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Characterization and microstructural evolution model of a Nb ferrite-bainite steel Gerami, Sepehr 2010

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Characterization and Microstructural Evolution Model of a Nb Ferrite-Bainite Steel by Sepehr Gerami a thesis submitted in partial fulfillment of the requirements for the degree of master of applied science in the faculty of graudate studies (Materials Engineering) the university of british columbia (Vancouver) September 2010 c© Sepehr Gerami, 2010 Abstract Complete microstructural evolution models for dual phase ferrite-bainite micro-alloy steels do not yet exist despite their widespread use. An attempt is made here to make a contribution towards development of a unified model. Transformation behaviour in a niobium bearing line-pipe steel is investigated. Grain growth and recrystallization studies are performed, and the results used to design continuous cooling transformation tests to study the effects of prior austenite grain size, cooling rate, retained strain, and niobium dissolu- tion on transformation behaviour in the steel. Existing modelling techniques are then applied to the experimental data in order to predict ferrite and bainite transformation start temperatures and transformation kinetics. ii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1 Semi-Empirical Models . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 Ferrite Formation Start . . . . . . . . . . . . . . . . . . 6 3.1.2 Transformation Kinetics . . . . . . . . . . . . . . . . . 8 3.1.3 Ferrite Stop/Bainite Start . . . . . . . . . . . . . . . . 12 3.2 Theoretical Approaches . . . . . . . . . . . . . . . . . . . . . . 13 3.2.1 Ferrite Formation . . . . . . . . . . . . . . . . . . . . . 13 3.2.2 Bainite Formation . . . . . . . . . . . . . . . . . . . . 21 3.3 The Role of Niobium . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.1 Niobium Precipitation and Interaction with Austenite Recrystallization . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 Effect of Niobium on the Austenite to Ferrite Trans- formation . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Experimental Methodology . . . . . . . . . . . . . . . . . . . 36 iii TABLE OF CONTENTS 4.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2.1 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2.2 Austenite Grain Growth Tests . . . . . . . . . . . . . . 37 4.2.3 Austenite Softening Tests . . . . . . . . . . . . . . . . 39 4.2.4 Continuous Cooling Transformation Tests . . . . . . . 41 5 Results and Data Analysis . . . . . . . . . . . . . . . . . . . 45 5.1 Preliminary Test Results . . . . . . . . . . . . . . . . . . . . . 45 5.2 CCT Test Results . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2.1 Niobium-in-Solution Tests . . . . . . . . . . . . . . . . 58 6 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.1 Ferrite Transformation Start . . . . . . . . . . . . . . . . . . . 62 6.2 Bainite Transformation Start . . . . . . . . . . . . . . . . . . 65 6.3 Ferrite and Bainite Growth . . . . . . . . . . . . . . . . . . . 70 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.1 Future Work Recommendations . . . . . . . . . . . . . . . . . 82 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 iv List of Tables 3.1 Variations of JMAK equation and associated parameters . . . 10 3.2 Nominal JMAK parameters for Umemoto model . . . . . . . . 11 4.1 Composition of sample steel (wt %) . . . . . . . . . . . . . . . 36 4.2 Etchants used for metallography . . . . . . . . . . . . . . . . . 39 5.1 Results of quantitative image analysis . . . . . . . . . . . . . . 57 5.2 Results of quantitative image analysis, Nb in solution . . . . . 60 6.1 Ferrite and bainite growth model parameters . . . . . . . . . . 78 v List of Figures 3.1 Fe-C phase diagram . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Ferrite start model . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Critical driving pressure vs bainite start temperature . . . . . 13 3.4 Iron-carbon phase diagram and concentration profiles . . . . . 16 3.5 Parabolic growth of allotriomorphic ferrite . . . . . . . . . . . 18 3.6 Model of Kamat et al. . . . . . . . . . . . . . . . . . . . . . . 19 3.7 Effect of austempering temperature on bainite start and finish. 29 3.8 Effect of deformation on precipitation kinetics . . . . . . . . . 31 3.9 Effect of niobium on austenite recrystallization . . . . . . . . . 32 3.10 Effect of Nb in Solution on Transformation . . . . . . . . . . . 35 4.1 Austenite grain growth test sample geometry . . . . . . . . . . 38 4.2 Double hit test . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.3 CCT test regimes . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.4 CCT test samples . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.5 CCT dilation data processing: Dilation data and lever rule (a); calculated CCT transformation curve (b). . . . . . . . . . 44 5.1 Austenite grain growth . . . . . . . . . . . . . . . . . . . . . . 46 5.2 Austenite softening at 850◦C . . . . . . . . . . . . . . . . . . . 48 5.3 CCT micrographs . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.4 Effect of cooling rate . . . . . . . . . . . . . . . . . . . . . . . 51 5.5 Effect of grain size . . . . . . . . . . . . . . . . . . . . . . . . 53 5.6 Photomicrographs of CCT samples, LePera etch . . . . . . . . 53 vi LIST OF FIGURES 5.7 Effect of strain . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.8 Photomicrographs of M/A fraction, effect of ǫ . . . . . . . . . 55 5.9 Nb-in-solution microstructures . . . . . . . . . . . . . . . . . . 59 5.10 Effect of Nb and Dγ . . . . . . . . . . . . . . . . . . . . . . . 61 6.1 Undercooling ∆T vs. log (D2effq) . . . . . . . . . . . . . . . . . 64 6.2 Obtaining Tfs . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.3 Relationship between ∆G∗bs and Tbs . . . . . . . . . . . . . . . 67 6.4 Comparison of ∆G∗bs in different studies . . . . . . . . . . . . 68 6.5 Calculating Tbs . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.6 Performance of bainite start model . . . . . . . . . . . . . . . 69 6.7 Schematic CCT diagram, plotted as T versus q. . . . . . . . . 71 6.8 Construction to determine n . . . . . . . . . . . . . . . . . . . 72 6.9 Calculated values of b versus T , Rios method . . . . . . . . . . 74 6.10 Calculated values of b versus T , modified Rios method . . . . 75 6.11 Temperature dependence of n . . . . . . . . . . . . . . . . . . 77 6.12 Ferrite start and growth models . . . . . . . . . . . . . . . . . 79 6.13 Bainite growth model . . . . . . . . . . . . . . . . . . . . . . . 80 vii Acknowledgements I would like to express my gratitude to my supervisor, Professor Matthias Militzer, for his continuous guidance and encouragement, without which this work would have certainly not been possible. My thanks to Dr. Fateh Fazeli for his infinite patience, and invaluable assistance. I am also grateful to Dr. Sujay Sarkar and Mr. Hamid Azizi- Alizamini for their advice and our fruitful discussions. I would like to thank Dr. Dongsheng Liu, Ms. Mary Fletcher, Mr. Ross McLeod, Mr. Carl Ng, and Mr. David Torok for their assistance in sample preparation and experimental work. Finally, I must state that I am eternally indebted to my beloved par- ents for their unwavering support throughout my studies, both material and otherwise. viii Chapter 1 Introduction Steel remains as the most ubiquitous class of alloys in use today, with a wide variety of applications ranging from building structures to auto-bodies. Lowering energy consumption (and thus carbon emissions) and reducing manufacturing costs provide incentives for continued investment in research and development of modern steels. Increasing commercial interest in high strength steels in the 1970’s led to the development of High Strength Low Al- loy (HSLA) steels, which are commonly created by micro-alloying low carbon steels with one or more elements such as niobium, titanium, or vanadium. In these steels, it is possible to achieve a significant improvement in yield strength through the combined effect of a refinement in grain size and dis- persion hardening by second phase precipitates in a typical microstructure of ferrite and pearlite by careful control of the hot rolling process (ie: temper- ature and strain) [1, 2]. The development of mathematical models meant to improve process control was begun in the 1980’s starting with works such as that of Sellars et al. [3] to describe the effect of hot rolling process variables, namely heating and cooling rates and strain and strain rates, on grain growth, recovery and recrystallization, and phase transformations in the steel. Com- plete computer process models were developed for the hot rolling of low carbon and HSLA steels [4, 5, 6]. 1 CHAPTER 1. INTRODUCTION More modern developments in steels have led to introduction of advanced high strength steels (AHSS), including dual phase (DP), transformation in- duced plasticity (TRIP) and complex phase (CP) steels. Applications for these steels range from automobile structures to oil and gas pipelines. The development of process models for these steels is still in its infancy [7], how- ever, some preliminary models have been proposed for ferrte/martensite DP steels [8, 9], TRIP steels [10, 11], and CP steels [12]. The strength and formability of the final product can be tailored to the application by adjusting processing parameters in order to modify the propor- tions of each microstructural constituent. A microstructure model that would describe the decomposition of austenite according to the process parameters is therefore highly desirable. The complexity of transformation behaviour in these alloys makes developing a process model quite challenging. The present investigation is concerned primarily on the effect of thermo- mechanical processing parameters on the phase transformation behaviour of a niobium bearing ferrite/bainite steel with a more complex-type microstruc- ture. There is a need for the development of models for ferrite-bainite steels, and so an attempt is made to utilize existing modelling techniques to repro- duce experimental data. 2 Chapter 2 Objectives The main objectives of this study are to: • Characterize the transformation behaviour of the complex phase steel - Investigate the effect of cooling rate, initial austenite grain size, and re- tained strain on austenite decomposition temperature, transformation kinetics, and final microstructure. • Quantify the effect of the state of niobium dissolution on the transfor- mation behaviour of the steel. • Utilize existing modelling techniques to develop a model that can pre- dict the transformation kinetics and final microstructure of the steel. 3 Chapter 3 Literature Review As face centred cubic (FCC) austenite (γ) is cooled beyond the A3 or Acm lines on the iron-carbon binary phase diagram (figure 3.1), it begins to trans- form to a body centred cubic (BCC) crystal structure referred to as ‘ferrite’ [13]. In a binary iron-carbon system at equilibrium, the steel is entirely BCC below ∼ 725◦C. Depending on the concentration of carbon and processing parameters, a certain amount of iron carbide (Fe3C) termed ‘cementite’ can precipitate upon cooling during and/or after transformation below the A1 and Acm lines in the phase diagram. At lower temperatures, metastable body centred tetragonal (BCT) martensite forms. Microstructural constituents consisting of these components are classified as grain boundary ferrite, grain boundary cementite, massive ferrite, Widmanstätten ferrite, Widmanstätten cementite, pearlite, upper bainite, lower bainite, lath martensite, and twinned martensite [14]. In the present study, grain boundary cementite, Widmanstätten cementite and massive ferrite are not encountered. At small undercoolings below A3, ferrite (α) nucleates on austenite grain boundaries and grows in a ‘blocky’ manner into approximately equiaxed grains[16]. Ferrite nucleating and growing on austenite grain boundaries un- der moderate undercoolings is referred to as grain boundary or ‘allotriomor- phic’ ferrite. Below the A1 line in the phase diagram (reported as 0.76wt% 4 CHAPTER 3. LITERATURE REVIEW Figure 3.1: The iron-carbon binary phase diagram [15] in figure 3.1) where untransformed austenite is supersaturated with carbon - due the bulk concentration of the steel or carbon rejection from ferrite to austenite during ferrite formation - a eutectoid product called ‘pearlite’ forms [16]. At higher cooling rates ferrite assumes non-polygonal acicular morpholo- gies. With a further increase in cooling rate, austenite decomposes into a needle or plate like ferritic structure that grows from existing ferrite al- lotriomorphs, referred to as ‘Widmanstätten ferrite’. At lower temperature under these higher cooling rates, a eutectoid product structurally distinct from pearlite, termed ‘bainite’, can form. The exact morphology of bainite is heavily dependent on its temperature of formation [16]; it is often cate- gorized as either upper or lower bainite. The general morphology is that of aggregates of ferritic platelets separated by regions of residual phases, usually consisting of untransformed austenite, martensite and/or cementite. These 5 CHAPTER 3. LITERATURE REVIEW aggregates are referred to as “sheaves” [17]. Widmanstätten ferrite is struc- turally similar to the ferritic portion of bainite, such that it can be difficult to distinguish the two under an optical microscope. Both semi-empirical and theoretical models have been developed in an attempt to predict phase transformation behaviour in steels. The following sections discuss some of these approaches. 3.1 Semi-Empirical Models Models for phase transformations in low carbon steels typically consist of distinct steps: Prediction of the ferrite transformation start, ferrite transfor- mation kinetics, pearlite and/or bainite transformation start, and pearlite and/or bainite transformation kinetics. 