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Modelling of austenite-to-ferrite transformation behaviour in low carbon steels during run-out table… Pandi, Rassoul 1998

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M O D E L L I N G O F A U S T E N I T E - T O - F E R R I T E T R A N S F O R M A T I O N B E H A V I O U R IN L O W C A R B O N S T E E L S D U R I N G R U N - O U T T A B L E C O O L I N G By Rassoul Pandi B .A.Sc , Tehran University, Tehran, Iran, 1987 M.Eng., McGil l University, Montreal, Canada, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Metals and Materials Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1998 © Rassoul Pandi, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) A B S T R A C T The need to manufacture high quality steel products that meet specific requirements dictates the control of steel processing. For flat products, controlled rolling in the finishing mill followed by accelerated cooling on the run-out table of a hot strip mill are the final processing steps before coiling the hot band. These three processing steps significantly influence the final microstructure and thus, the mechanical properties of the hot rolled steel. This work examines the austenite-to-ferrite phase transformation under run-out table conditions for two plain-carbon and two single microalloyed commercial low carbon steels. The austenite decomposition was quantified using diametral dilation measurements on a Gleeble 1500 thermomechanical simulator. The conducted tests were designed to simulate the microstructural conditions present at the exit of the finishing mill, i.e., the retained strain, the austenite grain size at the exit of finishing mill and the accelerated cooling conditions of the run-out table; the austenite decomposition kinetics were measured during the accelerated cooling simulation. Hot rolling which involves progressive stages of deformation and recrystallization of austenite during the concomitant reduction of temperature results in refined austenite grains. Refining the austenite grain raises the transformation temperature, increases the ferrite nucleation density and thereby refines the resulting ferrite grains. Accelerated cooling lowers the transformation temperature with associated ferrite grain refinement. A novel method was developed to characterize the austenite-to-ferrite phase transformation kinetics simulating the industrial, non-isothermal operating conditions. ii ABSTRACT iii This technique adopts the additivity rule, utilizing the grain size-modified Avrami equation, back-calculating the effective isothermal Avrami equation solely from continuous cooling test data. In this way, it permits the modelling of the austenite decomposition kinetics in low carbon steels where isothermal tests are difficult to perform. A more fundamental approach based on a carbon diffusion model incorporating a solute drag-like effect (SDLE) was also employed to describe the transformation kinetics of austenite to ferrite. The accuracy of the diffusion model could be improved by including the austenite grain size distribution rather than a mean grain size as an initial condition. For high strength, low alloy, Nb microalloyed (HSLA-Nb) steel, the presence of Nb retards austenite recrystallization, creating a temperature, T n r , below which the rolling strain will be accumulated as the steel progresses from stand to stand. The retained strain enhances the nucleation of the ferrite during austenite decomposition and results in enhanced strength and toughness properties. Rolling under no-recrystallization conditions with the accumulation of strain, i.e. controlled rolling, is a commonly employed rolling practice in the last stands of finish rolling. Thus, for the HSLA-Nb grade, the effect of retained strain on the austenite decomposition has been evaluated by performing continuous cooling transformation tests after deformation below T n r . Acceleration of the transformation and additional ferrite grain refinement was obtained as a result of the prior deformation which increased the ferrite nucleation rate by introducing additional nucleation sites both on the austenite grain boundary and within the deformed grains at crystallographic defects. However, the degree of grain refinement was strongly affected by the initial austenite grain size and the cooling conditions; the effect was small for fine austenite grains and accelerated cooling, whereas for larger austenite grains and lower cooling rates, significant additional grain refinement was observed which increased with increasing retained strain. It is important to note that the retained strain increases the austenite decomposition temperature for a given cooling rate and therefore augments the production of a more equilibrium microstructure, i.e., more polygonal ferrite and pearlite. T A B L E O F C O N T E N T S A B S T R A C T " T A B L E O F C O N T E N T S • v LIST O F F I G U R E S v i i LIST O F T A B L E S x i i i LIST O F S Y M B O L S x i v A C K N O W L E D G E M E N T x v i i i CHAPTER 1 1 INTRODUCTION 1 CHAPTER 2 8 LITERATURE REVIEW 8 2.1 ISOTHERMAL TRANSFORMATION OF PROEUTECTOID y >a 8 2.1.1 Carbon Diffusion Model 10 2.1.1.1 Solute Drag-like Effect (SDLE) 13 2.1.2 Johnson-Mehl-Avrami-Kolmogorov (JMAK.) Model 15 2.1.3 Grain Size-Modified Avrami Equation 19 2.1.4 Umemoto Equation 20 2.2 APPLICATION OF ISOTHERMAL TRANSFORMATION KINETICS TO DESCRIBE NON-ISOTHERMAL CONDITIONS 21 2.3 THE MORPHOLOGICAL CLASSIFICATION OF AUSTENITE DECOMPOSITION 24 2.4 AUSTENITE DECOMPOSITION ON THE RUN-OUT TABLE 26 2.5 EFFECT OF PROCESSING VARIABLES ON THE AUSTENITE DECOMPOSITION BF.HA VIOUR ON THE RUN-OUT TABLE '. 27 2.5.1 Chemistry 27 2.5.1.1 Plain-C-Mn Steels 28 2.5.1.2 High Strength Low Alloy (HSLA) Microalloyed Steels 30 2.5.2 Effect of Austenite Grain Size 33 2.5.3 Effect of Cooling Rate 34 2.5.4 Effect of Pre-strain 35 2.6 FERRITE GRAIN SIZE 39 CHAPTER 3 61 OBJECTIVES 61 CHAPTER 4 63 E X P E R I M E N T A L TECHNIQUES 63 4.1 MATERIALS 63 4.2 EXPERIMENTAL EQUIPMENT 64 4.2.1 Gleeble 1500 Thermomechanical Simulator 64 4.2.2 Torsion Test Apparatus 66 4.2.3 Microstructural Investigation 67 4.3 EXPERIMENTAL PROCEDURES 69 4.3.1 CCT Tests 69 4.3.2 Double Hit Compression Tests 72 4.3.3 Pre-strain Tests 74 4.3.3.1 Compression 74 4.3.3.2 Torsion 75 V TABLE OF CONTENTS vi C H A P T E R 5 83 C C T RESULTS 83 5. /. HEA T TREA TMENTSIMULA TION TO DEVELOP DESIRED A USTENITE GRAIN SIZE 83 5.2 CCT RESPONSE 87 5.2.1 Quantification of Transformation Start Temperature (A^) 89 5.2.2 Microstructural Evolution During CCT Testing 90 5.2.2.1 The Ferrite Grain Size and Volume Fraction 90 5.2.2.2 Transition From Polygonal to Non-Polygonal Microstructure 93 5.3 MODELING OF y->a TRANSFORMATION KINETICS 95 5.3.1 Transformation Start Temperature (A^) 95 5.3.2 Ferrite Growth Kinetics 97 5.3.2.1 Avrami Equation 97 5.3.2.2 Umemoto Equation 102 5.3.2.3 Grain Size-Modified Avrami Equation 103 5.4 COMPARISON OF THE TRANSFORMATION BEHA VIOUR OF THE FOUR STEELS 106 5.4.1 CCT Tests 106 5.4.2 Comparison Between DQSK and HSLA-V Steels 107 5.5 FERRITE GRAIN SIZE 108 C H A P T E R 6 134 RETAINED STRAIN RESULTS 134 6.1 DOUBLE HIT COMPRESSION TESTS 134 6.2 EFFECT OF RETAINED STRAIN ON THE A USTENITE DECOMPOSITION BEHA VIOUR FOR THE HSLA-Nb STEEL 136 6.2.1 Test Matrix 136 6.2.2 Effect of Retained Strain During Controlled Cooling 137 6.2.3 Effect of Combined Retained Strain and Accelerated Cooling on The Phase Transformation Behaviour and The Resulting Microstructure 142 6.3 EMPIRICAL MODELLING OF AUSTENITE-TO-FERRITE TRANSFORMATION KINETICS 146 6.3.1 Transformation Start Temperature 146 6.3.2 Ferrite Growth Kinetics 148 6.3.3 Modelling of Final Microstructure 151 C H A P T E R 7 169 C A R B O N DIFFUSION RESULTS 169 7. / CARBON DIFFUSION MODEL : 169 7.1.1 Model Assumptions 172 7.2 MODEL PREDICTIONS 173 7.2.1 Continuous Cooling Conditions 173 7.2.2 Effect of Austenite Grain Size Distribution 177 C H A P T E R 8 195 S U M M A R Y A N D CONCLUSIONS 195 8.1 SUMMARY. 195 8.2 CONCLUSIONS 197 8.3 FUTURE WORK 199 R E F E R E N C E S 201 APPENDIX 211 LIST OF FIGURES Figure 1.1: Schematic representation of a hot strip mill. 7 Figure 2.1: The ratio of the driving force for heterogeneous nucleation of grain corners ( A G * Q / A G * ( 1 0 I T 1 ) , grain edges (AG* E/AC-*hom) and grain boundaries ( A G * g / A G * j l o m ) to that for homogenous nucleation and as a function of the cosine of the contact angle, 9 [8]. 4 4 Figure 2.2: Schematic representation of fraction transformed as a function of time for a typical isothermal nucleation and growth phase transformation. 4 5 Figure 2.3: Fe-Fe3C phase diagram depicting equilibrium concentration for the formation of proeutectoid ferrite from austenite at Temperature T ] . 4 6 Figure 2.4: A proeutectoid portion of the Fe-Fe3C phase diagram showing the equilibrium, the critical cooling (r) and the critical heating (c) phase field boundaries for a rate of heating and cooling at 0.125 °C/min [ n l 47 Figure 2.5: Diagram showing the approximation of continuous cooling as the sum of a series of short time of isothermal increments 48 Figure 2.6: Schematic diagram of the formation process of a new phase during continuous cooling [4]. 49 Figure 2.7: Isothermal transformation diagram for a 1019 steel C66L 5 0 Figure 2.8: Modified CCT transformation diagram for 1017-1022 steels t 6 7 ] . 51 Figure 2.9: The Solubility products of aluminum, niobium, vanadium and titanium nitrides and carbides t 8 0 ! 52 Figure 2.10: CCT diagram for three steels which contain 0.2% wt.% C, 1.2% wt.% Mn and 0.11 wt.% Nb showing the effect of reheat temperatures of 1300 or 900 °C [92L 53 Figure 2.11: An early stage of ferrite transformation in 4 different austenite conditions; (a) undeformed condition; (b) a deformed condition in which the grains are elongated only; (c) a deformed condition in which grains are elongated and the rate of nucleation on grain boundaries is increased and (d) a deformed condition in which grains are elongated, the rate of nucleation on grain boundaries is increased and nucleation also occurs on deformation bands within the deformed grains [96]_ 54 Figure 2.12: The shape change of a spherical austenite grain by rolling with reduction p; (a) before rolling and (b) after rolling 55 Figure 2.13: The ratio of austenite grain boundary surface area per unit volume before and after rolling, as a function of rolling reduction, p [4]. 