P RODUCTION E NGINEERING A RCHIVES Bending fatigue strength coefficient the low carbon steel with impurities

The article discusses the results of a study investigating the effect of the number of fine non-metallic inclusions (up to 2 µm in size) on the fatigue strength of structural steel during rotary bending. The study was performed on 7 heats produced in an industrial plant. Fourteen heats were produced in a 100 ton oxygen converter. All heats were subjected to vacuum circulation degassing. Steel sections with a diameter of 18 mm were hardened and tempered at a temperature of 200, 300, 400, 500 and 600°C. The experimental variants were compared in view of the applied melting technology and heat treatment options. The heat treatments were selected to produce heats with different microstructure of steel, from hard microstructure of tempered martensite, through sorbitol to the duc-tile microstructure of spheroidite. The results were presented graphically, and the fatigue strength of steel with a varied share of non-metallic inclusions was determined during rotary bending. The results revealed that fatigue strength is determined by the relative volume of fine non-metallic inclusions and tempering temperature.


Introduction
Steel is one of the most popular constructional material. The properties and practical applications of all constructional materials, including steel, are determined mostly by their microstructure. The parameters of high-grade carbon steels are influenced by a combination of factors, including chemical composition and production technology (Ulewicz, 2016;Mazur et al., 2016;Gerasin 2015;Selejdak et al., 2014).
The impurity content is also a key determinant of the quality of high-grade steel. Inclusions may also play an important role, dependent on their type and shape. The quantity and quality of non-metallic inclusions is determined mostly by the steel melting technology. Inclusions may increase the strength of steel by inhibiting the development of micro-cracks. One of the most popular crack prevention methods involves the formation of a material discontinuity at the end of the crack (e.g. an opening in organic glass). The quantity of non-metallic inclusions in steel is relatively low, nevertheless, they have a significant impact on the structure, technological and strength parameters of the resulting alloy. An effective method for the complete elimination of non-metallic inclusions has not been developed to date (Murakami 2002;Lipiński et al., 2015;Lis, 2002).
Although high quality low carbon steel has a relatively small number of non-metallic inclusions, those impurities have a considerable impact on the material's technological and strength parameters, in particular fatigue strength and life. Non-metallic inclusions play a special role in the process of steel hardening. Due to differences in the physical properties of steel and inclusion-forming phases, structural stresses are formed along inclusion boundaries (Cummings et al., 1957;Zhang et al., 2005, Lipiński et al., 2012. Their negative impact on fatigue strength has been widely discussed in the literature (Beretta et al., 2001;Murakami 2002;Adamczyk et al., 2016), mostly in studies of hard-fatigue steels with low plasticity and inclusions larger than 5 µm. Selected authors have analyzed the purity and fatigue properties of steels with high plasticity. The effect of fine nonmetallic inclusions measuring up to 5 µm on the fatigue strength of steel has not been thoroughly investigated. Hebsur observed that fatigue crack propagation decreased in steels where fine non-metallic inclusions were irregularly distributed (Hebsur et al., 1980). According to , steels produced with the use of various methods contain mostly non-metallic inclusions of up to 2 µm in size. Highgrade steel contains fewer large-sized inclusions. Non-metallic inclusions generally exert a negative effect of fatigue strength Lipiński, 2015, Drozin, 2016Lenkovskiy et al., 2017). The above indicates that the dimensions of non-metallic inclusions significantly influence a material's fatigue strength.
The objective of this study was to determine the influence of fine non-metallic inclusions (up to 2 µm in size) on the fatigue strength of structural steel with high plasticity.

