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A study of austenite grain growth in a Ti-Nb HSLA steel Lechuk, Steven John 2000

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A STUDY O F A U S T E N I T E GRAIN G R O W T H IN A Ti-Nb H S L A S T E E L by STEVEN J O H N L E C H U K B.APSC., The University of British Columbia, Canada, 1996. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR T H E DEGREE OF MASTER OF APPLIED SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (DEPARTMENT O F METALS AND MATERIALS ENGINEERING) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA NOVEMBER, 2000 ©Steven Lechuk, 2000 In presenting this thesis in partial fulfilment of the , requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of V \g-V--\s C~A rV.W^"vW Ev\5',-.<>g.c:^ The University of British Columbia Vancouver, Canada DE-6 (2/88) 11 ABSTRACT Austenite grain growth kinetics have been studied in a Ti-Nb microalloyed low carbon steel in the temperature range of 1100 to 1250°C, employing a Gleeble® 1500 thermomechanical simulator. No significant grain growth has been observed below 1100°C. The onset of grain growth at 1150°C, both normal and abnormal, is related to the coarsening and dissolution of precipitates. This is confirmed and quantified by transmission electron microscopy analyses. For this purpose, the statistical grain growth model of Abbruzzese and Liicke is combined with the model by Cheng et al. for the coarsening and dissolution of precipitates. An austenite grain growth model has been developed which correlates the time and temperature dependence of the pinning force to the dissolution kinetics of the Ti-Nb carbonitrides in the steel. The model predictions are consistent with the experimental observations of grain size and particle size evolution. iii TABLE OF CONTENTS Abstract ii List of Tables v List of Figures vi List of Symbols ix Acknowledgements xii Chapter 1 Introduction 1 Chapter 2 Literature Review 4 2.1 Grain Growth 4 2.1.1 General Observations 4 2.1.2 Normal and Abnormal Growth 4 2.2 Particle Pinning 5 2.2.1 Zener Drag 5 2.2.2 Grain Size Dependent Pinning 6 2.3 Modelling Grain Growth 7 2.3.1 Empirical and Theoretical Relationships 7 2.3.2 Statistical Models 9 2.3.3 Other Grain Growth Models 12 2.4 Grain Growth in Austenite 12 2.4.1 Plain Carbon Steels 12 2.4.2 High Strength Low Alloy Steels 14 2.5 Precipitation in Austenite 16 2.5.1 Niobium 16 2.5.2 Titanium 18 2.5.3 Complex Carbonitrides 19 2.6 Dissolution 20 2.6.1 General Observations 20 2.6.2 Modelling 21 2.7 Coarsening 23 Chapter 3 Scope and Objectives 36 Chapter 4 Experimental 37 4.1 Material 37 4.2 Methodology 37 4.2.1 Austenite Grain Growth 37 4.2.2 Optical Microscopy 38 IV 4.2.3 Scanning Transmission Electron Microscopy 39 4.3 Quantitative Metallography 40 Chapter 5 Experimental Results 44 5.1 Starting Material Conditions 44 5.2 Experimental Observations 45 5.2.1 Austenite Grain Growth Investigations 45 5.2.2 Precipitate Investigations 46 5.2.2.1 Chemical Composition and Morphology 46 5.2.2.2 Size Distributions 47 5.2.3 Austenite Grain Growth Behaviour 49 5.3 Austenite Grain Size Distributions 51 5.3.1 Estimation of a Three Dimensional Distribution 51 5.3.2 Experimental Observations 52 5.4 Discussion of Experimental Errors 53 Chapter 6 Modelling 69 6.1 General Approach 69 6.2 Input Parameters 70 6.2.1 Material Parameters 70 6.2.1.1 Grain Boundary Energy and Mobility 70 6.2.1.2 Interfacial Energy 71 6.2.1.3 Diffusivity 71 6.2.1.4 Solubility Products 72 6.2.2 Initial Parameters 73 6.2.2.1 Initial Grain Size Distribution 73 6.2.2.2 Initial Particle Size Distribution 74 6.2.2.3 Initial Particle Volume Fraction 75 6.2.3 Pinning Parameter 75 6.3 Austenite Grain Growth Model Predictions 76 6.4 Sensitivity Analysis of the Precipitation Model 77 6.4.1 Solubility Products 77 6.4.2 Interfacial Energy 79 6.4.3 Diffusivity 79 6.5 Model Predictions 79 Chapter 7 Summary and Conclusions 95 Appendix A Summary of Experimental Measurements 99 References 101 LIST OF TABLES Table 2.1. Experimentally determined grain growth exponents. 24 Table 2.2. Solubility products of niobium carbide and niobium 25 carbonitride in austenite. Table 2.3. Solubility product of titanium nitride in austenite. 26 Table 2.4. Solubility product of titanium carbide in austenite. 26 Table 2.5. Diffusion coefficient of titanium and niobium in austenite. 27 Table 4.1. Chemical composition of HSLA steel (wt. percent). 42 Table 5.1. Comparison of austenite grain size measurements versus 55 number of grains counted. Table 6.1. Summary of empirical fitting parameters used in the austenite 83 grain growth model. Table 6.2. Selection of (Nb,Ti)C material parameters. 83 Table A . l . Measured austenite grain sizes. 99 Table A.2. Measured precipitate sizes. 100 LIST OF FIGURES VI Figure 2.1. Experimental data on the ratio of limiting grain radius to particle 28 radius, as a function of the volume fraction of particles. ^ Figure 2.2. The effect of grain size on the Zener pinning force for a given 29 particle distribution^ Figure 2.3. Relation between observed grain-coarsening temperature of 30 austenite and computed temperature for complete dissolution of the microalloy carbides/nitrides.^ Figure 2.4. Comparison of predicted and experimental grain growth 31 behaviour in a Ti-Nb-Mo microalloyed steel.[27] Figure 2.5. Solubility product of niobium carbide in austenite. 32 Figure 2.6. Solubility product of niobium carbonitride in austenite. 32 Figure 2.7. Solubility product of titanium nitride in austenite. 33 Figure 2.8. Solubility product of titanium carbide in austenite. 33 Figure 2.9. Comparison of titanium and niobium solubility products in 34 austenite. Figure 2.10. Comparison of niobium and titanium diffusivities in austenite. 35 Figure 4.1. Configuration of Gleeble® 1500 thermomechanical simulator 43 for austenite grain growth experiments. Figure 4.2. Schematic diagram of the (a) plan view and (b) elevation view 43 of the specimen and specimen holder. Figure 5.1. Optical micrograph of transfer bar microstructure (arrow 56 indicating the presence of TiN particles). Figure 5.2. Optical micrographs of the austenite microstructure at 1100°C 57 after (a) 1 second and (b) 600 seconds. Figure 5.3. Optical micrographs of the austenite microstructure at 1150°C 58 after (a) 120 seconds, (b) 600 seconds and (c) 1200 seconds. Figure 5.4. Optical micrographs of the austenite microstructure at 1200°C 59 after (a) 1 second, (b) 900 seconds and (c) 1200 seconds. Figure 5.5. Optical micrographs of the austenite microstructure at 1250°C 60 after (a) 1 second, (b) 120 seconds and (c) 600 seconds. Figure 5.6. T E M replica micrograph showing mixed precipitates at 1100°C 61 (arrows indicating co-precipitation of niobium-rich particles onto existing titanium nitrides). Figure 5.7. T E M replica micrographs of (Nb,Ti)C particles at 1100°C after 62 (a) 1 second and (b) 600 seconds. Figure 5.8. T E M replica micrographs of (Nb,Ti)C particles at 1150°C after 63 (a) 1 second and (b) 120 seconds. Figure 5.9. Precipitate size distributions at 1100°C for the smaller, spherical 64 Nb-rich particles after: (a) 1 second (591 particles counted) and (b) 600 seconds (280 particles counted) ; and for the larger, cuboidal Ti-rich (TiN) particles after (c) 1 second (98 particles counted). Figure 5.10. Measured austenite grain sizes as a function of reheat temperature 65 and time. Figure 5.11. Comparison of grain diameter and grain volume distributions 66 obtained from samples reheated at 1150°C for 120 seconds (ai, &2) and 600 seconds soaking time (bi, b2). Figure 5.12. Austenite grain size distributions obtained for samples reheated at 67 1200°C for (a) 60 seconds, (b) 900 seconds and (c) 1200 seconds soaking time. Figure 5.13. Austenite grain size distributions obtained for samples reheated at 68 1250°C for (a) 60 seconds, (b) 120 seconds and (c) 600 seconds soaking time. Figure 6.1. Interfacial energies estimated for various carbides and 84 nitrides in austenite (y) and ferrite (a). [ 6 5 1 Figure 6.2. Comparison of predicted and calculated particle pinning forces 85 for (Nb,Ti)Cat 1150°C. Figure 6.3. Comparison of model predictions and austenite grain size 86 measurements using empirical fit parameters listed in Table 6.1. V l l l Figure 6.4. Comparison of reported NbC solubility products on the prediction 87 of (a) mean particle diameter and (b) particle volume fraction at 1100°C. Figure 6.5. Comparison of reported NbC solubility products on the prediction 88 of (a) mean particle diameter and (b) particle volume fraction at 1150°C. Figure 6.6. Evaluation of the effect of changes in interfacial energy on the 89 (Nb,Ti)C particle volume fraction at (a) 1100 and (b) 1150°C. Figure 6.7. Evaluation of the effect of changes in diffusivity on the (Nb,Ti)C 90 particle volume fraction at 1150°C. Figure 6.8. Predicted (Nb,Ti)C pinning forces from the dissolution, growth 91 and coarsening model at (a) 1100 and (b) 1150°C. Figure 6.9. Comparison of model predictions and grain size measurements 92 using the dissolution model fit parameters at (a) 1100 and (b) 1150°C. Figure 6.10. Model predictions of (a) mean particle diameter and (b) particle 93 volume fraction as a function of time for TiN at 1250°C. Figure 6.11. Comparison of final pinning forces of 5 and 11 mm"1 at 1250°C. .94 LIST OF SYMBOLS A mean grain area A,,A2 constants used in Equation 2.13 Ap mean particle area a constant used in Equation 6.2 b Burger's vector C constant used in Equations 2.5 through 2.7 Co constant used in Equations 2.4 c* concentration field D general diffusivity Dg average grain diameter Dgb grain boundary diffusivity D, initial grain diameter D0 diffusivity pre-exponential constant d individual grain diameter d mean particle diameter dm mean three dimensional grain diameter do initial mean particle diameter dA equivalent area diameter dave mean grain diameter dg median grain diameter dy equivalent volume diameter driving force for grain growth of grains of size / relative to size j FP particle pinning force fj fraction of grains in size class j fi(d) probability function for a log-normal distribution Mr) probability function for a normal distribution K constant used in Equation 2.3 Ks solubility product K0 coarsening parameter h Boltzmann constant, 1.38066 x 10"23 JK"1 grain boundary mobility M0 grain boundary mobility pre-exponential constant "j number of grains per unit volume in size class j Ntot total number of grains per unit volume n grain growth exponent distribution of particles p particle pinning parameter Po initial particle pinning parameter PT total grain boundary pinning forces Pf final particle pinning parameter Pppt pinning forces related to particles Pr residual pinning forces Q activation energy for diffusion Qzb activation energy for grain boundary mobility xi R grain radius RG gas constant, 8.3144 tool"1K'1 Ri grain radius of size class i Rc critical grain radius Rum limiting grain radius due to particle pinning r particle radius f mean particle radius s standard deviation for a log-normal distribution T absolute temperature t time t0 initial time Wjj probability that grains i and j are neighbours a constant used in Equation 2.8 y precipitate/matrix interfacial energy ysb grain boundary interfacial energy ju arithmetic mean for a normal distribution v volume fraction of particles cr standard deviation of a normal distribution A CKNO WLEDGEMENTS The author wishes to express his sincere appreciation to his research supervisors, Professors Matthias Militzer and E. Bruce Hawbolt, for their guidance, valuable discussions, generous support and constant encouragement throughout the course of this research. The author would also like to express his thanks to Mr. R. Cardeno, Mr. B. Chau, Mr. R. McLeod, Ms. M . Mager, Mr. C. Ng and Mr. P. Wenman for their technical support. The author wants to express his gratitude to Dr. L. Cheng and Dr. D. Meade for their help in finishing this thesis. 