56 Figure 2.14: Effect of rolling reduction on the total effective nucleating area/vol., S v , for cube-shaped austenite grains of 20, 50 and 100 um [98] 57 Figure 2.15: Contribution of the increase in grain boundary area/vol., , and internal deformation band area/vol., S'fH, to the total nucleation area/vol., S'1"'"1, for an initial austenite grain size of 100 um [98]. 58 Figure 2.16: Comparison of measured ferrite grain size and model prediction U®\. 59 Figure 2.17: Difference of the calculated ferrite grain size, d c a | , from the value observed, d 0 b s , as a function of the dislocation density before the start of transformation [' 20]. 6 0 Figure 4.1: Schematic diagram of the tubular specimen support in the Gleeble test chamber. 77 vii LIST OF FIGURES viii Figure 4.2: Schematic diagram of axisymmetric compression testing in the Gleeble test chamber. 78 Figure 4.3: General overview of the MTS torsion machine at McGil l University; (1) hydraulic servovalve; (2) hydraulic motor; (3) rotating torsion bar; (4) turn potentiometer; (5) specimen; (6) stationary grip and (7) torque cell. 79 Figure 4.4: The (a) water quenched sample of HSLA-Nb steel showing ferrite outlining the original austenite grain boundaries and the (b) transparent tracing of the prior austenite grain boundaries for the HSLA-Nb steel. 80 Figure 4.5: Experimental dilation versus temperature results for the A36 steel after austenitizing at 950 °C. The solid lines indicate the extrapolations from the pre- and post-transformation regions (dy=l 8 um). 81 Figure 4.6: Typical double hit compression test performed at 850 °C for interpass times of I and 10 seconds for the A36 steel having an austenite grain size of 18 um and deformed at a strain rate of 0.1/s. 82 Figure 5.1: Schematic diagram for producing a small austenite grain size characteristic of that realized at the end of the finishing mill. 111 Figure 5.2: Schematic diagram for producing a 46 pm austenite grain size for the A36 steel.112 Figure 5.3: Austenite grain growth behavior for the HSLA-Nb steel obtained by Gleeble tests at a 5 °C/s heating rate and a 5 min. holding time, and H S L A - V steel, air furnace heated to the designated temperature and hold for 60 min. [135] 113 Figure 5.4: Continuous cooling transformation kinetics for the DQSK steel for initial austenite grain sizes of; (a) 38 um; (b)136 um and (c) 190 um. 114 Figure 5.5: Transformation kinetics for the air cooled («20 °C/s) DQSK steel for the range of initial austenite grain sizes, 38, 136 and 190 pm. 115 Figure 5.6: Transformation start temperature, Ar3, taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 36, 136 and 190 um for the DQSK steel. 116 Figure 5.7: Polygonal ferrite grain size and ferrite volume fraction for the DQSK steel obtained from CCT tests for three different initial austenite grain sizes of 38, 136 and 190 pm. 117 Figure 5.8: Microstructure obtained after continuous cooling tests on the DQSK steel having a 38 pm initial austenite grain size and subjected to different cooling rates; (a) I °C/s; (b) 87 °C/s and (c) 290 °C/s. 118 Figure 5.9: Microstructure obtained after continuous cooling tests on the A36 steel having an 18 um initial austenite grain size and subjected to different cooling rates; (a) I °C/s; (b) 19 °C/s; (c) 65 °C/s and (d) 122 °C/s. 119 Figure 5.10: The transition boundary for the polygonal to non-polygonal microstructure for each of the four steel grades for a range of initial austenite grain sizes and cooling rates. 120 Figure 5.11: Comparison between experimental data and predictions of Ar3 for the H S L A - V steel for different accelerated cooling conditions and initial austenite grain sizes.121 Figure 5.12: Behavior of the Avrami parameter b versus temperature for different CCT tests for the DQSK steel with a 38 pm initial austenite grain size, showing the effect of varying the time exponent n; (a) n=l . l ; (b) n=0.9 and (c) n=0.7. 122 Figure 5.13: Behavior of In b values versus supercooling for the DQSK steel with 38 pm initial austenite grain size and n=0.9. 123 Figure 5.14: Behavior of In b values versus supercooling for the H S L A - V steel with 36 pm initial austenite grain size and n=0.9. 124 Figure 5.15: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the DQSK steel having a 38 pm initial austenite grain size. 125 LIST OF FIGURES ix Figure 5.16: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the DQSK steel having a 38 um initial austenite grain size. 126 Figure 5.17: In b versus In d for the austenite-to-ferrite transformation. 127 Figure 5.18: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 136 urn austenite in the DQSK steel using the grain size-modified Avrami model predictions. 128 Figure 5.19: Comparison of the experimental results with the predictions obtained using the grain size-modified Avrami equation for the DQSK steel having a 38 um initial austenite grain size and m=2. 129 Figure 5.20: Comparison of the y decomposition kinetics obtained for the four candidate steels, each having a similar austenite grain size (38 um DQSK, 46 um A36, 36 urn H S L A - V and 44 um HSLA-Nb) and the same cooling conditions, 1 °C/s. 130 Figure 5.21: Comparison of the austenite decomposition kinetics for the DQSK and H S L A - V steels showing the effect of cooling rate for similar initial austenite grain sizes of 38 um for the DQSK and 36 um for the H S L A - V . 131 Figure 5.22: Microstructures obtained after CCT tests for; (a) DQSK steel having 38 um austenite grain size and subjected to 290 °C/s cooling rate; (b) H S L A - V steel having 36 um austenite grain size and subjected to 238 °C/s cooling rate, and industrial processed coil samples; (c) DQSK and (d) H S L A - V steels. 132 Figure 5.23: Comparison of the experimental ferrite grain size and predictions based on Eq. (5.13) for the HSLA-Nb steel as a function of the transformation start temperature 133 Figure 6.1: Double hit compression test for an interpass time of 10 seconds for the; (a) H S L A - V steel at 900 °C having a 36 um initial austenite grain size and for the (b) HSLA-Nb steel at 880 °C having an 18 um initial austenite grain size (ds/dt=0.1 s"'). 153 Figure 6.2: Austenite decomposition kinetics for the HSLA-Nb steel control cooled at I °C/s cooling rate after 0, 0.3 and 0.6 applied strain for; (a) 18, (b) 44 and (c) 84 um initial austenite grain sizes. 154 Figure 6.3: Microstructure of controlled cooled ((p=l °C/s) compression specimens of HSLA-Nb steel after deformation at 880 °C; (a) dy=18 um and e=0, (b) dy= 18 um s=0.6, (c), dy=84 um and s=0 and (d) dy=84 um e=0.6. 155 Figure 6.4: Effect of cooling rate on the austenite decomposition kinetics obtained from the HSLA-Nb steel with an 18 um austenite grain size and with; (a) 0.2 and (b) 0.5 retained strain. 156 Figure 6.5: Effect of cooling rate on the austenite decomposition kinetics obtained from the HSLA-Nb steel with an 84 um austenite grain size and with; (a) 0.2 and (b) 0.5 retained strain. 157 Figure 6.6: Effect of retained strain and cooling rate on the austenite decomposition kinetics obtained for the HSLA-Nb steel; (a) 18 um austenite cooled a t«100 °C/s and (b) 84 um austenite cooled at «20 °C/s. 158 Figure 6.7: Comparison of the microstructure of HSLA-Nb steels obtained in laboratory test with that of a industrially processed hot rolled coil; (a) continuous cooling test (dy=T8 um, retained 8=0.5, cp«100 °C/s) and (b) industrial processed coil sample. 159 Figure 6.8: The effect of retained strain and cooling rate on the ferrite fraction produced during the decomposition of 84 um austenite. 160 Figure 6.9: The effect of retained strain on the austenite grain size dependence of the critical cooling rate for polygonal or non-polygonal ferrite formation. 161 LIST OF FIGURES x Figure 6.10: Effect of austenite grain size, cooling rate and retained strain on the transformation start temperature, Ar3, (taken at the temperature of 5% transformation) for the HSLA-Nb steel with an 18 or 84 um austenite grain size. 162 Figure 6.11: Comparison of the experimental TQ QJ , Ar3 temperature for the HSLA-Nb steel versus equation (6.1) predictions for retained strain up to 0.6, austenite grain sizes varying between 18 and 84 um and a cooling rate of 1 °C/s. 163 Figure 6.12: Comparison of the experimental ferrite transformation kinetics for three different levels of applied strain (0, 0.3 and 0.6) with equation (6.2) predictions for the HSLA-Nb steel having an austenite grain size of 84 um cooled at 1 °C/s. 164 Figure 6.13: Comparison of the HSLA-Nb experimental ferrite transformation kinetics for different initial austenite grain sizes, cooling rates and levels of retained strain with model predictions based on equation (6.3). 165 Figure 6.14: Comparison of the HSLA-Nb experimental ferrite transformation kinetics for different initial austenite grain sizes, cooling rates and levels of retained strain with model predictions based on equation (6.4). 166 Figure 6.15: Ferrite grain size as a function of cooling rate for different levels of applied strain and; (a) 18, (b) 44 and (b) 84 um initial austenite grain sizes. 167 Figure 6.16: A comparison of experimental data and Eq. (6.5) predictions, showing the effect of cooling rate on the ferrite grain size for different austenite grain sizes of 18 um, 44 um and 84 um (e=0.5). 168 Figure 7.1: Schematic diagram of the hypo-eutectoid section of the iron-carbon equilibrium diagram showing the carbon diffusion gradients associated with the growth of ferrite at two different temperatures [L56]_ 181 Figure 7.2: Schematic diagram illustrating the tetrakaidecahedron shape attributed to an austenite grain and the spherical geometries used in the mathematical model [156]. 1 8 2 Figure 7.3: Schematic diagram illustrating the nodal arrangement and initial and boundary conditions for the spherical diffusion model [L56] 183 Figure 7.4: Comparison of the experimentally observed time to produce 50% ferrite with that predicted from the carbon diffusion model for the 0.17 wt %C with a dy=18 um (simulating the A36 steel) P ' ] . 