Abstract
This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.
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References
Sneddon I.N. (1951) Fourier Transforms. McGraw Hill, New York
Hwang K.C., Yu S.W. (1986) Elastic-Plastic Fracture Mechanics. Tsinghua University Press, Beijing
Hwang K.C., Yu S.W., Yang W. (1990) Theoretical investigation of crack-tip singularity fields in China. Appl. Mech. Rev. 43, 19–33
Hao T.H. (1992) An isolated crack normal to an interface of infinite extent under anti-plane shear. Theoret. Appl. Fract. Mech. 17, 233–238
Sih G.C., Liebowitz H. Mathematical Theories of Brittle Fracture, Fracture, vol. II. In: Liebowitz H (ed.) pp. 67-190. Academic, New York (1968)
Zak A.R., Williams M.L. (1963) Crack point stresses singularities at bimaterial interface. Trans. ASME J. Appl. Mech. Ser. E 30(1): 142
Muskhelishvili N.I. (1963) Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen
Savin G.N. (1961) Stress Concentration Around Holes. Pergamon Press, New York
Eshelby J.D. (1956) The Continuum Theory of Dattice Defects, Solid State Physics, Vol 3. Academic, New York
Cherepanov G.P. (1977) Mechanics of Brittle Fracture. McGraw-Hill, New York
Hao T.H. (1990) Near field behavior of in-plane crack extension in nonlinear incompressible material. Theoret. Appl. Fract. Mech. 12, 241–249
Hao T.H., Zhang X.T., Hwang K.C. (1992) In homogeneous behavior of antiplane shear crack in softening material with local unloading. Theoret. Appl. Fract. Mech. 17, 165–175
Yang W. (1995) Microscale and Macroscale Fracture Mechanics. Tsinghua University Press, Springer, Beijing
Lekhnitskii S.G. (1981) Theory of Elasticity of an Anisotropic Body, English edn. Mir, Moscow
Cook T.S., Erdogan F. (1972) Stresses in bounded materials with a crack perpendicular to the interface. Int. Eng. Sci. 10, 677–697, especially, p. 691
Hao T.H. (2006) New Method to Solve The Complex Elasticity. J. Donghua Univ. 2, 10
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Hao, T. Exact solution of plane isolated crack normal to a bimaterial interface of infinite extent. Acta Mech Mech Sinica 22, 455–468 (2006). https://doi.org/10.1007/s10409-006-0024-7
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DOI: https://doi.org/10.1007/s10409-006-0024-7