Mathematical Modeling and Computer Simulation of Steel Quenching

Abstract

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.

Design of advanced steels by integrated computational materials engineering

“…The following lists some applications. Material properties and fracture: for example, simulating the high‐speed tensile property, [100] crashworthiness, [101] ductile fracture, [102] buckling resistance, [103] the cyclic deformation behavior of TRIP steel [104] etc. Phase transformation: dealing with the stress and microstructure evolution during quenching [105,106] ; simulating the effects of the thermofluid field and thermal diffusion on the phase formation during welding [107] etc. Corrosion and fatigue: such as fatigue behavior [108,109] ; corrosion fatigue crack propagation behavior [110] ; dynamic bending fatigue test of wheels [111] ; and simulating localized and pitting corrosion [112,113] Material processing and forming: simulating the thermal distribution of steel products during quenching [106,114] or laminar cooling [115] ; analyzing the effect of electromagnetic stirring on liquid steel flow in the continuous casting mold [116] ; and simulating the material flow and the force load during the forging process [117] Industrial process optimization on various steel production processes by determining the best material behavior laws and process settings [118] …”

Artificial Neural Networks-Based Prediction of Hardness of Low-Alloy Steels Using Specific Jominy Distance

“…Cooling rate during the cooling from austenitizing temperature is adequately defined by cooling time from austenitizing temperature to temperature of 500 • C. This is further confirmed by the fact that prediction of the as-quenched hardness of steel based on cooling time from 800 • C to 500 • C is well known in the literature and practice, where as-quenched hardness at different workpiece points is estimated by the conversion of the cooling time to the hardness. This conversion is provided by the relationship between the cooling time and distance from the quenched end of the Jominy test specimen [4,12], making the cooling time to 500 • C, t 500 , good candidate for one of the main input variables in ANN for prediction of hardness. An equally important factor influencing the steel hardness is hardenability of steel.…”

“…Hardenability of steel can be involved in prediction model by taking into account the chemical composition. Additionally, hardenability of steel can be involved in prediction model by taking into account the specific Jominy distance, E d , which depends on chemical composition of steel and corresponds to the Jominy distance when 50% of the microstructure is martensite (Figure 1) [4,12,34]. Distance E d can be determined/estimated from the Jominy curve based on hardness of steel with 50% martensite in the microstructure, HRC 50%M [35]:…”

“…One of the most common semi-empirical methods for predicting hardness during continuous cooling is based on the continuous cooling transformation (CCT) diagrams [11]. Additionally, distribution of hardness in quenched steel can be predicted using the Jominy test results by transferring the results from the Jominy curve to the hardness values for different points of the steel specimen [4,12].…”

“…Hardness is often used as a basis for prediction of various elastic and plastic stressstrain as well as fatigue properties of steel [12,[29][30][31]. Hardness prediction is very important in heat treatment of steel.…”