###### Abstract  
Steel fatigue strength testing is a process that requires large amounts of time, resources and appropriate equipment. The industry seeks to replace cumbersome destructive testing with non-destructive testing. Coefficients were developed that allow the comparison of the parameters of material properties. One such factor is the fatigue strength coefficient, which allows the estimate of fatigue strength using the known hardness of a given material. The fatigue strength factor should be developed for conditions that are as close to the industrial conditions as possible. It should take into account not only the expected properties of the material and the technological process but also its imperfections, e.g., the share of non-metallic inclusions and the steel microstructure. This paper presents the results of research on the influence of non-metallic inclusions on the fatigue strength coefficient of structural steel subjected to rotary bending. The tests were carried out in seven heats obtained in a 140-ton electric furnace under industrial conditions. The steel was deslufurized and refined with argon. The paper presents the bending fatigue strength of hardened and tempered steel at temperatures from 200 \({}^{\circ}\)C to 600 \({}^{\circ}\)C as a function of the relative volume of inclusions. The non-metallic inclusions occurring in steel were determined qualitatively and quantitatively. The derived fatigue strength coefficient, k, for different tempering temperatures makes it possible to estimate the fatigue strength of the analyzed steel as a function of its hardness for various microstructures represented by the respective tempering temperatures. steel; fatigue strength; non-metallic inclusion +
Footnote †: journal: Applied  
1
Footnote 1: _Applied_  
13 September 2022  
16 September 2022  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. **1. Introduction**  
There are elements of machines operating at variable stresses. These stresses can be regular or irregular. Ensuring a high reliability of elements operating under variable loads requires the use of steel with high fatigue strength [1; 2; 3; 4; 5]. Work is underway to understand the factors that reduce the fatigue life of the material [6; 7; 8; 9; 10; 11]. One of the factors influencing the fatigue strength of steel, apart from the operating conditions, is non-metallic inclusions. There are many papers describing the influence of non-metallic inclusions on the development of microcracks and the fatigue strength of steel [12; 13; 14; 15; 16; 17]. The rate of microcrack development under variable stress conditions is a determinant of the material's resistance to fatigue [18]. The problem of the impact of non-metallic inclusions in steel on its fatigue strength is complex. Steels operating under variable loads are usually high-quality steels. Fatigue strength tests of various types of steel used in industry are carried out [19; 20]. Nevertheless, they have some amount of impurities. These impurities can significantly affect the properties of the material, in particular its fatigue strength. The shape, size, distribution, quality and quantity of non-metallic inclusions found in steel may vary depending on the manufacturing process [21; 22; 23; 24; 25; 26; 27; 28; 29]. Nodular inclusions are often observed in steels containing high levels of oxygen. The partial deoxidation of steel, e.g., with the addition of aluminum, favors the formation of small oxide inclusions on the boundaries of austenite grains. On the other hand, the addition of an excess of deoxidizers may lead to the formation of large faceted inclusions. The influence of non-metallic inclusions on the fatigue strength is closely related to the processes taking place in micro-areas. The complexity of the problem results, among others, from local plastic deformation, cyclic strengthening and weakening, nucleation and the development and joining of microcracks [6, 18, 30, 31, 32, 33].