An increase in technical requirements related to the prediction of mechanical properties of steel engineering components requires a deep understanding of relations which exist between microstructure, chemical composition and mechanical properties. This paper is dedicated to the research of the relation between steel hardness with the microstructure, chemical composition and temperature of isothermal decomposition of austenite. When setting the equations for predicting the hardness of microstructure constituents, it was assumed that: (1) The pearlite hardness depends on the carbon content in a steel and on the undercooling below the critical temperature, (2) the martensite hardness depends primarily on its carbon content, (3) the hardness of bainite can be between that of untempered martensite and pearlite in the same steel. The equations for estimation of microstructure constituents’ hardness after the isothermal decomposition of austenite have been proposed. By the comparison of predicted hardness using a mathematical model with experimental results, it can be concluded that hardness of considered low-alloy steels could be successfully predicted by the proposed model.

The purpose of this research is to upgrade the mathematical modeling and computer simulation of steel quenching. Based on theoretical analyses of physical processes that exist in quenching systems, the mathematical model for steel quenching is established and computer software is developed. The mathematical model of steel quenching is focused on physical phenomena, such as heat transfer, phase transformations, mechanical properties, and generation of stresses and distortions. The numerical procedure of computer simulation of steel quenching is divided into three parts: numerical calculation of transient temperature field, numerical calculation of phase change, and numerical calculation of the mechanical behaviors of steel during quenching. The numerical procedure is based on the finite volume method. Physical properties that were included in the model, such as heat conductivity coefficient, heat capacity, and surface heat transfer coefficient, were obtained by the inversion method based on the Jominy test results. By the completed algorithm, 3-D situation problems, such as the quenching of complex cylinders, cones, spheres, etc., can be simulated. The established model of steel quenching can be successfully applied in the practical usage of quenching.

The research main stream in this paper is to upgrade the mathematical modelling and computer simulation of quenching of steel. Based on theoretical analyse of physical processes which exist in quenching systems of steel workpieces, the mathematical model for computer simulation mechanical properties and distortions during the quenching has been developed. The mathematical model of steel quenching is focused on physical phenomena such as heat transfer, phase transformations, mechanical properties and generation of stresses and distortions. Because of that the numerical procedure of computer simulation of steel quenching is divided in three parts: numerical calculation of transient temperature field, numerical calculation of phase change and numerical calculation mechanical behaviours of steel. The numerical procedure is based on control volume method. Relevant physical properties about which cooling rate depends are specific heat capacity of steel, heat conductivity coefficient of steel, steel density, linear thermal expansion, transformation expansion, and heat transfer coefficient of quenchant. Also, the transformation plasticity has been included in the model. Physical and mechanical properties that were included in such model have been predicted by taking into account their temperature dependences. In the developed computer program for simulation quenching the hardness at different workpiece points is estimated by the conversion of the calculated cooling time from 800 to 500 °C, t _8/5 to the hardness by using both, the relation between cooling time, t _8/5 and Jominy distance and the Jominy hardenability curve. Other properties of steel have been estimated based on as quenched hardness of steel. Based on the developed algorithm, computer software is developed for simulation of 3D situation problems, such as the quenching of complex cylinders, cones, spheres, etc., can be simulated. The established numerical model and computer softwaire for simulation of steel quenching can be successfully applied in the practical usage of quenching.

Mathematical modelling of phase transformations and hardness distribution in non-monotonic quenched steel specimen was developed based on the results of simple experimental test i.e. Jominy test. The hardness in specimen points was estimated by the conversion of cooling time results to hardness by using both, the relation between cooling time and distance from the quenched end of Jominy specimen, and by using the Jominy hardenability curve. The cooling curve at the specimen point was predicted by numerical modelling of cooling by using the finite volume method. Developed numerical model for computer simulation of quenching was also experimentally verified. Limitations of proposed numerical model were found out as well. It has been shown that proposed numerical model can be successfully applied for purposes of simulation of continuous and interrupted quenching of carbon and low alloyed steel specimens.

The research purpose is to upgrade the mathematical modelling and computer simulation of quenching of steel. Based on theoretical analyze of physical processes which exist in quenching systems the mathematical model for steel quenching is established and computer software is developed. The mathematical model of steel quenching is focused on physical phenomena such as heat transfer, phase transformations, mechanical properties and generation of stresses and distortions. Physical properties that were included in the model, such as heat conductivity coefficient, heat capacity and surface heat transfer coefficient were obtained by the inversion method based on Jominy test results. The numerical procedure is based on finite volume method. By the developed algorithm, 3D situation problems such as the quenching of complex cylinders, cones, spheres, etc., can be simulated. The established model of steel quenching can be successfully applied in the practical usage of quenching.

Numerical model of controlled cooling in the production of steel hot rolled bars was developed. The numerical model and algorithm are completed to solve problems in controlled cooling of hot rolled bars in cooling beds. The controlled cooling is performed by special placement of hot rolled bars on cooling beds. By numerical model of controlled cooling is possible to predict a transient temperature field, microstructure evolution and hardness of round steel bars during their cooling in cooling beds. The numerical model of transient temperature field is based on control volume method. The hardness and microstructure distribution in steel bars has predicted by using equations of austenite decomposition kinetic. The algorithm for prediction is based the real chemical composition. Numerical model and computer program were experimentally verified by experimental work in a real industrial production of low-alloyed steel bars. The verification of developed numerical model was performed by comparison of simulated with experimentally evaluated results hardness and cooling curve.