In this paper, an axisymmetric torsion problem of a circular rigid disc of an elastic medium weakened by an external crack is presented. The mixed boundary-value problem is converted to a system of dual integral equations by using the Hankel integral transforms method. A system of Fredholm integral equations is obtained using the Abel integral equations formulas. The Jacobi polynomials series development is used for reducing the studied problem to a system of infinite algebraic equations. The latter system is solved numerically by the truncation method. Some physical quantities namely the displacement, the stress, and the stress intensity factor are obtained analytically and presented in the form of tables and graphs. A discussion is also followed dealing with the effect of the crack radius and the layer thickness on the rigidity of the medium. The results are validated with the particular case of the large thickness as well as with a comparison with those given by the finite element method.
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