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Flow stress, restoration and precipitation behavior, and modeling for two Ti-Nb stabilized IF steels… Huang, Chinfu 1999

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FLOW STRESS, RESTORATION AND PRECIPITATION BEHAVIOR AND MODELING FOR TWO Ti-Nb STABILIZED IF STEELS IN THE FERRITE REGION By CHTJNFU HUANG M. S., Central Iron and Steel Research Institute, Beijing, P. R. China, 1989 B. S., Central-south University of Technology, Changsha, P. R. China, 1983 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (The Department of Metals and Materials Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1999 ©Chunfu Huang, 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. The University of British Columbia Vancouver, Canada Department DE-6 (2/88) Abstract During the thermomechanical processing of steels in a conventional hot-strip mill or in a compact strip production line, the control of shape and gage, and the concomitant changes in microstructure, are essential for producing quality as-rolled steel strip or for providing good base materials for manufacturing cold-rolled and annealed steel sheet with excellent formability. This control is, in turn, based on a better understanding of the flow stress behavior, restoration behavior, microstructure evolution, and precipitation behavior of steels during the processing. Very few studies have dealt with the deformation and microstructure evolution occurring during the hot and/or warm rolling of IF steels. The flow stress behavior, static and dynamic restoration characteristics, precipitation behavior, and Compact Strip Production (CSP) rolling simulation behavior have been investigated on two Ti-Nb stabilized IF steels in this study. This was accomplished with the aid of axisymmetric compression tests, torsional rolling simulation tests, TEM observation on precipitation and substructures, and Kikuchi pattern analysis. Experimental tests were mainly carried out in the ferrite temperature range with the aim of providing guidance to the application of warm rolling of IF steels on a CSP line. The important results and conclusions of this research are as follows: (1) Both dynamic recrystallization and dynamic recovery contributed to the softening exhibited by the flow stress curves obtained in the austenite region. Dynamic recovery was the dominant softening mechanism in the ferrite region. The deformation activation energies were measured to be 302kJ/mole and ~240kJ/mole for deformation in the austenite and in the ferrite regions, respectively. The measured values of the deformation activation energies are similar to the self-diffusion energies and confirm that there is a close relationship between these two processes. The Zener-Hollomon value, Z, the temperature compensated strain rate, for the transition from dynamic recovery to dynamic recrystallization was determined as 8.23-lO'V in the austenite region for the Nb-rich Ti-Nb IF steel. The constitutive equation derived from dislocation theory fit the measured curves well. The comparison also suggests that other softening mechanisms, besides dynamic recovery, contributed to the flow stress behavior for deformation in the ferrite region, even though dynamic recovery is the dominant softening mechanism. (2) In the ferrite region, static recovery played a very important role in the softening process of IF steel; -40% of the softening was attributed to static recovery. Dynamic recovery during deformation reduced the effect of deformation strain on the recrystallization kinetics and intensified the effect of strain rate on the recrystallization kinetics. This effect was strengthened by the reduced solute Nb content in one of the steels studied. Static recrystallization progressed slowly in the ferrite temperature range, especially for the Nb-rich Ti-Nb IF steel, and at lower temperatures. In constrast, the Nb-lean Ti-Nb IF steel recrystallized fully in 100 seconds at 800°C. (3) Precipitates found in the two IF steels studied were TiN, TiS, Ti 4C 2S 2, Ti(CN), and Nb(CN). Among them, The Ti 4C 2S 2 particles (~50nm in size) were randomly distributed. Ti(CN), and Nb(CN) particles(<20nm in size) were found in specimens prior to the 'first hit' deformation and their sizes increased to ~10-35nm after the 'first hit' deformation and after different holding times. It is thought that Ti 4C 2S 2 was formed both by in situ transformation from TiS and by separate formation. Ti(CN), and Nb(CN) were found to co-precipitate with Ti 4C 2S 2 particles and to form as separate particles. Ti 4C 2S 2, Ti(CN), and Nb(CN) precipitates and solute Nb effectively retarded recrystallization in the ferrite region of the two IF steels studied. The 5% recrystallization time increased -30 times either by precipitate pinning or by a solute drag effect in the Nb-rich Ti-Nb IF steel, and increased 2.4 times either by precipitate pinning effect or by solute drag effects in the Nb-lean Ti-Nb IF steel. (4) Static and dynamic recovery dominated the softening process for early passes of the CSP rolling. An "apparent dynamic recrystallization" contributed to the flow stress reductions in the later passes, when the appropriate temperature and composition were obtained. Very fine quasi-equiaxed ferrite grains were obtained after the CSP rolling simulation and could be iii explained by "apparent dynamic recrystallization". This apparent recrystallization took place, aided by dynamic recovery. The IF steel with less solute Nb exhibited a lower flow stress and easier occurrence of apparent dynamic recrystallization. (5) The research suggests that warm-rolled IF steel bands with adequate microstructure and mechanical properties for cold-rolling and thinner hot strip products could be manufactured by CSP technology by optimizing the processing parameters to control precipitation distribution and microstructure. iv Contents ABSTRACT ii CONTENTS v LIST OF FIGURES vii LIST OF TABLES xv LIST OF SYMBOLS xvi ACKNOWLEDGMENT xxi Chapter I Introduction 1 1.1 IF steel development 1 1.2 CSP technology development 3 1.3 Modeling development , 5 Chapter II Literature Review 11 II. 1 Constitutive equations for steels 11 11.2 Recovery, recrystallization behavior in steels 18 11.3 Precipitation behavior in steels 29 11.4 CSP rolling and ferrite rolling 41 Chapter III Obj ective 55 Chapter IV Methodology 57 IV. 1 Materials 57 IV.2 Gleeble tests 58 IV.3 Torsion tests 63 IV.4 Optical and SEM Microstructure observations 65 IV.5 Carbon replica preparation and TEM observations 66 IV. 6 Thin foil and TEM (including Kikuchi pattern) analyses 67 Chapter V Flow Stresses Behavior during Compression Testing and Modeling 73 V. 1 Flow stress curves in the austenite region 73 V.2 Flow stress curves in the ferrite region 75 V.3 Modeling and Discussion 79 V.4 Summary 83 v Chapter VI Static Restoration Behavior 95 VI. 1 Double-hit test results 95 VI.2 Microstructure observation results 99 VI. 4 Summary 102 Chapter VII Precipitation Behavior I l l VII. 1 Solubility calculation for IF steels I l l VII.2 TEM observations 114 VII.3 Precipitation behavior modeling 118 VII.4 Discussions 124 VII. 5 Summary 125 Chapter VIII Ferrite Rolling (CSP) Simulations 142 VIII. 1 Flow stress curves 142 VIII.2 Microstructure observations 146 VIII.3 TEM and Kikuchi pattern analysis '. 148 VIII.4 Discussions 151 Chapter VIII.5 Summary 152 Chapter IX Summary, Conclusions and Recommendations 164 References 169 Appendix: Kikuchi Electron Diffraction and Analysis 175 vi LIST OF FIGURES Figure 1.1 Properties of super formable steel sheet. 8 Figure 1.2 Schematic comparison (a) CSP and (b) CCR strip production. 9 (G=gauge; M=microstructure; R=reduction; T=temperature.) 10 Figure 1.3 Schematic diagram of components of models for industrial hot forming processes. 11 Figure II. 1. The 0-a curves at different temperatures for mild steel. 45 Figure II.2 Form of stress-strain curves and microstructural changes during deformation at constant strain rate and temperature resulting from (a) work hardening and dynamic recovery only and (b) work hardening, slow dynamic recovery, and dynamic recrystallization. 46 Figure II.3 Flow curves of Nb-IF steel (0.029%Nb) subjected to direct heating and compression at temperatures (a) from 1100 to 935°C and (b) from 935 to 800°C, with a strain rate of 0.1 s"1. 47 Figure 11.4 Isothermal recrystallization of high-purity iron at various temperatures. 48 Figure II.5 JMAK plot for the series of IF steels coiled at 565°C, cold-rolled 75%, and isothermally annealed at 700°C. 48 Figure II.6 Static softening curves of the IF steel in austenite range. 49 Figure II.7 The development of microstructure during dynamic recrystallization (a-d) for a large initial grain size, and (e) for a small initial grain size. 49 Figure II.8 Flow curves for three steels tested in torsion at 900°C at strain rate of 2 s"1. 50 vii Figure II.9 Torsion generated flow curves for a Ti-, a Nb-, and a Ti+Nb-IF steel rolled according to a strip roughing schedule. 50 Figure 11.10 Torsion generated finishing flow curves for (a) Ti+Nb IF steel (b) Nb IF steel rolled according to typical strip rolling schedule and with the first and last finishing pass temperatures of 930°C and 888°C, respectively. 51 Figure II. 11 Torsion generated finishing flow curves for a hot/warm rolling schedule for a Ti IF steel. 51 Figure 11.12 Schematic illustration describing the starting temperatures for precipitation of possible precipitates in Ti- and Nb-added IF steels. 52 Figure 11.13 a) Typical TEM image of sandwich-like multi-phase particle in the 1220°C, 2min. re-heated condition; the outline shape of the particle is illustrated and b) Typical electron diffraction pattern showing the orientation relationship aTis||aH||atis-twin; CTis||CH||CTiS-twin- 53 Figure 11.14 Formation of carbosulfide and carbide in IF steels. 52 Figure II. 15 Schematic composition changes and concentration profiles from the interface during precipitation of a typical MC-type stoichimetric compound on a simplified Fe-M-C ternary system. 54 Figure 11.16 Relationship between r-value and precipitation ratio of TiC or Nb(C,N) which corresponds to solute carbon content. 54 Figure IV. 1 Microstructures of as-received IF steels. 69 Figure IV.2a Schematic diagram of the tubular transformation specimen support in the Gleeble test chamber. 70 vm Figure IV.2b Schematic diagram of the axisymmetric compression test geometry in the Gleeble test chamber. 70 Figure IV.3 Experimental dilation versus temperature measurements for the Nb-rich IF steel after reheating 5mins at 1200°C. The solid lines indicate the extrapolation from the pre- and post-transformation data. 71 Figure IV.4 Schematic thermomechanical schedules for axisymmetric compression tests. 71 Figure IV.5 Schematic representation of the thermomechanical schedule employed for the double-hit testing. 72 Figure IV.6 Schematic diagram of hot torsion system, HTS 100. 72 Figure V. l Flow stress versus strain curves obtained at Is"1 for different deformation temperatures. 85 Figure V.2 Flow stress vs strain curves deformed at 0.1 s"1 for different temperatures. 85 Figure V.3 ln(sinh(arjp)) versus 1/T for Nb-rich IF steel. 86 Figure V.4 Flow stress curves obtained at 1050 °C for different strain rates for the Nb-rich Ti-Nb IF steel. 86 Figure V.5 Flow stress curves obtained at 1150 °C for different strain rates for the Nb-rich IF steel. 87 Figure V.6 Flow stress curves obtained at 950 °C for different strain rates for the Nb-rich IF steel. 87 Figure V.7 ln(sinh(aap)) versus ln(strain rate) for the Nb-rich IF steel. 88 Figure V.8 Flow stress curves obtained at Is"1 at 1050 °C after two different reheating temperatures for the Nb-rich IF steel. 88 IX Figure V.9 Flow stress curves for the Nb-rich IF steel compressed at a strain rate of Is"1 after the specimens were reheated to 1200°C for 5 minutes and cooled to the deformation temperatures at 10°C/s. 89 Figure V.10 Flow stress curves for the Nb-rich IF steel compressed at a strain rate of Is"1 after the specimens were reheated to the deformation temperatures and held for 30 seconds. 89 Figure V . l l Relationship between ln(sinh(ctap)) versus 1/T for the Nb-rich IF steel deformed in the ferrite region. 90 Figure V.12 Flow stress curves of the Nb-rich IF steel compressed at 700°C at various strain rates after reheating to 1000°C for 5 minutes and cooled to the deformation temperature at 10°C/sec. 90 Figure V.13 Flow stress curves for the Nb-rich IF steel compressed at 700°C at various strain rates under direct reheating conditions. 91 Figure WA4 The relationship between ln(sinh(arjp)) and ln(strain rate) for the Nb-rich IF steel. 91 Figure V. 15 Relationship between peak stress and reheating condition. 92 Figure V.16a Relationship between the work-hardening rate and stress for the Nb-rich IF steel deformed in the austenite region. 93 Figure V. 16b Relationship between the work-hardening rate and the stress for the Nb-rich IF steel deformed in the ferrite region. 93 Figure V. 17a Comparison of predicted and measured flow curves for the Nb-rich IF steel deformed at 1050°C. 94 Figure V. 17b Comparison of predicted and measured flow curves for the Nb-rich IF steel deformed in the ferrite region. 94 Figure VI. 1 A schematic diagram showing back-extrapolation method for determining the recovery free softening fraction for a double-hit test 1 s"1 at 700°C on the Nb-rich Ti-Nb IF steel. 103 Figure VI.2 Relationship between F x and inter-hit time for the Nb-rich Ti-Nb IF steel deformed in the austenite region. 103 Figure VI.3 Relationship between F x and inter-hit time for Nb-rich Ti-Nb IF steel deformed in the ferrite region. 104 Figure VI.4 The JMAK and the S-F analysis of double-hit test data obtained for the Nb-rich Ti-Nb IF steel deformed in the ferrite region. 104 Figure VI.5 The recrystallization kinetics plotted as ln(ln(l/(l-Fx))) vs Int for the Nb-rich Ti-Nb IF steel deformed at 700°C. 105 Figure VI.6 The recrystallization kinetics plotted as ln(ln(l/(l-Fx))) vs Int for the Nb-lean Ti-Nb IF steel deformed in the ferrite region, first hit e=0.2. 105 Figure VI.7 The recrystallization kinetics plotted as ln(ln(l/(l-Fx))) vs Int for the Nb-lean Ti-Nb IF steel deformed in the ferrite region, first hit s=0.5. 106 Figure VI.8 Relationship between F x and inter-hit time for Nb-lean Ti-Nb IF steel deformed at 700°C. 106 Figure VI.9 Microstructures obtained after a 'first hit' test on the Nb-rich Ti-Nb IF steel at a strain arte of Is'1 to s=0.2 at 700°C for four different holding times. 107 Figure VI. 10 Microstructures obtained after a 'first hit' test on Nb-lean Ti-Nb IF steel at a strain rate of 1 s"1 to 8=0.2 at 800°C for two different holding times. 108 xi Figure VI. 11 Microstructures obtained after a 'first hit' test on the Nb-lean Ti-Nb IF steel at a strain rate of Is"1 to s=0.5 at 700°C for four different holding times. 109 Figure VI. 12 Effect of deformation temperature and strain on to.s on the Nb-lean Ti-Nb IF steel deformed in the ferrite region. 110 Figure VI. 13 Effect of deformation strain rate on t0.5 on the Nb-rich Ti-Nb IF steel deformed at 700°C. 110 Figure VII. 1 (TiNb)N particle and its EDS analysis on the Nb-rich Ti-Nb IF steel. 127 Figure VII.2 TiS particle and its EDS analysis on the Nb-rich Ti-Nb IF steel. 128 Figure VII.3 Morphology of small precipitates and their EDS analysis on the Nb-rich Ti-Nb IF steel after a deformation s=0.2 at 700°C at a strain rate of Is"1 and a holding time of 24 hrs. 129 Figure VII.4 Small precipitates in the Nb-rich Ti-Nb IF steel after a deformation s=0.2 at 700°C at a strain rate of 0.02s"1 and a holding time of 10 seconds. 130 Figure VII.5 Small precipitates and their EDS analysis for the Nb-rich Ti-Nb IF steel after a deformation s=0.2 at 800°C at a strain rate of Is"1 and a holding time of 10 seconds. 131 Figure VII.6 Morphology of the medium sized particles and their EDS analysis for the Nb-rich Ti-Nb IF steel after reheating to 1200°C for 5mins, e=0.2 deformation at 700°C and a strain rate of 1 s"1 and a holding time of 100 seconds. 132 Figure VII.7 Morphology of small particles and their EDS analysis for the Nb-rich Ti-Nb IF steel after reheating to 1200°C for 5mins, s=0.2 deformation at 700°C, Is"1 strain rate and a holding time of 10 seconds. 133 Figure VII.8 TiS particle in the Nb-lean Ti-Nb IF steel. 134 xii Figure VII.9 Small precipitates in the Nb-lean Ti-Nb IF steel before deformation. 135 Figure VII. 10 Small precipitates and their EDS analysis for the Nb-lean Ti-Nb IF steel after s=0.2 deformation at 700°C and a Is"1 strain rate and a holding time of 1000 seconds. 136 Figure VII. 11 Morphology of small particles and their EDS analysis for the Nb-lean Ti-Nb IF steel after reheating to 1200°C for 5 minutes, cooled to 700°C and holding for 30 seconds. 137 Figure VII. 12 (a) Morphology of particles for the Nb-lean Ti-Nb IF steel after reheating to 1200°C for 5minutes, s=0.2 deformation at 700°C and a Is"1 strain rate, and a holding time of lOseconds; (b) EDS analysis for the large particle in (a); (c) EDS analysis for samll particles in (a). 138 Figure VII. 13 Precipitates in thin foils made from both Ti-Nb IF steel specimens after simulated CSP rolling deformation at 800-750°C. 139 Figure VII. 14 The equilibrium precipitate mole fraction as a function of temperature, modified to include T12C2S2 precipitation for a Ti-stabilized ULC IF steel. 140 Figure VII. 15 Calculated precipitation start time, tn.05, and the static recrystallization start time, to.o5x, in the ferrite region for the Nb-rich Ti-Nb IF steel based on a modified Dutta and S ellars model. 141 Figure VIII. 1 Flow stress curves obtained during single twist ferrite deformation for the Nb-rich Ti-Nb IF steel and the associated temperature response. 154 Figure VIII.2 The flow stress curves obtained during ferrite (CSP) rolling simulation on the Nb-rich Ti-Nb IF steel. 154 xiii Figure VIII.3 The equivalent stress versus equivalent strain torsion results obtained for the Nb-rich Ti-Nb IF steel deformed in the austenite and the ferrite regions. 155 Figure VIII.4 Flow stress curves of the Nb-rich Ti-Nb IF steels deformed at different temperatures simulating austenite and ferrite (CSP) rolling. 155 Figure VIII.5 The flow stress curves obtained during a ferrite (CSP) rolling simulation on the Nb-lean Ti-Nb IF steel. 156 Figure VIII.6 SEM micrograph of the microstructure of the Nb-rich Ti-Nb IF steel after a single twist deformation. 156 Figure VIII.7 SEM micrographs of the Nb-rich IF Ti-Nb IF steel after ferrite (CSP) rolling simulations at different temperatures without prior austenite deformation. 157 Figure VIII.8 SEM micrographs for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel after prior austenite rolling deformation. 158 Figure VIII.9 SEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. 159 Figure VIII. 10 SEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation with passes at 800~750°C, without prior austenite deformation. 160 FigureVIII.il TEM micrographs of the Nb-rich IF Ti-Nb IF steel after a ferrite (CSP) rolling simulation- at different temperatures without prior austenite deformation. 161 Figure VIII. 12 TEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. 162 Figure VIII 13 TEM micrographs showing misorientation across specific grain boundaries for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel after prior austenite rolling deformation. 163 LIST OF TABLES Table II. 1 Formulae for predicting the grain size of IF hot-rolled band. 29 Table IV. 1 Chemistry of Ti-Nb IF steels used in this study (wt.%). 57 Table IV.2 Phase transformation temperatures for the Nb-rich IF steel. 60 Table IV.3 Torsion rolling simulation schedules in the austenite region. 65 Table IV.4 Torsion rolling simulation (CSP) schedules in the ferrite region. 65 Table V. l Values for constants in the hyperbolic sine law. 83 Table VII. 1 Solubility product equations and calculated T e q values for the two IF steels examined in this study. 113 Table VII.2 The values of constants in equation (VII.7) and (VII,8) used by Dutta for the Nb-microalloyed steels and by this study for the Nb-rich Ti-Nb IF steel. 122 xv LIST OF SYMBOLS A, A ] , A 2 Constants A' Constant ao, ai, a2, a^t aA> as Constants a.\ Activity of element i aa, ay Lattice constants of a and y, A B Constant b Burgers vector b0 Constant C Constant CR Cooling rate during y-a transformation, °C/s c, c0j ci, C2 Constants D Constant D(T) Self-diffusion coefficient, D*(> Imaginary y grain size just after hot rolling, urn D* Grain size of y, \xm D* Grain size of a, ixm DR Steady state grain size, ixm d0 Iinitial grain size, ixm d0 Constant in eq'n (II. 13) E Young's modulus, MPa xvi F a Solute drag force, MPa F p Particle pinning force, MPa F s Softening fraction F x Recrystallization fraction determined the by Perdrix method fi, I2,13, U, fs Exponents G Shear modulus, MPa AG 0 Standard Gibbs free energy, J AG* Critical driving force, J H Enthalpy, J h Work hardening coefficient, MPa I Steady state nucleation rate K Constant Ki Constant k Coherency factor ki ; k2 Constants ks Supersaturation ratio L Mean slip distance of dislocations in eq'n (11.26), nm L Gauge length, in eq'n (VIII. 1), mm M Taylor factor in eq'n (11.21), (V.7) M Mobility of the boundary in eq'n (11.26) m' Constant m Twist rate sensitivity in eq'n (VIII.2) N(t) Nucleation number xvii n Exponent n, ni_ n 2, n3> at Constants n' Constant Pj Material properties P s Start time for Ti(CN) precipitation, s p Exponent in eq'n (VII. 8) Qdef. Activation energy for hot working, kJ/mole Q g Constant R Gas constant r p Particle radius at time t, nm r Recovery rate S Entropy Sj Internal structure Sint Area fraction of the y/a interface T Torque in eq'n (VIII.2), M-kg T Temperature, °C or K T n r Non-recrystallization temperature for plate rolling condition, A r3 Start temperature for y-ct transformation, °C t Time, s to.5 Time for 50% recrystallization, s tn.05 Precipitation start time, s to.o5x Static recrystallization start time, s v Poisson's ratio xviii X Recrystallization fraction Y Intersheet spacing Z Zener-Hollomon parameter in eq'n (II.5), (11.6), (11.27), (V.14) Z Zeldovich factor in eq'n (11.42), (11.43) 0 Work-hardening rate a Constant P Constant in eq'n (11.6) P Frequency factor in eq'n (11.42), (11.43) E Strain sc The critical strain se The equivalent strain sp The strain at peak stress sr Characteristic strain s[ The Wagner interaction parameter between elements i and j s Strain rate A Interface movement distance, nm 8 Misfit parameter 0 Twist angle p Dislocation density, m/m pm Dislocation density of the deformed matrix, m/m Yb Surface energy, J/m a Stress, MPa xix G0 Stress at zero strain, MPa ai, o"2 The yield stresses for the first and the second stage of deformation in the double hit test, MPa CTI, an The yield stresses determined by the Perdrix method in the double hit test, MPa CTe Equivalent stress, MPa am The flow stress at the end of first deformation in the double hit test, MPa o~p Peak stress, MPa o~0p Internal stress, MPa CTS Steady state stress, MPa CTSS The steady-state stress after dynamic recrystallization has progressed through the material, MPa x Incubation time, s p a Shear modulus of ferrite, MPa xx ACKNOWLEDGMENT I would like to express my deepest gratitude to my supervisors, Professors E. B. Hawbolt and T. R. Meadowcroft. The successful completion of this thesis was due to their guidance, constant encouragement, and stimulating discussions throughout the course of this research. Further thanks to all the members of the hot strip mill modeling group who made a pleasant and cooperative atmosphere to discuss any technical problem. I wish to express my deep thanks to Dr. M. Militzer, Dr. W. Poole, and Dr. W. Sun for their interests in my work and their kindness and support. Many thanks to Mr. B. Chau, Dr. X. Chen, Mrs. M. Mager, Mr. R. Cardeno, Mr. P. Wenman, Mr. R. Mclead, Mr. C. Ng and Mr. R. Bennett for their technical assistances. I would like to thanks Mrs. J. Kitchen and all the office staff in the department for their assistance in administrative matters. I would like to acknowledge the financial support provided by the American Iron and Steel Institute, the United States Department of Energy, and Canadian Natural Sciences & Engineering Research Council. Last, but not the least, the great sacrifices and patience of all my family members and friends, especially my wife, is very appreciated. They have been a source of wisdom, understanding and strength throughout my studies. xxi Chapter I Introduction 1 Chapter I Introduction Success in the development of flat-rolled steel products relies primarily on the use of suitable process management in the rolling mills. A key role is played by a combination of mechanical and thermal processing. In the past quarter century, a tremendous amount of data has been accumulated on C-Mn steels and low carbon microalloyed steels from research and practical applications. Consequently, processes and products are constantly being optimized using the results of new research and increased technical capabilities in plant technology. Interstitial-free (IF) steels were developed over a quarter century ago as a means of providing improved formability in sheet products.1'2 The major industrial application of IF sheet steels has been as cold-rolled steel sheets used for deep drawing. Considerable work has been done on the recrystallization and texture formation during the annealing process after cold rolling. 3 ' 4 However, very few studies have dealt with the deformation and microstructure evolution occurring during the hot and/or warm rolling of IF steels. Final rolling in the ferrite temperature range, termed warm rolling, has recently been introduced in some hot strip mills. Ferrite rolling on a compact strip production (CSP) line will expand the range of mechanical properties available. IF steels are particularly suitable for this purpose because their Ar3 temperature is high.5 1.1 IF steel development The original IF steels were developed commercially with the introduction of vacuum degassing technology. In the early stages of development, the processing step resulted in interstitial C levels of 50-100ppm and nitrogen levels of 40-80ppm.''6'7'8 The IF steels produced commercially were Al-killed (0.02-0.07wt%Al) and alloyed with either Ti (generally 0.07-Chapter I Introduction - 2 0.12wt%) or Nb (generally 0.08-0.12wt%) or with binary additions of Nb+Ti (typically 0.05wt%Nb, 0.05wt%Ti). In these steels, if only Ti was added, the Ti scavenged both the C and N; if only Nb was added, the Nb scavenged only the C while the N was combined as AIN; if both Ti and Nb were added, the Ti scavenged both C and N, and if the Ti/(C+N) ratio was <4:1, the Nb would combine with the remaining C. Another distinguishing feature of these original IF steels was that they contained a considerable excess of the stabilizing elements Ti and/or Nb, which did not combine with either C or N and remained in solution. Initially these IF steels were processed in a batch annealing line. As compared with conventional steel grades, IF steels offered optimum cold formability, excellent strain hardening and complete resistance to aging. However, the metallurgical production process also involved certain constraints, i. e., the availability of vacuum facilities and the use of expensive alloying additions. The dynamic of subsequent technical innovations and industrial development of the use of IF steels is a typical example of the innovation process. This development required:9 increasingly stringent requirements with respect to the material properties of sheet steels; the improvement of secondary metallurgical processing equipment and capabilities of steel making; the introduction and widespread development of modern manufacturing and coating techniques for steel strip (continuous annealing, hot-dip coating); a deeper understanding and more effective utilization of the processes which occur in the steel through intensive physical and metallurgical research. The result of these improvements led to the introduction of extra low carbon (ELC) or ultra low carbon (ULC) IF steels in the early 1980's. In these steels, lower C and N levels (C<30ppm, N<30ppm) could be consistently attained, permitting the substantial reduction of solute additions (Nb and or Ti) to achieve the interstitial free state. Chapter I Introduction : : 3 While the ELC IF steels provide mean plastic strain ratio, rm, values which are relatively insensitive to coiling temperature and annealing method (continuous vs batch annealing), they require higher cold reductions to attain the levels of rm associated with ordinary IF steels. Strictly speaking, the ELC IF steels have somewhat lower rm values after continuous annealing, as compared to batch annealing. The planar anisotropy is also different for the two annealing methods as a result of small, but significant, differences in the textures produced. The planar anisotropy of cold rolled (CR), batch annealed (BA) ordinary Nb stabilized IF steels differs from that of the ELC Nb stabilized IF steels produced today. This is partly because the hot band of the latter grade contains a less intense {112}<110> texture component than that found in the hot band of ordinary Nb stabilized IF steels. A super extra deep drawing quality (EDDQ) grade of IF steel with even higher formability has been developed recently. For the super EDDQ grade, a surprisingly high formability is obtained, i. e., an average rm value (the index for deep drawability) of 2.2, and an average of total elongation (the index for stretchability) of 52%, as shown in Figure 1.1.10 The super EDDQ grade can be produced only when IF steel is annealed at high temperatures of 800~850°C. Based on a new precipitation mechanism in IF steels, a new stabilization map has been 11 12 established recently. ' The complete or partial stabilization of carbon, combined with a boundary concentration of highly segregating elements, such as B, C, and Nb, can be achieved through adjustment of the bulk composition. This map can be used to either analyze the behavior of existing steels or to design new high performance steels. 