Hidden ring crack in a rotating cylindrical shell under torsion

TL;DR

This paper models the behavior of a ring crack in a rotating cylindrical shell under torsion, providing analytical solutions for stress intensity factors and exploring how geometry and rotation affect crack extension.

Contribution

It introduces an analytical approach to evaluate crack behavior in rotating shells under torsion, including stress intensity factors and the influence of geometry and rotation.

Findings

Stress intensity factors depend on crack location and rotation frequency.

Crack extension is influenced by cylinder height and torsion load.

Model potential for fatigue crack analysis and detection methods.

Abstract

We consider the impact of a ring crack within a rotating hollow cylinder of fixed height under axisymmetric (torsion) loading. The form of the displacement is obtained from the equation of motion using the Fourier sin transform. The displacement jump over the crack is obtained from the boundary condition on the tangential stress, formulated as a singular integral equation which is solved by the method of orthogonal polynomials. The stress intensity factors on the opposing crack surfaces are calculated. The dependence of the crack extension on the problem geometry is investigated, including the impact of the crack's location, cylinder's height, torsion loading and rotation frequency. Possible extensions of the model to cover fatigue cracking are considered. A practical test to detect and locate cracks within a rotating cylinder is outlined.