Applied Science, Faculty of
Materials Engineering, Department of
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UBCV
Cheng, Leon Man Lung
Doctor of Philosophy - PhD
University of British Columbia
Owing to its significant effect on grain growth and recrystallization, both of which directly influence hardenability, ductility, texture formation and the mechanical properties of steels, the precipitation behavior of aluminum nitride (A1N) in steels is becoming of increasing practical importance. To improve the current understanding of the mechanisms and kinetics of precipitation, dissolution, growth and coarsening of A1N during the thermomechanical processing of low carbon steels, a comprehensive experimental and theoretical study has been carried out. Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) have been used, with the aid of the carbon extraction replica technique, to relate the observed morphologies, spatial distribution and particle size distribution of A1N precipitates in a low carbon, Al-killed steel to their thermal history. Experimental studies have been conducted on the precipitation, dissolution, growth and coarsening of A1N precipitates during isothermal annealing, reheating or continuous cooling of the steel at 650°C to 1350°C. The influence of prestraining on the kinetics of isothermal precipitation of A1N has also been studied using the Gleeble 1500 thermomechanical simulator and the stress relaxation technique. Generalized, theoretically based models have been developed in the present project to predict the kinetics of precipitation, dissolution, growth and coarsening of nitrides or carbides in low carbon or microalloyed steels undergoing thermomechanical treatments. The precipitation model takes into account the equilibrium thermodynamic properties of the systems, the precipitate morphology, the misfit strain energy (coherent or incoherent) and the interfacial energy. The precipitation kinetics is formulated using classical nucleation and growth theories. Both homogeneous and heterogeneous nucleation are considered. In the present work, the model is applied to study the precipitation behavior of A1N in low carbon, Al-killed steels during isothermal annealing and continuous cooling in both the austenite and ferrite regions. A theoretical model has also been developed to predict the dissolution, growth and coarsening behaviors and to simulate the size distribution evolution of nitrides and carbides in steels undergoing various heat treatment by using numerical integration methods on a multi-particle system. In this model, dissolution and coarsening are being treated as one continuous, simultaneous process. A set of diffusion, equilibrium and mass balance equations are solved simultaneously for each individual particle. The local equilibrium at the interface, curvature effects and diffusion along grain boundaries are taken into account. These models provide a physical basis for interpreting the influence of the thermomechanical variables on the stabilization of second phase particles in industrial hot strip mills. Theoretical predictions are in good agreement with the experimental measurements. These results lend support to several aspects of the models and to the assumptions incorporated in the models.
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STUDY OF THE KINETICS OF PRECIPITATION, DISSOLUTION AND COARSENING OF ALUMINUM NITRIDE IN LOW CARBON STEELS by LEON MAN LUNG CHENG M.Sc, University of California at Berkeley, 1992 B.Sc., National Taiwan University, 1990 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (DEPARTMENT OF METALS AND MATERIALS ENGINEERING) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1999 ©Leon Cheng, 1999 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 The University of British Columbia Vancouver, Canada DE-6 (2/88) 11 ABSTRACT Owing to its significant effect on grain growth and recrystallization, both of which directly influence hardenability, ductility, texture formation and the mechanical properties of steels, the precipitation behavior of aluminum nitride (A1N) in steels is becoming of increasing practical importance. To improve the current understanding of the mechanisms and kinetics of precipitation, dissolution, growth and coarsening of A1N during the thermomechanical processing of low carbon steels, a comprehensive experimental and theoretical study has been carried out. Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) have been used, with the aid of the carbon extraction replica technique, to relate the observed morphologies, spatial distribution and particle size distribution of A1N precipitates in a low carbon, Al-killed steel to their thermal history. Experimental studies have been conducted on the precipitation, dissolution, growth and coarsening of A1N precipitates during isothermal annealing, reheating or continuous cooling of the steel at 650°C to 1350°C. The influence of prestraining on the kinetics of isothermal precipitation of A1N has also been studied using the Gleeble 1500 thermomechanical simulator and the stress relaxation technique. Generalized, theoretically based models have been developed in the present project to predict the kinetics of precipitation, dissolution, growth and coarsening of nitrides or carbides in low carbon or microalloyed steels undergoing thermomechanical treatments. The precipitation model takes into account the equilibrium thermodynamic properties of the I l l systems, the precipitate morphology, the misfit strain energy (coherent or incoherent) and the interfacial energy. The precipitation kinetics is formulated using classical nucleation and growth theories. Both homogeneous and heterogeneous nucleation are considered. In the present work, the model is applied to study the precipitation behavior of A1N in low carbon, Al-killed steels during isothermal annealing and continuous cooling in both the austenite and ferrite regions. A theoretical model has also been developed to predict the dissolution, growth and coarsening behaviors and to simulate the size distribution evolution of nitrides and carbides in steels undergoing various heat treatment by using numerical integration methods on a multi-particle system. In this model, dissolution and coarsening are being treated as one continuous, simultaneous process. A set of diffusion, equilibrium and mass balance equations are solved simultaneously for each individual particle. The local equilibrium at the interface, curvature effects and diffusion along grain boundaries are taken into account. These models provide a physical basis for interpreting the influence of the thermomechanical variables on the stabilization of second phase particles in industrial hot strip mills. Theoretical predictions are in good agreement with the experimental measurements. These results lend support to several aspects of the models and to the assumptions incorporated in the models. iv TABLE OF CONTENTS Abstract ii List of Tables vi List of Figures vii List of Symbols xiv Acknowledgments xviii Chapter 1 Introduction 1 Chapter 2 Literature Review 5 2.1 Effects of AIN in Steels 5 2.2 Precipitation of AIN in Steels 8 2.3 Existing Kinetic Models of Precipitation 13 2.4 Dissolution, Growth and Coarsening 17 Chapter 3 Scope and Objectives 29 Chapter 4 Experimental Measurements 32 4.1 Material 32 4.2 Experimental Techniques 32 4.2.1 Gleeble Thermomechanical Simulator 32 4.2.2 Micrographs 33 4.2.3 Carbon Extraction Replica 34 4.3 Results and Discussion 36 4.3.1 Dissolution, Growth and Coarsening 36 4.3.1.1 Precipitate Distribution 36 4.3.1.2 Precipitate Morphology 40 4.3.2 Precipitation 41 4.3.2.1 Isothermal Precipitation 42 4.3.2.2 Continuous Cooling 44 4.3.2.3 Strain-Induced Precipitation 46 Chapter 5 Theoretical Model — Precipitation 73 5.1 Modeling 73 V Chapter 6 5.1.1 Nucleation 74 5.1.2 Chemical Driving Force 77 5.1.3 Interfacial Energy 80 5.1.4 Elastic Strain Energy 83 5.1.5 Critical Nucleus 89 5.1.6 Volume Fraction 91 5.2 Calculations 93 5.3 Results & Discussion 93 Theoretical Model — Dissolution, Growth & Coarsening 110 6.1 Modeling 111 6.1.1 Precipitates in Matrix 112 6.1.2 Precipitates on Grain Boundaries 119 6.2 Calculations 122 6.3 Results & Discussion 124 6.3.1 AIN in Austenite 124 6.3.2 AIN in Ferrite 127 Chapter 7 Summary and Conclusions 139 7.1 Summary 139 7.2 Conclusions 141 Chapter 8 Recommendations for Future Work 145 Appendix Nucleus Shape-dependent Parameters 147 References 149 LIST OF TABLES Table 2.1. Solubility of AIN in austenite. (see Figure 2 .2) Table 2 .2 . Calculated coefficients used in Duit et al.'s model[40]. Table 4.1. Chemical composition of DQSK steel (wt%). Table 5.1. List of thermodynamic parameters for AIN and the Fe-Al-N system. Table 5.2. Data used for calculation of interfacial energy for AIN in a-Fe and y Fe[76-80]_ Table 6.1. Diffusion coefficients of Al in austenite and ferrite, D = D0exp( Q/RT). V l l LIST OF FIGURES Figure 2.1. Effects of Al on hot ductility of steels after solution treatment for 5 22 min. at 1330°C. (Mintz and Arrowsmith[14]) Figure 2.2. Solubility of AIN in austenite. (see Table 2.1) 23 Figure 2.3. Effect of cooling rate on precipitation of AIN in C-Mn and Cr-Mo- 24 Ni steel. (Honar and Baliktay[27]) Figure 2.4. Comparison of PTT curves for the static and dynamic precipitation 25 of AIN: S: precipitation start; F: precipitation finish. (Michel and Jonas[31]) Figure 2.5. Comparison of observed precipitation start-time — temperature 26 curves in deformed austenite (closed points) with curves calculated from equation (2.4) with optimum value of B (half-open points) and mean value of B= 2.5xl010K3 (open points). (Dutta and Sellars[38]) Figure 2.6. Calculated and measured fraction of precipitated AIN as a function 27 of time. Isothermal annealing temperature: a) 750°C; b) 650°C (Duitera/.[40]). Figure 2.7. Calculated and measured values of free nitrogen as a function of 28 strip length and coiling temperature (Duit et al.[40]). Figure 4.1. Schematic of the specimen jaws in the Gleeble 1500 50 thermomechanical simulator. Figure 4.2. The extraction replica. The two-phase specimen (a) is etched (b) 51 and carbon coated (c). A further etch then lifts off the replica containing some second-phase particles (d). viii Figure 4.3. TEM micrographs of carbon replicas of as-received coil specimen; 52 showing fine AIN precipitates (indicated by arrows) along ferrite grain boundaries. Figure 4.4. TEM micrographs of AIN after (a) and (b) 4 hours at 650°C, (c) and 53 (d) 1 hour at 700°C, (e) and (f) 4 hours at 700°C and (g) and (h) 24 hours at 700°C. Figure 4.5. TEM micrographs of AIN after (a) and (b) 4 hours at 750°C, (c) and 54 (d) 24 hours at 750°C, and (e) and (f) 7 days at 700°C. Figure 4.6. Evolution of the size distribution of AIN precipitates after soaking 55 the coil specimens at 700°C for (a) 1 hour, (b) 4 hours, (c) 24 hours and (d) 7 days. Figure 4.7. Variation of mean diameter of AIN precipitates with annealing time 56 at 650°C, 700°C and 750°C. Figure 4.8. SEM micrograph of as-received DQSK coil specimen. 57 Figure 4.9. SEM micrographs of coil specimen after being annealed at (a) 57 700°C for 7 days and at (b) 750°C for 4 hours. Figure 4.10. STEM and TEM micrographs showing networks of AIN 58 precipitates in samples held for 24 hours at 700°C and then given different annealing times at 1000°C or 1100°C: (a) STEM, 30 min. at 1000°C, (b) STEM, 60 min. at 1000°C, (c) TEM, 90 min. at 1000°C and (d) TEM, 10 min. at 1100°C. Figure 4.11. Evolution of size distribution of AIN precipitates after soaking at 59 1000°C for a) t = 0s, b) t = 30 min., c) t = 60 min. and d) t = 90 min. ix Figure 4.12. TEM micrographs of AIN precipitates after 24 hours at 700°C and 60 then (a) 15 min. at 1100°C and (b) 30 min. at 1100°C. Figure 4.13. Optical micrographs of coil specimen after annealed at 700°C for 60 24 hrs and then 5 min. at (a) 1150°C and (b) 1350°C, respectively. Figure 4.14. TEM micrographs of replicas of specimens after a) 1 hour at 700°C, 61 b) 4 hours at 700°C, c) 24 hours at 700°C, d) 7 days at 700°C and e) and f) 24 hours at 750°C; showing the hexagonal-shape AIN precipitates. Figure 4.15. TEM micrographs showing rectangular-shaped AIN precipitates 62 after annealed for 24 hours at 700°C and then (a) 30 minutes at 1000°C, (b) 30 minutes at 1100°C and (c) and (d) 60 minutes at 1100°C. Figure 4.16. TEM micrograph showing AIN precipitate on MnS particle after 63 isothermally annealed for 30 minutes at 950°C. Figure 4.17. TEM micrographs showing AIN precipitates after isothermally 64 annealing the specimens at 900°C for (a) and (b) 15 minutes, (c) and (d) 30 minutes. Figure 4.18. TEM micrograph showing AIN precipitates after isothermally 65 annealing the specimen at 650°C for 1 minute. Figure 4.19. TEM micrographs showing AIN precipitates after isothermally 66 annealing the specimens at (a) 750°C for 10 min., (b) 750°C for 30 min., (c) 700°C for 10 min., (d) 700°C for 30 min., (e) 650°C for 10 min. and (f) 650°C for 30 min. Figure 4.20. Variation of mean diameter of AIN precipitates with annealing time 67 during isothermal precipitation at 650°C, 700°C and 750°C. Figure 4.21. A schematic of the temperature profile with different cooling rate 67 during austenite decomposition. Figure 4.22. TEM micrographs showing the effect of cooling rate during 58 austenite decomposition on the precipitation of AIN. Cooling rate = (a) 100°Cs"\ (b) 20°Cs"1, (c) and (d) 5°Cs\ (e) and (f) PCs"1. Figure 4.23. TEM micrographs showing AIN precipitates after isothermally 69 annealing the specimens for 10 minutes at (a) and (b) 850°C and (c) and (d) 800°C. Figure 4.24. A schematic of the thermomechanical profile for stress relaxation 70 test. Figure 4.25. Stress vs log(time) curve for the isothermal relaxation of DQSK 70 steel at 950°C with strain = 0.2 and strain rate = 0.2s"'. Figure 4.26. TEM micrographs showing strain-induced precipitation of AIN in 71 DQSK steel at 950°C, s = 0.2, s = 0.2 s"1: (a) 30 seconds, (b) 30 minutes after prestraining. Figure 4.27. Stress vs log(time) curves for the isothermal relaxation of DQSK 72 steel at 950°C with strain rate = 0.1s"1 and strain = 0.1 and 0.2. Figure 5.1. Schematic diagram of the free energy change, AG, for the 100 nucleation of a spherical nucleus as a function of the radius, r. Figure 5.2. Calculated interfacial energy of AIN in austenite (y-Fe) and ferrite 100 (cc-Fe). Figure 5.3. Effect of c/a on the precipitate morphology; (a) oblate spheroid (c/a 101 < 1) and (b) prolate spheroid (c/a > 1). Figure 5.4. Variation of misfit strain energy, E, with spheroid shape, c/a, (after 101 Nabarro[83]). X I Figure 5.5. Normalized strain energy of a coherent particle vs. aspect ratio for 102 three combinations of elastic constants (after Barnett et a/.[85]). Figure 5.6. Change of Gibbs energy, AG, as a function of a and c: surface plot 102 (left) and contour plot, i.e., iso-energy lines, (right). Figure 5.7. Calculated and measured fraction of precipitated AIN vs. isothermal 103 annealing time in a 0.09wt%C, 0.051wt%Al and 0.0073wt%N steel at 840°C and 1000°C, respectively (experimental data from Vodopivec[32]). Figure 5.8. Computed A G * / £ B T as a function of temperature for AIN nucleation 103 in austenite (0.09wt%C, 0.051wt%Al and 0.0073wt%N). Figure 5.9. Comparing calculated P - T - T diagram for AIN precipitation in 104 austenite (0.09wt%C, 0.051wt%Al and 0.0073wt%N) to experimental data; curve shows the onset of AIN precipitation, P S , and includes experimental data from Vodopivec[32]. Figure 5.10. Calculated fraction of AIN precipitates vs. isothermal annealing 105 time in austenite (DQSK: 0.038wt%C, 0.04wt%Al and 0.0052wt%N) at four different temperature. Figure 5.11. A G * / & B T as a function of temperature for AIN nucleation in 105 austenite (DQSK: 0.038wt%C, 0.04wt%Al and 0.0052wt%N). Figure 5.12. Calculated P - T - T diagram for AIN precipitation in austenite 106 (DQSK: 0.038wt%C, 0.04wt%Al and 0.0052wt%N); curve shows the onset of AIN precipitation (P S). Figure 5.13. Calculated P - T - T diagram for AIN precipitation in austenite in two 106 low carbon steels; curves show the onset of AIN precipitation (P S ). Figure 5.14. A G * / & B T for AIN nucleation at grain boundaries in austenite in two 107 low carbon steels as functions of temperature. X l l Figure 5.15. Calculated P-T-T diagram for A I N precipitation in ferrite in DQSK 107 steel: Ps and Pf represent 1% and 99% completion of precipitation. Figure 5.16. AG*/&BT as functions of temperature for homogeneous and grain 108 boundary nucleation of A I N in ferrite (DQSK steel). Figure 5.17. AG*/&BT as functions of temperature for grain boundary nucleation 109 of A I N in austenite (DQSK steel) for three different values of ygrj. Figure 5.18. Calculated P^ curves of the P-T-T diagram for A I N precipitation in 109 austenite in DQSK steel for three different values of ygb-Figure 6.1. Schematic diagram of the solute concentration in the vicinity of (a) 129 a dissolving precipitate and (b) a growing precipitate. Figure 6.2. Schematic concentration fields showing the effect of particle size 130 on the transformation mode, i.e., dissolution or growth, of an individual particle. Figure 6.3. Schematic diagram of a precipitate located on a grain boundary. 130 Figure 6.4. Flow chart illustrating the logic of the program. 131 Figure 6.5. Solubility products of A I N in austenite. 132 Figure 6.6. Evolution of size distribution of A I N particles after soaking at 133 1000°C for a) t = 0s, b) t = 30 min, c) t = 60 min and d) t = 90 min. Figure 6.7. Variation of mean diameter with reheating time at 1000°C. 134 Figure 6.8. Variation of A I N volume fraction with reheating time at 1000°C 134 (after annealed for 24 hours at 700°C). Figure 6.9. Size evolution of four selected A I N particles during soaking at 135 1000°C. Figure 6.10. Variation of mean diameter of A I N particles with reheating time at 136 xiii (a) 1100°C and (b) 1175°C, after an initial 24 hour annealing at 700°C. Figure 6.11. Variation of mean particle size with reheating time at 1000°C (after 137 initially annealed for 24 hours at 650°C). Figure 6.12. Evolution of the size distribution of AIN particles (initially 137 annealed for 24 hours at 650°C) after soaking at 1000°C for a) t = 0 s, b) t = 1 hour and c) t = 2 hours. Figure 6.13. Variation of mean diameter of AIN particles with annealing time at 138 700°C. Figure 6.14. Evolution of the size distribution of AIN particles after soaking at 138 700°C for a) t = 1 hour, b) t = 20 hours and c) t = 164 hours. LIST OF SYMBOLS1 A,B constants used in Equation (2.4) Agb grain boundary surface area eliminated by the present of the precipitate A„ pre-exponential factor used in Equation (2.9) A cross-section area of particle a radius of particle aP, a lattice parameters of precipitate and matrix, respectively c/a aspect ratio of precipitate C concentration field Ci, C2 constants used in Equation (2.1) c b solute concentration within grain boundary equilibrium solute concentration at planar interface Q solute concentration in the matrix at the interface CP,CM solute concentration in precipitate and in matrix, respectively C T total solute concentration d precipitate diameter d0 mean grain diameter d mean particle diameter d* critical diameter . D bulk matrix diffusivity Db grain boundary diffusivity E shape factor Eel elastic strain energy per unit length of a dislocation eT u uniform stress-free transformation strain f volume fraction of precipitate fo volume fraction of precipitate at time = 0 i . Al l symbols are in SI units, unless otherwise noted. XV / interface energy modifying factor G Gibbs free energy gf chemical potential (or partial molar free energy) of component i in phase (j) HfER enthaply ofthe stable state of component i at 1 atm. (O.lMPa) and 298.15 K I nucleation rate (per unit volume and unit time) k parameter used in Equation (6.10) kB Boltzmann's constant, 1.38066x 10"23 JK"1 ks supersaturation ratio K c coarsening parameter (Equation (2.14)) K°°,Ki solubility product for planar and non-planar precipitate/matrix interface, respectively Kp bulk modulus of the precipitate Ks solubility product /ds length of dislocation eliminated by the present ofthe precipitate L^* , L^e M regular solution type binary interaction parameters m constant exponent (Equation (2.3)) N number of atomic sites per unit volume on which the nucleation could have started n Avrami coefficient (Equation (2.9)) N A Avogadro's number, 6.02205xl023 mol'1 Ns atoms/unit area of surface Ny probable concentration of critical-sized nuclei in a unit volume Ps, P/ precipitation start and finish time, respectively Qn activation energy used in Equation (2.9) R gas constant, 8.3144 tool"'K"1 f arithmetic mean radius ofthe particle size distribution r* critical radius r radius of precipitate xvi s total surface area of precipitate T absolute temperature (K) t time t' incubation time V volume of a precipitate V A I N molar volume of AIN, 12.563xl0"6 m3mor' V e extended volume fraction of precipitate Vf volume fraction of precipitate v P ,v m molar volume of precipitate and matrix, respectively X ? , x° the equilibrium and original concentrations of element / in the respectively matrix, XP,XM concentration of precipitate forming element in precipitate and respectively matrix, mole fraction of component / in phase dp yf fraction of component i on the sublattice it occupies in phase dp Y Young's modulus ZH Zener-Hollomon parameter (Equation (2.4)) Z Zeldovich non-equilibrium factor Zt lattice coordination number Zs bonds per atom across the interface z fraction precipitated, 0 < z < 1 (Equation (2.9)) P* rate at which atoms impinge upon the critical nucleus X ' X excess and equilibrium vacancy concentration, respectively 5 grain boundary thickness A r volume misfit s, s strain and strain rate, respectively sT linear misfit strain xvu y precipitate/matrix interfacial energy (per unit area) ygb grain boundary surface energy (per unit area) yc chemical component of interfacial energy Yst structural component of interfacial energy an standard deviation of the particle size distribution Up, u shear moduli of precipitate and matrix, respectively vP, v Poisson's ratio of precipitate and matrix, respectively © percentage of the maximum possible nitrogen as AIN pi probability density of a log-normal particle size distribution pn probability density of a normal particle size distribution Q additional energy change produced when precipitates are formed at a high energy area £, growth parameter used in Equation (2.12) *F cooling rate (Kh"1) C, constant (Equation (2.3)) [i] concentration (wt%) of element i in solution AE heat of solution of precipitate Agchem chemical Gibbs free energy change for the precipitation of one mole of AIN AG Gibbs free energy change associated with the formation of a precipitate AGchem chemical free energy change per unit volume of precipitate AGS elastic misfit strain energy per unit volume of precipitate AGv a c free energy change associated with excess vacancies AG* critical formation energy AH heat of formation of precipitate X V l l l ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to his research supervisors, Professors E. B. Hawbolt and T. M. Meadowcroft, 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 Ms. M. Mager, Mr. B. Chau, Mr. R. Cardeno and Mr. P. Wenman for their technical support. Experiments in this research cannot be done without their assistance. The author wants to express his gratitude to Professors S. Dunbar, K. Pinder, D. Tromans, W. Poole, M. Wells, S. Cockcroft and M. Militizer for their critical questions and constructive advice during the departmental and final oral examinations and for their help in finishing this thesis. Special thanks to the external examiner, Dr. S. Argyropoulos of University of Toronto, for his constructive comments. Last, but not least, the author would like to delicate this work to his parents and to his wife for their love, support and encouragement to his study throughout these years. 