1.2 CSP technology development The conventional hot strip mill included a heavy slab caster, normally producing slabs in the 150mm to 250mm range, a slab storage and handling area, scarfing facilities for slab Chapter I Introduction ; ; 4 conditioning, slab reheat furnaces, a roughing stand group and a six or seven stand finishing train. Considerable strides have been made in producing defect-free slabs from continuous casting through modeling and controlling the steel liquid flow pattern in the tundish, using a submerged entry nozzle and protection powder, optimizing the mould shape and vibration modes, using combination electromagnetic stirrings, and strictly controlling the secondary zone cooling regime, etc. These improvements permitted direct linking of continuous casting and hot rolling. The first stage of this development involved hot charging conventional cast defect-free slabs into a reheating furnace followed by hot rolling. In the second stage, direct rolling techniques emerged in which hot slabs were delivered to hot-strip mills at rollable temperatures from the continuous casting machine, with only a quick temperature homogenization in between. Hot strip production from thin slab casting (continuous casting of 30-100mm thick slabs) is the technology being adopted in the new generation of hot-strip mills and is the most important development in steel production in our time. It eliminates the roughing mill and employs hot direct rolling, requiring only a homogenization furnace between the casting and finishing train. This practice reduces production time with resulting energy savings, improved performance, lower inventory costs and shorter delivery times. The Compact Strip Production (CSP) process consists only of a caster, a connecting system (the roller hearth furnace) and a finishing mill. A schematic comparison of conventional cold charge rolling (CCR) and CSP rolling is depicted in Figure 1.2.13 In CSP, ~50mm thick as-cast thin slabs are rolled directly to a final gauge of 2-16mm in a five or six stand tandem mill. Prior to rolling, the slabs, cast through a funnel-shaped continuous casting mould, are fed directly to an inline roller hearth furnace to be reheated for 12~20minutes to attain a temperature in the range of 1100 to 1150°C. As in CCR, after hot rolling, the hot strip is then cooled on the run-out table and coiled. The internationally patented funnel shaped mould and the roller hearth Chapter I Introduction ; ' 5 furnace are the heart of the CSP technologies. The funnel shape is proportional to the shrinkage of the shell during solidification and is designed to prevent the formation of bridges between the strand shell and nozzle. Also, the curvature ensures stress free solidification of the shell during withdrawal. Besides providing the means to maintain and equalize a uniform slab exit temperature of 1100°C prior to entry into the rolling mill, the roller hearth furnace also serves two other important functions: (i) It uncouples the casting operation (speed of 5-6 m/min) from the rolling mill (slab entry speed of 15 to 20 m/min.). (ii) It creates a buffer zone ahead of the mill to permit work roll changes while continuing casting.14'15 The successful rolling of high quality strip from thin slab casting can only result from a complete understanding and predictable controlling of the complex thermomechanical and metallurgical phenomena involved. Hot direct rolling is a relatively new technology, exhibiting some operational and metallurgical differences from cold-charge reheat rolling. The optimization of hot direct rolling and its extension into the high quality end of flat steel production is ongoing. The CSP hot strip mill not only employs hot direct rolling but also eliminates the roughing process, making it possible for as-cast slabs to be converted into quality hot band coils after five or six stand tandem rolling. Furthermore, there is the prospect of producing thin hot band coils (<lmm thickness) on CSP mills to compete with conventional cold rolled products. This can only be achieved by precise control of all hot rolling parameters to attain the stringent tolerances prescribed for cold rolled products. 1.3 Modeling development In order to control the microstructure, texture and properties of an alloy during a complex industrial thermomechanical treatment, there is a need for quantitative models that will accurately predict the effects of the processing parameters on the material that is produced. A Chapter I Introduction , 6 recent successful model has been developed for the hot strip mill. 1 6 In the hot strip mill, as the steel progresses from the roughing mill to the down coiler, many metallurgical reactions may occur, including austenite recrystallization and grain growth in the roughing and finishing mill, the austenite to ferrite transformation (or alternative phase transformations) and precipitation during the processing. The rates of all these reactions are very temperature sensitive. It is essential to develop an accurate temperature model that quantitatively links the processing parameters in the mill and the microstructural evolution of the strip. Computer modeling of the hot rolling process couples knowledge of mechanical and metallurgical engineering to simulate the temperature, deformation, microstructure evolution and their interactions on a real time basis. This has enabled a more complete understanding of the various physical processes that occur during rolling and cooling, as well as providing tools that can be used for analysis and control. 1 6 The outline of a macro model for industrial multi-pass hot rolling is shown in Figure 1.3. The overall model contains five sub-models. Among the five sub-models, the structure sub-model is an essential link in the series, interacting directly with the deformation, temperature, mechanics and behavior sub-models. It takes the external variables such as strain, strain rate, temperature and time from other sub-models, together with the microstructure, and using appropriate equations, it describes the microstructural changes, including dislocation content, grain and subgrain structure, texture and phase transformations occurring during processing.17'18'19 9ft Sellars and Whiteman have demonstrated that semi-empirical equations describing microstrucrural phenomena can be combined with a computer model of the thermal history to predict metallurgical changes that occur in steel during an industrial hot rolling operation. Jonas 91 and Sellars have compared the role of physical and computer modeling in the thermomechanical processing of steels. The power of computer models for setting up mills and Chapter I Introduction 7_ 22 for conducting off-line simulations has been recognized. Yada has developed a model for the hot rolling of C-Mn steel strip which assumes no thermal gradients through the strip thickness. Hodgson et al.2 3 have developed a model for the hot rolling of C-Mn and microalloyed steels in rod, bar, and plate mills. Work by Devadas et al. has made it possible to establish a very good off-line model.24'25'26 Models, such as those discussed above, have been successfully used in predicting the evolution of microstructure and mechanical properties of C-Mn, and microalloyed steels. Although much research has been done to quantify the recrystallization kinetics and evolution of texture during the annealing process after cold rolling of IF steels, the flow stress, recrystallization and precipitation behavior of IF steels during thermomechanical processing have not been well defined. It was widely concluded that the excellent formability of IF steels results because they are, in fact, merely free from interstitial C and N, and that the most important contribution of alloying with niobium and/or titanium is to maintain a fine grain size after hot rolling through precipitation of carbonitride particles.27'28 However, recent studies have shown that the precipitation behavior in IF steels during hot rolling is vastly different from those in other microalloyed steels.11'29 Furthermore, less research has dealt with the metallurgical behavior during ferrite or warm rolling of IF steels. As a result, the data describing microstructure evolution for a hot-rolled strip model for IF steel is incomplete. Chapter I Introduction 8 t - 0.8 mm 0) JD > C 2.5 2.0 1.5 i . o r Super EDDQ • A EDDQ DDQ DQ CQ J L JL • Recent data Figure 1.1 4 0 4 5 5 0 5 5 Total elongation (%) (JIS No. 5) Properties of formable steel sheets (from ref.10). Chapter I Introduction 9 (a) "Lift R = 40 - GO % o o g g o D o a o n o o 66663 D D P a n a n G =50 mm T= 1130-1100 *C G = 2-15mm M = As-cast y T=870-920*C T = <650*C M = Rec. r : T r a n s f . a Coiler R = 15 - 40 % R = 5 - 45 % % „ 9996999 n a n a a a a 6666566 n n n a a a a G =» 250 mm T = 1250*C M 3 y from RT a G = 30-40 mm T=1120 - 1050 *C M = Rec. y G 3 2 • 15 mm T = 870-920 "C M = Rec. y T = < 1550 *C M = Transf. a Figure 1.2 Schematic comparison (a) CSP and (b) CCR strip production (from ref. (G=gauge; M=microstructure; R=reduction; T=temperature.) Chapter I Introduction 10 INPUTS MODELS OUTPUTS Heat Transfer Equations Dimensions, Speed Constitutive Equations MiCTOStractural Equations TEMPERATURE L W MECHANICS a DEFORMATION s STRUCTURE Working Forces, etc € t Structure/Property Relationships BEHAVIOUR Product Properties S structure t time T temperature W work e strain t strain rate a stress Figure 1.3 Schematic diagram of components of models for industrial hot forming processes (from ref.18). Chapter II Literature Review 11 Chapter II Literature Review II. 1 Constitutive equations for steels In the hot-strip mill for rolling steel, the slab from a reheat furnace is reduced in thickness to the final gauge in roughing stands and successive finishing train stands. Of paramount importance in this operation is the shape and gauge control during rolling and the concomitant changes in microstructure which determines the final mechanical properties. Deformation of the steel in the roll bite provides the driving force for microstructural change and also has a profound influence on the shape and gauge of the product. The driving force for structure-modifying metallurgical phenomena, such as dynamic or static recovery and recrystallization, is the strain imparted by the deformation, the distribution of which is characterized by the reduction per pass, the rolling speed, the temperature distribution, and the steel composition. These variables also strongly influence the roll forces which, together with the design of the roll stands and the associated control systems, have an effect on gauge variations and the shape of the product. The theories proposed for predicting roll forces have, in general, assumed an average temperature within the roll bite or an average temperature through the thickness at any location in the roll bite for the purpose of calculating flow stress. The Sims model20 is one of the most widely used; it is based on the assumption of sticking friction at the interface and homogeneous deformation. The Sims equation utilizes an average value for the flow stress in the roll bite. In the application of rolling theories to hot rolling, there has been considerable uncertainty as to whether sticking or sliding friction prevails in the roll bite. Much of the confusion stems from the lack of data, owing to the difficulty of measuring coefficients of friction under hot rolling conditions. Another limitation of the earlier theories for rolling is the assumption of homogeneous deformation. There has been concern that, owing to the steep thermal gradients, the strain Chapter II Literature Review 12 distribution in a vertical slice may not be uniform. Thus, more recently, the finite element method has been applied to rolling in an attempt to provide a more accurate description of the distribution of strain in the roll bite. Irrespective of whether conventional rolling theories or finite element techniques are employed to predict roll forces, a knowledge of the flow stress behavior of the material at elevated temperatures is required. The plastic deformation of metals is a kinetic process in which the current strain rate is dependent on the stress, temperature, the instantaneous internal structure of the material (characterized by a set of state variables which may changes with time) and the material properties which do not vary. A general equation may, therefore, be written in the form:30'31 e = F(cr,T,Sl,PJ) ( L U ) where Pj characterizes the material properties such as lattice parameter, diffusion coefficient and elastic modulus. In general, the internal structure, Sj, of a deforming metal changes with time as the deformation proceeds. The rate of change is a function of stress, o, temperature, T, and the internal structure itself: ^ - = H,(<TtTtSnPj) (11.2) The coupled set of equations (II. 1) and (II.2) forms the constitutive law of the mechanism of deformation. It is, however, not easy to establish the constitutive law expressed by equation (II. 1) and (II.2), since the evolution of structure with strain or time is not understood sufficiently dS. well to formulate the expressions for —'-. Alternatively, simple empirical constitutive equations dt may be developed and applied in the analysis of metal-forming processes. Chapter II Literature Review 13 While early studies of constitutive relations applicable at high temperatures were aimed at developing a mechanical equation of state, a much simpler but useful set of relationships has been proposed and used. One equation describes the dependence of the material's flow on temperature and flow stress under hot working conditions. It is of the form: 1 9 ' 2 5 ' 3 0 ' 3 2 s — A(sinh aa)" exp(- ) (II.3) from which the flow stress is given by: a - —sinh" a £exp(Qdef/RT) i / n (II.4) The equation may be simplified at low and high stress levels, respectively by substituting Z = sexp(Qdef IRT) to give .30, 32 Z = Aa"' or Z = A2 exp(Ba) (11.5) (II.6) where A, Ai , A 2 and n, n' are constants, a and p are the constants related to the stress associated with the power-law breakdown, Z is the Zener-Hollomon parameter, Qdef is the activation energy for hot working. Although the constants A, a, n and Qdef depend on the material being considered, they are usually referred to as apparent values, because no account is generally taken of the internal microstructural state. Because it provides an upper bound for industrial application, it is common to use the peak stress, CTp, for developing Qdef-33 Mathematically, it can be formulated in the following equation ,34 Qdef=-R Sine S lnsinh(aa p) 8 In sit)h(aap) £(1/7/) (II-V) Chapter II Literature Review 14 In a recent investigation,31 it is shown that when the initial grain size and the dependence of Young's modulus on temperature are taken into account, a constant creep exponent, n=5, and the self-diffusion activation energy can be used to describe the peak stress, ap. The resulting unified expression is given as follows: £ =A D(T) sinh E(T) (II.8) Here, a o p is an internal stress associated with the peak stress, a P j that is related to the initial grain size via a Hall-Petch equation, E(T) is Young's modulus and D(T) is the self-diffusion coefficient in austenite. The latter is given by, D(T)=D0exp(-Qsd/RT) (II.9) where Qsd is self-diffusion activation energy. The Hall-Petch dependence of the internal stress, o"op, is given by the following: *ap=trl+Kd;1" (ii.io) where the constant K is, in turn, strain-rate dependent: K=3.94+0.451og(f) (11.11) i py where K is given in MPa mm and decreases when the strain rate is decreased. A more realistic description of the flow stress is obtained when it is expressed as a function of the Zener-Hollomon parameter, Z, as well as the current strain, s. Many approximate, empirical constitutive equations have been developed in which strain, strain rate, and temperature and even chemical composition are taken into consideration. Simple power or exponential relationships frequently describe the true-stress/true-strain curves: cr = a0e"> <j = al (\ + a2s)ni a = a3 - (a3 - a4) exp(a5 s) (II. 12) Chapter II Literature Review 15 (J = c0(cl +£)"' -c2£ni The following three other equations frequently mentioned in the literature25'34'35 are the Ludwik, Misaka, and Cingara equations: a=ao+boS04+Co+s08+doe1-2(Ludwik) (11.13) a = A'e"'em'exp(-^-) (Misaka) (11.14) RT olap = (£l£p)e~£l£p] (Cingara) (11.15) The Ludwik equation is based on a least squares method and is found to provide good agreement between the measured and calculated flow stress. The Misaka equation is based on the premise that the flow stress is influenced by temperature, strain, and strain rate in a mutually exclusive way. Inclusion of the term s" leads to an overestimation of the flow stress. The Cingara equation is valid in the range of the stress-strain curve up to the peak stress, if the peak stress and peak strain have been determined. The equations mentioned above for describing stress-strain behavior are empirical in nature and not based on any particular theoretical approach. Indeed, the deformation of steel during hot rolling is difficult to model because of the constant evolution of the internal structure. Different phenomena are involved, such as work hardening, dynamic recovery and dynamic recrystallization, and, in order to predict the flow behavior through a physical model, these mechanisms have to be considered. The slope of the stress vs plastic strain curves determined at constant strain rate and temperature corresponds to the work-hardening rate, 0 ; i.e.: 0 = — de (11.16) Chapter II Literature Review 16 C. Perdrix and his colleagues36'37 found that the 0-cr curve may be divided into successive linear portions with a negative slope up to the maximum of the C J - S curve (a=amax, 0=0), as shown in Figure II. 1. The change of the slope between segments of the 0-cr curve is more abrupt at high temperatures. TEM examination clearly associated the different parts of the 0 - G curve with different successive mechanisms of dynamic recovery. Their results seemed to confirm the validity of the Kocks and Mecking dynamic recovery model, ^ = kxpV2-k2p (11.17) as where ki=const. (strain hardening), k2 = k2(s,T) (dynamic recovery), p is dislocation density, and, ^ T = * 0 ( l - — ) (11.18) as as where o~-aGbp , 90=aGbki/2, o"s=aGb(ki/k2), G is the shear modulus and b is the Burgers vector. In each range, the integration of the linear relation gives a Voce type evolution law:36 a=ais{ l-exp[-Pi(s+80i)]} (11.19) where o~js is the saturation stress, Pi is a constant and s0i is an integration constant. Sellars19 pointed out that the combined effects of work hardening and dynamic recovery lead to the characteristic microstructural changes indicated in Figure II.2 (a). Initially, work hardening, h, is rapid and leads to a rise in dislocation density, p, and in flow stress, o~. As p increases, the recovery rate, r, increases, leading eventually at strain e>em to steady state conditions. In its simplest form, the relationship can be written as: dp=hds+rdt (11.20) Chapter II Literature Review 17 With the assumption that h is constant and rocp, this equation is easily integrated. Then substituting for p: a=aMGbpI/2 (11.21) where a is a constant (-0.15), M is the Taylor factor, G is the shear modulus, and b is the Burgers vector, leading to an equation of the form: a = a0 + (crv - a0)[1 - exp(-—)]°5 (11.22) £r where cjs is the steady state stress, a 0 is the stress at zero strain, and sr is a characteristic strain. Even though the equation provides a good description of the experimental curves in some cases, the assumptions used in deriving the equation are dubious.19 Laasraoui and Fabregue assumed that the work hardening law has the following form: ® = — -Ba (11.23) where A and B are constants. One form of the integration of the above equation is given by the following expression for the stress: oW(*) = fa-02 +(°SS,DRV2 - 0 ( l - exp ( - a f ) ) ] 0 5 (H-24) In this equation, rj0 is the stress level at the beginning of plastic deformation, a is a parameter which represents the capacity of the steel to recover dynamically during work hardening at high temperature, and OSS.DRV and a are deduced from A and B tlirough the following relationship: ° S S , D R V = A - ^ (II.25a) oc=-2B (II.25b) Chapter 11 Literature Review 18 II.2 Recovery and recrystallization behavior in steel The free energy of a crystalline material is raised during deformation by the increase of dislocation density and grain boundary area per unit volume. The material containing these defects is thermodynamically unstable. Although thermodynamics would suggest that the defects should spontaneously disappear, in practice, the necessary annealing mechanisms are often very slow at low homologous temperatures and may be incomplete between the rolling passes. As a result, unstable defect structures can be retained between hot rolling passes or after cold deformation. If the material is reheated or held at a high temperature after deformation, thermally activated diffusion processes provide mechanisms whereby the defects may be removed or alternatively arranged in configurations of lower energy. These processes involve loss of some or all of the stored energy and a corresponding change in microstructure. The stored energy, which provides the source of all microstructure and property changes that are typical of deformed metals, is derived from the point defects and dislocations generated during deformation. At first, the microstructure and also the properties may be partially restored to their original values by recovery, in which annihilation and rearrangement of the dislocations occur. The microstructural changes during recovery are relatively homogeneous and do not usually affect the original high angle grain boundaries between the deformed grains. A further restoration process called recrystallization may occur in which new dislocation-free grains are formed within the deformed or recovered structure. These grains then grow and consume the old grains, resulting in a new grain structure with a low dislocation density. Recrystallization may take place during deformation at elevated temperatures, in which dislocations in newly formed grains increase with further deformation, and this is termed dynamic recrystallization. Although recrystallization reduces the dislocation density, the material still contains grain boundaries, which are thermodynamically unstable. Further annealing may result in grain Chapter II Literature Review 19 growth, in which the smaller grains are eliminated, the larger grains grow, and the grain boundaries assume a lower energy configuration. In certain circumstances, this normal grain growth may give way to the selective growth of a few large grains, a process known as abnormal growth or secondary recrystallization. The microstructure evolution of IF steels during thermomechanical processing may involve some or all of the processes previously mentioned. They are discussed in detail in the following sections. II.2.1 Static and dynamic recovery Polycrystalline zone-melted iron has been shown to recover relatively easily with an activation energy increasing from 91.9 to 281.7 kJ/mole with decreasing purity; these activation energies correlate to vacancy migration and self-diffusion in iron, respectively.40'41 However, solute atoms and fine precipitate particles in alloy systems reduce the ease with which recovery occurs. A few ppm of interstitial impurities, carbon and nitrogen, when added to pure iron, show a strong effect in reducing recovery; this effect is more evident for nitrogen than for carbon.40,42'43 Solute additions are also found to exhibit similar retardation effects on recovery 4 4 Consequently, recovery effects are not normally important in low-carbon steels and low-carbon alloyed steels. The matrix of an IF steel is very low in interstitial atoms, and consequently, these alloys may undergo considerable recovery, comparable to that of pure iron. However, the recovery may be retarded due to any excessive stabilizing elements, e.g., a stoichiometric excess of Ti and/or Nb in iron after stabilizing all the interstitial C and N, particularly in ordinary IF steels. The presence of a fine precipitate distribution may also retard recovery in IF steels. The residual line Chapter II Literature Review ' 20 broadening measurements obtained by Satoh et al.45 on unstabilized and Ti-stabilized extra-low-carbon steels indicate that considerable recovery takes place prior to the onset of recrystallization and that Ti additions decrease the extent of recovery. The tensile strength and yield strength of a Nb-stabilized IF steel decrease by about 15% before the commencement of recrystallization, while no such recovery effects are visible in terms of the ratio of tensile strength to yield strength or the hardness measurements.40 Pan and Lenard46 investigated the flow behavior of three ultra low carbon (IF) steels containing Nb and Ti and a plain carbon steel during hot and warm working. When the steels are subjected to compression at constant strain rates in the austenite region, they exhibit typical work hardening and dynamic restoration behavior. When they are worked in the ferrite region, the dissolved niobium in the Nb-Ti IF steel retards the occurrence of dynamic recovery in ferrite, causing a rapid and quasi-linear increase of flow stress with small strain increments due to the fact that immobile dislocations accompanying pure work hardening are accumulated(Figure II.3). When the dislocation density reaches a critical value, metadynamic restoration takes place and causes the decrease of flow stress with further increasing strain. The shapes of these flow curves are different from those showing the typical work hardening and dynamic recovery. In addition, the yield stress shown in these curves is higher than in those exhibiting normal work hardening and dynamic recovery. The extent of retardation of the dynamic recovery of ferrite increases with increasing dissolved Nb content. When the dissolved Nb atoms precipitate before deformation or when the steel is free of Nb atoms, a typical strain hardening and dynamic recovery flow behavior is found in both the austenite and the ferrite regions. Chapter II Literature Review 2 1 II.2.2 Static recrystallization Recovery is a relatively homogeneous process in terms of both space and time. When viewed on a scale which is larger than the cell or subgrain size, most areas of a sample are changing in a similar way. Recovery progresses gradually with time and there is no readily identifiable beginning or end of the process. In contrast, recrystallization involves the formation of new strain-free grains in certain parts of the specimen and the subsequent growth of these to consume the deformed or recovered microstructure. The microstructure at any time is divided into recrystallized or non-recrystallized regions and the fraction recrystallized increases from 0 to 1 as recrystallization proceeds. The recrystallization characteristics of high purity iron after 60% cold working were investigated by Rosen et al.4 7 in the temperature range of 517 to 632°C. They observed the formation of nuclei only at certain boundaries of deformed grains; consequently, recrystallization is rapid for those grains, but very slow for others. These stable deformed grains are eventually consumed by the extremely slow growth of surrounding grains. They observe a decreasing isothermal growth rate and associate it with the very coarse grain size of the stable grains. Leslie et al. 4 4 observe recrystallization in iron to be a growth controlled process, with substantial nucleation at zero time. They attribute the measured decreasing isothermal growth rates to the reduction in driving force resulting from concurrent recovery. The Avrami equation has been shown to describe the kinetic measurements only at the beginning of recrystallization, as can be seen in Figure II.4. Two distinct stages can be seen in the Figure; the first is growth-controlled, and the second has been attributed to the lack of additional nucleation. A small amount of carbon added to high purity iron is reported to cause only a slight reduction in the recrystallization rate.42 This, in contrast with the stronger effect of substitutional Chapter II Literature Review 22 solutes, is partly explained in terms of the high mobility of interstitial atoms. It is further speculated that any reduction in grain boundary mobility caused by carbon would be compensated for by the greater stored energy in the system, due to the reduced recovery. Similar conclusions are made regarding the nitrogen addition, except for its stronger retarding effect on recrystallization.43 Ordinary IF steels are known to recrystallize in a very sluggish manner. The major retarding effect is caused by the type and amount of excessive stabilizing elements in the iron matrix and the size and distribution of the associated precipitates. Wilshysky-Dresler et al. 4 8 ' 4 9 studied the recrystallization kinetics of three Ti, Ti+Nb, Nb stabilized IF steels compared with unstabilized extra-low-carbon (0.004wt%C) steel. Their study illustrates two important points valid at all isothermal annealing temperatures: 1) The rates of recrystallization of the stabilized steels are retarded compared to the unstabilized steel, and the incubation times for recrystallization for the stabilized steels are much longer than that for the unstabilized steel, and 2) The recrystallization rates are independent of the hot band coiling temperature. Graphing log(ln—-—) against log t, where X is the fraction recrystallized and t is the recrystallization 1 — X time, yields linear plots (Figure II.5) with the recrystallization data for the stabilized IF steels exhibiting two distinct stages, each characterized by a different value of the time exponent, n, in the Avrami equation, X=l-exp(-bt"). The values of n are independent of coiling temperature and lower than the theoretical values for both stages of recrystallization. The calculation of precipitate pinning and solute drag forces reveals that the precipitate pinning force is larger than the solute drag force. This calculation, coupled with the correlation of the degree of retardation of recrystallization from a fine precipitate distribution, indicates that grain boundary pinning by Chapter II Literature Review 23 fine particles is the dominant mechanism by which stabilizing alloy additions in IF steels retard recrystallization. The studies by Tsunoyama et al. 5 0 and Hosoya et al.51 on extra-low-carbon (IF) steels (0.003wt%C) show that Ti or Nb addition to the steels results in a drastic increase of the recrystallization finishing temperature, TR. The TR contour lines have a specific relationship to the atomic ratio of the effective amount of Ti or Nb to C content. TR increases in proportion to the atomic ratio of Ti*(effective titanium content)/C or Nb/C. These studies, together with another similar study conducted by Takechi10 on recrystallization of Ti- and Nb-stabilized IF steels, indicate that Nb has the strongest retarding effect on recrystallization. Both Jonas52'53 and Bleck54 conclude that the recrystallization of IF steels is completed in less than 100 seconds when the IF steel has been pre-deformed and held in the austenite temperature range (Figure II.6). Jonas' results also indicate that the recrystallization behavior of IF steel is intermediate between that of the C-Mn steel and the Nb microalloyed steel. II.2.3 Dynamic and Metadynamic Recrystallization A simple description of dynamic recrystallization is: New grains originate at the original deformed grain boundaries, but, as the material continues to deform, the dislocation density inside the new grains increases. This reduces the driving force for their further growth, and the recrystalizing grains eventually cease to grow. An additional factor which may limit the growth of the new recrystallized grains is the nucleation of other grains at the migrating boundaries. In materials of lower stacking fault energy, such as austenitic steel, copper and nickel, recovery is slow due to the difficult climb and cross slip of dislocations and, as a result, the Chapter II Literature Review 24 dislocation density increases to the critical value necessary for dynamic recrystallization to occur. Dynamic recrystallization originates at high angle grain boundaries. Bulging of grain boundaries is frequently observed as a prelude to dynamic recrystallization and is consistent with the assumption that a mechanism closely related to Strain Induced Boundary Migration (SIBM) is operative.17 Then, the critical condition for nucleation becomes: > — ^ — r (11.26) s KMLGb where pm is the dislocation density of the deformed matrix, yb is the surface energy, K is a constant, M is the mobility of the boundary and L is the mean slip distance of dislocations. The stress-strain curve for a material which undergoes dynamic recrystallization generally exhibits a broad peak followed by a reduced flow stress, as shown in Figure II.2 (b). Under conditions of low Z (high temperatures and/or low strain rate), multiple peaks may be obtained at low strain. A critical deformation, ec, is necessary in order to initiate dynamic recrystallization, this value being obtained before reaching the peak of the stress-strain curve. 