1 CHAPTER 1 INTRODUCTION The use of steel as an engineering material continues to attract considerable interest for a wide variety of applications. Reasons for this arise from the broad range of mechanical and material properties which may be obtained at relatively low cost. Traditionally, there have been few alternative materials which offer such versatility and are economically feasible on similar production scales. Increasing property requirement demands continue to advance steels through constant improvements in design and production. High strength low alloy (HSLA) steels were developed in the 1960's where microalloy additions and thermomechanical processing have been combined to attain a set of desirable mechanical properties through microstructural control. HSLA steels are predominantly low in carbon (0.05 to 0.15 weight percent) and are alloyed with small quantities of elements such as niobium, titanium and vanadium (0.10 weight percent or less). Having excellent strength, coupled with good toughness and weldability, microalloyed steels are now used in many construction, transportation, and pipeline applications. The associated mechanical properties of HSLA steels are largely governed by microstructural changes that occur during the rolling process. These changes are dependent upon both processing conditions in the hot mill, as well as the effects of microalloying. Upon exiting the reheat furnace, deformation begins in the roughing mill where the steel slab is reduced in thickness by a series of rolling passes. Further 2 deformation occurs in the finishing mill until a desirable thickness is reached, after which the material is cooled by a series of water sprays on the runout table and then coiled on a down coiler. During hot rolling, austenite grain growth is the dominant microstructural phenomenon in both the reheat furnace and between rolling stands after completion of recrystallization. Since the austenite microstructure after rolling and cooling on the run out table determines the final ferrite grain size, this plays a key role in determining the final mechanical properties of the hot-rolled steel product. The presence of second phase particles can have a significant influence on the kinetics of austenite grain growth. Microalloying elements such as niobium, titanium and vanadium are known to be strong carbide and nitride formers which can exist as precipitates at various stages during rolling. The main purpose of microalloying is to assist in producing a fine, final ferrite grain structure. This is partially achieved by selecting a processing route which provides for an extremely fine dispersion of very small carbides and/or nitrides which effectively hinder austenite grain growth. The degree to which austenite grain growth is inhibited will depend upon the size and stability of these second phase particles. This, in turn, depends on the amount, type and number of alloying elements present, as well as, the processing history of the steel. Thus, important changes in the structure and properties of HSLA steels can be produced by the careful selection of these microalloy additions and the processing path. Much effort has been devoted to investigating methods which can be used to accurately predict austenite grain growth in low carbon microalloyed steels. The use of 3 computer models is becoming an increasingly important element in achieving this goal. It is the aim of process modelling to quantitatively link the process parameters in the mill to the properties of the hot rolled steel product. However, previous grain growth models based on empirical relations have been inadequate for quantitatively predicting austenite grain growth in microalloyed steels. This inadequacy is mainly attributable to the inability of these models to accurately account for the pinning effects of second phase particles. Recently, greater success in describing austenite grain growth has been seen with the use of statistical models which are able to account for such effects. However, these models are limited in the sense that very simplified assumptions have been made to describe particle pinning as a function of time and temperature without taking into account the actual precipitation and dissolution kinetics The present research involves the study of austenite grain growth in a commercial Ti-Nb HSLA steel. The aim of this work is twofold. An investigation of the kinetics of austenite grain growth is first performed through a series of experimental studies. This includes a series of austenite grain size measurements over a relevant temperature range, as well as, an analysis of microalloy precipitates using transmission electron microscopy. This information is used for modelling austenite grain growth based on the dissolution and coarsening kinetics of microalloy precipitates. In this way, an austenite grain growth model has been developed which correlates the time and temperature dependence of the pinning force to the dissolution kinetics of the Ti-Nb carbonitrides in the steel. 4 CHAPTER 2 LITERATURE REVIEW 2.1 Grain Growth 2.1.1 General Observations It is generally accepted that grain growth in polycrystalline materials results from a decrease in grain boundary surface energy corresponding to a decrease in the total grain boundary surface area with increasing grain size. Generally, grain structures must fulfill two basic requirements:1'1 volume conservation is maintained, i.e., all of the grains are connected along shared surfaces and there is an equilibrium of surface tensions between connected grains. Thus, an inherent distribution of grain sizes within a given structure arises from achieving a minimum total free energy of the system and meeting the above requirements. It is these size differences between grains which provide a driving force for grain growth. Those grains with a size advantage over their neighbours would experience significant growth. Larger grains would grow at the expense of smaller grains, leading to an overall increase in grain size. 2.1.2 Normal and Abnormal Growth Normal grain growth is characterized by the maintenance of a uniform grain structure in which the shape of the grain size distribution remains approximately constant while the average grain size increases. Alternatively, abnormal grain growth is a process in which a non-uniform grain size distribution develops by a select number of grains growing more rapidly at the expense of others. A necessary condition for the occurrence 5 of abnormal grain growth is that normal grain growth is inhibited.^ There are several ways in which grain growth can be retarded, but the only known method of completely inhibiting grain growth in bulk material (as opposed to thin films or filaments) is by the introduction of second phase particles.[3] The total boundary area arising from the location of a second-phase particle at a grain boundary is less than that which arises if the particle is situated elsewhere in the matrix-phase. Consequently, grain boundary migration will occur only if the driving force for grain growth exceeds the pinning (drag) force exerted by particles on the boundary. 2.2 Particle Pinning 2.2.1 Zener Drag Zener [4 ] was the first to treat the pinning effect of particles on a migrating grain boundary. Assuming that a boundary moves rigidly through an array of spherical particles, each of which exert a retarding force, it was proposed that normal grain growth would be completely inhibited when the grain size reached a critical maximum grain radius, Rnm, given by: 3v where r is the mean radius of the pinning particles and v is the volume fraction of particles. The average particle pinning force, Fp, may be related to the limiting grain radius such that: 6 F, (2.2) where y g b is the grain boundary interfacial energy. Equation 2.2 is known as the Zener pinning equation and is generally expressed as: where K is a dimensionless constant and m is the exponent for the particle volume fraction, v. An extensive review of Zener pinning by Manohar et a/. [ 5 ] suggests typical values of K and m (for v < 0.05) to be 0.17 and 1.0 respectively, as shown in Figure 2.1. More rigorous calculations concerning particle pinning have been attempted by many that the more sophisticated calculations do not lead to relationships which differ significantly from Equation 2.2. Various theoretical treatments of Zener pinning lead to the conclusion that the pinning force increases as the particle volume fraction increases and/or mean particle size decreases. 2.2.2 Grain Size Dependent Pinning Although a strong interaction between particles and grain boundaries has been well established, an accurate assessment of the pinning force is difficult since this is dependent on the details of the particle and grain arrangement. In very general terms, one of three cases are possible concerning the correlation between particles and grain (2.3) authors151 following the relationship first proposed by Zener. However, it is concluded 7 boundaries as a function of grain size. Either, the grains are much smaller than the particle spacing, the particle spacing and grain size are similar, or the grain size is much larger than the particle spacing. An analysis of the particle pinning force, as a function of grain size, was performed by Humphreys et al}® by considering a uniform distribution of particles within a cubic lattice. The effect of grain size on the Zener pinning force is shown schematically in Figure 2.2. As the grain size increases, a linear increase in pinning force occurs up to a maximum value corresponding to an equal grain size and interparticle spacing. At larger grain sizes, the pinning force falls in a non-linear manner. Although the actual value of the peak pinning force differs for each particle-grain boundary case, the principle that the pinning force varies in a manner similar to that shown in Figure 2.2 is undoubtedly correct.[6] 2.3 Modelling Grain Growth 2.3.1 Empirical and Theoretical Relationships Some of the first attempts to model grain growth were performed for aluminum-magnesium alloys and a 70-30 brass by Beck et al}1'9^ They were able to show that experimentally determined values of grain size during normal grain growth under isothermal annealing conditions fitted a power relationship such as: Dg=C0tn (2.4) where Dg is the average grain size for a given annealing time, /. C0 and n are parameters which are independent of grain size, but vary with the annealing temperature and 8 composition. Equation 2.4 was seen to be in good agreement with experimental findings as long as the initial grain size was small compared to the observed grain size being measured during grain growth. To account for deviations at shorter annealing times, Beck et a/.[7"9] proposed the more general form: where D, is the initial grain size. Grain growth relationships similar to Equation 2.5 have been derived from basic principles based on very simple assumptions. One such derivation has been given by controlling factor in normal grain growth. In their analysis, it is assumed that the effective radius of curvature of a grain boundary is proportional to the grain diameter and that the rate of grain boundary migration is inversely proportional to the grain diameter such that: Integrating Equation 2.6 and evaluating the integration constant at time t equal to zero leads to: (2.5) Burke and Turnbull [ l 0' 1 1 ] i in which grain boundary curvature is considered to be the D 2 -D? =Ct (2.7) 9 In general, grain growth data for a particular annealing temperature can be represented on a log Dg versus log t plot with Mn being the slope of a straight line with n having a theoretical value of 0.5. Numerous experimental studies^9'12"161 have been performed to determine n for a variety of materials. A summary of these findings is given in Table 2.1. The value of n is seen to approach 0.5 for select cases of high purity materials at high homologous temperatures. In most cases however, experimentally determined values of n vary considerably and are frequently less than the theoretical value. A summary of possible factors which may influence the value of n in high purity metals and solid solution alloys is given by Atkinson J 1 7 1 He suggested that the presence of solute atoms, solute segregation, second phase particles and texture effects are possible reasons for the variation of n and also are widely accepted as causes of grain growth inhibition. 2.3.2 Statistical Models A statistical approach to modelling isothermal grain growth was first proposed by Hillert [ 1 8 ] who considered the behaviour of individual grains within a range of grain sizes. Hillert makes the assumption that the size of an individual grain can be expressed by the radius, R, of an equivalent circle (or sphere) having the same area (or volume) in which the grain boundary velocity is proportional to the "pressure difference" caused by its curvature. It is also assumed that there is a critical grain size, Rc, for grain growth to occur, such that grains larger than this will exhibit growth and grains smaller than this will exhibit shrinkage. This leads to the following expression describing the average growth rate of all grains of size R: 10 dR dt • aMgbVgb \ R c R (2.8) where Mgn is the grain boundary mobility and a is a dimensionless constant. Equation 2.8 implies that grain growth is dependent on size differences between grains. Therefore it is important to consider the distribution of grain sizes within a material when attempting to model grain growth kinetics. Abbruzzese and Liicke [ l 9 ] extended Hillert's theory to account for the general case of grain growth including the effects of grain boundary pinning and texture. In their model, the actual grain structure is replaced by an equivalent spherical structure equal in grain volume in which the grain size distribution can be subdivided into discrete size classes. Each grain is surrounded statistically by grains of all other size classes. If a grain of size class i is.sufficiently larger than that of size class j, then a driving force, Fy, exists such that: Fu=rgb \RJ Ri J (2.9a) with and Fy = 0ifFy <0for R,> Rj (2.9b) FV = -FJI (2.9c) 11 where P is a pinning parameter. The growth (or shrinkage) rate of a grain of size / is given by: where wy is the probability that grains of size / and j are neighbours. The grain boundary mobility, Mgb, is related to the grain boundary diffusivity, Dgb, by: where b is the magnitude of the Burgers vector, T is the absolute temperature and kb is the Boltzmann constant. The probability, wy, that grains of size i and j are neighbours can be expressed for a random distribution by: (2.10) j (2.12) j where fj = N/N,0, represents the fraction of grains with size j, where Nj is the number of grains per unit volume in class j and N,0, is the total number of grains per unit volume. 