1 C H A P T E R 1 INTRODUCTION During the past decades, significant progress has been achieved in the development of microalloyed steels. It is well known that the precipitation of nitrides, carbides or carbonitrides of microalloying elements such as niobium, vanadium or titanium can have strong effects on the mechanical properties of steels due to their influence on recrystallization and grain growth during thermomechanical processing[1"3]. On the other hand, aluminum — which was used primarily for deoxidization purposes — is not usually classified as a microalloying element even though the precipitation of aluminum nitride (AIN) can have equally strong effects on the microstructure evolution and mechanical properties of steels. Due to its usefulness for controlling grain growth and recrystallization, which directly influence hardenability, hot ductility, texture formation and mechanical properties of steels, AIN precipitation has been of considerable interests to metallurgists^ 4"13^ In addition, Al-killed steels have been known to show improved strain aging resistance and enhanced deep drawability. The precipitation of AIN has also been held responsible for certain forms of cracking in continuously cast products. AIN also exerts important second order effects through its influence on the precipitation of other alloy nitrides or carbonitrides. Numerous studies have been conducted to deal with the effects of AIN on microstructure formation and the associated mechanical properties of steels. The size distribution, spatial distribution and morphological characteristics of the precipitates are Introduction 2 believed to markedly affect the mechanical properties of the steels after a variety of thermomechanical processing. However, the causes and effects of these nitride precipitates on microstructure development are still not yet fully understood; there is still much to investigate. To achieve an understanding of the mechanisms by which AIN precipitation or dissolution influence microstructure development during the thermomechanical processing of steels, one must first understand the precipitation and dissolution kinetics of AIN. Over the years, the mechanisms and kinetics of precipitation and dissolution/coarsening of AIN in steels have been investigated extensively by many researchers. It is generally acknowledged that alloy chemistry, temperature, holding time, strain, strain rate and cooling or heating rate play important roles on the precipitation or dissolution of AIN in steels during reheating, hot rolling, cooling and coiling. However, there still lacks a systematic study to quantify the influence of each of these variables as they relate to thermomechanical processing of steels. Consequently, there is scientific merit in combining an experimental and analytical study to characterize the precipitation and dissolution of AIN, and to develop appropriate models to determine quantitatively how variables such as composition, temperature, strain, strain rate and cooling rate affect the deportment of AIN during thermomechanical processing of steels. To improve the current understanding of the mechanisms and kinetics of precipitation, dissolution and coarsening of AIN during the thermomechanical processing of low carbon steels, a comprehensive experimental and theoretical study has been conducted. Introduction 3 Experimental studies have been carried out on the precipitation, dissolution, growth and coarsening of AIN precipitates during isothermal annealing, reheating or continuous cooling of a low carbon Al-killed steel. The effects of strain and strain rate on the strain-induced precipitation have also been studied using a stress relaxation technique. The carbon extraction replica technique combined with transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM) and energy dispensive X-ray (EDX) analysis have been used to investigate the morphology, composition, spatial distribution and particle size distribution of the AIN precipitates after different thermomechanical treatments. Although some models have been established for the kinetics of precipitation of nitrides or carbides in steels, most are empirical or semi-empirical (which are essentially curve-fitting models) and very few are fundamentally based. Through a series of experimental and theoretical studies, theoretically based models have been developed in the present project to predict the kinetics of precipitation, dissolution, growth and coarsening of AIN in low carbon steels incorporating processing variables, with all the parameters having appropriate physical significance. The precipitation model takes into account the equilibrium thermodynamic properties of the systems, the precipitate morphology, the misfit strain energy (coherent or incoherent) and the interfacial energy. The precipitation kinetics is formulated using classical nucleation and growth theories. Both homogeneous and heterogeneous nucleation during isothermal annealing and continuous cooling in both austenite and ferrite regions are considered. A theoretical-based model was also developed using numerical integration methods on a multi-particle system to predict the dissolution, Introduction 4 growth and coarsening behaviors and to simulate the size distribution evolution of nitrides or carbides in microalloyed steels. In this model, dissolution and coarsening are being treated as one continuous, simultaneous process. A set of diffusion, equilibrium and mass balance equations are solved simultaneously for each individual particle. In the case of precipitates on grain boundaries, the effect of grain boundary diffusivity is also considered. Good agreement is obtained between the theoretical predictions and the experimental measurements. These results lend support to several aspects of the model and to the assumptions incorporated in the model. Providing the basis for predicting the precipitation, dissolution and coarsening behavior, the results of this study will improve our ability to control and utilize the effects of AIN in steels. It will also assist in the optimization of microalloy design and will generate subsequent improvements to the current steelmaking and processing procedures. 5 C H A P T E R 2 LITERA TURE REVIEW 2.1. Effects of AIN in Steels The influence of AIN precipitation on microstructure evolution and the development of mechanical properties of low carbon, low alloy steels has been studied by many researchers[4"13]. These inclusions have an impact on the hot ductility of steel which is important in the production of sound, defect free products. Due to the low ductility of some low alloy steels at hot working temperatures, some severe cracking problems have arisen during continuous casting[4'5] and hot rolling[6], resulting in high wastage. The causes of the low hot ductility in these steels have been extensively investigated^ 5'7'8'. Microalloying composition and thermal history are known to have significant influence on the high temperature ductility[8]. However, the precipitation of AIN at austenite grain boundaries is believed to be one of the principal causes of low hot ductility in carbon and low-alloy steels in the temperature range 1100°C -700°C. There is general agreement1^ that for a given set of test conditions, increasing the aluminum content of steel causes a progressive reduction in the hot ductility. Mintz and Arrowsmith[14] have shown that the low ductility trough in plain iron-carbon alloys extends to higher temperatures with the addition of Al (Figure 2.1). Thermomechanical process variables, such as temperature, strain and strain rate during hot reduction and the cooling rate during controlled cooling affect the rate of precipitation of nitrides and the precipitate size which, in turn, govern the temperature range of the low hot ductility trough. Literature Review 6 It is believed that the low hot ductility associated with intergranular fractures in carbon and low-alloy steels during hot rolling and straightening of continuous cast products is caused by the grain boundary precipitation of aluminum nitrides which reduces grain-boundary mobility, inhibiting grain boundary migration, retarding dynamic recrystallization and leading to growth of voids around the precipitates, thus facilitating intergranular crack propagation^ 1'81. Croft et a/.[15] suggested that the AIN precipitates act as nuclei for intergranular cracks which are effectively constrained to the prior grain boundary region. Moreover, it is generally agreed that smaller AIN particles at the austenite boundaries cause poorer hot ductility than coarser particles[6]. Therefore, by controlling the precipitation of nitrides so that coarse precipitates are formed at the austenite grain boundaries, steels are less susceptible to cracking during hot deformation. In addition, the intervention of the y —» a transformation is associated with a further impairment in ductility, in part because of its significant accelerating effect on the precipitation of AIN. Even in the absence of AIN precipitation, it is suggested^ 10'161 that in the y + a range, strain concentration in the weaker and more ductile ferrite phase at the austenite grain boundaries leads to a marked reduction in hot ductility. The low hot ductility caused by the precipitation of AIN in the austenite, combined with that due to the y -» a transformation, widen the temperature range over which the steel has low hot ductility. However, Finkler and Rennollet[17] argued that AIN itself is not responsible for the impairment of hot ductility in steels. Instead, they suggested that nitrogen, especially at levels above 0.005wt%, is the cause of the ductility trough, even in the absence of nitride Literature Review 7 forming elements. They suggested that voids generated during the hot deformation process act as sites for the generation of molecular nitrogen, which then impedes dislocation movement. Nitrogen is also known to be responsible for the strain aging of steels. It is generally agreed that strain aging is due to the segregation of solute nitrogen and carbon atoms to dislocations, which results in an increase in flow stress and a decrease in toughness due to dislocation locking. However, the effect of nitrogen is usually more pronounced than that of carbon13'. It has been suggested13'18' that the addition of Al can improve the strain aging resistance of steels by forming AIN precipitates which reduces the amounts of dissolved, mobile nitrogen in solid solution. Aluminum nitride precipitates are also known to have significant effect upon the formation of the {111} recrystallized texture in cold-rolled and batch annealed sheets of aluminum-killed steel[11"13'. Taguchi et a/.[19' first utilized AIN and MnS as grain growth inhibitors during recrystallization to produce grain oriented silicon steels with a sharp {110}<001> texture. Furubayashi et a/.[20' claimed that plastic deformation provides dense nucleation sites for the formation of well-dispersed and fine precipitates of AIN, which are considered to be of major importance in the development of the preferred {111} texture. They also suggested a direct correspondence between the nucleation sites for precipitates and defects induced by deformation. Since the mechanisms by which these precipitates influence steel properties are still not yet fully understood, detailed studies ofthe precipitation behavior is critical in clarifying Literature Review 8 the effects of precipitates upon microstructure evolution and the associated development of the mechanical properties of the steels. 2.2. Precipitation of AIN in Steels The solubility of aluminum nitride plays a vital role in understanding the precipitation kinetics of AIN in steels. The driving force for precipitation is directly related to the solubility of the precipitates in steels. The solubility of AIN in steel can be expressed by the solubility product, Ks where [Al] and [N] are the contents (wt%) of Al and N respectively in solution, Ci aud C2 are two constants and T is the absolute temperature. Under equilibrium conditions, precipitation of AIN will occur when the solubility product is exceeded. in Table 2.1 and are shown in Figure 2.2. Except for the data from Darken et al}lli and Narita et al., the solubility data obtained by other investigators are in close agreement. Leslie et al.[22] suggested that the difference in solubility reported for the Darken data is not a result of the analytical technique, but most likely arises from local microsegregation of aluminum and nitrogen. Leslie et al. suggested that under practical heating conditions, due to local microsegregation of aluminum and nitrogen, the temperatures required for solution (2.1) The solubility data for AIN in austenite found in the literature[21 are summarized Literature Review 9 of AIN will be higher than those quoted by Darken et al. Thus, for practical heat treatment purposes, the solubility of AIN in austenite can be represented by[22] log K , = log [Al] [N] = + 1.03 (2.2) Over the past decades, a number of experimental studies have examined the precipitation and dissolution of AIN in steels, especially the effects of composition, temperature, cooling rate and deformation conditions on the kinetics of precipitation and dissolution^6"351. It has been shown that precipitation of AIN in austenite is particularly sensitive to the cooling rate126'; in some cases it can be suppressed entirely at cooling rates greater than about 65K/min[27]. Honer and Baliktay[27] demonstrated that the degree of precipitation of AIN is given by © = <;vPmxl00% (2.3) where 0 is the percentage of the maximum possible nitrogen as AIN, *F is the cooling rate (Kh"1), C, is a constant dependent on the initial nitrogen and aluminum levels, the primary grain size and the transformation behavior of the steel, and m is an exponent of value about -0.5. Their results for a C-Mn steel (C = 10.8, m = -0.49) and a Cr-Mo-Ni steel = 9.3, m = -0.55) are given in Figure 2.3. In Walker and Marshall's study[28] of AIN precipitation in steel upon thermal cycling, samples (0.41wt%C, 0.7wt%Mn, 0.28wt%Si, 0.038wt%Al & 0.0132wt%N) were Literature Review 10 first soaked at 1300°C for lmin., then were cooled rapidly to a temperature between 500°C and 750°C before immediately reheating to 1000°C, which is a typical strand straightening temperature. They found that if the temperature falls below the Ar3 temperature and the sample is subsequently reheated, then a significant increase in the fraction of aluminum nitrides is obtained with a corresponding decrease in the austenite grain size. However, this enhanced precipitation does not occur if the temperature does not fall below the A r 3 temperature. Since the a -» y reaction forms small grains just above the A C 3 temperature, they suggested that when these small austenite grains have formed, Al and N can diffuse more rapidly over the shorter distance to the grain boundaries and form AIN, which then pins the boundaries, preventing grain growth. If the thermal cycle does not include the temperature falling below the Ar3, then during subsequent reheating the small grains will not be present and Al and N must diffuse further to the more distant grain boundaries; thus, not as much AIN is formed. However, Gladman and Pickering^ 61 argued that significant AIN precipitation does not occur until the onset of the y —> oc transformation. It was also suggested that[I,I4] during the cooling of steel, AIN does not precipitate in unstrained austenite at the cooling rate normally applied in steel processing. Instead, strain-induced precipitation of aluminum nitride in austenite is the principal cause of low hot ductility. Mintz and Arrowsmith[14] have found that strain-induced precipitation occurs at higher temperatures as the strain rate decreases. Thus, a slower strain rate, as occurs during strand straightening, can shift the onset of low hot ductility to a higher temperature in the fully austenitic range. Literature Review 11 In the study by Dogan et al} J on AIN precipitation in low carbon steels, samples were first soaked at 1230°C for 90 min. and then hot-rolled into bars. Specimens taken from these bars were then reheated and isothermally annealed at high temperatures (1000°C -1100°C) for 15 to 180 minutes. They showed that for typical commercial aluminum-killed steels (Al=0.027wt%, N=0.007wt%), AIN precipitates were found to be distributed non-uniformly in the austenite, i.e., most of the precipitates were located on the grain boundaries. However, for steels with much higher Al and N contents (Al = 0.089wt%, N = 0.037wt%), the AIN precipitates are distributed quite randomly, with a much higher (10 times) AIN volume fraction. Yanovskaya[30] claimed that when a 3%Si steel (0.04-0.05%C, 0.03%A1 and 0.008%N) is cooled down after being solution treated at 1250°C, hexagonally-shapecl AIN particles are precipitated in the 1100 - 1000°C temperature range at cooling rates of 600 -300°C/min. She also claimed that rapid reheating of the steel to 1150°C and a 1-3 min. holding at this temperature results in the formation of an austenite/ferrite microstructure and partial or complete dissolution of the aluminum nitrides. When this steel is then subsequently cooled to 950°C at cooling rates of 300 - 600°C/min., an extremely high volume density of fine hexagonal particles is observed in the regions of decomposed austenite. A high volume density of AIN is also observed in the ferrite-austenite contact area after the phase transformation. However, fewer nitrides are precipitated in the ferrite that did not participate in the phase transition. Literature Review 12 It is generally acknowledged that the.hot deformation of Al-killed steels results in a marked increase in the kinetics of precipitation of A1N [ 3 1"3 6 ]. Michel and Jonas'^ found that during hot torsional deformation of a series of Fe-Al-N steels, the kinetics of the dynamic precipitation (i.e., precipitation occurring during deformation) of AIN in austenite can be increased by more than an order of magnitude over the corresponding static precipitation rates (Figure 2.4). Vodopivec[34] also reported an increased AIN nucleation rate during deformation without any alteration in the subsequent rate of precipitation. It was claimed that the onset of recrystallization during or immediately following the deformation would, by eliminating dislocation substructures, reduce the- subsequent precipitation rate to that typical of undeformed austenite. However, since hot deformation of steels at or below A 3 also accelerates the y —» a transformation, Kaspar et a/.