00 00 9fi ^ Typically, the critical strain, eC] is expressed as follows: ' ' ' ec=asp=Ad:-Zn (11.27) where ep is the strain at peak stress, d0 is the initial grain size and A, a, m, n are constants. When dynamic recrystallization contributes to softening after reaching the peak stress, the kinetics of dynamic recrystallization can be presented by an Avrami equation. ' ' ' For this purpose, it is assumed that the mechanical softening is directly proportional to the Chapter II Literature Review 25 recrystallized volume fraction. That is: (11.28) where crs is the peak stress and a s s is the steady-state stress after dynamic recrystallization has progressed through the material. By using the time for 50% recrystallization, to.5, equation (11.28) can be rewritten as follows: a=as-(as-ass)[l-exp(-0.693 • (— )k)] (11.29) 0^.5 where k is a constant associated with the nucleation mechanism. Microstructural evolution during dynamic recrystallization generally starts at the old grain boundaries, as shown schematically in Figure II. 7a. New grains subsequently nucleate at the boundaries of the growing grains (Figure II.7b), and in this way a thickening band of recrystallized grains is formed, as shown in Figure II.7c. If there is a large difference between the initial grain size ( D 0 ) and the recrystallized grain size (DR), then a "necklace" structure of grains may be formed (Figure II.7b-c), and eventually the material will become fully recrystallized (Figure II.7d). Unlike static recrystallization, the mean size of the dynamically recrystallized grains does not change as recrystallization proceeds. The steady state grain size (DR) during dynamic recrystallization is a strong function of the flow stress and is only weakly dependent on the deformation temperature. The empirical relation is often given as cr = KD-Rm (11.30) en t where m<l, K is a constant. Twiss examined the relation between the mean grain size and the flow stress for a number of materials and proposed a universal relationship which can be expressed in normalized form as Chapter II Literature Review 26 (11-31) where n=0.8 and Ki=15, G is the shear modules, and b is the Burgers vector. Whenever the critical strain for dynamic recrystallization is exceeded, recrystallized nuclei will be present in the material. If straining is stopped, but annealing continued, then these nuclei will grow with no incubation period into the heterogeneous, dynamically recovered 58 matrix. This phenomenon is known as metadynamic recrystallization. II.2.4 Dynamic behavior during hot and warm rolling of IF steels Dynamic recrystallization that takes place during hot-rolling of a steel is dependent on both the rolling conditions, such as strain (s), strain rate (e), temperature, interpass time, and the critical temperatures (e.g. Tnr, A^) of the steel. The critical temperature, Tnr, the temperature below which no recrystallization occurs and Ar3, the start temperature of the y to a transformation during hot rolling of IF steels, can be determined by plotting the mean flow stress (MFS) obtained for the plate rolling schedule as a function of the inverse absolute temperature.59 Typical flow curves for an IF steel, a plain carbon steel, and a Nb microalloyed steel are 52 1 compared in Figure II.8. At the applied strain rate of 2s" , the peak stress of the IF steel is attained at a strain of 0.65; this strain is frequently identified with the initiation strain for dynamic recrystallization. However, recrystallization is in fact initiated much earlier, at the critical strain, sc, which is usually 5/6 of the peak strain and appears to be relatively independent of strain rate. Figure II.9 illustrates the torsion generated stress-strain curves for three IF steels representing the seven roughing passes in the austenite range.59'60 An identical response is Chapter II Literature Review ; 27 obtained for the Ti and the Ti+Nb grade. At passes 6 and 7 (s>0.5), the three steels exhibit marked flow softening after reaching the maximum stress. This softening indicates that dynamic recrystallization has initiated during these passes. The flow stresses of the Nb stabilized IF steel are significantly higher than those of the other two Ti containing steels, probably reflecting the stronger solute strengthening effect of Nb compared to Ti and the fact that the Nb bearing steel has the highest excess concentration of microalloyed addition. Figure II. 10a and 10b show the stress-strain curves for two IF steels having first and last finishing pass temperatures of 930°C and 880°C, respectively.59 As can be seen, there is an accumulation of work hardening from the first finishing pass to the second, but after that, the maximum flow stress remains about the same. The lack of increase in flow stress with decreasing temperature indicates that dynamic recrystallization is taking place during deformation, followed by metadynamic recrystallization occurring between the passes. In order to reduce the production cost, there is an interest in employing warm-rolled deep drawn steel sheet in place of cold-rolled sheet. Hot rolling of IF steels in the ferrite range has been employed recently. The influence of the temperature of the first finishing pass on the stress-strain curves associated with the five finishing stands is illustrated in Figure II. 11 for a Ti-IF steel.61 As can be seen in the diagram, there is an accumulation of strain, i.e., work hardening, from the first to the second pass. There is no further increase in flow stress beyond the second pass, despite the approximately 15°C decrease in temperature associated with the final three passes. This lack of increase in flow stress suggests that some form of dynamic recrystallization is taking place during simulated rolling, as in the case of austenite,59 leading to a decrease in the isothermal flow stress and off-setting the effect of the decrease in temperature. It should be noted that although the reduction per pass is less than that required to initiate dynamic recrystallization, the relatively low temperatures and short interpass time (1 to 2sec.) allow the dislocation density to accumulate until it reaches and exceeds the critical level required for the propagation of this type of recrystallization. The occurrence of dynamic recrystallization during ferrite rolling of IF steels concluded by Najafi-Zadeh, is based primarily on the flow stress curves. Some recent research indicates that very small equiaxed grains are formed after severe deformation in the ferrite region of IF steels.62'63'64 The research concludes that the structures are equiaxed subgrains resulting from microband development, while other research confirms metallographically and crystallographically the occurrence of dynamic recrystallization (DRX) of ferrite in a Ti IF steel. Even though DRX occurs, the associated drop in the stress-strain curves is not observed. Limited work hardening of ferrite at large strains and inhibition of boundary migration by precipitates in the IF steel might be the reasons why the decrease in stress was small during DRX. An investigation of ferrite deformation behavior in a ferritic stainless steel reveals that the equiaxed fine grains resulted from apparent dynamic recrystallization aided by dynamic recovery.64 Some quantitative work has also been done on the recrystallization behavior of IF steels. According to Kino et al.,65 the grain size of hot-rolled bands in IF steels may be formulated as shown in Table II. 1. Hot rolling at low temperatures in the austenite (y) range contributes to the refinement of the y grain size (D*0), while the immediate and rapid cooling just after finishing hot rolling contributes to the inhibition of grain growth of the y grains and an increase of the y/a conversion ratio. Chapter II Literature Review 29 Table II. 1 Formulae for predicting the grain size of IF hot-rolled band''5 Steel A Steel B Imaginary y grain size just after hot rolling = 1.70xl04Z-018 = 1.26xl06Z"°-17 Grain growth of y grain after hot rolling 4= = |(4)2+154xl0,5exp(^)-j 4-= |(4)2+130xl014exp(^)-j Converting ratio y/oc *>; =9.88x 10"2(CR)° 2 8 2(D*)° 2 8 5 Da =1.48xl0-1(CR)0206(D*)033 Steel A: pure Ti-IF steel (e.g.: C/0.0010, Ti/0.02mass%); Steel B: Conventional Ti-IF steel(e.g.: C/0.003, Ti/0.05); Z = eexp(-^-), e: strain rate of final pass of hot rolling, RT Q=63.8kcal/mole, t: time, T: temperature(K), D: grain diameter in pm, CR: cooling rate during y—»a transformation. When the recrystallization and the phase transformations are complete, grain growth can take place, and has been described by the empirical equation: D" =D';i+ctzM-^) (11.32) kT OC £L£ iCT where c, n and Q g are constants. Different authors use different n values'0'00'60'0' and some suggest that grain growth can be divided into two stages and different c values applied.68 II.3 Precipitation behavior in steels Niobium, vanadium and titanium have different affinities for carbon and nitrogen in steel, producing different solubility products for the carbide and the nitride. These different solubility products result in a different precipitation behavior of these compounds. In the temperature range 1100-1250°C, commonly adopted as a slab reheat temperature, titanium nitride is the most stable compound and vanadium carbide the least stable in austenite. Niobium carbide and titanium carbide lie between these two compounds, and the amount of niobium or titanium dissolved in austenite at the reheating temperature can vary widely, depending on the temperature and carbon Chapter II Literature Review 30 content. The undissolved carbides and nitrides at the reheating temperature contribute to refinement of the initial austenite grain size. The carbides and nitrides of Ti, Nb and V are isomorphous with cubic structures and are soluble in each other. That is, the carbides or nitrides in steel often contain both nitrogen and carbon, and are often called carbonitrides. In commercial microalloyed steels, vanadium and niobium are precipitated as carbonitrides. Vanadium nitrides and niobium nitrides are seldom formed in commercial microalloyed steel, except in very low-carbon-high-nitrogen steel. On the other hand, in Ti-bearing steels, titanium nitride is formed first and after all the nitrogen is combined as titanium nitride, titanium carbide may subsequently precipitate with increasing Ti content. II.3.1 Classical Precipitation Calculations To quantify the precipitation behavior of the microalloying elements in steels, several methods are employed. The methodology frequently used is the experimental determination of the constants A and B in the solubility product equation log[M][I]=A+B/T65'69"73 Here, [M] and [I] are, respectively, the weight percentages of the metallic elements(Nb, Ti, V, or Mn), and the 12 interstitial elements (C, N, or C+—N). When the steel is held at a temperature lower than the calculated solution temperature, the nuclei of particles form and grow. If the steel is heated to a higher temperature, precipitate dissolution occurs. At temperatures lower than the calculated solution temperature, the dissolution rate is relatively slow and the dissolving particle seems to reach an equilibrium stable size. By contrast, at temperatures higher than the solution temperature, the precipitate dissolves quickly and completely. The above approach, however, is restricted to a relatively narrow composition range, defined by the composition of the steel tested and depends on the experimental accuracy. An Chapter II Literature Review 31 alternative approach employs thermodynamic principles to calculate the equilibrium between the various second-phase compounds and the matrix. By this means, the solubility of carbonitrides can be predicted in austenite with compositions not previously investigated in detail. Furthermore, this method can provide the calculated equilibrium composition of the precipitates. Finally, the equilibrium mole fractions of precipitates at a given temperature can be determined.74"76 The thermodynamic modeling assumes that (NbxTiyVi.x.y)(CaNp) is an ideal solid solution of six types of carbides and nitrides, i.e., NbCo.87, NbN, TiC, TiN, VC0.75 and VN, and Ti4C2S2, TiS, MnS and AIN are formed separately. Then, the equilibrium between austenite and precipitates can be described as: z[xAG"NbC + yAG°nc + (1 - x - y)AG°c ] + (1 - z)[xAG°NbN + yAG°m + (1 - x - y)AG"VN ] +RT[x lnx + ylny + (1 - x - y) ln(l - x - y) + a ln(——) + Bln(—^—)] (11.33) a + B a + 6 = RT[x\naNb + y\r\aTj +(1-x - y)h\av +a\nac + /?lnaw] AGA^-lnaAI+\naN (11.34) RT AG" M n S = In aUn + In as - £ In u (11.35) RT AG" ^ ^ = 41na7., ++21noc +2\nas -^ln(l-w)-lnv (11.36) RT = lna„ + lna s -^ln(l -u) + ln(l - v) (11.37) KI where AG°Nbc, AG°TiC, AG';c, AG°NbN, AG„W, AG°VN, AG°AIN, AG°NbS, A G " ^ , and AGrlS are the standard Gibbs free energies of formation of the respective subscript compound in Chapter II Literature Review 32 austenite, with infinite dilution as the reference state, a; is the activity of element i (i=C, N, Nb, Ti, V, Mn, S) in austenite, C\ is a modifier which takes into account the limited mutual solubility of the Mn- and Ti-based sulfides, z is the carbide fraction in the combined carbonitride and is related to a and p by a=(0.75+0.12x+0.25y)z P=l-z (11.38) u and v are defined as follows: U = f M n s / ( fruc2S2 +fTiS+fMns) V = / ( + f T i S ) (11.39) where fk is the number of moles of precipitate forming elements in compound k (k=MnS, Ti4C2S2 or TiS) normalized with respect to the total number of moles in the system. With the aid of the modified Wagner formalism, the activity of element i in austenite with respect to the infinite dilution reference state can be expressed as lna,= \nyFe+\nXi+fjsJiXJ (11.40) 7=1 where e\ is the Wagner interaction parameter between elements i and j , and lnype is the activity coefficient of the element in y-Fe, which can be calculated from ^YFe=-\zZzZ£j.XJX< (IL41) 1 7 = 1 '=1 where Xj is the mole fraction of element i in austenite, n is the number of alloying elements in the system; the subscript i represents the precipitate forming elements and the subscript/superscript j represents all the species considered in the system. All equations described above, together with the mass balance equation, can be simultaneously solved by Chapter II Literature Review ; 33 numerical methods. Good agreement between the theoretical predictions and the experimental data is obtained by Liu et al.74 "77 78 7Q Another approach developed by Kwon et al. ' ' combines classical nucleation theory and growth kinetics to determine the overall precipitation kinetics in Nb-microalloyed steels. Two types of NbC precipitation, i.e., interface and matrix nucleation, accompanying the y/a transformation are considered. For the calculation of time dependent nucleation rate (I) of NbC precipitate in ferrite, classical nucleation theory gives: I = Z - B-N(t)• exp(-AG* /kT)• exp(-r/t) (11.42) where the product of the Zeldovich factor (Z) and the frequency factor ((3),the incubation time for nucleation (x), and the nucleation number N(t) are expressed as follows: ZB = ^(^-y\NavRT)DeffXNb (11.43) A c KI T = £ — T (11.44) DeffXNhV2AG2 W) = Nmal+Nint (11.45) The critical driving force (AG*) was the sum of the chemical free energy change (AG^,C) and the strain energy (W-s) during the reaction of [Nb]+[C]->[NbC]: ~XNb(t)-Xce(t) AG»NbC=-f^\n\ e V e V ANb' A Ce (11.46) Ws = 9jua-S2 S = kamc a" (11.47) Chapter II Literature Review 34 where V m is the molar volume of NbC, the X; and eXj are the mole fractions of component i and its equilibrium value at a given temperature, respectively, u" is the shear modulus of ferrite, 8 is the misfit parameter, aNbc and aa are the lattice parameters of NbC and ferrite, respectively, and k is a coherency factor which varies from 0 to 1. The nucleation site density for interface NbC precipitates is: ^in,=%-7=%-4 ( I L 4 8 ) Q F e aFe Y The nucleation site density for matrix NbC precipitates is: Nmat=Xa{t)la] (11.49) where Sjnt. is the area fraction of the y/a interface, X a ( t ) is the volume fraction of the ferrite at time t, Y is the intersheet spacing and A is the interface movement distance. dV. The volumetric growth rate of precipitates, ——, is controlled by diffusion of Nb in dt austenite and applying Zener's steady state approximation gives: dVp . drp —p- = Awl — (11-50) dt " dt where drp/dt=Deff/rcr(t)[XNb(t)-eXNb]/(l-eXNb)- After growth is completed, assuming supersaturated solute atoms, particle coarsening occurs to reduce the total surface area of the 7 Q precipitates. The coarsening kinetics of alloy carbides is described by, , \6CTVDEFF eXm , [r (t)]3 = p—$- • {t - 1 „ ) + rl (II.51) 9RT (\-eXNbf Ci Ci where t c s is the coarsening start time, rcs is the initial radius of the precipitate and r p(t) is the radius of the precipitate at time, t. Chapter II Literature Review 35 By combining the nucleation and growth kinetics, the overall precipitation kinetics can be 7ft calculated, Xn"c^- = l-exp[-^I(t')V (t,t')At] (11.52) where XNbc is the volume fraction precipitated at time, t, XNbC(max) is the maximum volume fraction at a given temperature derived by the thermodynamic analysis, and V(t,t') is the volume of precipitate at time, t, which was nucleated at time, t', with the nucleation rate of I(t'). The Scheil's additivity rule was applied to calculate the non-isothermal precipitation behavior. Sun80'81 has developed a kinetic model for predicting the precipitation start time (Ps) under isothermal conditions, as well as the precipitation start temperature (TPs) during continuous cooling. The model has been successfully used to interpret the interaction between recrystallization and precipitation during rolling practice and has been applied in the commercial AISI model developed at the University of British Columbia.16 II.3.2 Characteristics of Precipitation in IF Steels The commonly accepted view of precipitation in IF steels has its origin in the precipitation behavior which is well established for HSLA steels. In the early days of research into precipitation in IF steels, most researchers drew similar conclusions to those that had been obtained from the research on HSLA steels. The main conclusions are summarized as follows: O Q (1) The precipitation reactions are assumed to be: A1+N->A1N Ti+N-»TiN Chapter II Literature Review 36 Ti+S->TiS Ti+C->TiC Nb+C+N->Nb(CN) (2) Based on the assumptions in (1), the soluble Nb or Ti in a is defined as follows:6'7'70'82'83 Nba(wt%)=Nb(wt%)-7.75C(wt%) (11.53) Tia(wt%)=Ti*(wt%)-4C(wt%) (11.54) where Ti* is the effective titanium available to combine with C and is defined as follows: Ti*(wt%)=Ti(wt)-(48/32)xS(wt%)-(48/14)xN(wt%) (11.55) Elimination of the interstitials C or N is accomplished by adding a sufficient amount of Ti or Nb to completely tie up the C and N; this is called the scavenging effect. (3) Precipitates in Ti-added IF steel are dispersed more coarsely than those in Nb-IF steel.50 This is because the sulfides in Ti- and Nb-added steels are mainly composed of Ti- and Mn-sulfides, respectively. Ti-sulfides are larger than the Mn-sulfides which form at lower temperatures. (4) The fraction of larger precipitates increases considerably by lowering the slab reheating temperature (SRT).84'85 It is believed that a low SRT helps keep TiC and NbC precipitates from going into solution. This effect is more pronounced in Ti-IF steels than in Nb-bearing steels. (5) Hot rolling with higher reductions and higher speeds significantly decreases the number of fine precipitates which are formed after hot rolling. The precipitates in steels hot-Chapter II Literature Review • ; 37 rolled with a low reduction and low speed, and followed by air-cooling, are smaller than lOnm in Nb-IF steel and frequently observed to be in rows.70'83 (6) The coiling condition is not critical for controlling the precipitation in IF steel when hot-rolling is conducted at temperatures higher than Ar3. However, when hot-rolling is conducted in the ferrite region, the precipitation behavior in IF steel strongly depends on the coiling temperature.86'87 Perera87 found that the morphology of the precipitates in a Ti+Nb IF steel hot-rolled in the ferrite region changes from a fine needle shape to spheres and polyhedral, when the aging temperature rises from 550~650°C to above 700°C.87 (7) In Ti-added steels, nitrides and sulfides can deposit at considerably higher temperatures than those in Nb-added steels, as schematically illustrated in Figure II. 12.50 In modern ULC IF steels, the levels of C, N, and S are not only lower than those in HSLA steels, but also the relative proportions of C to N to S are radically different. A typical HSLA steel might contain 0.05%C, 0.006wt%N, and 0.006wt%S, whereas a typical ULC IF steel contains <0.003%C, 0.003%N and 0.006%S. On an atomic weight percent basis, the ratios of C:N:S are consequently much different, i.e., C:N:S=22:2.5:1 for HSLA steels and 1.2:1.2:1 for ULC IF steels. Hence, carbon represents about 86% of the precipitate-forming atoms in HSLA steels, but only 35% in ULC IF steels. Consequently, nitrogen represents only 10% of the precipitate-forming atoms in HSLA steels, but 35% in ULC IF steels. Sulfur, on the other hand, represents only 4% in HSLA steels but 30% in ULC IF steels. Therefore, the precipitation in these two families of steels would be expected to be very different, and consequently, the well-established precipitation behavior in HSLA steels cannot be adopted for the new ULC IF steels. Recent work conducted by several authors reveals the importance of T14C2S2 as another 28 29 70 71 88 89 method of stabilizing carbon. ' ' ' ' ' In ULC IF steels containing Ti, the N is combined as Chapter II Literature Review ; 38 TiN, which precipitates in the liquid. The N, therefore, is fixed in the as-cast condition and very little, if any, is redissolved on subsequent reheating. The TiN particles formed have a diameter from 0.2 to 5.0pm. Although the TiN particles are very stable, they do contribute to the precipitation reactions which occur during subsequent processing; they act as nucleation sites for other precipitates. The most important view emerging from recent studies is that C is principally removed from solid solution by the formation of Ti4C2S2. while precipitation of MC(TiC, NbC) is observed to form epitaxially on the Ti4C2S2 particles, it represents a small percentage of the C-bearing precipitate and an insignificant percentage of the total Nb content..The work has also shown that Ti4C2S2 forms exclusively from TiS particles by an internal transformation. As illustrated in Figure 11.13, the particle transformation of TiS to Ti4C 2S 2 results in an "sandwich-like" precipitate. In the steels investigated, this precipitate transition was completed by about 900°C. The TiS responsible for the ultimate formation of Ti 4C2S2 is formed during reheating. Hence, the well-recognized influence of start rolling temperature (SRT) and Ti content on stabilization results from this mechanism. When stabilization occurs by the formation of Ti 4C2S2 and TiN, the amount of remaining, soluble titanium will be given by: Ti*(Wt%)=Ti(wt%)-2xl.5S(wt%)-3.42N(wt%) (11.56) When the Ti level in the IF steel is in excess of a critical level, this stabilization mechanism occurs and there is no further precipitation of particles other than those centered on the original sulfides and nitrides. Unlike HSLA steels, there is no strain-induced precipitation during rolling or precipitation during coiling. Chapter II Literature Review ; 39 When the ULC IF steel contains less Ti than required for stabilization through the formation of Ti4C2S2, a completely different situation is expected regarding precipitation. A critical amount of Ti would lead to incomplete stabilization of C by the Ti4C2S2 mechanism. The free C would then be available for the formation of a new and additional array of particles formed as strain-induced precipitates in the austenite during rolling or as precipitates formed in the ferrite during coiling. In summary, a schematic representation of the sequence of precipitation in a Nb+Ti IF steel, containing an excess of Ti, is presented in Figure 11.14. The sequence is quite different compared with that which occurs in HSLA steels. From the investigation of the Nb(CN) isothermal precipitation behavior in austenite, using two carbon grades of steel with different M/C atomic ratios, but having approximately equal products of [M] and [C], Akamatsu et al.9 0 found that the observed progress of precipitation in extra low carbon (IF) steel is much faster and the size of precipitates is apparently larger than those observed in steels with the higher carbon content corresponding to HSLA steels, even though their supersaturation is the same. To explain this phenomenon, the local equilibrium hypothesis at the austenite/Nb(CN) interface during precipitation has been introduced into the classical nucleation theory and the spherical growth theory, and an extended precipitation model has been proposed which can predict the precipitation behavior in IF steels, as well as in HSLA steels. If the local equilibrium compositions, bXj (j=Nb,C,N) and byj G=C,N), are used at the growing interface, it is reasonable to assume that the local equilibrium is applicable to the nucleation process. Then, the driving force, A G„ (J/mol), for nucleation of precipitates with composition byj from y of average composition aXj can be calculated by the following equation:90 Chapter II Literature Review : 40 f b „ ]„/- XNb' XC \ i b,, w XNb' XN XNb' XC XNb' AW (11.57) where 'XJ (j=Nb,C,N) is the initial composition in y before precipitation, b X j (j=Nb,C,N) is the local equilibrium composition of y at the nucleated interface, and byj (j=C,N) is the local equilibrium composition of Nb(CN). Then, the steady state nucleation rate, I(l/m3s), of Nb(CN) controlled by Nb diffusion in y can be described by the following equations: I=4^/^exp(^) (11.58) ay kT A G ' = ^ - j — ^ (11.59) 3 A"Gn/VmcN) where p is the dislocation density in y, ay the lattice constant of y, D N d the diffusion coefficient of Nb in y, a the y/Nb(CN) interfacial energy and VNb(CN) the molar volume of Nb(CN). The growth rate, v(m/s), of spherical precipitates with radius, R(m), controlled by Nb diffusion in y, is estimated as follows: Nb o b ^Nb~ ^Nb (11.60) T n I• Nb \ _ ^Nb ^Nb / T T / - U JNb= ~DNb • ( — T — ) r - « ~ 7, (1L61) a1 R where °CNb and b C N b are the Nb concentrations inside of the Nb(CN) and y at the interface, respectively, and °CNb =0.5A^Nb(CN), b C N b = b C N b /V y ; "C^ (the Nb concentration remote from the particle)=axNb/Vy. Chapter II Literature Review ; 4J_ Figure 11.15 shows a schematic phase diagram for a simplified Fe-M-C ternary system and the concentration profiles of solute M at the interface during precipitation of a typical MC-type (M=Nb, Ti; C=C,N) stoichiometric compound. The compositions shown for cases A and B correspond to the initial atomic ratio of constituents for precipitates M / O l (e.g. IF steel) and M/C<1 (e.g. HSLA steel), respectively. The boundary composition, B X M , given by an intersection of the solubility line for MC and the iso-activity line for C in austenite, differs from the equilibrium one, e X M . This difference is greater in the case of A, even under the same supersaturation of MC precipitation. As a result, the large concentration gradient of solute M is formed at the interface, and it accelerates the growth of the precipitate in the case A. Consequently, both the product, MC, and the ratio, M/C, are important factors affecting the kinetics of precipitation. II.4 CSP rolling and ferrite rolling As described in chapter I, CSP is a relatively new technology, exhibiting some operational and metallurgical differences from cold-charge reheat rolling. The optimization of CSP rolling, and its extension into the high quality end of flat steel production, is ongoing. Important rolling parameters, such as the homogenizing temperature, presence of de-scaling, number of finishing stands, permissible reduction per stand, rolling speed and run-out table cooling regime are still being experimented upon by various CSP mills. The temperature attained in the tunnel furnace, coupled with the residence time of the slab in the furnace, impacts on a host of operational and physical phenomena: precipitate redissolution, grain growth, scale morphology and growth. The scale morphology dictates the optimal design of the de-scaling unit. The number of roll stands have evolved from five to six and even seven stands. The Chapter II Literature Review 42 reduction per stand, particularly in the first and last stands, has changed considerably in an effort to reduce edge cracking and shape problems. On the run-out table, the cooling behavior is influenced by gauge, strip shape and flatness through their effects on the behavior of water on the strip surface. Poor cooling control may result in an unacceptable final microstructure and mechanical properties. A very important aspect of CSP rolling is the difference in grain evolution from finishing mill entry to the exit. The entry microstructure in a conventional mill originates from the reheated austenite and then undergoes a series of deformation, recrystallization and grain growth processes in the roughing mill. In the CSP mill, the entry microstructure is a virgin cast dentritic structure obtained from solidification during slab casting. This difference in microstructure has implications for the rolling process in terms of the deformation resistance and microstructural evolution, especially at the first pass. The range of steel grades produced in CSP plants is constantly growing. Weldable unalloyed steels, medium carbon steels, mild carbon steels, high-strength microalloyed steels for cold rolling and phosphorous-alloyed steels are being produced on CSP plants. Production trials have been made with silicon steels, alloyed steels for heat treatment, ferritic and austenitic stainless steels and high carbon steels. The resulting mechanical properties conform to those achieved in conventional hot strip production. Even