12 2.3.3 Other Grain Growth Models Although the use of statistical models has been emphasized in the present review, it is also important to comment on other types of models which have been developed for describing grain growth. Statistical models deal with an ensemble of probabilities for a collection of grains using a series of interrelated equations to define the behaviour of a typical grain in terms of a grain size class. "Probabilistic" or "stochastic" grain growth models have been developed^20'2'1 employing Monte Carlo computer simulations, which relate the probabilities of events on a microscopic, rather than a macroscopic scale. In general, a microstructure is mapped onto a discrete lattice in which each lattice site is assigned a number indicating the local crystallographic orientation. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest pairs of unlike crystallographic orientation. "Deterministic" or "vertex" grain growth models also exist which utilize equations of motion for the velocity of a grain boundary. [ 2 2'2 3 ] Basically, each subsequent configuration of the boundary network is exactly defined by a previous configuration; any particular grain boundary network configuration can only have arisen from one previous configuration. However, unlike statistical models, stochastic and deterministic models generally do not include pinning in a realistic way. 2.4 Grain Growth in Austenite 2.4.1 Plain Carbon Steels An extensive investigation of grain growth in austenite was conducted by Mil le r [ 2 4 ] for a variety of plain carbon and alloyed steels differing in mode of 13 deoxidization, alloy content and type of steelmaking process used for their production. Miller reported that steels fall into two general patterns of austenite grain growth, defined as "coarse-grained" and "fine-grained", usually set by the steelmaking practice. Austenite grain growth in a typical coarse-grained steel was gradual and continuous with increasing time or temperature. These alloys had been deoxidized with silicon and contained very small amounts (between 0.004 and 0.009 wt. percent) of aluminum. In a typical fine-grained steel, grain growth was more complex: at low austenitizing temperatures growth proceeded very slowly; at higher temperatures, a few grains grew very rapidly producing a mixture of small and large grains. This group of steels had been deoxidized entirely with aluminum (between 0.02 and 0.10 wt. percent) or at least partially with aluminum or zirconium (0.018 wt. percent Al , 0.04 wt. percent Zr). Miller postulated that the austenite grain growth behaviour of the fine-grained steels could be attributed to the inhibiting effect of particles of aluminum oxide or nitride. An investigation of the kinetics of austenite grain growth in a series of Al-killed plain carbon steels has been recently performed by Militzer et al.[25] It was found that, for all cases, austenite grain growth was strongly dependent on the preheating schedule, which in turn controlled the degree of A1N precipitation. Similar grain growth kinetics were also found among the different grades of steel. At lower reheat temperatures, austenite grain growth was effectively inhibited by the presence of A1N precipitates. At higher temperatures, both abnormal growth and a return to normal growth was observed which could be related to the coarsening and dissolution of the A1N particles. 14 2.4.2 High Strength Low Alloy Steels Within the past decade, considerable research has been conducted in understanding austenite grain growth behaviour in high strength low alloy steels.[26"291 Much of that effort has been directed towards quantifying the effects second phase particles have on the kinetics of grain growth. Traditionally, austenite grain growth behaviour has been described using empirical power law equations.[30 3 l ] However, factors such as grain growth inhibition and/or abnormal grain growth, attributed to the presence of second phase particles commonly observed in HSLA steels, are not accounted for in such models. More recently, efforts at modelling austenite grain growth have been made by considering these effects in microalloyed steels. t 1 9'2 6 - 2 9 1 Cuddy and Raley [ 2 6 ] considered the grain coarsening behaviour for a variety a low carbon steels containing small additions of Al , V, Ti or Nb. Over the range of compositions examined, a linear relationship was found between the austenite grain coarsening temperature (the temperature at which abnormal growth occurs) and the temperature for complete precipitate dissolution in each type of microalloyed steel (Figure 2.3). In conjunction with solubility relationships, Cuddy and Raley [ 2 6 ] were able to approximate the austenite grain-coarsening temperature in low carbon steels given the type and concentration of microalloying elements present under a given set of thermomechanical conditions. It was also observed that the higher the product of the concentrations of the interacting elements, the higher the grain coarsening temperature, with the least soluble particles impeding boundary motion to the highest temperature. 15 These findings corroborate in a qualitative way with other model predictions^29'321 for the pinning of grain boundaries by particles. A fundamental approach by Manohar et al.[27] was taken to predict austenite grain growth behaviour in the presence of second phase particles. Assuming equilibrium precipitation of TiN, a stable grain size was calculated employing a relationship for the limiting grain size, similar to that originally proposed by ZenerJ41 Thus, it was possible to model austenite grain growth as a function of temperature based on the dissolution and coarsening of microalloy precipitates, as shown in Figure 2.4. Manohar et al}27^ also observed three distinct stages in the grain growth behaviour of a Ti-Nb microalloyed steel: (i) marginal growth at lower temperatures, (ii) abnormal growth for intermediate temperatures in the range of 1100 - 1200 °C and (iii) a return to normal growth of coarse grains above 1200 °C. Recently, Militzer and Hawbolt [ 2 8 ] have employed the statistical grain growth model of Abbruzzese and Liicke^19] to describe austenite grain growth in microalloyed low carbon steels. This model has been successfully applied to capture austenite growth kinetics by incorporating a pinning parameter, P, related to the coarsening and dissolution of precipitates. However, no quantitative link was provided between the actual coarsening and dissolution kinetics of precipitates to a change in pinning force. Militzer and Hawbolt [ 2 8 ] considered the pinning parameter to be primarily a function of temperature; extremely simplified assumptions have been made to capture a potential time dependence of P at a given temperature by employing step functions or a linear 16 decrease of P with time. It is also noted that, similar to the findings of Manohar et al. [ 2 1 \ three distinct stages were observed for austenite grain growth in microalloyed steels. 2.5 Precipitation in Austenite 2.5.1 Niobium Niobium is known to have a high affinity for both carbon and nitrogen when added to steels. It has been well established that niobium carbide and niobium nitride are mutually soluble, forming a cubic-type crystal structure.[331 Since steels usually contain both carbon and nitrogen, it is often assumed that a carbonitride is formed, rather than a pure carbide or nitride or both. In reviewing published solubility data, Nordberg and Aronsson'-341 have indicated that the carbon-to-nitrogen ratio must be taken into consideration when discussing the precipitation of niobium compounds in low carbon steels. However, Irvine et alP5^ have suggested that the nitrogen content in a steel may be considered in terms of an equivalent carbon content, i.e., carbon equivalent = C + 12/14N, for the purpose of solubility calculations. The exact composition of niobium carbide, nitride or carbonitride with regard to stoichiometry is also an area of dispute. In many cases the solubility of niobium carbide in austenite has been experimentally determined by assuming a stoichiometric value. [ 3 4' 3 6 ] However, Mori et alP1^ have determined the non-stoichiometry of niobium carbide precipitates, having an average composition of NbCo.87 in the absence of nitrogen. Nordberg and Aronsson [ 3 4 ] have also indicated that niobium carbide is non-stoichiometric and that good agreement among previous solubility findings is obtained if they are 17 reinterpreted assuming the composition to be NbCo.87- Sharma et a/. [ 3 3 ] assume that the non-stoichiometry of the carbonitride is the same as that of the niobium carbide based on experimental observations. Thus, the composition of niobium carbonitride may be represented by Nb(CyNi.y)o.87 where the carbon and nitrogen randomly substitute for each other. Grain growth inhibition and abnormal grain growth due to particle pinning are largely controlled by the thermodynamic stability of second phase particles. For the dissolution of a simple carbide, M C , to its soluble components, the product of the soluble components (the solubility product, Ks) can be expressed as: log^=log[M][C] = ^ - ^ f (2.13) where Ai and A2 are constants known from published solubility data, and T is the absolute temperature. Solubility data from the literature133"371 for NbC and Nb(CN) in austenite are summarized in Table 2.2 and are shown in Figures 2.5 and 2.6, respectively. With the exception of Smith's results^341, the NbC solubility data obtained by other investigators are seen to be in good agreement. Solubility studies performed by Smith were based on pure alloys, most of which contained approximately 0.01 wt. percent carbon; however, the nitrogen content was not stated. Nordberg and Aronsson [ 3 4 ] suggest that a possible cause of the apparent discrepancy of Smith's data may be variations in the composition of 18 the precipitate. The low solubility values obtained by Smith deviate in a direction one would expect for a nitrogen-rich precipitate. The solubility product values for Nb(CN) reported by Mori et a/. [ 3 7 ] are seen to be somewhat lower than Nb(CN) data reported elsewhere.[34'35] This may be attributed to the relatively high nitrogen content reported by Mori et al.[37], resulting in the lower solubility values, as indicated by Figure 2.6. 2.5.2 Titanium Similar to niobium, titanium also has a high affinity for both carbon and nitrogen when microalloyed to HSLA steels. However, the precipitation behaviour of titanium nitride and titanium carbide differ considerably more than those of niobium nitride and niobium carbide. Titanium is bound preferentially to nitrogen as TiN at very high temperatures, forming a cubic-type crystal structure.^381 Experiments performed by Wada and Pehlke [39J in steels containing up to 0.10 wt. percent Ti suggest that the composition of titanium nitride is approximately TiNi.o at all temperatures in the austenite region. It was also observed that the TiN particle morphology was mainly cubic or rectangular-prism shaped. The crystal structure and composition of titanium carbide is the same as that of titanium nitride and can also be considered as being closely stoichiometric. It was demonstrated by Balasubramanian et al.[40] that the composition of T i C y varies from y = 0.920 to 0.965 in the austenite range for steels containing 0.1 to 2.0 wt. percent carbon. In general, the solubility of nitrides are seen to be significantly lower than those of the corresponding carbides. [ 3 5 , 3 6'3 9"4 2 ] This is specially true for titanium where TiN is 19 virtually insoluble in austenite at temperatures up to 1350°C. [ 2 9 1 Solubility data for TiN are presented in Table 2.3 and Figure 2.7. Investigations by Wada and Pehlke [ 3 9 ] led to TiN solubility values much larger than those of Kunze. [ 4 1 1 Kunze suggests that a possible reason for the difference may be the slow TiN formation due to its very low nucleation rate. This assumption is supported by the findings of Wada and Pehlke [ 3 9 ]; at a titanium content between 0.04 and 0.30 wt. percent, complete precipitation of titanium could only be obtained in particular cases. Kunze also suggests that the solubility data of Matsuda [42] may have been affected by a large scattering of the individual measurements. A list of solubility products for TiC is given in Table 2.4 and is illustrated in Figure 2.8. It can be seen from Figure 2.8 that the agreement between TiC solubility values from all of the investigations is reasonably good. A comparison of solubility products for titanium and niobium carbides, nitrides and carbonitrides is given in Figure 2.9. The solubility data presented in Figure 2.9 were chosen to reflect average values found for each type of precipitate. TiC and NbC are seen to possess similar solubility characteristics, with Nb(CN) being slightly less soluble than the pure carbides. It is also quite evident that TiN is considerably less soluble than the other types of precipitates considered. 2.5.3 Complex Carbonitrides Most commercial HSLA steels contain at least two carbide and/or nitride-forming microalloy additions. Many of these precipitates, such as Ti(CN), Nb(CN) and V(CN), are completely intersoluble, allowing for the formation of complex carbonitrides having a 20 wide range of composition and thermodynamic properties.