3.1.1 Ferrite Formation Start The ferrite transformation start temperature is often calculated thermody- namically; assuming equilibrium, the point at which ferrite formation starts is where the alloy temperature drops below the Ae3 line on the iron-carbon phase diagram [4, 5]. This approach does not take the condition of the austenite into consideration, however. Militzer et al. [18] suggested a method of predicting early growth of corner nucleated ferrite based on the austenite grain size and cooling rate. The approach assumes that nucleation site saturation is in effect beyond 5% of austenite decomposed, and that carbon diffusion is rate controlling. Under local equilibrium conditions, the temperature at which 5% of austenite has decomposed is taken as the experimentally detectable transformation start temperature TS, which is evaluated from: 6 CHAPTER 3. LITERATURE REVIEW Figure 3.2: An example of the ferrite start model of Militzer et al. [19] X∗C −X◦C = √ 2MP (X ∗ C −X◦C) φ1/2dγ √∫ TN TS DC XIC −X◦C XIC −XαC dT (3.1) where X◦C is the bulk concentration of carbon in the steel, X ∗ C is the limit- ing local carbon concentration at nucleation site saturation, MP ∼ 2 is the number of ferrite nuclei per austenite grain, φ is the cooling rate, dγ is the austenite grain diameter, TN is the temperature of nucleation, DC is the dif- fusivity coefficient of carbon in austenite, XIC is the concentration of carbon at the ferrite/austenite interface, and XαC is the concentration of carbon in ferrite. X∗C and TN are used as fit parameters. An example of the model is shown in is shown in figure 3.2. The points show experimental data, while the solid line represents the model. 7 CHAPTER 3. LITERATURE REVIEW 3.1.2 Transformation Kinetics The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [20, 21, 22, 23, 24] is often used to describe isothermal phase transformation kinetics. It pro- vides a less numerically intensive semi-empirical method of predicting trans- formation rates based on experimental data, without requiring diffusivity and mobility data. In general form, the JMAK equation is written as: Xα = 1− exp (−btn) (3.2) The constants b and n are often empirically determined, and are reflective of growth and nucleation conditions. The JMAK equation has been widely used to describe the formation of ferrite, pearlite, and bainite. Where more than one of these constituents is present, the JMAK equation is applied separately to each of them using different sets of parameters. Various modifications of the equation have been used. Table 3.1 lists some of the forms of the equation and their associated parameters available in literature. Commonly, the rate parameter b is defined as a function of chemical composition, temperature, carbon supersaturation, prior austenite grain size, strain, and/or cooling rate. In their application of the JMAK equation to ferrite transformation, Liu et al. [7] and Militzer et al. [19] normalized the fraction of ferrite formed to the equilibrium ferrite fraction Xe. They utilized a modified form of the JMAK equation proposed by Umemoto et al. [25]: X = 1− exp (−btn Dmγ ) (3.3) Nominal values for the parameters n and m in equation 3.3 are shown in table 3.2. Sarkar et al. chose to integrate the effect of Dγ into the parameter b. In the work of Han and Park [26] the values of b and n are functions of the 8 CHAPTER 3. LITERATURE REVIEW steel chemical composition. In contrast, the other authors chose a constant n independent of composition. Application of the Additivity Rule to the JMAK Equation Both nucleation and growth rates are temperature dependent. Consequently, they will be time dependent if the temperature of transformation varies with time. This makes application of the JMAK equation to continuous cooling transformations problematic. To counter this problem, Avrami [21] defined an “isokinetic” range of temperatures and concentrations in a given substance where the kinetics of phase change in the characteristic time scale remains unchanged; the relative internal history of the transformation is independent of the temperature path provided nucleation rate Ṅ and growth rate İ are proportional. Within this specific range, isothermal data can be used in conjunction with the principle of additivity [28] to describe the reaction under non-isothermal conditions. The principal requirement for additivity is: ∫ dt τ = 1 (3.4) That is, in a certain reaction where isothermal time τ results in a fraction transformed X◦, the reaction would reach X◦ under continuous cooling at a time t and temperature T where the above integral becomes unity. Cahn [29] suggested any reaction would be additive provided that the rate of transformation dX/dt was an exclusive function of temperature and the amount of parent material transformed: dX dt = [ dH(X) dX ] −1 h(T ) (3.5) 9 Table 3.1: Variations of JMAK equation and associated parameters in previous studies Alloy Composition (wt%) Transformation JMAK Equation and Parameters Han and Park [26] Fe-0.2C-1.97Si-1.52Mn-0.05Al-0.05Nb Ferrite X = 1− exp (−btn) ln b = 2.58445 + 1.845 ln(AGS)(4.5407 + 167.707[%Cγ ]− 67201[%Cγ ]1/2)× ln(TAe3 − T ) + (−35684− 877455[%Cγ ] + 374207[%Cγ ]1/2/T n = 0.8674 + 1.7506[%Cγ ] + 0.0583[%Mn] Militzer et al.[19] Fe-0.04C-0.30Mn-0.040Al Ferrite XXe = [ 1− exp ( 1 Dmγ (ξ)n )] Fe-0.045C-0.45Mn-0.08V-0.069Si-0.078Al Fe-0.08C-0.48Mn-0.036Nb-0.045Si-0.024Al Xe = XCγ −X C ◦ XCγ −X C α , n = 0.9 Fe-0.07C-0.76Mn-0.023Nb-0.013Ti-0.014Si-0.053Al Fe-0.07C-1.35Mn-0.086Nb-0.047Ti-0.14Si-0.044Al ξ = ∫ T TS exp[(b1(TAe3−T ′)−b2)/n] q(T ′) Liu et al.[7] Fe-0.07C-1.45Mn-0.73Si-0.05Al-0.01Ti Ferrite XXe = [ 1− exp ( −b tnDmγ )] Fe-0.06C-1.86Mn-0.077Si-0.043Al-0.011Ti-0.155Mo Xe = XCγ −X C ◦ XCγ −X C α , n = 1 b = expB◦ +B1(TAe3 − T ) +B2 X C ◦ 1−X Sarkar et al.[12] Fe-0.05C-1.88Mn-0.04Si-0.048Nb-0.49Mo-0.05Al Ferrite X = 1− exp (−btn) ln b = A0 +A1T +A2 lnDγ , n = 1.1 Bainite ln b = B0 +B1T +B2 ( XCγ ln (Dγ,rem) ) , n = 0.85, Dγ,rem = untransformed γ grain diameter 10 CHAPTER 3. LITERATURE REVIEW Table 3.2: Nominal JMAK parameters for Umemoto Model [27] Nucleation Site Site Saturation Nucleation & Growth n m n m Grain Surface 1 1 4 4 Grain Edge 2 2 4 2 Grain Corner 3 3 4 3 Avrami’s requirement that İ ∝ Ġ is rarely fulfilled in real reactions. However, in many cases of heterogeneous nucleation, the rate of nucleation is high, and potential nucleation sites are quickly exhausted as a consequence [30]. The reaction then becomes a function of growth rate only, which satisfies conditions for additivity. The JMAK equation in conjunction with the additivity principle is often used [7, 10, 12, 31, 32] as a convenient semi-empirical method to model the continuous cooling behaviour of austenite decomposition. In such a model, the reaction is broken down into isothermal increments, and the rate of trans- formation is calculated at each increment. The fraction transformed during each time increment is then simply the rate of transformation in that time increment multiplied by the length of the time increment. The b and n parameters in the JMAK equation are often optimized through mathematical means [33, 12]. Rios [34] devised a method of ex- tracting b and n from continuous cooling data which is based on a theoreti- cal rather than the usual mathematical approach. Some limitations to this model have been identified by Jia and Militzer [35], and some modifications have been made by the authors to address these limitations [35]. Descriptions of Rios’ approach, and said modifications, are provided in chapter 6. 11 CHAPTER 3. LITERATURE REVIEW 3.1.3 Ferrite Stop/Bainite Start The transition point between ferrite and pearlite and/or bainite transforma- tion is modelled by some authors [5, 4] by employing empirical relationships derived from experimental data in specific steels. There has been an effort by others [12, 10, 36], to utilize a more meaningful approach. The transition from ferrite to bainite is analyzed by these authors using the driving force for bainitic ferrite formation, as suggested by Ali and Bhadeshia [37]. Ali and Bhadeshia found that the free energy needed to obtain a detectable degree of bainitic ferrite formation could be approximated as a linear function of temperature, applicable to any low alloy steel. Bainite formation is assumed to take place under para-equilibrium con- ditions (carbon atoms may diffuse to reach a state of equilibrium but no diffusion of substitutional solutes takes place). Using thermodynamic data for the steel studied, the driving pressure ∆G for the formation of the bainitic ferrite can be calculated at any point during austenite decomposition, using the instantaneous temperature and carbon content in the remaining austen- ite. The critical driving pressure ∆G∗bs at which bainite formation starts is defined as the free energy calculated at an experimentally derived bainite transformation start temperature and corresponding austenite carbon con- centration. Plotting the critical driving pressure vs bainite start temperature, Sarkar, Liu, Fazeli and co-workers [12, 10, 36] found that a linear relation- ship existed between the two, regardless of carbon content and austenite microstructure, similar to the function found by Ali and Bhadeshia. These linear relationships can be seen in figure 3.3. Fazeli et al.[36] explained the discrepancy between their results and that of Ali and Bhadeshia [37] as a consequence of using different thermodynamic models and databases. 12 CHAPTER 3. LITERATURE REVIEW 500 520 540 560 580 600 620 640 0 200 400 600 800 1000 1200 G * [J /m ol ] T [°C] Sarkar and Militzer G* = 5.14Tbs - 3784 Liu et al, Fazeli et al G* = 3.64Tbs - 2840 Ali and Bhadeshia G* = 3.64Tbs + 2540 Figure 3.3: Critical driving pressure G∗ vs bainite start temperature Tbs from studies by Liu et al.[10], Fazeli et al.[36], Sarkar and Militzer [12] and Ali and Bhadeshia [37] 3.2 Theoretical Approaches 3.2.1 Ferrite Formation Nucleation The net free energy change during ferrite nucleation consists of several contri- butions: The volume free energy reduction V∆GV associated with formation of BCC crystal, the free energy increase Aσ due to the creation of an area A of FCC-BCC interface, the volume free energy change V∆GS associated with the misfit strain caused by the difference between the lattice parameter of the FCC and BCC crystals, and the free energy drop ∆Gd associated with 13 CHAPTER 3. LITERATURE REVIEW the destruction of austenite grain boundary[16]: ∆G∗ = −V∆GV + ∑ Aiσi + V∆GS + ∆Gd (3.6) The sum in the interfacial energy term in equation 3.6 reflects the fact that ferrite nuclei do not form with isotropic interfaces, but rather do so sur- rounded by interfaces of varying energy. By classical nucleation theory, the time-dependent nucleation rate is given by [38]: İ = NβZ exp ( −∆G ∗ kT ) exp ( −τ t ) (3.7) where N is the density of viable nucleation sites, β∗ is the frequency factor, Z is the Zeldovich non-equilibrium factor, τ is the incubation time, t is the isothermal reaction time, k is the Boltzmann constant, and T is temperature. Nucleation is considered to occur first on grain corners, followed by grain edges, and finally, grain faces. Before ∆G∗ can be calculated, information about the critical nucleus in- terface and shape is required. Assuming that the nucleus interface is isotropic would cause the interface to curve out evenly into the parent phase; as such, an incoherent ferrite nucleus on an austenite grain boundary can be assumed to be in the shape of two spherical caps. Clemm and Fisher [39] arrived at the following relation for ∆G∗: ∆G∗ = 4 (z2σαγ − z1σγγ)3 27z3∆G2V (3.8) where σαγ and σγγ are the interfacial energies for the ferrite/austenite inter- face and austenite grain boundaries, respectively. The parameters z1 through 14 CHAPTER 3. LITERATURE REVIEW z3 are factors dependent on the geometry of the nucleus and the ratio σαγ/σγγ. The misfit strain energy ∆GS is neglected. Although the spherical cap model is commonly used in classical analytical nucleation rate calculations, it fails to predict experimental data [40]. Lange, Enomoto and Aaronson [38, 41, 42, 40] developed a revision of the classical approach by using several different “pill-box” shaped nuclei of different geometries: either with a very low energy edge and two low energy planar faces, or with a low energy edge, a planar low energy face and a spherical cap high energy face. The authors reported good agreement of their model with experimental data for Fe-C and Fe-C-X alloys (where X represents some substitutional alloying element), provided nucleation was permitted at a very small fraction of the atomic sites available at grain faces. It must be noted, however, that in their observation of nucleation and growth kinetics of ferrite using X-ray diffraction patterns at a synchrotron facility, Offerman et al.[43] found that the activation energy for nucleation calculated by the method of Lange et al.[40] was two orders of magnitude larger than what they observed experimentally. Growth The hypoeutectoid portion of the iron-carbon phase diagram can be seen Figure 3.4 [32]. As a plain carbon steel with a carbon concentration of C◦ is cooled below the Ae3 line to T = T1 under equilibrium conditions, ferrite begins to precipitate and grow with a concentration given by the γ/γ + α phase boundary line at T1, Cα1. Carbon rejected from the ferrite diffuses into the parent austenite, such that the concentration of carbon in austenite immediately adjacent to the growing ferrite grain is given by the Ae3 (or γ + α/γ boundary) line at that temperature, Cγ1. Further cooling to T2 results in a carbon concentration of Cα2 in the ferrite, and Cγ2 in the austenite at the interphase. Under this mechanism, the transformation is said to be diffusion controlled. 15 CHAPTER 3. LITERATURE REVIEW Figure 3.4: Iron-carbon phase diagram and concentration profiles [32]. The lower part of figure 3.4 represents the carbon concentration profiles in the ferrite and austenite. It can be seen that the carbon concentration in austenite drops as one moves away from the growing ferrite grain. The shape of the carbon profile in the austenite is due to the diffusion of carbon atoms away from the enriched boundary and into the bulk of the parent austenite. The diffusion of carbon in austenite determines the degree of pile- up of carbon atoms at the interphase. Under these conditions, diffusivity in the austenite is therefore the rate limiting parameter in the formation of ferrite. During the initial stages of growth the bulk concentration of the austenite away from the interface C◦ does not increase by a significant amount, and is often considered constant. This simplification is problematic at later stages in the transformation, however, as will be discussed later. 