though the deformation rate from the thin slab right up to the finished product is markedly lower than that obtained in a conventional hot rolling plant, the hot strip rolled in a CSP mill exhibits a very fine-grained microstructure, which is the precondition for favourable combination of strength and ductility. For HSLA microalloyed steels, where the thin slab does not cool down below the precipitation temperature at any time prior to rolling, the microalloying elements remain in solution. They precipitate only during the rolling process and have exactly the desired effects on the microstructure and the mechanical Chapter II Literature Review 43 properties.91'92 Evaluation of the CSP produced hot band also shows that all of the material after 15 cold rolling is acceptable for automotive exposed large parts. As the demand for thinner hot strip products increases, operating hot mills at lower temperatures becomes a necessity if the final properties are not to vary significantly across the strip width. When these temperatures are low enough that a significant amount of ferrite is present, 'warm' rolling conditions are attained.93"95 Even on conventional mills, the reheating temperature in ferrite rolling could be lowered by about 200°C, which could result in a saving in the energy costs, a reduction in the scale loss, a reduction in the solute content and better control of texture fromation.96'97 Glover and Sellars 9 8 ' 9 9 studied the recovery and recrystallization during and after high temperature (500~800°C) deformation, of vacuum-melted iron and zone-refined iron in the early 1970s. Their results indicate that the transition from dynamic recovery to dynamic recrystallization occurs at higher values of Z (~1015 s"1 for high purity material compared with -5-1012 s"1 for low purity product) and hence at higher flow stresses for the higher purity material. For the same material, static recrystallization after deformation is faster in dynamically recovered than in dynamically recrystallized structures, due to a decrease in growth rate with time in the latter. Hashimoto et al. 1 0 0 ' 1 0 1 found that, compared with Al-killed ultra low carbon steel, ultra low carbon IF steel suffered much less r-value loss after annealing, when the rolling temperature was increased from room temperature to 700°C. The r-value deteriorated with increase in solute carbon content during hot rolling, as shown in Figure 11.16. Nagamichi et al. reached a similar conclusion.102 A detailed study on the texture formation in ferrite rolling by Senuma103'104 indicated that a cold rolled Ti bearing IF steel sheet that is obtained by prior warm rolling Chapter II Literature Review 44 showed a more favorable midplane recrystallization texture for deep drawability. Therefore, a cold rolled Ti-bearing IF steel sheet that is previously warm rolled under lubricated conditions to reduce the detrimental effect of the surface texture, and that is recrystallized after warm rolling, has a mean r-value which exceeds the values for 0.5-0.8 obtained from the same cold rolled steel sheet that was hot rolled in the y-region instead of in the oc-region. Chang105 compared the results of hot-direct rolling in the austenite region and in the ferrite region and found that an abnormal microstructure consisting of elongated coarse and mixed grains is obtained by hot direct rolling in the ferrite region. However, the abnormal grains left no traces in the annealed sheet after it is cold rolled to 75% and annealed at 830°c for 30 s. The mechanical properties of hot strip rolled in the ferrite region are inferior to those rolled in the austenite region. However, the properties are comparable after cold rolling and annealing. Yao 1 0 6 also concluded that the hot band microstructure has little effect on the mechanical properties of cold rolled and annealed steel sheets. Chapter II Literature Review 45 Figure II. 1. The 0-a curves at different temperatures for mild steel (from ref. ) Chapter II Literature Review 46 Grains Elongate Dislocation Ocnsity 1 Dislocation Ocnsity a Increases Subarains Devetoo • Constant Subarains Bmain j * v Equiaxed 1 ~ Canst. Mean Size Const. Mean Misori*ntn-1 1 i t Const. T Const. (a) STRAIN Original Grains Eton got* Dislocation Density Increases Poorly Formed Suboroins Develop Original Grqigs I Consumed • | Dynamic Recrystoltisation | Rex. Grains ~ Equiaxed . -» Const. Mean Size ' Heterogeneous I Substructure STRAIN Figure II.2 Form of stress-strain curves and microstructural changes during deformation at constant strain rate and temperature resulting from (a)work hardening and dynamic recovery only and (b) work hardening, slow dynamic recovery, and dynamic recrystallization. (from ref. 19) Chapter II Literature Review 47 compression at temperatures (a) from 1100 to 935°C and (b) from 935 to 800°C, with a strain rate of 0.1 s"1 (from ref46) Chapter II Literature Review 48 Recrystallization Time (Minutes) Figure II.4 Isothermal recrystallization of high-purity iron at various temperatures (from ref.47) i i • • 1 1 1 m i i i 1 1 1 1 n i i i 1 1 1 m i i i i I I i I I jmak. TcoH=565 C. Tanneal=70O C 10° 10' 10* 103 104 ilme (seconds) Figure II.5 JMAK plot for the series of IF steels coiled at 565°C, cold-rolled 75%, and isothermally annealed at 700°C (from ref.49) Chapter II Literature Review 49 Figure II. 6 Static softening curves of the IF steel in austenite range(from ref34) Chapter II Literature Review 50 Strain Figure II. 8 Flow curves for three steels tested in torsion at 900°C at a strain rate of 2 s (from ref52) Figure II.9 Torsion generated flow curves for a Ti-, a Nb-, and a Ti+Nb-IF steel rolled according to a strip roughing schedule (from ref.60) Chapter II Literature Review 51 Figure 11.10 Torsion generated finishing flow curves for: (a) Ti+Nb IF steel and (b) Nb IF steel rolled according to typical strip rolling schedule and with the first and last finishing pass temperatures of 930°C and 888°C, respectively (from ref.59) Figure II. 11 Torsion generated finishing flow curves for a hot/warm rolling schedule for a Ti IF steel (from ref31) Chapter II Literature Review 52 J Nb i NbC AIN MnS \ TiC TiS TiN J * L o w High — Starting temp, of precipitation Figure 11.12 Schematic illustration describing the starting temperatures precipitation of possible precipitates in Ti- and Nb-added IF steels (from ref.50) Process Figure II. 14 Formation of carbosulfide and carbide in IF steels (from ref28) Chapter 11 Literature Review 53 Figure 11.13 a) Typical TEM image of sandwich-like multi-phase particle in the 1220°C, 2min. re-heated condition; the outline shape of the particle is illustrated and b) Typical electron diffraction pattern showing the orientation relationship aTis||aH||atjs-rwin; cTis||cH||cTis-twin. (from ref.88) Chapter 11 Literature Review 54 Isoactivity line of Cin y IMC *(=» ^ A * ~—Q <CaseA> A — 0— <Case B> 0-Figure 11.15 Schematic composition changes and concentration profiles from the interface during precipitation of a typical MC-type stoichimetric compound on a simplified Fe-M-C ternary system, (from ref.90) 2J0 A0.OO4C B: * -0.11TI |- C: * -O.OSNb L D: * -0.04TL0.04Nb, I I 1.5 h 0 ^ Hot rolled at FET«700*te Annealed at 750°Cx3h 1 0 60 iob(%) <C>/<Ccr>or<Nb>/<Nbcr> Figure 11.16 Relationship between r-value and precipitation ratio of TiC or Nb(CN) which corresponds to solute carbon content, (from ref.100) 12 12 12 12 <C>=—<Ti>+—<Nb> (N - Nets AIN > < S > 18 93 14 32 Chapter III Objective 55 Chapter III Objective During the thermomechanical processing of steel in a conventional hot-strip mill or in a compact strip production line, the control of shape and gauge, and the concomitant changes in microstructure, are essential for producing quality as-rolled steel strip or providing good base material for manufacturing cold-rolled and annealed steel sheet with excellent formability. This control is, in turn, based on a better understanding of the flow stress behavior, restoration behavior, microstructure evolution, and precipitation behavior of steels during the processing. Extensive research has been done on recrystallization and texture formation during the annealing process after cold rolling of IF steels, because cold-rolled and annealed sheet steels find major applications in industry. However, very few studies have dealt with the deformation and microstructure evolution occurring during the hot and/or warm rolling of IF steels. Final rolling in the ferrite temperature range has recently been introduced to the hot strip mill; there is increasing interest in applying warm rolling in CSP technology. Thus, the objectives of this study are: (1) To measure and quantify the flow stress behavior of a Nb-rich Ti-Nb stabilized IF steel. (2) To study and model the static and dynamic restoration processes in two Ti-Nb stabilized IF steels. (3) To study the precipitation behavior and its effect on restoration behavior in two Ti-Nb stabilized IF steels. (4) To examine the ferrite (CSP) rolling behavior by using torsional rolling simulation based on the results of studies on flow stress, restoration and precipitation behavior. Chapter III Objective : 56 (5) To provide a guiding principle for producing a warm-rolled thinner IF steel strip or base material to be used for manufacturing cold-rolled and annealed IF steel sheet with excellent formability. Chapter IV Methodology 57 Chapter IV Methodology IV. 1 Materials The materials used in this study are two commercial Ti-Nb stabilized IF steels whose compositions are listed in Table IV. 1. Table IV. 1 Chemistry of Ti-Nb IF steels used in this study (wt%) Steels C Mn Si S P Al Cr Ni Nb-rich 0.0028 0.17 0.009 0.006 0.011 0.027 0.029 0.014 Nb-lean 0.002 0.106 0.010 0.008 0.010 0.033 0.019 0.010 Steels Ti Nb N Ti* Nb-rich 0.035 0.035 0.0029 0.007 Nb-lean 0.059 0.009 0.0041 0.021 Ti*=Titotai-3.42N-2(l .5S)=the Ti content available to tie up carbon. '' Both steels are typical ultra low carbon Ti-Nb stabilized steels, each with a carbon content 0.003%, and a nitrogen content <0.005%. Both steels will subsequently be referred to as IF steels in this thesis. The most significant difference between these two steels is their Nb content. The steel with 0.035%Nb will be referred to as the Nb-rich Ti-Nb IF steel and the one with 0.009%Nb will be referred to as the Nb-lean Ti-Nb IF steel. The materials obtained were in the form of a transfer bar with a thickness of about 30mm and were produced on commercial production mills. The Nb-rich Ti-Nb IF steel was manufactured by US Steel and the Nb-lean Ti-Nb IF steel was manufactured by LTV Steel Corporation. The microstructures of the transfer bar of both steels are shown in Figure IV. 1. Each consists of polygonal ferrite and some acicular ferrite. The ferrite grain sizes for the Nb-rich IF steel and Nb-lean IF steel are ~68pm and 78pm, respectively. Chapter IV Methodology 58 IV.2 Gleeble tests IV.2.1 Gleeble 1500 thermomechanical simulator The Gleeble 1500 thermomechanical simulator was used to perform instrumented hot compression and transformation tests. Figures IV.2a and IV.2b show schematic diagrams of the Gleeble jaws, anvil and specimen assembly for phase transformation tests and compression tests, respectively. The temperature of the specimen was controlled and monitored using an intrinsic chromel-alumel or platinum-platinum-rhodium thermocouple which was spot welded onto the surface of the specimen at mid-length. The specimen temperature was controlled by feedback temperature controlled resistive heating, which provided a rapid response for precise control of the specimen temperature during the test. For phase transformation tests, the electrical contact between the tubular specimen and the hollow anvils was provided by the spring (shown in Figure IV.2a). For compression tests, the electrical contact between the specimen and the deformation anvils was obtained initially by manually applying a small amount of axial compressive force at ambient temperature. Subsequent contact during the test cycle was carried out with aid of a pressurized air ram. The instantaneous diameter of the specimen was measured using a Linear Variable Differential Transducer (LVDT) that is attached to the central plane of the test sample. For compression tests, the displacement of the ram was also measured using another LVDT attached to the ram. The dilametral measurements were converted to cross-strain after correcting for the thermal expansion. This method was considered more accurate than the lengthwise strain obtained from the ram displacement measurement, since the latter presumes perfect translation of mechanical energy from the ram to the sample. For compression tests, the load on the ram (referred to as the standard load) and on the Chapter IV Methodology : ; 59 fixed anvil (referred to as the auxiliary load) were measured by a load cell at the end of the ram fixture and at the end of the fixed anvil, respectively. The true stress was computed by converting the measured diameter into area and dividing the auxiliary load by this area. The auxiliary load measurement was considered a more accurate measurement because the motion of the movable ram could lead to inaccuracies in the standard load measurement, due to the friction associated with the moving parts. To minimize oxidation during testing, the test chamber was evacuated to a pressure less than 3 millitorr, then back filled with high purity argon. After back filling with argon, the Gleeble machine parameters were re-zeroed. Subsequent controls were carried out by a pre-programmed computer schedule and the test data was acquired by the same computer. IV.2.3 Phase transformation temperature tests In order to determine the austenite-to-ferrite transformation temperatures of the IF steels, diametral dilatometric tests were performed on the Gleeble 1500 thermomechanical simulator using tubular specimens. The bulk samples were heated to 1200°C, held for 1 hour and quenched to water to dissolve the carbide and carbonitride precipitates before being machined to the tubular specimens. The purpose of this treatment was to standardize the thermal and mechanical history of the specimens without introducing decarburization in the tubular samples. The transformation tests involved stabilizing the tubular sample at the different austenite temperatures for 5mins, after which the specimens were cooled to 500°C by one of three cooling rates, i.e., 2°C/sec, air cooling, or 10°C/sec. During each test, the temperature and mid-plane diameter of the specimen was recorded as a function of time. Figure IV.3 shows a typical dilation measurement as a function of temperature for the Nb-rich Ti-Nb IF steel. At high temperatures, in the austenite region, the diameter of the specimen decreases approximately linearly with Chapter IV Methodology \ 60 decreasing temperature. The slope of the curve corresponds to the thermal contraction coefficient of austenite (fXy). During the austenite decomposition, the dilation curve shows an increase due to the increasing atomic volume of the ferrite.107 After the austenite decomposition reaction was completed, the diameter of the specimen again decreases linearly with temperature, reflecting the thermal contraction coefficient of ferrite (aa). The phase transformation start and finish temperatures are determined at the points where the diameter of the specimen deviates from the linear relationship. The measured phase transformation temperatures, Tstart (Ar3) and TfmiSh, as a function of cooling rate, for the Nb-rich IF steel are listed in Table IV.2 Table IV.2 Phase transformation temperatures for the Nb-rich IF steel Cooling rate 5mins@1200°C 5mins@1100°C 5mins@1000°C Tstart* °C T op 1 finish; Tstart* °C T op 1 finish* ^ Tstart) °C Tfinishj C Air cooling 856 801 864 770 868 803 10°C/sec. 864 789 866 788 874 813 2°C/sec. 868 816 879 829 882 835 IV.2.3 Axisymmetric compression tests Solid cylindrical specimens, 10mm diameterx 15mm length, were machined from the transfer bar and subjected to compression tests. The bulk samples were initially heated to 1200°C, held for 1 hour and quenched to water to dissolve the carbide and carbonitride precipitates before machining to the compression specimens. The purpose of this treatment was to standardize the thermal and mechanical history of the specimens without introducing decarburization into the cylindrical samples. The axisymmetric compression deformation was conducted using a Gleeble 1500 thermomechanical simulator. The specimens were separated from the Inconel anvils using tantalum sheet to prevent welding and to reduce friction. The combination of the specimen geometry and the use of the tantalum sheet was very effective in Chapter IV Methodology 6 1 decreasing friction and, hence, minimizing barreling effects during high temperature compression testing. The calculated standard deviations of peak flow stresses were 1.4MPa and 7.1 MPa in the austenite and ferrite region, respectively. A schematic diagram of the basic deformation simulation test is illustrated in Figure IV.4. Two series of tests have been carried out; one was under reheating conditions, the other under direct heating conditions. For the reheating condition, the specimen was reheated to 1200°C or 1000°C for 5 minutes and then cooled to the deformation temperature. Most of the specimens were deformed up to s=1.0 in the ferrite temperature region from 600°C to 850°C. The strain rate employed for the deformation tests was varied from 0.02 s"1 to 10 s"1. Some specimens were deformed in the austenite temperature region. For the direct heating condition, the specimen was reheated to the deformation temperature and held for 30 seconds, then deformed up to s= 1.0 in the ferrite temperature range. The strain rate was varied from 0.02 s"1 and 10 s"1. IV.2.4 Double-hit tests The softening taking place between each stand in a hot strip rolling operation can be simulated using double-hit, hot compression experiments conducted on the Gleeble 1500 thermomechanical simulator. Solid specimens, 15mm in length and 10mm in diameter, were employed for this purpose. The relevant thermomechanical schedule is illustrated schematically in Figure IV.5. The applied strain during the first hit of this test does not exceed the peak strain. Any softening occurring during the holding interval between the first and second hit was expected to be mainly due to static recovery and recrystallization. Considering that the yield strength at high temperature is a sensitive measurement of the microstructural state of the steel, the fractional softening, Fs, can be evaluated by the following expression: where a m is the flow stress at the end of the first stage of deformation, and ai and 02 are the yield stresses determined at an offset strain of 0.002 for the first and second stage of deformation, respectively. Several sets of laboratory double-hit experiments were designed to investigate the effects of deformation temperature, applied strain, and strain rate on the kinetics of recrystallization. The deformation temperature was in the ferrite region, i.e., from 600°C to 800°C. The strain for the first hit was 0.2 or 0.5; the high strain was employed only for the high strain rate (=ls"1) cases to avoid the occurrence of dynamic recrystallization. The strain rate employed for double hit tests was varied from 0.02 s"1 to 1 s"1. For each set of strain, strain rate and temperature test conditions, different holding intervals have been chosen based on the expected softening behavior for this condition. The softening fraction versus holding interval was plotted to describe the softening curves. The results have been analyzed using alternative relationships between to.5 vs s, logt.0.5 vs logs and to.5 vs y to interpret the recrystallization kinetics of the steels. IV.2.4 Microstructural observation for recrystallization To check the results of the double-hit tests, microstructural observations have also been carried out using special double-hit test conditions. Smaller solid cylindrical specimens, 6mm in length and 4mm in diameter, were employed in these tests. The selected double-hit thermal and mechanical test conditions for the first hit of the double-hit test were employed on the smaller specimen. Following the so-called 'first hit' deformation, the specimen was held for different times at the same temperature and then helium quenched to ambient temperature. The specimens Chapter IV Methodology : 63 were then cut in half along the longitudinal axis, the exposed surface being prepared for microstructure and precipitation examination. IV.3 Torsion tests IV.3.1 Torsion test apparatus, HTS 100 The HTS 100 is a newly designed hot torsion system capable of simulating high strain deformation. A schematic diagram showing the principle of the system is shown in Figure IV.6. On the left is the axially movable and rotational end. The axial movement permits the installation and removal of the specimen. Axial load and torque are measured by the axial load cell and the torque cell, respectively. In the center, the specimen is screwed into the stationary grips and is kept within an evacuated, back filled chamber. The optical encoder on the right hand end can be translated in order to control and measure the twist of the specimen. For the purpose of control and to enable data acquisition, this system is interfaced with a Dell Computer operating in a Windows environment. The torsion specimen had a 12.7mm reduced gauge length and a 10mm diameter. The thermocouple for furnace control was spot welded on the specimen surface at the mid-length of the gauge. Another thermocouple was spot welded on the specimen surface close to the left hand end of the reduced section; this thermocouple could be used to monitor the temperature gradient in the gauge range and to correct the temperature when the center thermocouple was broken off due to the high strain torsional twisting. A pyrometer is also installed to permit inspection of the surface temperature of the mid-length of the specimen. Both twist rate and angle of rotation can be programmed to simulate multi-stages of deformation. The resulting torque and twist can be converted to true stress and strain data. Chapter IV Methodology 64 To minimize oxidation during the experiment, the test chamber is evacuated to a pressure less than 100 millitor, then back filled with a protective gas, e.g., high purity argon or a 3% hydrogen+high purity argon mixture. This procedure is repeated before each test commences. IV.3.2 Single twist test Single twist testing was carried out on the torsion system to check the results of flow behavior that had been obtained by compression testing; the latter was limited to a maximum strain of 0.6. Machined specimens of the Nb-rich Ti-Nb IF steel were heated to 1200°C for 30 minutes and helium quenched to ambient temperature and then reheated to 1000°C for 5 minutes to duplicate that used in a compression test. After being reheated to 1000°C for 5 minutes, the specimen was cooled to 730°C and held for 30 seconds to homogenize the temperature across the transverse section. Then, the specimen was deformed to a high strain, s=4.9, at 1 s"1 and subsequently helium quenched to ambient temperature immediately after the deformation. IV.3.3 Ferrite (CSP) rolling simulation Ferrite (CSP) rolling simulations were performed on both the Nb-rich Ti-Nb IF steel and the Nb-lean Ti-Nb IF steel. For the Nb-rich Ti-Nb IF steel, two series of tests have been carried out. In the first series of tests, the specimens were reheated to 1200°C for 30 minutes and then directly cooled to a deformation temperature in the ferrite region. In the second series of tests, the specimens were reheated to 1200°C for 30 minutes and then cooled to 1085°C~925°C and subjected to a simulated austenite rolling deformation in this temperature range, prior to execution of the simulated ferrite rolling deformation. So, the initial ferrite grain size attained prior to the simulated ferrite rolling deformation for the first series of tests was larger than that obtained for the second series of tests. The simulated austenite rolling deformation and the simulated ferrite rolling deformation schedules are listed in Table IV.3 and Table IV.4, Chapter IV Methodology 65 respectively. For the Nb-lean Ti-Nb IF steel, the specimens were reheated to 1200°C for 30 minutes and then cooled to a temperature in the ferrite region and then subjected to the simulated ferrite rolling deformation in this temperature range. Thus, the results obtained for the Nb-lean Ti-Nb IF steel will be comparable to the case with the large initial ferrite grain size in the Nb-rich Ti-Nb IF steel. Table IV.3 Torsion rolling simulation schedules in the austenite region Fl F2 F3 F4 F5 F6 F7 reduction, % 44.4 33.2 30.3 24.7 18.7 15.2 10.4 s 0.67 0.47 0.42 0.33 0.24 0.19 0.13 At, sec. 2.87 1.97 1.37 1.02 0.82 0.82 s, s"1 1 1 1 1 1 1 1 CR=5°C/sec, Tro,iing=1085/925oC Table IV.4 Torsion ro ling simulal ion (CSP) schedules in t he ferrite region Fl F2 F3 F4 F5 F6 reduction, % 32.0 55.0 55.0 49.3 30.7 17.2 8 0.45 0.92 0.92 0.79 0.42 0.22 At, sec. 9.56 4.30 1.93 .96 .96 s, s"1 1 3 3 3 3 3 CR=3°C/sec; (TroiHng=850/800, 800/750, 75 0/700, 700/650°C) IV.4 Optical and SEM microstructure observations Specimens from the transfer bar, so-called 'first hit' tests, phase transformation tests and all torsion tests were prepared for microstructural examination. For the transfer bar (as-received material), the observation surface was parallel to the rolling direction. For the 'first hit' test samples, the tested samples were cut in half along the longitudinal direction and microstructural examination was performed in the center of the exposed face. For the torsion test specimens, the following three observation surfaces have been examined; the transverse surface, the longitudinal surface (exposed by cutting the specimens along the centre line) and the tangential surface (the Chapter IV Methodology 66 subsurface parallel to the torsion rotation direction). It was found that the tangential surface best represented the deformation microstructure evolution. As a result, all microstructural observations were performed on the tangential subsurface of the torsion test specimens. The microstructure specimens were set in cold-mount and then polished initially using 120, 180, 320, 600 and 800 grinding paper and finally 5 and 1pm diamond suspension polishing cloths. The newly polished specimens were etched in 5vol.% Nital for 30-60 seconds for the fully recrystallized samples. For the deformed or partially recrystallized samples, the newly polished specimens were etched in 5 vol.% Nital for 20-30 seconds and then etched in Marshal's reagent for 3-5 seconds. In general, it was necessary to repeat several times the 1pm polishing and the etching in Nital and Marshal's reagent with shorter etching times to obtain a satisfactory microstructure. The etched surfaces were recorded using optical and SEM microscopy. However, for most cases, the microstructure was better delineated using SEM procedures. This resulted from the fact that the etched surfaces were usually uneven because deep etching had to be applied to reveal the clean grain boundaries of the IF steels. IV.5 Carbon replica preparation and TEM observations The 'first hit' test specimen surfaces were examined using carbon replica techniques for revealing precipitation. The specimens were mounted and polished following the microstructure polishing schedule, but short polishing times were used to avoid the loss of particles. The newly polished surfaces were etched in 2 vol.% Nital for a few seconds and then a thin carbon layer was deposited on the sample surface. Chapter IV Methodology 67 The coated samples were then scratched with a sharp knife to remove the graphite coated layer away from the area of interest. The remaining coated layer was divided into several 2mm squares and then several drops of 5 vol.% Nital was applied onto the surface. The separation of the carbon replica from the sample surface was performed in distilled water. The separated carbon replicas were washed in ethanol and used for the TEM examination. The replicas thus produced were examined in a 'Hitachi H-800' scanning transmission electron microscope operated at an accelerating voltage of 100 kV. In addition to the images obtained at magnifications of from 2 k to 50 k, an EDX analysis was also performed on some of the precipitates. Using the above examination procedures, the precipitation behavior in the IF steels was examined. IV.6 Thin foil and TEM (including Kikuchi pattern) analyses The thin foils prepared for TEM investigation were prepared from the torsion rolling simulation test specimens. Thin sub-surface slides, that were parallel to the longitudinal direction, were cut from the torsion specimens using a slow speed diamond saw. Discs 3 mm in diameter were cut from the slides using electron discharge machining. These discs were mounted and mechanically thinned in small increments of 30-50um using a 'Gatan' disc grinder. Wet grinding was done alternatively on both surfaces until a final thickness of approximately ~60u,m was achieved with a surface finish of 600grit. The ground discs were then electropolished to perforation in a 'Struers Tenupol-2' jet polishing unit using an electrolyte of 5% perchloric acid and 95% glacial acetic acid (by volume) at a polishing current of 60-80mA (Potential of 70V) maintained at a cold water temperature of~12-15°C. Chapter IV Methodology ; 68 The thin foils thus produced were examined in a 'Hitachi H-800' scanning transmission electron microscope operated at an accelerating voltage of 100 or 200 kV. In addition to the images obtained at magnifications of from 5 k to 50 k, a limited number of Kikuchi patterns were also obtained for selected specimens. The Kikuchi patterns obtained were analyzed with the aid of Excel. The detailed analysis methodology is presented in the Appendix. Chapter IV Methodology 69 (a) Nb-rich steel (b) Nb-lean steel Figure IV. 1 Microstructures of as-received IF steels. Chapter IV Methodology 70 Specimen Spring Helium gas used to quench Cu electrical contacts Thermocouple Crosswise strain measurement Anvil Helium gas out Figure IV.2a Schematic diagram of the tubular transformation specimen support in the Gleeble test chamber. Stainless steel jaw Clamp Crosswise strain/ measurement \ Load cell Specimen Anvil Figure IV.2b Schematic diagram of the axisymmetric compression test geometry in the Gleeble test chamber. Chapter IV Methodology 71 0.037 -r 0.036 + 0.027 -I 1 1 — : 1 1 1 700 750 800 850 900 950 Temperature, °C Figure IV.3 Experimental dilation versus temperature measurements for the Nb-rich IF steel after reheating 5mins at 1200°C. The solid lines indicate the extrapolation from the pre- and post-transformation data. As Figure IV.4 Schematic thermomechanical schedules for axisymmetric compression tests. Chapter IV Methodology 72 Reheating 1st hit — w 2nd hit -A/V Holding Air cooling Time Figure IV.5 Schematic representation of the thermomechanical schedule employed for the double-hit testing. Axial Loadcell Torque Cell Pyrometer Optical Encoder for Twist Control and Measurement Thermocouples Type K or TypeS Axially Movable and Rotationally Fixed End Rotating End Figure IV.6 Schematic diagram of hot torsion system, HTS 100. Chapter V Flow stress behavior during compression testing and modeling 73 Chapter V Flow Stress Behavior during Compression Testing and Modeling This chapter deals with the flow stress behavior of the Nb-rich Ti-Nb IF steel. The axisymmetric compression tests were carried out on the Gleeble thermomechanical simulator to determine the flow stress curves for different deformation conditions of the Nb-rich Ti-Nb IF steel. The measured flow stress curves were compared with calculated curves based on constitutive equations. The activation energies for deformation in austenite and in ferrite were calculated from the measured data. The critical conditions for the transition from dynamic recovery to dynamic recrystallization were determined. The constitutive equations were derived from dislocation theory. V . 