184 Figure 7.5: The effect of Mn segregation, quantified by the segregation energy, E, on the local equilibrium carbon concentration at the austenite/ferrite interface in the A36 steel; the broken line indicates the carbon bulk concentration, C^ P ' l . 185 Figure 7.6: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.038 wt.% C, simulating the DQSK steel with 38 um initial austenite grain size. 186 Figure 7.7: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.17 wt.% C, simulating the A36 steel with 18 um initial austenite grain size. 187 Figure 7.8: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.045 wt.% C, simulating the H S L A - V steel with 36 um initial austenite grain size. 188 Figure 7.9: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.082 wt.% C, simulating the H S L A -Nb steel with 18 um initial austenite grain size. 189 Figure 7.10: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.045 wt % C , simulating the H S L A - V steel with 120 urn initial austenite grain size (cp=l °C/s). 190 LIST OF FIGURES xi Figure 7.11: The three-dimensional austenite grain size distribution for the H S L A - V steel; (a) for a reheating temperature of 950 °C and holding time of 2 minutes (giving an average y grain size of 36 pm) and (b) for a reheating temperature of 1150 °C and holding time of 30 seconds (giving an average y grain size of 120 pm). 191 Figure 7.12: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.045 wt % C , simulating the H S L A - V steel using 80, 100, 120 and 140 pm as an average for the initial austenite grain size and a cooling rate of 1 °C/s. 192 Figure 7.13: The volume fraction of each grain size class for the H S L A - V steel reheated to 1150 °C and held for 30 seconds, giving an "average y grain size" of 120 pm. 193 Figure 7.14: Comparison of the experimental results with the predictions employing 120 pm average austenite grain size and austenite grain size distribution for the 0.045 wt % C , simulating the H S L A - V steel (cp=l °C/s). 194 Fig. App. 1: Transformation kinetics for the air cooled («20 °C/s) A36 steel for the range of initial austenite grain sizes, 15, 18 and 46 pm. 211 Fig. App. 2: Transformation kinetics for the air cooled («20 °C/s) H S L A - V steel for the range of initial austenite grain sizes, 36, 85 and 120 pm. 212 Fig. App. 3: Transformation kinetics for the air cooled («20 °C/s) HSLA-Nb steel for the range of initial austenite grain sizes, 18, 44 and 84 pm. 213 Fig. App. 4: Transformation start temperature, A ^ , taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 15, 18 and 46 pm for the A36 steel. 214 Fig. App. 5: Transformation start temperature, Ar3, taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 36, 85 and 120 pm for the H S L A - V steel. 215 Fig. App. 6: Transformation start temperature, Ar3, taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 18, 44 and 84 pm for the HSLA-Nb steel. 216 Fig. App. 7: Polygonal ferrite grain size and ferrite volume fraction for the A36 steel obtained from CCT tests for three different initial austenite grain sizes of 15, 18 and 46 pm. 217 Fig. App. 8: Polygonal ferrite grain size and ferrite volume fraction for the H S L A - V steel obtained from CCT tests for three different initial austenite grain sizes of 36, 85 and 120 pm. 218 Fig. App. 9: Polygonal ferrite grain size and ferrite volume fraction for the HSLA-Nb steel obtained from CCT tests for three different initial austenite grain sizes of 18, 44 and 84 pm. 219 Fig. App. 10: Behavior of In b values versus supercooling for the A36 steel with 18 pm initial austenite grain size and n=0.9. 220 Fig. App. 11: Behavior of In b values versus supercooling for the HSLA-Nb steel with 18 pm initial austenite grain size and n=0.9. 221 Fig. App. 12: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the A36 steel having a 18 pm initial austenite grain size. 222 Fig. App. 13: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the H S L A - V steel having a 36 pm initial austenite grain size. 223 Fig. App. 14: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the HSLA-Nb steel having a 18 pm initial austenite grain size. 224 Fig. App. 15: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the A36 steel having a 18 pm initial austenite grain size. 225 LIST OF FIGURES xii Fig. App. 16: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the H S L A - V steel having a 36 um initial austenite grain size. 226 Fig. App. 17: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the HSLA-Nb steel having a 18 um initial austenite grain size. 227 Fig. App. 18: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 18 um austenite in the A36 steel with the grain size-modified Avrami model predictions. 228 Fig. App. 19: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 36 um austenite in the H S L A - V steel with the grain size-modified Avrami model predictions. 229 Fig. App. 20: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 18 urn austenite in the HSLA-Nb steel with the grain size-modified Avrami model predictions. 230 Fig. App. 21: Comparison of the experimental y—>a transformation results with the predictions obtained using the grain size-modified Avrami equation for the A36 steel having a 18 um initial austenite grain size and m=2. 231 Fig. App. 22: Comparison of the experimental y->a transformation results with the predictions obtained using the grain size-modified Avrami equation for the H S L A - V steel having a 36 um initial austenite grain size and m=2. 232 Fig. App. 23: Comparison of the experimental y—»a transformation results with the predictions obtained using the grain size-modified Avrami equation for the HSLA-Nb steel having a 18 um initial austenite grain size and m=2. 233 L I S T O F T A B L E S Table 2.1: The exponent n of the Avrami equation for the y-»a transformation. 18 Table 2.2: Empirical equations for predicting ferrite grain size. 41 Table 4.1: Chemical compositions (in wt.%) of the steels investigated. 63 Table 5.1: Heat treatment schedules to develop the specified mean, volumetric austenite grain sizes. 85 Table 5.2: Parameters A and B for Eq. ( 5 . 6 ) . 96 Table 5.3: Parameters C, D and E for Eq. ( 5 . 7 ) . 97 Table 5.4: Parameters F and G for Eq. ( 5 . 1 0 ) . 101 Table 5.5: Exponent m and parameters F and H for Eqs. ( 5 . 1 1 ) and ( 5 . 1 2 ) . 104 Table 5.6: Parameters F and H for Eq. ( 5 . 1 2 ) . 105 Table 5.7: The ferrite volume fraction, F, and J, K and r| fitting parameters for Eq. (5.13) [ 1 4 7 ] . 110 Table 6.1: The experimental conditions for quantification of the effect of retained strain on the austenite decomposition kinetics and resulting microstructure for the HSLA-Nb steel. 137 Table 7.1: Parameters E Q , E I of Eq. ( 7 . 5 ) . 176 Table 8.1: Effect of processing variables on the phase transformation behaviour. 198 xiii L I S T O F S Y M B O L S b Kinetic parameter in Avrami equation Carbon content in mole fraction c 0 Initial concentration of carbon C a Concentration of carbon in ferrite Cy Concentration of carbon in austenite deff. Effective austenite grain size (um) d a Ferrite grain size (um) dy Austenite grain size (um) D(T) Diameter of specimen at temperature T (mm) Drc Diffusion coefficient of carbon in austenite (m^s'l) G Growth rate AG Free energy change (kJ/mole) AH The change in enthalpy I Nucleation rate (s~l) J Diffusion flux of carbon in austenite (genres" 1) k Rate constant in grain size-modified Avrami equation m Growth geometry-dependent factor in grain size-modified Avrami equation n Kinetic parameter in Avrami equation N Number of nuclei per volume N 0 Available number of potential nuclei N L R Number of grain boundary intercept per unit length along the rolling direction N L Z Number of grain boundary intercept per unit length along the rolling thickness direction xiv LIST OF SYMBOLS N L T Number of grain boundary intercept per unit length along the transverse rollin direction p Rolling reduction Q Activation energy (kJ/mole) R Gas constant (J/°Cmole) R Rolling reduction S Fractional softening S Thickness of planar ferrite precipitation (m) s v Total effective area per unit volume (mm^/mm^) SV(GB) Grain boundary area per unit volume (mra^/mm^) SV(IPD) Intragranular planar defect area per unit volume (mm^/mm^) S gb Surface area of the austenite grain boundary AS The change in entropy t Time (s) ts Non-isothermal incubation time (s) T(T) Isothermal incubation time at temperature T (s) At Time increment (s) T Temperature (°C or °K) AT Temperature change (°C) T A c i Ferrite to austenite transformation start temperature during heating (°C) T A C 3 Ferrite to austenite transformation finish temperature during heating (°C) T A e i Austenite-pearlite equilibrium transformation temperature (°C) T A e 3 Austenite-ferrite equilibrium transformation temperature (°C) T A r i Austenite to ferrite transformation finish temperature during cooling (°C) T A r 3 Austenite to ferrite transformation start temperature during cooling (°C) T E Equilibrium temperature T 1 1 nr Temperature of no recrystallization (°C) LIST OF SYMBOLS xvi X Diffusion distance (m) X Fraction transformed a Symbol denoting ferrite a Parabolic rate constant of ferrite ap Thermal expansion coefficient of produced phase Cty Thermal expansion coefficient of austenite phase s Applied strain <P Cooling rate (°C/s) Y Symbol denoting austenite a Flow stress (M Pa) In the name of Allah, the Beneficent, the Merciful To the memory of my father this thesis is dedicated xvii A C K N O W L E D G E M E N T I would like to express my sincere thanks to my supervisors, Professors E. B. Hawbolt and M . Militzer. 