16 CHAPTER 3. LITERATURE REVIEW One dimensional diffusion across the interphase is described by: ∂C ∂t = ∂ ∂x ( DγC ∂C ∂x ) (3.9) where C is the concentration of carbon in austenite, t is time, x is the distance away from the interphase into the austenite, and DγC is the diffusivity of carbon in austenite. For a spherical particle with radius r: δC δt = δ δr ( DγC δC δr ) + 2DγC r δC δr (3.10) In reality, the transformation of austenite to ferrite involves two mech- anisms: the diffusion of carbon from the ferrite product into the austenite parent, and the rearrangement of the FCC austenite crystal lattice into the BCC ferrite crystal lattice. In the carbon diffusion controlled mechanism discussed above, the greater proportion of the energy of transformation is dissipated through diffusion of solute through the solid. Where the rear- rangement of atoms at the interface becomes significant, the reaction be- comes ‘mixed mode’. It is also possible for the transformation to become interface controlled. [44] Under diffusion control, growth of the critical nucleus can be simplified as an advancing planar front. Zener [45] approximated the rate at which the front advances as: v = XγC,eq −X◦C√( X◦C −XαC,eq ) ( XγC,eq −XαC,eq )√D/t (3.11) 17 CHAPTER 3. LITERATURE REVIEW Figure 3.5: Parabolic growth of allotriomorphic ferrite. S/2 = αt0.5 and L/2 = βt0.5 are the half-thickness and half-length of the allotriomorphs. α and β are the parabolic growth rate constants for thickening and lengthening [46]. where XγC,eq and X α C,eq are the equilibrium concentrations of carbon in austen- ite and ferrite, and X◦C is the bulk carbon concentration of the alloy. The above simplification is not a solution of the underlying diffusion prob- lem; however, analytical solutions of the diffusion problems confirm parabolic growth rates before soft impingement takes place [9]. This has also been ver- ified experimentally. The data of Bradley and Aaronson [46], for instance clearly shows a parabolic relationship (figure 3.5). The use of the carbon diffusion model to describe ferrite transformation is quite common. An example of an application is the work of Kamat et al. [32], who developed a finite difference model based on equations 3.9, 3.10 for isothermal transformation in grade 1010 and 1020 steels. Their results can be seen if figure 3.6. While the planar geometry model gives good initial agreement, later stages of the reaction are better described by the spherical geometry model. 18 CHAPTER 3. LITERATURE REVIEW Figure 3.6: Model of Kamat et al.[32] Investigating a ternary Fe-C-X system (where X represents a substitu- tional alloying element) presents complications over the simple binary Fe-C system, due to the much higher diffusivity of interstitial carbon relative to substitutional alloying elements. Since carbon diffusion is very rapid, full equilibrium can be assumed in the case of Fe-C alloys for most of the trans- formation. However, it is not reasonable to expect full equilibrium in sub- stitutional alloys, since transformation rates exceed the rate of diffusion of some components in the system. Furthermore, the rate of diffusion of inter- stitial atoms is much higher than that of substitutional atoms. Three con- ditions could occur during ferrite formation: ortho-equilibrium (OE), para- equilibrium (PE) and negligible partitioning local equilibrium (NPLE) [47]. Under ortho-equilibrium, each component has equivalent chemical po- 19 CHAPTER 3. LITERATURE REVIEW tentials in both the parent and product phases. Both interstitial and sub- stitutional components diffuse during transformation. Under PE, only the interstitial component (carbon) reaches a state of equilibrium; substitutional atoms are essentially immobile, such that the concentration of substitutional elements in the parent remains unchanged after transformation. Transfor- mations under PE tend to proceed at higher rates. The third case, NPLE, is an intermediate condition between the two extremes of OE and PE; substi- tutional atoms can diffuse locally, but cannot reach equilibrium in the bulk phases. In systems under NPLE conditions that lie closer to PE, limited local diffusion of substitutional solutes creates a sharp spike-like pile-up of solute atoms in front of the advancing ferrite interface, yet the lack of long range diffusion leaves the bulk substitutional composition of the alloy unchanged [48, 49, 47]. In their study of ferrite growth in Fe-C-X steels, Enomoto and co-workers [38, 41, 42] carried out their calculations under OE, PE and NPLE. They found that reaction kinetics followed NPLE at higher transformation temper- atures, and PE at lower transformation temperatures. A later investigation by Tanaka et al.[50, 51, 52] of transformations in quaternary Fe-C-Mn-X sys- tems found somewhat consistent results, showing a gradual shift away from PE as transformation temperatures were increased. Rates predicted by these models typically exceed that of experimental results. This is explained by the authors as a solute drag like effect (SDLE). In this theory, the ’spike’ like pileup of substitutional atoms tends to interact with the advancing phase boundary [53], reducing the interface mobility, and therefore the transforma- tion rate. The model of Kamat et al.[32], was applied by Militzer et al. [18] to A36 (Fe-0.17C-0.74Mn-0.012Si-0.040Al wt%) and DQSK (Fe-0.038C-0.30Mn-0.025Ni- 0.033Cr-0.040Al wt%) steels transforming under continuous cooling. It was found that for the more manganese rich A36 steel, the carbon diffusion model predicted transformation rates in excess of what was experimentally observed 20 CHAPTER 3. LITERATURE REVIEW in the earlier stages of growth; this was attributed to the modification of car- bon diffusion by solute drag due to manganese, and it was therefore neces- sary to reconsider the equilibrium conditions at the interphase. Considering a steady state enrichment of manganese at the interphase due to segregation, the thermodynamic conditions at the interphase were re-assessed by includ- ing a ’segregation factor’ dependent on the ability of manganese to follow the movement of the interphase. Hutchinson et al.[44] developed a carbon diffusion based model describing Fe-C-Ni alloys where they identified a transition from PE to NPLE during isothermal growth of ferrite, where the local diffusion of nickel was rate- controlling. Growth was initially fast and fit PE conditions; as growth slowed later in the reaction (presumably due to a reduction in driving force) nickel atoms had time to diffuse through the interface and a nickel spike formed in front of the interface, promoting interfacial conditions to evolve towards NPLE. The authors found good agreement with their experimental data. 3.2.2 Bainite Formation As mentioned earlier, Widmanstätten ferrite is structurally similar to bai- nite. It seems to be generally accepted that Widmanstätten ferrite nucleates and grows through diffusional processes [54, 55, 49, 56]. While authors agree that the ferrite portion of bainite also nucleates through a diffusive process, there is disagreement on the growth mechanism of bainite. Two competing theories exist. The first describes bainite formation as a partially displacive mechanism where ferrite sheaves form in a manner similar to that of marten- site followed by diffusion of interstitial carbon atoms into the surrounding austenite and later precipitation of cementite [55]. The second theory pro- poses that the ferrite in bainite (referred to hereafter as bainitic ferrite) forms by a ledge-wise diffusion mechanism, and that it is simply a microstructural continuum of pearlite [48, 57]. 21 CHAPTER 3. LITERATURE REVIEW Displacive Theory In displacive transformations, there is a crystallographic dependence; the habit plane of martensite is macroscopically undistorted. That is, the habit plane is common to both the austenite parent and the martensite. This is due to the displacive transformation occurring by a homogeneous shear that is parallel to the habit plane. The displacive transformation therefore induces an Invariant Plane Strain (IPS), as there are no strains in-plane. It is important to note that this requires the interphase to be glissile. As a direct consequence of the IPS, the intersection between the surface of a specimen and of a BCC crystal growing displacively within that spec- imen will cause a rotation at the surface, about its intersection with the growing crystal’s habit plane. This phenomenon is referred to as the surface relief effect. Reliefs on the surface of samples that have undergone bainitic transformation are cited as evidence for the displacive formation of bainite [49]. The sheaf-like morphology of the ferrite plates is attributed to deforma- tion in the untransformed austenite as ferrite plates form; the FCC-BCC transformation is accompanied by significant dilation normal to the habit plane, which requires plastic accommodation in the adjacent austenite. Dis- locations formed in the austenite cause a loss of coherency in the interphase, halting the growth process. Further growth of ferrite must then come from sympathetic nucleation of new plates, causing the sheaf-like morphology of bainite [17]. In experiments carried out by Shipway and Bhadeshia [58] bainitic ferrite formation was reduced in samples that were plastically de- formed in the austenitic range, despite increased nucleation of bainite sub- units due to the higher dislocation density. The authors attributed this to dislocation forests interfering with glissile requirement of the interphase. Ferrite plates form in a displacive manner such that no diffusion of sub- stitutional atoms, including iron atoms, takes place, and interstitial atoms diffuse only after the initial displacive reaction [59]. According to the pro- 22 CHAPTER 3. LITERATURE REVIEW ponents of the displacive mode of transformation, carbon diffusion is much slower than bainitic ferrite growth, as justified by direct atomic resolution image and atomic resolution chemical analysis experiments [49]. The dis- placively formed ferrite plates would therefore be supersaturated with car- bon, which later diffuses to the austenite/ferrite interface and enriches the untransformed austenite, or precipitates as cementite. Carbon enrichment of the residual austenite can reach a level that stabilizes the austenite; the final fraction of bainite is therefore dependent on the composition of the final austenite [60]. In upper bainite, carbon is partitioned into the residual austenite, and the ferrite is largely carbide free. Cementite precipitation becomes thermo- dynamically possible when carbon concentration in the austenite reaches the solubility limit. Where no kinetic hindrances are present, carbide formation accompanies ferrite growth, until some limiting temperature. The precipi- tation of carbides from residual austenite prompts formation of secondary ferrite. Given the very low diffusivity of iron and substitutional atoms at the temperatures involved, and the supposed absence of incoherent inter- faces or grain boundaries to start the process, the secondary ferrite is not likely to form through a diffusive mechanism and is far more likely to form displacively [49]. Nakamura and Nagakura [61] suggest that cementite forms directly from austenite on the ferrite-austenite interface, and grows by rapid diffusion. Ohmori and Maki [62] describe a mechanism where platelets form on the edges of the growing ferrite prior to impingement. In lower bainite, there is a fine dispersion of plate-like carbides inside the ferrite plates, arranged along the same crystallographic direction as the ferrite plates they populate. In-situ hot-stage TEM by Kang et al.