1 Flow stress curves in the austenite region The phase transformation temperature tests showed that the Ar3 for the Nb-rich Ti-Nb IF steel was 882°C for a 2°C/sec. cooling rate. To avoid the occurrence of strain induced transformation, the austenite was deformed in the temperature range from 950°C to 1200°C. V . l . l Effects of deformation temperature on the flow stress Flow stress versus strain curves for the Nb-rich Ti-Nb IF steel deformed at Is"1 for different temperatures are presented in Figure V.L Prior to deformation, the specimens were reheated to 1200°C for 5 minutes and cooled to the deformation temperature at 10°C/s. As shown in the figure, the flow stresses increase with decreasing temperature. When the temperature is below 1000°C, the flow stress increases with increasing strain. When the deformation temperature is at 1050°C, the flow stress reaches a steady state. When the deformation temperature is 1100°C and 1150°C, a peak stress is attained, after which the flow Chapter V Flow stress behavior during compression testing and modeling 74 stress decreases with increasing strain. When the deformation temperature is at 1200°C, the flow stress reaches a peak, decreases and then reaches another steady state where the flow stresses flatten out. It should be pointed out that the temperature on the specimen's surface didn't increase during the deformation because of the high heat loss in this temperature range. Thus, it is assumed that the decreasing stress resulted only from dynamic recrystallization. Flow stress versus strain curves for the Nb-rich Ti-Nb IF steel deformed at 0.1/sec. for different temperatures are presented in Figure V.2. The reheating conditions were the same as those used in Figure V . l . Again, the flow stress increased with decreasing temperature. Compared with the flow stress curves in Figure V . l , the strain at peak stress was attained earlier than that deformed at 1/sec. When the temperature was below 950°C, the flow stress reached a steady value with no further increase with increasing strain. . Figure V.3 shows the results from Figure V. l and V.2 plotted as ln(sinh(ao"p)) versus 1/T. For both strain rates, a linear relationship fits very well, which suggests that the deformation activation energy, Qdef,. for the Nb-rich Ti-Nb IF steel is constant for different strain rates. From this figure, the value of Qd e f . for the Nb-rich Ti-Nb IF steel deformed in the austenite region was calculated to be 302kJ/mole. V. 1.2 Effect of strain rate on flow stress The effect of strain rate on flow stress was found at three different temperatures, i.e., 1150°C, 1050°C, and 950°C. The reheating condition for these tests was the same as that used in Figure V . l . The test results for the three temperatures are shown in Figure V.4, V.5, and V.6. At 1150°C (Figure V.4), the flow stress curves exhibit dynamic recrystallization behavior for strain rates of 0.1s"1 and Is"1 At 1050°C (Figure V.5), the flow stress curves exhibit dynamic recrystallization when the deformation strain rate is lower than 0.1s"1, and exhibit dynamic Chapter V Flow stress behavior during compression testing and modeling ; 75 recovery when the deformation strain rate is above Is"1. At 950°C (Figure V.6), the flow stress curves exhibit dynamic recovery behavior for strain rates of 0.1s"1 and Is"1. Figure V.7 shows the Figure V.4, V.5 and V.6 data plotted as ln(sinh(ao~p)) vs. Ine for the Nb-rich Ti-Nb IF steel. At 1050°C, the linear relationship is followed; the slopes at the other two temperatures are similar to that obtained at 1050°C. This result indicates that the n value in equation (II.3) is a constant for the temperature range studied. V.1.3 Effect of reheating conditions on the flow stress Different reheating conditions result in different initial austenite grain sizes prior to deformation. Figure V.8 shows the effect of reheating temperature on the flow stress behavior. The specimens were reheated to either 1100 or 1200°C for 5minutes and then cooled to 1050°C and held for 30 seconds prior to deforming at Is"1 to E=1.0. The lower reheating temperature gives a higher flow stress due to the smaller initial austenite grain size. However, the material with the lower reheating temperature attains a peak stress and starts to soften earlier than the sample experiencing the higher reheating temperature. In austenite, dynamic recrystallization originates at high angle grain boundaries and bulging of grain boundaries is observed as a prelude to dynamic recrystallization. Smaller initial austenite grain sizes offer more nucleation sites for dynamic recrystallization of the deforming material and the material softens earlier. V.2 Flow stress curves in the ferrite region The typical deformation temperature range for ferrite rolling is from 600°C to 800°C and was applied to investigate the flow behavior of IF steels in this study. The experiments in the ferrite region were divided into two series. In the first series, the specimens machined from the solution treated bars were reheated to different reheat conditions, cooled to the deformation Chapter V Flow stress behavior during compression testing and modeling 76 temperature, held for 30 seconds, and deformed at different strain rates. In the second series, the specimens machined from the solution treated bars were directly reheated to the deformation temperature and held for 30 seconds, followed by deformation at different strain rates. V.2.1 Effect of deformation temperature on the flow stress Figure V.9 shows the true stress-strain curves of the Nb-rich Ti-Nb IF steel compressed at a strain rate of 1/sec. in the temperature range from 600°C to 800°C; the materials were initially reheated to 1200°C for 5minut.es and cooled to the deformation temperature at 10°C/sec. To homogenize the specimens, they were held at the deformation temperature for 30 seconds prior to deformation. The flow stress decreased with increasing deformation temperature and all curves exhibited typical dynamic recovery behavior without any significant flow stress decrease once the steady state stresses were attained. Figure V.10 shows the true stress-strain curves of the Nb-rich Ti-Nb IF steel compressed at a strain rate of 1/sec. in the temperature range from 600°C to 800°C; the test samples were initially directly reheated to the deformation temperature and held for 30seconds. The flow stresses obtained for this condition were higher than those found under reheating conditions (40~50MPa in the range of 600~650°C, 10~20MPa in the range o f 700~800°C). When the deformation temperature was higher than 750°C, the flow stress curves exhibited a peak followed by a small decrease in flow stress. Recorded sample temperatures indicated that deformation heating contributed to the post peak softening when the deformation temperature was below 750°C. At 800°C, no significant temperature increase was recorded during the deformation. So, the post peak softening at 800°C doesn't result from temperature increase, but may result from dynamic recrystallization. Chapter V Flow stress behavior during compression testing and modeling 77 Figure V . l l shows the relationship of ln(sinh(aap)) versus 1/T using data from Figures V.9 and V.10 for the Nb-rich Ti-Nb IF steel for different reheating conditions. The value of Qdef. calculated from the figure for the Nb-rich Ti-Nb IF steel deformed in the ferrite region is 241kJ/mole for the reheating condition and 246kJ/mole for the direct heating condition. The difference in the calculated value is small and both values are lower than that of the steel in the austenite region. The deformation activation energy is closely related to the self-diffusion activation energy. The small difference in Qdef. in the ferrite region is thought to originate from the different initial ferrite grain size and the different solute Nb content in the matrix due to the different reheating conditions. The large difference in Qdef. for the austenite and the ferrite regions results from the different crystal structures. The self-diffusion activation energy of pure iron in the ferrite region (bcc) is 239kJ/mole; it compares favorably with the measured 241 and 246 kJ/mole obtained for the Nb-rich Ti-Nb IF steel. This value is lower than the self diffusion activation energy of 284kJ7mole in the austenite region (fee), which compares reasonably to the measured 302 kJ/mole for the Nb-rich Ti-Nb IF steel.108 V.2.2 Effect of strain rate on flow stress Figure V.12 shows the true stress-strain curves for the Nb-rich Ti-Nb IF steel compressed at 700°C at various strain rates after the samples were initially reheated to 1000°C for 5minutes and cooled to the deformation temperatures at 10°C/s. To homogenize the specimens, they were held at the deformation temperature for 30 seconds prior to deformation. The flow stress increased with increasing strain rate and reached a steady state stress at strain rates from 0.1s"1 to 10s"1. When the strain rate was lower than 0.02s"1, the flow stress curve reached a peak stress and then decreased with increasing strain. At this low strain rate, no deformation heating was observed. This suggests that dynamic recrystallization is present besides dynamic recovery. Chapter V Flow stress behavior during compression testing and modeling ; 78 Figure V.13 shows the true stress-strain curves of the Nb-rich Ti-Nb IF steel compressed at 700°C at various strain rates after the samples were reheated to the deformation temperature and held for 30 seconds. The flow stress increased with increasing strain rate and reached a steady state after a very small strain increment. When the strain rate was lower than 0.1s"1, the flow stress curves reached a peak stress and then decreased with increasing strain. Again, no evidence of deformation heating was measured and the softening mechanism may again result from dynamic recrystallization. Figure V.14 shows the relationship between the peak flow stress and strain rate for the Nb-rich Ti-Nb IF steel compressed at 700°C. The peak stress increased as the strain rate increased. Generally speaking, the peak stress under direct heating conditions was higher than that obtained under reheating and cooling conditions. The non-linear relationship between the ln(sinhaa) and Ins suggests that the restoration mechanisms are different for low and high strain rates. At a high strain rate, dynamic recovery was the only restoration process, and both dynamic recovery and dynamic recrystallization may have played a role in the restoration process at low strain rates. V.2.3 Effect of reheating conditions on flow stress Three reheating conditions were applied for investigating this effect. Figure V. 15 shows that the effect of the reheating condition on the peak stress at the higher deformation temperatures was small; the reheating effect became more significant with decreasing deformation temperature. At higher temperatures, dynamic restoration took place readily and the effect of the initial microstructural state, prior to deformation, diminishes with the combined effect of deforming and softening. It can be inferred from these results that the variations in the initial strip condition don't affect the rolling forces during ferrite rolling, when the rolling 79 Chapter V Flow stress behavior during compression testing and modeling temperature is high enough. This is important for IF steels, because IF steel is characterized by a high Ar3 and therefore the ferrite rolling can be carried out at high temperatures. V.3 Modeling and Discussion The deformation of metals at elevated temperatures shows work hardening to a peak stress, after which there is either a monotonic decrease in stress to a steady state stress or there is a cyclic stress behavior; the latter also settles down to a steady state value at large strains. In general, the multi-peak behavior occurs under slow strain rate and high temperature conditions, whereas, the single peak behavior is observed for most forming/working conditions. The most widely used criterion for determining single peak behavior is: 1 7 ' 1 0 9 D0>2DSS (V.l) where D 0 is the initial grain size (pm) and D s s is the steady state grain size (pm). Current flow stress curves and microstructure observations satisfy the above criteria.1 All flow stress curves exhibiting a peak reached a steady state without cyclic behavior because the initial grain size was much larger than those obtained after deformation. The flow curves suggest that dynamic recovery is dominant during axisymmetric compression deformation. The flow stress response arises from the combined effects of work hardening and dynamic recovery. The evolution of the dislocation density with strain is generally considered to depend on two components: ' ' dp dp de de storage dp de (V.2) recovery The slope of the stress versus plastic strain curves determined at a constant strain rate and 1 The initial ferrite grain size, D 0, was measured ~80um and the steady state grain sizes, D s s , were estimated <10um. Chapter V Flow stress behavior during compression testing and modeling 80 temperature correspond to the work-hardening rate, 0; i.e., da 0 = de (V.3) Figures V.l6 a, b shows the relationship between the work-hardening rate and the stress for the Nb-rich Ti-Nb IF steel deformed in austenite and ferrite, respectively. The initial values of the work-hardening rate are high and decrease rapidly with increasing stress. Examining the curves in terms of the dependence of the work-hardening rate on stress, as proposed by Kocks (a linear 0-cr relation) and by Roberts (a 0-1 fa dependence relation), it is assumed that the work-hardening law has the following form: 0 - — - Ba (V.4a) a Phenomenologically, the linear 0-cr relation is consistent with an equation of the form, ^- = (kxJp~-k2p)lb (WAV) de and the 0-1 fa dependence relation is consistent with an equation of the form, ^f = kR,-kR1Jp~ (V.4c) de In a similar way, equation (V.4a) can be interpreted in terms of the following equation: ^- = h-rp (V.5) de where h and r represent the work hardening and softening terms, respectively. For the material with precipitates and a fine grain size, the mean free path of the dislocations is a geometrically imposed constant, and the dislocation storage rate is assumed to be a constant. For the second term, it is assumed that dynamic recovery follows first-order kinetics. So, h and r in equation (V.5) are considered as constants. The integration of equation (V.5) gives: Chapter V Flow stress behavior during compression testing and modeling 81. p=p0e-rE+(h/r)(l-e-rE) (V.6) where p0 is the initial dislocation density. At high temperatures, the effective stress is negligible compared to the internal stress, so that the applied stress can be related directly to the square root of the dislocation density; i.e.: rj=aMGbp1/2 (V.7) where a is a constant, M is the Taylor factor, G is the shear modulus, and b is the Burger vector. Combining equation (V.6) and (V.7), the flow stress in terms of the strain can be given by the following expressions: a=[aoers+(aMGb)2(h/r)(l-erE)]I/2 (V.8) or a=[a02+(as2-a02)(l-e-rE)]1/2 (V.9) where the initial stress, a0, and the saturation stress, as, are ctMGbp01/2 and aMGb(h/r)1/2, respectively. When dynamic recrystallization contributes to softening, the kinetics of dynamic recrystallization can be represented by an Avrami equation. For this purpose, it is assumed that the mechanical softening is directly proportional to the recrystallized volume fraction. That is: tr, -cr — = X (V.10) By using the time for 50% recrystallization, to.5, equation (V.10) can be rewritten as follows: a=as-(as-ass)[l-exp(-0.693 • (—)k)] (V.l 1) ^0.5 Chapter V Flow stress behavior during compression testing and modeling 82 where G s s is the steady-state stress after dynamic recrystallization has progressed through the material, k is a constant associated with the nucleation mechanism and to.s is determined by the strain difference between the strain at the peak stress, CTs, and the strain that the flow stress reaches a s s. To correlate the flow stress and strain rate at constant temperature, the following equation has been proposed by several authors:24"25'30"32'38 e =A(sinh oca)" (V.12) The above equation can be extended to cover a range of temperatures and still follows the hyperbolic law: A(sinh aa)"= s exp(-^-) =Z (V. 13) RT where A, a, n, R are constants and Z is the Zener-Hollomon parameter. The calculated values for the constants in the hyperbolic law are listed in Table V . l . The apeak was used to calculate the deformation activation energy, Qdef, because it provided an upper bound for industrial application. The lower Qdef found for the ferrite region not only conforms to the relationship with self-diffusion, as discussed in the previous section, but also suggests that the thermally activated deformation mechanism occurs more easily in the ferrite region. The calculated a and n values in the austenite region and in the ferrite region for reheating specimens to 1200°C, holding for 5 minutes and cooling to the deformation temperature are close to values (n«5.0 and a«0.0T25) reported for low carbon steels.110 However, the calculated a value is higher and the n value is smaller for the direct heating condition (Table V.l) and further work is needed. With the constants shown in Table V. l and the measured flow stress curves for Chapter V Flow stress behavior during compression testing and modeling 83 deformation in the austenite region, the transition Z value for dynamic recovery to dynamic recrystallization can be calculated. The value obtained is 8.23-10ns-1. Table V. 1 Values for constants in the hyperbolic sine law Austenite Ferrite* Ferrite** A= 1.49E+11 8.86E+10 8.87E+10 n= 4.64 4.73 2.49 Q(kJ) 302+0.9 241±3.2 246±2.6 a= 0.0125 0.0125 0.0170 * Reheating condition: 1200°C for 5mins, then cooling to the deformation temperature. **Direct heating condition: direct heating to the deformation temperature Examples of the predicted flow stress curves, based on the above equations, are compared in Figure V.l7a and V.l7b with the experimental measurements for the Nb-rich Ti-Nb IF steel for deformation both in the austenite and in the ferrite regions. The parameters a0, as, and r in equation (V.9) were obtained by curve fitting. The predicted curves provide good fit to the measured ones over the temperature range examined. In the ferrite region, the predicted stress is higher than the measured value in the medium strain range; the prediction before the peak is based on dynamic recovery only, which suggests that another softening process, other than dynamic recovery, is present. V.4 Summary Axisymmetric compression tests were carried out using the Gleeble thermomechanical simulator to determine the flow stress curves at different deformation conditions for the Nb-rich Ti-Nb IF steel. The principal conclusions drawn are as follows: Chapter V Flow stress behavior during compression testing and modeling 84 (1) Both dynamic recrystallization and dynamic recovery contributed to the softening exhibited by the flow stress curves in the austenite region. The dynamic recrystallization kinetics could be predicted using the Avrami equation. (2) Dynamic recovery was the dominant softening mechanism for axisymmetric compression deformation in the ferrite region. (3) The deformation activation energies calculated were 302kJ/mole and ~240kJ/mole for deformation in the austenite and in the ferrite regions, respectively. The measured values of the deformation activation energy are similar to the self-diffusion energies and it confirms that there is a close relationship between thermally activated deformation and self-diffusion processes. (4) The Zener-Hollomon value, Z, the temperature compensated strain rate, for the transition from dynamic recovery to dynamic recrystallization was determined as 8.23-10us"! in the austenite region for the Nb-rich Ti-Nb IF steel. (5) The constitutive equations derived from dislocation theory agreed well with the measured curves. The experimental results also suggested that other softening mechanisms besides dynamic recovery contributed to the flow stress curve behavior for deformation in the ferrite region, even though dynamic recovery was the dominant softening mechanism. Chapter V Flow stress behavior during compression testing and modeling 85 140 • 950°C • 1000°C A1050°C o1100°C x1150°C • 1200°C 0.1 0.2 0.3 Strain 0.4 0.5 0.6 Figure V. l Flow stress versus strain curves obtained at Is" for different deformation temperatures. 120 100 ^ffaasataaui wuwuu »—| Figure V.2 Flow stress vs strain curves deformed at 0.1s"1 for different temperatures. Chapter V Flow stress behavior during compression testing and modeling 86 «?• 1.6 B -2. 1.2 -0.4 0.6 0.65 0.7 0.75 1000/T 0.8 0.85 0.9 Figure V.3 ln(sinh(arjp)) versus 1/T for the Nb-rich IF steel. Figure V.4 Flow stress curves obtained at 1150 °C for different strain rates for the Nb-rich IF steel. Chapter V Flow stress behavior during compression testing and modeling 87 160 140 120 100 oj 80 oio/sec. o 1/sec. • 0.1/sec. A0.05/sec. Figure V.5 Flow stress curves obtained at 1050 °C for different strain rates for the Nb-rich Ti-Nb IF steel. 160 Figure V.6 Flow stress curves obtained at 950 °C for different strain rates for the Nb-rich IF steel. Chapter V Flow stress behavior during compression testing and modeling 88 -0.6 -3 -1 0 ln(strain rate) Figure V.7 ln(sinh(aap)) versus ln(strain rate) for the Nb-rich IF steel. 120 -i Chapter V Flow-stress behavior during compression testing and modeling 89 250 -r 200 S. 150 I 100 « © o o o o o • ' o o o o o o o o o o o o o o o o o o o o o o o x X X X x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O600 °c • 650 °C A 700 °C X750 °C O800 "C 0.1 0.2 0.3 Strain 0.4 0.5 0.6 Figure V.9 Flow stress curves for the Nb-rich IF steel compressed at a strain rate of Is"1 after the specimens were reheated to 1200°C for 5 minutes and cooled to the deformation temperatures at 10°C/s. 300 250 200 j> 150 +, m (3 o 0 e o ° ° 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • • a • ° • • • • • • o D a D D a D D D D D D a D a D D D o ° n o D Q Q D r j o o o A A A A A r faT^po o ° 0 ° o o o o o o o o o o o A A A A A A A A A A A A A A A A A A A A A A A A A A A A 50 x X x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x o o o o o o o o o o o o o o o o O600 °C • 650 °C A 700 °C X750 °C O800 °C 0.1 0.2 0.3 Strain 0.4 0.5 0.6 Figure V.10 Flow stress curves for the Nb-rich IF steel compressed at a strain rate of Is"1 after the specimens were reheated to the deformation temperatures and held for 30seconds. Chapter V Flow stress behavior during compression testing and modeling 90 reheating direct heating 2.5 b a ~£ 1.5 0.5 0.9 0.95 1.05 1000/T 1.1 1.15 1.2 Figure V. 11 Relationship between ln(sinh(aap)) versus 1/T for the Nb-rich IF steel deformed in the ferrite region. CD CL 160 140 120 100 g 80 I 60 LL 40 -fr 20 0 • • q Hi "k * * i A 4 A » Q O ° o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o • 10/sec. o 1/sec. »0.1/sec. o 0.02/sec. 0.1 0.2 0.3 Strain 0.4 0.5 0.6 Figure V.12 Flow stress curves of the Nb-rich IF steel compressed at 700°C at various strain rates after reheating to 1000°C for 5minutes and cooled to the deformation temperature at 10°C/s. Chapter V Flow stress behavior during compression testing and modeling 91 200 180 160 140 120 r ^ -I 100 t-tn S 80 60 i 40 20 0 ° o o O 0 O O a Q O Q n ° o o O O o o o o o o o o o o <> 10/sec. ° 1/sec. A 0.1/sec. o 0.02/sec. 0.1 0.2 0.3 Strain 0.4 0.5 0.6 Figure V.l3 Flow stress curves for the Nb-rich IF steel compressed at 700°C at various strain rates under direct reheating conditions. 1.8 1.6 1.4 1.2 c •2- 0.8 0.6 0.4 0.2 -2 -1 0 ln(strain rate) - • — Direct heating o - Reheated Figure V.l4 The relationship between ln(sinh(aap)) and ln(strain rate) for the Nb-rich IF steel. Chapter V Flow stress behavior during compression testing and modeling 92 • Q+H SQ+A+C1 • Q+A+C2 800°C 700°C 600°C Figure V. 15 Relationship between peak stress and reheating condition. Q+Ff=direct reheating; Q+A+Cl=austenizing 1000°C for 5min & cooling @10°C/sec; Q+A+C2=austenizing 1000°C for 5min & cooling @2°C/sec. Chapter V Flow stress behavior during compression testing and modeling 93 0 " 2 0 4 0 6 0 80 100 120 140 CT, MPa Figure V.l6a Relationship between the work-hardening rate and stress for the Nb-rich IF steel deformed in the austenite region. 0 50 100 150 200 250 300 CT, MPa Figure V.l6b Relationship between the work-hardening rate and the stress for the Nb-rich IF steel deformed in the ferrite region. Chapter V Flow stress behavior during compression testing and modeling 94 140 120 100 £ 60 40 20 0.1 0.2 • 10/sec. measered 10/sec. predicted • 1/sec. measured 1/sec. predicted 0.1/sec. measured - - - 0.1/sec. predicted o 0.05/sec. measured — - 0.05/sec. predicted 0.3 0.4 0.5 0.6 Strain Figure V.l7a Comparison of predicted and measured flow curves for the Nb-rich IF steel deformed at 1050°C. 250 • 600°C measured -600°C predicted o 700°C mesured 700°C predicted a 800°C measured - - - 800°C predicted 0.2 0.3 Strain 0.4 0.5 0.6 Figure V.l7b Comparison of predicted and measured flow curves for the Nb-rich IF steel deformed in the ferrite region. Chapter VI Restoration Behavior 95 Chapter VI Static Restoration Behavior The major aim of this part of the research work is to study the static restoration behavior of the two IF steels included in this study. Double-hit tests were carried out to determine the softening fraction for different holding times. Static recovery and recrystallization kinetics are presented by analyzing the double-hit test data. The effects of strain, strain rate and temperature on the static restoration kinetics are discussed. Microstructure observations were performed on selected cases to check the double-hit test results and to help to understand the restoration mechanisms. It was found that static recovery played a very important role in the softening process of the IF steel after deformation in the ferrite region. The static recrystallization progressed slowly in the ferrite temperature range, especially at lower temperatures. VI. 1 Double-hit test results The fractional softening, Fs, shown in expression (IV. 1) is a measurement of the combined effects of static recovery and recrystallization. According to Perdrix , translating an initial stress-strain curve onto the second deformation curve, as shown by the dotted line in Figure VI. 1, to make it coincide with the stress-strain curve of the second deformation, defines a new stress value, an, which can be employed to determine the extent of restoration excluding static recovery. This method, which is termed the back-extrapolation method, gives a static restoration index, Fx, defined as follows: (VI.l) a —a m Chapter VI Restoration Behavior 96 where rjm is the flow stress at the end of the first stage of deformation, CTI is the yield stress determined at an offset strain of 0.002 for the first deformation, and o"n is the back-extrapolation yield stress determined as shown in Figure VI. 1. Comparison of F s and F x provides a measurement on the softening fraction attributed to static recovery. The relationship of F x and F s is defined as follows: F = F v " Fr (VI.2) * \-Fr where F r is the recovery softening fraction. The computed softening fraction obtained from current tests indicated that recovery played an important role in the restoration process of the IF steels studied. This static recovery followed dynamic recovery that had occurred during deformation. For plain carbon steels, recrystallization in the austenite is found to start at a softening ratio, F s, of -20%. In the present study, the softening fraction of the Nb-rich Ti-Nb IF steel due to static recovery was -35% in the austenite region and -40% in the ferrite region. VI. 1.1 Double-hit test results for the Nb-rich Ti-Nb IF steel Figure VI.2 shows the relationship between F x and inter-hit time for the Nb-rich Ti-Nb IF steel deformed in the austenite region. Prior to the double-hit deformations, the specimens were reheated to 1200°C and held for 5 minutes, then cooled to the desired deformation temperature and held for 30 seconds to homogenize the temperature. The strain during the first hit was 0.2 with a strain rate of Is"1. At higher temperatures (1150°C, 1050°C), the material recrystallized rapidly and reached full recrystallization in -10 seconds. At lower temperature (950°C), recrystallization progressed slowly in the beginning and then rapidly in the later stage. The slow recrystallization progress in the early stage might have resulted from the interaction between recrystallization and precipitation, which will be discussed in chapter 7. Chapter VI Restoration Behavior 97 Figure VI.3 shows the relationship between F x and inter-hit time for the Nb-rich Ti-Nb IF steel deformed in the ferrite region. The reheating conditions for this series of tests involved holding at 1000°C for 5minutes, then cooling to the desired deformation temperature and holding for 30 seconds. The strain during the first hit was 0.2 with a strain rate of Is"1. Generally speaking, the recrystallization process was slower in the ferrite region compared to that in the austenite region. The recrystallization kinetics increased slightly with increasing temperature for the temperature range studied for the Nb-rich Ti-Nb IF steel. The recrystallization kinetics obtained at each double-hit test condition could be characterized in terms of the JMAK equation and/or the S-F (Speich and Fisher) equation,40 X = 1 - exp(-bt") (JMAK equation) (VI.3) = ktm (S-F equation) (VI.4) 1 — X where X is the recrystallization fraction, b and k are temperature dependent constants, and n and m are constants related to the nucleation mechanism. Figure VI.4 shows a comparison of the JMAK and the S-F kinetics characterization for the Nb-rich Ti-Nb IF steel for the testing conditions shown in Figure VI.3. The linear relationship was well maintained, confirming that the recrystallization kinetics could be depicted by both the JMAK and the S-F equations: the n and m values were independent of the test temperature. This further indicates that the Perdrix calculation method is valid in representing the recrystallization fraction. In the remaining part of this thesis, the JMAK equation will be used to quantify