical crack in an anisotropic elastic body,” Int. J. Solids Struct., 14, No. 11, 925–934 (1978).
V. S. Kirilyuk, “On the stress state of an orthotropic medium with a penny-shaped crack,” Int. Appl. Mech., 40, No. 12, 84–91 (2004).
V. S. Kirilyuk, “The stress state of an elastic orthotropic medium with an elliptic crack under tension and shear,” Int. Appl. Mech., 41, No. 4, 358–366 (2005).
V. S. Kirilyuk, “On the influence of the orientation of spheroidal hollows and rigid inclusions in orthotropic media on stress concentration,” Strength Mater., 38, No. 1, 39–47 (2006).
V. S. Kirilyuk, “Static equilibrium of an elastic orthotropic medium with an elliptic crack under bending,” Int. Appl. Mech., 41, No. 8, 895–903 (2005).
L. J. Willis, “The stress field around the elliptical crack in an anisotropic medium,” Int. J. Eng. Sci., 6, No. 5, 253–263 (1968).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body [in Russian], Nauka, Moscow (1977).
T. Mura, Micromechanisms of Defects in Solids, Martinus Nijhoff, Boston; London (1987).
Author information
Authors and Affiliations
Additional information
__________
Translated from Problemy Prochnosti, No. 4, pp. 146–159, July–August, 2007.
Rights and permissions
About this article
Cite this article
Kirilyuk, V.S., Levchuk, O.I. & Tkachenko, V.F. On the static equilibrium of an elastic orthotropic medium with an arbitrarily oriented elliptical crack. Strength Mater 39, 443–453 (2007). https://doi.org/10.1007/s11223-007-0050-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11223-007-0050-0