[63] showed that lower bainite ferrite remains supersaturated with carbon for some time after completion of growth. The carbides in the final product are mostly cementite, however, ǫ transition carbides have also been detected. A model, proposed by Matas and Hehemann [64] involves the formation of carbides 23 CHAPTER 3. LITERATURE REVIEW which then transform to cementite at a later time. There are two cases in the formation of carbides in lower bainite, that of high dislocation density, and that of low dislocation density [49]. In their model, Rees and Bhadeshia [60] consider the activation energy of bainite to be directly proportional to the driving force for bainite transfor- mation. The nucleation mechanism of bainite is held to be identical to that of Widmanstattätten ferrite. Nucleation is therefore only possible below the Widmanstattätten ferrite start temperature WS. A function GN(T ) is de- fined that describes the universal value of the minimum free energy change for displacive nucleation of ferrite. Ali and Bhadeshia [37] propose a lin- ear relationship between GN and temperature, based on experimental data. Work by Sarkar and Militzer [12] seems to confirm this. The model of Rees and Bhadeshia [60, 65] is as follows. The nucleation rate I is given by equation 3.12: I◦ = K1 exp [ −K2 RT − K2∆Gm rRT ] (3.12) where r, K1 and K2 are empirical constants. K1 is representative of the density of potential sites for nucleation, and at WS, I = K1. ∆Gm is the maximum free energy available for para-equilibrium nucleation, calculated using a parallel tangent construction [66]. For nucleation to proceed, ∆Gm < GN . Driving force for nucleation decreases as the transformation proceeds due to carbon enrichment of the parent austenite. This is represented by incor- porating the associated free energy change into ∆Gm. Buildup of carbon on the ferrite/austenite interfaces contributes to a drop in local driving force for nucleation on previously formed ferrite plates (auto-catalysis). An auto- catalysis factor β is defined that is empirically related to the mean concen- tration of the alloy. The effect of auto-catalysis is then modelled by equation 24 CHAPTER 3. LITERATURE REVIEW 3.13. I = I◦ (1− βθξ) (3.13) The overall growth rate is given by dξ dt = uK1 θ (1− ξ) (1 + βθξ) exp [ −K2 RT ( 1 + ∆G◦m r ) + Γξ ] (3.14) where Γ is given by equation 3.15. Γ = K2 (∆G ◦ m −GN) rRT (3.15) The above model assumes that carbon that diffuses out of the ferrite plates is uniformly distributed within the remaining austenite, which is not entirely true. Some of the austenite, supersaturated with carbon, remains in the form of isolated films between ferrite plates [65]. Para-equilibrium conditions are assumed, and so the carbon composition of the austenite films is arrived at by thermodynamic equilibrium calculations. Diffusional Theory In the diffusional theory of bainite transformation, the formation of bai- nite takes place through a random walk of atoms across the phase interface, with a bias towards the product phase. The bainite reaction is considered as a competitive eutectoid reaction, as opposed to a cooperative eutectoid transformation such as pearlite [48]. Proponents of the diffusional theory cite experimental evidence [67, 68] to support the lengthening and thicken- ing of bainite plates at diffusion controlled rates. Specifically, the diffusion 25 CHAPTER 3. LITERATURE REVIEW of carbon in austenite is most likely the rate determining mechanism [53]. Furthermore, experimental evidence is referred to where bainite plates have been observed to grow continuously, which would not be compatible with the step-wise growth suggested by the displacive theory of transformation [69]. The dominant effect on the driving force available for nucleation is that of the interfacial energy; in order to minimize the interfacial energy, the critical nuclei of a precipitate must be as coherent as possible with the ma- trix, resulting in nucleation with detectable kinetics, and prejudicing growth towards partial coherency [70]. However, once beyond the nucleation stage, growth of the precipitated phase is influenced more by the orientation depen- dence of the ferrite-austenite boundary mobility [48]. Precipitated crystals can be enclosed entirely by full or partially coherent boundaries. Given that the stacking sequence on the two sides of these boundaries is different, the boundaries are entirely immobile in the direction normal to themselves [54]. Misfit dislocations exist at the interphase, and measurements and observa- tions suggest that these dislocations are sessile [71]. The ferrite-austenite boundaries must therefore be displaced through the ledge mechanism [48], where plate growth is achieved through lateral diffusional migration of the ledges. This is in direct conflict with the displacive theory, which holds that the interphase is glissile. According to authors advocating the diffusional mechanism of transfor- mation, there is no fundamental difference in the mechanism of formation of Widmanstätten ferrite, upper bainite and lower bainite; at temperatures where bainite forms, there is no break in the edgewise growth rate as un- dercooling increases that would indicate a change of mechanism. Also, the edgewise growth of ferrite plates is too slow to cause carbon supersaturation in the ferrite [72]. The surface relief effect which is cited as a major piece of evidence by displacive theory advocates is questioned by Aaronson and co-workers [54]. Indeed, it is claimed by the diffusive camp that bainite formation does not 26 CHAPTER 3. LITERATURE REVIEW fulfil the phenomenological theory of martensite crystallography (PTMC), which is necessary for a displacive mechanism (the sessile austenite-ferrite interfaces being one violation of PTMC). Furthermore Muddle et al.[73] claim that PTMC is not a reliable indicator of a martensitic type of transformation. Aaronson et al.[74] point out that some diffusional phase transformation have crystallography that is predictable by PTMC due to the fact that their habit planes appear to be invariant planes. The displacive theory’s treatment of the incomplete transformation phenomenon is also questioned; by the diffusional theory, it is possibly due to a solute drag like effect [46]. Hillert [75] states that there is no clear signs of carbon supersaturation in bainitic ferrite during growth, and that kinetic indications exist that show that the ferrite/austenite interface is not closely related to interface features present in lath and plate martensite. In more recent work, Hillert and co- workers cite new metallographic evidence of carbon diffusion during ferrite growth [76]. They are convinced that Widmanstätten ferrite and the ferritic portion of bainite are the same structure [56]. Several authors have presented approaches to modelling the growth of plates by diffusion [77, 78, 79, 80, 81, 82]. A fairly recent model by Quidort and Brechet [53] expands upon the method used by Trivedi [81] where a simplified expression is used for the growth rate, assuming infinite mobility of the interface and neglecting capillary effects. The growth rate v is given by the solution of an expression of the dimensionless Peclet number p given by equation 3.16. p = 9 16π Ω2 ∗ = ρv 2DC (3.16) where ρ is the curvature at the plate growth tip, DC is the diffusivity coeffi- cient of carbon in austenite, and Ω∗ is an algebraic combination of the solute supersaturation in austenite, and is given by 27 CHAPTER 3. LITERATURE REVIEW Ω∗ = Ω◦ 1− 2 2 pi Ω◦ − 12piΩ2◦ (3.17) The solute supersaturation in austenite is defined as: Ω◦ = xγαC − x̄C xγαC − xαγC (3.18) The variables xγαC , x̄C , and x αγ C represent the atomic fraction of carbon in austenite at the interface, the average atomic fraction of carbon, and the atomic fraction of carbon in ferrite at the interface respectively. The values of xγαC and x αγ C are calculated assuming para-equilibrium at the ferrite/austenite interface. The assumption is made that the system selects a critical tip curvature ρC that gives the maximum rate of growth v◦. Then, v = v◦ = 27DΩ3 ∗ 256πρC (3.19) The authors include an adjustment of the carbon concentrations at the interface to account for an acceleration due to cementite precipitation based on a mass balance at the ferrite/austenite interface. They find, however, that the model predicts transformation rates significantly higher than shown by experimental data. They suggest that interaction of substitutional elements with the moving interface must be causing a solute drag like effect. They also suggest that the simplified thermodynamic conditions at the interface which were assumed for the model are not sufficiently accurate, and that for a general case, concentrations at the interface should be calculated with con- sideration of several interacting processes such as diffusion of several different elements, solute drag, and the FCC to BCC atomic rearrangement. 28 CHAPTER 3. LITERATURE REVIEW Figure 3.7: Dependence of bainite start and finish on austempering tem- perature. Solid lines show predictions calculated by the diffusional model, dotted lines show predictions calculated by the displacive model. TRIP steel (Fe-0.19C-1.45Si-1.54Mn-0.032Al wt%)1[83]. Minote et al.[83] examined bainite transformation in TRIP steel. Samples were austempered at temperatures between 300◦C and 450◦C and the bainite transformation was observed. The authors found that neither the diffusional, nor the displacive theory described the bainite transformation start and finish times over the entire temperature range. Rather, the diffusional theory was found to be sufficient above 350◦C while the displacive theory performed better below. A summary of these results can be seen in figure 3.7. 3.3 The Role of Niobium One of the main goals in thermomechanical processing of micro-alloyed steels is to achieve a fine microstructure in the final product. Higher strength and 1Original published in ISIJ International. 29 CHAPTER 3. LITERATURE REVIEW greater resistance to brittle fracture are two of the important benefits af- forded by smaller grain sizes [84]. The addition of micro-alloying elements such as titanium, niobium, aluminum, and vanadium is a common method of increasing the strength and brittle fracture resistance of steels through refinement of the final microstructure, achieved through the prevention or re- tardation of austenite recrystallization after deformation, or austenite grain growth during the reheat stage. Furthermore, an even distribution of fine stable carbonitride particles can be achieved during thermomechanical pro- cessing that serves to strengthen the steel [1]. Niobium in solid solution and niobium carbonitride precipitates have a significant effect on the condition of austenite [1, 84, 85, 86, 87, 88, 89], and on the nucleation and growth of the product phases [1, 90, 91, 92, 93, 94]. It is thus a very common micro-alloying element in low alloy steel grades with applications ranging from automotive to oil and gas line-pipes. Niobium is an alloying element in the steel stud- ied in this work; a brief review has therefore been made of its role in the thermomechanical processing of micro-alloy steels. 3.3.1 Niobium Precipitation and Interaction with Austen- ite Recrystallization At equilibrium, the concentrations of niobium present in austenite either as a solute in the matrix or in precipitate form can be calculated using the solubil- ity product of niobium carbonitride in austenite [1]. The solubility product can be derived using thermodynamic calculations, or experimentally, and will vary with the alloy composition. The precipitation of niobium carbonitride is heterogeneous in nature, and will typically occur at crystalline defects such as grain boundaries, incoherent twin boundaries, sub-grain boundaries, and dislocations. Interphase precipitation can also take place during the austenite to ferrite transformation; precipitates form on the advancing boundary be- tween austenite and ferrite, and are left behind in the ferrite as the boundary passes [1, 95]. 30 CHAPTER 3. LITERATURE REVIEW Figure 3.8: Effect of deformation on precipitation kinetics [2] The kinetics of precipitation of niobium carbonitrides in micro-alloyed austenite is typically rather sluggish due to the close proximity to the solvus while in the austenite phase field [1]. However, the introduction of defor- mation promotes nucleation of precipitates by increasing the availability of potential nucleation sites, which is of great significance in thermomechanical processing. This is demonstrated in figure 3.8 for a steel with alloy compo- sition (in wt%) of 0.17C-0.04Nb-0.011N[2]. Palmiere et al.[84] determined that localized precipitation of Nb(CN) was greater at favoured nucleation sites than in the bulk of the matrix by a factor of 1.5 − 2. Speer and Hansen [86] concluded that strain induced precipita- tion of niobium carbonitrides occurs in two stages. During the first stage, immediately after deformation, precipitates nucleate at grain boundaries and deformation bands. The second stage of precipitation occurs within grains. Should recrystallization precede the second stage of Nb(CN) precipitation, precipitation will occur in the matrix at a sluggish rate. However, if precipi- tation occurs before recrystallization, nucleation of Nb(CN) particles occurs 31 CHAPTER 3. LITERATURE REVIEW Figure 3.9: Effect of niobium on austenite recrystallization for a deformation temperature of 954◦C.[86]. on the sub-grain boundaries within unrecrystallized grains. The fine disper- sion of particles thus formed is capable of providing recrystallization growth retarding forces comparable in magnitude to the driving force for recrystal- lization. Essentially, Nb(CN) precipitation and austenite recrystallization are coupled. The formation of fine precipitates promoted by the substructure of deformed, unrecrystallized austenite serves to retard or temporarily halt the recrystallization process through grain boundary pinning [1, 84, 85, 86, 87]. The effect of the presence of Nb(CN) precipitates on recrystallization can be seen in figure 3.9. In the figure, the curve to the far left belongs to a steel with composition (in wt%) of 0.087C-1.90Mn-0.23Si. The middle and right curves belong to a steel with composition (in wt%) of 0.012C-1.98Mn- 0.28Si-0.11N-0.26Nb. Recrystallization occurs rapidly in the C-Mn steel. In the case of the far right curve, labelled “Precipitation Occurs,” all of the niobium is in solution prior to deformation, and thus precipitation of fine Nb(CN) is induced by deformation. The middle curve, labelled “Precipi- tation Cannot Occur” represents the case where Nb(CN) precipitation and 32 CHAPTER 3. LITERATURE REVIEW coarsening has been permitted prior to deformation, such that niobium in the austenite has equilibrated. By “Precipitation Cannot Occur” it is meant that no precipitation occurs during deformation, as all Nb(CN) that could have precipitated during deformation is already in precipitate form. Refer to the far right curve in figure 3.9. The deformation-induced precip- itation of niobium carbides significantly retards recrystallization, such that it is not complete until 104 seconds have passed. Where particles are coarse and wide-spaced, they have little effect on the recrystallization behaviour in the steel; however observing the middle curve in the figure, it can be seen that despite the lack of effective precipitates, recrystallization kinetics in the Nb steel are still slower than they are in the C-Mn steel. In order to ex- plain this, it must be noted that the niobium content of the steel is quite high relative to its carbon content (0.26wt% Nb versus 0.012wt%C): A large proportion of the niobium in the steel remains in solution throughout the process. The slower recrystallization kinetics relative to that of the C-Mn steel is explained by the solute drag effect of niobium on the migrating grain boundaries [1, 85, 86]. Conclusions from figure 3.9 can be summarized as follows: Although both solute atoms and precipitates can suppress recrystallization, fine precipi- tates are far more effective at slowing recrystallization than solute atoms. In the steel shown in the figure, the precipitation of 0.01wt% of the niobium dissolved in the steel as carbonitrides on the substructure of deformed the austenite (far right curve), prior to recrystallization, was more effective at suppressing recrystallization than keeping 0.20wt% niobium in solid solution (middle curve)[86]. 