Approximation method for arbitrary-shaped stress concentration source; application of physical and mathematical approximations of arbitrary parent–child notch

Abstract

The degree of stress concentration in structures is of critical importance in safety designs. Many stress concentration factors for various shapes of notches with defined their geometry have been published, and if not published, the stress concentration factors can be obtained by FEM. However, when a complex, non-reproducible, and diverse notch exists on the surface of an actual machine that has undergone processing or is in a corrosive environment, it is usually more rational to use an immediate approximate solution rather than a rigorous but time-consuming analytical solution. There are two methods proposed for obtaining such approximate solutions. Although physical and mathematical approximate methods are separately used to estimate stress concentration factors in a specific-shaped notch, the application limits to arbitrarily sized and shaped notches are not yet clarified. In this study, we first extended the double-notch concept to the “parent–child notch” concept in the mathematical method, and then conducted finite element modelling for typical and complex notches. Further, we introduced the two representative lengths in the stress distribution induced by the parent notch from the mechanical consideration, and we deductively and inductively elucidated the application limits of the physical and mathematical approximations for an arbitrary parent–child notch. It was finally found that the stress concentrations of an arbitrary parent–child notch could be estimated only with the physical or mathematical approximation. Furthermore, a method for predicting fatigue limits of real structures subjected to cyclic loading was also proposed based on the present results.