K
III
-Deformation modes in internal oblique cracks under plane-stress conditions |
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Authors: | Pericles S Theocaris |
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Institution: | (1) Athens National Technical University, P.O. Box 77230, GR 175-10 Athens (P. Phaleron), Greece |
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Abstract: | The exact shape of the deformed internal oblique crack in an infinite elastic plate under conditions of plane stress was studied.
The Muskhelishvili potential function yielded the exact stress and displacement field around the crack. While in previous
papers by the author the study was mainly concerned with the definition of the in-plane shape of the deformed crack and important
properties were disclosed concerning especially the contribution of the shear loading of the crack, in this paper the out-of-plane
component of displacements is determined and its influence on the exact shape of the deformed crack in space is presented.
It is shown that, as soon as shear displacements appear in the cracked plate under plane stress, out-of-plane shear displacements
are a compulsory consequence for plane-stress conditions of the plate. The elliptic form of the deformed internal crack was
twisted out of the plane of the plate with its zero twisting displacement near the new crack tip of its deformed shape corresponding
to the vertex of the ellipse. The points of maximum and minimum out-of-plane displacements were placed close to the vertices
of the ellipse at polar angles, θ, depending only on the eccentricity of the ellipse and displaced always on both sides of
the vertices. The compulsory coexistence of mode II and mode III deformations makes the internal crack in plane stress to
present a complicated pattern of deformation at its deformed crack tips. All of these results are amply supported by experimental
evidence with caustics, which always show either a simple mode I pattern or a complex mode II and III pattern as soon as shear
interferes in the mode of deformation of the plate. |
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