Yoshihiko Mukai

A New Conception on Fatigue Plasticity and Its Application to Notch Problems

A hypothesis of fatigue plastic adaptation is proposed and modeled as one idea that is available to combine microscopic and macroscopic approaches on fatigue plasticity. The hypothesis expresses that, at the positions of a surface layer, a notch root and a fatigue crack tip, elastic deformation arising at the maximum stress is transformed into the localized inhomogeneous plastic deformation inherent in fatigue. On the basis of the hypothesis, an equivalent stress ratio is formulated as a parameter for the correspondence between the cyclic stress conditions of notched and unnotched specimens, and it is applied to some published fatigue data on the different loading types of tension-compression, torsion, bending and their combinations.

Practical Criterion for Estimation of Notch Fatigue Strength: Fatigue Diagrams and Material-Dependency of Notch Effects

In the previous paper, authors considered a notch fatigue criterion on the basis of an equivalent stress ratio which was newly proposed as the parameter for the correspondence between cyclic stress conditions of a notched and unnotched specimen. The equivalent stress ratio is represented as a function of a nominal stress ratio and a theoretical stress concentration factor of a notched specimen. It could be derived without difficulty from a hypothesis of plastic adaptation which was newly proposed by the authors and the mechanical models which reflected the hypothesis. In the present paper, in order to confirm the applicability of the equivalent stress ratio, a wide range of published fatigue test data is rearranged on the diagram where the abscissa represents the equivalent stress ratio and the ordinate does the notch-root-concentrated stress range. As a result, the consistent relation proper to material is obtained in spite of the difference of a notch stress concentration factor, a specimen type (a plate or a round-bar) and a loading type (axial, bending, torsional or their combined loading). The relation is formulated in a simple form as an empirical equation. Such a result leads to a notch fatigue criterion that 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. Moreover, the equation for estimation of a fatigue strength reduction factor can be derived by relating its definition with the notch fatigue criterion. As a result, it is shown that a usually defined fatigue strength reduction factor is represented by multiplying the theoretical stress concentration factor by the unnotched specimen’s fatigue strength ratio which is dependent upon the mean stress. Accordingly, it is clear that the material-dependency of notch effects can be characterized by the steepness of slope of the unnotched specimen’s fatigue strength diagram.Copyright

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.Copyright