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The diffusional transformation kinetics of C-Mn steels during continuous cooling have been measured and predicted in this study for predicting the non-isothermal multi-stage cooling transformation kinetics.
A suitable thermodynamic model is assessed for determining the driving force of austenite to ferrite transformation and the austenite/ferrite interface concentrations under various equilibrium constraints, which are essential to determine the diffusion-controlled transformation kinetics.
The continuous cooling transformation (CCT) curves of C-Mn steels are determined using dilatometric method. Pham’s empirical growth model is found most suitable for describing the start and finish transformation curve. The Avrami equation, common-used for isothermal transformation, is found to be applicable to the continuous cooling transformation. The Avrami exponents, nF and nP, for ferrite- and pearlite- dominant CCT, respectively, are close to the isothermal ones reported in the literature. The Avrami constant, b, increases with decreasing austenitizing temperature, indicating a fast progress of transformation. Combining Pham’s empirical growth model with Avrami equation, the CCT kinetics of C-Mn steels can be predicated well.
The examination on the microstructural evolution during CCT suggests that the transformation of austenite to grain boundary allotriomorphs of ferrite (GBAF) can be divided into (1) nucleation and growth (NG) stage, (2) growth only (site saturation, SS) stage, and (3) coalescence stage. In the NG stage, the oblate ellipsoid aspect ratio of GBAF remains 3:1 until all the nucleation sites are exhausted., i.e. the onset of SS stage, then gradually decreases in the SS stage. Once the aspect ratio approaches unity, the coalescence starts to operate. Based on this observation, a physical base model is developed for predicting the austenite to GBAF CCT. This model possesses the capability to predict the start and finish transformation temperatures, the fraction transformed, and the final ferrite grain size. Although such model failed to predict the whole range of CCT curve due to the fact that only the GBAF transformation is included at present stage, it is still highly recommended for microstructural control.
In order to completely predict the whole CCT curves, a semi-empirical physical base model is adopted. In addition, the methodology to predict multi-stage cooling transformation from CCT curves is also derived based on additivity rule and the concept of ideal TTT diagram. Associated with the additivity rule and the concept of ideal TTT diagram, such empirical model is validated to be applicable for the prediction of CCT and step wise cooling transformation.
The latent heat is calculated using thermodynamic software for the accurate control of cooling history of the medium carbon steels which usually releases an abundance of latent heat. Associated with the semi-empirical transformation model, the calculation of latent heat is integrated into a heat transfer model and successfully implemented in a mill operation.

ABSTRACT I
ACKNOWLEDGEMENTS III
CONTENTS IV
TABLE CONTENTS VIII
NOMENCLATURE IX
CHAPTER 1 INTRODUCTION 1
1.1 Background 1
1.2 Motivation and Objectives 2
CHAPTER 2 LITERATURE SURVEY 4
2.1 Measurement of kinetics of phase transformation 4
2.2 Characteristics of austenite transformation 5
2.3 Nucleation kinetics and Incubation time 5
2.3.1 Enomoto‘s model 6
2.3.2 Bhadeshia's model 7
2.3.3 Kirkaldy's model 7
2.3.4 Pham's model 8
2.4 Thermodynamic basis of the volume free energy change 8
2.5 Isothermal transformation kinetics 9
2.5.1 Classic growth kinetics 9
2.5.2 Johnson-Mehl-Avrami equation 10
2.6 Non isothermal transformation 12
2.7 Ideal (true) TTT diagram 13
2.8 Factors affecting the transformation kinetics 14
2.8.1 Chemical compositions 14
