PSI - Issue 43

Kamila Kozáková et al. / Procedia Structural Integrity 43 (2023) 178–183 Kamila Koza´kova´ / Structural Integrity Procedia 00 (2023) 000–000

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Many theories have been developed so far. For example, Z. Kne´sl proposed stability criterion of average opening stress, which is used for the assessment of sharp notches [6]. J. Klusa´k published criterion for general singular stress concentrators [7]. D. Taylor proposed the theory of critical distances, where the most popular approaches are the Point method and the Line method. Later, these approaches were applied by Susmel to fatigue problems. These approaches use averaging distances l for fatigue lifetime predictions. There are many formulas how to determine the length parameter. For example, D. Taylor considers the length parameter as another material parameter. In this case, the predictions are not satisfactory, because the length parameter depends on the number of cycles to fracture [8, 1, 2]. The article describes the method for determination of this parameter from experimental data of AW 7075 aluminum alloy and fatigue lifetime predictions of notched specimens. Fatigue tests were performed in the areas of high-cycle, and gigacycle fatigue (10 5 − 10 10 cycles). It is hardly possible to reach this area in real time with conventional machines. For that reason, fatigue tests were performed using an ultrasonic fatigue testing machine, which works at a loading frequency of 20 kHz. By using this machine it is possible to achieve one billion cycles in 14 hours. Fully reversed push-pull loading was applied (stress ratio R = − 1).

Nomenclature

σ y ( l ) average stress over the critical distance σ a the amplitude of failure loading σ n a

the amplitude of failure loading of the notched specimen

σ s a

the amplitude of failure loading of the smooth specimen σ y , nom nominal (average) stress over the cross-section of the notched specimen σ y axial stress L the length of specimen l the length parameter N f number of cycles to fracture R radius of the specimen in the narrowest diameter r notch radius x distance from the notch tip

We can distinguish various crack initiation regions in relation to the stress amplitude level and a number of cycles to fracture. In the area of low cycle fatigue, multiple cracks often initiate at the surface. In the area of high cycle fatigue, one crack is usually initiated at the surface, whereas in the area of gigacycle fatigue, internal failure can be observed as smaller defects play more important roles. Internal fracture is usually initiated at inclusions or voids.

2. Prediction method

Fatigue lifetime can be predicted using the average stress over averaging distance l . The whole process for fatigue lifetime predictions can be divided into a few steps (see Fig. 1). In the present study, length parameter l is determined from experimental fatigue data of smooth specimens and notched specimens with notch radius r = 0 . 2 mm, and from knowledge of corresponding axial stress distribution of notch with the same notch radius ( r = 0 . 2 mm). Length parameter l is considered to be the material parameter, but it will be shown that it depends on the number of cycles to fracture N f . The parameter is applied to axial stress distributions of various notch radii to predict their fatigue lifetimes.

2.1. Experimental data and an analysis of axial stress distributions

Fatigue tests were performed on aluminum alloy AW 7075 which has good notch sensitivity. An ultrasonic fatigue testing machine working at a frequency of 20 kHz was used. All specimens were designed so that their intrinsic frequencies of longitudinal oscillations were equal to or close to 20 kHz. The length L of the notched specimens