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 modelling group who made a pleasant and cooperative atmosphere to discuss any technical problems. I wish to express my thanks to Professors T. R. Medowcroft and J. K. Brimacombe for their interests in my work and their kindness and support, especially during the later stages of this work when I was not in a good health situation. Many thanks to Mr. B. Chau, Dr. X . Chen, Mr. R. Cardeno and Mr. P. Wenman for their technical assistant. Special thanks to Mr. H. Rastgar for his encouragement and assistance in preparation of this document. I would like to thank Mrs. J. Kitchener 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 and the United States Department of Energy. Last, but not the least, the great sacrifices and patience of all my family members and friends, especially my mother, my parents-in-law, my wife and my daughters are very much appreciated. They have been a source of wisdom, understanding and strength throughout my studies. xviii CHAPTER 1 I N T R O D U C T I O N The hot strip mill provides the main industrial processing path for producing steel in the form of sheet. This process usually consists of five stages of operation: reheating, rough rolling, finish rolling, run-out table cooling and coiling. A schematic diagram of a hot strip mill process is shown in Fig. 1.1. In the reheating furnace, the continuously cast slab is heated to approximately 1250 °C to provide a sufficiently high temperature to permit easy deformation Dl and to ensure the dissolution of soluble precipitates formed during casting and cooling. Through the either reversing or tandem roughing mill, by multi-pass deformation, the slab is reduced from a thickness of approximately 250 mm to a transfer bar which is 20 to 50 mm thick. Finish rolling takes place at temperatures between 1100 and 850 °C in a tandem mill with four to seven successive finishing stands and the final thickness can range from approximately 1 to 10 mm. The rolling schedule in the finishing stands, i.e., the amount of reduction applied in each pass, depends on the desired final thickness, usually leaving the last two passes with lower reduction to ensure surface quality and shape control. The steel strip then enters the run-out table where it is control cooled by a combination of water sprays and air cooling between the spray banks. The cooling rate of the strip is determined by the strip thickness and the velocity as well 1 Chapter 1 INTRODUCTION 2 as the flow rate of the water. The average cooling rates for accelerated cooling are usually in the range 10-150 °C/s; the maximum cooling rates obtained directly under the water sprays. During the initial heating of the slab in the reheating furnace, significant growth of the austenite grains occurs. Grain growth may also occur between the roughing passes where the temperature is high and the interpass time is relatively long (>30 seconds), providing appropriate conditions for austenite grain growth. During rough rolling which can be both reversing or tandem, the deformation usually causes work hardening which is followed by dynamic recovery, and subsequent static recovery and recrystallization; the latter usually takes place between deformation passes. However, dynamic recrystallization can occur during rough rolling at high temperatures and low strain rates [2], followed by metadynamic recrystallization between passes. At the lower temperatures (<1100 °C) and the higher strain rates (>10 s~l) employed for finish rolling, work hardening and dynamic recovery predominate with or without static recovery and recrystallization between the stands, depending on steel chemistry, temperature and interpass time. Following hot deformation in the austenite phase field, the subsequent decomposition of the austenite is initiated on the run-out table during accelerated cooling and completed before or during coiling '. The final microstructure resulting from the phase transformation is determined by the steel chemistry, the austenite grain size, the retained strain (i.e., the stored strain energy related 1 Dual-phase steels are intentionally rolled in the intercritical (OC+Y) two-phase field. These steels are not considered in this thesis. Chapter 1 INTRODUCTION 3 to the deformed and unrecrystallized austenite), the state of precipitation in high strength low alloy (HSLA) steels and the cooling conditions. Accelerated cooling on the run-out table was originally developed to keep the length of a hot strip mill within reasonable limits [3]. Later on it was discovered that this cooling regime has an important influence on the properties of the hot rolled strip; as a result, several cooling systems were developed. Since the run-out table is part of an integrated system, it is important to realize that the metallurgical events occurring during accelerated cooling can be affected by earlier processing in the furnace and in the roughing and finishing passes. The most important initial parameters on the run-out table are chemistry, finishing mill exit temperature, prior austenite grain size, retained strain and state of precipitation of the microalloying elements. For a given initial condition at the exit of the finishing mill, the accelerated cooling pattern on the run-out table and the coiling temperature are the most important factors controlling the metallurgical events taking place in the final stages of the hot strip mill process. Process modelling is an effective method to relate chemistry and processing variables to the mechanical properties of the produced steel. From a metallurgical perspective, the models should describe the thermal history and associated microstructural changes occurring during reheating, hot working in the roughing and finishing mills, during accelerated cooling on the run-out table and coiling to finally relate the resulting microstructure to the mechanical properties of the hot-rolled product [4]. Such a hot strip mill process model is currently being developed in the Centre for Metallurgical Process Engineering at the University of British Columbia (UBC) as part of the Advanced Process Control Program (APCP) of the American Iron and Steel Institute Chapter 1 INTRODUCTION 4 (AISI) supported by the United States Department of Energy (DOE). To achieve this goal, the research team at U B C is collaborating with the National Institute of Standards and Technology (NIST) in Boulder, Colorado and the United States Steel (USS) Corp. in Pittsburgh, Pennsylvania. USS supplies the steels and the mill data used in this study, NIST is responsible for quantifying the constitutive behaviour of these steels and the mechanical properties and U B C develops the thermal, deformation and microstructure models. The latter requires extensive physical metallurgy research and simulation testing to model the grain growth, recrystallization, phase transformation and precipitation occurring during hot rolling, run-out table cooling and coiling. The modelling of the phase transformation kinetics and the resulting microstructure in two plain-carbon (DQSK and A36) and two microalloyed steels (HSLA-V and HSLA-Nb) is the focus of this thesis; the author of this work is a member of the physical metallurgy research team. Plain-carbon steels are essentially iron-carbon-manganese alloys. Reducing the carbon level in plain-carbon steels improves properties such as weldability (related to hardenability) and formability (related to plastic ductility). Formability is a generic term related to a number of properties i.e., bendability, stretch-forming and deep-drawing characteristics [5]. In the hot strip mill processing of plain-carbon steels, austenite grain refinement is achieved as a result of progressive deformation (hot rolling) and subsequent recrystallization of austenite at reducing temperatures. Decreasing the austenite. grain size increases the austenite grain boundary area per unit volume, this being the main site for nucleation of ferrite. The resulting ferrite grain size is then controlled by the austenite grain size obtained during the austenite-to-ferrite transformation, the cooling profile being Chapter 1 INTRODUCTION 5 the most important parameter determining the austenite decomposition temperature and the subsequent ferrite nucleation rate. Although low carbon (<0.2 wt% C) plain-carbon steels dominate hot rolled production, their lack of strength is a major drawback [6]. This problem and the requirement for a steel having improved weldability, formability and strength, encouraged the steel makers to develop a new generation of steels called HSLA steels. These steels are low carbon steels (<0.1 wt.% C) containing microalloying elements such as V , Ti and Nb and have an improved strength-to-weight ratio. This allows, for example, the use of thinner-gauge sheets in the automotive industry, resulting in lighter and more fuel-efficient automobiles. The improved strength in HSLA steels is derived from ferrite grain refinement and precipitation strengthening. While the former results from an increased ferrite nucleation rate during the austenite-to-ferrite transformation, the latter is predominantly caused by microalloyed carbonitrides precipitated in the ferrite phase during run-out table cooling and/or coiling. In HSLA-Nb steels there is a temperature below which recrystallization does not occur during the short interpass times in the final passes in the finishing rolling stands. This temperature is called the no recrystallization temperature, Tm, and results when Nb in solution and/or precipitates of Nb(C, N), reduces the mobility of the austenite grain boundary thereby preventing recrystallization in the available interstand time. Therefore, during hot rolling of HSLA-Nb steels, deformation can be applied either above T n r where recrystallization is usually completed between the roll passes or below T n r (between T n r Chapter 1 INTRODUCTION 6 and A r 3 ) where plastic strain is accumulated in the final stands of the mill, prior to the austenite decomposition. The latter processing path is referred to as controlled rolling. Deformation in the finishing mill between T n r and A r 3 produces elongated austenite grains called "pancaked" austenite. In hot strip mill controlled rolling processing of H S L A steels, usually most of the deformation is employed above T n r , with only the last few stands operating between Tm and A r 3 17]. The retained strain from deformation between Tm and A r 3 can substantially increase the number of available ferrite nucleation sites at the austenite grain boundaries and within the austenite grains at twin boundaries and/or at deformation bands. Accelerated cooling after hot rolling is recognized as an advanced thermal treatment in the hot-rolling process. The accelerated cooling reduces the temperature of the austenite-to-ferrite transformation, enhancing the ferrite nucleation rate, thereby producing a finer ferrite with higher strength and improved toughness. High strength steel with good formability