The paper presents a multi-scale mathematical model dedicated to a comprehensive simulation of resistance heating combined with the melting and controlled cooling of steel samples. Experiments in order to verify the formulated numerical model were performed using a Gleeble 3800 thermo-mechanical simulator. The model for the macro scale was based upon the solution of Fourier-Kirchhoff equation as regards predicting the distribution of temperature fields within the volume of the sample. The macro scale solution is complemented by a functional model generating voluminal heat sources, resulting from the electric current flowing through the sample. The model for the micro-scale, concerning the grain growth simulation, is based upon the probabilistic Monte Carlo algorithm, and on the minimization of the system energy. The model takes into account the forming mushy zone, where grains degrade at the melting stage – it is a unique feature of the micro-solution. The solution domains are coupled by the interpolation of node temperatures of the finite element mesh (the macro model) onto the Monte Carlo cells (micro model). The paper is complemented with examples of resistance heating results and macro- and micro-structural tests, along with test computations concerning the estimation of the range of zones with diverse dynamics of grain growth.
The article discusses the development of an approximation model of selected plastic and mechanical properties obtained from compression tests of model materials used in physical modeling. The use of physical modeling with the use of soft model materials such as a synthetic wax branch with various modifiers is a popular tool used as an alternative or verification of numerical modeling of bulk metal forming processes. In order to develop an algorithm to facilitate the choice of material model to simulate the behavior of real-metallic materials used in industrial production processes the induction of decision trees was used. First of all, the Statistica program was used for data mining, which made it possible to determine / find the relationship between the percentage of particular constituents of the model material (base material and modifiers) and yield strength, critical and maximum strain, and provide the opportunity to indicate the most important variables determining the shape of the stress – strain curve. Next, using the induction of decision trees, an approximation model was developed, which allowed to create an algorithm facilitating the selection of individual modifying components. The last stage of the research was verification of the correctness of the developed algorithm. The obtained research results indicate the possibility of using decision tree induction to approximate selected properties of modeling materials simulating the behavior of real materials, thus eliminating the need for costly and time-consuming experiments carried out on metallic material.
A mathematical model of austenite - bainite transformation in austempered ductile cast iron has been presented. The model is based on a model developed by Bhadeshia [1, 2] for modelling the bainitic transformation in high-silicon steels with inhibited carbide precipitation. A computer program has been developed that calculates the incubation time, the transformation time at a preset temperature, the TTT diagram and carbon content in unreacted austenite as a function of temperature. Additionally, the program has been provided with a module calculating the free energy of austenite and ferrite as well as the maximum driving force of transformation. Model validation was based on the experimental research and literature data. Experimental studies included the determination of austenite grain size, plotting the TTT diagram and analysis of the effect of heat treatment parameters on the microstructure of ductile iron. The obtained results show a relatively good compatibility between the theoretical calculations and experimental studies. Using the developed program it was possible to examine the effect of austenite grain size on the rate of transformation.