[35] suggested that the enhanced AIN precipitation during hot deformation of steel at or below A3 is due to the acceleration of the y -» a transformation instead of due to dynamic precipitation. In addition, Michel and Jonas[31] reported that at high strain rates (MO 'V 1 ) , no dynamic precipitation of AIN occurred before recrystallization, while at low strain rates (<3xlO"V'), dynamic precipitation of AIN can occur, and even be completed, before the initiation of recrystallization. Literature Review 13 2.3. Existing Kinetic Models of Precipitation Numerous different kinetic models have been established for the precipitation of second phase particles, especially nitrides and carbides in steels[37"40]. Akamatsu et alP1^ developed a mathematical model for predicting the isothermal precipitation of NbC in deformed austenite in a microalloyed low carbon steels. Their model, based on experimental precipitation studies, uses classical nucleation and growth theories. The effect of hot deformation is correlated into the model by using dislocation density as a parameter. The chemical driving force for nucleation was determined from the equilibrium solute content which was obtained from the experimental solubility product. However, four fitting parameters are needed to fit the calculation to the experimental results. Dutta and Sellars[38], on the other hand, derived a semi-empirical kinetic model for strain-induced niobium carbonitride (Nb(C,N)) precipitation on the basis of diffusion controlled nucleation theory. The effect of strain rate on precipitation was introduced by using the Zener-Hollomon parameter^ 411. They proposed the following strain-strain rate sensitive expression for the time to form 5% of the total precipitation of Nb(C,N) at temperature, T, in austenite: ArxTun-i - i 7 -0-5 270000 B t0.05=A[Nb] e ZH exp r t e x P T 3 ( l n ^ ) 2 ( 2 - 4 ) Literature Review 14 where ZH = s exp is the Zener-Hollomon parameter; Taef is the absolute temperature R T d e f of deformation; [Nb] is the soluble niobium content (wt%); s is the strain; s is the strain rate; k„ is the supersaturation ratio which is calculated from the solubility product; and A and B are constants with optimum values determined by fitting the precipitation-time-temperature curve to experimental data. Their calculated precipitation-time-temperature curves are compared to experimental data in Figure 2.5. However, Arieta and Sellars[42] stated that the excess vacancies (non-equilibrium vacancies) generated during deformation can enhance the driving force for the nucleation of incoherent/semi-coherent precipitates. It is because the annihilation of the excess vacancies at the incoherent precipitate/matrix interface can relieve the elastic strain created by the nucleation. By considering the effect of excess vacancies, they modified the above equation to become t5% =A[Nbr1s-1r05 exp (-200000^ 1 exp 167t(y/) RT 3 1_ D N b e x P V 270000 RT J ,3&BT(AGchem + AG v a c) J (2.5) where E>Nb is the diffusion coefficient of Nb in the austenite matrix; %ex and %e are the excess and equilibrium vacancy concentration, respectively; y is the interface energy between austenite and Nb(C,N); / is an interface energy modifying factor; kB is the Literature Review 15 Boltzmann's constant and the chemical driving force, AGChem V V P ; h\ks where Vp is the molar volume of the precipitate. The free energy change associated with the presence of excess vacancies, AGvac, for an incoherent precipitate is deduced by Russell[43] as AG v a c = -——RTln— 9(RT^-)2 — - (2.6) V3C Vp X e X e 4Y(Vp)2 where Y and v are the Young's modulus and the Poisson's ratio of the matrix, respectively, and AT is given by where V p and V m are the molar volumes of the nucleating phase and the matrix, respectively. Liu and Jonast39] developed a kinetic model to predict the starting time for the strain-induced precipitation of Ti(C,N) in austenite. In this model, the classical nucleation theory was modified and the chemical driving force was calculated by a thermodynamic approach, instead of using the solubility product. The chemical driving force, AGChem, was expressed as Literature Review 16 AG RT chem 2V„ In / Y e A A T i v X T i y -i-yln 23 + (l-y)ln A N (2.8) where V p is the molar volume of the Ti(C,N) precipitate, and X° are the equilibrium and original concentrations of element / (i = Ti, C or N) in the matrix, respectively, and y is the mole fraction of carbon in the nucleus of Ti(C,N). However, in both Jonas' and Sellars' models, only the nucleation ofthe precipitates was considered. The growth of the precipitates was ignored. Therefore, these kinetic models can only be applied at the early stage of precipitation. Moreover, a number of parameters in these models were determined by curve-fitting. Duit et a/.[40] developed a simple kinetic model, which is based on the Avrami equation, to predict the fraction of aluminum nitride precipitated. For isothermal precipitation behavior, z=l-exp{-(t/t0)n} (2.9) where z = fraction precipitated (0 < z < 1); t is the isothermal annealing time; n is the Avrami coefficient; t0 = A n exp 9SL V R T y , where An is a pre-exponential factor; Qn is the activation energy; R is the gas constant; and T is the absolute temperature. For non-isothermal precipitation, the additivity rule and infinitesimal increments of time were used: Literature Review 17 (2.10) n such that z = 1 - exp<! - J exp Q n dt (2.11) RT(t) where the function T(t) depends on the specific thermal route. The parameters An, Qn and n were calculated by fitting the model to measured AIN precipitation data obtained for different thermal processes. Values of An, Qn and n calculated by Duit et al. are shown in Table 2.2. A comparison of their measured and calculated results for isothermal annealing and hot rolled coils is given in Figure 2.6 and Figure 2.7. Although this model can be used to predict AIN precipitation in some cases, it is basically an empirical formula. The effect of chemical composition is ignored. Moreover, since this is essentially a curve-fitting method, this model cannot be used to describe alternate thermomechanical processes, or even similar processes with different conditions, unless the associated empirical parameters are known. 2.4. Dissolution, Growth and Coarsening There are generally two different mechanisms responsible for the growth or dissolution of the precipitates[44]. For interface controlled growth, the growth rate is controlled by the mechanism that allows the solute atoms to cross over from the matrix to Literature Review 18 the precipitate. On the contrary, for diffusion controlled transformation, the interface reaction is much faster than the diffusion process and the diffusion rate of transport of atoms to the growing precipitate becomes the dominant factor. Since the nitrides and carbides possess a composition significantly different from that of the steel matrix, it is generally believed[44"47] that the growth or dissolution of the precipitates is diffusion controlled. Although exact solutions for growth or dissolution depend on the boundaries and initial conditions, Zener[48] has shown that whenever the growth is controlled by a simple diffusion process, the growth rate varies inversely as the square root of the time. In their studies of Ti(C,N) and MnS precipitates in steels, Jonas et a/.[45,49] confirmed that the time dependence of the mean diameters of the growing precipitates follows a parabolic law. They described the growth rate as where a is the radius of the particle and h\ is the growth parameter dependent on the effective diffusion coefficient of the rate controlling element and its supersaturation in the matrix. The mean diameter of the growing precipitates was described as da _ h\ (2.12) dt a ( J ) 2 + ( a d ) 2 - ( ^ ) 2 = 8 ^ ( t - t 0 ) (2.13) Literature Review 19 where d is the mean diameter, ad is its standard deviation, d* is the critical diameter and to is the average nucleation time for a given steel at a given temperature. After the nucleation and growth processes, precipitates with various sizes are dispersed in the matrix. There is a tendency for the smaller particles to shrink and the larger ones to grow. This process is known as coarsening or Ostwald ripening and is driven by the minimization of the total surface free energy of the system. According to the classical Lifshitz-Slyozov-Wagner (LSW) theory^ 50'511 for particle coarsening, under steady state conditions and a limiting case of zero volume fraction of precipitates, the mean particle diameter, d , increases with time according to a cubic law: where d0 is the initial mean diameter at time, to, and Kc is a coarsening parameter that depends on interfacial energy, diffusion coefficient and other variables. In this model, a steady-state size distribution is predicted to be approached irrespective of the initial size distribution, with a maximum particle size of 1.5 f, where r is the mean particle radius. By modifying the LSW equation, Sun et al}49^ described the coarsening kinetics of precipitates after precipitation as (d ) 3 =(« / 0 ) 3 +K c ( t - t 0 ) (2.14) d-df=Kc(t-?f) n (2.15) Literature Review 20 where df is the mean diameter of the precipitates at the precipitation finish time, Py. The denomination of the fractional exponent, n, in this equation depends on the specific rate-limiting mechanism: n = 3 if the coarsening is controlled by bulk diffusion, n = 4 if controlled by grain boundary diffusion and n = 5 if controlled by pipe diffusion. However, it was shown[52'53] that the coarsening rate of the largest particles initially increases rather rapidly, then passes through a maximum and slowly approaches zero for long periods of time. The value of the coarsening rate predicted by the LSW theory is reached shortly before reaching the maximum rate. Moreover, in most cases, the observed size distributions are wider than those predicted by the LSW theory. Furthermore, an extended distribution of large sized particles is observed, in contradiction to the LSW theory. Literature Review Author logKs = log[Al][N] Darken et a/.[21] -7400/T+ 1.95 Leslie et al.[22] -6770/T+ 1.03 Shimose & Narita[23] -7184/T+ 1.79 Uimerefa/.[24] -7750/T+1.80 Erasmus[25] -6180/T +0.725 Gladman & Pickering[26] -7500/T+ 1.48 Honer & Baliktay[27] -9200/T + 2.923 Table 2.1. Solubility of AIN in austenite. (see Figure 2.2) treatment coefficients Qn [kJ/mol] n A„ [s] isothermal annealing 228 3.1 8.7xl0"10 hot rolled coil 260 0.44 4.3xl0"10 batch annealing 150 0.41 1.6xl0"14 continuous annealing 276 1.1 1.2xl0"12 Table 2.2. Calculated coefficients used in Duit et al.'s model[40]. Literature Review 22 Figure 2.1. Effects of Al on hot ductility of steels after solution treatment for 5 minutes at 1330°C. (Mintz and Arrowsmith[14]) Literature Review 23 T e m p e r a t u r e . °C 1300 1200 1100 1000 900 850 i x IO"'. K - 1 Figure 2.2. Solubility of AIN in austenite. (see Table 2.1) Literature Review 24 ST 2 h at 13S0°C ST 2 h at 13S0°C Cooled to 400°C. FC Cooled to tOOO'C. WQ A r ' A r ' Q 450 330°C a 0 7 7 0 6 9 0 ° c Maximum possible AIN I I 1 1 1 —J 2000 1500 TSO 400 ISO 20 Approximate equivalent diameter of air cooled bar, mm Figure 2.3. Effect of cooling rate on precipitation of AIN in C-Mn and Cr-Mo-Ni steel. (Honar and Baliktay[27]) Literature Review 25 Figure 2.4. Comparison of PTT curves for the static and dynamic precipitation of AIN: S: precipitation start; F: precipitation finish. (Michel and Jonas1 J) Literature Review 26 1100 U 1 0 0 0 r Ui a. 2 lit 900 800 1100 <_> 1O0O 3 < id a. 2 i - 9O0H 8001-TIME TIME.s Figure 2.5. Comparison of observed precipitation start-time — temperature curves in deformed austenite (closed points) with curves calculated from equation (2.4) with optimum value of B (half-open points) and mean value of B= 2.5xl010K3 (open points). (Dutta and Sellars[381) Literature Review 27 Figure 2.6. Calculated and measured fraction of precipitated AIN as a function of time at isothermal annealing temperature of: a) 750°C; b) 650°C (Duit et al.m). Literature Review 28 I J ' 'l '* T- -f^- ' ' I I ' 1 I ' ' 1 1 1 1 ' 0 100 200 300 4B0 500 600 700 d i s t a n c e f r o m s t r i p he&d Cm) Figure 2.7. Calculated and measured values of free nitrogen as a function of strip length and coiling temperature (Duit et al.[40]). 29 C H A P T E R 3 SCOPE AND OBJECTIVES Extensive studies have been conducted on the precipitation, dissolution, growth and coarsening behaviors of nitrides and carbides in microalloyed steels. However, the mechanism and kinetics of the formation and evolution of these nitrides or carbides are still not yet fully understood, particularly as they relate to thermomechanical processing parameters. Some models have been established for the kinetics of precipitation of nitrides or carbides in steels, but most are empirical or semi-empirical and very few are fundamentally based. Although the empirical or semi-empirical models are sometimes able to predict the onset of precipitation successfully, they are essentially curve-fitting models, valid only for the experimental conditions employed. Besides the volume fraction of the precipitates, the size and/or size distribution of the precipitates and the distance between the precipitates are also important factors in determining the microstructure and mechanical properties of the steels. Dissolution, growth or coarsening of the precipitates may occur during cooling, reheating or coiling of the steels. Although models have been developed for these processes, most of these models only focus on the mean precipitate size and its variation with time. Very little information regarding the size distribution of the precipitates can be obtained from these models. Despite the extensive studies on precipitation of aluminum nitrides in steels, no fundamentally-based model has been developed to explain the kinetics of AIN precipitation, dissolution, growth or coarsening in steels. Very few systematic studies combining both the Scope and Objectives 30 thermodynamics and the kinetics of AIN precipitation or dissolution/coarsening in steels have been carried out. In particular, the role of chemical composition, temperature, and heating/cooling rate have not been clearly resolved. In order to predict the behavior of AIN precipitation, dissolution, growth or coarsening in low carbon steels undergoing thermomechanical treatments, a systematic thermodynamic and kinetic approach is required. Through a series of experimental and theoretical studies, the present research intends to accomplish the following objectives: i) To improve the current understanding of the mechanisms of precipitation, dissolution, growth and coarsening of aluminum nitride in steels; ii) To relate the observed size, distribution and morphology of AIN in various specimens to their thermal history; iii) To clarify the effects of various thermomechanical processing variables on the precipitation kinetics; iv) To develop a theoretically based model to predict the kinetics of the precipitation-temperature-time (PTT) behavior of AIN in steels incorporating processing variables, with all parameters having appropriate physical significance; v) To develop a theoretically based model to predict the dissolution and coarsening behavior and to simulate the size distribution evolution of AIN in low carbon steels for a given reheat temperature and time at temperature, with growth, Scope and Objectives 31 dissolution and coarsening being treated as one continuous, simultaneous process. While this study concentrates on the precipitation and dissolution behavior of AIN, its results are expected to be generally applicable to the entire class of alloy nitrides, carbides and carbonitrides in steels. A model capable of predicting the AIN precipitation and/or dissolution behavior should be valuable for generating subsequent improvements to current steelmaking and processing procedures, and thus have engineering relevance. 32 C H A P T E R 4 EXPERIMENTAL MEASUREMENTS 4.1. Material Experiments in the present research were carried out on a commercially produced, drawing quality special Al killed (DQSK) steel obtained from US Steel. The chemical composition of this steel is given in Table 4.1. After hot rolling, the material was coiled at a coiling temperature of 650°C. Both transfer bar (product at the end of roughing mill) and coiled sheet (product after hot strip mill processing) samples were obtained, along with the mill data pertinent to each sample. Cylindrical specimens (dpiOmmx 15mm) were machined from the transfer bar and specimens 4mmx4mmx6mm were machined from the as-received coil sheet. Cylindrical specimens were used with the Gleeble thermomechanical simulator (section 4.2.1), while the 4mmx4mmx6mm coil specimens were used for heat treatment in furnace. To prevent oxidation during heat treatment, 4mmx4mmx6mm specimens were encapsulated in evacuated (or fdled with high purity Ar gas) quartz capsules. 4.2. Experimental Techniques 4.2.1. Gleeble Thermomechanical Simulator In this study, controlled heating/cooling or hot-deformation experiments were carried Out on the Gleeble 1500 thermomechanical simulator. A schematic of the Gleeble Experimental Measurements 33 1500 machine is shown in Figure 4.1. The temperature of the specimen was controlled and monitored using an intrinsic Pt-Pt/Rh thermocouple which was spot welded onto the outer surface ofthe specimen at mid-length, as shown in Figure 4.1. The resistive heating design, together with the temperature feedback control system provided rapid response for precise control of specimen temperature during heating, isothermal holding and cooling. During deformation, the linear displacement of the anvils was controlled and programmed and the applied force and diametrical strain were measured using an axial load cell and a crosswise strain device, respectively. 4.2.2. Micrographs After each thermal/mechanical experiment, each specimen for metallographic examination was cut from the mid-length, using an AI2O3 cut-off wheel. A direct spray coolant was used to protect the specimen from overheating during cutting. The specimen was cold mounted in a resin polymer and then ground progressively using 60 through 600 grit silicon carbide papers and then polished with 6 um and 1 um diamond paste. Quantitative analysis of the resulting microstructure was carried out utilizing a C-Imaging System image analyzer. For grain size measurements, a 2% Nital solution was used as an etchant to reveal the ferrite grain boundaries. From the ferrite microstructure, the mean grain area was determined and from this mean area, the mean equivalent area diameter, EQAD, was obtained. At least 300 ferrite grains were analyzed to obtain the ferrite grain size. Experimental Measurements 34 To measure the austenite grain size, a different technique was used. After a water-quenched specimen was polished, it was first etched with a 2% Nital solution and then with a 10% N a 2 S 2 0 5 solution to enhance the contrast between the pearlite/bainite and the ferrite phase (formed during quenching) which outlines the prior austenite grain boundaries. 