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Three-dimensional stress and displacement fields near an elliptical crack front

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Abstract

Local stress and deformation fields for an elliptical crack embedded in an infinite elastic body subjected to normal, shear and mixed loads are considered. Particular emphasis is placed on the direction of propagation of points along the crack border. A confocal curvilinear coordinate system related to a fundamental ellipsoid, and a local spherical coordinate system attached to the crack border are adopted. Using asymptotic analysis, this paper obtains the stress and displacement fields in a plane inclined to the 3D crack front. Results show that the present solutions are independent of the curvature of the ellipse, and different from those given by Sih (1991). Based on two different fracture criteria, crack growth analysis shows that a 3D crack would propagate in the direction of the normal plane along the crack front. As a result, the fracture initiation and propagation of a 3D flat crack can be analyzed in the plane normal to the crack front, and the local fields in the normal plane are the linear superposition of the plane strain mode-I, mode-II, and mode-III crack-tip fields.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of South Carolina, Columbia, SC, 29208, USA

    X.K. Zhu & Y.J. Chao

  2. Department of Hydraulic Engineering, Tsinghua University, Beijing, 100084, China

    G.T. Liu

Authors
  1. X.K. Zhu
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  2. G.T. Liu
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  3. Y.J. Chao
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Zhu, X., Liu, G. & Chao, Y. Three-dimensional stress and displacement fields near an elliptical crack front. International Journal of Fracture 109, 383–401 (2001). https://doi.org/10.1023/A:1011030615958

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