Practical Criterion for Estimation of Notch Fatigue Strength

In the present study, a practical criterion for the estimation of the fatigue strength of notched specimens is discussed from a practical standpoint of design and maintenance of machines and structures. First of all, a hypothesis of “Fatigue Plastic Adaption” is proposed as one idea that is available to combine microscopic and macroscopic approaches to fatigue plasticity. The hypothesis expresses that, at a surface layer and at a notch root, elastic deformation arising at the cyclic maximum stress is transformed into local and inhomogeneous plastic deformation. Based on the hypothesis, mechanical models are constructed in order to simulate cyclic stress behavior at the surface layer and at the notch root. As a result, “Equivalent Stress Ratio” is formulated as a parameter for correspondence of cyclic stress conditions between notched and unnotched specimens. Moreover, on the basis of the hypothesis of the plastic adaptation, the equation of the equivalent stress ratio is also derived for the case of biaxial stress cycling in torsion, and it is finally expanded for the general case of proportional multiaxial stress cycling. The published fatigue data concerning tension-compression, bending, torsion and their combined loading are rearranged on the diagram where an abscissa indicates the equivalent stress ratio and an ordinate indicates the stress range at the notch root. As the result, it is recognized that the relation between the equivalent stress ratio and the notch-root-concentrated stress range is shown by a certain curve proper to material in spite of difference of stress concentration factors, loading types and mean stresses. Consequently, a criterion for notch fatigue strength is described on the basis of the equivalent stress ratio, i.e., the notch-root-concentrated stress range at the fatigue strength of the notched specimen for any nominal stress ratio is identical with the fatigue strength of the unnotched specimen for the equivalent stress ratio.