[43'44] Unfortunately, little information has been published concerning the chemistry and stability of these complex carbonitrides. As a result, their behaviour are invariably based on simplified solubility relationships for single-metal particles. Houghton et a /J 4 4 ] investigated the effects of various heat treatments on the precipitating phases in a number of Ti-Nb microalloyed steels. Although their analysis showed a wide range of particle compositions, no attempt was made to develop thermodynamic relationships concerning particle chemistry and stability. Strid and Easterling[43] have reported similar findings, using scanning transmission electron microscopy and energy dispersive spectroscopy techniques to study complex particle dispersions and compositions for a large number of particles in various Ti-V and Ti-Nb bearing steels. However, no solubility or precipitation data for these complex carbonitrides were reported. 2.6 Dissolution 2.6.1 General Observations Since nitrides, carbides and carbonitrides possess a composition significantly different from that of the steel matrix, it is generally believed that the dissolution process is diffusion controlled.[45] The magnitude of the diffusion coefficient, D, is indicative of the rate at which atoms diffuse. The temperature dependence of diffusion is: D = D 0 exp-\ R G T J (2.14) 21 where D0 is a temperature-independent pre-exponential, Q is the activation energy for diffusion, RQ is the universal gas constant.1^61 Since the diffusion rates of carbon and nitrogen are generally orders of magnitude faster than those of substitutional solutes such as niobium and titanium, it is assumed that the rate of precipitate dissolution will be controlled by the slower diffusing species. Diffusion data reported in the literature^47"501 for niobium and titanium in austenite are summarized in Table 2.5. As shown in Figure 2.10, reasonable agreement is seen between niobium diffusivity values. 2.6.2 Modelling A theoretical model has been developed by Cheng [ 5 1 ] to predict the dissolution, growth and coarsening behaviour of nitrides and carbides in low-carbon and microalloyed steels using numerical integration methods on a multi-particle system. The model takes into account the equilibrium thermodynamic properties of the system, the local equilibrium at the particle interface, curvature effects and diffusion along grain boundaries. The size of a particular particle is determined by the simultaneous solution of a set of diffusion, equilibrium and mass balance equations for each individual particle. Originally developed to study the dissolution and coarsening behaviour of aluminum nitride in an Al-killed plain carbon steel, the model can be modified to apply to other steel compositions. Basic assumptions of the dissolution, growth and coarsening model follow; a detailed mathematical description may be found elsewhere.1521 The diffusion-controlled dissolution and growth of a particle in a matrix requires the solution of Fick's second law: DV2C*JC dt 22 (2.15) where D (assumed to be independent of composition) is the interdiffusion coefficient in the matrix and C is the concentration field in the matrix surrounding the precipitate. For simplicity, all precipitates are assumed to be uniformly distributed in the matrix and are spherical in shape. When a particle is located on a grain boundary, both grain-boundary and bulk diffusion can occur simultaneously. The model considers a grain-boundary precipitate to be a sphere with a thin slab of material (i.e., the grain boundary) attached along its equator. When both grain-boundary and bulk diffusion occur, the concentration field can be approximated as the sum of two solutions. One solution is that without the grain boundary, the other is for the grain boundary only. Moreover, it is assumed that the diffusion of solute along the surface of the precipitate is sufficiently rapid that the spherical shape is maintained. Other dissolution models have been reported in the literature153'54^ based on principles differing from those used by Cheng. [ 5 1 ] Myhr and Grong [ 5 3 ] have proposed a model for nucleation, growth (or dissolution) and coarsening for diluted alloys based on the finite difference method. Assuming an array of spherical particles with uniform thermodynamic properties, a particle distribution is divided into a series of discrete size classes, each representing a control volume. From this, the flux of particles in and out of the control volume is calculated at each time step for a given thermal history. When considering the dissolution of carbide species, Voice and Faulkner [54] have reported that the assumption of a constant equilibrium solute concentration cannot be made. Taking 23 this into consideration, a computer simulated dissolution model has been developed based on the diffusion of solute away from a carbide particle across discrete shell elements. 2.7. Coarsening Lifshitz and Slyozov [ 5 5 ] and Wagner[561 have developed a detailed theory for the process of particle coarsening. Widely known as Ostwald ripening, this process is driven by the minimization of the total surface free energy of a system of particles. According to the classical Lifshitz-Slyozov-Wagner (LSW) theory for particle coarsening, the mean particle diameter, d , increases with time according to: where dn is the initial mean diameter at time to, and Ko is a coarsening parameter related to interfacial energy, diffusion and other variables. The LSW theory is strictly valid only for volume fractions approaching zero under steady state conditions. Several extensions of the LSW theory have been developed to treat the effect of a finite volume fraction on diffusion-controlled coarsening.1571 Although the authors of these theories use different approaches to analyze the coarsening problem, they all produce the d ~ r 1 / 3 law. (2.16) Table 2.1. Experimentally determined grain growth exponents. Material n Temp. Range Author (Homologous) oc-brass 0.21 0.45 - 0.70 Beck et al. [9] Al (zone-refined) 0.29 0.36-0.68 Gordon et al. [ 1 2 ) Sn (zone-refined) 0.5 0.72 - 0.95 Holmes et al. [13] Pb (zone-refined) 0.43 0.64 - 0.92 Drolet et al. [14] Pb (zone-refined) 0.4 0.51 -0.97 Boiling etal.[15] Ti 0.33 0.24 - 0.36 Hu et al.[l6] 25 Table 2.2. Solubility products of niobium carbide and niobium carbonitride in austenite. Solubility Product log K-Nb(CN) Temperature Range Method Author (°C) [Nb][C] 2.9- 7500/T 900 - 1200 A de Kazinczy et al.[34] [Nb][C] 3.04 -7290/T 900 - 1300 B Meyer [ 3 4 ] [Nb][C] 3.7- 9100/T 1000- 1300 C Smifh [ 3 4 ] [Nb][C] 3.42 -7900/T 800- 1300 D Narita [ 3 6 ] [Nb][C] 2.96 -7510/T E Nordberg et al.[34] [Nb][C] 0 8 7 3.18 -7700/T 1000- 1300 B Mori etal.[37]' [Nb][C] 0 8 7 3.11 -7520/T E Nordberg et al. [34] [Nb][C] 0 8 7 2.81 -7020/T F Sharma et al.[33] [Nb][C] 0 8 3 [N] 0 1 4 4.46 -9800/T 950- 1225 B Mandry et al.[34] [Nb][C + 12/14N] 2.26 -6770/T 900- 1300 B Irvine et al. [35^ [Nb][C] 0 2 4[N] 0 6 5 4.09-•10400/T 1000- 1300 B Mori et al.[37] [Nb][C+N] 1.54 - 5860/T 900 - 1200 B Meyer [ 3 4 ] A. Hardness measurements B. Chemical separation and isolation of precipitate C. Gas equilibrium D. Chemical analysis E. Statistical treatment of previous solubility products F. Thermodynamic calculation 26 Table 2.3. Solubility product of titanium nitride in austenite. Solubility Product log K T j N Temperature Range Method Author [Ti][N] 0.32 - 8000/T 1150- 1430 A Matsuda et al.[42] [Ti][N] 5.19 - 15490/T 1100- 1350 B Kunze [ 4 1 ] [Ti][N] 4.94 - 14400/T 1000 - 1290 B Wada et al. [39] [Ti] [N] 5.0 - 14400/T C Roberts [41] A. Atomic absorption spectroscopy B. Gas equilibrium C. Thermodynamic calculation 9 Table 2.4. Solubility product of titanium carbide in austenite. Solubility Product log K T i c Temperature Range (°C) Method Author [Ti][C] 2.75 - 7000/T 950- 1350 A Irvine et al.[35] [Ti][C] 4.1 -9070/T 1000 - 1200 B Kirkaldy et al. m [Ti][C] 5.33 - 10475/T 900- 1300 A Narita [ 3 6 ] [Ti][C] 4.2 - 8970/T Ohtani et al. m [Ti][C] 3.23 - 7430/T Ohtani et al.[40] A. Chemical analysis B. Gas equilibrium 27 Table 2.5. Diffusion coefficient of titanium and niobium in austenite. Species D0 Q Author (mm2/s) (kJ/mole) Ti 15 250 Moll et al. [47] Nb 560 286 Oikawa [ 4 8 ] Nb 492 285 Subramanian et al.[49] Nb 5.3 xlO 4 343 Sparke et al.[50] Nb 75 264 Kurokawa et al.[50] 28 10000-1000-N V Ng A AI/CuAlj A a-Fe/FesC V Al/AI^ O, T AI/AJjNi • Fe-NI-Cr/carbldes • y-Fe/MnS • Y-Fe/fTi.Nb)CN O y-Fe/AIN » O a-Fe/Fe,C %% • a-FeA'N O Y-FG/AIN 100-10-5 : : . , . „ \ 1- V — i 1 1 r 0.0001 0.001 0.01 0.1 Volume fraction Figure 2.1. Experimental data on the ratio of limiting grain radius to particle radius, as a function of the volume fraction of particles. [ 5 ] 29 Figure 2.2. The effect of grain size on the Zener pinning force for a given particle distribution.^ 30 Figure 2.3. Relation between observed grain-coarsening temperature of austenite and computed temperature for complete dissolution of the microalloy carbides/nitrides.[26] 31 1 6 0 0 H 1 1 1 j 1 j 1 1 1 1 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 Temperature (C) Figure 2.4. Comparison of predicted and experimental grain growth behaviour in a Ti-Nb-Mo microalloyed steel.[27] 32 Figure 2.5. Solubility product of niobium carbide in austenite. Figure 2.6. Solubility product of niobium'carbonitride in austenite. 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 1 /'A 'Matsuda et al.[42] ^unze 1 4 ' 1 3Wada etal.[39] 'Roberts14'1 5 6 7 8 9 10000/T (1/K) Figure 2.7. Solubility product of titanium nitride in austenite. 4.5 4.0 3.5 3.0 2.5 2.0 1.5 -1.0 -0.5 0.0 ''rvine et al[35] 2Kirkaldy et al.m 6) JNarita13' l'5Ohtani et al. [40] 7 8 10000/T (1/K) Figure 2.8. Solubility product of titanium carbide in austenite. 7.0 6.0 5.0 4.0 3.0 2.0 1.0 H 0.0 TiN 1 3 9 1 Nb(CN) 1 3 5 1 NbC [ 3 7 ] T i c [ 4 0 ] 1 7 8 9 10 10000/T (1/K) Figure 2.9. Comparison of titanium and niobium solubility products in austenite. -16 -21 4 , , , , 1 6.4 6.6 6.8 7.0 7.2 7.4 10000/T (1/K) Figure 2.10. Comparison of niobium and titanium diffusivities in austenite. 36 C H A P T E R 3 SCOPE AND OBJECTIVES Considerable research has been conducted on the influence of second phase particles on austenite grain growth in HSLA steels. However, very few studiesp8] have attempted to provide a quantitative link between the mechanisms which govern the evolution of these particles and their effect on the kinetics of austenite grain growth. Of the models which have been developed for austenite grain growth predictions, most take an empirical approach to account for the presence of second phase particles. Incorporating the kinetics of particle coarsening and dissolution would be the next logical step in developing a refined austenite grain growth model for microalloyed steels. Through a series of experimental and theoretical studies, the present research intends to accomplish the following objectives: i) To experimentally determine the kinetics of isothermal austenite grain growth in a Ti-Nb microalloyed steel over a series of relevant temperatures; ii) To experimentally determine the size and distribution of Ti-Nb carbonitride precipitates for a variety of grain growth conditions; iii) To combine the Abbruzzese and Liicke^191 statistical grain growth model with a model describing coarsening and dissolution of precipitates15'1, to provide a reasonable description of the kinetics of austenite grain growth. 37 C H A P T E R 4 EXPERIMENTAL 4.1 Material Experiments were carried out using a Ti-Nb microalloyed high strength low alloy (HSLA) steel supplied by Lake Erie Steel Co. Ltd, a subsidiary of Stelco Inc. All tests were performed on as-received hot rolled transfer bar material with the chemistry given in Table 4.1. 4.2 Methodology 4.2.1 Austenite Grain Growth For the grain growth tests, rectangular samples (3mm x 6mm x 15mm) were machined from the transfer-bar material. This specimen design was chosen for two reasons. First, it was possible to obtain sufficiently high cooling rates required for revealing the austenite microstructure by the use of a water quench; second, the given dimensions allowed for a statistically adequate number of measurable grains across the thickness, while minimizing thermal gradients during cooling. All isothermal austenite grain growth tests were performed on a Gleeble® 1500 thermomechanical simulator. A schematic of the Gleeble® 1500 machine and experimental set up is shown in Figure 4.1. Grain growth samples were placed between two 10 mm diameter cylindrical anvils each containing a small ledge for the sample to sit on (Figure 4.2). Prior to heating, a small force between the anvils was applied to ensure 38 good conduct between the contact surfaces. The samples were thermally cycled on the Gleeble by the use of resistance heating. Test temperatures were continuously monitored using a Pt-Pt/Rh thermocouple spot welded to the upper surface at the mid-length of each sample. The use of resistive heating in combination with the temperature feedback control system ensured precise specimen temperature control during heating and isothermal holding. Prior to heating, the specimen chamber was held in a vacuum of less than 10"4 Torr and then backfilled with argon in order to minimize the effects of decarburization and oxidation. Isothermal austenite grain growth experiments were performed between 1100°C and 1250°C for holding times ranging from 1 to 1200 seconds. Samples were heated from room temperature at a constant rate of 5°C/s to the desired test temperature. Upon completion of the desired heat treatment, the specimens were cooled rapidly using a manually operated water quench in order to obtain a martensitic microstructure. From this quenched microstructure the prior austenite grain boundaries were revealed using procedures described below. 