The solution of the branched crack problem for an isotropic material, employing the dislocation method as developed by Lo (1978), results in a singular integral equation in which the slope of the crack-opening displacement is the unknown. In this brief note, using the function-theoretic method, the behavior of this unknown function is investigated at the corner where the branched and main crack meet and it is shown that the order of stress singularity obtained at the reentrant corner of the branched crack is given by the Williams’ (1952) characteristic equation for the isotropic wedge.

Issue Section:
Brief Notes
Topics:
Corners (Structural elements), Fracture (Materials), Stress singularity, Wedges, Dislocations, Displacement, Integral equations
1.
Chatterjee
S. N.
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The Stress Fields in the Neighborhood of a Branched Crack in an Infinite Elastic Sheet
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2.
Grenestedt
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Hallstrom
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Crack Initiation from Homogeneous and Bimaterial Comers
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3.
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K.
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Energy Release Rate and Crack Kinking
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5.
Lo
K. K.
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Analysis of Branched Cracks
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6.
Muskhelishvili, N., 1992, Singular Integral Equations, Dover, New York.
7.
Selvarathinam, A.S., 1995, “A Generalized Linear Elastic Fracture Model for Advanced Materials,” Ph.D. dissertation, Clemson University, Clemson, SC.
8.
Selvarathinam, A.S., and Goree, J.G., 1998, “T-stress Based Fracture Model for Cracks in Isotropic Material,” Engineering Fracture Mechanics, In press.
9.
Timoshenko, S.P., and Goodier, J.N., 1982, Theory of Elasticity, McGraw-Hill, New York.
10.
Williams
M. L.
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1952
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Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
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