4.2.3. Carbon Extraction Replica The evolution of the precipitate size distribution and the microanalysis of the precipitates were studied by transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) on carbon extraction replicas of the specimens. The general principles of the extraction technique are shown in Figure 4.2. To prepare the replicas, the specimen is first ground and then polished with diamond paste (6 pm and 1pm) to obtain a flat surface. The specimen is then etched in a 2% Nital solution for 5 seconds such that the particles are exposed and stand proud of the surface. After evaporating a thin film (~20nm) of carbon onto the etched surface, the carbon film is scored with a sharp point into 2-3mm squares and the specimen is etched again in a 5% Nital solution until the replicas lift off. The specimen is then slid into a dish of distilled water so that the replicas can float off onto the water surface. Finally, the replicas are picked up on 3mm Cu grids for examination using transmission electron microscopy. The investigations were performed at an operating voltage of lOOkV to 200kV in a transmission electron microscope equipped with an energy dispensive X-ray (EDX) analysis system. Experimental Measurements 35 Using TEM micrographs of the replicas, the area of each AIN precipitate, A, was determined and the equivalent area diameter, d, was obtained for each precipitate using the following relation: At least 200 AIN precipitates were analyzed to obtained the size distribution for each specimen. Compared to the thin film TEM specimen, the carbon extraction replica has two advantages. First, it is easier to prepare an extraction replica than to prepare a thin film specimen. It takes much less time and several replicas can be made at the same time. Secondly, the extraction replica can provide a much larger area for studying in the TEM. However, despite its advantages, there is an uncertainly on the reliability of this method, particularly regarding the detection of very fine particles (d < 5 nm). It is possible that the presence of very fine particles may not always be detected due to physical loss or partial dissolution during the preparation of the extraction replicas. In their study of Nb(C,N) in HSLA steels, Arieta and Sellars[42] had difficulty in extraction of precipitates smaller than 5nm. However, in the present study a high density of fine AIN precipitates can be observed (e.g., Figure 4.26(a)); therefore, loss of fine precipitates is believed to be insignificant during the current procedure, although sometimes there is difficulty in identify the particle using the EDX microanalysis system. (4.1) Experimental Measurements 36 4.3. Results and Discussion 4.3.1. Dissolution, Growth and Coarsening To study the growth of AIN precipitates in ferrite, coil specimens (encapsulated in evacuated quartz) were isothermally annealed at 650°C to 750°C for times ranging from 1 hour to 1 week. Another set of specimens was first isothermally annealed in a furnace at temperatures between 650°C and 750°C for 24 hours to obtain different initial particle size distributions. These annealed specimens were then heat-treated at a temperature between 1000°C and 1350°C (either in a high purity argon atmosphere or encapsulated in quartz) for increasing holding times, and then rapidly cooled by water quenching to study the dissolution and coarsening of AIN in austenite. 4.3.1.1. Precipitate Distribution Replicas of the as-received coil specimens revealed very few AIN particles. The visible precipitates were usually very fine (d < 10 nm) and were apparently located along the ferrite grain boundaries (Figure 4.3). However, both the amount of visible AIN precipitates and the average size of the precipitates increased dramatically after the specimens were annealed at 650°C to 750°C for a period of time. Figure 4.4 and Figure 4.5 show the typically fine dispersion of AIN precipitates resulting from annealing of the coil specimens at 650°C to 750°C for various times. It can be seen from these figures that most of the AIN precipitates are still distributed along the ferrite grain boundaries after annealing, while a small amount of precipitates can be found in the matrix (Figures 4.5 (b) and (c)). Experimental Measurements 37 The high density of visible precipitates after aging suggests that the AIN was not completely precipitated during the coiling of the steel. Thus, the low density of precipitates in the as-received specimen is believed to be due to incomplete precipitation during coiling of the steel. Comparing the as-received specimen (Figure 4.3) to that obtained after annealing at 700°C (Figures 4.4 and 4.5), it seems that although the mean AIN particle size increases dramatically shortly after being heated to 700°C, the mean particle size increases very slowly upon further aging. The mean particle diameter increases from less than 10 nm to 31 nm after 1 hour at 700°C. However, there is only an additional 15 nm change in the mean particle diameter even after annealing at 700°C for 7 days. Distributions of the particle size after aging at 700°C for various times are shown in Figure 4.6. As seen in the figure, not only did the mean size increase with holding time at the test temperature, the shape of the distribution also changed. After short annealing times, the distribution has a highly asymmetric shape which tails off at large particle sizes. However, as annealing time increases, the distribution develops into a more symmetric shape, i.e., the small precipitates dissolve during the coarsening process. In Figure 4.7, the mean size ofthe AIN precipitates, plotted as a function of time for three different reheating temperatures — 650°C, 700°C and 750°C — shows a similar trend in precipitate size evolution. For all three temperatures, there is a rapid initial growth of the precipitates, followed by a relatively slow coarsening process. In addition, by comparing the size distribution obtained after the same annealing time at 650°C, 700°C and 750°C, it can be seen that the mean particle size increases with Experimental Measurements 38 annealing temperature for the same reheating time. This difference can be attributed to the relatively high diffusivity of Al in ferrite at higher temperatures, which in turn, contributes to a higher growth/coarsening rate. An SEM micrograph of the as-received coil specimen is shown in Figure 4.8. The mean ferrite grain diameter is approximately 10 um. SEM micrographs of specimens after annealing at 750°C for 4 hours or at 700°C for 7 days are shown in Figure 4.9. Comparing the ferrite grain sizes of these specimens to that of the as-received coil, there is no significant difference in the ferrite grain size, even after aging at 700°C for 7 days. It seems that grain growth in the ferrite in this temperature range is inhibited by the pinning effects ofthe AIN precipitates on the grain boundaries. In another set of tests, after being annealed at 700°C for 24 hours, specimens were rapidly heated to a high temperature (1000°C to 1350°C) in the austenite region and isothermally held at that temperature for up to 2 hours before being water cooled to room temperature. As seen in Figure 4.10, networks of AIN precipitates can be found in the final microstructures, if the precipitates are not completely dissolved. It is believed that these networks represent the prior ferrite grain boundaries (before reheating to the austenite region) where the AIN precipitates first formed. Particle size distributions of the AIN precipitates after different annealing times at 1000°C are shown in Figure 4.11. The resulting microstructures after holding at 1000°C for 30min., 60 min. and 90 min., show that although the mean size of the precipitates increases with time, the total number of precipitates decreases. This suggests that a partial dissolution of the AIN precipitates Experimental Measurements 39 occurred during the early stage of annealing at 1000°C accompanied by coarsening of the undissolved precipitates. Because of the high solubility of AIN in austenite, compared to that in ferrite, all AIN precipitates start to dissolve once the specimen is reheated to the high temperature. As the matrix solute concentration increases and approaches the equilibrium value, the process gradually shifts from dissolution to coarsening, i.e., a process in which small particles shrink and large particles grow in order to minimize total surface energy. During austenitizing of this steel, the presence of the pre-existing AIN precipitates can inhibit the growth of the austenite grains. In their study of austenite grain growth in this DQSK steel, Giumelli[54] and Militizer et a/.[55] showed that there is very little grain growth during isothermal annealing at temperatures below 1100°C. The mean grain diameter remains below 40 um after 10 min. However, at a higher temperature (1150°C), rapid grain growth takes place. The mean grain diameter reaches more than 200 um after 10 min. They attributed these results to the complete dissolution of AIN at temperature higher than 1100°C. These findings agree with our observations. TEM micrographs of the AIN precipitates after different annealing times at 1100°C (Figure 4.12) show that the AIN precipitates are not completely dissolved at this temperature after 30 min. However, in another test, after aging for 24 hours at 700°C and then isothermally annealing at 1150°C for 30 min., no AIN precipitates could be found in the replicas. The mean austenite grain size after 5 min. at 1150°C and 1350°C were found to be 120 um and 350 um, respectively (Figure 4.13). According to the solubility product of AIN in steel obtained by Leslie et al}22\ complete dissolution of AIN in this DQSK steel should occur at about 1160°C. Experimental Measurements 40 Using a thermodynamic model (see Chapter 5) developed by the author, the equilibrium solubility temperature is determined to be approximately 1120°C. In spite of this difference in solubility temperature, both approaches support the observations that complete dissolution takes place at temperatures higher than 1100°C. 4.3.1.2. Precipitate Morphology Concerning the morphology of precipitates visible in replicas, AIN precipitates in the as-received coil appear plate-like. However, after aging at 650°C to 750°C, two other shapes can be found; hexagonal and rectangular/cuboidal (Figures 4.5 and 4.14). Using EDX microanalysis, it has been confirmed that these precipitates are Al-rich with no other metal elements. In Figure 4.14(a), hexagonal-shaped precipitates can clearly be seen after 1 hour at 700°C. Moreover, it seems that the higher the temperature or the longer the aging time in the ferrite region, the more sharply defined hexagonal-shaped precipitates (Figure 4.14) can be found in the replicas. However, if the specimens are heated up to the austenite region after long aging in the ferrite region, the hexagonal-shaped AIN precipitates start to change shape again. Rectangular precipitates can be found after isothermal annealing at 1000°C and 1100°C (Figure 4.15). During the early stage of precipitation of the AIN precipitates, the shape of the precipitates is not only determined by the interfacial energy, but also by the misfit strain energy. However, during further annealing, relaxation will cause the misfit strain to diminish. Shapes of the precipitates are then primary determined by the interfacial energy. For crystalline solids, surface energy varies with the Experimental Measurements 41 crystallographic orientation, i.e., some orientations have a higher surface energy than others. Therefore, there is a tendency for the shape of the precipitates to change such that a preferred orientation is achieved in order to lower the overall interfacial energy. In addition, since ferrite is bcc and austenite is fee, the orientation relationship between AIN (hep) and ferrite is expected to be different from that between AIN and austenite. This may explain the change from a hexagonal to a rectangular shape after annealing in the austenite region. 4.3.2. Precipitation Prior to testing, specimens (encapsulated in evacuated quartz) were solution-treated at 1250°C in a furnace for 30 min. and then water quenched to completely dissolve the AIN precipitates present in the DQSK steel. Isothermal precipitation was carried out at temperatures between 650°C and 1050°C using the Gleeble thermomechanical simulator. Specimens were first heated to 1250°C at 10°Cs"1 and then annealed at 1250°C for 3 min. before being cooled to the testing temperature at a rate of about -100oCs_1. After different holding times at the isothermal temperature, specimens were helium quenched (~ -160°Cs"1) to room temperature. Extraction replicas were then obtained from the final microstructures to study the AIN precipitates. Using different cooling rates to the test temperature, the effect of cooling rate on precipitation was studied. The effects of prestraining on the precipitation kinetics were studied using the stress relaxation technique. Experimental Measurements 42 4.3.2.1. Isothermal Precipitation No AIN precipitates were observed in the replicas after the samples were held for 30 min. at 1000°C or above, although some large MnS particles can be seen. However, after holding the specimen at 950°C for 30 min., a few AIN precipitates were found on MnS particles, as seen in Figure 4.16. Although it is thermodynamically favorable for AIN precipitates to form below 1100°C in DQSK steel, as discussed in the previous section, difficulty in nucleation, which is due to a high precipitate/matrix interfacial energy and misfit strain, retards the onset of precipitation. Details regarding the interfacial energy and misfit strain energy will be discussed in Chapter 5. It is believed that the MnS particles provided preferable nucleation sites for the precipitation of AIN. However, due to the low density of MnS particles, the total amount of AIN precipitates is believed to be very small. Ushioda et alP® also reported the observation of AIN precipitation on grain boundary MnS particles during isothermal annealing in austenite. They suggested that this is due to the relatively low interfacial energy between AIN and MnS as compared to that between MnS and y-Fe. Thus, the energy required to form an AIN nucleus on a MnS particle is lower than that for grain boundary or homogeneous nucleation. On the other hand, after holding the DQSK specimen at 900°C for 15 min., very fine AIN precipitates were found (Figure 4.17 (a) and (b)). These observations suggest that the precipitation kinetics increase as temperature decreases in the austenite region. At a lower temperature, the chemical driving force for nucleation increases, which reduces the nucleation barrier. Therefore, it is easier for the AIN precipitates to nucleate. Figure 4.17 Experimental Measurements 43 (c) and (d) show the AIN precipitates after annealing at 900°C for 30 min. Both the number and size of the AIN precipitates increased after a longer annealing time. Although the density of the AIN precipitates was low, it can be seen that the AIN precipitates were formed along some lines, which are believed to be the prior austenite grain boundaries. It can be seen in the next chapter that the nucleation barrier associated with grain boundary nucleation of AIN is much lower than that associated with homogeneous nucleation in austenite at this temperature. However, when the samples were isothermally annealed in the ferrite region after solution treatment, the onset of precipitation occurred at a much shorter holding time than those annealed in the austenite region. Traces of very fine AIN precipitates can be found after holding the specimen at 650°C for 1 minute (Figure 4.18). Moreover, a much higher density of AIN precipitates can be observed as compared to those samples held in the austenite region for the same holding time. Figure 4.19 shows the AIN precipitates after the samples were held at 650°C to 750°C for 10 min. or 30 min. The AIN particles were primarily precipitated along the ferrite grain boundaries, although fine AIN precipitates can be found in the ferrite matrix. It is believed that both homogeneous and grain boundary nucleation occurred during the precipitation of AIN in ferrite; however, the precipitation kinetics is dominated by grain boundary nucleation with a small fraction of homogeneous nucleation. Comparing samples annealed at 650°C, 700°C and 750°C for the same holding time, it seems that although the amount of AIN precipitates increases as temperature decreases, Experimental Measurements 44 the mean size of the AIN precipitates decreases with temperature in this temperature range. The measured mean diameters ofthe AIN precipitates are shown in Figure 4.20 as functions of annealing temperature and holding time. For a fixed isothermal annealing temperature, the mean particle size increases with time. It can also be seen from Figure 4.20 that the mean size increases at a slightly faster rate at higher temperatures. These observations agree with the classical nucleation and growth theory. As temperature decreases, due to a higher chemical driving force and a smaller nucleation barrier, the nucleation rate increases. Thus, more fine precipitates are nucleated at a lower temperature. On the other hand, the diifusivity of Al, which directly affects the growth rate of the precipitate, increases as temperature increases. Thus, a higher growth rate is expected at a higher temperature. 4.3.2.2 Continuous Cooling Since the precipitation of AIN is much faster in ferrite than in austenite, the y -» a transformation plays an important role on the precipitation kinetics during continuous cooling. Thus, experiments were carried out to study the effect of cooling rate during austenite decomposition on the precipitation of AIN. After solution-treatment at 1250°C for 3 minutes, specimens were cooled to 900°C at 25°C s"1. Then different cooling rates were used to cool the specimens to 725°C, followed by a helium quench (~ -160°Cs"1) immediately after reaching 725°C. A schematic of the temperature profile is presented in Figure 4.21. Experimental Measurements 45 With a cooling rate of 100°C s"1 (Figure 4.22 (a)) or 20°C s"1 (Figure 4.22 (b)) during austenite decomposition, no AIN precipitates were found in the ferrite. However, for 5°C s"1, a high density of fine AIN was found in the ferrite matrix (Figure 4.22 (c) and (d)). With a cooling rate of l0Cs"', an even higher density of AIN precipitates was in the ferrite matrix (Figure 4.22 (e) and (f)). With a cooling rate of 25°Cs"1, there was not sufficient time for AIN to precipitate above 900°C, thus, all the AIN should be precipitated during the austenite decomposition. As shown in Figure 4.22, there were clusters of AIN precipitates at the low cooling rate, but bands of AIN precipitates can also be found. It is possible that those bands of AIN precipitates represented the prior austenite grain boundaries. During the early stage of austenite decomposition, small ferrite grains were formed at the austenite grain boundaries. It is unclear whether the AIN precipitates nucleated at the moving austenite/ferrite interface or nucleated in the newly formed ferrite. Further investigations into the precipitation mechanism of AIN during austenite decomposition are needed. Figure 4.23 (a) and (b) show the AIN precipitates after the sample was isothermally annealed at 850°C, which is just below Ar3, for 10 minutes. Bands of AIN precipitates were found. However, when the sample was isothermally annealed at 800°C for 10 minutes (Figure 4.23 (c) and (d)), there was no band of AIN precipitates. Clusters of AIN precipitates were found. These observations seem to support the suggestion that bands of AIN precipitates were found just below Ar3 when small ferrite grains were formed along the austenite grain boundaries. Experimental Measurements 46 Although more studies are needed to investigate the precipitation kinetics of AIN in the austenite/ferrite two phases region, this may not have a great influence in an industrial hot strip mill, especially for DQSK steel. In a typical mill, the cooling rate at the run-out table is usually higher than 25°Cs_1, thus, the precipitation of AIN during austenite decomposition has little effect on the final microstructure. 