Simplified Method of Forecasting the Influence of Cooling Intensity During Hardening on the Mechanical Properties of Steel Products

The object of research is the structure and mechanical properties of steel at the central points of hardened products. In this work, a technique has been developed based on comparing the cooling rate in the central region of the product with the cooling rate of a test sample with a diameter of 5–6 mm, investigated in laboratory conditions. By this time, this approach was not possible, since two main problems had not been resolved. The transition from a small sample to a real product during quenching was scientifically unreasonable due to the great complexity of the problem. There were no known mathematical relationships for calculating the cooling rate when quenching products of arbitrary shape in liquids. Recently, these problems have been solved and steel with optimal harden-ability has appeared, which can be cooled very quickly. This simplified the solution to this problem. The technique developed in this work helps to temper metal products in such a way that there are large compressive residual stresses on the surface, and in the middle there is a bainite structure of high strength and increased toughness. This allows to increase the service life of hardened products, reduce the percentage of alloying elements, and also maintain a clean environment. In this regard, based on the achievements of science in recent decades, a method is proposed for predicting the structure and mechanical properties of steel during quenching of real parts. This technique can be used to increase the durability of machine parts and tools. The work also notes the prospects of using aqueous solutions of low-concentration polymers for intensive hardening of steel products. In this case, when simulating the cooling rate during quenching of real products, test samples are quenched in aqueous solutions of the same polymers of increased concentration in order to form a stable vapor film. The stable vapor film ensures a stable heat transfer coefficient. This increases the accuracy of modeling and expands the capabilities of the proposed calculation method.


Introduction
The main idea of this work is to combine advances in the fields of bainitic and martensitic transformations based on effective control of phase transformations in the core of hardened products. Great achievements have been obtained in the strengthening of rolled products, where the main emphasis is on achieving a high-strength and plastic bainitic structure [1,2]. At present, special attention is paid to bainitic transformations, since the bainitic structure provides higher strength and plastic properties of the material than the martensitic structure of the material can provide [3]. When discussing this important problem with the author of [3], it turned out that to obtain a bainitic structure, it is necessary to apply rapid cooling in order to avoid pearlite transformations. As a rule, upon rapid cooling, martensite immediately appears on the surface of the items to be hardened instead of bainite. Therefore, in most cases, to obtain a viscous bainitic structure, expensive isothermal quenching in baths is carried out at a temperature equal to or higher than the temperature of the onset of the martensitic transformation М s . In this case, alloyed and high-alloyed steels are used. The bainitic structure along the entire section of the product under conditions of rapid cooling can be obtained by quenching steels in liquid media under pressure [4]. But such a process is expensive and requires the manufacture of special equipment. This problem is easily solved by combining both directions. As is known, during the quenching of steels with low hardenability, a thin layer of martensite appears on the surface of products, while the core remains viscous, consisting of bainite and pearlite [5][6][7]. This leads to the creation of compressive stresses on the surface of hardened parts [8,9]. Moreover, the authors of [10][11][12] have shown by computer simulation that intense hardening creates high compressive stresses on the surface of products and super-strengthens the material. Very important experiments by the authors of [13][14][15] have confirmed this. This leads to significant savings in alloying elements. Therefore, in studies [16,17], a steel with optimal hardenability was developed and a quenching medium for its hardening was proposed, which The object of research is the structure and mechanical properties of steel at the central points of hardened products. In this work, a technique has been developed based on comparing the cooling rate in the central region of the product with the cooling rate of a test sample with a diameter of 5-6 mm, investigated in laboratory conditions. By this time, this approach was not possible, since two main problems had not been resolved. The transition from a small sample to a real product during quenching was scientifically unreasonable due to the great complexity of the problem. There were no known mathematical relationships for calculating the cooling rate when quenching products of arbitrary shape in liquids. Recently, these problems have been solved and steel with optimal hardenability has appeared, which can be cooled very quickly. This simplified the solution to this problem. The technique developed in this work helps to temper metal products in such a way that there are large compressive residual stresses on the surface, and in the middle there is a bainite structure of high strength and increased toughness. This allows to increase the service life of hardened products, reduce the percentage of alloying elements, and also maintain a clean environment. In this regard, based on the achievements of science in recent decades, a method is proposed for predicting the structure and mechanical properties of steel during quenching of real parts. This technique can be used to increase the durability of machine parts and tools. The work also notes the prospects of using aqueous solutions of low-concentration polymers for intensive hardening of steel products. In this case, when simulating the cooling rate during quenching of real products, test samples are quenched in aqueous solutions of the same polymers of increased concentration in order to form a stable vapor film. The stable vapor film ensures a stable heat transfer coefficient. This increases the accuracy of modeling and expands the capabilities of the proposed calculation method.
Keywords: method of modeling the structure formation, bainitic and martensitic transformations, heat treatment, high strength.
ISSN 2664-9969 is a 1 % aqueous solution of a polymer of reverse solubility. These achievements have been discussed internationally in leading physics journals [18,19].
When choosing a cooling mode for metal products in the implementation of hardening heat treatment, the following main criteria are traditionally guided by the choice of a cooling medium: -requirement for the absence of any vapor film during the hardening process, which creates a uniform and intensive cooling of steel products [10]; -economic feasibility of implementing the selected development, which is primarily due to the cost of the cooling medium and its operation; -manufacturability of the cooling medium, which is determined by the following main parameters: operating temperature; acceptable concentration of components (for various aqueous cooling media); the ability to monitor the cooling capacity of the medium; -environmental safety of the cooling medium during its preparation, operation and disposal; -fire safety during storage and operation. An increase in the degree of metal alloying or the use of additional technologies for surface hardening of the working surfaces of metal products (in addition to traditional types of heat treatment) significantly increases the cost and complicates the technology of their manufacture. Saving metal became possible due to the discovery of the phenomenon of super-hardening of steel during intense hardening [17,18]. And also the formation of high compressive residual stresses on the surface of heat-strengthened products has been proven [19,20].
To control the microstructure and mechanical properties of steel in the center of hardened products, it is necessary to cut the hardened part and make test samples from the core of the material. This is a very expensive and painstaking job. Therefore, it is relevant to accurately predict the structure and mechanical properties in the center of hardened products.
Long-term studies of the authors [3,17,20] have created the basis for the implementation of such forecasts. Thus, the object of research is the structure and mechanical properties of steel at the central points of hardened products. The aim of this research is to develop a technique for modeling the processes of phase transformations in the center of hardened large products in laboratory conditions.