the recrystallization kinetics. Figure VI.5 shows the recrystallization kinetics plotted as ln(ln(l/(l-Fx))) versus Int for the Nb-rich Ti-Nb steel deformed at 700°C with different strain rates. The strain during the first hit was 0.2. The recrystallization rate decreased significantly with decreasing strain rate, which could result because the slower strain rate permitted more dynamic recovery before Chapter VI Restoration Behavior 98 recrystallization was initiated. The lower stored deformation energy in the dynamically recovered structures reduced the driving force both for recrystallization nucleation and for grain growth. VI. 1.2 Double-hit test results for the Nb-lean Ti-Nb IF steel It is well known that Nb has a strong effect on the y-»a transformation in low-alloy steels. Small Nb additions retard ferrite formation. This is surprising since Nb is a ferrite stabilizer, i.e., the ^temperature increases as Nb is added. This apparent contradiction is explained by the fact that Nb affects the growth rate of ferrite, although the detailed mechanism is still not known. However, it seems reasonable to believe that the effect is caused by solute drag of Nb. 1 1 1 The fact that solute Nb increases the recrystallization temperature of cold-rolled ultra low carbon steel is well known and studied. However, the effect of solute Nb on the recrystallization behavior in the ferrite region during warm rolling remains unreported. Figure VI.6 shows the recrystallization kinetics plotted as ln(ln(l/(l-Fx))) versus Int for the Nb-lean Ti-Nb IF steel deformed in the ferrite region. The reheating conditions for this series of tests involved holding at 1200°C for 5minutes, then cooling to the desired deformation temperature and holding for 30seconds. The strain during the first hit was 0.2 with a strain rate of Is"1. Generally speaking, the recrystallization rate was much faster than that found in the Nb-rich Ti-Nb IF steel under the same testing conditions. The recrystallization rate increased with increasing temperature. Figure VI.7 shows the recrystallization kinetics plotted as ln(ln(l/(l-Fx))) versus Int for the Nb-lean Ti-Nb IF steel deformed at almost the same test conditions, except using a different first hit strain=0.5. The recrystallization behavior was similar to that obtained using a first hit strain=0.2. This is uncommon, as recrystallization rate generally increases with increasing retained strain. This will be discussed in more detail in the next section. Chapter VI Restoration Behavior 99 Figure VI.8 shows the recrystallization kinetics plotted as ln(ln(l/(l-Fx))) versus Int the Nb-lean steel deformed at 700°C for two different strain rates. The first hit strain was 0.5. The strain rate did not have a strong effect on the recrystallization behavior, which could result because both materials had a more dynamically recovered structure due to the high strain before recrystallization was initiated. In addition, the reduced solute Nb content in the Nb-lean steel would also encourage recovery. VI.2 Microstructure observations To check the results of the double-hit tests, microstructural examination was carried out using selected double-hit test conditions on smaller specimens and quenching the specimens after the 'first hit' and after different holding times. These so called 'first hit' test results indicated that recrystallization progressed very slowly in the ferrite region, especially for the Nb-rich Ti-Nb IF steel. Significant recrystallization occurred only at higher temperatures (>800°C) and/or longer holding times (annealing in furnace for 3—25 hrs) for both the Nb-rich and the Nb-lean Ti-Nb IF steels. Figure VI.9 shows microstructures obtained after a 'first hit' test on the Nb-rich Ti-Nb IF steel at a strain rate of Is"1 to s=0.2 at 700°C for different holding times. After holding for 100 seconds, a few smaller recrystallization islands can been seen in the deformed microstructure. The recrystallization fraction obtained was ~5% and was lower than the 16.7% obtained in the double hit test. After holding for 1000 seconds, the recrystallization fraction increased to -20%, similar to the 26.6% obtained in the double hit test. Hardness tests on the quenched specimens indicated that the hardness decreased significantly, even though no recrystallization structure was found in the quenched specimen. This result confirms that static recovery plays an important role during inter-hit time, this simulating the inter-pass time during the ferrite rolling. A fully Chapter VI Restoration Behavior 100 recrystallized structure was obtained after annealing the specimens for 25 hrs in a furnace at 700°C. Figure VI. 10 shows the microstructures obtained after a 'first hit' test on the Nb-lean Ti-Nb IF steel at a strain rate of Is"1 to 6=0.2 at 800°C for two different holding times. After holding for 100 seconds, significant recrystallization occurred in the quenched microstructure and complete recrystallization was obtained after holding the specimen for 600 seconds. These results are consistent with double hit test results using the same test conditions. Figure VI. 11 shows the microstructures obtained after a 'first hit' test on the Nb-lean Ti-Nb IF steel at a strain rate of Is"1 to 8=0.5 at 700°C for four different holding times. The material did not recrystallize before holding 100 seconds. The recrystallization fraction for holding times of 1000 seconds and 3 hrs was -40% and -65%, respectively; this is similar to the double hit test results. In general, the recrystallized fraction calculated using Perdrix's method was similar to the recrystallized fraction obtained by microstructure observation; this provided justification that the results using Perdrix method could be used to quantify the recrystallization kinetics. VI.3 Discussion The static restoration processes in deformed material are thermally activated diffusion processes that are dependent on holding temperature, time and initial microstructural state. This initial state, in turn, is dependent on the deformation temperature, strain, strain rate, and initial structure before deformation. By using the time for 50% static recrystallization, to.5, a general equation presenting the effects of deformation temperature, strain, strain rate and initial state can be written as follows: 2 6 ' 3 7 ' 5 5 ' 6 7 ' 1 1 2 ; 0 , = / , ^ H / j e x p ( / 5 - % (VI.5) Chapter VI Restoration Behavior 101 where fi, f2, f?, f4, fs are exponents, d0 is the initial grain size before deformation, and Q s t is the static recrystallization activation energy. This equation has been widely used to model the C-Mn steels and high strength low alloyed steels by determining the exponents and Qst. For most steels, the coefficients are constants and Q s t is a function of the steel chemistry. A few ppm of interstitial impurities, carbon and nitrogen, when added to pure iron, showed a strong effect in reducing recovery; this effect was more evident for nitrog;en than for carbon.40,42'43 Solute additions were also found to cause a similar retardation effect on recovery.44 Consequently, the recovery effects are less important in low C-Mn and low-carbon alloyed steels. The reduced recovery in these steels resulted in a strong deformation strain (high f2 values) effect and a weak strain rate (low f3 values) effect on to.5. The matrix of IF steel is very low in interstitial atoms, and consequently these alloys may undergo considerable recovery. As pointed out in the previous section, the softening fraction of the Nb-rich Ti-Nb IF steel due to recovery was ~35% in the austenite region and -40% in the ferrite region. These values are higher than the typical value of 20% obtained for low C-Mn steels. A significant contribution from recovery in IF steels in the ferrite region is also reflected in the effect of deformation strain and strain rate on the static recrystallization behavior. Figure VI. 12 shows that deformation strains in the range 0.2 to 0.5 had little effect on to.5. For the Nb-lean Ti-Nb IF steel, the lower solute Nb content permitted more dynamic recovery during deformation and reduced the effective strains, even though the applied strains were different. The flow stress curves in the previous chapter indicated that the flow stress in the ferrite reached a steady state quickly and the flow stresses at s=0.2 and 0.5 were almost the same. The effect of deformation strain rate on to.5 for the Nb-rich Ti-Nb IF steel deformed at 700°C is illustrated in Figure VI. 13. The to.5 increased significantly with decreasing strain rate. A Chapter VI Restoration Behavior 102 slow strain rate gave more time for the deformed material to recover, which reduced the effective retained strain. The static recrystallization driving force is proportional to the stored energy which is directly related to the retained strain. VI.4 Summary Double-hit tests on two IF steels were carried out to determine the softening fraction for different holding times. Recovery and recrystallization kinetics were determined by analyzing the double-hit test data. Microstructure observations were performed on selected samples to check the double-hit test results and to clarify the restoration mechanism. The main conclusions of these tests are as follows: (1) The Perdrix back-calculation method can be used to quantify double hit test results and to represent the recrystallization kinetics. (2) Static recovery plays a very important role, contributing to approximately 40% of the softening process in IF steel deformed in the ferrite region. (3) Dynamic recovery during deformation reduced the effect of deformation strain on the recrystallization kinetics and intensified the effect of strain rate on the recrystallization kinetics of the IF steels. These effects were more pronounced due to the reduced solute Nb content in the Nb-lean IF steel. (4) Recrystallization progressed slowly in the ferrite temperature range, especially for the Nb-rich Ti-Nb IF steel and at lower temperatures. The Nb-lean Ti-Nb IF steel could recrystallize fully in 100 seconds at 800°C. Chapter VI Restoration Behaviors 103 160 140 120 100 80 60 40 20 -Measured back extrapolation 0.05 0.1 0.35 0.4 0.15 0.2 0.25 0.3 Strain Figure VI. 1 A schematic diagram showing the back-extrapolation method for determining the recovery-free softening fraction in a double-hit test 1/sec. at 700°C on the Nb-rich Ti-Nb IF steel. 1 -i u." 0.5 0.1 1 10 100 inter-hit time, sec. Figure VI.2 Relationship between F x and inter-hit time for the Nb-rich Ti-Nb IF steel deformed in the austenite region. Chapter VI Restoration Behaviors 104 0.35 0.25 0.15 0.05 1000 Figure VI.3 Relationship between F x and inter-hit time for Nb-rich Ti-Nb IF steel deformed in the ferrite region. -1.5 Figure VI.4 The JMAK and the S-F analysis of double-hit test data obtained for the Nb-rich Ti-Nb IF steel deformed in the ferrite region. 10 100 1000 Figure VI.5 Recrystallization kinetics plotted as ln(ln(l/(l-Fx))) versus Int for the Nb-rich Ti-Nb IF steel deformed at 700°C. 1000 Figure VI.6 Recrystallization kinetics plotted as ln(ln(l/(l-Fx))) vs. Int for the Nb-lean Ti-Nb IF steel deformed in the ferrite region, first hit s=0.2. Chapter VI Restoration Behaviors 106 5- -0.5 1000 Figure VI.7 Recrystallization kinetics plotted as ln(ln(l/(l-Fx))) vs. Int for the Nb-lean Ti-Nb IF steel deformed in the ferrite region, first hit 8=0.5. 1000 Figure VI.8 Recrystallization kinetics plotted as ln(ln(l/(l-Fx))) vs. Int for the Nb-lean Ti-Nb IF steel deformed at 700°C. Chapter VI Restoration Behaviors 107 0 sec. lOOsec. 1000 sec. 25 hrs Figure VI.9 Microstructures obtained after a 'first hit' test on the Nb-rich Ti-Nb IF steel at a strain rate of Is"1 to s=0.2 at 700°C for four different holding times. Chapter VI Restoration Behaviors 108 100 sec. Figure VI. 10 Microstructures obtained after a 'first hit' test on Nb-lean Ti-Nb IF steel at a strain rate of Is"1 to e=0.2 at 800°C for two different holding times. Chapter VI Restoration Behaviors 109 0 sec. lOOsec. 1000 sec. 10000 sec. Figure VI. 11 Microstructures obtained after a 'first hit' test on Nb-lean Ti-Nb IF steel at a strain rate of Is"1 to s=0.5 at 700°C for four different holding times. Chapter VI Restoration Behaviors 110 500 7 0.9 0.95 1 1.05 1.1 1.15 1.2 1000/T, 103K"1 Figure VI. 12 Effect of deformation temperature and strain on to.5 on the Nb-lean Ti-Nb IF steel deformed in ferrite region. 1.00E+07 1 1.00E+06 1.00E+05 1.00E+04 1.00E+03 -I • : 1.00E+02 • 1.00E+01 • 1.00E+00 J 1 0.01 0.1 1 strain rate Figure VI. 13 Effect of deformation strain rate on to.5 on the Nb-rich Ti-Nb IF steel deformed at 700°C. Chapter VII Precipitation behavior 111 Chapter VII Precipitation Behavior The precipitation behavior in steels is important to characterize because of the strong interaction between recrystallization and precipitation. In this chapter, the solubility product of IF steels is calculated based on classical theory. Then, TEM observations on the precipitation behavior of the two IF steels examined are compared with the results of precipitation behavior modeling. It is found that Ti4C2S2, Ti(CN), and Nb(CN) precipitates effectively retard recrystallization of the two IF steels in the ferrite region. Solute Nb in the Nb-rich Ti-Nb IF steel may contribute a similar retardation effect as precipitates. VII. 1 Solubility calculation for IF steels The solubility product can be derived from an analysis of the Gibbs free energy, AG0, for the following dissolution reaction, AxBy(s)=xA(ss)+yB(ss) (VII.l) At equilibrium, we have AG 0 = AH" -TAS° = -RTlnK = -RTIn[^] (VII.2) ttA,By where AH 0 and AS0 are the standard enthalpy and entropy of the reaction, respectively, while [aA] and [as] denote the chemical activities of elements A and B in the matrix in equilibrium with pure A x B y . When pure AxBy is used as a standard state, the activity of the precipitate, aA B , is equal to unity. In addition, if the activity of the solute is referred to a 1% hypothetical solution (as is assumed in most precipitation situations) it is a fair approximation to set aA«[CA] and aB«[CB] at high dilutions, where [CA] and [CB] are the equilibrium concentrations either in Chapter Vll Precipitation behavior 112 wt.% or at.% of elements A & B at infinite dilution. Hence, the solubility product can be written as: l o g [ C J * [ C f l ] ' = ^ - ^ (VII.3) Within a system containing more than two alloying elements, different types of mixed precipitates may form. Assuming that some precipitates are ideal solutions of different types of precipitates, and/or the precipitates are formed separately, similar equilibrium equations to (VII.3) can be established. These, together with the mass balance equations, can be simultaneously solved by numerical methods.74"76 This method has been successfully applied to model the precipitation behavior of microalloyed steels and extended to explain Ti4C2S2 precipitation in IF steels.113 However, difficulties were found in applying this method to the IF steels examined because of the absence of thermodynamic data. An alternative method to characterized the precipitation behavior is to experimentally determine the constants A and B by rewriting equation (VII.3) as follows: \og[CAY[CBy=A-j (VII.4) Table VII. 1 lists the published equations applicable to IF steels and the T e q values calculated using these equations for the two IF steels examined in this study. The calculated T e q values in Table VII. 1 are based on the nominal compositions of the two steels. In fact, the precipitation sequence in the two IF steels decreases the actual precipitation start temperature of certain precipitates by consuming or even depleting some elements in the matrix. On the other hand, boundary segregation and heterogeneous nucleation may increase the precipitation start temperature of certain precipitates. Based on a study on precipitation of Nb(CN) in an IF steel, S. Akamatsu90 concluded that local equilibrium at the austenite/Nb(CN) interface during precipitation had to be introduced into the classical Chapter VII Precipitation behavior 113 nucleation theory to calculate the driving force, A b G n , for the nucleation of precipitates. This approach resulted in an increased precipitation start temperature and accelerated the precipitation growth kinetics. Table VII. l Solubility product equations and calculated T e q values for the two IF steels examined in this study. Solubility production equations References T e q(°C) of Nb-rich Ti-Nb IF steel T e q(°C) of Nb-lean Ti-Nb IF steel log[Ti][C]=-7000/T+2.75 49,113 762.5 775.0 log[Ti][C]=-10475/T+5.33 49 848.5 858.3 log[Ti][C]=3.14-7400/T(in y) 10 762.0 773.8 log[Ti][C]=5.032-10793/T(in a) 10 920.7 931.4 log[Ti] [N]=-165 86/T+5.90 114 1403.3 1332.0 log[Ti][N]=4.04-13900/T(in y) 10 1457.1 1542.3 log[Ti][N]=7.38-18372/T(in a) 10 1342.2 1282.1 log[Nb][C]=-6770/T+2.26 49,90 806.8 693.3 log[Nb] [C]=-10960/T+5.43 49 888.0 804.0 log[Nb][C]=3.7-9100/T 46,49,70 907.3 804.4 log[Nb][C]=l .3-5000/T(in y) 10 668.7 554.0 log[Nb][C]=3.312-8793/T(in a) 10 928.0 818.2 log[%Nb][%N]=3.82-9940/T 90 999.0 931.3 log[Nb][N]=3.78-9850/T(in y) 10 994.0 926.2 log[Nb][N]=5.96-13069/T(in a) 10 1039.9 984.3 log[Nb][C] 7[N]3=-6113/T+1.45 49 847.6 728.8 log[Nb][C]'83[N] 14=1.178-5529/T 10 809.3 680.4 (in y) 901.2 log[Nb][C] 83[N] l4=3.153-9128/T 10 1015.6 (in a) log[Nb] [C+12114N]=-6770/T+2.26 46,49 856.5 758.2 log[Ti][S]=-3252/T-2.01 65 1676.7 2197.9 log[Ti][C] 5[S] 5=-5208/T-0.78 65 1427.0 1556.1 Chapter Vll Precipitation behavior 114 VII.2 TEM observations The precipitation behavior for both Ti-Nb IF steels was examined using replicas prepared from 'first hit' specimens. Thin foil TEM observations on samples from the torsion simulation tests also revealed the precipitate morphology after deformation and helped to clarify the precipitation behavior in industrial practice. Several large (~150nm) cubic particles were observed in replicas made from 'first hit' specimens of both IF steels. EDS analysis confirmed that they contained only Ti or Ti+Nb, as shown in Figure VII. 1. The morphology and composition of these particles suggested that they were TiN or (Ti,Nb)N that were formed in the liquid steels. The size of these particles was too large and the number of particles was too few to influence the recrystallization behavior of either IF steel. VII.2.1 TEM observations on the Nb-rich Ti-Nb IF steel Four series of tests were chosen to examine the effect of reheating and deformation on the precipitation behavior in the Nb-rich Ti-Nb IF steel. In the first series of tests, the specimens machined from solution heat-treated (1200°C for lhr) bar were reheated to 1000°C for 5 minutes, then cooled to 700°C and held for 30 seconds before applying a deformation strain of 0.2 at a strain rate of Is"1. After the 'first hit' deformation, the specimens were held at 700°C for different times and helium-quenched to room temperature. The precipitate morphology prior to 'first hit' deformation was observed. It was found that there were a few large particles, -0.5-1 pm in diameter, thought to be TiS as shown in Figure VII.2. Some precipitates appear to be growing epitaxially On the TiS, as can be seen in Figure VII.2. Also, several medium sized particles (~30-50nm, identified by arrows) can be seen in the figure; these particles appeared in all specimens under this reheating condition for different 115 deformation and holding times. These particles are important and will be discussed later. At the same time, many very small precipitates could be seen in the specimens. These precipitates were <20nm in size and were thought to be Ti(CN) and/or Nb(CN), even though they were too small for EDS analysis. The TEM observation on specimens held for 0 seconds and 10 seconds indicated that the precipitate morphology didn't change significantly; more small precipitates appeared after holding for 100 seconds. The precipitate size also increased with holding time. Figure VII.3 shows the morphology of the small precipitates and their EDS analysis after a holding time of 24 hrs. The precipitate size had increased to ~10nm-35nm and the EDS analysis indicated that these precipitates contained Ti, Nb, and/or S. In the second series of tests, the specimens underwent the same reheating and deformation conditions as employed in the first series of tests, except a lower strain rate of 0.02/sec. was applied during the 'first hit' deformation. TEM observations indicated that the size and distribution of the precipitates in this series were almost the same as those of the first series. However, the small precipitates appeared earlier than they did in the first series of tests, due to the slow strain rate. More small precipitates were present, even after holding for only 10 seconds, as shown in Figure VII.4. In the third series of tests, the specimens machined from the solution treated rods were reheated to 1000°C for 5mins, then cooled to 800°C and held for 30seconds before applying a deformation s=0.2 at a strain rate of Is"1. After the 'first hit' deformation, the specimens were held at 800°C for different times and helium-quenched to room temperatures. Besides the medium sized precipitates that appeared in the first and seconds series of tests and contained Ti, Nb, and S, some very small precipitates could be seen and EDS established that they contained only Ti and Nb, as shown in Figure VII.5. These precipitates sized ~20-40nm were thought to be Ti(CN) and/or Nb(CN). The higher deformation and holding temperature Chapter Vll Precipitation behavior 116 provided the conditions for these precipitates to coarsen large enough to be detected by EDS. On the other hand, the precipitate density at 800°C seemed lower than that o f the first t w o series due to coarsening. In the fourth series of tests, the reheating temperature was increased to 1200°C and held for 5mins. The samples were then cooled to 700°C and held for 30seconds before applying a deformation s=0.2 at a strain rate of 1/sec. After the 'first hit' deformation, the specimens were held at 700°C for different times and helium-quenched to room temperatures. The particle size obtained for this series was different from that obtained in the first three series of tests. The medium sized particles contained Ti, and S and were fewer but larger (-30-60nm) than those found in the first three series, as shown in Figure VII.6. It is shown in the next section that these particles are Ti4C2S2. The larger size of these particles resulted from the higher reheating temperature. At the same time, it was found that small precipitates determined by EDS to be Ti(CN) and/or Nb(CN) were also larger (~10-35nm) than those found in the first three series, as shown in Figure VII.7. The number of this kind of precipitate was higher also. This observation suggested that more C was available to form Ti(CN) and Nb(CN) under this reheating condition. VII.2.2 TEM observations on the Nb-lean Ti-Nb IF steel Two series of tests have been carried out to examine the precipitation behavior in the Nb-lean Ti-Nb IF steel. In the first series of tests, the specimens were reheated to 1000°C for 5 minutes, cooled to 700°C and held at 700°C for 30 seconds before applying s=0.2 at a strain rate of Is"1. After the 'first hit' deformation, the specimens were held at 700°C for different times and helium-quenched to room temperature. The morphology of the precipitates existing prior to the 'first hit' deformation (as-quenched) was first examined. Several large TiS particles were found in the as-quenched specimen. The morphology of these particles was Chapter VII Precipitation behavior 117 similar to that found in the Nb-rich Ti-Nb IF steel, as shown in Figure VII.8. It should be emphasized that these TiS particles were observed in all specimens after deformation and different holding times. The morphology of the medium sized particles ~40nm (thought to be Ti4C2S2) was the same as those observed in the Nb-rich Ti-Nb IF steel. Many small precipitates were also observed in this specimen. They were thought to be Nb(CN) and/or Ti(CN) according to their sizes, as shown in Figure VII.9. The size of these precipitates was <20nm. After the 'first hit' deformation and holding for different times, these small precipitates grew to larger precipitates (~15-35nm in diameter) and they were deteimined by EDS to be Ti(CN) and or Nb(CN) precipitates, as shown in Figure VII. 10. However, the number of precipitates decreased. In the second series of tests, the reheating temperature was increased to 1200°C and held for 5 minutes. The deformation parameters and holding times were the same as those adopted in the first series of tests. The morphology of the large TiS particles in the specimens of this series of tests was the same as that observed in the first series. Fewer medium sized particles were found in this series. Instead, many small precipitates, sized ~15-25nm, could be observed in specimens before or after the 'first hit' deformation. A distinctive distribution was observed for these precipitates. Most of these precipitates formed in chains, as shown in Figure. VII.l 1. These particles were thought to be Ti 4C 2S 2, Ti(CN) and Nb(CN) by EDS analysis. The precipitate chains were connected to each other (Figure VII. 12) as though they were located along grain boundaries. The present replica work couldn't ascertain whether or not they were along the original austenite grain boundaries or along the ferrite grain boundaries. Small precipitates were also presented homogeneously throughout the matrix, but were smaller than those formed in the chains. The morphology of the small precipitates did not change after Chapter Vll Precipitation behavior 118 holding at 700°C for 1000 seconds; smaller precipitates inside the matrix seemed to exhibit some growth after holding at 700°C for 3hrs. VII.2.3 TEM observations on thin foils made from samples used for torsion rolling simulations in the ferrite region A precipitation examination was also performed on thin foils made from torsion rolling simulation samples on both Ti-Nb IF steels in the ferrite region. Figure VII. 13 shows the precipitates in the thin foils made from the torsion specimens of the Nb-rich Ti-Nb IF steel that were reheated to 1200°C for 30 minutes, subjected to a simulated CSP rolling deformation at 800-750°C, and helium-quenched to ambient temperature. Many precipitates were observed in the Nb-rich Ti-Nb IF steel and a few precipitates were observed in the Nb-lean IF steel. VII.3 Precipitation behavior modeling It has been assumed by many early investigators of IF steels that these steels can be considered as dilute microalloyed HSLA steels.115'116 In other words, the precipitation behavior in these two types of steel were thought to be similar, if not identical, except for the amount of precipitates formed. This concept has been proved untrue for modern ULC IF steels because of 11 9R 90 71 RR subtle differences in compositions between microalloyed and IF steels. ' " ' ' ' For example, in Ti and/or Nb microalloyed HSLA steels of typical S, C, and N contents (atomic ratio S:C:N«1:10:10), the major C-bearing precipitates are free-standing carbonitride (MCN) particles that formed by the classic nucleation and growth process. On the other hand, in modern ULC steels with atomic ratio S:C:N«1:1:1, particles of TiS and T12C2S2 were found. 11,28-29,71,88, In the present study, TiS and Ti2C2S2 particle were observed in all specimens after the 'first hit' tests. Large TiS particles are believed to be formed during solidification of the liquid Chapter VII Precipitation behavior 119 steel. According to Hua et al., the in situ transformation from TiS to Ti2C2S2 is the primary process responsible for the stabilization of C at high temperatures (1220°C to 930°C) and the stabilization process continues through the epitaxial growth of carbides on fully transformed Ti2C2S2 at low temperature (<930°C).29'88 TEM observation in the present IF steels revealed that large particles, thought to be TiS, did not fully stabilized C and S by the in situ transformation from TiS to Ti2C2S2 after the 1200°C and 1000°C reheating conditions for both Ti-Nb IF steels. Many separate medium size particles (~30-60nm), thought to be Ti2C2S2, were observed. The epitaxial growth of Ti2C2S2 and/or carbides on TiS was also observed in the present study (Figure VII.2). However, it was believed that in situ transformed and epitaxially grown Ti2C2S2 contributed only a small stabilization of C. The size range and dispersions of Ti2C2S2 observed in the present study are very similar to those obtained by Subramanian et al. 71 72 in a Ti stabilized IF steels. ' The Ti2C2S2 particles that precipitated during reheating affect the austenite grain size and recrystallization during reheating and deformation of these steels due to their relatively small size and wide dispersion. Figure VII. 14 shows the equilibrium precipitate mole fraction as a function of temperature, modified to include Ti2C2S2 precipitation for a Ti-stabilized ULC IF steel. The precipitation start and finish temperatures for T14C2S2 are 1270°C and 980°C, respectively. This result indicates that the equations log[Ti][S]=-3252/T-2.01 and log[Ti][C] 5[S] 5=-5208/T-0.78 presented in Table VII. 1 could be used to calculate equilibrium [Ti], [C], and [S] in solution of the IF steels studied. Then, the supersaturation ratio, kS; at a temperature is defined as the ratio of the actual amount of [Ti][S] and [Ti][C]°'5[S]05 to the equilibrium amount of [Ti][S] and [Ti][C]05[S]05 in solution, i.e., k,(TV5) = [Ti][S]S(An /IO"3 2 5 2"'"2 0 1 (VII.5) Chapter Vll Precipitation behavior ; 120 ks(Ti4C2S2) = [r/][C] 0 5[S] 0 5, oi„ / i o " 5 2 0 8 ' ™ (VII.6) Based on the above equations, the equilibrium content of the elements in solution in different thermal stages can be calculated. Table VII.2 lists the calculated equilibrium wt% of elements in solution for both the Nb-rich and the Nb-lean Ti-Nb IF steels. It can be seen from the table that some Ti and S remain in solution after solution heat treatment, even after reheating at 1000°C for 5 minutes. This could explain why many small precipitates containing Ti, S, and Nb were found in the same sample, indicating that Ti2C2S2 could co-precipitate with Ti(CN) and Nb(CN). The calculated results also indicate that the C contents are very low, except for the Nb-rich Ti-Nb IF steel after a 1200°C reheating condition. This result explains why only a few precipitates could be detected as pure Ti(CN) and/or Nb(CN) in the TEM observations. This also reinforces the significance of Ti2C2S2 precipitation in the IF steels examined. The calculated compositions in Table VII.2 also showed that most Nb remained in solution due to the very low C content in the IF steels being studied. The effect of solute Nb on recrystallization was well known and this will be discussed in next section. Chapter VII Precipitation behavior 121 Table VII.2 Calculated equilibrium contents (wt%) of elements in both Ti-Nb IF steels. Nb-rich Ti-Nb IF steel Nb-lean Ti-Nb IF steel Ti content after TiN precipitation 0.025 0.045 Ti content after 1200°C solution heat treatment 0.01815 0.0332 C content after 1200°C solution heat treatment 0.00193 0.00052 S content after 1200°C solution heat treatment 0.00368 0.00406 Ti content after 1000°C for 5 minutes reheating 0.01121 0.02960 C content after 1000°C for 5 minutes reheating 0.00106 7.25E-05 S content after 1000°C for 5 minutes reheating 0.00136 0.00286 TEM observations indicated that separate Ti(CN) and/or Nb(CN) precipitates were found in the specimens before and after the 'first hit' deformation. Table VII.2 also showed that some solute C was retained after reheating, especially for the Nb-rich Ti-Nb IF steel; for example, [C]soin=0.0019 after the 1200°C solution heat treatment. This solute C will combine with the remaining solute Ti and/or Nb to form separate Ti(CN) and Nb(CN) precipitates. Dutta and Sellars 1 1 7 have shown that this small precipitate played an important role in retarding recrystallization at temperatures typical of the finish controlled rolling operation either in the austenite region or in the ferrite region. They derived a precipitation-time-temperature relationship for Nb(CN) precipitation on the basis of thermodynamics and diffusion to examine the influence of composition and process variables on the temperature at which recrystallization was retarded and effectively stopped by strain induced precipitation. If Chapter Vll Precipitation behavior . 