3.3.2 Effect of Niobium on the Austenite to Ferrite Transformation Niobium carbonitride precipitates serve as additional nucleation sites for fer- rite, in polygonal, acicular or bainitic morphologies. Furthermore, their exis- 33 CHAPTER 3. LITERATURE REVIEW tence tends to raise transformation start temperatures and thus promote the growth of higher temperature transformation products [1, 90, 91, 92, 93]. It has been suggested that the presence of fine deformation induced precipitates could later serve to slow the reaction through a boundary pinning mecha- nism [93] or through changes in local matrix chemistry and carbon fluxes caused by precipitation process. A recent study by Bréchet and co-workers [96] points to the contrary, however; in contrast to their appreciable effect on grain boundary motion, niobium carbonitride precipitates did not dis- cernibly effect the motion of the interphase during the austenite to ferrite transformation. Niobium in solid solution in austenite tends to suppress ferrite formation [1, 90, 91, 92, 93]. As the concentration of niobium in solution increases, transformation start temperatures are lowered, and the transformation pro- ceeds at a slower pace. The hardenability of micro-alloyed steels containing niobium can therefore be increased by dissolving a greater portion of nio- bium prior to transformation. The reduction in kinetics is more pronounced at lower cooling rates, where the driving force for transformation is low [91]. Figure 3.10 shows the effect of increasing amounts of niobium in solution on the transformation rate during an isothermal treatment at 670◦C; varying amounts of niobium in solution were achieve by holding samples for a range of holding times at 900◦C. There seems to be a lack of consensus on the mechanism by which niobium in solid solution suppresses the austenite to ferrite transformation. While some authors propose a solute drag mechanism on interphase boundaries [94, 93], others reject this [90, 91]. Authors who disagree with the solute drag mechanism propose the following: The misfit strain around niobium atoms that have segregated to austenite grain boundaries interact with and lower the surface energy of grain boundaries, and thus reduce the potency of nucleation sites. Additionally, niobium solute atoms at grain boundaries might be interacting with carbon atoms, either lowering the driving force 34 CHAPTER 3. LITERATURE REVIEW Figure 3.10: Effect of Nb in Solution on Transformation2 [4] for ferrite formation, or limiting the diffusion of carbon away from ferrite nuclei[90]. The solute drag theory is rejected by proponents of the displacive forma- tion theory for bainite. The presence of niobium solutes delays the onset of bainite formation; the diffusional solute drag theory is incompatible with the displacive mechanism[90]. 2Original published in ISIJ International. 35 Chapter 4 Experimental Methodology 4.1 Materials The experimental work was carried out on a low-carbon line-pipe grade steel sample provided by Essar Steel Algoma (see Table 4.1 for composition). Table 4.1: Composition of sample steel (wt %) C Mn S P Si Nb 0.06 1.49 0.002 0.009 0.2 0.047 Al Cr Cu Ti V N 0.038 0.02 0.02 0.001 0.003 0.0094 The dependence of the transformation behaviour of the steel on austenite grain size, retained strain, and cooling rate was investigated by conducting Continuous Cooling Transformation (CCT) tests. CCT tests were also used to evaluate the effect of niobium dissolution in austenite on austenite de- composition. In brief terms, the tests involved samples being machined from the above steel, austenitized, deformed, and cooled using different reheat conditions, strain levels, and constant cooling rates. Designing the CCT test regimes required data on austenite grain growth 36 CHAPTER 4. EXPERIMENTAL METHODOLOGY during the reheat stage, and austenite softening behaviour following deforma- tion. Preliminary experiments were therefore carried out prior to designing the CCT tests in order to generate the aforementioned data. They are dis- cussed in the following sections. 4.2 Simulations 4.2.1 Apparatus All simulations were carried out on a Gleeble 3500 Thermomechanical Simu- lator. Samples were held in water cooled copper grips, and heated resistively using an adjustable electrical current. Temperature control was achieved by varying the current passing through the samples according to feedback from a thermocouple welded on to the surface of the sample. For cooling regimes requiring high cooling rates, either compressed helium gas or wa- ter was used as a quench medium. A computer controlled hydraulic system applied compressive strain to the sample through the sample grips. Simula- tions were conducted either under vacuum (10−4torr/0.013Pa) or in an argon atmosphere. A dilatometer was used to measure diametric dilation of the sample dur- ing the simulation. A strain measuring device was substituted for cases where sample strains exceeded the range limits of the dilatometer and high sensitivity was not required. 4.2.2 Austenite Grain Growth Tests Rectangular test samples measuring 3mm x 6mm x 15mm were machined from the provided steel plate. See figure 4.1. Prior to each test, a Pt/Pt-Rh thermocouple was welded at the sample surface. The samples were heated at 5◦C/s to specific austenitizing temperatures and held there for a period of 5 minutes to allow for grain growth, after 37 CHAPTER 4. EXPERIMENTAL METHODOLOGY Figure 4.1: Austenite grain growth test sample geometry which time they were water-quenched to room temperature. The range of austenitizing temperatures used was 950◦C to 1250◦C, with tests carried out at 50◦C increments. The prior austenite grain size was measured using image analysis. In order to improve the definition of the prior austenite grain boundaries, the samples were annealed at 550◦C for 24 hours in an argon atmosphere fur- nace. The samples were then sectioned, ground, polished and etched using a saturated aqueous picric acid solution (see table 4.2 for etchant details). Photomicrographs of random locations on the etched samples were generated using an optical microscope. The prior austenite grain boundaries where then highlighted, and Clemex image analysis software was used to measure the av- erage prior austenite grain size (EQAD), according to procedures outlined in ASTM standard E 1382-97 1. 1E 1382-97: Standard test methods for determining average grain size using semi- automatic and automatic image analysis; ASTM International, 2004. 38 CHAPTER 4. EXPERIMENTAL METHODOLOGY Table 4.2: Etchants used for metallography Use Etchant and Composition Notes Revealing prior austenite - 100mL Saturated Aqueous Picric Acid Swab sample surface grain boundaries - 80 mg CuCl2 with NaOH after etching - 3 mL Wetting Agent Revealing ferrite/ferrite 2% Nital and ferrite/cementite boundaries - 98 mL Ethyl Alcohol - 2 mL Nitric Acid Revealing martensite/ LaPera’s Etchant retained austenite Equal Proportions of: - 4g Picric Acid + 100mL Ethyl Alcohol - 1g Sodium Metabisulphate + 100 mL Water 4.2.3 Austenite Softening Tests The experiments conducted to investigate austenite softening behaviour fol- lowed established procedures for “Double-Hit” tests: Cylindrical samples 1cm in diameter and 1.5cm in length were machined from the sample material. A Pt/Pt-Rh thermocouple was welded to the surface of each sample. Samples were then mounted in the Gleeble between hydraulically operated anvils. A diametric strain gauge was used to measure the strain in the sample, a load cell in line with the sample was used to measure compressive forces applied on the sample. See figure 4.2a for sample geometry. The samples were heated and held at austenitization temperatures ac- cording to the selected reheat regimes discussed above, then cooled to 850◦C at 10◦C/s. Once the samples’ temperatures were stabilized for 2 seconds at 850◦C, they were subjected to a strain of 0.3 at 1s−1 in the first “hit.” Following several different holding times (5 through 60 seconds), the samples were strained again in a second “hit”, this time past their yield point. See figure 4.2b for a schematic diagram of the test regime. 39 (a) (b) (c) Figure 4.2: Double hit test. (a) Sample geometry, (b) Test regime, (c) ex- ample of results 40 CHAPTER 4. EXPERIMENTAL METHODOLOGY Values for true stress and true strain were calculated for each sample using load and deformation data acquired during each test. The yield stress at each ‘hit’ was defined as the stress at an offset strain of 0.002. The degree of softening in a sample was defined by: Softening = σmax − σy,2 σmax − σy,1 (4.1) where σy,1 and σmax are the yield stress and maximum stress during the first hit, and σy,2 is the yield stress during the second hit. The variables σmax, σy,1, and σy,2 are shown in figure 4.2c. 4.2.4 Continuous Cooling Transformation Tests The data generated in the experiments described above were used to de- termine the appropriate regimes for the CCT tests. Schematics of the test regimes can be seen in figure 4.3a. The samples were heated to 1000◦C or 1100◦C, cooled at 10◦C/s to 850◦C, left undeformed or deformed to a strain of 0.3 or 0.6 at 1s−1 and the immediately cooled at 50◦C/s to 800◦C to avoid softening in the deformed samples. The samples were then cooled to room temperature at constant cooling rates of 1◦C/s to 50◦C/s. (a) (b) Figure 4.3: Test regimes. (a) CCT (b) Nb-in-solution CCT regime 41 CHAPTER 4. EXPERIMENTAL METHODOLOGY (a) Sample for tests without deformation (b) Sample for tests with deformation Figure 4.4: CCT test samples Two different sample geometries were used: Hollow cylindrical tubes for tests that did not require deformation (figure 4.4a), and solid cylindrical bars for tests that required deformation (figure 4.4b). Niobium Dissolution Continuous Cooling Transformation Tests Investigating the effect of niobium dissolution on the transformation be- haviour of the steel required changes to the established CCT test procedures explained above. It was determined that 1 minute at 1200◦C was sufficient to dissolve all niobium carbonitride precipitates [97]. In order to assure full dissolution of niobium, a hold time of 2 minutes at 1200◦C was selected. The austenite grain growth data for the steel showed however that this would result in a large austenite grain size in excess of 100µm, and would not be reflective of industrial conditions. A grain refining step was therefore introduced: Once the niobium dissolution procedure was complete, samples were cooled at 10◦C/s to 1050◦C and subjected to a strain of 0.3 at a rate of 1s−1 in order to induce recrystallization of the austenite grains. Once deformed, the samples were held for a predetermined period of time to allow for full recrystallization 42 CHAPTER 4. EXPERIMENTAL METHODOLOGY of the austenite grains. The samples were then either cooled at 50◦C/s to 850◦C, left undeformed or subjected to a strain of 0.3 at a rate of 1s−1, then cooled at 50◦C/s to 800◦C to avoid softening. All samples were then cooled to room temperature at constant cooling rates between 5◦C/s and 50◦C/s. A schematic of the test regime can be seen in figure 4.3b. The time for full recrystallization was determined from double hit tests at 1050◦C. Assuming that 100% softening corresponded to a fully recrystallized condition in the austenite, an optimal holding time at 1050◦C. Several niobium-in-solution CCT samples were water quenched immedi- ately after the recrystallization step and etched with a picric acid solution to reveal the recrystallized austenite grains. The recrystallized grain size was then measured by image analysis using the same methods as previously described. Data Processing During cooling, dilation data acquired during each test were plotted against the corresponding sample temperatures. See figure 4.5a for an example. Two linear portions can be seen in the plot. The linear region at higher temperatures shows the thermal contraction of the sample in the austenitic region, while the linear region at lower temperatures shows that in the ferritic region. The transition region between the two linear regions corresponds to the transformation of the austenite FCC structure to BCC structure in the ferrite; the expansion of the sample in this region is associated with the greater atomic volume of the BCC structure relative to the FCC structure. This transition region was used to track the decomposition of the austenite through a simple application of the lever rule (figure 4.5a). Figure 4.5b shows an example of a transformation curve calculated from dilation and temperature data. Analysis of the transformation dilation data was supplemented by quan- titative analysis of sample microstructures. Each sample was sectioned, 43 CHAPTER 4. EXPERIMENTAL METHODOLOGY (a) (b) Figure 4.5: CCT dilation data processing: Dilation data and lever rule (a); calculated CCT transformation curve (b). polished, and etched in a 2% nital solution to delineate ferrite/ferrite and ferrite/cementite boundaries to allow identification of ferrite and bainite. Optical micrographs of the etched surfaces were used to measure the frac- tion of ferrite in each sample, using the point count method outlined in the ASTM standard E 562. The samples were then re-polished and etched once more, this time in LePera’s solution, revealing regions of martensite/ retained austenite (MA). Image analysis software was used to measure the fraction of MA in each sample. The remaining fraction of the microstructure in each sample was considered to be bainite. 