FATIGUE SAFETY COEFFICIENTS FOR ULTRA-HIGH REGION OF LOAD CYCLES

In this paper the authors introduce results from the field of the fatigue safety of selected steels in the region of ultra high number of loading cycles. The fatigue tests were carried out at high frequency tension compression loading (f = 20 kHz, T = 20 ± 5°, R = -1) in the region from N = 10 to N = 10 cycles. The fatigue safety coefficients were calculated by four methods (Goodman, Gerber, ASME elliptic and Soderberg). The percentage reduction of the fatigue safety coefficients (N = 10 vs. N = 10 cycles) was at Goodman, 7.99 ÷ 10.83 %, Gerber, 5.27 ÷ 8.26 %, ASME, 1.89 ÷ 6.42 % and Soderberg, 6.51 ÷ 10.25 %.

used in various industries. They have a specific place in the field of rails, tires, wings and hull transport. With regard to this state area of application, these steels are required to have a long service life and high reliability and safety, [8]. Determining the fatigue safety factor is important both from a theoretical point of view and from a practical point of view [9][10][11][12][13]. In this paper the authors introduce their own results from the field of the fatigue safety of selected steels in the region of ultra -high number of loading cycles.

Experimental
Experimental works, the qualitative and quantitative chemical analysis, tensile tests, fatigue test and the fatigue coefficient ku calculations, were carried out on eight structural steels including high strength steels (DOMEX 700MC, HARDOX 400, HARDOX 450). Chemical analysis was performed with help of the emission spectrometry on an ICP (JY 385) emission spectrometer, using a fast recording system Image. Tensile tests were carried out on a ZWICK Z050 testing machine at ambient temperature of T = 20 ± 5 °C, with the loading range in interval F = 0 -20 kN and the strain rate of . s 10 The round cross -section specimens were used, the shape and dimension of specimens have met requirements of the EN 10002 -1 standard (3 specimens for each steel were used). The fatigue tests were carried out at high -frequency sinusoidal cyclic tension -compression loading (f = 20 kHz, T = 20 ± 5 °C, R = -1, cooled by distilled water with anticorrosive inhibitor) and with use of the ultrasonic fatigue testing device. Smooth round bar specimens (minimum 10 pieces) with diameter of 4 mm, ground and polished by metallographic procedures, were used for the fatigue test [14][15]. The investigated

Introduction
Fatigue is the dominant degradation mechanism during the operation of components and mechanical constructions. More than 90 % of all the fractures are caused by fatigue of the applied material. Targeted research, both theoretical and experimental, of the low -cycle and high -cycle fatigue of structural steels, began in the mid -19 th century. For the area of the high cycle fatigue, the fatigue limit c v was defined as the largest fluctuating stress at certain mean stress m v that the structural steel withstands for an infinite number of cycles. For steels, the so -called basic number of cycles N c , in the range from N c = 10 6 to 10 7 cycles, was recommended for an infinite number of cycles. However, research institutes have demonstrably noticed that fractures caused by fatigue occur in structural steels far beyond the so -called basic number N c = 10 7 cycles. Conclusions on the safe loading and permanent fatigue strength beyond this cycle limit are inaccurate and incomplete. In view of this fact, at the end of the 20 th century, both theoretical and experimental research of ultra -high -cycle fatigue, in the range from N = 10 7 to N = 10 10 loading cycles, began. Questions are being verified, such as what is the course of dependence a v = f (N), the physical nature of the fatigue limit c v , the existence of the fatigue limit, degradation fatigue mechanisms at very low values of the plastic deformation amplitude, propagation of short fatigue cracks at extremely low rates, the role of inclusions, long grain boundaries, pores, surface and subsurface initiation of fatigue cracks, etc. after the so -called basic number N c = 10 7 load cycles in structural steels. The course of the dependence a v = f (N), including the step -wise or duplex curves with a "plato" is discussed [1][2][3][4][5][6][7]. High -graded steels of medium and high strengths are where: a v is the stress amplitude, m v is the mean stress, c vl is the fatigue limit, Rm is the ultimate tensile strength, Re is the yield point.
region of number of cycles ranged from N 10 6 . to 10 9 cycles of loading.
The fatigue safety coefficient was calculated with regard to work [12], Figure 1, with the using equations: (1) Goodman, (2) Gerber, (3) ASME and (4) Soderberg. v v =^h [12]   were exhibited by the structural steels of higher strength, what is related to their higher sensitivity to both surface and internal defects (micro -impurity, microstructural heterogeneity, pores, grain size, inclusions). These statements are in accordance with the works of the authors [1][2][3][4][5][6][7]9]. It is clear from results (Figures 2 to 5, Tables 3 to 6) that Goodman and Soderberg methods are suitable methods (criteria) for evaluation of the fatigue safety of selected structural steels in the region of the high number of cycles. The Soderberg criterion checks the occurrence of any deformation. Lower values of k u ensure that no fatigue failure or accidents would occur during the considered ultra -high number of load cycles. The Goodman criterion is very strict, but it is one of the best known criteria that allows for a simple analytical solution of fatigue tasks. The American Society of Mechanical Engineers (ASME) has addressed the issue of fatigue safety, which is a more conservative criterion but does not have sufficient margin to determine the fatigue safety coefficient for an ultra -high number N = 10 9 of cycles. The Gerber criterion seems to be the least suitable, because approaching the limit state of fatigue safety and at an ultra -high number of cycles fatigue fracture accidents can occur [9][10][11][12][13]. Application of the above described experimental work was executed on a screw joint, which is, during the operation, loaded by a cyclic stress in superposition with the preload. The material parameters of the screw were taken from Table 1, where values of Re and Rm of experimental materials are given.

Results and discussion
Results of qualitative and quantitative chemical analysis (chemical composition), tensile tests (ultimate tensile strength R m , yield point R e ) and high -frequency fatigue tests , , , 10 10

Conclusions
Taking into account the performed experimental work, the following can be stated: