The torsion problem of a disk bonded to a dissimilar shaft

Abstract

The torsion of an infinitely long elastic shaft bonded to an elastic disk of finite width and of different elastic constants is considered. The contact may be accomplished through bonding or shrink-fit. First the general problem with the axisymmetric edge cracks on the contact area is formulated. This problem is shown to reduce to a singular integral equation with a simple Cauchy-type singularity. In limit, when the contact is along the entire width of the disk, it is shown that the dominant kernel of the integral equation is of generalized Cauchy-type and the solution has a singularity of the form (c2−x2)−γ, where 2c is the width of the disk and 0 < γ < 12. A series of numerical examples is worked out with or without the edge cracks and under symmetric and anti-symmetric external loads. A variation of the torsion problem, namely, the problem of two semi-infinite strips under anti-plane shear loading is then considered. Again, the results of a series of numerical examples are given to show the effect of the geometry and the material properties on the stress intensity factor.