A Simple Engineering Estimate of the Fatigue Notch Factor of Arbitrary Stress Concentrators

Abstract

Since the early 1930s, much energy has been devoted to the basic engineering problem of accurately computing stress concentrations at-possibly complex-design features; it shall suffice here to mention such classic contributions as those by Neuber, [1,2] Peterson, [3] and Williams. [4] The maximum stress in an arbitrary notch is mainly influenced by depth, radius, and flank angle of the notch. [5] In fatigue life estimates, the task is further complicated as the fatigue stress endured at the hot spot is usually higher than what is predicted by the elastic stress concentration factor. [6] The difference between the elastic stress concentration factor and the fatigue notch factor is usually computed by means of averaging [2] or gradient [6] theories; for very sharp notches, the issue of non-propagating cracks is also relevant. [7,8] Neuber's [2] and Novozhilov's [9] ideas of introducing an effective stress by averaging the actual stress field over a characteristic microstructural length have recently experienced a reappraisal. [10] Ongoing discussion of the physical relevance of such a length notwithstanding, the concept provides, at the very least, a practical regularization method whose single parameter-the microstructural length-is easily determined from the analysis of macroscopic test data. Recent research efforts [11,12] have yielded a complete, but still somewhat involved framework for such computations. The present contribution aims at complementing the aforementioned approach by a mathematically simple but yet accurate engineering assessment of the fatigue notch factor of arbitrarily shaped notches. To this purpose, we proceeded the following three steps: characterization of the elastic near-tip notch field of arbitrary notches; computation of the fatigue stress factor by averaging over the characteristic microstructural length; finally, discussion of the limits of validity of the resulting solution. Characterization of the Elastic Near-Tip Stress FieldFollowing Williams, [4] sharp corners with vertex angles higher than 1808 exhibit a stress singularity, with the exponent m depending on the vertex angle and the stress range Ds at a distance x from the vertex being conveniently characterized by the range of the notch stress intensity factor DK [13] DsðxÞ ¼ DK½2px m ðþH:O:T:ÞThis gives a linear graph of stress versus vertex distance in a bilogarithmic chart (Fig. 1), with its slope corresponding to the exponent m. For the case of a crack with parallel flanks (3608 flank angle), the classical square root singularity m ¼ À1/2 and the conventional stress intensity factor are obtained. Clearly, this stress distribution neglecting nonsingular higher order terms does not yield the correct far-field stress and is therefore only valid for the near-tip stress field.The notch stress intensity is proportional to the notch depth t, the far-field stress Ds 1 , and a geometric correction factor Y [13]

A State‐of‐Art Review on Prediction Model for Fatigue Performance of Welded Joints via Data‐Driven Method

“…Therefore, the effective processing of the fatigue performance database is the first task to realize accurate prediction. As shown in Figure and Table 1 , there are several approaches to establish a reliable fatigue performance database, which can be divided into three main categories: independent (experiment and simulation), [ 1,4,5,9,29,54–74 ] literature based, [ 13,75–85 ] and data augmentation based. [ 86–94 ] Even an efficient data‐driven method cannot construct an effective model via an insufficient database; thus, the establishment of a high‐quality database is quite important.…”