A critical plane gradient approach for the prediction of notched HCF life

Abstract

A new approach, which uses the Findley critical plane damage parameter along with the stress gradient at the notch, was developed for predicting notched HCF life. The proposed approach and methodology for HCF notch analysis accounts for: (i) the multiaxial stress state at the notch, (ii) the notch size effect, and (iii) the effect of fatigue stress ratio. Two fatigue failure criteria based on the critical distance method were used to define a notch gradient parameter, G F. It was shown that G F is invariant with notch geometry and fatigue stress ratio. This invariance of G F was used to successfully and consistently analyze and predict notched HCF life of the titanium alloy Ti–6Al–4V for: (i) different notch geometries, and (ii) different fatigue stress ratios. For a notch under a general 2-dimensional stress state subjected to constant amplitude fatigue loading, the current approach can be performed in closed-form. Closed-form equations were developed for the fatigue notch factor K f, and the Findley gradient factor, G F, as a function of the critical distance, a c, the notch radius, ρ, the stress concentration factor K t, and the stress ratio, R. The proposed approach can be applied equally well using either finite element analysis or the closed-form analysis. A relationship was also established between G F and the notch sensitivity of a material. A new Findley notch sensitivity parameter, Q F, given by (2- G F) was proposed as a convenient and a more robust measure of the notch sensitivity than the classical notch sensitivity parameter, q, which can vary with the applied fatigue stress ratio.