Methods of research
During the study, samples with a diameter of 5-6 mm are used, which are cooled in the laboratory at a rate equal to the cooling rate in the center of large items during quenching.
This paper discusses studies in relation to technologies of hardening heat treatment of various metal products, in which water or aqueous solutions of polymers of very low concentration are used as a quenching medium. To optimize the proposed approach, the authors propose a new simplified technique for studying the effect of cooling intensity under conditions of hardening heat treatment on the mechanical properties of steel products. The essence of the new technique is outlined below.

Research results and their discussion
3.1. Simplified method for predicting the mechanical properties of the material in the core of hardened products. To predict the strength properties of the material in the core of large products, it is necessary to create conditions for cooling test samples equal to those for cooling the core of products. It is enough to calculate the cooling rate of the core of large products and the cooling rate of samples and create conditions for their equality.
The proposed calculations are based on the theory of thermal conductivity and the theory of regular thermal regime [21,22].
To carry out such calculations Tables 1-3 show the thermophysical properties of copper, silver and supercooled austenite, which are used in this research.
To calculate the cooling rate of test samples and real parts, let's use the generalized dependence (1), which is valid for any size and shape of products [11,21,22]: where v -cooling rate; а -coefficient of thermal diffusivity of steel; Kn -Kondratiev number; K -Kondratiev form factor in m 2 ; T -current temperature; Т m -temperature of the quenching bath.
Since the cooling process must be interrupted, below is also a generalized relationship (2) for calculating the cooling time for products of various configurations under different heat transfer conditions [11,12]:   where where t -cooling time in seconds; Bi V -dimensionless generalized Biot number; k = 1, 2, 3 -coefficients for bodies of plate, cylindrical and spherical shape; a -heat transfer coefficient; l -thermal conductivity of steel; S -surface; V -volume.