44 Chapter 5 Results and Data Analysis 5.1 Preliminary Test Results Austenite Grain Growth A brief study of austenite grain growth was conducted on the steel in order to determine the appropriate reheat conditions for the CCT tests. Observation of the austenite grain growth test samples revealed a range of average equiva- lent austenite grain diameters Dγ (EQAD) between 10µm and approximately 150µm for 5 minute holding times between 1000◦C and 1250◦C. Image anal- ysis was carried out on samples showing austenite grain sizes relevant to industrial processes (10 - 40µm). Figures 5.1a and 5.1b show the distribution of EQAD’s for holding tem- peratures of 1000◦C and 1125◦C respectively. Increasing the holding temper- ature resulted in larger austenite grain sizes. This trend can be seen in figure 5.1c, which shows the mean EQAD’s for the reheat temperatures analysed. The trend resembles an exponential function. It was observed that greater reheat temperatures gradually shifted the grain size distributions away from normality; a ‘tail’ developed in the grain size histograms, due to the onset of abnormal grain growth. 45 CHAPTER 5. RESULTS AND DATA ANALYSIS 5 10 15 20 25 0 20 40 60 80 100 120 140 160 180 N um be r o f G ra in s Austenite Grain EQAD [ m] (a) 0 20 40 60 80 100 0 10 20 30 40 N um be r o f G ra in s Austenite Grain EQAD [ m] (b) 1000 1050 1100 1150 10 20 30 A us te ni te  G ra in  E Q A D  [ m ] Holding Temperature [°C] (c) Figure 5.1: Austenite grain size distributions after 5 min at 1000◦C (a), 1125◦C (b). Mean grain diameter for range of holding temperatures plotted in (c). 46 CHAPTER 5. RESULTS AND DATA ANALYSIS Reheat conditions were selected for the CCT tests that produced suffi- ciently uniform austenite grain size distributions: 5 minutes at 1000◦C and 5 minutes at 1100◦C, resulting in mean Dγ’s of 10µm and 17µm. Attempts to produce Dγ’s beyond 17µm by adjusting the holding time and/or temper- ature failed to produce sufficiently uniform grain size distributions. Austenite Softening Recrystallization in austenite following deformation during CCT simulations was of concern; it was necessary to preserve the flattened austenite grain structure in order to measure the effect of retained strain on phase trans- formation behaviour in the steel. Softening following deformation is a direct consequence of recovery and recrystallization. “Double-Hit” tests measuring the degree of softening (as described in the preceding chapter) were utilized to investigate recrystallization kinetics in the steel. The calculated results can be seen in figure 5.2. The initial 10 - 20 % of the softening was assumed to be due to recovery, while the remainder was attributed to recrystallization [98]. Samples with an initial average austenite EQAD of 17µm were somewhat more resistant to recrystallization in comparison to samples with that of 10µm. While the cause of this difference in recrystallization kinetics was not investigated in the present study, it was taken into consideration when de- signing the following CCT test procedures. It is likely that the finer austenite grains produced at 1000◦C promoted recrystallization. The Niobium-in-solution CCT tests included an additional grain-refinement step involving a strain of 0.3 at 1050◦C, followed by holding at 1050◦C for a predetermined time to allow recrystallization. The time required for recrys- tallization was determined by performing ’double-hit’ tests, as described in the previous chapter. Test results suggested an optimum holding time of 20 seconds for full recrystallization. 47 CHAPTER 5. RESULTS AND DATA ANALYSIS 10 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 D eg re e of  S of te ni ng Inter-hit Time [s]  D  = 10 m  D  = 17 m Figure 5.2: Austenite softening behaviour at 850◦C, for initial γ - EQAD’s of 10 and 17µm. 5.2 CCT Test Results CCT tests were carried out for each of the 10 and 17µm initial grain diam- eters with three different levels of applied strain: ǫ = 0, 0.3, and 0.6. Each initial austenite grain size and strain level was then subjected to cooling rates between 5 and 50◦C/s. It was not possible to separate the ferrite and bainite portions of the trans- formation using the dilation response of the sample. The transition from fer- rite to bainite was smooth, and no transformation stasis was observed. The fraction of each constituent was instead measured through image analysis. However, the smooth transition complicated the image analysis also; identi- fication of bainite was made difficult by the presence of highly non-polygonal ferrite phases that were at times indistinguishable from the bainite (see fig- 48 CHAPTER 5. RESULTS AND DATA ANALYSIS ure 5.3). An effort was made to remain consistent in identifying the phases, yet it was recognized that any measurements made would be approximate at best. An error of 10% in the measurement was considered appropriate. It was assumed that all ferrite formed did so prior to the onset of pearlite and/or bainite formation. The final fraction of ferrite would therefore be present at the pearlite/bainite transformation start temperature, or equiv- alently the ferrite transformation stop temperature Tfs. The value of Tfs could then be approximated by comparing the fraction of ferrite in each sam- ple measured by image analysis to the transformation curve of that sample calculated using its dilation response. It was found that the decreasing the prior austenite grain size Dγ and increasing the amount of strain imparted on the austenite ǫ had similar effects on the transformation behaviour in the steel. An effective grain size Deff was therefore introduced to combine the initial austenite grain size Dγ with strain ǫ, where [99]: Deff = Dγ exp(−ǫ) (5.1) Equation 5.1 can be applied under no-recrystallization conditions only. This was confirmed for the present CCT tests by austenite softening tests as discussed previously. Effect of Cooling Rate Transformation start temperatures Ts were lowered by as much as 59 ◦C (for Deff = 17µm), and ferrite stop temperatures Tfs were lowered by as much as 73◦C (for Deff = 5µm) as the cooling rate was increased from 5 ◦C/s to 50◦C/s. Plotting austenite fraction transformed vs temperature over the course of the transformation (figure 5.4), the effect of cooling rate on austenite decomposition can be seen clearly. Metallographic observation of the test samples revealed that lower tem- perature transformation products were present in greater amounts at higher 49 (a) Dγ = 10µm, ǫ = 0, q = 5 ◦C/s (b) Dγ = 10µm, ǫ = 0, q = 50 ◦C/s (c) Dγ = 10µm, ǫ = 0.6, q = 5 ◦C/s (d) Dγ = 10µm, ǫ = 0.6, q = 50 ◦C/s (e) Dγ = 17µm, ǫ = 0, q = 5 ◦C/s (f) Dγ = 17µm, ǫ = 0, q = 50 ◦C/s (g) Dγ = 17µm, ǫ = 0.6, q = 5 ◦C/s (h) Dγ = 17µm, ǫ = 0.6, q = 50 ◦C/s Figure 5.3: Photomicrographs of CCT samples, 2% nital etch 50 CHAPTER 5. RESULTS AND DATA ANALYSIS 450 500 550 600 650 700 750 800 0.0 0.2 0.4 0.6 0.8 1.0  50 °C/s  20 °C/s  5 °C/s Fr ac tio n Tr an sf or m ed Termperature [°C] Figure 5.4: Effect of cooling rate on transformation for Dγ = 17µm and ǫ = 0. cooling rates; the fraction of polygonal ferrite decreased, as can be seen in figures 5.3a and 5.3f, and figures 5.3e and 5.3f. The photo-micrograph in 5.3e shows the microstructure resulting from cooling unstrained austenite with an average grain diameter of 17µm at a rate of 5◦C/s. The product microstruc- ture is composed primarily of polygonal ferrite (90%). Figure 5.3f shows the product of cooling austenite in the same condition as that of 5.3e at a rate of 50◦C/s; in this case there is very little polygonal ferrite present, and the structure consists mainly of bainite(74%). The effect of cooling rate on the fraction of bainite was more pronounced in coarser, undeformed austenite grains. Deformation and austenite grain refinement seemed to reduce the effect of the cooling rate on the fraction of constituents formed. In all cases, increasing the cooling rate refined the final microstructure. Figures 5.3c and 5.3d, shows the effect of cooling rate on the resultant mi- crostructures of austenite with an average grain diameter of 10µm subjected 51 CHAPTER 5. RESULTS AND DATA ANALYSIS to a strain of 0.6, cooled at 5◦C/s and 50◦C/s, respectively. Although both cooling rates result in a microstructure consisting mainly of polygonal fer- rite, increasing the cooling rate from 5◦C/s to 50◦C/s serves to refine the microstructure. Etching the same samples to reveal martensite and retained austenite (M/A) showed an increase in the fraction of M/A with rising cooling rates. The M/A that formed under higher cooling rates was also finer and more evenly distributed. Effect of Initial Austenite Grain Size It was found that samples with Dγ = 10µm transformed at higher tempera- tures than those with Dγ = 17µm. Figure 5.5 shows austenite decomposition versus temperature for undeformed samples cooled at 50◦C/s. The shift in transformation temperatures associated with a change in Dγ can be observed in the transformation curves. This change can be explained by noting the greater grain boundary area density in finer grained materials which serves to increase the availability of nucleation sites. Higher transformation temperatures in samples with Dγ = 10µm resulted in greater fractions of polygonal ferrite. The effectiveness of lowering Dγ on increasing the fraction of ferrite was much more pronounced at higher cooling rates. Whereas the difference in the fraction of ferrite after cooling undeformed austenite at 5◦C/s is essentially equivalent for both Dγ’s - the difference in results is within experimental error - cooling undeformed austen- ite at 50◦C/s resulted in an appreciable increase in the fraction of ferrite after a drop of Dγ from 17µm to 10µm: At ǫ = 0 and q = 50 ◦C/s, Xf = 0.72 for Dγ = 10µm, versus Xf = 0.20 for Dγ = 17µm. Respective photomicrographs are shown figures 5.3a and 5.3b. Reducing the initial austenite grain also significantly increased the frac- tion of M/A in the samples; this was attributed to the greater carbon en- richment in untransformed austenite due to the early formation of greater 52 500 550 600 650 700 750 800 0.0 0.2 0.4 0.6 0.8 1.0  D  = 10 m  D  = 17 m Fr ac tio n Tr an sf or m ed Temperature [°C] Figure 5.5: Effect of Dγ on transformation in samples with ǫ = 0 and q = 50◦C/s. (a) (b) Figure 5.6: Photomicrographs of CCT samples for ǫ = 0, q = 50◦C/s, Dγ = 10µm (a), and ǫ = 0, q = 50◦C/s, Dγ = 17µm (b). LePera etch. 53 CHAPTER 5. RESULTS AND DATA ANALYSIS fractions of polygonal ferrite, and the lack of carbide precipitation which would have otherwise occurred during bainite formation [100]. Figure 5.6 shows an etch of undeformed samples with Dγ = 10µm and Dγ = 17µm, cooled at 50◦C/s. The light phase is M/A and the dark background is ferrite and bainite. The figure shows a rather dramatic case of the effect of Dγ on the fraction of M/A: An M/A fraction of 0.06 for Dγ = 17µm and 0.11 for Dγ = 10µm, at an equivalent cooling rate, and no deformation. Effect of Strain Introducing strain in the austenite at 850◦C (in effect flattening the austenite grains) shifted the transformation to higher temperatures. Much like reduc- ing the initial grain size, introducing greater amounts of strain ǫ promoted the growth of finer, more polygonal ferrite, and suppressed the formation of bainite. The effect of ǫ on the start temperature and kinetics of transforma- tion is illustrated in figure 5.7. The transformation curve is shifted to lower temperatures by up to 100◦C. Referring once more to figure 5.3 and comparing photomicrographs of samples with identical Dγ and q, the effect of introducing ǫ can be readily observed. Samples that have undergone deformation show finer, more ferritic microstructures. For the case of Dγ = 17µm and q = 50 ◦C/s, the measured fraction of bainite decreased from 0.74 to 0.15 with the introduction of a strain of 0.6. The effect of ǫ on the fraction of bainite is more pronounced in samples with Dγ = 17µm, however the most fine, ferritic microstructure after q = 50◦C/s (Xf = 0.72, XM/A = 0.11) was achieved with Dγ = 10µm and ǫ = 0.6. Introducing ǫ from 0 to 0.6 doubled the fraction of M/A (from 0.06 to 0.12), in a manner similar to reducing Dγ (figure 5.8). Table 5.1 shows a summary of test conditions and results. In the table, Xf , XM/A, and Xother are the fractions of ferrite, M/A and ‘other’ constituents, respectively. The term ‘other’ used here is a feature of the methodology used 54 500 550 600 650 700 750 800 0.0 0.2 0.4 0.6 0.8 1.0   = 0   = 0.3   = 0.6 Fr ac tio n Tr an sf or m ed Temperature [°C] Figure 5.7: Effect of ǫ on transformation in samples with Dγ = 17 and q = 50◦C/s. (a) (b) Figure 5.8: Photomicrographs showing the effect of ǫ on the M/A fraction (light phase) in samples with Dγ = 17, and q = 50 ◦C/s. (a) ǫ = 0; (b) ǫ = 0.6. 55 CHAPTER 5. RESULTS AND DATA ANALYSIS to measure the constituents. Ferrite and M/A were measured directly, while pearlite/bainite fractions were calculated as the remainder of the sample. It is assumed that pearlite constitutes the ‘other’ phase at transformation temperatures above ∼ 650◦C, while below it is assumed that bainite forms. Assuming that ferrite formed first in the absence of any other reactions, the temperature at which ferrite formation stopped in each sample Tfs was extracted from its transformation curve using its measured value of Xf . The ±10% Xf measurement error is recorded in table 5.1. Note that it reflects in the values of Xb, and the extracted values of Tfs, also shown in the table. 