4.2.2 Optical Microscopy Specimens to be used for subsequent grain size measurements were cut at the thermocouple position and prepared for metallographic examination. The surface of interest was cold mounted in an acrylic resin and then progressively ground on silicon carbide papers to a 600 grit finish and finally polished using a 6 um and 1 urn diamond slurry. 39 Prior austenite grain boundaries in the resulting martensitic microstructure were revealed using the following etchant:[58] 2 g picric acid 1 mL hydrochloric acid 1 g dodecylbenzenesulfonic acid 100 mL distilled water Etching was accomplished at room temperature by immersing the specimens in this solution from 300 to 600 seconds. 4.2.3 Scanning Transmission Electron Microscopy The mean particle size and particle size distribution were assessed by scanning transmission electron microscopy using carbon extraction replicas. To prepare carbon extraction replicas, the specimens were first ground and polished as previously described and then lightly etched in 2% nital. A thin film of carbon approximately 200 A thick was then deposited on the surface of each sample using a vacuum evaporator. The carbon coated surface was scored with a sharp point into 2-3 mm squares. The extraction replicas were released by re-etching the samples in 5% nital and then placing them in distilled water. Finally, each replica was picked up on a 3 mm copper grid for subsequent examination. All electron microscopy work was performed at an operating voltage of 200 keV on a Hitachi H-800 transmission electron microscope equipped with an H-8010 scanning system and an energy dispersive X-ray (EDX) analysis system. 40 4.3 Quantitative Metallography Quantitative analysis of the mean austenite grain size, austenite grain size distribution, mean precipitate size and precipitate size distribution were carried out using a C«IMAGlNG L C Image Analysis System. A S T M standard grain size measurements were performed employing the method of Jeffries.[59] The sum of all the grains included completely within the area of measurement plus one half the number of grains intersected by the perimeter of the area of view gives the number of equivalent whole grains. From this, the mean grain area, A, is obtained from which the equivalent area diameter (EQAD), d.A, is calculated by: (4.1) A corresponding grain size distribution of each sample was generated based only on grains completely within the area of measurement. An average of approximately 450 grains were included in each analysis. From T E M micrographs of the replicas, an equivalent area precipitate diameter was obtained using Equation 4.1, where A is replaced by the mean precipitate area, Ap. All of the precipitates analyzed were completely within the area of measurement. The number of precipitates included in each analysis differed significantly for different reheat temperatures. An average of approximately 400 niobium-rich precipitates were measured at 1100°C; whereas, an average of only 60 precipitates were measured at 1150°C. An 41 average of approximately 100 titanium-rich particles were measured at all temperatures of interest. 42 Table 4.1. Chemical composition of HSLA steel (wt. percent). c Mn Si Nb Ti N P s 0.06 1.37 0.1 0.068 0.038 0.0073 0.008 0.002 43 Figure 4.2. Schematic diagram of the (a) plan view and (b) elevation view of the specimen and specimen holder. 44 C H A P T E R 5 EXPERIMENTAL RESULTS 5.1 Starting Material Conditions All experimental studies were performed on the as-received transfer bar material. Since the transfer bar provided the starting material condition, it was important to characterize its initial microstructure. Exiting the reheat furnace at approximately 1240°C, the material was rough rolled down to approximately 1130°C. Following rough rolling, the slab tail was sheared and quenched in a water bath. Photomicrographs of the transfer bar structure were taken using an optical microscope, as illustrated in Figure 5.1. The quenched structure was seen to be relatively uniform, consisting mostly of bainite with some ferrite nucleated along the prior austenite grain boundaries. Vickers hardness measurements were made to help identify the phases present. An estimate of the prior austenite grain size was approximated to be 40 jam. Large cube-shaped particles approximately 1 jam in diameter were also observed in the as-received material. Carbon extraction replicas were prepared and examined using a scanning transmission electron microscope for the presence of second phase particles. The larger particles were identified as being predominantly titanium, presumably TiN. Some mixed titanium-niobium, cube-like and irregularly shaped precipitates, approximately 100 to 300 nm in diameter, were also seen. There was no evidence of any fine scale precipitation. r i 45 5.2 Experimental Observations 5.2.1 Austenite Grain Growth Investigations Isothermal austenite grain growth experiments were performed between 1100 and 1250°C for holding times ranging from 1 to 1200 seconds. A summary of all experimental measurements is given in Appendix A. Samples were heated to the desired test temperature at 5 °C/s and water quenched following holding. The evolution of the austenite grain structure as a function of temperature and time is illustrated by a sequence of photo micrographs shown in Figures 5.2 through 5.5. Little change in grain structure was observed at the 1100°C reheat condition. As evident from Figure 5.2, a relatively fine, homogeneous austenite microstructure is maintained for all holding times at this temperature, with very little growth occurring between 1 and 600 seconds. At the higher reheat temperatures, grain growth can be seen to be occurring in stages, exhibiting both normal and abnormal behaviour. For holding times of up to 300 seconds at 1150°C, a relatively homogeneous increasing austenite grain structure is maintained during grain growth. As reheat times are further increased between 300 and 1200 seconds, a non-uniform, or duplex microstructure develops. The austenite microstructure consists of a few extraordinarily large grains surrounded by a matrix of equiaxed fine grains (Figure 5.3c), a grain size distribution typical of abnormal grain growth behaviour. Initially, on attaining 1200°C, a uniform grain distribution is obtained as shown in Figure 5.4a. With increasing time, a continuous increase in the austenite grain size is observed. However, for holding times of more than 600 seconds, abnormal growth is obtained as indicated by the development, of a non-homogeneous 46 microstructure with a mixture of fine and coarse grains as shown in Figures 5.4b and 5.4c. The grain growth behaviour at 1250°C is similar to that obtained at 1150 and 1200°C. The grain size distribution remains fairly uniform throughout at short reheat times, followed at longer times by the development of several very large irregular-shaped grains, shown in Figure 5.5c. 5.2.2 Precipitate Investigations Electron microscopy replica studies were carried out for a select number of austenitizng conditions in order to investigate the possible presence and effect of precipitates during grain growth. A semi-quantitative analysis of particle composition was made for most precipitates through the use of energy-dispersive X-ray (EDX) techniques. Unfortunately, only a partial analysis of the metallic component was possible, since elements lighter than sodium (i.e., carbon and nitrogen) were not detectable with the available equipment. Mean particle sizes and particle size distributions were quantified from measurements made from the T E M replica micrographs. Large differences in precipitate size, composition and morphology were observed between many of the austenite grain growth samples examined. These observations have been divided into two general categories based primarily on particle composition. 5.2.2.1 Chemical Composition and Morphology Large numbers of relatively small, spheroidal-shaped precipitates were seen at the lower reheat temperatures. Difficulties arose in identifying some of the particles due to their extremely small size (less than 10 nm in diameter). However, of the particles that 47 were analyzed, all were composed mainly of niobium usually accompanied with small amounts of titanium. These Nb-rich particles remained spherical in shape, independent of the titanium content. A relatively sparse, stable population of large cube-shaped particles, were also present in all of the samples examined. These were identified as being predominantly titanium, presumably TiN. In most cases, very little if any niobium was detected in the larger cube-shaped titanium-based particles. The larger Ti-rich particles were consistently cuboid or rectangular in form. The present observations are consistent with other studies[43'44], reporting similar findings of small spherical Nb-rich particles with much larger Ti-rich cuboidal precipitates. In many instances, the smaller niobium-rich spheroidal precipitates could be visually identified as precipitated onto existing TiN particles, as shown in Figure 5.6. 5.2.2.2 Size Distributions The distribution of particles and particle sizes as a function of temperature and time was also examined. Figure 5.7 depicts T E M replica micrographs taken from austenite grain growth samples at the 1100°C reheat condition. A very fine dispersion of predominantly Nb-rich spherical particles, presumably (Nb,Ti)C, were present in all specimens at this temperature. As evident from Figures 5.7a and 5.7b, precipitate alignment and clustering of Nb-rich particles was often observed. Particle diameters increased from a mean of approximately 9 nm at 1 second up to a mean of 20 nm accompanied by larger Nb-rich particles of 50 to 60 nm after 600 seconds, indicating possible coarsening effects. All of the Nb-rich particles observed remained spherical or near spherical in shape. The dissolution of (Nb,Ti)C with time accompanied by 48 coarsening of a few larger particles was also evident at the 1150°C reheat condition. Measured mean precipitate diameters ranged from approximately 40 to 50 nm at this temperature (Figure 5.8). Although little change in mean particle size was seen, a visual assessment of the volume fraction indicated a significant decrease in the number of (Nb,Ti)C precipitates as compared to that observed at 1100°C and a further reduction after hold times of 60 seconds. Additional T E M tests at 1150°C indicated that all of these particles had gone into solution between 300 and 900 seconds. Fewer (Nb,Ti)C precipitates were visible for short holding times at 1200°C, these disappearing after 30 seconds. No evidence was found of any (Nb,Ti)C precipitates at 1250°C. As indicated previously, a very stable population of larger cuboidal Ti-rich (TiN) particles were also observed in all the grain growth samples. No marked variations in the mean, larger, cuboidal Ti-rich precipitate diameter were observed from 1 second at 1100°C up to holding times of 1200 seconds at 1250°C. Measured particle size distributions for the smaller, spherical Nb-rich (Nb,Ti)C particles at the 1100°C reheat condition are shown in Figures 5.9a and 5.9b. As seen in these figures, not only does the mean (Nb,Ti)C particle size increase with holding time, the size of the distribution also changes. It is observed that an essentially normal distribution of (Nb,Ti)C precipitates is maintained at holding times of 1 to 600 seconds. The size distribution of the larger, cuboidal Ti-rich (TiN) particles after 1 second at 1100°C is shown in Figure 5.9c. Similar, very symmetric TiN particle distributions were measured at all times and temperatures of interest. 49 5.2.3 Austenite Grain Growth Behaviour Results of the isothermal austenite grain growth experiments conducted at temperatures between 1100 and 1250°C are given Figure 5.10. As expected, it is generally observed that with increasing temperature or hold time, there is a corresponding increase in the average austenite grain size. However, the kinetics of austenite grain growth are seen to change significantly depending on the experimental conditions of interest. As indicated in Figure 5.10, the 1100, 1150 and 1250°C grain growth curves show a significant change in growth rate after 60 seconds. This appears to be a "critical" reheat time of initial inhibition of austenite grain growth where, the initially high grain growth rate decreases. This would suggest that pinning effects due to the presence of second phase particles can have a major influence on austenite grain growth in microalloyed steels. At 1100°C, austenite grain growth is suppressed by the presence of a fine dispersion of (Nb,Ti)C precipitates. Marginal grain growth from 22 to 37 um is seen to take place at holding times of 1 to 600 seconds. It is uncertain what effect the larger TiN particles have at the 1100°C reheat temperature. Although the location of austenite grain boundaries were not visible in the T E M replica micrographs, the TiN particles appeared to be aligned in many of the micrographs examined. Presumably, at 1100°C, the larger TiN particles had much less of an effect on austenite grain growth compared to the relatively small size and large volume fraction of Nb-rich precipitates. 