Abstract
Torsion of a cracked elastic body by an embedded semi-infinite rigid cylinder is studied. A coaxial penny-shaped crack is situated in the plane of the end of the cylinder. The problem is reduced to a system of dual integral equations including Hankel and Weber–Orr transforms and then, by using ansatzs, to an integral equation of the second kind with Hankel integral operator given on a semi-infinite interval or to an equivalent infinite system of linear algebraic equations with a Hankel matrix. A detailed investigation allowed us to suggest efficient methods for solving equations for any size of the crack. In particular, accurate approximate formulas for the stress intensity factor and the contact stresses are derived, as well as an asymptotic formula for the stress intensity factor when a crack is large. Analytical estimations and calculations manifest a strong increase in the stress intensity factor and the contact stress at the end of the cylinder as the crack tip is very close to the cylinder surface.
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