at low temperature and superior weldability can be produced by an optimum combination of controlled-rolling and accelerated cooling. Quantifying the effect of cooling rate, austenite grain size and retained strain on the subsequent decomposition kinetics of austenite and on the resulting microstructure in two low carbon plain-carbon steels (DQSK and A36) and two single microalloyed HSLA (HSLA-V and HSLA-Nb) steels are the objectives of this thesis. In pursuance of these objectives, a number of experimental simulation tests were conducted followed by mathematical modelling of the results to describe the austenite-to-ferrite transformation behaviour of the four steels in this study. CHAPTER 2 LITERATURE REVIEW 2.1 ISOTHERMAL TRANSFORMATION OF PROEUTECTOID y—»cc Isothermal transformation tests are usually employed to provide a better understanding of the y-»a proeutectoid transformation mechanism. The austenite-to-ferrite phase transformation occurs by nucleation and growth. In the absence of austenite deformation, austenite grain corners, grain edges and grain boundaries have been observed as preferred sites for ferrite nucleation [8]. The free energies for nucleation on these sites are reduced by elimination of the boundaries originally present. Cahn [8] determined the ratios of the critical free energy of nucleation at the grain corner, grain edge and grain boundary to the homogeneous nucleation ( A G * c / A G * n o m , AG*£/AG*hom a n d ^Cr*g/AG*h 0m' respectively) as a function of the cosine of the contact angle, 0, as shown in Fig. 2.1. The resulting reduced free energy associated with heterogeneous nucleation starting at grain corners followed by grain edges and boundaries results in a smaller critical nucleus size when compared to homogeneous nucleation [9]. Thus, the heterogeneous ferrite nucleation is initiated first at grain corners, followed by 8 Chapter 2 LITERATURE REVIEW 9 grain edges and then grain boundaries, reflecting the decreased free energy required for nucleation for each nucleation site as compared to that for homogeneous nucleation. Generally, the isothermal transformation kinetics shows a sigmoidal shaped curve, such as that illustrated in Fig. 2.2. Depending on the carbon content and temperature, the isothermal y—»a transformation may also exhibit a pre-transformation incubation period, prior to the start of transformation. This incubation time increases with increasing carbon content and approaches the minimum for pure iron. At the early stages of transformation, the rate of transformation (the derivative of the fraction transformed with time) increases rapidly. This is primarily due to the increasing nucleation rate. Following the early stages, the transformation rate reaches a nearly constant value reflecting the balanced combination of nucleation and growth or early site saturation and growth and, finally decreases to zero. At the later stages of the transformation, the carbon diffusion fields from adjacent ferrite grains, each being created by rejection of carbon into the remaining y phase at the growing a interface, overlap. This effect reduces the carbon gradient at the interface and thus diminishes the driving force for diffusion. This phenomenon is known as soft impingement. Growth stops when one ferrite growing interface impinges on another; this is called hard impingement. There are two fundamental mechanisms proposed for the diffusive redistribution occurring at the transformation interface H^]. in the first one, the substitutional elements are redistributed to maintain thermodynamic equilibrium at the cc /y interface. This is full partitioning of alloying elements called orthoequilibrium (OE). In the second case, as a kinetics point of view, there is no redistribution and therefore partitioning of substitutional elements. Two distinct limiting constraints have been recognized to define Chapter 2 LITERATURE REVIEW 10 no-partition states U®\. The first is designated as paraequilibrium (PE) and the second is designated no-partition local equilibrium (NPLE). PE is a limiting state defined by a uniform carbon chemical potential and a continuous substitutional element to iron mole fraction ratio at the transforming interface. For paraequilibrium, the boundary may migrate with an equilibrium carbon interface composition but virtually no substitutional solute partitioning in the bulk of the two phases P 2> 1 3 L NEPE is a kinetics state defined by a no-partition local equilibrium for all components at the interface which requires a corresponding steep diffusion profile spike of alloying elements ahead of the interface. 2.1.1 Carbon Diffusion Model Carbon diffusion in austenite as the rate determining step has been used in a number of ferrite growth models [ 1 2 , 1 4 - 1 6 ] . These models assume early nucleation site saturation and equilibrium carbon concentrations at the a/y interface (local equilibrium). After nucleation and site saturation of ferrite at the austenite grain boundaries, the subsequent ferrite growth rate controls the transformation kinetics. A schematic diagram of the formation of proeutectoid ferrite from austenite at temperature T\ with the initial carbon content of C Q is shown in Fig. 2 . 3 . In the austenite-to-ferrite transformation, after step quenching of austenite to temperature T\, the carbon content in the untransformed austenite increases with increasing ferrite; the transformation ceases when the carbon content in the untransformed austenite reaches the equilibrium composition for a given Chapter 2 LITERATURE REVIEW 11 temperature. The ferrite fraction at any stage of transformation can be expressed by the lever law as follows M : where V a ( t ) is the ferrite volume at time t, V Q is the total volume of a specimen, C Q is the initial carbon content, Cy and C a are the equilibrium carbon concentration in the austenite and ferrite respectively, and Fp(t) is the transformed fraction at time t. Zener used a linearized carbon gradient in the austenite at the a/y interface to approximate the carbon diffusion controlled growth rate of ferrite t 1?]. The half-thickness, R, (planar) of the ferrite at time t was expressed by: R = atm (2.2) where a is the parabolic rate constant given as [6]: DU2(Cr-C0) (cr-cjl2(c0-cay « = ~ : , n ' w, (2.3) where D is the diffusivity of carbon in y. Equation (2.3) is a reasonable approximation only for the early stages of transformation where the carbon diffusion fields in the y from Chapter 2 LITERATURE REVIEW 12 separate ferrite growth centers do not overlap each other. However, in low carbon plain-carbon steels, the parabolic rate constant given by Eq. (2.3) can be used until near the end of transformation [18]. A more exact expression for the parabolic rate constant for thickening ferrite, though still based on the assumption that carbon diffusion is rate controlling and the carbon diffusivity is independent of carbon concentration, has been derived H ]^; C -C C -C f - V ' 2 D K V J a = T e x P | f 2 \ a erfc a 2 D 1/2 (2.4) where D is the weighted average diffusivity of carbon in austenite. Kamat et al. [12] developed a model based on carbon diffusion controlled growth to predict the isothermal decomposition kinetics of austenite to ferrite at different temperatures. In this model, it was assumed that the austenite grains have a spherical geometry and, owing to symmetry, there is no carbon redistribution at the center of the sphere. The model also assumed a local carbon equilibrium at the ferrite/austenite interface. The details of this model development will be given in Chapter 7. Kamat et al. [12] found a reasonable agreement between the experimental data and the model predictions for 1010 and 1020 steels. However, results for higher alloyed grades indicate a reaction rate slower than that expected from carbon diffusion [20]. This is consistent with the findings of Silalahi et al. [14] who have shown a relatively poor agreement Chapter 2 LITERATURE REVIEW 13 between experimental results and carbon diffusion model predications. The differences were expected to be attributed to a solute drag-like effect (SDLE) of the alloying element, Mn, on the a/y interface [21] which will be discussed in the next section. As mentioned above, by increasing supercooling the transformation shifts from orthoequilibrium (partitioning of Mn) to paraequilibrium (no partitioning of Mn) conditions. The SDLE reflects the intermediate growth regime between Mn diffusion controlled at low supercooling and carbon diffusion controlled at high supercooling. 2.1.1.1 Solute Drag-like Effect (SDLE) When the interphase boundary moves, the solute atoms migrate along with the grain boundary and exert a drag that reduces the boundary velocity [22]. The magnitude of the drag will depend on the concentration and binding energy of the solute atom to the boundary. Investigations of Fe-C-X alloys have shown that the abnormal slow ferrite allotriomorphs' nucleation [23] and growth kinetics can be ascribed to a SDLE [24, 25]. Under transformation conditions in which there is not enough time for redistribution of the solute elements, the substitutional alloying elements can be concentrated at the a/y interface. These elements lower the activity of carbon at the a/y boundaries and diminish the activity gradient of carbon in y which drives ferrite growth [20]. Since this gradient (dCldx) is responsible for the driving force and instantaneous diffusion flux (J = -DdC I dx), absorption of the solute elements at the a/y interface reduces the ferrite growth kinetics. In extreme cases, ferrite growth ceases altogether [24]. Chapter 2 LITERATURE REVIEW 14 The influence of alloying elements on the kinetics of ferrite growth in Fe-C-X alloys, where X is the substitutional solute, has been studied by a number of investigators [16, 26-29] -phe experimental ferrite growth rates were up to four orders of magnitude faster than that predicted for the full partitioning of the substitutional solute (i.e., Mn, N i , A l , Mo, etc.) [3°]. Aaronson et al. t 2 0 ] found that in Fe-C-X (i.e., where X is Mn, Si, Cr or Ni), the austenite-to-ferrite transformation rate is much slower than in the Fe-C, carbon diffusion controlled binary alloy, which agrees with other work investigating the Mn [21] and Nb microalloy [31] SDLE. Reynolds and Aaronson [32] examined the plate-lengthening kinetics of Widmanstatten ferrite and they found that the addition of a substitutional element can decrease the a/y interface growth rate dramatically i.e., by a factor of 20, in agreement with the existence of a SDLE. Shiflet et al. [33] suggested interface boundary carbide precipitation and segregation of added alloying elements to disordered y / a boundaries to be responsible for lowering the ferrite growth rate. Mainly, however, these discrepancies are attributed to a SDLE. The addition of substitutional microalloying elements, (Ti, Nb and V), can significantly retard the austenite decomposition behaviour [6]. Microalloying elements, in particular Nb and V , which can be in solid solution during austenite decomposition, can also have a major impact on the morphology of the final microstructure i.e., shifting from the polygonal shaped ferrite to acicular (needle-like) ferrite structure [25, 34]. T h u s , because of the SDLE, the microalloyed Nb and V steels exhibit a greater tendency to form a more refined, higher strength acicular ferrite structure. Chapter 2 LITERATURE REVIEW 2.1.2 Johnson-Mehl-Avrami-Kolmogorov ( J M A K ) Model 15 In addition to the fundamental approach to describe phase transformation kinetics, several attempts have been directed, even in recent years, to employ empirical or semi-empirical equations to predict the phase transformation kinetics [4> 35-37] y^g empirical equations are more flexible, having been applied to different chemistries [35-37] a n c j include industrial process parameters such as retained strain [37]. Johnson and Mehl [38] , Avrami [39, 40] and Kolmogorov [41] were pioneers in the development of a semi-empirical equation to describe isothermal transformation kinetics as a function of extended volume. The extended volume is the sum of the volumes of a transformed phase provided that the second phase would nucleate and grow completely independently. In other words, grains can grow without impingement and nucleate everywhere in the parent phase, including in the already transformed volume. By making the following assumptions, i) the nucleation is completely random; ii) the transformation growth rate is isotropic; thus, the produced phase has spherical geometry; iii) the nucleation and growth rates are constant; and iv) an increment of extended volume is formed by totally random nucleation, the volume of a cell at time t nucleated at time zero will be given by: 4 4 / v V =-W^ =-7r(Gt) 3 3 v ' (2.5) Chapter 2 LITERA TURE REVIEW 16 where G is the growth rate. A cell which does not nucleate until time x will have a volume: V = ^ nrG\t-rf (2.6) The number of nuclei that formed in a time increment of dx will be Idt per unit volume of untransformed phase. Thus, i f the particles do not impinge on one another, for a unit total volume: X = ^ V ' = -7TIG3 \{t-rfdz (2.7) 3 o or X = -IGY (2.8) 3 This equation will only be valid for X « l (very small t). As time passes the produced grains will eventually impinge on one another and the rate of transformation will decrease again. The equation valid for randomly distributed nuclei for both long and short time is as follows [42]; Z = l - e x p - - / G V (2.9) Chapter 2 LITERA TURE REVIEW 17 This equation was developed for homogeneous transformations which exhibit a constant nucleation rate, I, and a linear growth such as the austenite-to-pearlite transformation. Avrami [39, 43] examined the described treatment to include a variable nucleation rate based on the number of nucleation sites available. For the case of most of the nucleation sites being consumed in the early stages of the transformation (early site saturation), the following equation was obtained: (An \ X = l - e x p - — N0G3t3 (2.10) V 3 where N Q is the available number of potential nuclei. He then proposed a general relation to calculate the phase transformation kinetics [39, 43]• X = \-exp(-bt") (2.11) where b is a temperature-dependent parameter and n is a parameter descriptive of the mode and geometry of the transformation, which can be calculated from isothermal experimental measurements. This widely used phenomenological description, Eq. (2.11), is commonly known as the Johnson-Mehl-Avrami-Kolmogorov (JMAK) [38-41, 43] equation, or simply the Avrami equation. It is found that 3<n<4 was adequate for three-dimensional growth, 2<n<3 for two-dimensional and l<n<2 was valid for one-Chapter 2 LITERATURE REVIEW 18 dimensional growth [44]. Exact experimental measurements of n for different kinds of transformations and geometries are available in the literature [44]. Cahn [9] also examined the effect of different nucleation sites on the exponent n. He found that in the case of site saturation, n=l, 2 and 3 are appropriate exponents for nucleation at grain boundaries, grain edges and grain corners, respectively. The Avrami equation, Eq. (2.11), has been shown to satisfactorily characterize the kinetics of the isothermal austenite-to-pearlite transformation [35, 36] \± has also been applied to describe the long-range diffusion controlled transformation of austenite-to-ferrite transformation in low carbon steels [13, 35, 45, 46] Since austenite grain boundaries are preferred sites for ferrite nucleation [47, 48] ; m e exponent n of the Avrami equation for the Austenite-to-ferrite transformation should be close to 1; this has been confirmed by experimental measurements [36, 49, 50] j h e exponent n values for several hypoeutectoid steels are summarized in Table 2.1. Table 2.1: The exponent n of the Avrami equation for the y-»a transformation. Grade n Ref. 1038 0.88 [49] 1020 1.17 [49] 1025 1.33 [36] 1010 1.00 [50] Little published information is available on using the Avrami equation to model phase transformation kinetics in the presence of deformation. Collins et al. [37] adopted Chapter 2 LITERATURE REVIEW 19 the Avrami analysis to describe the austenite decomposition kinetics in deformed austenite when the austenite grain size and temperature were constant. However, because of the limitations in performing isothermal tests, they could not fully investigate the behaviour of the temperature-dependent parameter, b. Further, there is no information in the literature utilizing the Avrami based model to describe the austenite decomposition kinetics, including the effect of retained strain reflecting the industrial processing conditions. 2.1.3 Grain Size-Modified Avrami Equation Since solid state transformations are almost always initiated by heterogeneous nucleation at grain corners, grain edges or grain boundaries, the grain size is another factor which should be included to model the phase transformation kinetics and final microstructure. In a long-range diffusion controlled phase transformation such as the y-»a proeutectoid transformation in low carbon steels, as the austenite grain size increases the transformation rate decreases. Umemoto et al. [54] used this concept and modified the Avrami equation, Eq. (2.11), to include an austenite grain size parameter, d; the new equation known as the grain size-modified Avrami equation [55]5 is: X = 1 - exp kt" (2.12) Chapter 2 LITERATURE REVIEW 20 where k is the rate constant and m is a fitting parameter depending on the growth geometry. This algorithm has been used to model the phase transformation kinetics occurring during industrial processing conditions [56, 57] 2.1.4 Umemoto Equat ion The application of the Avrami equation, Eq. (2.11), for the austenite-to-ferrite transformation is necessarily an empirical fit. Umemoto et al. [58] investigated the kinetics of the austenite-to-proeutectoid ferrite reaction for 0.2 and 0.43 wt.% C plain-carbon steels. They found that the Avrami equation predicted faster transformation rates in the later stages of the transformation. The slower rate of ferrite growth observed in the last stage of the austenite-to-ferrite transformation resulted from soft impingement i.e., the overlapping of the diffusion fields from adjacent ferrite grains which is consistent with the other findings [59]. Thus, they derived an equation to account for soft impingement effects by multiplying Avrami rate equation by (l-X)P, as follows [58]; — = (nbt"-l)(\-Xy+p (2.13) dt where experimentally, p was found to be 0.5. Chapter 2 LITERATURE REVIEW 21 2.2 APPLICATION OF ISOTHERMAL TRANSFORMATION KINETICS TO DESCRIBE NON-ISOTHERMAL CONDITIONS The austenite to ferrite portion of the Fe-Fe3C equilibrium diagram is shown in Fig. 2.4 [H] , the A3 or A e 3 temperature being the temperature/composition boundary describing the austenite in equilibrium with ferrite. The A r 3 temperature is the non-equilibrium austenite-to-ferrite transformation start temperature obtained during cooling. Because the austenite decomposition to.ferrite is diffusion controlled requiring time at a given temperature, during cooling or heating there is a lag between the equilibrium and the observed critical temperatures. As the cooling or heating rates are accelerated, larger differences will be obtained in the magnitude of the supercooling or superheating, respectively. This effect is described using the processing-dependent critical temperatures, A c 3 for heating and A r 3 for cooling. The letter "c", represents the French word "chauffage", meaning heating and the letter "r", represents the French word "refroidissement", meaning cooling. Phase transformation kinetics obtained under non-isothermal conditions have not been as extensively studied as have isothermal transformation kinetics. In isothermal experiments, because the temperature, one of the most fundamental physical parameters controlling the nucleation and growth rates, is kept constant, the interpretation of phase transformation behaviour is simpler. However, since continuous cooling transformations are widely used in industrial processing, the use of isothermal transformation information to investigate continuous cooling transformation behaviour was recognized. The study of Chapter 2 LITERA TURE REVIEW 22 non-isothermal transformations started with Scheil [60], who proposed a method for predicting the transformation start temperature during continuous cooling based on the incubation period associated with the isothermal transformation. He proposed that on