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An integral representation of the stress intensity factors for three-dimensional static problems

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Abstract

For finding suitable expressions for the stress intensity factors (SIFs) under a general three-dimensional condition, the first stress invariant and the displacement tangent to a crack edge are analyzed. By using Green's theorem, the SIFs are expressed by integrals for the most general situations. K I and K II are expressed by integrals of the first stress invariant and its partial derivative. K III is expressed by an integral of the displacement tangent to the crack edge and its partial derivative. The integrals include a surface integral on a smooth surface of arbitrary shape, and a line integral along part of the surface's boundaries. The expressions are valid for an arbitrarily shaped elastic medium with stationary cracks of arbitrary shape. The expressions provide a new approach for the determination of the SIFs.

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Authors and Affiliations

  1. Computational Mechanics Center, Georgia Institute of Technology, 30332-0356, Atlanta, GA, USA

    Xiaoyuan Dong

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  1. Xiaoyuan Dong
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Dong, X. An integral representation of the stress intensity factors for three-dimensional static problems. Int J Fract 69, 189–199 (1994). https://doi.org/10.1007/BF00035029

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  • DOI: https://doi.org/10.1007/BF00035029

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