The use of the theory of critical distance and the stress-gradient approach in the fatigue life estimation of notched components

Fatigue life prediction for machine components is a fundamental factor in the industrial world, and therefore several methods can be traced in technical literature to estimate life of notched components. The present paper correlates the classical stress-gradient approach, or support factor method, proposed by Siebel, Neuber and Petersen with the more recent theory of critical distance approach by Tanaka and Taylor. On one hand, the main asset of the support factor method is the punctual information about the stresses needed to estimate the effective stress, namely the maximum stress and stress gradient at the hot spot. By contrast, the theory of the critical distance needs the calculation of the stress distribution for a finite depth inside the material. The main drawback of the support factor method is that the material parameter rho* is available only for a limited series of materials. In order to overcome this limitation, the paper investigates the correlation between the material parameter rho* and the critical distance L by relying on a parametric stress function. The proposed correlation aims at giving a simple method for the industrial engineers, which often needs straightforward methods to tackle practical problems. A comparison between the two methods is carried out by considering three different benchmark geometries: a typical V-notched specimen, a vessel under internal pressure and a complex industrial hydraulic control valve. In the first two benchmarks, the effective stresses are analytically retrieved and compared using both methods while an elastic finite element analysis is performed for the last one. The close match of the fatigue life prediction between the methods supports the possibility to exploit the data available in literature for the critical distance in order to estimate the effective stresses with the support factor method.