continuous cooling, nucleation will occur when the sum of the consumed fractional incubation times become unity, where t s is the non-isothermal incubation time i.e., the start of transformation, T ( T ) is the isothermal incubation time at temperature T and dt is the time increment spent at each temperature, T, during continuous cooling. The prediction of non-isothermal phase transformation kinetics using this approach is based on the additivity principles. The additivity approach involves the summation of short-term isothermal steps as a way of describing continuous cooling conditions, as schematically shown in Fig. 2.5 [4]. During cooling, the new phase nucleates and/or grows at each temperature with the corresponding nucleation and growth rates for that temperature. For example, at Tj, the new phase is nucleated at a rate Is(Tj) and grows at a rate oc(Tj), as shown schematically in Fig. 2.6 [4]. Describing continuous cooling as the summation of a series of isothermal steps is a useful approach to model the non-isothermal transformation kinetics using the Avrami equation, Eq. (2.11). Cahn [61] formulated that the additivity principle could be satisfied (2.14) Chapter 2 LITERATURE REVIEW 23 when the instantaneous transformation rate is a function solely of the amount already transformed and the temperature i.e., dX/dt=f(X, T). Christian [9] postulated that a transformation will be additive i f the reaction rate can be expressed as two independent functions, one in terms of fraction transformed and the other in terms of temperature, M=EZI (2.i5) dt G(X) where H(T) is a function of temperature only and G(T) is a function of fraction transformed only. It can be shown that the Avrami equation, Eq. (2.11), having a constant exponent n obeys the criterion proposed by Christian [9]. Rearranging the Avrami equation, Eq. (2.11): (2-16) Differentiating Eq. (2.11) with respect to t: dY — = -exp(-bt")(-nbt"-]) (2.17) dt Substituting Eq. (2.16) into Eq. (2.17) dX _ n(-b)~" dt ( 1 ^ v l n ( l - X ) y n-l (2.18) Thus, i f n=constant and b=f(T), the Avrami equation satisfies Eq. (2.15). Chapter 2 LITERATURE REVIEW 24 Several attempts have been reported to predict the continuous cooling transformation (CCT) kinetics from experimental isothermal transformation data for interface as well as diffusion controlled growth t l 2> 35, 36, 49, 54, 62-65] Hawbolt et al. [35] successfully applied the Avrami equation using the additivity principle to predict the continuous cooling austenite-to-ferrite transformation kinetics in a 1025 plain-carbon steel being cooled at rates of 2-23 °C/s. Campbell et al. [49] satisfactorily applied the principle of additivity adopting the Avrami equation to predict the ferrite portion of austenite decomposition in 1020 and 1038 steels with a variety of cooling rates up to 50 °C/s. The Umemoto equation, Eq. (2.13), was also applied to continuous cooling conditions for hypoeutectoid steels to describe the austenite-to-ferrite transformation kinetics [58]. There was a reasonable agreement between the experimental results and predictions for slow cooling rates of 0.1 and 0.5 °C/s. 2.3 THE MORPHOLOGICAL CLASSIFICATION OF AUSTENITE DECOMPOSITION In low carbon, plain-carbon steels, a polygonal ferritic microstructure results from the y—»a phase transformation occurring at comparatively small undercooling. Figure 2.7 shows an example of an isothermal time temperature transformation (TTT) diagram for a low carbon plain-carbon (1019) steel [66]. Above A e 3 the austenite is stable. Just below the A e 3 , the transformation to low carbon ferrite occurs by rejecting the remaining carbon Chapter 2 LITERATURE REVIEW 25 to the untransformed austenite. At high super cooling below Aej , the high carbon austenite transforms to pearlite. The use of CCT diagrams is more appropriate to investigate the resulting microstructure obtained from industrial processes where the materials are continuously cooled. Figure 2.8 illustrates an example of a modified CCT curve for 1017-1022 steels austenitized at 900 °C [67]. As can be seen, there is a maximum cooling rate below which an equilibrium microstructure, ferrite plus pearlite, can be produced. Beyond this cooling rate, non-equilibrium microstructures, bainite and martensite, form. Reducing the interstitial carbon content enhances the formation of polygonal ferrite, improving the weldability [68] and the formability of the final product [69]. Polygonal ferrite is a relatively low strength phase, its strength increases with grain refinement [70] or by changing the morphology from polygonal to acicular [6]. Ferrite nucleates at corners, edges and grain boundaries of austenite and grows in a blocky manner. Thus, one austenite grain can yield a few ferrite nuclei. Therefore, one of the most effective methods to refine the ferrite grain size is to reduce the austenite grain size by recrystallization at relatively lower temperatures in the austenitic region. The finer austenite grains produce an enhanced nucleation site density for ferrite which improves the mechanical properties. Chapter 2 LITERATURE REVIEW 26 2.4 AUSTENITE DECOMPOSITION ON THE RUN-OUT TABLE The austenite decomposition on the run-out table occurs under non-isothermal conditions and is affected by various factors i.e., the chemistry, the austenite grain size, the cooling conditions and the presence of retained strain and/or precipitates in the austenitic region prior to the transformation. In this case, the usage of TTT and CCT diagrams are limited. The TTT diagrams are strictly valid only for the specific chemistry, austenite grain size and cooling rate from the austenite to the transformation temperature [71]. The CCT diagrams are also valid for a specific chemistry, initial austenite grain size and cooling condition used [72]. The fact that on the run-out table, the phase transformation kinetics occurs under continuous cooling conditions (the resulting microstructure is thermal path dependent), makes the task of predicting the microstructural evolution during cooling a difficult one. In addition to cooling conditions, the austenite grain size and retained strain vary from point to point and thus, quantifying the relationship between phase distribution and variables would require a very large number of measurements. In low carbon, plain-carbon steels, the austenite grains are completely recrystallized during hot rolling. The lower the recrystallization temperature, the smaller the y grain size, yielding a smaller resulting ferrite grain size; this improves the mechanical properties of the final product [73]. Accelerating the cooling rate results in additional ferrite grain refinement through enhanced nucleation due to the increased supercooling of the transformation [21, 52, 53] j n t hj s case, the austenite grain size and Chapter 2 LITERATURE REVIEW 27 cooling rate play a major role in determining the transformation kinetics and the resulting microstructure. Under continuous cooling conditions, the transformation start temperature, A r 3 , decreases as the austenite grain size and/or the cooling rate is increased [51,74]. In HSLA microalloyed steels, in addition to the ferrite grain refinement resulting from a smaller austenite grain size and the higher degrees of supercooling associated with accelerated cooling, the application of deformation below T n r (actually between T n r and A r 3 ) further increases the ferrite nucleation enhancing ferrite grain refinement [5U 53] The addition of microalloyed elements, particularly Nb, raises the T n r temperature dramatically [75]. This gives greater opportunity to deform the material in this temperature range (between T ^ and A r 3 ) in the industrial process during finish rolling. Following hot rolling, the steel strip progresses onto the run-out table of a hot strip mill, where the austenite-to-ferrite transformation initiates and is usually completed under continuous cooling, non-isothermal conditions. 2.5 EFFECT OF PROCESSING VARIABLES ON THE AUSTENITE DECOMPOSITION BEHAVIOUR ON THE RUN-OUT TABLE 2.5.1 Chemistry When interstitial and substitutional alloying additions are made to pure iron, the stability range of the new phases can change and new phases can form. The versatility of Chapter 2 LITERATURE REVIEW 28 steels depends to a large extent on the wide variety of microstructures and mechanical properties that can be obtained as a result of the decomposition of the high temperature austenite phase. Carbon and manganese in plain-carbon steels and microalloying elements (i.e., Ti , Nb and V) in low carbon H S L A microalloyed steels are the most important alloying elements in weldable, formable sheet steels. 2.5.1.1 Plain-C-Mn Steels Plain-carbon steels can be classified into three categories based primarily on the carbon level. Low carbon steels with less than 0.25 wt.% C, intermediate carbon steels with a carbon level from 0.25 to 0.6 wt % C and high carbon steels with a carbon level of 0.6 to 2 wt.