Surface tractions for unsymmetrical nominally flat contacts under partial reverse slip conditions

Abstract

Dovetail regions in blade-disk joints of aircraft engines are prone to damage due to stress concentration and steep stress gradients. Evaluation of contact tractions (pressure and shear) is an essential first step towards an accurate estimation of stresses, in order to estimate the life of the components. They are modeled as unsymmetrical nominally flat contacts (different edge radii) that experience moment and bulk stress in addition to normal and tangential loads. Existing solution for pressure in a symmetrical nominally flat contact is modified to obtain a closed-form solution for pressure in an unsymmetrical nominally flat contact. A new analytical solution for shear traction under partial reverse slip (large bulk stress) conditions is obtained by approximating the contact pressure into equivalent Hertzian and square flat distributions in the central flat and rounded edges, respectively, thereby avoiding the logarithmic and other complicated terms. Limiting/ transition bulk stresses that determine various regimes of partial reverse slip conditions are evaluated and used to determine the shear case for given loading.