4.3.2.3. Strain-Induced Precipitation To study the effects of strain and stain rate on the precipitation kinetics of AIN, a stress relaxation technique developed by Liu and Jonas[57] to determine the precipitation start (Ps) and finish (Pj) times was adopted. In the present study, preliminary experiments were carried out using the Gleeble 1500 machine. Prior to testing, specimens (encapsulated in evacuated quartz) were solution-treated at 1250°C in a furnace for 30 min. and then water quenched to completely dissolve the AIN precipitates presented in the DQSK steel. Using the Gleeble machine, the specimen was first heated to 1250°C at 10°Cs"' as can be seen from the thermomechanical profile presented in Figure 4.24. After solution treatment for 3 minutes, the specimen was cooled to the test temperature at 25°Cs"\ On attaining the test temperature, a 10% or 20% prestrain was applied at a strain rate of 0.1 s"'or 0.2 s"1. Following such a prestrain, stress relaxation begins and the relevant data was recorded. The experimental stress relaxation data acquired in this way at 950°C is shown in Figure 4.25. As described by Liu and Jonas[45'57], the points indicated by arrows on the relaxation curves in Figure 4.25 can be identified as the precipitation start (Ps) and the finish times Experimental Measurements 47 (Pf). After a strain is applied, creep of the specimen allows the elastic part of the strain to be relieved, which causes the stress to decrease or relax. As shown in Figure 4.25, the stress first decreases quickly before Ps. When precipitation begins, which can retard the progress of relaxation, the stress relaxation decreases and an inflection develops in the relaxation curve. After the precipitation is complete at Pf, the slope of the relaxation curve changes again. The evolution of the size distribution of the AIN precipitates was followed with the aid of extraction replicas. The samples were helium quenched after increasing times at the isothermal temperature. Figure 4.26 shows the distribution of AIN precipitates at 30 seconds and 30 minutes after prestraining at 950°C. It can be seen in Figure 4.26 (a) that few AIN precipitates exist after 30 seconds. Comparing the precipitation of AIN in deformed and undeformed materials at the same isothermal temperature, it clearly shows that deformation can dramatically enhance the precipitation kinetics. Two other sets of relaxation data are shown in Figure 4.27. The two samples were prestrained at 950°C with a strain rate of 0.1s'1 and a strain of 0.1 and 0.2, respectively. With the same strain rate, a higher strain seems to shift the onset of precipitation (Ps) to a shorter time. Comparing Figure 4.27 to Figure 4.25, it seems that with the same isothermal temperature and strain, the difference in strain rate does not have any significant effect on the precipitation kinetics. However, this may due to the small difference in strain rate (i.e., 0.1 s"1 vs. 0.2 s'1). Experimental Measurements 48 Although further studies are needed to clarify the effects of strain and strain rate on the mechanisms and kinetics of strain-induced precipitation, it is suggested that deformation can enhance the precipitation kinetics by two ways. First, deformation can create a high density of dislocations which can act as preferred nucleation sites due to their high strain energy. Secondly, dislocations can provide a rapid diffusion path for the Al. This enhanced diffusivity can accelerate both the nucleation rate and growth rate. Experimental Measurements c Mn Si Al S Cr N 0.038 0.30 0.009 0.040 0.008 0.033 0.0052 Table 4.1. Chemical composition of DQSK steel (wt%). Experimental Measurements 50 W and Ta foils to stop welding to anvils Inoonel 718 Anvils Crosswise Strain Measurement (LVOT) P t - P t 1 0 % R h Thermocouples CLAMP ;ure 4.1. Schematic of the specimen jaws in the Gleeble 1500 thermomechanical simulator. Experimental Measurements 51 Figure 4.2. The extraction replica. The two-phase specimen (a) is etched (b) and carbon coated (c). A further etch then lifts off the replica containing some second-phase particles (d). Experimental Measurements 52 Figure 4.3. T E M micrographs of carbon replicas of as-received coil specimen; showing fine AIN precipitates (indicated by arrows) along ferrite grain boundaries. Experimental Measurements 53 Figure 4.4. TEM micrographs of AIN after (a) and (b) 4 hours at 650°C, (c) and (d) 1 hour at 700°C, (e) and (f) 4 hours at 700°C and (g) and (h) 24 hours at 700°C. Experimental Measurements 54 (a) 2<M> nm . % (b) 1 /'* V 1* t 200 nm ^ % (C) - • ; , 200 nm ( d ) ^ * - M # . 2un run (e) i ; - >/*< 2 ^ p i J£S • -.—4 * 200 nm Figure 4.5. T E M micrographs of AIN after (a) and (b) 4 hours at 750°C, (c) and (d) 24 hours at 750°C, and (e) and (f) 7 days at 700°C. Experimental Measurements 55 80 120 d i a m e t e r (nm) 80 120 d i a m e t e r ( n m ) 40 80 120 d i a m e t e r (nm) 160 80 120 d iamete r (nm) Figure 4.6. Evolution of the size distribution of AIN precipitates after soaking the coil specimens at 700°C for (a) 1 hour, (b) 4 hours, (c) 24 hours and (d) 7 days.. Experimental Measurements 56 60 T 50 | 40 % 30 +' ro T3 20 --10 --0 • 12 24 annealing time (hours) A 650°C • 700°C • 750°C days Figure 4.7. Variation of mean diameter of AIN precipitates with annealing time at 650°C, 700°C and 750°C. Experimental Measurements 57 Figure 4.8. S E M micrograph of as-received DQSK coil specimen. Figure 4.9. S E M micrographs of coil specimen after being annealed at (a) 700°C for 7 days and at (b) 750°C for 4 hours. Experimental Measurements 58 2.0 um 3.0 um « * *• 1 •I ; ' / ' j * i . ' . 1.0 um Figure 4.10. S T E M and T E M micrographs showing networks of AIN precipitates in samples held for 24 hours at 700°C and then given different annealing times at 1000°C or 1100°C: (a) STEM, 30 min. at 1000°C, (b) S T E M , 60 min. at 1000°C, (c) T E M , 90 min. at 1000°C and (d) T E M , 10 min. at 1100°C. Experimental Measurements 59 25 --20 --15 --10 -- r—I (a) 40 80 120 d i a m e t e r ( n m ) 160 40 80 120 d iam e t e r ( n m ) 160 40 80 120 d i a m e t e r ( n m ) 40 80 120 160 diam e t e r ( n m ) Figure 4.11. Evolution of size distribution of AIN precipitates after soaking at 1000°C for a) t = 0s, b) t = 30 min., c) t = 60 min. and d) t = 90 min. Experimental Measurements 60 Figure 4.13. Optical micrographs of coil specimen after annealed at 700°C for 24 hours and then 5 min. at (a) 1150°C and (b) 1350°C, respectively. Experimental Measurements 61 Figure 4.14. T E M micrographs of replicas of specimens after a) 1 hour at 700°C, b) 4 hours at 700°C, c) 24 hours at 700°C, d) 7 days at 700°C and e) and f) 24 hours at 750°C; showing the hexagonal-shape AIN precipitates. Experimental Measurements 62 ^ ^ ^ ^ t 400 nm 160 400 nm 500 nm Figure 4.15. T E M micrographs showing rectangular-shaped AIN precipitates after annealed for 24 hours at 700°C and then (a) 30 minutes at 1000°C, (b) 30 minutes at 1100°C and (c) and (d) 60 minutes at 1100°C. Experimental Measurements 63 Figure 4.16. T E M micrograph showing AIN precipitate on MnS particle after isothermally annealed for 30 minutes at 950°C. Experimental Measurements 64 Figure 4.17. T E M micrographs showing AIN precipitates after isothermally annealing the specimens at 900°C for (a) and (b) 15 minutes, (c) and (d) 30 minutes. Experimental Measurements 65 Figure 4.18. TEM micrograph showing AIN precipitates after isothermally annealing the specimen at 650°C for 1 minute. Experimental Measurements 66 Figure 4.19. T E M micrographs showing AIN precipitates after isothermally annealing the specimens at (a) 750°C for 10 min., (b) 750°C for 30 min., (c) 700°C for 10 min., (d) 700°C for 30 min., (e) 650°C for 10 min. and (f) 650°C for 30 min. Experimental Measurements 67 50 x 40 + ¥ r 3 0 + £ E .<$ 2 0 T J C CO <0 E 10 4 D A Q -+- •+-10 20 30 40 annealing time (min.) 50 60 A 650°C • 700°C • 750°C Figure 4.20. Variation of mean diameter of AIN precipitates with annealing time during isothermal precipitation at 650°C, 700°C and 750°C. 3 min. @1250°C / \25°C/sec / \ CR= 1,5,20, 100 °C/sec / 900°C V _ / \ C R / ,725°C / \ ~160°C/sec Figure 4.21. A schematic of the temperature profde with different cooling rate during austenite decomposition. Experimental Measurements 68 Figure 4.22. T E M micrographs showing the effect of cooling rate during austenite decomposition on the precipitation of AIN. Cooling rate = (a) 100°Cs"1, (b) 20°Cs"1, (c) and (d) 5°C&\ (e) and (f) PCs" 1 . Experimental Measurements 69 Figure 4.23. T E M micrographs showing AIN precipitates after isothermally annealing the specimens for 10 minutes at (a) and (b) 850°C and (c) and (d) 800°C. Experimental Measurements 70 3 min. @1250°C / \,25°C/sec / \S,S / Vv T , t \ /lO°C/sec \ / r Figure 4.24. A schematic of the thermomechanical profile for stress relaxation test. 30 \ h 1 1 1 1 1 1 10° 101 102 103 t i m e ( s e c ) gure 4.25. Stress vs. log(time) curve for the isothermal relaxation of DQSK steel at 950°C with strain = 0.2 and strain rate = 0.2s"1. Experimental Measurements 71 Figure 4.26. T E M micrographs showing strain-induced precipitation of A I N in DQSK steel at 950°C, 8 = 0.2, s = 0.2 s"1: (a) 30 seconds, (b) 30 minutes after prestraining. Experimental Measurements 72 T=950°C t i m e ( s e c ) Figure 4.27. Stress vs log(time) curves for the isothermal relaxation of DQSK steel at 950°C with strain rate = 0.1s"1 and strain = 0.1 and 0.2. 73 C H A P T E R 5 THEORETICAL MODEL —PRECIPITATION A theoretically based model was developed to predict the precipitation kinetics of nitrides and carbides in microalloyed or low carbon steels undergoing various heat treatments. This model takes into account the equilibrium thermodynamic properties of the systems, the precipitate morphology, the interfacial energy and the misfit strain. The precipitation kinetics is formulated using classical nucleation and growth theories. Both homogeneous and heterogeneous nucleation are considered. In the present work, the model is applied to study the precipitation behavior of aluminum nitride (AIN) in Al-killed low carbon steels. 5.1. Modeling Gibbs first described the two fundamental modes of solid-state precipitation reactions. In the first of these reactions, now usually described as a nucleation and growth reaction, a small region of a new phase forms from within the matrix phase. The new region, the nucleus, has, in general, a different composition and structure from the parent phase. The nucleus is separated from the parent matrix by an interface which will have an interfacial energy, y. This type of transformation is initiated by composition fluctuations which are large in magnitude but localized in extent. The second mode of transformation is typified by a composition fluctuation within an unstable region of a free-energy curve. This type of reaction, where the disturbance is limited in magnitude but delocalized in space, is Theoretical Model —Precipitation 74 described as spinodal decomposition. It is generally believed that the precipitation of nitrides or carbides in steels can be described as a nucleation and growth reaction. 5.1.1. Nucleation All structural transformations are driven, at constant temperature and pressure, by the possible reduction in Gibbs free energy, G, from the original to the final structure. During nucleation of a second phase particle, the driving force is the decrease in the volume free energy due to the formation of a more stable phase from a less stable matrix. However, due to the increase of the interfacial area between the two phases, there is an increase in the interfacial free energy. Moreover, there is generally a misfit or elastic strain energy associated with the nucleation of a new phase from a solid parent phase. Both the interfacial energy and strain energy act as barriers to the transformation. For a homogeneous nucleation, the change of Gibbs free energy, AG, associated with the formation of a precipitate of volume, V, and total surface area, S, may be written as AG = V(AGchem + AGS) + Sy (5.1) where AGChem is the chemical free energy change (or chemical driving force) associated with the formation of one unit volume of precipitate, AGS is the elastic strain energy generated by the formation of a unit volume nucleus and y is the interfacial energy per unit area of the matrix/precipitate interface. Theoretical Model —Precipitation 75 The volume ofthe nucleus, V, increases as the third power of the nucleus size while the area term, S, increases only as the second power of the nucleus size. The plot of free energy change versus nucleus radius for a spherical nucleus in Figure 5.1 shows that at small radii the nucleus is unstable and tends to redissolve in the matrix; only when the precipitate has reached the critical radius, r*, does the nucleus become capable of metastable existence, and after addition of one atom (r > r*) it can grow with a continuous decrease of free energy. The critical formation energy, AG*, accompanying the formation of a critical sized nucleus can be obtained by solving Equation (5.1) for the condition According to classical nucleation and growth theory[43'44'58], the formation of a nucleus can be considered to be produced by thermally activated heterophase fluctuations. Before a nucleus becomes stable, it must first reach the critical size. Using statistical mechanics, at thermal equilibrium, the probable concentration of critical-sized nuclei, Nv, in a unit volume is given by N v = Nexp f AG^ (5.3) Theoretical Model —Precipitation 76 where N is the number of atomic sites per unit volume on which the nucleation could have started, ICB is the Boltzmann's constant and T is the absolute temperature. The rate of nucleation is then the product of this concentration of critical nuclei and the rate of atomic addition to the nuclei to make them supercritical. Thus, the general, time-dependent equation for the rate of isothermal nucleation may be given as I = ZP Nexp exp[-yj (5.4) where I is the nucleation rate (per unit volume and unit time), Z is the Zeldovich non-equilibrium factor, p* is the rate at which atoms impinge upon the critical nucleus, and t' is the incubation time. The quantities Z, p , AG and t' are all specific to the system and to the type of nucleation process158"621 (see Appendix). In addition, preexisting high energy sites such as lattice defects, inclusions, etc. can act as heterogeneous sites for nucleation. According to Cahn's analysis^ 631, when the nucleus forms on a preexisting defect, the energy of formation of the nucleus is reduced by that proportion of the defect energy that is consumed by the nucleus as it is formed. Therefore, for heterogeneous nucleation, Equation (5.1) can be re-written as AG = V(AGchem + AGS) + Sy + Q (5.5) Theoretical Model —Precipitation 11 where Cl is the additional energy change produced when precipitates are formed at a high energy area (grain boundary, dislocation, interface, etc.). For example, for nucleation on grain boundaries, Cl can be set as -AgbYgb, where ygb is the grain boundary energy per unit area and Agb is the grain boundary surface area eliminated by the presence of the precipitate. For nucleation on dislocations, Cl can be set as -/dSEei where Eei is the elastic strain energy per unit length of the dislocation and /ds is the length of dislocation eliminated by the presence ofthe precipitate. Since nucleation on heterogeneous sites usually lowers the barrier for nucleation (i.e., Cl < 0), the critical energy for heterogeneous nucleation, AG*heter, is usually smaller than that for homogeneous nucleation, AG*h0mo- Since I oc exp f AG*A it is clear that V kBTj AG* plays a vital role in the nucleation rate. Therefore, by nucleation on heterogeneous sites, the nucleation rate can be enhanced significantly. 5.1.2. Chem ical driving force The chemical driving force, AGChem, can be calculated by using equilibrium thermodynamics^ 4"691. For the case of AIN in a Fe-Al-N system, the precipitation of AIN from aluminum and nitrogen dissolved in ferrite or austenite can be written as A1* + N4->A1N* (5.6) where § = y (austenite) or a (ferrite). The chemical Gibbs free energy change for the Theoretical Model —Precipitation 78 precipitation of one mole of AIN, AgChems can then be given as Agchem - g l l N S A I § N (5.7) where g/ is the chemical potential (or partial molar free energy) of component / in phase <(). Because of the low concentrations of both Al and N in the solid solution, the chemical potential of Fe in both the original and the remaining matrix is assumed to have no significant difference and thus can be neglected. The chemical driving force per volume of AIN, AGChem, is AGChem = AgCh e mA^AiN where V A I N is the molar volume of AIN. Furthermore, assuming that the precipitates are of equilibrium composition, the chemical driving force becomes where gA1N is the chemical potential of an equilibrium, stoichiometric AIN compound. The chemical potential, gA1N , can be written as where gA1N and aA1N are the standard state Gibbs energy and the activity of AIN, respectively. Since AIN is treated as a strictly stoichiometric compound of fixed concentration, aA1N = 1. Values of gA1N can be obtained from the equation developed by A8chem - S A I N ~ § A I ~ S N (5.8) g A I N = g A l N + l n [ f l A l N ] (5.9) Theoretical Model —Precipitation 79 Hillert and Jonsson[68]: S A I N - H S E R =-345837+ 359.862T-54.3087TlnT + 8.56xlO"4T2 + 2.326 xl0 6T _ 1 (5.10) -1.26 x 108 T"2 (J / mole of AIN) where T is the absolute temperature and Ffb K represents H A , +}H^ . H, is the enthaply of the stable state of component / at 1 atm. (O.lMPa) and 298.15 K. To describe the Gibbs energy of Al and N in an Fe-Al-N system, a two-sublattice regular solution model developed by Hillert and Staffansson[70] was used. Since in the present study the concentrations of both Al and N are very low, ternary interactions can be neglected. Thus, gM and gN can be obtained from the binary Fe-Al and Fe-N systems as follows: g* =gSf+RTln 2 - y M i (5.ii) S: ^d gA1 = g°t +RTlnyN +(yfe)Z4e)A1 ' (5.12) where L^ v and Lp e A ] are regular solution type binary interaction parameters. The parameter L^e M is concentration dependent and can be described as Theoretical Model —Precipitation 80 4e,A, * °4.^+ 14..Ai(yJ. - y t i ) (5-i3) The term y, represents the fraction of component / on the sublattice it occupies and is related to the ordinary mole fractions as S i X A \ "*~*Fe yii=-rLr y A . + y F e = i (5.i5) where xf is the ordinary mole fraction of component i, ss and Sj are constants describing the number of lattice sites and interstitial sublattice sites. For austenite (fee), ss = Sj = 1, for ferrite (bec), ss = 1 and s, = 3. Values of the standard Gibbs free energy and interaction parameters can be obtained from the literature[64"69] and are listed in Table 5.1. 5.1.3. Interfacial Energy For crystal-crystal interfaces, the atomic matching ranges from perfect, as in fully coherent interfaces, through less perfect matching in semicoherent interfaces, to random matching in fully incoherent interfaces. The energy of an interphase boundary depends on many parameters, e.g., interfacial misfit, the type of atomic bonding between and within the phases, etc. Turnbull^ 71' considered the interfacial energy of semicoherent interphase boundaries to consist of two additive components; a chemical term (yc) for the coherent Theoretical Model —Precipitation 81 interface and an additional structural term (yst) due to the cross-grid of edge dislocations: The chemical component, which corresponds to the energy associated with a fully coherent interface, is given as where AE is the heat of solution of the precipitate, Ns is the number of atoms per unit area of surface, Zt is the lattice coordination number, Zs is the number of bonds per atom across the interface, N A is the Avogadro's number and X p and X M are the concentration (mole fraction) of the precipitate forming element in the precipitate and matrix, respectively. For AIN precipitates in low alloy steels, X p = 0.5 and X p » XM. AE can be evaluated from the respective heat of formation of AIN, AH, using AE = -AH. The structural component, yst, in Eq.(5.16) is associated with the array of interfacial dislocations which accommodate the mismatch lattices between the two phases. It can be estimated[72] as y = yc + ys St (5.16) (5.17) Yst = l + ^ - f l + y2 ) 2 (5.18) J Theoretical Model —Precipitation 82 with 27iAr (5.19) 3(1-v*) 1 1 1 (5.20) + — U- Up 2 1 1 (5.21) a* a aP and v * = ( V + V p ) (5.22) where A is the volume misfit between the two lattices, (i and |j,p are the shear moduli of the matrix and precipitate, v and vP are the Poisson's ratio of the matrix and precipitate and a and aP are the lattice parameters of the matrix and precipitate, respectively. There is considerable evidence[73'74] which supports the view that most of the carbides and nitrides in microalloyed steels have definitive orientation relationships with respect to the austenite or ferrite matrix. For the case of hep AIN in fee y-Fe, it is believed that there is a correlation between the {0001} hep planes and the {111} fee planes. For the hep/bec precipitate-matrix pairs in the AIN/a-Fe system, the {1100} hep planes and the {110} bec planes are believed to be parallel and form the habit plane. As a result, in the present calculation, Z\ = 3, Zg = 4, Z) = Z" = 12 and V 3 a p 2 (5.23) Theoretical Model —Precipitation 83 and 2 (5.24) For the calculation of the interfacial energy, the heat of formation of AIN can be derived from the numerical data in Ref. 75. Other data used for the calculation are summarized[76"80] in Table 5.2. The calculated interfacial energies are shown in Figure 5.2. It can be seen in Figure 5.2 that the interfacial energy is a function of temperature. It increases slightly as temperature decreases in both austenite and ferrite regions. It also shows that the interfacial energy of the AIN/ct-Fe interface is higher than that of the AlN/y-Fe interface even at the same temperature. However, this difference in interfacial energy may be in the same order of magnitude of the error introduced by the approximation used during the calculation. 