Kn Bi
Bi Bi The author of [20] proposes a criterion for intense cooling (4), at which both film boiling and unsteady nucleate boiling during quenching in liquid media are absent: where ϑ β l ϑ ϑ where ϑ I . ; R -radius; T I -surface temperature at the beginning of nucleate boiling; T oinitial temperature; T S -saturation temperature.
When quenching sheet metal, well-known data on the effect of pressure in a sprayer on the intensity of convective heat transfer can be used (Fig. 1) [23]. According to the proposed method, this means that the sheet core has the same mechanical properties as the 6 mm sample after quenching in water at 60 °С.
To facilitate similar calculations in relation to the semiaxles of trucks in Tables 4, 5 show comparable cooling rates of semi-axes and samples.  It should be noted that along with the improvement of the mechanical properties of the core of the semi-axles of cars, high compressive stresses arise on their surface, increasing the service life of the semi-axes. Some experimental data are given in Table 6. Table 6 Residual circumferential compressive stresses in MPa on the surface of different products after their intense hardening [11] No. Product Circumferential compressive stresses in MPa on the surface of intensely hardened products Thus, the mechanical properties of the core of an intensely cooled 20 mm thick sheet correspond to the mechanical properties of a cylindrical sample 6 mm in diameter quenched in a hot hearth with a heat transfer coefficient of 750 W/m 2 K. To simulate the process of cooling the core of the semi-axes, cooling of the samples is required at lower heat transfer coefficients.
It should also be noted that it is very incorrect and erroneous to attempt to use the heat transfer coefficients obtained when testing a 20 mm diameter silver ball on any steel samples. The thermal conductivity of silver is 20 times higher than the thermal conductivity of steel, which means that silver will have a more developed vapor film and a different heat transfer coefficient compared to steel.