Materials and Methods
The experimental material consisted of steel products in an industrial plant. In the third process, steel was melted in a 100ton oxygen converter and deoxidized by vacuum. Steel was cast continuously and square 100x100 mm billets were rolled with the use of conventional methods. Billet samples were collected to determine: • chemical composition. The content of alloy constituents was estimated with the use of LECO analyzers, an AFL FICA 31000 quantometer and conventional analytical methods, • relative volume of non-metallic inclusions with the use of the extraction method.
The number of particles range 2 μm and smaller was the difference between the number of all inclusions determined by chemical extraction and the number of inclusions measured by video method.
Analytical calculations were performed on the assumption that the quotient of the number of particles on the surface divided by the area of that surface was equal to the quotient of the number of particles in volume divided by that volume [20].
In aim of qualification of fatigue proprieties from every melting was tested 51 sections. The sections had the shapes of cylinder about 10 mm diameter. Their main axes were directed to direction of plastic processing simultaneously. The observations of microsections etched with nital revealed that steel tempering at various temperatures significantly affected the material's phase structure.It consisted in hardening from austenitizing by 30 minutes in temperature 880°C after which it was followed quenching in water, for which a drawing was applied . Tempering consisted in warming by 120 minutes material in temperature 200, 300, 400, 500 or 600°C and cooling down on air.
Fatigue strength was determined for all the heats. Heat treatment was applied to evaluate the effect of hardening on the fatigue properties of the analyzed material, depending on the volume of fine non-metallic inclusions. During a heat treatment, steel sections were hardened and tempered at a temperature of 200, 300, 400, 500 and 600°C. The application of various heat treatment parameters led to the formation of different microstructures responsible for steel hardness values ranging from 271 to 457 HV.
Examination was performed with the use of a rotatory curving machine with a frequency of pendulum cycles of about 6000 periods on minute. Fatigue defining endurance level of 10 7 cycles was accepted as its basis. The level of fatigue-inducing load was adapted to the strength properties of steel. Maximum load was set as follows: • for steel tempered at a temperature of 200°C -650 MPa, • for steel tempered at a temperature from 300°C to 500°C -600 MPa, • for steel tempered at a temperature of 600°C -540 MPa.
During the test, the applied load was gradually reduced in steps of 40 MPa (to support the determinations within the endurance limit). Load values were selected to produce 10 4 -10 6 cycles characterizing endurance limits. Coefficients c and p were substituted with coefficient k to convert equation (6) to (7). (1) The significance of correlation coefficients r was determined on the basis of the critical value of the Student's t-distribution for a significance level α=0.05 and the number of degrees of freedom f = n-2 with formula (2). (2) The average diameter of inclusion was calculated by means of the following formula: ( 3) where: nj -counts of inclusions, lj -average diameter of inclusions, µm

Results and discussions
The average chemical composition of the analyzed steel is presented in Table 1. Statistically significant the bending fatigue strength relationship of steel hardened and tempered at 300°C in dependence on the volume of impurities ranging up to 2 µm, is presented in Fig. 2, and regression equation with corre-lation coefficients r at (5). k(300)=0.4706d+0.0134 with r=0.7304 (5)

Fig. 2.
Bending fatigue strength of steel hardened and tempered at 300°C subject to inclusions diameter k, µm Statistically significant the bending fatigue strength relationship of steel hardened and tempered at 400°C in dependence on the volume of impurities ranging up to 2 µm, is presented in Fig. 3, and regression equation with corre-lation coefficients r at (6). k(400)=0.4706d+1.3568 with r=0.6519 (6) Fig. 3. Bending fatigue strength of steel hardened and tempered at 400°C subject to inclusions diameter k, µm Statistically significant relationship bending fatigue strength of steel hardened and tempered at 500°C in dependence of volume the impurities range to 2 µm is presented in Fig. 4, regression equation and correlation coefficients r at (7). k(500)=05368d+0.0624 with r=0.8451 (7) Statistically significant the bending fatigue strength relationship of steel hardened and tempered at all temperatures in de-pendence on the volume of impurities ranging up to 2 µm, is presented in Fig. 6, and regression equation with corre-lation coefficients r at (9). The parameters representing correlation coefficients are present at Table 2. The regression equations, correlation coefficient r (3) -(9) was correlated with tempering temperature, correlation coefficient r. All regression equations were characterized by a high correlation coefficient of over 0.65, which points to high statistical significance confirmed by Student's t-test. The above data indicate that the equations describing parameter k at different tempering temperatures, where r=0.70, can be replaced with a single equation for all tempering temperatures (9).

Conclusion
1. This study demonstrated correlations between the diameter of impurities and the bending fatigue coefficient of non-metallic inclusions measuring at all range for high grade and high purity steels. 2. The proposed linear regression equations supported the determination of fatigue strength coefficient k and diameter of impurities with sufficient accuracy for every tempering temperature for high purity steels. 3. The influence of impurities on the fatigue strength coefficient of steel depends on its microstructure (tempered temperature). 4. With the decrease of plasticity of steel (matrix of impurities), the impact of diameter of impurities is more intense.