Issue 46

G. Deng et alii, Frattura ed Integrità Strutturale, 46 (2018) 45-53; DOI: 10.3221/IGF-ESIS.46.05 46 fatigue life when the stress level is near to the bending fatigue strength. On the basis of fracture mechanics and the research of Nisitani [7], the mechanical factors determining fatigue breakage are not only the actual stress but also its distribution. At present, the actual stress and its distribution can be easily and accurately calculated for any machine component, but they have not yet been used in bending fatigue strength design. To develop a general bending fatigue strength evaluation method applicable to machine components with a wide range of geometries, the actual stress and its distribution should be considered as very important factors. Nisitani [3,7] and Tanaka [8] carried out many studies on bending fatigue strength evaluation, where the strengths were defined on the basis of the criteria of crack initiation or the arrest of crack propagation, and they presented a method of obtaining the fatigue strength from the threshold stress intensity factor. Because of the difficulty of determining the threshold stress intensity factor and because fatigue strength design allowing the existence of a non-propagating crack is unrealistic considering safety, their method is not practically used. Kato [9] introduced the use of the initial crack length to evaluate the qualities of a surface and presented a fatigue life simulation method under the assumption that the progress of fatigue involves only the progress of crack propagation. However, many problems remain in deciding the initial crack length, which is very sensitive to the simulation conditions. The purpose of this study is to search for a general method for bending fatigue strength design applicable to machine components with a wide range of geometries that considers the effects of the actual stress and its distribution on fatigue crack initiation. As the first stage of this study, three-point bending specimens with notches of different shapes are used to obtain bending fatigue limit stresses, which are expressed as the maximum stress at the critical point on the notch surface, and an approach to estimating the tension fatigue strength of a smooth specimen is presented, which will be the basic material property used in general bending fatigue design. C ONSIDERATION OF THE STRENGTH AND CRITERIA FOR BENDING FATIGUE Bending fatigue limit stress and bending fatigue load capacity hanges in the shape of a machine element, such as the introduction of a notch, a hole, or a corner, will decrease the bending fatigue strength expressed by the nominal stress as, stated in fatigue design documents, and this phenomenon is evaluated using the fatigue stress concentration factor. However, if the actual stress at the critical point is used in fatigue strength evaluation, the limit stress for bending fatigue breakage will increase owing to the existence of a feature such as a notch or stress concentration [10]. To avoid introducing the misunderstanding that the stress concentration increases the fatigue strength of a machine element, the bending fatigue limit stress and bending load capacity are used to indicate the maximum actual stress and the bending load without fatigue breakage, respectively. Thus, the stress concentration due to the introduction of such notches, holes, or corners will increase the bending fatigue limit stress but decrease the bending load capacity. Factors affecting the initiation of a fatigue crack Many studies have shown that the fatigue crack initiation life accounts for a large proportion of the fatigue life, particularly when the stress level is close to the fatigue strength, and that a fatigue crack will not stop growing unless the shape around the critical point is very sharp [3]. Thus, fatigue crack initiation may be a sufficient condition for bending fatigue breakage, which means that whether or not bending fatigue breakage occurs depends on the initiation of a surface fatigue crack, and the criteria for the initiation of a fatigue crack can be used for bending fatigue strength design. Fatigue crack initiation and growth depend on the stress intensity factor in fracture mechanics [11,12]. On the basis of linear elastic fracture mechanics, the stress intensity factor is related to the potential energy release rate and elastic properties of the material. The potential energy release rate is also strongly related to the distribution of the stress around the tip of the crack or the critical point. Consequently, t he initiation of a fatigue crack depends not only on the actual surface stress but also on its distribution. Fig. 1 shows images of the stress distributions around notches with small and large radii that have sharp and gentle stress gradients, respectively. The change in the potential energy release rate owing to the initiation is related to the hatched area. If the threshold value of the potential energy release rate for fatigue crack initiation is constant ( e 1 = e 2 ), a larger surface stress with a high gradient will exist on the surface of the notch with the smaller radius, and a smaller stress with a gentle stress gradient will exist on the surface of the notch with the larger radius. This is considered to be the main reason why the fatigue strength expressed by the actual stress at the critical point varies for different shapes. In the evaluation of the effect of the stress distribution on bending fatigue crack initiation, we think that only a very small region around the critical point should be considered since the length of the initiated crack is only micrometer order; and on the basis of the linear-elastic analysis results of stress distributions in depth direction for the typical shapes such as that C