56 CHAPTER 5. RESULTS AND DATA ANALYSIS Table 5.1: Results of quantitative image analysis Deff (µm) q ( ◦C/s) Ts ( ◦C) Xf Xb XM/A Tfs( ◦C) 5 5 771 0.84± 0.084 0.10± 0.084 0.06 714+10 −20 5 20 745 0.83± 0.083 0.10± 0.083 0.07 656+16 −25 5 50 734 0.75± 0.075 0.14± 0.075 0.11 651+13 −17 7 5 768 0.85± 0.085 0.09± 0.085 0.06 712+9 −15 7 20 746 0.79± 0.085 0.16± 0.085 0.05 675+10 −18 7 50 721 0.59± 0.059 0.30± 0.059 0.11 662−9 −9 9 5 762 0.89± 0.089 0.05+0.089 −0.050 0.06 682 +17 −47 9 20 736 0.80± 0.080 0.08± 0.080 0.12 626+15 −17 9 50 713 0.73± 0.073 0.15± 0.073 0.12 618+12 −14 10 5 736 0.83± 0.083 0.05+0.083 −0.050 0.12 681 +10 −15 10 20 722 0.86± 0.086 0.1± 0.086 0.04 643+13 −25 10 50 696 0.72± 0.072 0.18± 0.072 0.10 629+10 −12 13 5 755 0.83± 0.083 0.12± 0.083 0.05 673+15 −34 13 20 715 0.74± 0.074 0.20± 0.074 0.06 621+11 −12 13 50 704 0.61± 0.061 0.30± 0.061 0.09 627+7 −10 17 5 713 0.90± 0.090 0.09± 0.090 0.01 610+20 −49 17 20 702 0.33± 0.033 0.62± 0.033 0.05 658+4 −4 17 50 682 0.20± 0.020 0.74± 0.020 0.06 646+2 −2 57 CHAPTER 5. RESULTS AND DATA ANALYSIS 5.2.1 Niobium-in-Solution Tests The CCT tests discussed in the previous section were not designed with niobium dissolution in the austenite in mind. Niobium-in-solution tests were designed to investigate the effect of niobium dissolution on the transformation of the austenite. However, Dγ achieved by the grain refining step, 40µm, was much larger than the 10 and 17 µm average austenite grain diameters in the conventional CCT tests. Further grain refinement would have required strains exceeding the limits of the simulation equipment. Consequently, it was not possible to compare the results of the two sets of tests in terms of niobium dissolution exclusively; the influence of Dγ was also present. The effect of cooling rate on transformation temperatures was pronounced for both the deformed and undeformed cases. Increasing the cooling rate from 5◦C/s to 50◦C/s resulted in a decrease in Ts of 62 ◦C for austenite deformed to ǫ = 0.3 and 64◦C for undeformed austenite. This is reflected in the final microstructures of the test samples. There is a considerable difference between the microstructures achieved after cooling at 5◦C/s and 50◦C/s. See figure 5.9; 5.9a-5.9d show ferrite and bainite fractions, 5.9e and 5.9f show M/A (light phase). Whereas after 5◦C/s ferrite is present in appreciable quantities, 35% for ǫ = 0 and 78% for ǫ = 0.3, microstructures after 50◦C/s contained much reduced quantities of ferrite, 4% for ǫ = 0 and 16% for ǫ = 0.3. The greater fraction of ferrite in the lower cooling rate tests led to a greater fraction of M/A. In both cases, the fraction of M/A more than doubled with an increase of the cooling rate from 5◦C/s to 50◦C/s. The results also show that introducing a strain of 0.3 has a significant effect on austenite decomposition. The transformation start temperature was increased rather consistently across the cooling rates: 49◦C for 50◦C/s, and 47◦C for 5◦C/s. As would be expected, there was an associated increase in the relative quantity of ferrite in the product microstructure. Interestingly, in this case the M/A fraction did not increase appreciably. A summary of results for the Niobium-in-solution tests can be seen in 58 (a) ǫ = 0,q = 5◦C/s (b) ǫ = 0,q = 50◦C/s (c) ǫ = 0.3,q = 5◦C/s (d) ǫ = 0.3,q = 50◦C/s (e) ǫ = 0,q = 5◦C/s (f) ǫ = 0,q = 50◦C/s Figure 5.9: Nb-in-solution microstructures. (a)-(d): 2% nital etch showing ferrite, bainite; (e),(f): LePera etch showing M/A (light phase). 59 CHAPTER 5. RESULTS AND DATA ANALYSIS table 5.2. Table 5.2: Results of quantitative image analysis, Nb in solution Deff (µm) q ( ◦C/s) Ts ( ◦C) Xf Xb XM/A Tfs( ◦C) 30 5 730 0.78± 0.078 0.17± 0.078 0.05 611+11 −12 30 20 694 0.26± 0.026 0.68± 0.078 0.06 642+4 −5 30 50 668 0.16± 0.016 0.83± 0.078 0.01 633+3 −3 40 5 683 0.35± 0.035 0.60± 0.078 0.05 638+3 −2 40 20 652 0.10± 0.010 0.87± 0.078 0.03 638+3 −1 40 50 619 0.04± 0.0040 0.94± 0.078 0.02 626+2 −2 Effect of Initial Austenite Grain Size and Nb Dissolution Comparing the data from the niobium-in-solution tests to the data from the conventional tests in order to evaluate the coupled effect of the much coarser Dγ and Nb in solution, it was observed that transformation proceeded at lower temperatures. For instance, Ts for undeformed austenite cooled at 50◦C/s was 63◦C higher for Dγ = 17µm than Dγ = 40µm. The fraction of bainite formed in the sample was thus significantly greater. As can be seen in figure 5.9 lower bainite was present in large quantities in the niobium-in- solution tests, whereas it was almost absent in the conventional CCT tests. Also, due to their more ferritic character, the fractions of M/A were greater in the conventional CCT tests. It is not known to what extent these results can be attributed to either the greater grain size in the niobium-in-solution tests or the different states of dissolution of niobium in austenite. It is necessary to isolate these conditions by carrying out further tests where samples with Dγ = 40µm have niobium 60 CHAPTER 5. RESULTS AND DATA ANALYSIS 300 350 400 450 500 550 600 650 700 750 0.0 0.2 0.4 0.6 0.8 1.0  D  = 17 m, Nb precipitated  D  = 40 m, Nb in solution Fr ac tio n Tr an sf or m ed Temperature[ C] Figure 5.10: Coupled effect of Dγ and niobium dissolution on transformation in samples with ǫ = 0 and q = 50◦C/s. precipitated in order to reliably analyse the effect of niobium dissolution on the decomposition of austenite. The precipitation of niobium in the form of carbonitrides can be achieved by precipitation treatment at ∼ 900◦C. 61 Chapter 6 Model The overall transformation model consists of four individual parts. The first predicts the ferrite transformation start temperature, and the second de- scribes the ferrite growth. The third part of the model predicts the bainite transformation start temperature and the final fraction of non-bainitic fer- rite, which are assumed to be coincident. The final part describes bainite growth. The order in which the constituents of the model are presented in this chapter does not reflect their order of application in the model. 6.1 Ferrite Transformation Start The ferrite transformation start temperature is predicted using the approach of Militzer et al [18], previously mentioned in the literature review. Assuming that carbon diffusion is rate controlling, for a spherical nucleus, the steady state growth rate is given by: dRf dt = Dc xic − x◦c xic − xαc 1 Rf (6.1) 62 CHAPTER 6. MODEL Rf is the radius of the ferrite particle, Dc is the diffusion coefficient of carbon in austenite, x◦c is the average carbon bulk concentration, x α c is the equilib- rium carbon concentration in ferrite, and xic is the interfacial concentration of carbon, affected by manganese segregation. Integrating for a constant cooling rate q, where TN is the temperature of nucleation, Rf = √ 2 q ∫ TN T Dc xic − x◦c xic − xαc dT (6.2) Where r is the radius of the carbon diffusion field, the carbon concentration profile around the growing ferrite grain is given by xc(r) = ( xic − x◦c ) (Rf r ) + x◦c (6.3) The temperature corresponding to 5% ferrite transformation, defined as the cessation of nucleation (site saturation), is considered as the transfor- mation start temperature. Nucleation sites are steadily occupied, and in- creasing carbon concentration of austenite near nuclei due to the ejection of carbon from ferrite lowers the local driving force. These complex processes are simplified by introducing a critical carbon concentration x∗c above which no nucleation can occur. A critical radius r∗ corresponding to x∗c can be defined: r∗ = x∗c − x◦c xIc − xαc Rf (6.4) Then, the transformation temperature TS can be determined from: 63 CHAPTER 6. MODEL 2 3 4 5 60 90 120 150 180 210  D  = 10 m,  = 0  D  = 10 m,  = 0.3  D  = 10 m,  = 0.6  D  = 17 m,  = 0  D  = 17 m,  = 0.3  D  = 17 m,  = 0.6  D  = 40 m,  = 0  D  = 40 m,  = 0.3 T [C ] log(D2 eff q) Figure 6.1: Undercooling ∆T vs. log (D2effq) x∗c − x◦c = √ 2MP (x ∗ c − x◦c) q1/2Dγ √∫ TN TS Dc xic − x◦c xic − xαc dT (6.5) where x∗c and TN are used as fit parameters, and MP ≃ 2 is the number of nuclei per austenite grain and Dγ is the austenite grain diameter. When MP r ∗2 = D2γ, further nucleation is impossible. Figure 6.1 shows the experimentally measured undercooling required for transformation start, along with the model predictions. The effective austen- ite size Deff concept was used to combine the effects of initial austenite grain size and strain. Despite some scatter, single values of x∗c = 2.4x ◦ c and TN = 1050K seem to sufficiently predict transformation start in most 64 CHAPTER 6. MODEL cases. 6.2 Bainite Transformation Start Assuming that bainite nucleation and Widmanstätten ferrite are similar, the method of Ali and Bhadeshia [37] can be used to predict the bainite start temperature [36, 10, 12]. Ali and Bhadeshia proposed that the nucleation of Widmanstätten ferrite is similar to that of martensite; that is, the activa- tion energy for nucleation varies directly with the magnitude of the chemi- cal driving force, the difference being that Widmanstätten ferrite nucleates under para-equilibrium conditions where carbon diffuses in contrast to the diffusion-less nucleation of martensite. They found that the critical free en- ergy required to obtain a detectable degree of transformation is a linear func- tion of temperature, and independent of chemical composition for low alloy steels. It is therefore possible to predict the onset of Widmanstätten ferrite nucleation by comparing the chemical driving force for the FCC-BCC trans- formation with critical free energy of nucleation; where the chemical driving force exceeds the critical free energy, Widmanstätten ferrite nucleation has begun. Applying this approach to the onset of bainite formation requires quan- tifying the dependence of the critical free energy for bainite transformation start on temperature. The necessary data is extracted from experiments. As discussed in the previous section, the final fraction of ferrite in each experimental sample was measured using quantitative image analysis. As- suming that ferrite formed exclusively prior to all other microstructural con- stituents, the measured final fraction of ferrite Xf can be used to extract the temperature at which ferrite formation ceased, from the associated trans- formation curve constructed from dilation data. This is a simple matter of finding the temperature on the X vs. T curve (figure 6.2) that corresponds to the value of Xf . Bainite is assumed to form immediately after ferrite. The 65 CHAPTER 6. MODEL  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  600  620  640  660  680  700 Fr ac tio n Tr an sf or m ed Temperature [°C] Figure 6.2: Obtaining Tfs from transformation curve using Xf , measured through image analysis. temperature corresponding to Xf can then be equated with the temperature of bainite formation start, Tbs. Assuming also that all carbon atoms are ejected from ferrite into the remaining austenite during transformation, the concentration of carbon in the austenite xγc at the point where ferrite formation ceased can be calculated from Xf and the bulk carbon concentration x ◦: xγc = 1 1−Xf (6.6) Knowing T and xγc allows the calculation of the chemical free energy for transformation, ∆G, using phase equilibria generated by ThermoCalc software. A set of values for the critical free energy for bainite start ∆G∗bs is thus generated. Plotting ∆G∗bs versus Tbs (figure 6.3), the linear relationship is immediately apparent, and is given by: ∆G∗bs = 2570− 3.27Tbs (6.7) 66 CHAPTER 6. MODEL  350  400  450  500  550  600  650  590  600  610  620  630  640  650  660  670 ∆G  [J /m ol] Temperature [°C] Figure 6.3: Relationship between critical driving force for bainite formation ∆G∗bs and the temperature of bainite formation start Tbs Refer to figure 6.4. The critical driving force for bainite start ∆G∗bs eval- uated in this study (solid line) is compared to literature data (dotted and dashed lines) [37, 36, 10, 12]. The dashed lines indicate data for CP, DP, and TRIP steels. The close proximity of the lines seems to indicate independence from chemical composition, at least for the low alloy steels studied. The model divides the transformation path into individual time-steps. At each time-step, the temperature and concentration of carbon in austenite (calculated from the fraction of austenite remaining, as predicted by the ferrite model discussed in the next section) are used to calculate the chemical driving force for the FCC-BCC transformation ∆G. A ∆G versus T curve can then be constructed for the transformation path. This is shown as the solid line in figure 6.5. The dotted line in figure 6.5 represents the temperature dependence of ∆G∗bs given by equation 6.7. Where ∆G is greater ∆G ∗ bs, ferrite formation has ended, and bainite formation has begun. The intersection of the two curves is taken as Tbs. 67 CHAPTER 6. MODEL 500 520 540 560 580 600 620 200 400 600 800 1000 1200 Present StudyG * [J /m ol ] T [ C] Liu et al, Fazeli et al G* = 3.64T - 2840 Ali and Bhadeshia G* =3.637T - 2540 Sarkar and Militzer G* = 5.14T - 3784 Figure 6.4: Comparison of critical driving force for bainite formation with those used in other studies. The performance of the model can be seen in figure 6.6. Experimentally measured values of Xf are plotted on the abscissa, and model predicted values of Xf are plotted on the ordinate. The solid line represents a slope of unity and perfect agreement between experiment and model. For two of the transformation paths, the model values do not agree with experimentally measured values. This can be associated with the aforementioned image analysis measurement errors. 68 500 550 600 650 700 0 100 200 300 400 500 600 700 800 T bs G G  [J /m ol ] Temperature [°C] G*bs Figure 6.5: Calculating Tbs for the case of Dγ = 10µm, ǫ = 0.6, q = 20.  