3.2.
Prediction of mechanical properties in the core of large products by quenching and laboratory testing of small test samples. Prediction of the structure of steel and its hardness at the central points of products can be carried out using the Jominy method, which has been discussed many times in the literature [24][25][26]. Let's propose a simpler forecasting technique, which consists in comparing the cooling rates obtained when testing small samples in hot water and the calculations performed to calculate the cooling rate of the core of a real part when it is quenched in real conditions. It is known from the technical literature that the cooling capacity of water significantly depends on its tempera-ture during the quenching cooling of parts. The results of experiments [27] carried out on a silver ball 20 mm in diameter are shown in Fig. 2. Fig. 2. Curves of changes in the cooling rate of a 20 mm diameter silver ball when it is cooled in water with different temperatures depending on the temperature of the center of the thermal probe [27] The work [28] investigates the uniformity of cooling of a steel strip from a temperature of 800 °С according to the values of the ultimate strength along its thickness depending on the water temperature. Digits on the curves in Fig. 3 show the water temperature in °С. Fig. 3. The uniformity of metal cooling from a temperature of 800 °С according to the values of the ultimate strength along the width of the steel strip, depending on the temperature of the quenching medium [28] This is an extremely costly and painstaking work that takes a long time, measuring the mechanical properties of materials over the entire section of the steel strip. Therefore, let's suggest the opposite procedure. By quenching cylindrical samples 6 mm in diameter in various quenching media and measuring their cooling rate, as well as their mechanical tests, it is possible to restore the distribution of strength in the steel strip using the proposed method of simplified calculations. More detailed information on the quenching of steels in liquid media, taking into account modern mathematical models, is discussed in [29]. In the calculations, one can use experiments carried out on cylindrical samples with a diameter of 6 mm, which are shown in Fig. 4 and in Table 7. Research can also be used [26,27,30].
In Fig. 4    Note: the numerator shows the values for heat-strengthened metal, and the denominator -after heat-strengthening and subsequent tempering at 500 °С To implement the proposed technique, let's experimental data on testing the mechanical properties of steel and its fine structure after quenching small samples in hot water (Fig. 4, Table 7). As seen from Fig. 4, even within the same steel grade, the mechanical properties of the steel vary greatly, which the Jominy method does not take into account. In addition, the known method does not operate with such concepts as the plastic properties of the material, the level of microdeformations and the density of dislocations (Fig. 4, Table 7). The proposed technique makes it possible to transfer the obtained studies to real parts, in which the cooling rate during quenching is the same as the cooling rate of small samples.
In recent decades, in the practice of heat treatment, aqueous solutions of polymers have been actively used as cooling media. The results of recent studies show the promise of using aqueous solutions with a low concentration of polymers, which provide intense and uniform cooling of various steel metal products during quenching [18,19].
Additional information concerning uniform cooling and predicting the structure and mechanical properties of the material in the volume of heat-strengthened products is presented in [18,19].
The algorithm of the developed technique is demonstrated by the example of intensive hardening of steel products of a ring shape (Fig. 5). Let's suppose that at the enterprise the specified products are cooled with water jets (Fig. 1) under conditions Bi → ∞.  Table 8 shows the cooling rates of ring-shaped products at a temperature of 700 °С depending on the dimensions of the products that are hardened under conditions. Let's suppose that it is necessary to study the structure and measure the mechanical properties in the center of a large ring, which has the following dimensions: outer diameter D 2 = 0.1 m, inner diameter D 1 = 0.02 m, and ring height 0.04 m ( Table 8). The cooling rate in the center of such a ring at a temperature of 700 °С is 42 °С/s. Similarly, Table 9 shows the cooling rates of small samples for rupture depending on their dimensions and cooling conditions, that is, the heat transfer coefficient. Comparing Table 8 and Table 9, it is necessary to find equal cooling rates and thus figure out what the small sample should be for testing and under what conditions it should be cooled. For the case under consideration, a small sample with a diameter of 5 mm is suitable, which must be cooled with a coefficient of 300 (Table 9).
The proposed method, in comparison with the Jominy method, is simpler and allows one to obtain broader and more important information about the tested steel (Fig. 4, Table 7). This work continues the development of the method for predicting the structure and mechanical properties of steel in the core of hardened products in a more simplified version, which was described in [26]. Especially this method is very important when using steel with optimal hardenability and the method of its choice depending on the shape and size of the hardened products, which were patented in [16].

ISSN 2664-9969
As a rule, such steel is subjected to intense quenching, which provides for the creation of high compressive stresses in the surface martensite layer and a softer core consisting of a mixture of pearlite and bainite or pure bainite of increased strength and ductility [16,17]. In this regard, it is important to have a simple and easily realizable technique for studying the mechanical properties of the core of hardened products without resorting to their destruction.
At present, there are already ready-made developments for the large-scale introduction of intensive technologies and steels with optimal hardenability into world practice on the basis of existing equipment or simple new equipment. It is planned to use low concentrations of aqueous solutions of polymers of reverse solubility as a quenching medium. Employees of Intensive Technologies LTD (ITL, Kyiv, Ukraine) have developed computer programs for calculating cooling modes in quenching media for parts of various configurations and sizes. Also, a quenching medium for intensive quenching based on aqueous solutions of polyacrtlamide of very low concentration (0.001-0.005 %) has been proposed [31,32].
It should be borne in mind that the proposed calculation technique is very approximate. At the modern level, when calculating temperature fields and cooling rates, it is necessary to solve the hyperbolic equation of heat conduction and use computer simulation [33,34]. It is also important to use modern methods of testing quenching media [35][36][37]. All this should be taken into account in further research.

Conclusions
The paper proposes a simple technique for modeling the formation of the structure and mechanical properties of the material in the core of various steel products during their quenching in liquid media. The essence of the technique is that first, the rate of cooling of the core of the hardened products is calculated at temperatures of 700 °С and 300 °С. Then the calculation of the cooling rate of small samples with a thickness of 5-6 mm is carried out, which are cooled under conditions where similar cooling rates are achieved for small test samples at temperatures of 700 °С and 300 °С. It is also proposed to combine the achievements in the field of bainitic and martensitic transformations during quenching in order to maximize hardening of the quenched products.