2.8.2 Austenite grain size 15
2.8.3 Energy status of austenite 15
2.9 Prediction of diffusional transformation of austenite 15
2.9.1 Theoretical modelling of CCT 17
CHAPTER 3 COMPARISON OF THERMODYNAMIC MODELS 26
3.1 Introduction 26
3.2 Comparison of available thermodynamic models 26
3.2.1 Hillert-Staffanson subregular model 26
3.2.2 Quasi-chemical model 29
3.2.3 Wagner formula 31
3.3 Calculation of equilibrium and driving force 32
3.3.1 Calculation of equilibrium 32
3.3.2 Thermodynamic equilibrium constraints 32
3.3.3 The Gibbs free energy change associated with austenite to ferrite transformation 33
3.4 Thermodynamic data used 34
3.4.1Thermodynamic data of pure iron 34
3.4.2 Thermodynamic data of carbon 35
3.4.3 Thermodynamic data of substitutional elements 36
3.4.4 Wagner parameters 36
3.5 Comparison of various thermodynamic solution models 38
3.5.1 Phase diagrams 38
3.5.2 The driving force associated with austenite to ferrite transformation. 38
3.5.3 Thermodynamic calculation for transformation kinetics 39
3.6 Summary 39
CHAPTER 4 EMPIRICAL MODELING OF CONTINUOUS COOLING TRANSFORMATION OF AUSTENITE IN STEELS 47
4.1 Introduction 47
4.2 Literature survey 47
4.2.1 Empirical nucleation models 47
4.3 Experimental procedure 49
4.3.1 Materials preparation 49
4.3.2 Measurement of transformation kinetics 49
4.4 Results and discussion 49
4.4.1 Continuous cooling curves 49
4.4.2 Nucleation 49
4.4.3 Growth kinetics 51
4.5 Prediction of CCT curves 55
4.6 Limitation of such approach 55
4.7 Summary 56
CHAPTER 5 MICROSTRUCTURAL EXAMINATION OF NUCLEATION AND GROWTH OF FERRITE IN PLAIN CARBON STEELS 76
5.1 Introduction 76
5.2 Experimental procedure 76
5.2.1 Materials preparation 76
5.2.2 Measurement of transformation kinetics 76
5.2.3 Quantitative microscopy 77
5.3 Results and discussion 78
5.3.1 Microstructural evolution during continuous cooling in steel AL 78
5.3.2 Grain density and volume fraction change 80
5.3.3 Effect of C content and austenitizing temperature on the microstructural evolution 82
5.4 Summary 84
CHAPTER 6 THEORETIC MODELLING OF CONTINUOUS COOLING TRANSFORMATION 106
6.1 Introduction 106
6.2 Review of modelling of transformation kinetics 106
6.2.1 Concept of extended volume 106
6.2.2 Nucleation kinetics 107
6.2.3 Growth kinetics 108
6.2.4 Umemoto's extended volume approach for iso- and noniso- thermal ferrite transformation 109
6.2.5 Liu's site saturation model for non-isothermal ferrite transformation 112
6.2.6 Approach used in this study 115
6.3 Validation of prediction models 115
6.3.1 Umemoto's NG model 115
6.3.2 Liu's SS model 116
6.3.3 Modification of Liu's SS model 117
6.3.4 Limitation of first principle physical base model 119
6.4 Summary 119
CHAPTER 7 ASSESSMENT OF ADDITIVITY RULE TO STEELS 131
7.1 Introduction 131
7.2 Basic approaches 132
7.2.1 Examination of Nucleation Models 132
7.2.2 Methodology of Calculating Ideal TTT Diagrams 133
7.2.3 Prediction of Transformation Diagrams Using Ideal TTT Diagrams 135
7.3 Results and discussion 136
7.3.1 Start Transformation Model 136
7.3.2 Ideal TTT Diagrams 137
7.3.3 Effect of consumed incubation fraction during cooling on TTT diagrams 138
7.3.4 TTT and CCT Diagrams Predicted Using Ideal TTT Diagrams 139
7.3.5 Implement of ideal TTT concept and additivity rule 140
7.4 Summary 142
CHAPTER 8 APPLICATION AND EVALUATION OF LATENT HEAT IN C-MN STEELS 166
8.1 Introduction 166
8.2 Basic approaches 167
8.2.1 Thermodynamic model 167
8.2.2 Calculation of latent heat 168
8.3 Experiments 170
8.3. Materials 170
8.3.1 DTA measurements 170
8.4 Results and discussion 171
8.4.1 Thermodynamic calculation 171
8.4.2 DTA results 172
8.4.3 Effects of chemical compositions 174
8.4.4 Implementation of transformation model coupled with latent heat 176
8.5 Summary 180
CHAPTER 9 CONCLUSIONS AND FURTHER WORK 198
REFERENCES 200

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