5.1.4. Elastic strain energy In general, there are two different origins of strain that can be developed by the formation of a new phase in a matrix phase, when both are crystalline. In the first type, misfit between two coherent phases causes the straining of both lattices. The second type of strain is that caused when the new phase occupies a different volume from the region of the matrix that it has replaced. Theoretical Model —Precipitation 84 As we can see later in this section, the strain energy associated with a coherent particle is usual larger than that for an incoherent particle. We have noticed, however, that the interfacial energy of an incoherent boundary is larger than that of a coherent boundary, and this opposes the strain energy factor. Since strain energy is proportional to the volume of the particle but surface energy is proportional to the surface area of the particle, the surface energy term will predominate at sufficiently small sizes, and the first nuclei may be coherent. As the nucleus grows, the strain energy will increase until it becomes more favorable energetically for the particle to become incoherent with the matrix. An incoherent precipitate is stressed in a purely hydrostatic fashion along its interface with the surrounding matrix. If the matrix is treated as an isotropic elastic continuum, the elastic strain energy (per unit volume) in the precipitate/matrix assembly for an incoherent precipitate can be given by[44] AGS = — uC(Ar)2E (5.25) with C= 3 K p 3KP+4|i where A r is the volume misfit, \i is the shear modulus of the matrix, Kp is the bulk modulus ofthe precipitate and E is a shape factor. In this model, each precipitate is considered to be an oblate or prolate spheroid[81,821 (Figure 5.3). The spheroid is described on the x\ - X2 - X3 orthogonal coordinate system as Theoretical Model —Precipitation 85 2 2 + 2— < 1 where a and c are the two principal radii. The values of the aspect ratio, c/a, are indicative of the shape of the precipitate, i.e., c/a -> 0 represents a disk, c/a = 1 is a sphere and c/a —» oo is a needle. By considering a family of spheroids, Nabarro[83] has shown that the shape factor, E, is a function of c/a, and he obtained values for the function E(c/a) for some limiting cases. When c/a -» oo (i.e., needle), E(c/a) = -|. For a sphere, E(c/a) = 1. Nabarro also showed that for a spheroid with c/a = 1 + 4, E(c/a) differs from unity only in terms of order of h\ when £, is small, so that E(c/a) is a slowly changing function near c/a = 1. Furthermore, when c/a « 1 (i.e., disk), Nabarro obtained an approximate solution for this case in which A smooth graph through these points leads to the variation of E(c/a) as a function of c/a shown in Figure 5.4. To obtain a value for E(c/a) in the current calculation, the following relationships are arbitrarily used: E(c/a) = 3TIC ( c /a« 1) (5.26) 4a when c < a E(c/a) = i (5.27) 3 1 fc —+—exp - — 4 4 Va J when c> a Theoretical Model —Precipitation 86 These equations provide approximate values for E(c/a) which agree with Nabarro's findings. The strain energy associated with a coherent precipitate has been studied by many researchers. According to Eshelby^ 841 and Barnett et alJS5\ for a pure, uniform dilatational transformation, which only alters the size but not the shape of the particle, the uniform stress-free transformation strain, ej-, is ej = eT8„ (5.28) [1 when i = j and 5- = < 10 when i ^ j where sT is the constant linear misfit strain. If the elastic constants are isotropic and the same in both particle and matrix, the coherent strain energy per unit volume of precipitate, A G C = A G O = M ± Z ) 0 L X ( 5 . 2 9 ) 1 - V where |u is the shear modulus, and v is the Poisson's ratio. In this case, AG^ is independent of the shape of the precipitate. In fact, AG^ is identical to the strain energy of an incoherent spherical precipitate if the same elastic properties are used for precipitate and matrix in Equation (5.25) and if sT is taken as Ar/3, where AT is the volume misfit. Theoretical Model —Precipitation 87 However-, Barnett et al.[85] have shown that AGCS is shape dependent when the particle and the matrix have different elastic constants: AG:=3(sT)2cop 1-- 1 1 + 20 + 1 1-v cop vqp + r ( 0 - l ) l + v -1 (5.30) where co = u. 1 + v l - 2 v l + vr co = n p " p l-2v. (5.31) r = l l-(c/a)2 c/a _, -372-cos (c/a); l-(c/a)' c/a < 1 c/a = l 1 + ——cosh '(c/a); c/a>l l-(c/ay (c/a) -1 3 / 2 (5.32) and 1 + - 1 2(1-v) ^ - 1 V ll J f(5-4v) 3(3r -1) 2(1 -(c/a)2). 1 + - 1 2(1 - v) ^ - 1 V P J f (i-r)(i-2v)+- 2 r - 3 r - i l -^/a) 2 ; (5.33) Theoretical Model —Precipitation 88 When the matrix and precipitate are elastically identical (fx = pp, v = vp), then Equation (5.30) becomes identical to Equation (5.29). Figure 5.5 is a plot of A G ^ / A G s vs. c/a for three different Up/jo, ratios. It can be seen that when the precipitate is harder than the matrix (up > u), A G j associated with a disk (c/a « 1) is greater than that associated with a sphere (c/a =1) ; the reverse is true when the matrix is the harder phase. Moreover, for a spherical precipitate, the elastic strain energy is a maximum for a soft precipitate (|xp < u) and a minimum for a hard precipitate (up > u). However, most coherent interfaces involve both shear and dilatational transformation strains. It has been shown[84] that the shear component of the coherent misfit strain energy also depends on the particle shape. For a single set of tensor shear strains ( e i 3 = eL )» m e shear strain energy is minimized for a disc located in the plane of shear[43]. If the elastic constants are the same in both particle and matrix, the coherent shear strain energy, A G ' ' 8 , is[43] A G c , s = *H(2-v) 2 | V | s 2(l-v) UJ (5.34) The shear strain energy goes to zero as the particle becomes disc-like (i.e., c/a —> 0). In the present study, only the dilatational component is considered. In the temperature range that we are concerned with, the shear modulus of AIN is much greater than those ofthe austenite or ferrite matrix (see Table 5.1). Comparing Theoretical Model —Precipitation 89 Equation (5.30) to Equation (5.25) for an AIN precipitate in steel, it can be seen that the coherent strain energy, AG\, is always larger than that for an incoherent particle, AGS, for all values of c/a, although AG^ » AGS when c/a = 1. Moreover, if we compare the coherent strain energy to the chemical driving force for AIN in austenite, it can be seen that the coherent strain energy is at least in the same order of magnitude as the absolute value of the chemical driving force. In most cases, AG^ is in fact larger than |AG c h e m | . Therefore, it is reasonable to believe that the precipitate/matrix interface can maintain its coherency only when the nucleus is very small. 5.1.5. Critical nucleus Since the elastic strain energy (coherent or incoherent) is not only a function of size but also a function of shape, if AG is plotted as a function of size and shape of the precipitate, the combination of size and shape which gives a "min-max" (saddle-point) value of AG must be found. The AG* value at this point in the energy field is associated with the formation of a critical sized nucleus and it represents the activation energy for nucleation by the most favorable path. For the spheroid described in the previous section, the volume, V, and surface area, A, can be given as V = ^ - ^ (5.35) Theoretical Model —Precipitation 90 2ua2 + 71c2 , (1 + s -<1 and A = 47ia2 when — - 1 a (5.36) 27ia2 + 27tac • sin s s 2 when — > 1 a respectively. Therefore, using Equation (5.1) or Equation (5.5), the Gibbs free energy change, AG, can be calculated as a function of a and c in the cases of homogeneous or heterogeneous nucleation. In the present model, the energy change associated with the formation of a coherent particle, AGC, and that associated with an incoherent particle, AG1, are both calculated. AG is then determined as the minimum of the two values, i.e., AG = min( AG 0, AG1). For example, the calculated Gibbs energy change, AG, for nucleation of AIN along austenite grain boundaries in DQSK steel at 900°C is shown in Figure 5.6. The saddle point in Figure 5.6 represents the lowest activation barrier[82] for nucleation, i.e., AG*. The energy at this point should be a maximum with respect to changes in size and a minimum with respect to changes in shape. The values of a and c for the corresponding critical nucleus (in this case, a disk-shape nucleus) can be obtained by solving the non-linear equations Theoretical Model —Precipitation 91 S A G = 0 and S A G = 0 (5.37) da 5.1.6. Volume fraction In Equation (5.4), the number of atomic sites per unit volume on which the nucleation could have started, N, is considered to be a constant. However, during precipitation, the value of N decreases in two ways. First, some of these sites become critical nuclei due to the nucleation of the precipitates. Secondly, sites can also be swallowed by the growing precipitates. Moreover, due to impingement with other precipitates, the growing of the newly formed precipitates can be completely stopped or significantly slowed along the area of contact. To take these into account, the concept of extended volume fraction[86~88] is applied. The extended volume fraction, Ve, is defined as the sum of the volume of all the transformed phase divided by the total volume, assuming that the transformed phase never stops growing and that new nuclei keep nucleating at the same rate in both transformed as well as untransformed material. The extended volume fraction at time, t, can be expressed as (5.38) o where I(x) is the nucleation rate at time, x, V(t,x) is the volume of a particle at time, t, which began growth from a nucleus at time, x. If there are different nucleation sites (i.e., bulk Theoretical Model —Precipitation 92 matrix, grain boundary, dislocation, etc.), additivity of the extended volume can be where i represent the different nucleation sites. The volume of a particle at time, t, can be determined by using the growth equations shown in the next chapter (Equations (6.10) and (6.29)). To simplify the model, an equivalent sphere with the same volume as the critical nucleus is used as the initial size and the sequential calculations of volume are based on spherical particles. To determine the volume fraction of precipitates, the Johnson-Mehl-Avrami-Kolmogorov (JMAK)[86,87] model for phase transformations is applied. The actual volume fraction ofthe transformed phase, Vf, is expressed as In the present study of AIN in DQSK steel, since the maximum volume fraction of AIN is very small (i.e., ~ 10"4), the actual volume fraction and the extended volume fraction is virtually identical, i.e., assumed[88'89], i.e., Ve=I>i (5.39) V f =l-exp(-Ve) (5.40) V f «V e (5.41) Theoretical Model —Precipitation 93 5.2. Calculations Since an exact solution for Equation (5.38) cannot be obtained, a numerical integration method is used to predict the precipitation behavior of AIN. During the calculation, after each infinitesimal increment of time, At, the nucleation rate at that time and the new volume of all the previously nucleated particles are calculated, as well as the new solute concentration in the matrix. By repeating these calculations for each time step, the extended volume fraction, and in turn, the actual volume fraction, can then be obtained as functions of time. For non-isothermal (e.g., continuous cooling/heating) conditions, temperature (as a function of time) is recalculated after each infinitesimal time step and all other parameters are recalculated based on the new temperature. For nucleation on grain boundaries, the grain boundary surface energy are taken from the literatures^ 90'911 and are considered to be constants — Ygb = 0.75Jm"2 and Ygb = 0.8Jm"2. The effect of y g b on the precipitation kinetics will be discussed later. 5.3. Results and Discussion The theoretical model is first compared to experimental data for isothermal AIN precipitation in a 0.09wt%C, 0.051wt%Al and 0.0073wt%N steel[32]. Specimens were first solution treated at 1300°C for 2 hours before being quenched to the isothermal annealing temperature. The calculated and measured fraction of precipitated AIN vs. isothermal annealing time at 840°C and 1000°C, respectively, are shown in Figure 5.7. The N A i N / N t o t a i ordinate in Figure 5.7 shows the ratio between the amount of nitrogen as AIN and the total Theoretical Model —Precipitation 94 nitrogen content in the steel. For this composition, the calculated A G * / £ B T for both homogeneous and grain boundary nucleation in austenite are shown in Figure 5.8 as functions of temperature. Although both homogeneous and heterogeneous nucleation are considered during the calculation, it can be seen from Figure 5.8 that the critical energy barrier, A G , for bulk matrix (homogeneous) nucleation is an order of magnitude higher than that for nucleation at grain boundaries. Thus, the nucleation kinetics are completely dominated by nucleation of AIN at austenite grain boundaries. In fact, the values of A G for homogenous nucleation at these temperature are so high that homogeneous nucleation is ( A G * ^ virtually impossible (i.e., exp V kBT j —> 0). Comparing the prediction to the experimental data in Figure 5.7, it shows good agreement. No fitting parameter is used in the model to obtain these calculated results. A calculated Precipitation-Time-Temperature (P-T-T) diagram for the isothermal precipitation of AIN in this steel in the austenite region is shown in Figure 5.9, and compared with the two experimental points at 840°C and 1000°C, respectively. The onset of precipitation (P5) is set as 1% of the total precipitation. Calculated volume fractions of AIN precipitate in DQSK steel as a function of isothermal annealing time at various temperatures (in austenite) are shown in Figure 5.10. As in the previous case, A G * for homogeneous nucleation is much larger than that for grain boundary nucleation (Figure 5.11). Thus, precipitation is dominated by nucleation at grain boundaries. The equilibrium solution temperature for AIN in this steel is determined to be about 1120°C. However, it can be seen from Figure 5.10 that the precipitation of AIN is Theoretical Model —Precipitation 95 extremely slow even at 960°C. There is no significant precipitation until holding for more than a day (« 9xl04 sec.) at the isothermal temperature. These predictions suggest that although thermodynamically it is energetically favorable for AIN to precipitate below 1120°C, the precipitation is retarded by the high nucleation energy barrier. The values of exp f AG* A V ^ B T J 8 1 A -18 at 880°C, 960°C and 1000°C are calculated to be in the order of 10, 10 and 10"35, respectively. However, the diffusivity of Al in austenite only changes by a factor of 5 over this same temperature range. A calculated Precipitation-Time-Temperature (P-T-T) diagram for the isothermal precipitation of AIN in the DQSK steel in the austenite region is shown in Figure 5.12. The onset of precipitation (Ps) is set as 1% of the total precipitation. This figure shows that the P-T-T curve does not follow the classical C-curve behavior; instead, it resembles the upper half of a C-curve. This suggests that the kinetics of precipitation in this temperature range is controlled, not by the diffusivity of Al, but by the nucleation rate which increases substantially as the temperature decreases. By assuming a stable austenite phase below Ae3 (i.e., no y -> a transformation), the current model suggests that precipitation indeed follows the classical C-curve behavior and a maximum rate can be achieved at about 800°C to 820°C. It has been shown that the precipitation of AIN during isothermal transformation in a 0.2C-0.05A1-0.024N steel follows classical C-curve behavior[18], giving a maximum rate of precipitation in austenite at about 1100°C. However, even at this temperature, the rate of precipitation is still slow, with more than 6 hours needed to precipitate all the possible AIN. Theoretical Model —Precipitation 96 The calculated P-T-T curves for the isothermal precipitation of AIN for the two previously examined low carbon steels in the austenite region are compared in Figure 5.13. It clearly shows the effect of the Al and N content on the precipitation kinetics. With higher Al and N contents, the curve shifts to shorter time (because of higher nucleation rate) and higher temperature (because of higher solution temperature). As shown in Figure 5.14, the values of A G * / £ B T for grain boundary precipitation in the 0.051A1-0.0073N steel is much lower than that for the precipitation in the DQSK steel, especially at higher temperatures. Since A G S and y do not change much with this composition difference, it is mainly the difference in the chemical driving force, AGChem> that contributed to the difference in A G * . In Figure 5.15, calculated P^ and P/ curves for AIN precipitation in DQSK in the ferrite region are shown. It can be seen from this figure that the precipitation of AIN in ferritic DQSK follows the classical C-curve behavior with the nose at about 630°C. Compared to Figure 5.12, this figure shows that AIN precipitation is much faster in ferrite than in austenite. Moreover, although the kinetics are still dominated by grain boundary nucleation, the calculation shows that at the early stage of precipitation, homogeneous nucleation occurs and contributes a small fraction of the total precipitation. This can be explained by the difference in nucleation barrier, A G * . In Figure 5.16, A G * / A : B T for homogeneous and grain boundary nucleation are plotted as functions of temperature. Although the nucleation for homogeneous nucleation is still higher than that for grain boundary nucleation, the difference between them is not as large as that for nucleation in austenite. Because of the much higher number of homogeneous nucleation sites, the Theoretical Model —Precipitation 97 homogeneous nucleation rate is comparable (10 ~ 100 times smaller) to the grain boundary nucleation rate, such that both homogeneous and grain boundary nucleation can occur simultaneously. As shown in the previous chapter, there is evidence that AIN precipitates exist in the ferrite matrix after isothermal precipitation in the ferrite region. Since the barrier to nucleation on a grain boundary is reduced by the elimination of grain boundary energy as the nucleus is formed, the value of the grain boundary energy is important in determining the critical energy, A G * . In Figure 5.17, A G * / £ B T is plotted as a function of temperature for 3 different values of ygb, 0.65Jm"2, 0.75Jm"2 and 0.85Jm"2. It can be seen that at the same temperature, a higher ygb leads to a lower nucleation barrier with the difference being more significant at high temperatures. Since the formation of a nucleus is driven by the reduction of total Gibbs free energy, then at high temperature, because ofthe low chemical driving force, the reduction of grain boundary energy becomes more important. However, at low temperature, due to the high chemical driving force, the effect of the reduction in grain boundary energy on A G * becomes less significant. The calculated P-T-T diagram for the precipitation of AIN in DQSK steel is shown in Figure 5.18, using the three different values of ygb. It can be seen that a higher ygb shifts the Vs curve to the left (shorter time). At low temperature in the austenite region, the change in P^ is small (within the same order of magnitude), however, at high temperature, the deviation among the curves becomes significant. Theoretical Model —Precipitation R e f Fee (J/mol) S N -Ig^f = " 3 7 2 0 2 + 179.756T- 13.071nT 64,6.5 LFN%= -26150 64,65 gAi - H A I R = -2132.5-14.767T-0.0247T2 69* ° L F e > A i = -96053 +18.408T 67 l L F e , A i = 31654-19.474T 67 Bcc (J/mol) g N a -ygnf =21378 +139.858T-10.9077TlnT 64,65 = 0 64,6:5 g AT-g A i = 10083-4.8116T 67 ° L F e , A i = _ 1 1 5 7 1 3 + 26.604T 67 ,LaFe>AI=31729-19.421T 67 AIN (J/mol of AIN) g° iN ~(H^R +iH^R) = -345837 + 359.862T-54.3087TlnT + 8.56xl0"4T2 + 2.326 x 106 T"1 -1.26x108T"2 N2, gas (J/mol) 950K < T < 3350K jg° g a s - jH^ E R =-7358.85 + 17.2003T-16.3699TlnT 2 2 66 -6.5107 xlO"4T2 +3.0097 xlO"8T3 +563070T"1 298.15K<T<950K | g ° g a s - | H ^ E R = -3750.675-9.45425T-12.7919TlnT 2 & N 2 2 N 2 6 6 -0.00176686T2 + 2.680735 x 10"9T3 -32374T"1 * equation derived from tabulated data in Ref. 69. Table 5.1. List of thermodynamic parameters for AIN and the Fe-Al-N system. Theoretical Model —Precipitation 99 AIN (hep) y-Fe (fee) ct-Fe (bec) Lattice parameter a = 0.3111 a = 0.364 (nm) c = 0.4975 Shear modulus, \i 1.28 x l O 5 8.1 x l O 4 (MPa) a = 0.2866 1-0.91-T - 3 0 0 1810 6.4xlO q 1-0.81 T - 3 0 0 1810 - 3.2 x 10~2 (T - 573)2 - 2.4 x 10~2 ( T - 923)2 Poisson's ratio, v 0.25 0.29 when T > 573K when T > 923K 0.29 Table 5.2. Data used for calculation of interfacial energy for AIN in a-Fe and y-Fe[76"80]. Theoretical Model —Precipitation 100 Figure 5.1. Schematic diagram of the free energy change, AG, for the nucleation of a spherical nucleus as a function of the radius, r. 0.81 0.3-1 1 1 1— 550 750 950 1150 temperature (°C) Figure 5.2. Calculated interfacial energy of AIN in austenite (y-Fe) and ferrite (a-Fe). Theoretical Model —Precipitation 101 Figure 5.3. Effect of c/a on the precipitate morphology; (a) oblate spheroid (c/a < 1) and (b) prolate spheroid (c/a > 1). EA Figure 5.4. Variation of misfit strain energy, E, with spheroid shape, c/a, (after Nabarro[83J). Theoretical Model —Precipitation 102 v = v p = 0.291 H = 8.6xl0"dyn/cm 2 o.ol | I I | I I I // I 0 . 