50 Grain growth at 1150°C can be thought of as occurring in various stages. As reheat times are increased between 60 and 300 seconds, the grain growth rate becomes more sluggish, resulting in the formation of a plateau in the grain growth curve at around 70 um. Grain boundaries continue to be pinned by (Nb,Ti)C, but at a larger grain size than that obtained for the 1100°C reheat temperature. This apparent decrease in pinning force may be explained by the observed increase in mean particle size from 9 to 40 nm and an assumed increased particle solubility with increasing temperature. As holding times are increased between 300 and 1200 seconds, the Nb-rich carbides continue to dissolve, further decreasing the grain boundary pinning force. The driving force for grain growth eventually exceeds the precipitate pinning force, allowing austenite grain growth to occur. Those grains with a significant size advantage are able to grow at a very rapid rate at the expense of the finer surrounding grains. This is clearly illustrated in Figure 5.10 where, after 300 seconds, enhanced grain growth is observed implying that a significant proportion of the niobium precipitates have gone into solution. At the higher reheat temperatures of and 1200 and 1250°C, very few, if any, (Nb,Ti)C particles remain to retard austenite grain growth. For the 1200°C reheat temperature, a continuous increase in grain size is generally observed between 1 and 1200 seconds. Between 600 and 900 seconds, a marginal increase in austenite grain size from 158 to 165 Lim is seen, resulting in a plateau similar to that observed at 1150°C. However, this appears to be an anomaly which may be related to the decreasing number of grains being counted for the larger grain sizes. Initially, normal grain growth at 1250°C occurs at appreciably larger rates than that observed at the lower reheat temperatures. 51 However, similar to 1100 and 1150°C, grain growth appears to become inhibited at a reheat time of 60 seconds. This associated "critical" grain size would indicate some type of particle pinning, which presumably could be attributed to the presence of TiN. Abnormal growth behaviour is also observed at 1200 and 1250°C after 600 seconds, which would also suggest that normal grain growth has been inhibited in some manner. 5.3 Austenite Grain Size Distributions 5.3.1 Estimation of a Three Dimensional Distribution All grain size measurements from the quantitative image analysis were made on planar sections through the austenite microstructure, resulting in a two dimensional (2-D) grain size distribution from which an equivalent area diameter (EQAD) was obtained. Equivalent measurements made in three dimensions (3-D) would be preferred, since this would give a more realistic representation of the actual grain structure and provide a 3-D grain size distribution applicable to the statistical grain growth model of Abbruzzese and Liicke. [ 1 9 ] Since a 3-D determination is not practical from direct measurements for multiple samples, several procedures have been developed to estimate a 3-D volumetric grain size, dy, from 2-D EQAD measurements. Matsuura and Itoh [ 6 0' 6 1 ] have estimated a 3-D grain size distribution with discrete size classes, using the measured mean grain area, A, and the associated grain size distribution. Since this method requires the integration of a probability function for each of these size classes, a computer program written by Giumelli [ 6 2 ] has been employed for such calculations.[60] 52 5.3.2 Experimental Observations Further information may be gained concerning austenite grain growth behaviour by considering changes in the austenite grain size distribution with temperature and time. In those cases where a uniform microstructure or normal grain growth was observed, a log-normal grain size distribution would be expected. Alternatively, abnormal grain growth, characterized by duplex microstructures, would lead to non-uniform or possibly bimodal grain size distributions. Two methods of representing austenite grain size distributions were considered in the present research. The first was to estimate a 3-D grain diameter distribution from the measured 2-D data using the method of Matsuura and Itoh [601; this was then plotted against the frequency of grains measured for each size class. A second approach taken, using the same number of size classes, was to convert the 3-D grain diameters into equivalent volumes and graphically plot the grain volume fraction for each size class against the total volume of grains considered. A comparison of the resulting austenite grain diameter and austenite grain volume distributions is made in Figure 5.11 for two heating times at 1150°C. Figure 5.11(ai, &2) compares the distribution obtained for a normal grain growth condition. Generally, the shape of the two distributions is similar for both methods considered. The two grain size distributions in Figure 5.11(bi, b2) were obtained for a condition in which abnormal grain growth was observed. It is quite clear that the method using grain volumes gives a much better indication of the presence of abnormal growth with a characteristic bimodal distribution. As a result, the 53 comprehensive investigation into changes in austenite grain size distribution with temperature and time was performed employing the grain volume procedure. Figures 5.12 and 5.13 depict the evolution of the volumetric austenite grain size distribution obtained after reheating at 1200 and 1250°C. As shown in Figures 5.12a, and 5.13a, the austenite grain size distributions for 60 seconds soaking time are seen to be essentially log-normal. For longer holding times of 900 seconds at 1200°C (Figure 5.12b) and 600 seconds at 1250°C (Figure 5.13c) a shift to a bimodal grain size distribution develops, indicative of abnormal grain growth. This is consistent with observations from Figure 5.10, indicating a critical time range between 60 and 600 seconds. As shown in Figure 5.12c, after 1200 seconds soaking time, a very wide distribution of grain size has developed, possibly indicating a trend towards normal growth of the very large grains. 5.4 Discussion of Experimental Errors It is important to consider the magnitude and effect errors in measurements may have when interpreting experimental data. Austenite grain sizes were measured using A S T M standard methods, which recommend that at least 50 grains are visible in each field being analyzed.1391 However, for higher orders of accuracy, it is suggested that areas containing 500 to 1000 or more grains may be needed. A comparison made between grain size measurements containing statistically significant different sample population sizes is shown in Table 5.1. Measurements performed on samples which showed abnormal growth behaviour gave consistently higher average grain size values with increased sample population size. This is partly attributed to the fact that a larger number 54 of irregularly large grains are more accurately accounted for when larger areas are examined. With the exception of the data obtained on samples reheated for 120 seconds at 1250°C, very little difference between measured grain sizes as a function of the number of grains counted, was seen in specimens possessing a homogeneous microstructure. Although the number of grains counted between sets of data differed, an average of the differences in mean grain size in Table 5.1 indicates an accuracy of measurement of approximately 10 %. An assessment of the accuracy of particle size measurements was not performed. This is difficult since a relatively small number of particles (less than 100) were measured in many cases. Similar to grain size measurements, statistics would suggest that 500 to 1000 particles are needed to perform an accurate assessment. 55 Table 5.1. Comparison of austenite grain size measurements versus number of grains counted. Temp. CQ Time (s) Measured E Q A D * (Lim) Ave. number of grains per field Tot. number of grains measured Difference in grain size (%) Comments on microstructure 1150 600 91.3 31 374 15.6 non-homogeneous 108.2 535 1070 1200 300 122.7 69 346 1.8 homogeneous 125.0 438 875 1200 600 131.5 60 361 16.8 non-homogeneous 158.1 270 540 1250 60 136.3 56 334 1.0 homogeneous 134.9 363 726 1250 120 127.8 63 317 9.9 homogeneous 141.9 290 579 1250 300 145.3 49 343 7.6 non-homogeneous 157.2 266 531 1250 600 203.3 25 175 7.6 non-homogeneous 220.0 72 143 i Jeffries' method Figure 5.1. Optical micrograph of transfer bar microstructure (arrow indicating the presence of TiN particles). Figure 5.2. Optical micrographs of the austenite microstructure at 1100°C after (a) 1 second and (b) 600 seconds. ~20i As 2 0 0 M * X iff? 200um Figure 5.3. Optical micrographs of the austenite microstructure at 1150°C after (a) 120 seconds, (b) 600 seconds and (c) 1200 seconds. Figure 5.4. Optical micrographs of the austenite microstructure at 1200°C after (a) 1 second, (b) 900 seconds and (c) 1200 seconds. 60 Figure 5.5. Optical micrographs of the austenite microstructure at 1250°C after (b) 1 second, (b) 120 seconds and (c) 600 seconds. Figure 5 . 6 . T E M replica micrograph showing mixed precipitates at 1100°C (arrows indicating co-precipitation of niobium-rich particles onto existing titanium nitrides). 62 Figure 5.7. T E M replica micrographs of (Nb,Ti)C particles at 1100°C after (a) 1 second and (b) 600 seconds. Figure 5 . 8 . T E M replica micrographs of (Nb,Ti)C particles at 1150°C after (a) 1 second and (b) 120 seconds. 64 Particle diameter (nm) 2.5 7.9 25.1 Particle diameter (nm) 79.4 125.6 Particle diameter (nm) 397.2 Figure 5.9. Precipitate size distributions at 1100°C for the smaller, spherical Nb-rich particles after: (a) 1 second (591 particles counted) and (b) 600 seconds (280 particles counted); and for the larger, cuboidal Ti-rich (TiN) particles after (c) 1 second (98 particles counted). 65 350 0 200 400 600 800 1000 1200 1400 Time (s) Figure 5.10. Measured austenite grain sizes as a function of reheat temperature and time. 66 71.3 225.4 G r a i n diameter (nm) 0.3 -. s o 0.25 -0.2 -E 0.15 -> 0.1 -a 'a 0.05 -o 0 -(a.) i—i—i—i—i—i—r 3.4E-02 1.1E+00 3.4E+01 1.1E+03 Grain volume (mm 3) xio' 0.25 0.2 S 0.15 (bi) La 0.1 0.05 0 20.0 63.3 200.1 632.8 G r a i n diameter (uni) c .2 0.5 -""S cc L . 0.4 -B 0.3 -O > 0.2 -= u 0.1 -o 0 -3.0E+00 9.6E+01 3.0E+03 9.6E+04 G r a i n volume (mm 3) x lO 6 Figure 5.11. Comparison of grain diameter and grain volume distributions obtained from samples reheated at 1150°C for 120 (a,, a2) seconds and 600 seconds soaking time (bi, b2). 67 I.4E-01 4.3E+00 1.4E+02 4.3E+03 Grain volume (mm 3) x l u ' -i—i—r 6.0E+00 .9E+02 6.0E+03 .9E+05 Grain volume (mm3) xlO 6 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 (C) - i — i — i — r =f=T= 2E+01 3.8E+02 1.2E+04 3.8E+05 Grain volume (mm3) x lO 6 Figure 5.12. Austenite grain size distributions obtained for samples reheated at 1200°C for (a) 60 seconds, (b) 900 seconds and (c) 1200 seconds soaking time. 68 3.0E+00 9.6E+0 Grain volume (mm ) xlO 0.25 c O ' ti 0.2 « 0.15 E © 0.1 > "3 0.05 O 0 (b) 3.0E+00 9.6E+01 3.0E+03 9.6E+04 Grain volume (mm 3) xlO 6 o cs o > 0 "I 1—i—I r 3.0E+00 9.6E+01 3.0E+03 9.6E+04 Grain volume (mm 3) xlO 6 Figure 5.13. Austenite grain size distributions obtained for samples reheated at 1250°C for (a) 60 seconds, (b) 120 seconds and (c) 600 seconds soaking time. 69 CHAPTER 6 MODELLING 6.1 General Approach An attempt at modelling the austenite grain growth kinetics in the present microalloyed steel has involved the combination of two separate computer models. The dissolution, growth and coarsening model developed by Cheng et a/. [ 5 2 ] is employed to quantify the experimentally observed kinetics of niobium and titanium microalloyed precipitates. Using this model, a mean particle size, r , and volume fraction, v, can be determined as a function of time and temperature, thereby providing an input to quantify a pinning parameter, P. Consequently, the actual time and temperature dependence of P has been established based on predicted particle dissolution, growth and coarsening kinetics. This information is then incorporated into the statistical grain growth model of Abbruzzese and Liicke. [ 1 9 ] Two methods are attempted in relating the dissolution, growth and coarsening of precipitates to the kinetics of austenite grain growth. First, an empirical set of fit parameters related to particle pinning is determined based on austenite grain size measurements. A comparison is then made between these values and those predicted independently by the dissolution, growth and coarsening model. 