Sharif Digital Repository

In this study, a model is developed to predict austenite phase transformation by means of Avrami's model and the finite element method. For doing so, the Avrami-type rate equation is evaluated with the modified Euler's method to handle the kinetics of phase change under non-isothermal conditions. Also, to simultaneously consider the effect of temperature variations on austenite decomposition, heat conduction equation is solved using a two-dimensional finite element approach. To establish the reliability of theoretical results, a comparison is made between simulated and experimental cooling curves for two grades of carbon steel. © 2003 Elsevier B.V. All rights reserved  

Knowledge of process parameters during and after hot rolling is a significant requirement in order to produce a material with the desired microstructures and mechanical properties. In continuous hot rolling mills, different stages may exist, including water descaling, rolling stands, interstand sections, and run-out table. In each of these sections, various thermal and/or mechanical conditions are applied on the rolling metal that would affect material response in successive stages. In other words, an integrated model should be employed in hot rolling operations to evaluate metal behavior and microstructural events at the same time. Therefore, the thermal-mechanical response as well as... 

In this paper, a mathematical model has been developed to determine temperature distribution on the run-out table. The variational formulation and the finite element method have been employed to solve the governing conduction-convection equation. In order to avoid numerical instabilities due to the convection term, the heat transfer equation is first transformed to the standard form and then Raylieght-Ritz approximation technique and the finite element method have been utilized to solve the equation. To include the effect of phase transformation during cooling of steel, a second-order rate equation for describing austenite decomposition kinetics is coupled with the heat transfer model. A... 

A thermo-elastic analysis coupled with a phase change model is employed to evaluate thermal stresses as well as progress of austenite decomposition after hot strip rolling operations. The thermo-mechanical finite element analysis is utilized to assess the distributions of temperature and thermal stresses during cooling while at the same time, a model based on the additivity rule is used to determine the rate of austenite to ferrite decomposition. The proposed model is applicable to multi-pass rolling schedules while the effects of different process parameters including the rolling speed and cooling configuration of the run-out table can be taken into account. In order to verify the... 

Transformation of austenite to ferrite under continuous cooling condition was investigated. The heat conduction problem was managed by finite element method while two-dimensional cellular automata modeling was simultaneously performed to predict the progress of austenite decomposition using a two-step algorithm to reduce surface-to-volume ratio. Continuous cooling experiments on low carbon steel were made and the ferrite structure was determined and compared with the simulation data. The predicted and the experimental results demonstrated an acceptable consistency and the activation energy for ferrite growth was determined as 171 kJ/mole. The rate of ferrite transformation increased under... 

Transformation of austenite to ferrite under continuous cooling condition was investigated. The heat conduction problem was managed by finite element method while two-dimensional cellular automata modeling was simultaneously performed to predict the progress of austenite decomposition using a two-step algorithm to reduce surface-to-volume ratio. Continuous cooling experiments on low carbon steel were made and the ferrite structure was determined and compared with the simulation data. The predicted and the experimental results demonstrated an acceptable consistency and the activation energy for ferrite growth was determined as 171 kJ/mole. The rate of ferrite transformation increased under... 

This paper presents a mathematical model for prediction of temperature history, final microstructures, and transformation kinetics in steel rods subjected to non-uniform cooling conditions. To achieve this goal, a mathematical model based on two-dimensional finite element method is developed to solve the governing heat conduction equation with non-uniform boundary conditions. The additivity rule is coupled with the finite element analysis to assess the kinetics of austenite decomposition during continuous cooling. The effect of decarburization during heating stage is also considered in the model employing Fick's second equation. To verify the predictions, time-temperature histories during...