0 1.0 2 . 0 3iO 4 . 0 5 . 0 6 .0 7 0 to ( D i s c ) (Sph t re ) c /a ( N e t d t o ) Figure 5.5.Normalized strain energy of a coherent particle vs. aspect ratio for three combinations of elastic constants (after Barnett et a/.[85]). Theoretical Model —Precipitation 103 time (sec) Figure 5.7. Calculated and measured fraction of precipitated AIN vs. isothermal annealing time in a 0.09wt%C, 0.051wt%Al and 0.0073wt%N steel at 840°C and 1000°C, respectively (experimental data from Vodopivec^ 32 )^. i o ° 4 1 1 1 1 900 950 1000 1050 1100 temperature (°C) Figure 5.8. Computed A G * / £ B T as a function of temperature for AIN nucleation in austenite (0.09wt%C, 0.051wt%Al and 0.0073wt%N). Theoretical Model —Precipitation 104 1050 x 1000 o V 9 5 0 LB 3 re k_ o a. £ 900 4-850 4-800 10u 101 102 103 104 10 s t i m e ( s e c ) Figure 5.9. Comparing calculated P-T-T diagram for AIN precipitation in austenite (0.09wt%C, 0.051wt%Al and 0.0073wt%N) to experimental data; curve shows the onset of AIN precipitation, Ps, and includes experimental data from Vodopivec[32]. Theoretical Model —Precipitation 105 time (sec) Figure 5.10. Calculated fraction of AIN precipitates vs. isothermal annealing time in austenite ( D Q S K : 0.038wt%C, 0.04wt%Al and 0.0052wt%N) at four different temperature. • J Q O - I 1 1 1 1 1 850 900 950 1000 1050 1100 temperature (°C) Figure 5.11. A G * / £ B T as a function of temperature for AIN nucleation in austenite ( D Q S K : 0.038wt%C, 0.04wt%Al and 0.0052wt%N). Theoretical Model —Precipitation 106 1000 T 950 4-V 900 3 o a. E o 850 4-800 4-750 -I 1 1 1 1 1 10 1 10 2 1 0 3 1 0 4 1 0 s 10 6 t i m e ( s e c ) Figure 5.12. Calculated P-T-T diagram for AIN precipitation in austenite (DQSK: 0.038wt%C, 0.04wt%Al and 0.0052wt%N); curve shows the onset of AIN precipitation (Ps). 1000 -980 - ^ ^ 0 . 0 5 1 %AI, 0.0073%N 960 -940 - / ^^^^ 920 -/ / / 0 . 0 4 % A I , 0 . 0 0 5 2 % N 900 -880 -860 -840 - 1 1 1 1 1 1 1 0 ° 10 1 10 2 10 3 10 4 10 5 10 6 t i m e ( s e c ) Figure 5.13. Calculated P-T-T diagram for AIN precipitation in austenite in two low carbon steels; curves show the onset of AIN precipitation (Ps). Theoretical Model —Precipitation 107 875 925 975 1025 1075 temperature (°C) Figure 5.14. AG*/#BT for A I N nucleation at grain boundaries in austenite in two low carbon steels as functions of temperature. Figure 5.15. Calculated P-T-T diagram for AIN precipitation in ferrite in DQSK steel: Vs and P/represent 1% and 99% completion of precipitation. Theoretical Model —Precipitation 108 AG* 25 20 15 10 bulk matrix grain boundary 580 630 680 730 temperature (°C) 780 Figure 5.16. AG*/A:BT as functions of temperature for homogeneous and grain boundary nucleation of AIN in ferrite (DQSK steel). Theoretical Model —Precipitation 109 0.65Jlnf 0.75Jlnf 0.85J/rrf 900 950 1000 1050 1100 t e m p e r a t u r e ( °C) Figure 5.17. A G * / & B T as functions of temperature for grain boundary nucleation of A I N in austenite (DQSK steel) for three different values of ygb. 1000-r O o IF 3 2 8. E fi 950+ 900+ 850-1 0 ' 1 0 ' 0 . 8 5 J m 0 . 7 5 J m 1 0 J 1 0 ' time(sec) 1 0 A 1 06 1 0 7 Figure 5.18. Calculated curves of the P - T - T diagram for A I N precipitation in austenite in DQSK steel for three different values of ygb. 110 CHAPTER 6 THEORETICAL MODEL —DISSOLUTION, GROWTH & COARSENING The size distribution of nitride or carbide precipitates is an important microstructural parameter in determining the mechanical properties of low carbon or microalloyed steels after a variety of thermomechanical processes. During reheating of the steels, the pre-existing precipitates may dissolve due to increasing solubility. In addition, there is a tendency for the smaller particles to shrink and the larger ones to grow. This process is known as coarsening or Ostwald ripening and is driven by the minimization of the total surface free energy of the system. Although models have been developed for these two phenomenon, they are often modeled as two separate processes^ 50'92"951. In reality, dissolution and coarsening usually overlap and occur simultaneously. In such a case, neither conventional dissolution nor Ostwald ripening models can be applied. In the present work, a theoretical model was developed to predict the dissolution, growth and coarsening behavior of nitrides or carbides in low-carbon and microalloyed steels undergoing thermomechanical treatment by using numerical integration methods on a multi-particle system. Dissolution and coarsening are treated as one continuous, simultaneous phenomenon and the two processes are simulated in a natural sequence. This model takes fully into account the equilibrium thermodynamic properties of the system, the local equilibrium at the interface, curvature effects and diffusion along grain boundaries. Theoretical Model —Dissolution, Growth & Coarsening 111 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. This model is applied to study the dissolution and coarsening behavior of aluminum nitride (AIN) in a DQSK Al-killed low carbon steels. The predicted results are then compared to experimental measurements made on the same system. 6.1. Modeling Based on the measured mean diameter and the standard deviation of the initial size distribution, an assembly of n particles can be defined according to a presumed particle size distribution. The form of the initial size distribution depends on the initial experimental conditions. However, in most cases, the distribution of nitrides or carbides in steels can be well-represented by either a normal distribution or a log-normal distribution. For a normal distribution, the density function can be written as: Pn = 1 exp (6.1) where pn is the probability density of a normal particle size distribution, a is an individual particle radius, f is the arithmetic mean radius of the distribution and a n is the standard deviation. For log-normal distribution, the density function is Theoretical Model —Dissolution, Growth & Coarsening 112 1 Pi =-/== e x P | (hm-n) 2 2G2 (6.2) where p, is the probability density of a log-normal particle size distribution, \x is the arithmetic mean of the distribution of ln(a) and a, is the standard deviation of the normal distribution of ln(a). 6.1.1. Precipitates in Matrix For both dissolution and growth, the diffusion controlled transformation of a particle in a matrix requires the solution of Fick's second law, DV ' C = f ( 6 . 3 ) where D (assumed independent of composition) is the interdiffusion coefficient in the matrix and C = C(r,t) is the concentration field in the matrix surrounding the precipitate. For an MX type precipitate in an Fe-M-X ternary system, where M is the substitutional alloy element (e.g. Nb, V, Al, etc.) and X is the interstitial element (e.g. C and N), the diffusivity of the interstitial elements is usually several orders of magnitude higher than that of the substitutional elements. It is reasonable to assume that the kinetics of the particle dissolution and/or coarsening process is controlled by the slower diffusion rate of Theoretical Model—Dissolution, Growth & Coarsening 113 the substitutional alloying element and the concentration gradient of the interstitial element in the matrix can be ignored. For simplicity, all precipitates are assumed to be spherical and that during dissolution/growth the precipitates remain spherical. For such a spherically symmetrical system, Equation (6.3) becomes D d2C 2 dC — + dt2 r dt dC For precipitates in a finite matrix, the precipitates are assumed to be uniformly distributed in the matrix. For mathematical simplicity, each particle can be considered to be at the center of a spherical cell with radius, I, where 21 is the initial average inter-particle distance. Let a be the radius of a particle within the spherical cell. If I» a, then within a short period of time, the solute concentration at the cell wall, C M , can be approximated as a constant, although it changes slowly with time. Under this situation, the bouadary conditions for Equation (6.4) become C = Ci when r = a (6.5a) and C = C M when r = I (I»a) (6.5b) Schematic concentration profiles around a precipitate in these conditions are shown in Figure 6.1, where Cp is the solute concentrations in the precipitate and Q is the solute concentration in the matrix at the particle/matrix interface. Theoretical Model—Dissolution, Growth & Coarsening 114 If Ci and C M are assumed to be constants, then the concentration profile can be determined by following the stationary interface (invariant size) approximation[92] developed by Whelan. In this approach, the diffusion field around a precipitate with radius, a, is assumed to be the same as that which would exist if the precipitate/matrix interface had been fixed at a from the start, i.e., by restricting the diffusion field to have no memory of the past motion of the interface. Thus, for constant Q and C M , Equation (6.4) can be solved to obtain the concentration profile for r > a, C-CM=(C,-CM)-erfc r (6.6) where the complementary error function, erfc(x), is defined as erfc(x) = -= f°exp(-t2)dt (6.7) Due to mass conservation of the solute in the matrix, the flux of solute at the interface is equal to the rate of loss (or gain) of solute in the precipitate. Thus, for a spherical particle, the condition of flux balance at the interface can be written as - Ana 1 (CP - Cj )da = -4na 2D dC dr dt (6.8) r=a Theoretical Model —Dissolution, Growth & Coarsening 115 which can be rewritten to obtain the rate of migration (or velocity) of the precipitate/matrix interface, v, as v = • da _ D aC dt ~ C P - Cj dr (6.9) Having obtained — from Equation (6.6), — can be obtained from Equation (6.9) as 8r dt da dt~ -k I D f D^2 a \nts (6.10) C - C with k= 1 c - c (6.11) In equation (6.10), the term in t 2 arises from the transient part of the diffusion field. For steady-state, Equation (6.10) becomes da dt = -k- D a (6.12) Equation (6.10) is the solution for an isolated particle in an infinite matrix where both Q and C M do not vary with time. However, under local equilibrium conditions at the precipitate/matrix interface, the Gibbs-Thomson equation shows that the equilibrium Theoretical Model —Dissolution, Growth & Coarsening 116 composition in the matrix at the curved precipitate/matrix interface, Q, varies with precipitate radius, a, as[96] Ci =C" exp ' 2 Y V (6.13) where y is the precipitate/matrix interfacial energy, Vp is the molar volume of the precipitate, R is the gas constant, T is the absolute temperature and is the equilibrium solute concentration at a planar interface. In the case of dissolution, the presence of the curvature effect tends to speed up the rate of dissolution, being particularly important for small particles. For an MX type precipitate, the solubility product for a non-planar precipitate/matrix interface, Ki, can be written as[47] K, = [M]I[X]I = K<° -expf^y (6.14) V RTa J where [M]j and [X]} are the equilibrium contents (wt%) of M and X, respectively, in the matrix at the curved precipitate/matrix interface and K°° is the solubility product for a planar interface. Values of can be derived from experimental data or calculated from thermodynamic data. Theoretical Model —Dissolution, Growth & Coarsening 117 Moreover, in a finite, dilute solution, although the diffusion fields surrounding the precipitates would not seriously overlap, the solute concentration in the matrix will still vary with time due to the dissolution or growth of the precipitates. In the case of dissolution, the increase of solute concentration in the matrix tends to slow down the rate of dissolution. As the solute concentration increases and reaches the equilibrium value, then the total volume fraction of the precipitates will remain constant. On the other hand, in the case of a growing precipitate, the decrease of solute concentration in the matrix tends to slow down the growth rate. If the solute concentration in the matrix is fixed, the particles will never stop shrinking (or growing) which does not agree with reality. Therefore, in an attempt to take into account the effects of variation in Q and CM on the rate of dissolution, Equation (6.10) is modified. Although strictly speaking, Equation (6.10) is only valid when & is a constant (i.e, Cp, Q and CM are all constants), it is reasonable to believe that[93'94] within a very short period of time, Equation (6.10) can still be a good approximation for the rate of dissolution (or growth) for the case where both Q and CM change only slowly with time. Therefore, during the calculation, Q in Equation (6.10) is replaced by Equation (6.13) to include the effect of curvature. Both Q and CM are updated after each infinitesimal increment of time. For AIN in the DQSK steel, CM only changes from 0.04wt% for no precipitation to 0.029wt% for complete precipitation. However, for example, at 700°C, Q can change from 0.03wt% at a planar interface to 0.078wt% at the interface of a 5nm radius particle. Clearly the change in the curvature of the precipitate has a stronger effect on the rate of dissolution than the change in the solute concentration in the matrix. Theoretical Model —Dissolution, Growth & Coarsening 118 If there is no new precipitate formed during dissolution or coarsening, the volume fraction of precipitates at time, t, is f (t) = f0 f " E v i ( t ) i=l Z V . o (6.15) where fo is the volume fraction of precipitates at t = 0, Vj(t) and Vi0 are the volumes of particle i at time = t and 0, respectively. During the calculation, CMO) is considered as the average solute concentration in the matrix which can be determined from f(t) and the total solute content in the system, i.e., CM(t) = C T - ^ (6-16) where C T is the total solute concentration. It can be seen from Equation (6.10) that a precipitate is dissolving when k > 0 and growing when k < 0. For most MX type precipitates, Cp is normally considered as constant. Since Q is a function of a and C M is a function of time, so k - k(a, t). Therefore, for a multi-particle system, whether an individual particle may dissolve or grow depends on its radius, as illustrated in Figure 6.2. Thus, it is possible that one particle dissolves while some other particles are growing at the same time. Moreover, each individual particle may Theoretical Model —Dissolution, Growth & Coarsening 119 have a different growth or dissolution rate. The size of each individual precipitate, a\, can be determined by integrating Equation (6.10) numerically for each precipitate. 6.1.2. Precipitates on Grain Boundaries When a particle is located on a grain boundary, both grain boundary and bulk diffusion can occur simultaneously. During dissolution, solute atoms can flow from the particle's surface to the matrix or can diffuse along the grain boundary. The solute atoms can also flow from the grain boundary to the matrix. Similar situations also arise for a growing particle, but instead of flowing away from the particle, the solute atoms flows towards the particle. A dissolving particle located on a grain boundary is shown schematically in Figure 6.3. In the present model, a grain boundary precipitate is considered as a sphere with a thin slab of material (i.e., grain boundary) attached along its equator[97], as shown in Figure 6.3. 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, as described in the previous section. The other is the solution 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. The concentration profile in the grain boundary can be determined by examining a volume element within the boundary[97], such as that shown in the lower right corner in Theoretical Model —Dissolution, Growth & Coarsening 120 Figure 6.3. Let Nr and Nr+dr be the number of atoms per unit time entering and leaving the volume element at the points r and r+dr, respectively, dNc be the amount of solute per unit time diffusing from the boundary element to the bulk matrix and dNb be the change in amount of solute in the boundary element per unit time. Conservation of solute implies that Nr - N r + d r - dNc = dNb (6.17) Since N r = - D b A c ^ - (6.18) or d N b = 5 A c ^ (6.19) and dNc can be approximated^ 981 as d N c « ^ ( C b - C M ) d A s (6.20) « 0 where Cb = Cb(r,t) is the solute concentration within the grain boundary, CM is again the average solute concentration in the matrix, Db is the grain boundary diffusivity, 8 is the thickness of the grain boundary, A c and dAs are the cross sectional area and surface area of the volume element, respectively and d0 is the mean grain diameter. Theoretical Model —Dissolution, Growth & Coarsening 121 From the geometry depicted in Figure 6.3, A c =27rr5 (6.21) and dAs - 2rardr (6.22) Using Equation (6.17) to Equation (6.22), one can obtain (*2 d'Cb 1 dCb 4D ar2 r or 6</0Db ^ DC, dt (6.23) Within a short period of time, CM can be assumed to be constant. With the boundary conditions that Cb - CM and Cb = Ci when r » a when r = a (6.24a) (6.24b) Equation (6.23) can be solved to obtain the concentration profile within the grain boundary as M (6.25) where (3 4D (6.26) Theoretical Model —Dissolution, Growth & Coarsening 122 and the modified Bessel function, KQ(X), can be approximated as (6.27) when x > 1. Although Equation (6.27) is only valid for large x, the error in using this approximation is small (i.e. less than 10%) even when* < 1. Considering the mass conservation of the solute over the whole surface of the particle, the condition of solute balance can be written as -47ta 2(CP-C I)da = 47ifl2D ac dr 27ia8Db acb dt dt (6.28) where C(r=a, t) = Cb(r=a, t) = Q. Combining Equation (6.25) to Equation (6.28) with the results from the previous section, the growth (or dissolution) rate of the precipitates can be approximated as do dt" = -k D 5Db 5Dbp — + —f- + ——+ a 4a' 2a I V 2 (6.29) 6.2. Calculations The theoretical model described in the preceding section has been applied to the dissolution and coarsening of aluminum nitride (AIN) in both austenite (y) and ferrite (a) in DQSK steel. The predictions are based on a 2000 particles assembly. A flow chart for the Theoretical Model —Dissolution, Growth & Coarsening 123 computer program is shown in Figure 6.4. During the calculation, based on the values of a and Ci for each particle, as well as CM, at time, t, the new values of all a at t + At can be determined using Equations (6.12) or (6.29), where At is an infinitesimal increment of time. The new value of CM at t + At can also be calculated from the new volume fraction. By repeating these calculations for each time step, the size evolution of each particle can then be obtained. The diffusion coefficients of Al in a bulk matrix^9'100-1 or along a grain boundary in austenite and ferrite are shown in Table 6.1. For diffusion of Al along a grain boundary, because of lack of experimental data, self-diffusion data for Fe along a grain boundary were used[101]. The equilibrium between AIN and the Fe-Al-N system can be determined by using the method described in the previous chapter. AIN and the matrix are in chemical equilibrium when Agchem - 0 in Equation (5.7). Using this relation, the equilibrium solubility of AIN in both austenite and ferrite (for planar precipitate/matrix interfaces) can then be calculated and presented in the usual form as logK^ = log{[wt%Al][wt%N]} = A - ® (6.30) where A and B are constants. The solubility products of AIN in austenite and ferrite are determined as Theoretical Model —Dissolution, Growth & Coarsening 124 logK" =log{[wt%Al][wt%N]} = 4.5989-11568 (6.31) T and logK^ =6.1061- 14442 (6.32) T respectively. Equation (6.31) is compared to literature data[21'26'27'64] in Figure 6.5. 