Calculation of fatigue limits of case-hardened specimens with consideration of mean stresses and residual stresses

Abstract

The strength of case-hardened parts under cyclic loading can be determined in an experimental manner, but this can produce a large amount of costs due to the expenditure of material and testing time. Therefore, a calculation method is developed, that strongly reduces the number of experiments. The presented model is based on Weibull's weakest-link concept and allows to compute the survival probability of a case-hardened part which is loaded close to the fatigue limit. The essential quantities in this model are the distribution of Vicker's hardness of the material, the exponents of the Weibull distribution of the volume and the surface, the residual stress state, the surface roughness and the surface oxidation depth. By integrating the survival probabilities of the surface and the volume, the survival probability of the entire specimen or part can be calculated, which allows to compute the fatigue limit. The necessary parameters have to be determined from reference specimens. The model is successfully examined by comparing experimental and calculated results of smooth and notched case-hardened specimens under alternating torsion, rotating bending, repeated tension and tension-compression.