Abstract

An infinite homogeneous wedge containing an edge crack of length ′𝑎′, subjected to concentrated loads at two points, is analyzed for stresses and displacement due to Elastostatic deformation. The series expressions for the stresses  everywhere in the body are then computed for use in estimating other fracture parameters. The wedge contains a crack of length “a” lying along the ray  The problem is formulated by an infinite Mellin transform, and transformed into an integral parameter plane where the transformed problem is solved to get the displacement by the WienerHopf technique. These produced a two-dimensional Neumann boundary value problem in terms of the only non-zero displacement component, . The presence of the crack motivates the expectation of different transform plane displacement,  Mellin transform is next applied, where 𝑠 is the transform parameter, which introduces four coefficients,   that are evaluated by the Wiener-Hopf technique using given boundary conditions. A series of closed-form solutions was thereafter obtained for displacement and stresses that were used to analyze the fracture parameters. The stress field at the crack tip of the wedge is employed to compute the mode III stress intensity factor, . The result is that along the crack region, the displacements  which implies discontinuity of the displacement field and that the tearing stress  along the region is zero. Also, at the region ahead of the crack,   implies the continuity of the displacement fields, and that the tearing stress  It is also continuous there. We then conclude that, as a result of the crack, there are different fracture parameter responses at every region of the wedge material. It is also found that the stress intensity factor,  It is independent of the material property, but depends linearly on the concentrated load. Therefore, irrespective of the structural material, there are always certain fracture responses due to the application of load.

Keywords

References

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