0  0.2  0.4  0.6  0.8  1  0  0.2  0.4  0.6  0.8  1 X Fe rri te , M od el X Ferrite, Experiment Figure 6.6: Performance of bainite start model 69 CHAPTER 6. MODEL 6.3 Ferrite and Bainite Growth Considering an isothermal reaction at some temperature T where the time required to obtain a certain fraction transformed X is known to be τ(X,T ), it is possible, using the additivity rule, to find the time required to obtain X under a constant cooling rate q = (dT/dt). In this case, equation 3.4 can be used to arrive at [34]: τ(X,T ) = ( ∂T ∂q ) X (6.8) Applying 6.8 to the JMAK equation, it is possible to express X as a function of q and T . X(τ, T ) = 1−exp [b(T )τn(T )] → X(q, T ) = 1−exp [ b(T ) ( ∂T ∂q )n(T ) X ] (6.9) The parameters b(T ) and n(T ) are written here as a function of tem- perature due to the fact that nucleation and growth are often temperature dependent. Rios [34] devised a method to extract the isothermal data required to ap- ply equation 6.9 from experimental continuous cooling transformation data. Where nucleation site saturation is present, the dependence of growth rate on temperature can be readily obtained from continuous cooling data. A special CCT diagram is constructed from experimental data for the transformation of concern. As opposed to the conventional method of mapping data on the T − t plane, it is more convenient that the data be plotted as T vs. q. An example constructed from experimental data is shown in figure 6.7. Each solid contour line in figure 6.7 represents a single fraction trans- formed. Rearranging equation 6.9, and taking the logarithm of both sides provides a useful relation: 70 CHAPTER 6. MODEL 0 3 6 9 12 15 640 660 680 700 T/ q(665°C,0.10)  4.9sT em pe ra tu re  [° C ] Cooling Rate [°C/s] X = 0.10X = 0.25X = 0.50 q(665°C, 0.10)  6 °C/s Figure 6.7: Schematic CCT diagram, plotted as T versus q. ln ln ( 1 1−X ) = ln b(T ) + n(T ) ln [( ∂T ∂q ) X ] (6.10) In equation 6.10, fixing T results in a linear relationship whose slope is given by n(T ). For cases where n is independent of temperature and therefore constant, the reaction is isokinetic, and equation 6.10 can be written as: ln ln ( 1 1−X ) = ln [ b(T ) ( |q(X0, T )| ( ∂T ∂q ) X0 )n] − n ln (|q(X,T )|) (6.11) where X0 is some fixed volume fraction. The value of n at some T can therefore be determined by plotting ln ln ( 1 1−X ) against ln q(X,T ) for that T . Doing so, however, requires knowledge of cor- responding values of X and q. This information is extracted from the con- 71 CHAPTER 6. MODEL 0.5 1.0 1.5 2.0 2.5 -2.5 -2.0 -1.5 -1.0 -0.5 0.0  T = 680°C  T = 650°C  T = 665°C ln ln  1 /(1 -X ) ln q Figure 6.8: Construction to determine n for continuous cooling transforma- tion in figure 6.7 tinuous cooling transformation diagram in figure 6.7. Intersections with the iso-X contour lines and horizontal lines (indicated in the figure with hollow circles) drawn at several temperatures within the range for which data is required, in this case 680◦C, 665◦C and 650◦C, give values of q which would yield the fractions transformed represented by the contour lines at those tem- peratures. Figure 6.8 shows plots of ln ln ( 1 1−X ) versus ln q(X,T ) for 680◦C, 665◦C and 650◦C. For this temperature range, n ≃ 1.78 and is constant. This is an indication that the reaction is effectively isokinetic - n does not vary with temperature. If n is known, b(T ) can be calculated by setting X = X0 in equation 6.11. Rearranging gives 72 CHAPTER 6. MODEL b(T ) = ln ( 1 1−X0 ) ( ∂T ∂q )n X0 (6.12) Values of ∂T/∂q are extracted from the CCT data in a manner similar to that by which q was obtained above. The value of ∂T/∂q for T = 650◦C and X = 0.10 is indicated in figure 6.7. Calculated values of b(T ) for a narrow range of ferrite transformation, in the case of Dγ = 10µm, ǫ = 0, and q = 5◦C/s, are plotted in figure 6.9. In the figure, for the above range of temperatures in this particular reaction, b is an exclusive function of T to a very good approximation. For this case, the differential form of the JMAK equation can be written as: ( dX dt ) = b(T ) 1 n · [ n(1−X)[ln(1−X)]n−1n ] (6.13) It is quite possible however, that dX/dt is not an exclusive function of T , as is assumed by the Rios method. Conceivably, the rate of decomposition of austenite can in some cases be affected by the fraction transformed. Lusk and Jou [101] showed that the rule of additivity remains valid in cases where the rate of transformation is affected by both T and X, provided that it is a separable function of T and X. That is, dX dt = H(T )L(X) (6.14) Jia et al [35] suggested a modification of the Rios method, where b would be considered as a separable function of T and X. In essence: b = f(T )g(X) (6.15) The differentiated form of the JMAK equation would then become: 73 CHAPTER 6. MODEL 640 650 660 670 680 690 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0 ln  b Temperature [°C]  X = 0.10  X = 0.50  X = 0.25 Figure 6.9: Calculated values of b versus T for the continuous cooling trans- formation in figure 6.7, where b is an exclusive function of T dX dt = b(X,T ) 1 n · { n(1−X)[− ln(1−X)]n−1n } 1 + (1−X) ( ∂b ∂X ) [ ln(1−X) b ] (6.16) where ∂b ∂X = f(T ) dg dX = b · [( dg dX ) g(X) ] (6.17) Taking the logarithm of equation 6.15, and substituting into equation 6.16 yields: ln ln ( 1 1−X ) = F (T ) +G(X) + ln [ q (X0, T ) ( ∂T ∂q ) X0 ]n − n ln [q(X,T )] (6.18) 74 CHAPTER 6. MODEL 640 650 660 670 680 690 700 710 720 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 ln  b Temperature [°C] Figure 6.10: Calculated values of b versus T , where b is a function of both T and X The parameters n and b (in the form of ln b(T,X) = F (T ) + G(X)) can be determined by following the methodology of the Rios, should n not vary with T . Rather, they must be obtained numerically. Figure 6.10 shows a plot of b(T,X) versus T for a reaction in which b is strongly dependent on X. This was the case for the majority of experimental data in this study, for both ferrite and bainite. Implementation of Modified Rios Method Transformation data sets acquired from experiments during the present study are divided into ferritic and bainitic sections. Austenite decomposition is assumed to begin with the formation of ferrite, and transition to bainite at later stages of transformation. The fraction transformed for each of the two constituents is normalized by a different method. For ferrite formation, 75 CHAPTER 6. MODEL the experimental fraction of austenite transformed Xexp at each recorded temperature datum is divided by the para-equilibrium ferrite fraction XPE at that temperature, such that the normalized fraction of ferrite Xα is given by: Xα = Xexp XPE (6.19) The normalized bainite fraction transformed Xb, on the other hand, is defined as Xb = Xexp −Xf 1−Xf (6.20) where Xf is the previously defined final fraction of ferrite. CCT dia- grams were constructed and n was extracted following the Rios method. It was found that n values for both the ferritic and bainitic portions of the transformation curve showed some temperature dependence, suggesting that additivity might not be fulfilled. This result was not surprising for the bainitic case, where sympathetic nucleation of ferrite plates invalidates the assumption of site-saturation, and the shifting morphologies and mechanisms affect growth rates. For the ferrite case, the temperature dependence of n might be explained by referring to the microstructural morphology of the product. Figure 6.11 shows an extreme example of the temperature depen- dence of n encountered during analysis. The range of constituents defined for this model as ‘ferrite’ is quite broad, encompassing morphologies from polygonal ferrite to acicular ferrite and structures at the transition point to bainite. It was found, however, that selecting an average value of n for each one of the ferritic and bainitic reactions yielded satisfactory predictions. The rate parameter b is extracted from the data as previously discussed. As expected, b shows a significant dependence on the fraction transformed, especially for cases where little polygonal ferrite is present. The modified form of the Rios treatment is therefore implemented. An equation that in- 76 CHAPTER 6. MODEL 1.5 2.0 2.5 3.0 3.5 4.0 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0  T = 700°C  T = 725°C  T = 750°C ln ln  1 /(1 -X ) ln q n = 0.91 n = 1.34 n = 1.76 Figure 6.11: Temperature dependence of n. Data shown is for Dγ = 10µm, ǫ = 0.6. cludes the effect of both T and X is used to fit the calculated b values, where: ln b = a(T − T0)2 + c ln(1−X) + d (6.21) The fit parameters T0 and c have been found to be independent of the initial conditions of the austenite. Single values of T0 and c are established for each of the ferritic and bainitic transformations. Parameters a and d on the other hand show strong dependence on the initial austenite conditions. To account for this in the ferritic portion of the transformation, the effective austenite grain size Deff , defined previously, is added to equation 6.21, such that: 77 CHAPTER 6. MODEL Table 6.1: Ferrite and bainite growth model parameters Parameter Ferrite Bainite n 1 0.5 a1 −1.41× 10−4 9.3× 10−6 a2 1.56× 10−4 1.62× 10−6 T0 602 884 c 0.1 0.35 d1 −0.05 −0.11 d2 0.52 0.01 ln b = [a1 lnDeff + a2] · (T − T0)2 + c ln(1−X) + d1Deff + d2 (6.22) In the bainite model, Deff is replaced by Drem, or the effective average diameter of remaining austenite, assuming spherical geometry. This is done to account for the reduced size of the austenite after ferrite formation has proceeded, assuming ferrite grows on the austenite grain boundaries towards the centre of spherical austenite grains. Drem is defined as Drem = Deff (1−Xf ) 1 3 (6.23) Values for n and the parameters describing b are listed in table 6.1. A value of n ≃ 1 for the ferrite portion of transformation is consistent with results from other studies [7, 10, 12, 35]. This value suggests the presence of site-saturation and one-dimensional growth of ferrite from austenite grain boundaries [19]. The bainitic transformation n ≃ 0.5 is slightly lower than values reported in literature [12, 35] for low alloy steels. Figure 6.12 shows some calculated transformation fractions compared to experimental data for the ferrite portion of the reaction. Examples of predic- 78 CHAPTER 6. MODEL 550 600 650 700 750 800 0.0 0.2 0.4 0.6 0.8 1.0  D  = 10 m,  = 0.6, q = 20 oC/s  D  = 17 m,  = 0.3, q = 12.5 oC/s  D  = 10 m,  = 0, q = 50 oC/s  Model Fr ac tio n Tr an sf or m ed Temperature [ C] Figure 6.12: Experimental data, prediction of ferrite start and growth mod- els. tions by the bainite growth model are shown in figure 6.13. Generally good agreement is achieved for most data sets. The use of the JMAK equation and additivity principle seems to offer an adequate prediction of the transfor- mation kinetics. Not all predictions are good, however; the ferrite prediction for the case of Dγ = 10µm/ǫ = 0/q = 50 ◦C, shown in figure 6.12, is such an example. An effort is made to formulate fit parameters that would help avoid discrepancies between calculated and experimental values for industri- ally relevant cases. In the more relevant cases where deformation is present, the model provides good agreement with experiments. Improvement of the model fit requires a more in-depth study of the effects of the initial austenite condition (Dγ,ǫ) and fraction transformed on the rate parameter b. The form of equation 6.22 is empirical. A more theoretical approach could yield better results. Furthermore, the effects of niobium in solution and niobium carbonitride precipitates on b were not considered in 79 CHAPTER 6. MODEL 450 500 550 600 650 700 0.0 0.2 0.4 0.6 0.8 1.0  D  = 17,  = 0, q = 20°C/s  D  = 40,  = 0, q = 12.5°C/s  D  = 40,  = 0.3, q = 50°C/s  Model Fr ac tio n Tr an sf or m ed Temperature [°C] Figure 6.13: Experimental data, and predictions of bainite growth model. the present model. A study of literature suggests significant influence of the state of niobium on transformation behaviour. The solute drag effect of niobium on the advancing interphase, serves to slow growth, while fine niobium carbonitride precipitates serve as extra nucleation sites. It is expected that as the initial austenite grain size is increased beyond those studied in this investigation, increased sympathetic nucleation during bainite formation will effect the quality of the model predictions. However, these grain sizes are not of major concern, as its not expected that they will be encountered during hot-rolling. 80 Chapter 7 Conclusions Experiments were conducted on a Ferrite-Bainite steel to investigate its transformation behaviour under varying processing conditions including re- heat temperature, degree of strain, and cooling rate. To this end, data has been acquired for austenite grain growth, softening following deformation in the austenite, and the kinetics and proportions of ferrite and bainite in the steel. Based on the data, the effect of varying the initial austenite con- ditions (austenite grain size and retained strain), and cooling rate on the transformation behaviour of the steel have been reported and analysed. Existing techniques for predicting the transformation start temperature, ferrite growth, bainite formation start temperature, and bainite growth have been used to model the decomposition of austenite. The model can be used to predict the temperature and kinetics of transformation, and the final fractions of ferrite and bainite in the steel. As study of the effect of the state of niobium dissolution in the austen- ite during transformation on transformation behaviour has been initiated. Further tests in this area are required in order to make any meaningful con- clusions. 81 CHAPTER 7. CONCLUSIONS 7.1 Future Work Recommendations The following are recommended as improvements to the model, and extension of the experiments: • The fit function describing the JMAK equation rate parameter b in the ferrite and bainite models could be improved. Although the cur- rent form seems to provide a satisfactory fit for industrially relevant conditions, it does not perform ideally for all cases. Further study of the effect of initial austenite grain size and retained strain on b is recommended. • Reducing the rather large measurement error for the final fraction of ferrite would significantly improve its predictive capabilities. An EBSD technique utilizing misorientation gradients has been investigated by Zaefferer et al [102] as a method to determine the fraction of bainite; an attempt could be made to implement this technique to supplement image analysis to this end. • Further study of the effect of the state niobium dissolution in austenite on transformation behaviour is necessary for any meaningful analysis of the subject, or its implementation in the model. CCT tests could be devised that follow the same procedures for austenitization, niobium dissolution and austenite grain refinement as the niobium-in-solution tests, with the modification that samples are held above the Ae3 tem- perature for enough time to ensure full precipitation of niobium car- bonitrides. In this way data can be generated for cases where niobium is precipitated, but where the initial austenite grain size is identical to the 40µm in the niobium-in-solution samples. 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