Three-Dimensional Cracks: Further Concepts
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In Chapter 6 the basic principles of the distributed dislocation (loop) technique for three-dimensional crack problems were described, where the stress due to an infinitesimal dislocation loop of unit strength was used as the kernel function of the singular integral equation. The technique was employed to solve the crack problems under opening mode loading only. This approach will now be extended to a more general case, where a planar crack of arbitrary shape is subjected to mixed-mode loading. As the crack faces will in general experience both opening and shearing displacements, the basic infinitesimal dislocation loop to be employed to model the three relative displacements of the crack faces will have an arbitrary Burgers vector b, i.e. it is no longer perpendicular to the slip plane. To derive the associated singular integral equations we must first find the stress field due to an infinitesimal dislocation loop with arbitrary Burgers vector.
KeywordsStress Intensity Factor Burger Vector Slip Plane Crack Front Singular Integral Equation
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