70 6.2 Input Parameters 6.2.1 Material Parameters Material input parameters necessary for the grain growth and dissolution models are discussed in the following sections. As a starting point, initial possible material parameter values are considered as suggested in the literature. However, the correct choice of values are not necessarily obvious. This is particularly true for the dissolution, growth and coarsening model, due to the complexity of the particle system considered. Consequently, a sensitivity analysis is performed to determine a set of reasonable material parameter values which demonstrate consistent predictions compared with the experimental data. 6.2.1.1 Grain Boundary Energy and Mobility Values of grain boundary energy and mobility are needed as input parameters for the grain growth model. The grain boundary energy has been determined by Gjostein et a/. [ 6 3 ] to decrease with carbon content (for C < 0.8 wt. percent) according to the relationship: 7^=(0.8-0 .35C 0 6 8 ) (6.1) where C is the carbon content in weight percent. Consequently a grain boundary energy value of 0.75 J/m 2 is used for the present calculations. The grain-boundary mobility, Mgb, can be expressed as: 71 M g b = f - M 0 z J - ^ \ (6.2) Equation 6.2 is assumed to be independent of composition, where M0 = 0.89 cm2/s, Qgb = 1.66 eV, and a Burger's vector b = 2.58 A are parameters estimated from pure iron. [ 6 4 ] 6.2.1.2 Interfacial Energy An interfacial energy term, y, used in the dissolution, growth and coarsening model, is associated with the boundary of the precipitate/matrix interface and is related to the atomic matching of this crystal-crystal interface. A theoretical analysis of y has been performed by Sun et alS6^ for various carbides and nitrides formed in microalloyed steels; the results are presented in Figure 6.1. From Figure 6.1, y is seen to be a function of the matrix phase (austenite or ferrite) and temperature, decreasing slightly with increasing temperatures in each matrix phase region. Figure 6.1 would indicate typical interfacial energy values of 0.5 and 1.0 J/m 2 for NbC and TiN precipitates, respectively. However, since these values are not exactly known for the particle system considered, several trials were performed in which y was varied at 1100 and 1150°C for the (Nb,Ti)C precipitates, as discussed below. 6.2.1.3 Diffusivity Some variation was found to exist in Table 2.5 for reported diffusivity values for niobium in austenite. As shown in Figure 2.10, a general comparison made between niobium and titanium diffusivities seems to indicate that titanium is the slower diffusing 72 species. Since the experimental evidence indicated that many of the Nb-rich particles contained significant amounts of titanium, it is assumed that Ti-containing particles would dissolve more slowly than pure niobium precipitates. A s a result, model trials were performed employing the lowest reported diffusivity values for Nb (Kurokawa et al.t50]), as well as a diffusivity value for T i (Moll et a/. [ 4 7 ]). 6.2.1.4 Solubility Products A n Energy Dispersive X-ray (EDX) analysis of precipitates showed that, in this particular microalloyed steel, the majority of these contain a mix of niobium and titanium in varying amounts. Since limited data could be found concerning these complex precipitates, and exact particle compositions are not'known, simplified assumptions have been made regarding the particle chemistries. Upon precipitation from the melt, it is assumed that all of the nitrogen is bound to titanium as T i N . Titanium is known to have a much higher affinity for nitrogen, as compared to niobium, consistent with its considerably lower solubility in austenite. These precipitates were also larger and cube-shaped in nature, consistent with reported characteristics of T i N . A l l solubility data obtained for T i N predict complete particle dissolution above 1400°C, well above the temperature range (1100-1250°C) examined in this study. The fraction of niobium not in solution at a given temperature is considered to be precipitated as a carbide. Any remaining titanium is assumed to be in the form of a mixed Nb-Ti precipitate or possibly T i C . However, for the purpose of selecting solubility products for the model, these precipitates were treated as N b C . This seems reasonable 73 since the solubility of niobium and titanium carbide is relatively similar, as indicated in Figure 2.9. With the exception of the data reported by Smith1 3 4 1, the solubility data listed in Table 2.2 for NbC suggest complete dissolution between 1100 and 1200°C for the present composition. An evaluation of the reported NbC solubility product data is given in the following sections. 6.2.2 Initial Parameters 6.2.2.1 Initial Grain Size Distribution The 3-D austenite grain size distribution is approximated by a log-normal distribution: where dg is the peak grain radius and s characterizes the width of the distribution. The average grain size is given by: (6.3) dave = d g exp (In,)2 (6.4) 2 Using methods outlined by Giumelli [ 6 1 ], estimates of s for the initial grain size distribution at each temperature were made from experimental measurements. Since 74 variations between initial grain size distribution widths were small, an average of 0.3 was used in the model for all calculations. All grain growth model predictions are based on the average three dimensional grain diameter, dave. For purposes of comparison, average 3-D grain diameter estimations have been made from the experimental EQAD grain size measurements using the following relation proposed by Giumelli et al.[62]: 6.2.2.2 Initial Particle Size Distribution Based on the measured mean diameter and the standard deviation of the initial particle size distribution, an assembly of np particles may be generated to adequately represent the experimental measurements. In general, the distribution of carbides and nitrides in steels are usually well represented by a normal distribution. For a normal distribution, the probability function,/,^,,can be expressed as: (6.5) (6.6) where r is an individual particle radius, u. is the arithmetic mean radius of the distribution and a is the standard deviation. For modelling purposes, a generated normal distribution of 2000 particles was used for each trial. 75 6.2.2.3 Initial Particle Volume Fraction As a starting condition for the dissolution, growth and coarsening model, the initial particle size distribution and initial volume fraction were needed as inputs. Since no direct experimental data on initial particle volume fractions was obtained, initial (Nb,Ti)C and TiN precipitate volume fractions at 1100 and 1250°C respectively were calculated from equilibrium solubility equations and stoichiometric relationships}66^ An initial (Nb,Ti)C particle volume fraction at 1150°C has been evaluated from the measured austenite grain growth data. Molar volumes of 6.68 xlO"6, 12.8 xlO"6 and 11.9 xlO"6 m3/mol for austenite'67^, NbC^68^ and T i N ^ respectively were used in the model calculations. 6.2.3 Pinning Parameter It is important to note that pinning values obtained from the dissolution and coarsening model account only for those effects caused by particles. In consideration of pinning forces other than those arising from particles, a general expression for grain boundary pinning may be described by: PT=Pppt+Pr (6-7) where PT is the total pinning force associated with Zener particle pinning, PPPT, due to (Nb,Ti)C precipitates, and residual pinning forces, P R , related to solute drag and/or the presence of TiN particles. Based on the measured austenite grain growth data at 1150 and 1200°C, an estimate of the residual pinning force was obtained. For the longer reheat 76 times at 1150 and 1200°C, the final pinning force would not be affected by the presence of (Nb,Ti)C particles since all of these would have gone into solution. Consequently, a and 1200°C reheat temperatures. In addition, a scaling factor of 5.9 (i.e. K = 0.17"') based on experimental work outlined by Manohar et al.^\ has been applied to particle pinning values based on Equation 2.3. Using the mean particle radius and volume fraction data generated from the dissolution, growth and coarsening model for (Nb,Ti)C at 1150°C, the time dependence of particle pinning has been determined based on the particle dissolution kinetics. As shown in Figure 6.2, the general time evolution of P during precipitate dissolution can been described by the exponential function: where P0 and Pj are the initial and final pinning parameters respectively, and a is a constant which is dependent on diffusivity and particle solubility. 6.3 Austenite Grain Growth Model Predictions Equation 6.8 is used in the Abbruzzese-Liicke model to describe changes in pinning force as a function of time for the temperatures of interest. From this, a set of empirical fit parameters, given in Table 6.1, has been determined based on the measured austenite grain sizes. As shown in Figure 6.3, reasonable agreement is seen between residual pinning force of 11 mm" was estimated from model trials performed at the 1150 (6.8) 77 predicted and experimental results using the values listed in Table 6.1. P0 and Pj are taken to be constant at 1100°C, suggesting little change in particle pinning forces at this temperature. This is consistent with experimental observations, indicating the presence of a fine dispersion of (Nb,Ti)C for all holding times at 1100°C. At 1150 and 1200°C, pinning values are seen to decrease with increasing hold times, which can be attributed to the dissolution and coarsening of the (Nb,Ti)C particles. The value of a dictates the rate at which pinning forces decrease. This drops significantly from 500 at 1100°C to 200 s"1 at 1200°C, indicating an increase in particle dissolution rates with increasing reheat temperatures. It is interesting to note that, a final pinning force of 11 mm"1 was obtained for both the 1150 and 1200°C reheat conditions. This value would not be affected by the presence of (Nb,Ti)C particles as these were shown to go into solution after 300 seconds. Therefore, a value of 11 mm"1 may be associated with residual pinning effects related to solute drag or possibly from the presence of TiN. At the 1150 and 1250°C reheat temperatures, the experimental data indicates the formation of a plateau in the grain growth curve followed by an increased rate of austenite grain growth. The Abbruzzese-Liicke model does not reflect this behaviour, but rather predicts a continuous increase in grain size with increasing hold time, typical of normal growth. This would suggest an inability to predict abnormal growth behaviour using the present grain growth model. 6.4 Sensitivity Analysis of the Precipitation Model 6.4.1 Solubility Products An evaluation of the reported NbC solubility product data is shown in Figures 6.4 and 6.5. It is clear that predictions using the values reported by de Kazinczy et alP^ and 78 Nordberg et alPA^ are consistent with the experimental studies. Model predictions using the solubility data reported by Mori et al.[37] show extremely different results, suggesting that the dissolution, growth and coarsening model is very sensitive to the choice of solubility products. As shown in Figure 6.4b, following an initial decrease in volume fraction (presumably from a number of the smallest particles disappearing), a gradual increase in volume fraction is observed, indicating growth at 1100°C. Model predictions of an increase in mean particle size from 9 to approximately 30 nm after 600 seconds is in reasonable agreement with the experimental data. As shown in Figure 6.5a, complete precipitate dissolution at 1150°C is predicted at 370 seconds by Nordberg et a/. [ 3 4 ] and 700 seconds by de Kazinczy et alP^ This is consistent with observed dissolution occurring between 300 and 900 seconds. As evident in Figure 6.5a, the measured mean particle diameters at 1150°C were seen to be consistently larger than those predicted by the model. This discrepancy may in large part be due to the relatively small number of particles included in the experimental study to determine these particle sizes (typically 60 particles for each), resulting in statistical-related errors. However, it was also noticed from the measured distributions that as the number of precipitates in the smaller size classes continuously diminished over time, the number of precipitates in the larger size classes remained relatively constant, leading to an overall increase in particle size for holding times up to 300 seconds. 79 6.4.2 Interfacial Energy As shown in Figure 6.6a, significant changes in (Nb,Ti)C particle volume fraction predictions at 1100°C were caused by relatively small changes in interfacial energy values. At 1150°C however, changes in interfacial energy were seen to have little effect on the particle dissolution kinetics. This would suggest that precipitate growth and coarsening is much more sensitive to changes in interfacial energy as compared with particle dissolution. 6.4.3 Diffusivity As shown in Figure 6.7, several model trials were performed in which the niobium diffusivity reported by Kurokawa et alP0^ was varied by a factor of two and three at 1150°C. The diffusive of titanium reported by Moll et a/. [ 4 7 ] is also included in this plot. It is clear that changes in diffusivity have a strong effect on the kinetics of precipitate dissolution. As would be expected, the rate of particle dissolution is seen to decrease with slower diffusion rates. 6.5 Model Predictions Taking into consideration results from the sensitivity analysis, as well as comparisons of model predictions with experimental measurements. A set of material input parameters which best describes the dissolution, growth and coarsening behaviour of (Nb,Ti)C precipitates in the present microalloyed steel is given in Table 6.2 (note that diffusivity values listed in Table 6.2 are reduced by a factor of three for the model trials). The resulting (Nb,Ti)C predicted pinning forces using these values at 1100 and 1150°C 80 are shown in Figure 6.8. At 1100°C, the model predicts an essentially constant pinning force of 70 mm"1. This is in good agreement with empirical model predictions of 65 mm" A dramatic decrease from an initial pinning force of 308 mm"1 occurs within 40 seconds. However, this is seen to have little effect on austenite grain growth predictions. At 1150°C, the pinning force falls from 36 to 11 mm"1, yielding a rate constant of 350 s"1. This is seen to be slightly lower than the empirical value of 500 s"1, indicating that the dissolution, growth and coarsening model overpredicts dissolution rates. A comparison of measured and predicted grain sizes based on the dissolution model parameters is given in Figure 6.9. Since no experimental data was obtained concerning initial particle volume fractions, an estimate of the initial volume fraction was made based on Zener drag relations. This was calculated as 1.90 xlO"4. As shown in Figure 6.9b, a range of model predictions are given by varying a from 350 to 500 mm"1. The particle dissolution, growth and coarsening model predicts a rate constant of approximately 350 mm"1. However, a value of 500 mm"1 appears to give a more appropriate description of the observed grain growth behaviour. As indicated from experimental observations, a very stable population of TiN particles were present for the entire range of temperatures considered. Model predictions for TiN at 1250°C are shown in Figure 6.10. Following a slight decrease at initial times, the model indicates that the mean particle diameter begins to stabilize at approximately 180 nm, consistent with the experimental results. 