A simplified approach to apply the theory of critical distance to notched components under torsional fatigue loading

摘要

In the present study, the use of the theory of critical distances (TCD) was extended to notched components subjected to torsional fatigue loading. Initially, using some basic solid-mechanics arguments, it was demonstrated that the reference stress to use for assessing notched components under torsional fatigue loading is the fully-reversed plain torsional fatigue limit. Secondly, some data sets taken from the literature were used to show that the characteristic material length constant under torsion is different from that under uniaxial fatigue loading. This experimental evidence was shown to be in agreement with several results of previously published investigations. Finally, the material cracking behaviour under pure torsional loading was reviewed, showing that the characteristic material length constant under cyclic shear stress cannot be easily calculated using linear elastic fracture mechanics (LEFM) concepts (as can be done for uniaxial fatigue loading), mainly due to the lack of experimental data generated under Mode III loading. To overcome this problem, two different hypotheses were proposed: (i) that the critical distance under torsion is the same as that under uniaxial fatigue loading; (ii) that the critical distance under torsion can be calculated using an effective threshold value of the stress intensity factor which accounts for the experimental evidence that the torsional fatigue limit for a crack subjected to cyclic shear stress is determined by the non-propagation of Mode I branched cracks. Comparison with experimental data found in the literature showed that both of these hypotheses gave reasonable predictions of the fatigue limit, with hypothesis (ii) being somewhat better than hypothesis (i). This result is very useful, because it allows engineers engaged in fatigue assessment of real components to predict the effect of torsion, by using material constants derived from uniaxial fatigue tests and by simply post-processing information obtained from linear elastic FE models.