6.3. Results and Discussion 6.3.1. AIN in austenite To study the dissolution and coarsening of AIN in austenite, specimens obtained from a coil of DQSK steel were first heat treated at 700°C for 24 hours to obtain an initial size distribution of the AIN particles; the samples were then immediately heated to 1000°C. Both measured and predicted size distributions of AIN after the steel is soaked at 1000°C for different holding times are shown in Figure 6.6. Based on these size distributions, the mean diameter of the AIN is calculated and plotted as a function of holding time in Figure 6.7. It can be seen that the mean diameter of the AIN particles decreases slightly during the initial stage of annealing and then increases. The initial size distribution, as shown in Figure 6.6(a), is obtained by annealing the coil material at 700°C for 24 hours. Using the measured values of mean radius and standard deviation, a normal distributed particle size is established to initiate the simulation. Comparing the predictions to observations at t = 30 min., 60 min. and 90 min. (Figure 6.6(b) to 6.6(d)), a reasonably good agreement is Theoretical Model —Dissolution, Growth & Coarsening 125 obtained. Although there are differences between the measured and predicted mean size, the distributions are very similar. Once the specimen is rapidly heated to the test temperature, all particles start to dissolve (decrease in mean diameter) initially due to the high solubility and low solute concentration in the matrix (i.e., high k values). As the precipitates dissolve, the solute concentration in the matrix, CM, increases (i.e., the volume fraction of AIN decreases) and gradually reaches a stable level. The predicted volume fraction of undissolved AIN particles in the steel is shown in Figure 6.8. The total volume fraction decreases very quickly during the early stage of annealing and then stays at an almost constant level throughout the rest of the annealing. The size evolution of 4 selected AIN particles are shown in Figure 6.9. It can be seen that after the initial stage, the dissolution rates of the smaller ones (particles C & D) decrease as CM increases (lower k values). However, as the particles become very small, the curvature effect causes the dissolution rate of these particles to increase rapidly. While the smaller particles are completely dissolved, the larger ones (A & B) start to coarsen after shrinking slightly in the early stage (Q becomes lower than CM, i.e., k changes from +ve to -ve). Moreover, it can also be seen in Figure 6.9 that particle B, as it becomes one of the "smaller" particles among the remaining particles, starts to shrink near the end of the simulation, while particle A keeps growing. These predicted behaviors are not only in agreement with our knowledge of dissolution and coarsening kinetics of second-phase particles, they also indicate the Theoretical Model —Dissolution, Growth & Coarsening 126 capability of the present model to treat dissolution and coarsening as one continuous process, with no clear separation between the two. The size evolution of AIN at two other temperatures, 1100°C and 1175°C, is shown in Figure 6.10. Although both start with the same initial size distribution, because ofthe higher solubility and higher diffusivity, the mean size of AIN at 1100°C is much larger than that at 1000°C for the same holding time. However, for the case of 1175°C, the soaking temperature is sufficiently high to dissolve all AIN particles. From Equation (6.31), the equilibrium solution temperature for AIN in this steel is determined to be approximately 1120°C. Thermodynamic properties of the system not only determine the equilibrium condition, they also play a major role on the dissolution or growth rate. Dissolution and coarsening of AIN at 1000°C was also studied with a different initial size distribution. In these tests, specimens were first solution-treated at 1250°C for 30min., and then quenched to and held at 650°C for 24 hours to obtain the initial particle size distribution. In this case, the measured initial size distribution is best fitted by a log-normal distribution for the simulation. Figure 6.11 shows the variation of mean particle size with reheating time. The size distributions of AIN particles for different times at the soaking temperature are shown in Figure 6.12. Although the mean sizes are different (due to different initial sizes), the curve shown in Figure 6.11 is similar in shape to that shown in Figure 6.7. Both curves exhibit a small initial decrease in the mean size followed by an increase of the mean size (i.e., shifting from a dissolution-dominated to a coarsening-dominated process). Theoretical Model —Dissolution, Growth & Coarsening 127 6.3.2. AIN in ferrite The capability of the present model to simulate the size evolution of second-phase particles along grain boundaries is demonstrated by the following study of the coarsening of AIN precipitates along ferrite grain boundaries during annealing of the steel at 700°C. Specimens were first solution-treated at 1250°C for 30min. and then quench to and held at 700°C for up to 7 days. SEM micrographs of the specimens indicate that there is no significant difference in the ferrite grain size throughout the test, possibly due to the pinning effect of the AIN precipitates. Therefore, during the calculation, the average ferrite grain size is taken to be constant (d0 «10um) and the precipitates are considered to be stationary along the grain boundaries (i.e., precipitates remain on the grain boundaries throughout the anneal). The size evolution and distribution of AIN precipitates are shown in Figure 6.13 and Figure 6.14, respectively. In the present model, it is assumed that no new nucleation occurs during the annealing. For this test condition, it has been determined that precipitation should be completed within approximately 30 minutes. Thus, a log-normal size distribution is established from the measured size distribution of AIN precipitates obtained after 1 hour at 700°C (Figure 6.14(a)) to initiate the simulation. As shown in Figure 6.13, the coarsening of AIN particles is rapid during the early stage of annealing and slows down at longer times. Moreover, unlike those previous cases, there is no initial decrease of the mean diameter at early annealing times. This indicates that the growth mechanism is dominated by coarsening throughout the whole period. Theoretical Model —Dissolution, Growth & Coarsening D0 (m2/s) Q (kJ/mol) Ref. austenite, matrix 2.51xl0"4 253.4 99 austenite, grain boundary 3.0x10'4 167.4 101 ferrite, matrix 5.31xl0~8 196.5 100 ferrite, grain boundary 5.82x10"8 143.8 101 Table 6.1. Diffusion coefficients of Al in austenite and ferrite, D = D0exp(-Q/RT). Theoretical Model —Dissolution, Growth & Coarsening 129 Figure 6.1. Schematic diagram of the solute concentration in the vicinity of (a) a dissolving precipitate and (b) a growing precipitate. Theoretical Model —Dissolution, Growth & Coarsening 130 Figure 6.2. Schematic concentration fields showing the effect of particle size on the transformation mode, i.e., dissolution or growth, of an individual particle. Figure 6.3. Schematic diagram of a precipitate located on a grain boundary. Theoretical Model —Dissolution, Growth & Coarsening 131 ( START ) i Input initial data I ~ Read parameters Setup particle assembly t = 0, initialization Calculate T(t), C e ' I Calculate f, C M I first particle, i = 1 Calculate Q and new a at t = t + At for the i * particle No i = i+ 1 Simulation ends No t = t + At Plot ( END j Figure 6.4. Flow chart illustrating the logic of the program. Theoretical Model —Dissolution, Growth & Coarsening -3 + O .4 -Honere f a/. [27] -Darken ef a/.[21] •Gladman ef a/. [26] Hillert ef a/.[64] - present work 7 8 9 -1-4 it A \ 10 l/T^CTIC1) Figure 6.5. Solubility products of AIN in austenite. Theoretical Model —Dissolution, Growth & Coarsening 133 30 y 25 -20 > s O c 15 -0) 3 t T O 10 -£: 5 -0 -(a) A ] measured - calculated 40 80 120 d i a m e t e r ( n m ) 160 (b) 80 120 d i a m e t e r ( n m ) 25 25 0 40 80 120 160 (d) d i a m e t e r ( n m ) Figure 6.6. Evolution of size distribution of AIN particles after soaking at 1000°C for a) t = 0s, b) t = 30 min, c) t = 60 min and d) t = 90 min. Theoretical Model —Dissolution, Growth & Coarsening 134 80 G) E ro c ro a> E 40 20 calculated + measured 2000 4000 reheating time (sec) 6000 Figure 6.7. Variation of mean diameter with reheating time at 1000°C. 3.5 i 2000 4000 reheating time (sec) 6000 Figure 6.8. Variation of AIN volume fraction with reheating time at 1000°C (after annealed for 24 hours at 700°C). Theoretical Model —Dissolution, Growth & Coarsening 135 Figure 6.9. Size evolution of four selected AIN particles during soaking at 1000°C Theoretical Model —Dissolution, Growth & Coarsening 136 Figure 6.10. Variation of mean diameter of AIN particles with reheating time at (a) 1100°C and (b) 1175°C, after an initial 24 hour annealing at 700°C. Theoretical Model —Dissolution, Growth & Coarsening 137 80 E c L_ d) <D E ro T3 c (0 (U E 40 t 20 calculated + measured 2000 4000 reheating time (sec) 6000 Figure 6.11. Variation of mean particle size with reheating time at 1000°C (after initially annealed for 24 hours at 650°C). • measured - * — calculated 30 40 80 120 d i a m e t e r (nm) 160 ] measured • calculated ^ T V T » I » I » I > I » I » I > 80 120 d i a m e t e r (nm) 160 40 35 -f Figure6.12. Evolution of the size distribution 3 Q of AIN particles (initially annealed for 24 hours S 2 5 at 650°C) after soaking at 1000°C for a) t = 0 s, | b) t = 1 hour and c) t = 2 hours. 80 120 d i a m e t e r ( n m ) Theoretical Model —Dissolution, Growth & Coarsening 138 0 1 : 1 1 1 1 0 50 100 150 annealing time (hrs) Figure 6.13. Variation of mean diameter of AIN particles with annealing time at 700°C. Figure 6.14. Evolution of the size distribution of AIN particles after soaking at 700°C for a) t = 1 hour, b) t = 20 hours and c) t = 164 hours. 0 40 80 120 160 (c) diameter (nm) 139 CHAPTER 7 SUMMARY AND CONCLUSIONS 7.1. Summary The behavior of aluminum nitride (AIN) precipitates in aluminum-killed steels has been the subject of much investigation because the precipitates are known to have significant effects upon recrystallization and grain growth which directly influence hardenability, ductility, texture formation and other mechanical properties of steels. Although aluminum nitride is beneficial in that it restricts grain growth, it can cause embrittlement problems, particularly during continuous casting and hot rolling. It has been suggested that the AIN precipitates cause low hot ductility by inhibiting dynamic recrystallization and by grain boundary pinning which is considered to facilitate void formation. The size distribution, spatial distribution and morphological characteristics of the precipitates are believed to markedly affect the mechanical properties of the steels after a variety of thermomechanical processing. Thus, an understanding of the precipitation, dissolution, growth or coarsening kinetics could markedly facilitate the development of optimum heat treatment schedules. Although the literature of AIN in steels is extensive, the mechanisms and kinetics of precipitation, growth, dissolution and coarsening of AIN in steels are not yet fully understood. To improve the current understanding of these mechanisms and kinetics during Summary and Conclusions 140 the thermomechanical processing of low carbon steels, a comprehensive experimental and theoretical study has been carried out. An objective of the present study is to relate the observed size, distribution and morphology of aluminum nitride in various specimens to their thermal history. With the aid of the carbon extraction replica technique, a detailed study of the morphology, spatial distribution and size distribution of the AIN particles in a drawing quality special Al killed (DQSK) steel has been carried out via TEM and STEM high magnification microscopy and microanalysis. Experimental works have been conducted on the precipitation, dissolution, growth and coarsening of AIN precipitates during isothermal annealing, reheating or continuous cooling of the steel. The influence of prestraining on the kinetics of isothermal precipitation of AIN has also been studied using the Gleeble 1500 thermomechanical simulator and the stress relaxation technique. Instead of using a semi-empirical, curve-fitting approach commonly used by many researchers, it is the intention of this study to develop a generalized, theoretically-based model to predict the precipitation kinetics of nitrides and carbides in microalloyed low carbon steels undergoing thermomechanical treatments. In the present work, the model is applied to study the precipitation behavior of AIN in low carbon, Al-killed steels during isothermal annealing and continuous cooling in both austenite and ferrite regions. This model takes into account the equilibrium thermodynamic properties of the systems, the precipitate morphology, the misfit strain energy (coherent or incoherent) and the curvature effects, etc. The precipitation kinetics are formulated using classical nucleation and growth Summary and Conclusions 141 theories. Both homogeneous nucleation and grain boundary nucleation are considered. A theoretical-based model was also developed by using numerical integration methods on a multi-particle system to predict the dissolution, growth and coarsening behaviors and to simulate the size distribution evolution of nitrides or carbides in microalloyed steels. In this model, dissolution and coarsening are being treated as one continuous, simultaneous process. A set of diffusion, equilibrium and mass balance equations are solved simultaneously for each individual particle. In the case of precipitates on grain boundaries, the effect of grain boundary diffusivity is also considered. Calculations are compared to experimental observations for AIN dissolution and growth in both austenite and ferrite. Various initial size distributions and reheating temperatures are used in the tests. 7.2. Conclusions Based on the experimental and theoretical works carried out in this study for the precipitation, dissolution, growth and coarsening of AIN in low carbon steels, the following conclusions are drawn: 1) Aluminum nitride nucleates with difficulty in austenite. In the DQSK steel used in the present work, AIN should be stable at below about 1120°C. However, due to the high nucleation barrier, precipitation of the AIN is retarded until at low temperatures (near Ae3) in the austenite region. When precipitation occurs, the AIN precipitates are formed by heterogeneous nucleation — primarily by grain boundary nucleation, but some AIN nucleates on pre-existing MnS particles; Summary and Conclusions 142 Deformation can enhance the precipitation kinetics of AIN. A higher strain shifts the onset of precipitation to a shorter time. It is believed that prestraining enhances the precipitation of AIN by introducing a high density of dislocations. The dislocations can act as preferred nucleation sites which lower the nucleation barrier and they can provide a rapid diffusion path for the Al which, in turn, accelerates both nucleation rate and growth rate; Precipitation of AIN is much faster in ferrite than in austenite. The majority of the AIN precipitates are found to be distributed along the ferrite grain boundaries, although a small amount of AIN is found in the matrix. The AIN precipitates inhibit ferrite grain growth during aging in the ferrite region. The AIN precipitates grow rapidly during the early stage of annealing in the ferrite region followed by a slow coarsening process during further aging; In continuous cooling, the cooling rate during austenite decomposition has a significant effect on the precipitation of AIN. At a high cooling rate, there is no precipitation of AIN during the y -> a transformation. At a slow cooling rate (=S5°C s"1), a high density of fine AIN precipitates can be found. At an even slower cooling rate (~1°C s"1), AIN precipitates appear to form in bands; When isothermally annealed at 850°C (just below Ae3), AIN precipitates seem to form along bands, just like the case with slow cooling. On the other hand, clusters of AIN precipitates are found in the matrix when isothermally annealed at 800°C. It Summary and Conclusions 143 is believed that at 850°C, AIN nucleates at the small ferrite grains which form along the austenite grain boundaries; During isothermal annealing in the austenite region (after long-time aging in ferrite), networks of AIN precipitates are found in the austenite matrix. These networks represent the prior ferrite grain boundaries. Below about 1150°C, the AIN precipitates are found to be partially dissolved during the early stage of annealing, accompanied by coarsening of the undissolved precipitates. The AIN precipitates are found to be completely dissolved at temperatures higher than 1150°C; Depending on the heat treatment and processing conditions, different morphologies of AIN precipitates can be found. In ferrite, the higher the temperature and the longer the reheating time, the more hexagonal-shaped precipitates are visible in the replicas. If the specimen is heated up to the austenite region after annealing in ferrite, hexagonal-shaped precipitates change to a rectangular shape during annealing. This change in shape is believed to be caused by the tendency to achieve a preferred orientation relationship between the precipitates and the matrix, driven by the reduction of total interfacial energy; Theoretical models have been developed to predict the precipitation, dissolution, growth and coarsening behaviors of AIN in low carbon steels. Predictions and experimental observations are in good agreement. The precipitation kinetics is shown to be a strong function of solute concentration, temperature and initial microstructure; Summary and Conclusions 144 9) For the DQSK steel used in the present study, the calculations reveal that in undeformed austenite, AIN must nucleate on the austenite grain boundaries, the nucleation barrier associated with homogeneous nucleation is too large to allow any nucleation. In ferrite, both homogeneous and grain boundary nucleation are possible, although the precipitation is dominated by grain boundary nucleation. The model also shows that the P-T-T diagram for AIN precipitation in ferrite follows the classic C-shape with the nose at about 630°C; however, in austenite, the precipitation start time decreases as temperature decreases; 10) Dissolution, growth and coarsening can be treated as one continuous, simultaneous process with no clear separation between these phenomena. Alloy composition, temperature and initial particle size distribution affect the resulting particle size distribution; 11) These models provide a physical basis for quantifying the effects of many of the variables encompassing typical thermomechanical processing on the mechanisms and kinetics of precipitation, dissolution, growth and coarsening of nitrides, carbides and carbonitrides in steels. The satisfactory agreement between calculations and experimental data lend support to several aspects of the models and to the assumptions involved. 145 CHAPTER 8 RECOMMENDATIONS FOR FUTURE WORK Although it has been shown that prestraining can enhance the precipitation of AIN in steels, the mechanism is still unclear. In particular, the roles of strain and strain rate have not been clearly resolved. Further investigations, both experimental and theoretical, are needed to quantify the influence of strain and strain rate on the strain-induced precipitation of nitrides, carbides and carbonitrides in steels during thermomechanical processing. Since both recovery and recrystallization can occur during or after deformation, the effects of recovery and recrystallization on strain-induced precipitation should also be taken into account. In some thermomechanical treatments, deformation occurs during the transformation of austenite. Thus, the precipitation of nitrides or carbides in the two phases region may have great importance on the resulting microstructure. A detailed study of the mechanism and kinetics of precipitation of nitrides or carbides during austenite decomposition can improve our understanding of these phenomena and will generate subsequent improvements to the current processing procedures. Although the theoretical models developed in the present study are capable of predicting the precipitation and dissolution kinetics of AIN in steels, they are simplified models restricted by the assumptions. To improve these models, fundamental studies ofthe Recommendations 146 interfacial energy, misfit strain energy and the degree of interphase boundary coherency are necessary. The dissolution model can be improved by taking into account the non-spherical shape of the precipitates. Instead of assuming a uniform distribution, incorporating the actual spatial distribution of the precipitates and the influence of overlapping diffusion fields into the model may help develop a more generalized model and provide better insight into the behavior of realistic systems. 147 APPENDIX NUCLEUS SHAPE-DEPENDENT PARAMETERS The parameters Z, P* and t' in the general, time-dependent equation for the rate of nucleation (Equation 5.4) have been shown to be depended on the shape of the critical nucleusf58~62 .^ The Zeldovich non-equilibrium factor, Z, is given as[43J 2nkBT V dn2 , 1 2 (Al ) n where n is the number of atoms in an embryo and n* is the number of atoms in the critical nucleus. For a sphere-based critical nucleus during homogeneous nucleation, Z can be approximated as[61,62] 1 ( A G c h e m + A G s )2 - ( V p / N A ) ( A 2 ) S n l(c/a)(3-(c/a)2) (^Ty3)" where c/a is the aspect ratio, Vp/NA is the atomic volume ofthe precipitate. Typically, Z « 10"2. 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Study of the kinetics of precipitation, dissolution and coarsening of aluminum nitride in low carbon steels
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