122 the precipitation start time, to.os, is less than the static recrystallization start time, to.osx, static recrystallization is retarded or stopped. The relationship for to.os and to.osx are as follows: t005 = A[NbYx s-'Z'05 cxp(QNb I RT) • exp( B ) (VII.7) T (In*,) W - ^ > - " e x p ( ^ ) - e x p | e ( n T C 1 r»5 ^ def 2 75-10 ( —185)-[M>] (VII.8) where A, B , C are constants, n, p are exponents, 8 is strain, d0 is the initial grain diameter (pm), Z is the Zener-Hollomon parameter, ks is the supersaturation ratio, Q N d is diffusion activation energy of Nb, Qdef is the deformation activation energy, and [Nb] is solute the Nb content. The values of constants in equation (VII.7) and (VII.8) used by Dutta and Sellars in the austenite region for the Nb-microalloyed steels and required for coincidence of predicted and observed times in the ferrite region for the Nb-rich Ti-Nb IF steel are listed in Table VII.3. Table VII.2 The values of constants in equation (VII.7) and (VII.8) used by Dutta and Sellars for the Nb-microalloyed steels and by this study for the Nb-rich Ti-Nb IF steel. Constant For the microalloyed steel (in the austenite region)117 For Nb-rich Ti-Nb IF steel (in the ferrite region)* A 3.010"6 1.5-10"6 B 2.5-1011 9.3-10" C 6.75-IO"20 2.02-10"18 n 2 2 P 4 0.5 Q N b , J/mol 270,0.00 293,000 Qdef, J/mol 300,000 240,000 *Constants A, B , C are estimated from the 'first hit' microstructure and precipitation observation; p and Qdef are values obtained in this study; Q N d is from reference69. Chapter Vll Precipitation behavior 123 Figure VII. 15 shows the calculated tn.05 and to.osx values for the Nb-rich Ti-Nb IF steel based on this modified Dutta and Sellars' model. At higher temperature range (e.g. 800°C), to.05 for the Nb(CN) is much larger than to.osx- This is consistent with the microstructure observation that this steel recrystallized rapidly at 800°C. When the temperature was around 700°C, recrystallization occurred before precipitation initiated but was retarded by the occurrence of precipitation in the later stage of recrystallization. When the temperature is lower than 675°C, precipitation occurred earlier than recrystallization and recrystallization was retarded significantly. This is also consistent with the microstructure observation that recrystallization of this steel progressed very slowly in the lower temperature range. Roucoules118 used a model developed by Liu and Jonas113 to predict the start time, Ps, for Ti(CN) precipitation: KC* PS=H- (pTty exp(250000 / RT) exp( ) (VII.9) kT Here, H=0.0156 A G . = 16,(0.25^ 3(AGchcm + AG£)2 p = 1.68(1 + 577) exp(^^) x 109 m"2 (VII. 11) RT where a is the interface energy, AGChem is the chemical driving force for nucleation, AGe is the volume strain energy associated with the formation of the nucleus and p is the dislocation density. The start precipitation time for Ti(CN) of the steel examined could be calculated if the thermodynamic data was obtained. Chapter VII Precipitation behavior 124 VII.4 Discussions The retardation of recrystallization in a steel becomes more pronounced as the precipitate distribution becomes finer and denser and the solute content in the bulk increases. In the Ti-Nb IF steels studied, the retardation of recrystallization is caused by precipitation of Ti4C2S2, Ti(CN) and Nb(CN) particles, while the retardation of recrystallization is also caused by solute Nb, according to the calculated precipitation behavior and TEM observations. Kwon has incorporated solute drag and pinning effects into a kinetic equation to evaluate the recrystallization behavior of Nb microalloyed steels.77'78 The 5% recrystallization time for Nb microalloyed steels is given as follows: to.o5x=(to.o5x)c-Mn-exp[CNb-(A7T-B)]-exp[Cppt/rp-(C/T-D/rp)] ' (VII. 12) (W)c-W„ =6.75-10VoV4exp(3-105/i?r) (VII.13) where A, B, C, D are constants, CNb, C p p t are the concentrations (wt%) of the dissolved and precipitated Nb, and rp is the precipitate radius. The terms exp[CN0-(A/T-B)] and exp[Cppt/rp-(C/T-D/rp)] represent the solute drag and pinning effects, respectively. Because most Nb remained in solution, the solute drag term at 700°C is 30.4 and 2.4 for the Nb-rich and the Nb-lean Ti-Nb IF steel, respectively. This suggests that recrystallization for the Nb rich Ti-Nb IF steel is delayed by one order of magnitude due to solute drag. By assuming that 1/3 of the Nb is precipitated in the steels, the precipitate pinning effect term at 700°C is 31.7 and 2.4 for the Nb-rich and the Nb-lean Ti-Nb IF steels, respectively. This calculation result indicates that the solute Nb retards the recrystallization as effectively as precipitation pinning in the IF steels studied. TEM observations also indicated that precipitation was concentrated on boundaries for the Nb-lean Ti-Nb IF steel after reheating to 1200°C, holding for 5 minutes, and cooling to Chapter Vll Precipitation behavior 125 deformation temperatures in the ferrite region. These precipitates retard recrystallization more effectively than randomly distributed precipitates do. In order to obtain the desired microstructure and mechanical properties of the steel, it is important to control the chemistry of the steel and the thermomechanical processing parameters according to the present study. For example, a lower Nb content and higher coiling temperatures should be adopted if low yield strength, soft hot-rolled steel sheet is to be produced. To produce steel sheets with good formability, a lower reheating temperature, a higher deformation temperature, a lower coiling temperature and an adequate amount of Ti+Nb addition should be adopted. A lower reheating temperature and a higher deformation temperature increases Ti 4C2S2 precipitation and reduces Ti(CN) and Nb(CN) precipitation inside the grains. Reduced precipitation inside the grains will decrease the undesired texture formation initiated at deformation bands.119 A lower coiling temperature guarantees a hot-rolled microstructure similar to a cold-rolled one and favorable texture formation in as-annealed cold-rolled steel sheets. VII. 5 Summary TEM observations on the precipitation behavior of the two IF steels studied were carried out and compared with the results from a precipitation model. These observations support the following conclusions: (1) The precipitates found in the IF steels studied mainly consisted of TiN, TiS, T14C2S2, Ti(CN), and Nb(CN). Among these, the T14C2S2 particles were ~50nm in size and were randomly distributed. The Ti(CN), and Nb(CN) particles of <20nm were found in specimens before the 'first hit' deformation and their size increased to ~10-35nm after the 'first hit' deformation and different holding times. Chapter Vll Precipitation behavior 126 (2) It is thought that T14C2S2 was formed both by in situ transformation from TiS and by separate formation. Ti(CN), and Nb(CN) might precipitate epitaxially on the Ti4C2S2 particles but separate Ti(CN), and Nb(CN) precipitates were detected also. (3) A modified Dutta and Sellars' model can be used to interpret the interaction between precipitation and recrystallization. (4) Solute Nb in the IF steel studied contributed the same retardation effect as precipitates. The calculated 5% recrystallization time increased -30 times either due to precipitate pinning or solute drag in the Nb-rich Ti-Nb IF steel. The retardation increased 2.4 times either due to precipitate pinning effect or due to the solute drag effect in the Nb-lean Ti-Nb IF steel. (5) Based on the present study, the desired microstructure and associated mechanical properties of IF steels could be obtained by optimizing the chemistry and processing parameters. Chapter Vll Precipitation behavior 127 Nb Ld i T ,K« FeK« CuK< 0.00 2.5< 5.12 10.2: Figure VII.l (TiNb)N particle and its EDS analysis for the Nb-rich Ti-Nb IF steel. Chapter VII Precipitation behavior 128 Chapter VII Precipitation behavior 129 NbL« S K « TiK« FtK« I ( J I J i l l || i IF" ' 8.06 i.'Si 5'. 12 ?'.<S8 10.22 Figure VII.3 Morphology of small precipitates and their EDS analysis on the Nb-rich Ti-Nb IF steel after a deformation e=0.2 at 700°C at a strain rate of Is"1 and a holding time of 24 hrs. Chapter Vll Precipitation behavior 130 Figure VII.4 Small precipitates in the Nb-rich Ti-Nb IF steel after a deformation s=0.2 at 700°C at a strain rate of 0.02s"1 and a holding time of 10 seconds. Chapter VII Precipitation behavior 131 Figure VII.5 Small precipitates and their EDS analysis for the Nb-rich Ti-Nb IF steel after a deformation 8=0.2 at 800°C at a strain rate of Is'1 and a holding time of 10 seconds. Chapter Vll Precipitation behavior 132 s y « TiK« CuK4 I 1 i | J 0.00 2.5< 5.12 ?-<8 10.22 Figure VII.6 The medium sized particles and their EDS analysis for the Nb-rich Ti-Nb IF steel after reheating to 1200°C for 5mins, s=0.2 deformation at 700°C and a strain rate of Is"1 and a holding time of 100 seconds. Chapter VII Precipitation behavior 133 NbL« I, Tik< FtK< I I i 1 PF1' I 0 .00 2.'S< 5 . 1 2 ?'. 68 1 0 . 2 2 Figure VII.7 Small particles and their EDS analysis for the Nb-rich Ti-Nb IF steel after reheating to 1200°C for 5mins, s=0.2 deformation at 700°C, Is"1 strain rate and a holding time of 10 seconds. Chapter Vll Precipitation behavior 134 Figure VII.8 TiS particle in the Nb-lean Ti-Nb IF steel. Chapter Vll Precipitation behavior 135 Figure VII.9 Small precipitates in the Nb-lean Ti-Nb IF steel before deformation. Chapter Vll Precipitation behavior 136 seconds. CuL« F t L « Nb L4 T • 1 B. r r i 0.00 1 . 28 2.5(5 3.84 5.18 Figure VII. 11 Morphology of small particles and their EDS analysis for the Nb-lean Ti-Nb IF steel after reheating to 1200°C for 5mins, cooled to 700°C and holding for 30 seconds. Chapter VII Precipitation behavior 138 mm I, i tit T K< tit 5 . 1 2 (b) Tik« u 1 i 5 , 1 2 (c) Figure VII. 12 (a) Morphology of particles for the Nb-lean Ti-Nb IF steel after reheating to 1200°C for 5mins, s=0.2 deformation at 700°C and a Is"1 strain rate, and a holding time of 10 seconds; (b) EDS analysis for the large particle in (a); (c) EDS analysis for the small particle in (a). Chapter Vll Precipitation behavior 139 M M m • i ft .fin Figure VII. 13 Precipitates in thin foils made from Nb-rich Ti-Nb IF steel specimens after simulated CSP rolling deformation at 800-750°C. Chapter VII Precipitation behavior 140 700 600 500. Steel 1.0. H7 C N T l S 0.0042 0.0017 0.068 0.013 T OO 0.2 0.4 0.6 OB 1.0 1.2 PPT. MOLE FRACTION, 2 x 1000 Figure VII. 14 The equilibrium precipitate mole fraction as a function of temperature, modified to include Ti2C2S2 precipitation for a Ti-stabilized ULC IF steel. Chapter VII Precipitation behavior 141 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 t, sec. Figure VII. 15 Calculated precipitation start time, to.05, and the static recrystallization start time, tn.osx, in the ferrite region for the Nb-rich Ti-Nb IF steel based on a modified Dutta and Sellars model. Chapter Vlll Ferrite (CSP) Torsion Rolling Simulations 142 Chapter VIII Ferrite (CSP) Torsion Rolling Simulations First, the CSP (ferrite) torsion rolling simulation results will be described including the flow stress behavior and microstructural evolution. The restoration mechanisms operative during the rolling simulation will be discussed using recovery and recrystallization theories. An apparent dynamic recrystallization is suggested to explain the flow stress drop observed during the rolling deformation. Finally, optimization of the chemistry and processing parameters for ferrite (CSP) rolling practice is discussed based on the torsion rolling simulation results and the results on flow stress, static and dynamic restoration, and precipitation behavior presented in the previous chapters. VIII.l Flow stress curves VIII. 1.1 Single twist test results and discussion The torsional flow behavior of steel is presented using equivalent stress, ae> and equivalent strain, ee, and is calculated based on the following equations:120 E' = 7rr ( V , I U ) ° e = r-(3 + m + n) (V1II.2) 27ta where a is the gauge radius, L is the gauge length,, 6 is the twist angle, T is the torque, m is the twist rate sensitivity and n is the exponent. In chapter V, axisymmetric compression tests were carried out to determine the flow behavior of the Nb-rich Ti-Nb IF steel. Single twist deformation has also been performed using the hot torsion system to check the results obtained in the axisymmetric compression tests. A more important purpose of the hot torsion tests is to determine the accumulated strain needed to Chapter Vll l Ferrite (CSP) Torsion Rolling Simulations 143 initiate dynamic recrystallization because the maximum strain is limited in the axisymmetric compression tests. The reheating condition adopted was similar to that used for the axisymmetric compression test. Figure VIII. 1 shows the measured temperature during deformation, and compares the measured equivalent stress versus equivalent strain curves, corrected for temperature variation, with that predicted by equation. Any heating that occurred within the specimen due to deformation can cause flow softening. In the present torsion deformation equipment, the calculated values of equivalent stress and equivalent strain represent those that occurred at the surface of the test specimen.120 Fortunately, a thermocouple was welded on the specimen surface during all torsional deformation; this made it possible to monitor the surface temperature variation during deformation. It was found that the temperature increased by up to 32°C on deforming to a strain of 4.9 (Figure VIII. 1). This temperature increase resulted in significant flow softening (as illustrated by the measured flow stress curve in Figure VIII. 1); a correction has to be applied to the test data to account for this. The magnitude of the associated softening was estimated from the following equation: Q , 1 1 A C = T7~ ^ T i A T (VIII.3) n a R T T + A T v y Values for the deformation activation energy, Q, the exponent, n, and the constant, a, which appeared in a hyperbolic sine equation (V.14), were previously determined using the axisymmetric compression tests. By correcting the flow stress to a constant temperature, the shape of the flow stress curve resembled that of a curve exhibiting dynamic recovery even though a small flow stress reduction is apparent after a large strain (e>2.5). This suggests that dynamic recovery is the dominant restoration mechanism during the early deformation stage, and another softening mechanism is present at large strains. The work hardening during torsional Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 144 deformation is slower than that of axisymmetric compression deformation. The strain at peak stress is larger than that which is present in axisymmetric compression tests. Thus, the expected accumulation of strain needed to initiate another softening mechanism, besides dynamic recovery, for industrial rolling should be smaller than the value obtained in Figure VHI.l. The constitutive equations (V.9) and (V.l2) derived in chapter V were used to predict the flow stress curve for this test. As shown in Figure VIII. 1, the predicted curve fits the measured one very well. However, the comparison between the measured and the predicted curves emphasizes that another softening mechanism, besides dynamic recovery, is present during the deformation; the predicted curve is based on dynamic recovery only and the predicted stress is higher than the measured one at large strains. The explanation of the softening mechanism will be presented in the next section dealing with the microstructural observations. VIII. 1.2 Ferrite (CSP) rolling simulation flow stress curves Two series of torsion tests have been carried out on the Nb-rich Ti-Nb IF steel. In the first series of tests, the specimens were reheated to 1200°C, held for 30 minutes, and cooled to the desired deformation temperature at 3°C/s. This reheating regime produced large austenite grain sizes before the transformation to ferrite and resulted in large initial ferrite grain sizes prior to the ferritic rolling simulations. The ferrite grain size obtained was ~160pm. However, the ferrite grain size in industrial CSP rolling may be even larger than this because the ferrite structure is transformed from the coarse grained solidification structure. In the second series of tests, the specimens were subjected to a rolling simulation deformation in the austenite region before they were cooled to the desired ferrite rolling deformation temperature. The ferrite grain size obtained for this regime was ~40pm. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 145 Figure VIII.2 shows the equivalent stress-strain curves for the Nb-rich Ti-Nb IF steel with large initial ferrite grains. The flow stress increased rapidly in the first deformation pass as the strain increased. The flow stress after the second pass was higher than that after the first pass, not only because of additional work hardening due to the strain accumulation, but also because the strain rates for the 2nd to 6th passes were higher than those of the first pass. In the second pass, the flow stress still increased with increasing strain. However, it did not increase significantly after the third pass. Another significant feature of the flow behavior was that there was no significant softening during the interpass time. It was also noted that the flow stresses of the last two passes were significantly smaller when the deformation temperatures were above 750°C. The stress-strain response for the last two passes was essentially constant when the deformation temperature was below 700°C. Figure VIII.3 shows the equivalent stress versus equivalent strain torsion generated curves for the Nb-rich Ti-Nb IF steel deformed with an austenite rolling simulation. The flow stress in the ferrite region was lower than that of the last three passes in the austenite region, even though the deformation temperature varied from 1085°C to ~925°C in the austenite region and was ~800°C in the ferrite region. Therefore, the rolling force in the final rolling passes would be lower if ferrite rolling was employed for IF steels. Figure VIII.4 shows the equivalent stress versus equivalent strain curves for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel, after the steel had been subjected to an austenite rolling deformation simulation. As illustrated in the figure, there was significant softening during each interpass time in the austenite region (the first six passes), but no significant softening during the interpass time in the ferrite region. The flow stresses obtained in the ferrite region were similar in magnitude to those obtained for the same steel not Chapter Vlll Ferrite (CSP) Torsion Rolling Simulations 146 subjected to austenite rolling (Figure VIII.2). In addition, the flow stresses decreased in the last two passes when the deformation temperature was above 750 °C. For the Nb-lean Ti-Nb IF steel, the ferrite rolling simulation was conducted only on the large initial grain sized material; i.e., that not subjected to an austenite rolling simulation. The resulting equivalent stress versus equivalent strain curves are presented in Figure VIII.5. Generally speaking, the flow stresses behaved similar to those obtained for the Nb-rich Ti-Nb IF steel deformed in the ferrite region, and the values of the flow stresses were lower than those obtained for the Nb-rich Ti-Nb IF steel deformed in the same temperature region. However, the flow stresses for the last two passes during the rolling simulations were significantly lower, even though the deformation temperature was as low as 650°C. All o f the flow stress curves indicated that static recrystallization did not play an important role during the ferrite deformation. Static and dynamic recoveries are the dominant softening mechanisms. However, the flow stress decrease observed in the last two passes cannot be explained by recovery alone. Some recent research ' revealed the same behavior for IF steels deformed in the ferrite region. The single twist test indicated that the flow stress decreased after large strains (Figure VIII.l). Because static recrystallization did not play an important role during ferrite deformation, the strain was accumulated from the 1st pass to the last pass. This high strain accumulation may result in other softening mechanisms, besides recovery, in the last two passes. V.III.2 Microstructure observations Figure VIII.6 shows a SEM micrograph of the polished and nital etched surface of the Nb-rich Ti-Nb IF steel after the single twist deformation. Very fine, quasi-equiaxed grains are Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 147 delineated in the micrograph. These quasi-equiaxed grains had very sharp grain boundaries even though they exhibited a little elongation along the torsional shearing direction. This is surprising because the microstructure obtained was that quenched in immediately after a large strain deformation, with no time for static recrystallization to occur. Figure VIII.7 shows the SEM micrographs of the Nb-rich IF Ti-Nb IF steel after ferrite (CSP) rolling simulations at different temperatures without prior austenite deformation. It was found that quasi-equiaxed grains were obtained throughout the sample when it was deformed in the range of 850-800°C. The microstructure of samples deformed in the range of 800-750°C consists of quasi-equiaxed grains and deformation bands. The associated microstructure exhibited deformation bands when the material was deformed at lower temperatures (<700°C). Figure VIII.8 shows the SEM micrographs for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel after the steel had been subjected to a prior austenite rolling simulation. The microstructures exhibited more quasi-equiaxed grains compared with those obtained at the same temperatures without prior austenite rolling deformation. According to dynamic recrystallization theory, dynamic recrystallization occurs more readily in material with a smaller initial grain size. These results provide additional evidence that some kind of dynamic recrystallization occurs during the ferrite (CSP) rolling simulation. Figure VIII.9 shows the SEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. The microstructures were more quasi-equiaxed than those seen in the Nb-rich Ti-Nb IF steel (Figure VIII.7). Even though the deformation temperature was as low as 650°C, the microstructure showed a predominantly quasi-equiaxed structure. For the Nb-lean IF Ti-Nb steel, the solute Nb content in the matrix is much lower than that for the Nb-rich Ti-Nb IF steel. The reduced solute Chapter Vlll Ferrite (CSP) Torsion Rolling Simulations : 148 Nb drag in the Nb-lean IF steel would have less retardation on any restoration process during and/or after deformation. This result supports the occurrence of dynamic recrystallization during the ferrite (CSP) rolling simulation. The microstructure evolution was examined on the Nb-lean IF steel for the ferrite (CSP) rolling simulation at 800°C~750°C. The microstructure obtained after different passes was revealed on specimens quenched immediately after deformation. Figure VIII. 10 shows the SEM micrographs obtained after passes 1, 2 and 3. After the 1st pass, only few grains exhibited deformation and most of the grains remained in their original shape (Figure VIII. 10a). After the 2 n d pass, many grains exhibited severe deformation, while some grains showed only limited deformation (Figure VIII. 10b). Tsuji et al.'s study121 on an ultra low carbon ferritic stainless steel indicated that the degree of deformation in individual grains was dependent on the initial grain orientation. The present results are consistent with their conclusion. After the 3 rd pass (Figure VIII. 10c), all grains exhibited deformation and some quasi-equiaxed grains appeared inside the large deformed grains. This evolution process led to a quasi-equiaxed grain structure after the 4th and 5th passes. VIII.3 TEM and Kikuchi pattern analyses The microstructure observation obtained using optical and scanning electron microscopy presented some important evidence that another restoration mechanism, besides dynamic recovery, was contributing to the softening of the steels during a ferrite (CSP) rolling simulation. However, the evidence did not present a clear picture as to show which restoration mechanism was enhancing the softening process. The following TEM and Kikuchi pattern analyses was conducted to provide more information to clarify the mechanism. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations ; 149 Figure VIII. 11 shows the TEM micrographs of the Nb-rich Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. The microstructure of the material deformed at higher temperatures (800~750°C) revealed a quasi-equiaxed grain structure and the microstructure of the material deformed at lower temperatures (700~650°C) exhibited elongated structure. Figure VIII. 12 shows the TEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. Both microstructures exhibit mainly quasi-equiaxed grains, even for the material deformed as low as 650°C. Figure VIII. 13 shows TEM micrographs and the misorientation across specific grain boundaries for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel after prior austenite rolling. Both microstructures showed quasi-equiaxed grains, albeit the boundaries of the material deformed at higher temperature are sharper and the shape of the grains is more equiaxed than that obtained in the material deformed at the lower temperatures. Misorientation measurements across specific grain boundaries are shown in the TEM micrographs; neighboring grains were misoriented in the range of 10.9° to 63.0°. Most of the boundary misorientations were larger; whereas only a few boundary misorientations were close to typical values -10° for subgrains. This observation confirmed that a large fraction of the grains contained high angle boundaries and are, therefore, not subgrains. This also explains why the boundaries of these quasi-equiaxed grains could be revealed by normal chemical etching techniques and were delineated well in the SEM micrographs. The materials with quasi-equiaxed microstructures relate to the flow stress curves in which a significant stress decrease is realized in the last two passes. The same features were 199 observed in warm rolled low carbon steel by Sakai et al. and in warm rolled Ti stabilized IF Chapter Vll l Ferrite (CSP) Torsion Rolling Simulations 150 steels by Y. Matsubara et al. and G. H. Akbrari et al. . Sakai suggested that recrystallized grains (2-1 Oum) in the severely sheared region of the quenched sheet had structural features peculiar to dynamic recrystallization and were probably dynamically recrystallized grains. Matsubara62 believed that the equiaxed grains obtained by them resulted from the occurrence of dynamic recrystallization of ferrite in a Ti-added IF steel; this was confirmed by metallographic and crystallographic analysis. G. H. Akbari63 held that they were equiaxed subgrains resulting from microband development. A. Belyakov et al.6 4 revealed that the equiaxed fine grains obtained by them resulted from the formation of dense dislocation walls at low strains and subsequently of microbands and their clusters at moderate strains, followed by the evolution of a fragmented structure inside the clusters of the microbands at high strains. This evolution process was assisted by dynamic recovery and was called "an apparent dynamic recrystallization". In the present study, the flow stress decrease was more apparent in the Nb-lean Ti-Nb IF steel which contained lower soluble Nb and therefore less potential for retardation of dynamic recovery. Also, fine ferrite grains were only obtained when the strains were large and the deformation temperatures were high. Furthermore, the measured misorientation between grains was larger than values typical for subgrains. The grain misorientation was also larger when deformation temperatures were higher and dynamic recovery was going on more easily. Thus, it can be concluded that the fine quasi-equiaxed grains obtained during CSP rolling could be explained by apparent dynamic recrystallization. This conclusion was further confirmed by the fact that the materials with a smaller initial ferrite grain size, obtained by subjecting them to the prior austenite rolling deformation, featured flow stress decreases in the last two passes and exhibited more quasi-equiaxed grains when they were deformed at the same temperature range for samples without austenite rolling simulation. The smaller initial grains rendered more Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 151 original grain boundaries where apparent dynamic recrystallization occurred more easily. VIII.4 Discussion The higher Ar3 and lower flow stresses observed for the IF steels studied creates a tremendous advantage for warm rolling applications. Warm rolling of IF steels in the ferrite temperature range has two important future applications in industry. The first is the production of a soft hot-rolled band that is produced on a CSP line, to be used as a raw material for cold-rolled and annealed IF steels with high formability. Another important advantage of this technology is the lower reheating temperature, which could result in a saving in the energy cost, a reduction in the scale loss, a reduction in the solute content and even better control of texture formation.96'97 The second is the production of warm-rolled thinner hot strip obtained by operating the hot mills at lower temperatures assuming the final properties do not vary significantly across the strip width.93-95 Several investigators100"106 have indicated that, even though an abnormal microstructure consisting of elongated coarse and mixed grains was obtained by warm rolling IF steel in the ferrite region, when the deformation and coiling temperatures were lower, the abnormal grains left no trace in the cold-rolled and annealed IF sheet steels. A detail study by Senuma103'104 on the texture formation obtained by ferrite rolling indicated that a cold rolled Ti bearing IF steel sheet, when warm rolled, showed a more favorable recrystallization texture at its midplane for deep drawability. The cold rolled Ti-bearing IF steel sheet that was warm rolled under lubricated conditions, to reduce the detrimental effect of the surface texture, and was recrystallized after warm rolling had a mean r-value 0.5-0.8 higher than that obtained in a cold rolled steel sheet that was hot rolled in the y-region instead of the ct-region. The present study has not examined the Chapter Vlll Ferrite (CSP) Torsion Rolling Simulations 152 effect of hot band microstructure on the mechanical properties obtained in the final cold-rolled and annealed IF sheet steels. However, TEM observation of precipitation behavior in the 'first hit' tests and in specimens subjected to the torsional ferrite rolling simulation indicated that reducing the reheating temperature resulted in more Ti4C2S2 precipitates and less Ti(CN) and/or Nb(CN) precipitates inside the grains. The later precipitates could contribute to the formation of an undesired texture during cold rolling and annealing. This condition can be reduced by optimizing the reheating, deformation and coiling temperatures. IF steel is one of the best steel grades that could be produced on a CSP line and is excellent material for producing cold-rolled and annealed sheet steel with excellent formability. Recent research106 concluded that a fully recrystallized microstructure was obtained for an IF steel by increasing the finishing and coiling temperatures in the ferrite region. This resulted from the high A r i and Ar3 temperatures of the IF steel due to its ultra low carbon content. These properties make it possible to produce as warm-rolled thinner strip product with adequate formability. However, the grains of a fully recrystallized microstructure are large and the steel becomes soft. Torsional CSP ferrite rolling simulations found that a dynamically recrystallized microstructure could be obtained by applying very high strains at higher temperatures in the ferrite region. These dynamically recrystallized grains are very small and equiaxed. This suggests that as warm-rolled thinner strip products with an adequate formability might be manufactured by CSP technology without loss of product strength. VIII.5 Summary Ferrite (CSP) rolling simulations were carried out on the hot torsion system for both the Nb-rich and the Nb-lean Ti-Nb IF steels. Optical microscopy, SEM and TEM were used to Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 153 reveal the microstructure evolution during the rolling simulations. The following main conclusions can be drawn: (1) Dynamic recovery and apparent dynamic recrystallization occurred during the single twist deformation in the ferrite region and very fine grains were observed in the quenched material. (2) Static and dynamic recovery dominated the softening process for the early passes of the CSP rolling and an apparent dynamic recrystallization contributed to a flow stress reduction in the later passes, when the appropriate temperature and composition were obtained. (3) Very fine quasi-equiaxed ferrite grains were obtained after the CSP rolling simulation and could be explained by apparent dynamic recrystallization. This apparent recrystallization took place aided by dynamic recovery. (4) Material with a smaller initial ferrite grain size did not exhibit an increase in the flow stress during ferrite rolling simulation; this was due to the easier occurrence of apparent dynamic recrystallization. (5) Material with a lower soluble Nb content exhibited lower flow stresses and an easier occurrence of apparent dynamic recrystallization. (6) As warm-rolled IF steel bands with adequate microstructure and mechanical properties for cold-rolling and annealing, and thinner as warm-rolled strip products could be manufactured by CSP technology by optimizing operation parameters to control precipitation distribution and microstructures. