TECHNICAL PAPERS
Mar 1, 1989

Stress Interference in a Transversely Isotropic Body under Axisymmetric Loading

Publication: Journal of Engineering Mechanics
Volume 115, Issue 3

Abstract

An unbounded homogeneous transversely isotropic body of revolution containing two twin spheroidal cavities is subjected to an axisymmetric loading. The axis of loading symmetry coincides with the axis of elastic symmetry of the material and the axis of revolution of the body. The elasticity solution is obtained in series form utilizing the displacement potential representation for the equilibrium of transversely isotropic solids, and numerical results are presented for the cases of two spherical cavities perturbing uniaxial and hydrostatic tension fields in certain hexagonal crystals and in isotropic materials. Of primary interest is the influence of cavity spacing and material type on the degree of stress interference between the two perturbations.

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References

1.
Atsumi, A. (1960). “Stress in a circular cylinder having an infinite row of spherical cavities under tension.” J. Appl. Mech. 27, 87–92.
2.
Chen, W. T. (1968). “Axisymmetric stress field around spheroidal inclusions and cavities in a transversely isotropic material.” J. Appl. Mech. 35, 770–773.
3.
Chen, W. T. (1971). “Elastic analysis of an axisymmetric stress field perturbed by a spheroidal inhomogeneity.” Quart. Appl. Mech. 517–525.
4.
Choi, B. I., and Earmme, Y. Y. (1985). “An elastic solution for two spherical precipitates embedded in infinite matrix.” Mech. Res. Comm. 12, 127–134.
5.
Elliott, H. A. (1948). “Three‐dimensional stress distributions in hexagonal aeolotropic crystals.” Proc. Cambridge Phil. Soc. 44, 522–533.
6.
Elliott, H. A. (1949). “Axial symmetric stress distributions in hexagonal aeolotropic crystals. The problem of the plane and related problems.” Proc. Cambridge Phil. Soc. 45, 539–547.
7.
Eshelby, J. D. (1957). “The determination of the elastic field of an ellipsoidal inclusion, and related problems.” Proc. Royal Soc., Series A, 241, 376–396.
8.
Eshelby, J. D. (1959). “The elastic field outside an ellipsoidal inclusion.” Proc. Royal Soc., Series A, 252, 561–569.
9.
Eshelby, J. A. (1961). “Elastic inclusions and inhomogeneities.” Progress in solid mechanics, Sneddon and Hill, eds. North‐Holland Publishing Company, Amsterdam, The Netherlands, 2, 89–140.
10.
Eubanks, R. A. (1965). “Stress interference in three‐dimensional torsion.” J. Appl. Mech. 32, 21–25.
11.
Goree, J. G., and Wilson, H. B. (1967). “Axisymmetric torsional stresses in a solid containing two partially bonded rigid spherical inclusions.” J. Appl. Mech. 34, 313–320.
12.
Greenberg, H. (1965). “An engineering basis for establishing radiographic acceptance standards for porosity in steel weldments.” J. Basic Engrg. 87, 887–893.
13.
Hamada, M., and Kodama, J. (1985). “Axisymmetric tension of an infinite body containing two spherical cavities.” Bull. JSME 28, 408–413.
14.
Hashin, Z. (1965). “On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry.” J. Mech. Phys. Solids 13, 119–134.
15.
Hashin, Z. (1979). “Analysis of properties of fiber composites with anisotropic constituents.” J. Appl. Mech. 46, 543–550.
16.
Hashin, Z., and Rosen, B. W. (1964). “The elastic moduli of fiber‐reinforced materials.” J. Appl. Mech. 31, 223–232.
17.
Heinrich, S. M., and Eubanks, R. A. (1985). “Stress interference in axisymmetric torsion of a transversely isotropic body.” Civ. Engrg. Studies, Struct. Res. Series No. 518, University of Illinois, Urbana, Ill.
18.
Hellwege, K. H. (1979). Landolt‐Börnstein numerical data and functional relationships in science and technology. New series, 11, Springer‐Verlag, Berlin, W. Germany.
19.
Hill, J. L. (1966a). “The effect of two rigid spherical inclusions on the stresses in an infinite elastic solid (Discussion).” J. Appl. Mech. 33, 715–718.
20.
Hill, J. L. (1966b). “Pure torsion of an infinite solid containing two rigid spherical inclusions.” J. Appl. Mech. 33, 201–203.
21.
Hill, R. (1964). “Theory of mechanical properties of fibre‐strengthened materials: I. Elastic behaviour.” J. Mech. Phys. Solids 12, 199–212.
22.
Hobson, E. W. (1931). The theory of spherical and ellipsoidal harmonics. Macmillan, New York, N.Y.
23.
Hu, H.‐C. (1953). “On the three‐dimensional problem of the theory of elasticity of a transversely isotropic body.” Acta Scientia Sinica 2, 145–151.
24.
Johnson, W. C., and Lee, J. K. (1982). “An integral equation approach to the elastic interaction of two precipitates.” Physica Status Solidi, a 71, 589–602.
25.
Lapkin, V. P. (1975). “Effect of transverse isotropy on the stress and strain state of a soil base loaded by a strip foundation.” Soil Mech. Found. Engrg. 12, 201–207.
26.
Lekhnitskii, S. G. (1981). Theory of elasticity of an anisotropic body. Mir Publishers, Moscow, U.S.S.R.
27.
Miyamoto, H. (1957). “On the problem of the theory of elasticity for a region containing more than two spherical cavities.” Trans. JSME 23, 431–436 (in Japanese).
28.
Moon, P., and Spencer, D. E. (1971). Field theory handbook, 2nd Ed. Springer‐Verlag New York, Inc., New York, N.Y.
29.
Moschovidis, A. A., and Mura, T. (1975). “Two‐ellipsoidal inhomogeneities by the equivalent inclusion method.” J. Appl. Mech. 42(12), 847–852.
30.
Nisitani, H. (1963). “On the tension of an elastic body having. an infinite row of spheroidal cavities.” Trans. JSME 29, 765–768 (in Japanese).
31.
Peterson, R. E. (1965). “The interaction effect of neighboring holes or cavities, with particular reference to pressure vessels and rocket cases.” J. Basic Engrg. 87, 879–884.
32.
Pickering, D. J. (1970). “Anisotropic elastic parameters for soil.” Geotech. 20(3), 271–276.
33.
Shelley, J. F., and Yu, Y. Y. (1966). “The effect of two rigid spherical inclusions on the stresses in an infinite elastic solid.” J. Appl. Mech. 33, 68–74.
34.
Sternberg, E., and Sadowsky, M. A. (1952). “On the axisymmetric problem of the theory of elasticity for an infinite region containing two spherical cavities.” J. Appl. Mech. 19, 19–27.
35.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed. McGraw Hill Book Co., New York, N.Y.
36.
Willis, J. R. (1975). “The interaction of gas bubbles in an anisotropic elastic solid.” J. Mech. Phys. Solids 23, 129–138.
37.
Zureick, A. H., and Eubanks, R. A. (1988). “Spheroidal cavity with prescribed asymmetric tractions in three‐dimensional transverse isotropy.” J. Engrg. Mech., ASCE, 114, 24–48.

Information & Authors

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 115Issue 3March 1989
Pages: 555 - 577

History

Published online: Mar 1, 1989
Published in print: Mar 1989

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Authors

Affiliations

S. M. Heinrich, Associate Member, ASCE
Asst. Prof., Dept. of Civ. Engrg., Marquette Univ., Milwaukee, WI 53233
J.‐Y. Wang
Grad. Student, Dept. of Civ. Engrg., Marquette Univ., Milwaukee, WI 53233

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