Analysis of three-dimensional edge cracks under tensile loading |
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Authors: | Yonglin Xu Brian Moran and Ted Belytschko |
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Institution: | (1) Department of Civil Engineering, Northwestern University, 60208 Evanston, IL |
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Abstract: | Three-dimensional edge cracks are analyzed using the Self-Similar Crack Expansion (SSCE) method with a boundary integral equation
technique. The boundary integral equations for surface cracks in a half space are presented based on a half space Green's
function (Mindlin, 1936). By using the SSCE method, the stress intensity factors are determined by the crack-opening displacement
over the crack surface. In discrete boundary integral equations, the regular and singular integrals on the crack surface elements
are evaluated by an analytical method, and the closed form expressions of the integrals are given for subsurface cracks and
edge crakcs. This globally numerical and locally analytical method improves the solution accuracy and computational effort.
Numerical results for edge cracks under tensile loading with various geometries, such as rectangular cracks, elliptical cracks,
and semi-circular cracks, are presented using the SSCE method. Results for stress intensity factors of those surface breaking
cracks are in good agreement with other numerical and analytical solutions. |
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Keywords: | Self-similar crack expansion boundary integral equation |
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