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 154 Strain Measured - Corrected by T Predicted -Temperature 900 850 800 750 700 B 650 600 550 500 Figure VIII. 1 Flow stress curves obtained during single twist ferrite deformation for the Nb-rich Ti-Nb IF steel and the associated temperature response. 0 -I 1 1 1 1 i — : i = =H 0 0.5 1 1.5 2 2.5 3 3.5 4 Equivalent Strain Figure VIII.2 The flow stress curves obtained during ferrite (CSP) rolling simulation on the Nb-rich Ti-Nb IF steel. Chapter Vlll Ferrite (CSP) Torsion Rolling Simulations 155 1200 0 1 2 3 4 5 6 Equivalent strain Figure VIII.3 The equivalent stress versus equivalent strain torsion results obtained for the Nb-rich Ti-Nb IF steel deformed in the austenite and the ferrite regions. 250 200 o 7 0 0 ° C / 6 5 0 ° C a 7 5 0 ° C / 7 0 0 ° C o 8 0 0 ° C / 7 5 0 ° C • 8 5 0 ° C / 8 0 0 ° C ra 0. in in <D 150 0) > LU 100 50 Equivalent strain Figure VIII.4 Flow stress curves of the Nb-rich Ti-Nb IF steel deformed at different temperatures simulating austenite and ferrite(CSP) rolling. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 156 200 180 160 140 120 </> 100 Equivalent strain Figure VIII.5 The flow stress curves obtained during a ferrite(CSP) rolling simulation on the Nb-lean Ti-Nb IF steel. Torsional shear direction Figure VIII.6 SEM micrograph of the microstructure of the Nb-rich Ti-Nb IF steel after a single twist deformation. Chapter Vlll Ferrite (CSP) Torsion Rolling Simulations 157 (a) 850~800°C (b) 800~750°C (c)750~700°C (d) 700~650°C Torsional shear direction ^. Figure VIII.7 SEM micrographs of the Nb-rich IF Ti-Nb IF steel after ferrite (CSP) rolling simulations at different temperatures without prior austenite deformation. Chapter Vll l Ferrite (CSP) Torsion Rolling Simulations 158 (a) 850~800°C (b) 800~750°C (c) 750~700°C (d) 700~650°C Torsional shear direction — Figure VIII.8 SEM micrographs for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel after prior austenite rolling deformation. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 159 (b)700~650°C Torsional shear direction p. Figure VIII.9 SEM micrographs ofthe Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. Chapter Vll l Ferrite (CSP) Torsion Rolling Simulations 160 (c) Pass 3 Figure VIII. 10 SEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation with passes at 800~750°C, without prior austenite deformation. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 161 (a) 800~750°C (b) 700~650°C Figure VIII. 11 TEM micrographs ofthe Nb-rich IF Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. Chapter VIII Ferrite (CSP) Torsion Rolling Simulations 162 (b) 700~650°C Figure VIII. 12 TEM micrographs of the Nb-lean Ti-Nb IF steel after a ferrite (CSP) rolling simulation at different temperatures without prior austenite deformation. Chapter Vll l Ferrite (CSP) Torsion Rolling Simulations 163 (b) 750~700°C Figure VIII 13 TEM micrographs showing misorientation across specific grain boundaries for different deformation temperatures in the ferrite region for the Nb-rich Ti-Nb IF steel after prior austenite rolling deformation. Chapter IX Summary and Recommendations 164 Chapter IX Summary and Recommendations IX. 1 Conclusions The flow stress behavior, static and dynamic restoration characteristics, precipitation behavior, and Compact Strip Production (CSP) rolling simulation behavior have been investigated on two Ti-Nb stabilized IF steels. This was accomplished with the aid of axisymmetric compression tests, torsional rolling simulation tests, TEM observation on precipitates and substructures, and Kikuchi pattern analysis. Experimental tests were mainly carried out in the ferrite temperature range; some were also carried out in the austenite temperature range for comparison purposes. The results were assessed with the aim of providing adequate guidance to the application of warm rolling of IF steels on a CSP line; this production path has many advantages over the conventional rolling mill. The important results and conclusions of this research are summarized as follows: (1) Both dynamic recrystallization and dynamic recovery contributed to the softening exhibited by the flow stress curves obtained in the austenite region. The dynamic recrystallization kinetics can be predicted using an Avrami equation (2) The deformation activation energies were measured to be 302k.f/mole and ~240kJ/mole for deformation in the austenite and in the ferrite regions, respectively. The lower value of the deformation activation energy in the ferrite region confirms the close relationship between deformation activation and self-diffusion energies. (3) The Zener-Hollomon values, Z, the temperature compensated strain rate, for the transition from dynamic recovery to dynamic recrystallization was determined as 8.23-1011s"1 in the austenite region for the Nb-rich Ti-Nb IF steel. Chapter IX Summary and Recommendations 16b (4) A constitutive equation derived from dislocation theory fit the measured curves well both in the austenite and in the ferrite region. The comparison also suggests that other softening mechanisms, besides dynamic recovery, contributed to the flow stress behavior for deformation in the ferrite region, even though dynamic recovery is the dominant softening mechanism. (5) The Perdrix calculation method was used to quantify the double hit tests both in the austenite region and in the ferrite region; fractional softening in the results provided a good represention of the recrystallization kinetics. (6) Static recovery played a very important role in the softening process in the IF steel. The softening fractions attributed to static recovery of IF steel in the ferrite region is -40%. (7) Dynamic recovery during deformation reduced the effect of deformation strain on the recrystallization kinetics and intensified the effect of strain rate on the recrystallization kinetics of the IF steels. This effect was strengthened by the reduced solute Nb content in the Nb-lean steel. (8) Static recrystallization progressed slowly in the ferrite temperature range, especially for the Nb-rich Ti-Nb IF steel and at lower temperatures. The Nb-lean Ti-Nb IF steel can recrystallize fully in 100 seconds at 800°C. (9) Precipitates found in the two IF steels studied were TiN, TiS, Ti 4C2S2, AIN, Ti(CN), and Nb(CN). Among them, Ti4CiS2 (~50nm in size) was randomly distributed. Ti(CN), and Nb(CN) (<20nm in size) were found in specimens before the 'first hit' deformation and their sizes increased to ~10-35nm after the 'first hit' deformation and after different holding times. Chapter IX Summary and Recommendations 166 (10) It is thought that T14C2S2 was formed both by in situ transformation from TiS and by separate formation. Ti(CN), and Nb(CN) could have co-precipitated with Ti4C2S2 particles and separate Ti(CN), and Nb(CN) precipitates were also detected. (11) Solute Nb in the Nb-rich Ti-Nb IF steel contributed a similar retardation effect on recrystallization as precipitates. The calculated 5% recrystallization time increases ~30 times either by precipitate pinning or by a solute drag effect in the Nb-rich Ti-Nb IF steel, and increases 2.4 times either by precipitate pinning effect or by solute drag effects in the Nb-lean Ti-Nb IF steel. (12) Dynamic recovery and apparent dynamic recrystallization occurred during the single twist deformation in ferrite and very fine grains were observed in the quenched material. (13) Static and dynamic recovery dominated the softening process for early passes of the ferrite (CSP) rolling and an "apparent dynamic recrystallization" contributed to the flow stress reductions in the later passes, when the appropriate temperature and composition were obtained. (14) Very fine quasi-equiaxed ferrite grains were obtained after the ferrite (CSP) rolling simulation and could be explained by "apparent dynamic recrystallization". This apparent recrystallization took place aided by dynamic recovery. (15) Material with a smaller initial ferrite grain size did not exhibit an increase in the flow stress during rolling simulation due to the easier occurrence of apparent dynamic recrystallization. Chapter IX Summary and Recommendations 167 (16) The Nb-lean IF steel with the lower solute Nb content, exhibited lower flow stresses and easier occurrence of apparent dynamic recrystallization during ferrite rolling simulation. (17) The research suggests that as warm-rolled IF steel bands with adequate microstructure and mechanical properties for cold-rolling and thinner hot strip products could be manufactured by CSP technology by optimizing the processing parameters to control precipitation distribution and microstructure. IX.2 Recommendations The present research was restricted to laboratory tests because IF steels have not been industrially produced on a CSP line. IF steel thin slabs or strips cast on a CSP line are still unavailable. However, some important findings in this research revealed that IF steels would have tremendous advantages if they were produced on a CSP line by using warm rolling technology. The following recommendations are suggested: (1) An industrial trial should be performed on producing IF steel on a CSP line by using ferrite rolling. Based on the present research results, precise control of the rolling and coiling temperatures, and very high strain should be employed in the trial. (2) A more detailed investigation of restoration characteristics should be carried out to reveal the static recovery and static recrystallization processes. An in-depth study on static recovery kinetics during the ferrite rolling processes should be performed. (3) A quantitative investigation on precipitation during reheating and rolling using industrial cast thin slabs produced on a CSP line should be carried out. This should Chapter IX Summary and Recommendations 168 include determining operating parameters to control precipitation either along grain boundaries or in the matrix. (4) A comprehensive investigation of dynamic recrystallization phenomenon should be initiated, aimed at producing high strength IF steels on a CSP line by refining grain size through dynamic recrystallization. The final goal of this study is to produce as warm-rolled thinner strips for direct application. (5) The texture formation obtained at different stages of processing should be studied. 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Kong: "Precipitation behavior of carbides and nitrides in interstitial free steel with co-addition of titanium and niobium," Proc. Conf. on the 3rd HSLA Steel'95, CMS, Beijing, 1995, pp. 199-202. 90. S. Akamatsu, T. Senuma and M. Hasebe: "Mathematical modeling of Nb(C,N) precipitation applicable to extra low carbon steels," Proc. Intern. Symp. on Low-Carbon Steels for 90's, edited by R. Asfahani and G. Tither, TMS, 1993, pp. 187-194. 91. G. Flemming F. Hofrnann, W. Rohde and D. Rosenthal: CSP plant technology and its adaptation to an expanded production programme," MPT (Verlag Stahleisen, Diisseldorf) vol. 16, 1993, No.2, pp.2-11. References 173 92. W. Rohde and G. Flemming: "Current state, capabilities and further developments of the CSP technology," MPT (Verlag Stahleisen, Dusseldorf) vol. 18, 1995, No.4, pp.82-98. 93. Ph. Harlet F. Beco, P. Cantinieaux, D. Bouqugneau, P. Messien and J. C. Herman:"New soft steel grades produced by ferritic rolling at Cockerill Sambre," Proc. Intern. Symp. on Low-Carbon Steels for the 90's, edited by R. Asfahani and G. Tither, TMS, 1993, pp.389-396. 94. M. R. Barnett and J. J. Jonas: "Influence of ferrite rolling temperature on microstructure and texture in deformed low C and IF steels," ISIJ International, vol.37, 1997, No.7, pp.697-750. 95. M. R. Barnett and J. J. Jonas: "Influence of ferrite rolling temperature on grain size and texture in annealed low C and IF steels," ISIJ International, vol.37, 1997, No.7, pp.706-714. 96. O. Kwon and G. Kim: "Controlled rolling of hot strips in the ferrite region," Procof the Application of the Latest Technological Innovations and Processes for the Production of Iron, Steel, and High Quality Product-Mix Conference, TMS, Nov. 1992, pp. 163-168. 97. T. A. Bloom and R. W. Nuske: "Effect of thermomechanical processing on the structure and properties of ultra low carbon Ti-stabilized steel," Proc. 32th Mechanical Working and Steel Processing Conference, 1990, ISS, pp.229-238. 98. G. Glover and C. M. Sellars: "Recovery and recrystallization during high temperature deformation of a-iron," Metallurgical Transactions, vol.4, March, 1973, pp.765-775. 99. G. Glover and C. M. Sellars: "Static recrystallization after deformation of a-iron," Metallurgical Transactions, vol.3, Aug., 1972, pp.2271-2280. 100. S. Hashimoto T. Yakushiji, T. Kashima and K. Hosomi: "Effect of solute carbon and hot rolling temperature on recrystallization texture of hot rolled and annealed extra low carbon sheet steels," Proc. 8 t h International Conference on Texture of Materials (ICOTOM 8) edited by J. S. Kallend and G. Gottstein, The Metallurgical Society, 1988, pp.673-678. 101. S. Hashimoto T. Kashima, N. Nakajima, H. Shirasawa and M. Miyahara: "Effect of ferrite-phase hot rolling on the ductility of ultra-low-carbon steel," Proc. Conf. on Metallurgy of Vacuum-Degassed Steel Products, edited by R. Pradhan, TMS, 1990, pp.357-369. 102. T. Nagamichi, N. Komatsubara and K. Kunishige: "Effect of ferrite-region hot-rolling on r-value of Ti and Nb bearing ultra-low carbon hot-rolled sheet steels," Proc. Conf. on the Processing, Properties and Applications of Metallic and Ceramic Materials, vol.II, Birmingham, UK, Sept., 1992, pp.1037-1042. 103. T. Senuma: "Influence of a region hot rolling on the rolling and recrystallization texture of cold rolled Ti-bearing extra low carbon steel sheets," Materials Science Forum, vol. 157-162, 1994, pp.1051-1056. 104. T. Senuma H. Yada, R. Shimizu and J. Harase:"Textures of low carbon and titanium bearing extra low carbon steel shees hot rolled below their A R 3 temperatures," Acta Metall. Mater., vol.38, No.12,1990, pp.2673-2681. 105. S. K. Chang, H. J. Kang: "Hot direct rolling in ferrite region in extra low-carbon steel," Steel Research 6, 1995, No.11, pp.463-469. 106. Z. Yao and B. K. Zuidema: "Ferrite rolling of interstitial free steels," THERMEC '97, International Conference on Thermomechanical Processing of Steels & Other Materials, edited by T. Chandra and T. Sakai, TMS, 1997, pp.595-601. 107. R. Pandi: "Modeling of Austenite-to Ferrite Transformation Behavior in Low Carbon Steels during Run-out Table Cooling," Ph. D. thesis, University of British Columbia, 1998. 108. P. Shewmon: Diffusion in Solid, 2 n d edition, TMS, PA, 1989, pp.89. 109. P. D. Hodgson, D. C. Collinson and B. A. Parker: Conf. Proc, Advances in Hot Deformation Textures and Microstructures, Ed. by J. J. Jonas, T. R. Bielerand K. J. Bowman, TMS, 1994, pp.41-61. 110 AISI project reports, Department of Metals & Materials Engineering, University of British Columbia, 1996, 1997. 111. M. Suehiro, Z.-K. Liu and J. Agren: "Effect of niobium on massive transformation in ultra low carbon steels: a solute drag treatment," Acta Mater., vol. 44, 1996, No. 10, pp.4241-4251. 112. B. Donnay J. C. Herman, V. Leroy, U. Lotter, R. Grossterlinden and H. Pircher: "Microstructure evolution of C-Mn steels in the hot deformation process: the STRIPCAM model," Proc. 2 n d International Conf. on Modeling of Metal Rolling Process, Dec, 1996, London, pp.23-35. 113. W.J. Liu, S. Yue, and J. J. Jonas: "Characterization of Ti carbosulfide precipitation in Ti microalloyed steels," Metallurgical Transactions A, vol. 20A, Oct., 1989, pp.1907-1915 114. H. Kobayashi:"Microstructure development in Ti bearing interstitial free steel with simulated hot rolling practice," ISIJ International, vol.32, No.7, 1992, pp.873-881 References 174 115. Technology of Continuously Annealed Cold-rolled Sheet Steel, Ed by R. Pradhan, TMS-AIME, Warrendale, PA, 1990 116. Metalluygy of Vacuum-Degassed Steel Products, Ed by R. Pradhan, TMS-AIME, Warrendale, PA, 1995 117. B. Dutta and C. M. Sellars: "Effect of composition and process variable on Nb(CN) precipitation in niobium microalloyed austenite," Materials Science and Technology, vol. 3, March, 1987, pp. 197-206. 118. C. Roucoules, S. Yue, and J. J. Jonas: "Effect of alloying elements on metadynamic recrystallization in HSLA steels," Metall. and Mater. Trans. A, vol. 26A, Jan., 1995, pp.181-190. 119. Y. Hosoya and Y. Nagataki: "Probable mechanism on the recrystallizationx texture formation in IF-steel," Proc. of 37 t h Mechanical Working and Steel Processing Conf., ISS, Vol. XXXIII, 1996, pp.915-925. 120. J. A. Bailey: "Fundamental Aspects of Torsional Loading," Metals Handbook, vol.10, 9 t h Edition, ASM, 1989, pp. 139-144. 121. N. Tsuji, Y. Saito and T. Shinmiya: "Initial orientation dependence of recrystallization in hot-deformed ferrtic steel," THERMEC 97, Proc. of Intern. Conf. on Thermomechanical Processing of Steels & Other Materials, edited by T. Chandra and T. Sakai, TMS, 1997, pp.403-409. 122. T. Sakai: "Deformation and recrystallization behavior of low carbon steel in high speed hot rolling," Transactions ISIJ, vol. 28, 1988, pp.1028-1035. Appendix: Kikuchi Electron Diffraction and analysis 175 Appendix: Kikuchi Electron Diffraction and Analysis* A. 1 Geometry of formation The name Kikuchi lines are given to the patterns of lines that are obtained in electron diffraction from fairly thick crystals after their discovery in 1934 by Kikuchi. Their mechanism of formation is as follows: The electron beam, on entering a specimen, suffers inelastic and incoherent scattering by interaction with the atoms. These electrons can be subsequently re-scattered coherently when Bragg's law is satisfied at a suitable set of reflecting planes. Cones of radiation are emitted, and if the incident waves are symmetrically impinging on the plane AB, cones of equal intensity are scattered, with semi-vertex angles of (90-0) (Figure A. la), to each side and bisecting the reflecting plane, AB. If, however, the waves impinge on an inclined reference plane AB (Figure A. lb), then most of the electrons are initially sceittered into the direction K i and relatively few into the forward direction K2. Under normal conditions, and on a positive print, one then observes a bright line corresponding to K i near the Bragg spot and a dark line corresponding to K2 near the origin. The intersection of the cones of Kikuchi radiation with the reflecting sphere produces hyperbolic which are almost straight lines due to the small 9 angles and the large radius of the sphere for fast electrons. These lines are actually straight on the photographic plate for the usual angles recorded in a pattern (-9° at 100 kV for A,L=2Acm). Each reflection (hkl) thus gives rise to a pair of Kikuchi lines, hkl and (hkl), whose respective intensities depend principally upon the orientation, perfection, and thickness of the crystal. Figures A. 2a and 2b show the geometry for crystals oriented symmetrically and at the exact Bragg condition. These are really the only two orientations that are needed during electron microscopy applications; case (b) should be used * Adapted from G. Thomas: "Kikuchi Electron Diffraction and Application" in Diffraction and Imaging Techniques in Materials Appendix: Kikuchi Electron Diffraction and analysis 176 when crystallographic data is needed and case (a) is the two-beam situation necessary for contrast analysis. It should be noted that in the case of rescattering of inelastic beams, the specimen acts as a monochromator, i.e., the planes (hkl) reflect electrons which are satisfied by Bragg's law for the wavelengths involved: 2d sin (0)' = nA'. Since, typically, the characteristic energy losses are of the order of tens of volts, then X'&X (incident), and the same reflecting sphere-reciprocal lattice construction describing the spot pattern can be used for the Kikuchi pattern (Figures. 2a, b). Kikuchi patterns are always produced even in thin crystals, but the specimen must be thick enough in order that a sufficiently intense Kikuchi cone be observed on the photo plate. Furthermore, the specimen should be relatively free from long range internal strains (e.g., elastic buckling, a high dislocation density), otherwise, the Kikuchi cones will be incoherently scattered and may become too diffuse to be observed. The absence of observable Kikuchi lines, or the appearance of very broad diffuse lines from heavily dislocated structures, e.g., ferrous martensite, is due to incoherent scattering. As the thickness of the foil increases, the diffraction pattern changes from spots, to Kikuchi lines and spots, to Kikuchi lines or bands, until finally complete absorption within the foil occurs. The thickness limits for these events increase with increasing voltage, due to enhanced penetration. It can be seen from Figures A. 2a and 2b, that on tilting the specimen in one sense, the Kikuchi lines sweep across the pattern in the opposite sense. In Figure A. 2a the crystal has been tilted by Ghki-clockwise so as to excite the first order (hkl) refection. The Kikuchi origin is fixed in the crystal so that as the crystal is tilted, the cones sweep across the pattern as, if rigidly "fixed" to the specimen. Thus, the Kikuchi pattern is extremely useful in determining the precise Science, eds. S. Amelinckx, R. Gevers and J. van Landuyt, North-Holland Publishing Company, 1978, pp399-427. Appendix: Kikuchi Electron Diffraction and analysis 177 orientation, as well as for calibrating tilt angles, etc. Since each Kikuchi line in a pair bisects the reflecting plane, then the angle subtended by each pair is always 29, independent of the crystal orientation. Furthermore, the Kikuchi pattern represents the traces of all reflecting planes in the crystal and can thus be directly compared to the appropriate stereographic projection. The Kikuchi lines are also parallel to the Bragg extinction contours. Applying Bragg's law, and the appropriate structure factor rules, enables one to plot the complete Kikuchi pattern, Figure A.3 is derived to scale for the first order Kikuchi reflections for Al at 100 kV. Tilting the crystal tilts the reciprocal lattice in the same sense and magnitude. The spot pattern thus translates only slightly on tilting, since each spot rotates on tilting about an arc of radius |g| centered at the origin (Figure A.2b). The Kikuchi pattern, however, shifts in an easily observable manner («1 cm per 1° tilt for A.L«2 Acm). The Kikuchi lines associated with a particular reflection, hkl, always lie perpendicular to g (hkl), i.e., on a line through the origin and normal to the Kikuchi pair. The centers of symmetry of the spot pattern and the Kikuchi pattern thus coincide only in symmetrically oriented foils. For accurate determinations of orientation relationships, the foil can be tilted until the symmetrical situation appears on the screen. A.2 The precise determination of orientations The general method of solving a Kikuchi pattern and determining the precise foil orientation is similar to the method for solving spot patterns. Since the spacing of each Kikuchi pair is proportional to 29 (Figure A.la), then we have for different sets of Kikuchi pairs of spacings,/?//>2, etc., Appendix: Kikuchi Electron Diffraction and analysis 178 px = K20x p2 = K292 p3 = K20, where K is the effective camera length, L. Thus if the reflections hjkjl/ —h„k„ln, are identified, the pattern can be calibrated in terms of distances on the plate and corresponding angles. The identification of the Kikuchi reflections is done as follows. Suppose in Figure A.4 there are three sets of intersecting Kikuchi lines at angles a, p, y; the points of intersection, A, B, C, are zone axes (Kikuchi poles). If the crystal is cubic, then since px oc l/dhkl , etc., we have pidi=XL, p2d2=XL— pndn=XL, or P\ J h 2 + k 2 + l 2 ^ P x _^h2+k2+lf Pi jh2+k2 +l2 Ps ^Jh2+k2+l2 and so on. Measure the spacings, p\$2, and P 3 , take their ratios and then, by using tables of d-spacing ratios, the tentative indices hikiU, etc., are assigned. The correctness of the assignment is then made by measuring the angles a, p, y, and comparing them to the calculated values based on h\k]li, \i2k2h, etc. cos« = (/2,/23 + £ , # 3 +lxl3)/(-yJhx2 + k2 +/,2 • *Jh2 + k2 +l2 This process can be time consuming, as it is often a question of trial and error in order to obtain the correct solution. The results can be checked by measuring other Kikuchi lines in the pattern. Once the lines are indexed, the poles A, B, C are obtained by taking the respective cross products, e.g. A=[/j/&y//]x [T f^ok]- Let these poles be piqfi, P2q2f2 and piqsri. The indices of the direction of the beam through the crystal (i.e., where the transmitted beam intersects the pattern at O) can be found either by calculation or by Stereographic analysis. Both require measurement Appendix: Kikuchi Electron Diffraction and analysis 179 of the angles OA>OB >OC (^&ure Measure the distances OA, OB and convert to angles using either the calibration, p/ =K29, or by measuring distances, AB-BC-CA, and convert these into angles, since the angles AB>BC>CAcan ^ e calculated once, A, B, C are indexed. Let [uvw] be the axis O, then if 916263 are the angles QAOBOC qp, + vqx + wrx Ju2 + v2 + w2 //>, + t f up2 +vq2 + wr2 + v2 + w2 \pl+ql + r22 up3 +vq3 + wr3 Ju2 + v2 + w2 y cos<93 and uvw is determined by solving these equations. Once uvw of an individual grain was determined, the misorientation between adjacent grains could be easily calculated using similar cosine formula. An example of this calculation process is illustrated in the attached spread sheet using MS Excel software. Appendix: Kikuchi Electron Diffraction and analysis 180 Incident beom Reflecting plane Troce of reflecting plone AB Specimen Photo plate Figure A. 1. Geometry of formation of Kikuchi lines, a. Incident beam is inelastically scattered; inelastic electrons are then rescattered coherently by plane AB to produce cones of radiation which intersect the reflecting sphere as slightly curved lines, which bisect the reflecting plane. Each Kikuchi pair corresponds to a unique reflecting plane, b. Diffraction representation for crystal oriented for Bragg diffraction. In this case, more electrons are scattered into the diffracting direction so that the Kikuchi lines Ki are bright, and K2 dark. Appendix: Kikuchi Electron Diffraction and analysis 181 Figure A.2. Reciprocal lattice-reflecting sphere construction showing relation of Kikuchi pattern to spot pattern for, (a) exact Bragg two-beam orientation, and lb) the symmetrical orientation. The spacing of Kikuchi lines is independent of crystal orientation. Appendix: Kikuchi Electron Diffraction and analysis 182 Figure A.3. Stereographic projection of first order Bragg contours (and Kikuchi pairs) drawn to scale for 100 kV electrons in aluminum up to (h2 +1C2+l2) = 27 Appendix: Kikuchi Electron Diffraction and analysis 183 Figure A.4. Sketch to illustrate indexing of any Kikuchi pattern. If the poles A, B, C do not appear on the plate, use tracing paper to extend the Kikuchi lines through points of intersection. 

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