This singular integral equation, whose solution is also given, is basic in a class of problems involving the interface crack under load. In order to give proper credit to former endeavors, please let us follow the present "Q&A" question.
With the given f(t), we have in closed forms the dislocation densities, relative displacements of the faces of the crack and crack-tip stresses. The calculation of the crack extension force is under way.
The crack extension force is obtained. The presentation of the study will be given in due course. .
This solution is used in a paper intitled "Interface crack loaded in tension: introducing an internal shear stress promoted by the Poisson's effect"; see our contributions in ResearchGate
Internal shear stresses develop on both sides of the interface loaded in tension as the result of a difference in the Poisson's contractions in the media. Attached is an image of this internal shear stress. The value of the crack extension force is significantly modified by this shear stress: see our contribution " Interface crack loaded in tension: introducing an internal shear stress promoted by the Poisson's effect" for details.
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