81 The modelling of austenite grain growth kinetics at 1100 and 1150°C was based on the dissolution and coarsening of (Nb,Ti)C microalloyed precipitates. This is not the case for grain growth predictions at 1200 and 1250°C however, since essentially none of these particles remain at the higher reheat temperatures. Therefore, other possible causes of grain boundary pinning must be considered. One possibility is the effect of solute drag. Solute atoms have been shown to decrease grain growth similar to particle pinning. ^ Another possibility is a particle pinning force related to the presence of TiN. In an attempt to verify the presence of TiN as a possible pinning source, estimations of the interparticle spacing and limiting grain size (based on Equation 2.1) were made based on a measured mean particle size and calculated volume fraction. Both estimates indicated particle pinning to occur at a grain size of less than 50 urn. This is seen to be significantly smaller than what was observed from the experimental investigations. However, it is important to note that extremely large titanium particles with a radius in the order of 1 urn present during the grain growth experiments were not taken into account during T E M investigations. Assuming that austenite grain growth behaviour at 1200 and 1250°C is controlled by the presence of TiN, it must be considered that the interparticle spacing is in the order of the grain size. As outlined by Humphreys et al.[6], Zener pinning would not apply in this case and an increase in pinning force will occur up until a maximum value corresponding to an equal grain size and interparticle spacing. The present time-dependent pinning force relationship is not able to account for such effects. 82 From the T E M investigations, some (Nb,Ti)C were noticed for very short heating times at 1200°C. This would indicate an initial pinning force greater than Pr but less than P0 at 1150°C. The value of the time constant, a, was selected on the basis of a best fit to the measured data. Pinning forces due to TiN were predicted to be essentially constant during grain growth at 1250°C. The dashed line in Figure 6.11 are grain growth predictions using a constant pinning force of 11 mm"1. Although agreement with grain growth measurements up to 300 seconds is reasonably good, it does not reflect any increase in grain size corresponding to longer hold times. It is possible that austenite grain sizes at 1250°C have exceeded the mean TiN interparticle spacing and therefore, a decrease in pinning force similar to that shown in Figure 2.2 would be expected. Taking this into consideration, model predictions using a smaller final pinning force of 5 mm"1 (shown by the solid line) is used to give a more accurate description of the kinetics of austenite grain growth. 83 Table 6.1. Summary of empirical fitting parameters used in the austenite grain growth model. 1100°C 1150°C 1200°C 1250°C P 0 (mm ') 65 28 19 11 Pf (mm" ') 65 11 11 5 a (s"1) 500 200 750 Table 6.2. Selection of (Nb,Ti)C material parameters. Parameter Value Reference Nb diffusivity constant (£> „) 75 (mm2/s) [50] Nb diffusivity activation energy (Q) 264 (kJ/mol) [50] NbC solubility product 2.9 - 7500/T (wt. %) [34] NbC interfacial energy (y) 0.5 J/m 2 [65] ;ure 6.1. Interfacial energies estimated for various carbides and nitrides austenite (y) and ferrite (a). [ 6 5 ] 85 0 100 200 300 400 500 600 700 Time (s) Figure 6.2. Comparison of predicted and calculated particle pinning forces for (Nb,Ti)C a t l l 5 0 ° C . 86 400 0 200 400 600 800 1000 1200 1400 Time (s) Figure 6.3. Comparison of model predictions and grain size measurements using empirical fit parameters listed in Table 6.1. 87 S u £ H o s-C3 a, H Z c cs 40 30 20 10 (a) 2.5e-4 2.0e-4 -2 1.5e-4 1.0e-4 1 5.0e-5 D 0 = 75 mm2/s, Q = 264 kJ/mol1501 y = 0.5 J/m 2 [ 6 5 ! de Kazinczy et al.* Nordberg et all34] — - Mori etalm • experimental measurements 100 200 300 400 500 Time (s) 600 700 (b) de Kazinczy et al.[j4' Nordberg et a/. [ 3 4 ] — • - Mori etalw] 0.0 D 0 = 75 mm2/s, Q = 264 kJ/mol[501 y = 0.5 J/m21 0 100 200 300 400 500 600 700 Time (s) Figure 6.4. Comparison of reported NbC solubility products for (a) mean particle diameter and (b) particle volume fraction at 1100°C. 88 200 de Kazinczy et a/.1341 Nordberg et al[34] Mori etal.[3?I • experimental measurements D 0 = 75 mm2/s, Q = 264 kJ/mol[501 y = 0.5 J/m 2 [ 6 5 ] 400 Time (s) 600 800 2.5e-4 g 2.0e-4 4 l-5e-4 (b) 200 de Kazinczy et al. [j41 Nordberg et al.[34] Moriera/. [ 3 7 ] D 0 = 75 mm2/s, Q = 264 kJ/mol[50] y = 0.5 J/m 2 t 6 5 ] 400 Time (s) 600 800 Figure 6.5. Comparison of reported NbC solubility products for (a) mean particle diameter and (b) particle volume fraction at 1150°C. 89 1.8e-4 1.6e-4 1.4e-4 1.2e-4 1.0e-4 8.0e-5 6.0e-5 4.0e-5 2.0e-5 0.0 (a) D 0 = 75 mm2/s, Q = 264 kJ/mol [ 5 0 1 logK N b C = 2.9 - 7500/T1 3 4 1 — y = 0.4 J/rn • • Y = 0.5 J/m 2 -• - y = 0.45 J/m 2 0 100 200 300 400 Time (s) 500 600 700 75 mm7s, Q = 264 kJ/mol logK N b C = 2.9 - 7500/T1 3 4 1 y = 0.4 J/m' Y = 0.5 J/m 2 Y = 0.6 J/m 2 [50] 50 100 150 200 Time (s) 250 300 Figure 6.6. Evaluation of the effect of changes in interfacial energy on the (Nb,Ti)C particle volume fraction at (a) 1100 and (b) 1150°C. 90 2.5e-4 1200 Time (s) Figure 6.7. Evaluation of the effect of changes in diffusivity on the (Nb,Ti)C particle volume fraction at 1150°C. Figure 6.8. Predicted (Nb,Ti)C pinning forces from the dissolution, growth and coarsening model at (a) 1100 and (b) 1150°C. 92 a in a 03 fl cu tn S 05 o 1. CU E 2 > 100 80 60 40 A 20 (a) • measured grain sizes model predictions • • , • 200 400 Time (s) 600 250 200 400 600 800 1000 1200 1400 Time (s) Figure 6.9. Comparison of model predictions and grain size measurements using the dissolution model fit parameters at (a) 1100 and (b) 1150°C. 93 200 190 180 170 160 150 140 (a) • model predictions 1 — • experimental measurements 200 400 600 800 Time (s) 1000 1200 1400 6e-4 5e-4 4e-4 3e-4 H 2e-4 le-4 0 200 400 600 800 1000 1200 1400 Time (s) Figure 6.10. Model predictions of (a) mean particle diameter and (b) particle volume fraction as a function of time for TiN at 1250°C. 94 Figure 6.11. Comparison of final pinning forces of 5 and 11 mm"1 at 1250°C. 95 CHAPTER 7 SUMMARY AND CONCLUSIONS Austenite grain growth in low carbon microalloyed steels has been a subject of much interest because of its effect on the final microstructure, and hence final mechanical properties, of many commercial steel products. A considerable amount of this research has been conducted on the influence of second phase particles. However, very few attempts have been made to provide a quantitative link between the actual coarsening and dissolution of precipitates and its effect on austenite grain growth. The present research work has looked at austenite grain growth behaviour in a Ti-Nb HSLA steel. The objectives of this were to experimentally determine the effect Nb-Ti carbonitride precipitates had on the kinetics of isothermal grain growth and use this information to combine the statistical grain growth model of Abbruzzese and Liicke [ 1 9 ] with a model describing the coarsening and dissolution of precipitates^51^ thereby providing a reasonable description of austenite grain growth. Based on the experimental and theoretical works carried out in this study, the following conclusions are drawn: 1) The formation of complex second phase particles resulting from the addition of multiple microalloying elements are seen to have a significant effect on the kinetics of austenite grain growth in low carbon steels. The presence of niobium-rich precipitates has a very strong influence on grain growth over the temperature range of 1100 to 1150°C. This has been correlated to a relatively small mean particle diameter in addition to a high particle volume fraction. The influence of 96 these precipitates decreases significantly at 1200 and 1250 °C due to the higher solubility of niobium at these higher reheat temperatures. However, austenite grain size measurements at 1200 and 1250 °C also seem to be influenced by particle pinning forces. This may possibly be attributed to the presence of a very stable population of TiN particles observed over the entire range of temperatures and times considered. 2) The model developed by Cheng et al}52^ was successfully applied to capture the dissolution, growth and coarsening kinetics of (Nb,Ti)C and TiN precipitates, in a microalloyed steel. From this, predicted changes in particle pinning forces with hold time using a Zener drag relationship could be approximated by an exponential-type function based on an initial and final pinning parameter, as well as, a rate constant which is dependent on particle diffusivity and solubility. It was seen that the predicted pinning parameters generated by the model served as adequate input values for describing austenite grain growth using a time-dependent pinning force. 3) Model results of mean particle diameter and particle volume fraction were extremely sensitive to material input parameters. Large differences in model predictions were observed between different choices of NbC solubility product data. However, a select number of these data gave comparable predictions with experimental results at both the 1100 and 1150°C reheat temperatures. Variations in interfacial energy were seen to have a much larger effect on model predictions 97 at 1100°C than at 1150°C. This would suggest that particle growth and coarsening are much more sensitive to interfacial energy values as compared to particle dissolution. It was also observed that the kinetics of particle dissolution were strongly dependent on the choice of diffusivity values. Based on experimental evidence and model trials, the presence of titanium in the niobium-rich carbides seems to significantly reduce the diffusivity of niobium, and hence, decrease particle dissolution rates. 4) The statistical grain growth model of Abbruzzese and Liicke [ l 9 ] gives a reasonable description of austenite grain growth behaviour in the present material considered. However, the model did not seem to be able to accurately reflect the onset of abnormal grain growth behaviour characterized by a change in grain growth rates. Instead, grain growth predictions were similar to that of normal growth behaviour. It is recommended for future work that further investigations be made in both the experimental and modelling aspects of this project. One of the key parameters needed to accurately describe particle pinning forces is the initial precipitate volume fraction. It would be very beneficial to experimentally determine particle volume fractions in order to improve model predictions. For example, focused ion beam (FIB) technology may be utilized to prepare T E M specimens with known dimensions thereby enabling to experimentally determine precipitate volume fractions. Since it is postulated that austenite grain growth at 1200 and 1250°C may be dependent on the presence of TiN particles, further T E M studies are also needed to confirm exactly the effect of these 98 particles on the kinetics of austenite grain growth. It is also recommended for future work that a sensitivity analysis should be performed for the Abbruzzese-Liicke model to evaluate the effects of changes in initial grain size distribution on model predictions. APPENDIX A SUMMARY OF EXPERIMENTAL MEASUREMENTS Table A . l . Measured austenite grain sizes. Temp. Time Measured Tot. number of E Q A D * grains measured* (°C) (s) (Lim) 1100 1 22.4 379 10 22.5 374 30 23.7 337 60 27.3 498 120 24.7 510 300 26.9 515 600 36.9 364 1150 1 33.1 449 10 48.4 666 30 56.3 575 60 64.4 439 120 65.9 479 300 77.0 395 600 108.2 1070 900 143.5 312 1200 177.6 225 1200 1 67.7 464 10 73.0 399 30 80.3 412 60 90.1 640 120 100.0 520 300 125.0 875 600 158.1 540 900 164.9 510 1200 191.0 357 1250 1 80.7 358 10 94.2 292 30 104.6 567 60 134.9 726 120 141.9 579 300 157.2 531 600 220.0 143 900 247.8 101 1200 328.0 127 Jeffries' method 100 Table A.2. Measured precipitate sizes. Temp. Time Meas. (Nb,Ti)C Tot. number of Measured TiN Tot. number of ppt. diameter (Nb,T')C ppts. meas. ppt. diameter TiN ppts. meas. (°C) (s) (nm) (nm) 1100 1 9.1 591 183.3 91 30 11.9 408 120 21.5 268 300 19.6 280 151.6 106 1150 1 40.3 87 199.5 89 60 50.3 57 120 46.9 63 300 50.9 45 1200 1 192.7 99 1250 1 170.7 98 120 180.1 109 1200 185.3 103 101 REFERENCES 1. A. 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