Stress Concentrations in Fillets

The stress concentrations arising in the fillets of fan and turbine blades, tie down rods, and bolt heads from axially symmetric centrifugal or static force loadings are treated two dimensionally by photoelastic and theoretical methods. The effects of the fillet radius, the height of the base, the mode of application of retention forces, and the distance between the retention reactions and fillet tangencies are considered. The stress concentration factor, K, was found to increase with decreasing radius and decreasing base height and, for small radii, to decrease at first with the distance between the reaction and fillet tangency but, in general, to increase with this distance. Comparisons with other experiments and stress concentration configurations are also made. An approximate theoretical solution is derived by selecting a convenient region from the whole base and replacing, where necessary, the exact boundary conditions with relaxed or integral conditions. The problem is formulated in terms of the classical Airy stress function. Agreement between theory and experiment is reasonable