% C. Increasing the carbon level lowers the Ae3 temperature dramatically as shown in the Fe-Fe3C phase diagram in Fig. 2.4, and reduces the driving force for austenite decomposition at any temperature [76]. The addition of carbon shifts the CCT diagram to longer time which gives more opportunity for hardenability and the formation of non-equilibrium microstructures i.e., bainite and martensite. Kirkaldy et al. [77] proposed an empirical formula to describe the Ae3 temperature as a function of carbon content for Fe-C alloys as: Ae3 (°K) = 1115-150.3(wr%C) + 216(0.765 - wt%C)4: (2.19) Chapter 2 LITERATURE REVIEW 29 The commercial plain-carbon steels, in addition to carbon, contain intentional additions of Mn, which affects the phase boundaries, the transformation behaviour and the final microstructure. Manganese in the range of 0.25% to 1% is one of the most important elements which exists in all commercial plain-carbon and microalloyed steels. Manganese combines with sulfur present in steel to produce manganese sulfide, MnS, as a non-metallic inclusion. These inclusions are much less damaging to mechanical properties than is the alternative low-melting FeS compound that forms in the absence of Mn at the austenite grain boundaries and melts at hot rolling temperatures (hot shortness). The substitutional alloying element manganese, that is in excess of forming MnS, further strengthens the steel through solid solution-hardening and grain refinement due to depression of the y-»a transformation temperature which modifies the transformed microstructure 178]. Increasing the ratio of manganese to carbon in low carbon steels gives rise to lower temperature transformation products, such as acicular ferrite or bainite [78]. Kirkaldy et al. [77] formulated the A e 3 temperature based on the thermodynamics of the ternary Fe-C-X system for a wide range of alloying elements, including the Fe-C-Mn plain-carbon steels. They also found that in the commercial steels, the addition of Mn diminishes the A e 3 substantially. The required equations and thermodynamic information for calculation of the A e 3 temperatures are available in the literature [77]. Based on experimental results, Andrews [79] has reported empirical relationships between chemistry and the approximate A e 3 temperature for different steels as following: Chapter 2 LITERA TURE REVIEW 30 Ae„=9\3- 25 Mn -UCr- 20C« + 605/ + 60Mo + 40W + 100V + 700P 3 (2.20) - (250Al + 1 2 0 ^ + 40077) Mn can be seen to play an important role in suppressing the austenite decomposition temperature. Since the A e 3 temperature decreases dramatically and non-linearly with carbon content therefore, the effect of carbon on the A e 3 was given explicitly in the literature 179]. 2.5.1.2 High Strength Low Alloy (HSLA) Microalloyed Steels The chemical compositions of HSLA microalloyed steels were developed primarily to produce the desired strength, toughness, ductility and weldability. The common microalloying elements in HSLA steels are Ti , V , Nb and are present in amounts less than 0.1 wt.%. However, even at these levels, they can exert a remarkable influence on the microstructure and properties, primarily by enabling ferrite refinement and precipitation strengthening. The dominant microstructure in low carbon HSLA steels produced by controlled-rolling is polygonal ferrite. This is also the microstructure which is produced in plain-carbon steels. Decreasing the carbon content can yield pearlite-reduced or pearlite-free steels, thereby enhancing the ductility and toughness of the product. Microalloying elements have different affinities for carbon and nitrogen in austenite, as indicated by the carbide and nitride solubility products shown in Fig. 2.9 [80]. In hot strip mill processing, prior to hot rolling, the slabs are heated in a reheating Chapter 2 LITERATURE REVIEW 31 furnace to temperatures in the range of approximately 1200-1250 °C. Because of the extreme low solubility of TiN, it remains as a stable precipitate in the reheating period. This precipitation can pin the austenite grain boundary and prevent austenite grain coarsening [81]. Among the microalloying precipitates, V C has the maximum solubility and dissolves at relatively low reheating temperature. The other nitride or carbide precipitates (TiC, Nb(C, N) and VN) have intermediate solubilities between V C and TiN, and the amount of microalloying element dissolved in the austenite can vary widely with the reheating temperature, carbon and nitrogen contents. Depending on the levels of the microalloying elements, C and N , and the cooling rate, either one of the following three conditions can happen, i) The microalloyed elements can be presented as precipitates in the austenite phase; ii) microalloyed carbides or carbonitrides can precipitate during y—>a transformation and iii) microalloyed carbides or carbonitrides can precipitate in a after the completion of austenite decomposition [78]. The effect of Nb content and temperature on the austenite restoration in low carbon HSLA-Nb steels has been systematically studied by Yamamoto et al. [82]. For a given strain and strain rate, as the Nb content increases, the onset of recrystallization is prolonged markedly. This is attributed to both precipitation of Nb(C, N) and solute drag from the excess solute niobium atoms. Depending on the reheating temperature and the level of Nb, the niobium precipitated in the as-cast slab can remain or be partially or totally dissolved in the matrix. For example, for the HSLA-Nb microalloyed steel with 0.082 wt.% C, 0.0054 wt.% N and 0.036 wt.% Nb used in this study, a minimum reheating temperature of 1100 °C is required to dissolve the Nb(C, N) precipitates. If Nb is dissolved in the matrix, it can precipitate as strain induced niobium carbonitrides in the Chapter 2 LITERATURE REVIEW 32 austenite during hot rolling or can form during the y—>a transformation [83] as a result of decreasing solubility. The strain-induced precipitation prevents recrystallization during hot finish rolling resulting in retained strain. The retained strain results in more boundaries, dislocations and the formation of internal deformation bands, providing more nucleation sites for ferrite. This can improve the mechanical properties of the final product by ferrite grain refinement as well as precipitation strengthening. However, a powerful hot rolling mill with very high load capacity at each deformation stand is required. In the industrial process the reheating temperature is relatively high and the combined addition of Ti and Nb microalloying elements is an appropriate technique to produce very high strength steels. The addition of Ti is beneficial to improve the strength by limiting austenite grain growth which enhances subsequent ferrite grain refinement and the presence of Nb has contributed to higher mechanical properties not only by grain refinement but also by precipitation strengthening. Vanadium is usually added and retained in solid solution in austenite down to relatively low temperatures. The V(C, N) precipitates are predominantly formed during the austenite-to-ferrite transformation, or in ferrite. Thus the addition of V enhances the strength of ferrite by precipitation strengthening [84] and not by austenite grain refinement. For structural sections not requiring a high strength material, there is a preference for the use of V instead of other microalloying elements. This is due to: (1) the ease of casting of V microalloyed steels, (2) the relative ease of dissolving V(C, N) during reheating due to its lower precipitation temperature and (3) the lower rolling loads Chapter 2 LITERATURE REVIEW 33 required during hot finishing rolling, as V does not retard recrystallization to the extent that other microalloying elements do [84]. Yue et al. [75] employed multipass torsion testing techniques to investigate the effect of microalloying elements on the no-recrystallization temperature, T n r . In this method, the specimens are continuously cooled from the reheating temperature (1260 °C) at 1 °C/s cooling rate while a series of 17 passes of deformation, each with a strain of about 0.3 and an interpass time of 30 second. They found the following correlation between T ^ and the chemical composition [75]; Tnr = 887 + 464C + (6445M> - 644^Nb) + (732V - 230-Jv) + 89077 + 3 63.4/ - 3575/ (2.21) The addition of Nb has the strongest influence, followed by Ti, as seen in Eq. (2.21). At levels above 0.1 wt.%, V also has a weak, but significant tendency to increase the T n r . Increasing the T ^ expands the no-recrystallization region giving more opportunity for controlled rolling which has a major impact on the rolling process and on the resulting microstructure. 2.5.2 Effect of Austenite Grain Size To produce a fine ferrite grain size with its associated enhanced strength and toughness, minimizing the prior austenite grain size is essential. On cooling through the intercritical zone, the growth of proeutectoid ferrite from austenite occurs by long range Chapter 2 LITERATURE REVIEW 34 diffusion following heterogeneous nucleation, mainly at the grain corners, edges and boundaries and at crystalline defects within the austenite grains. Decreasing the y grain size increases the y grain boundary area per unit volume, which provides an increase in the number of potential nucleation sites, and therefore accelerates the nucleation rate resulting in ferrite grain refinement [85-87, 88-90] i t j s a j s o established that decreasing the y grain size increases the transformation rate [51,54, 55] b y increasing the ratio of the nucleation rate to the growth rate [91]. The increase of austenite grain size, resulted from higher reheating temperature, reduces the transformation start temperature and increases the transformation start time for a given cooling condition, as is shown in Fig. 2.10 [92]. This increased hardenability also changes the resulting microstructure as well. A large austenite grain size will depress polygonal ferrite formation and increase the percentage of non-polygonal (Widmanstatten) ferrite at lower cooling rates [93]; the larger austenite grain size would also increase the amount of martensite formed at higher cooling rates [88]. 2.5.3 Effect of Cooling Rate The cooling rate has a strong effect on the phase transformation kinetics through its effect on the transformation start temperature, Ar3 U^]. Since the austenite-to-ferrite phase transformation is a thermally activated process, the ferrite requires time to initiate and grow. By increasing the cooling rate, there is less time available for the transformation to initiate and therefore, the Ar3 decreases [21, 51, 52] During cooling, Chapter 2 LITERATURE REVIEW 35 the magnitude of the carbon content of the austenite in equilibrium with ferrite at the growing interface increases, increasing the carbon gradient in the austenite and resulting in a more rapid transformation. However, at very low temperatures, i.e., very high supercoolings, due to the reduced carbon diffusivity, the transformation rate decreases. Accelerated cooling in the austenite to ferrite transformation range is also an important thermal treatment for controlling microstructure and mechanical properties. It is established that accelerated cooling following finishing rolling reduces the ferrite grain size significantly [51> 52, 94] a n ( ^ enhances the strength of the final product 178, 45] The enhancement of the mechanical properties of accelerated cooled products has been attributed to two metallurgical factors: the ferrite grain refinement and the formation of lower temperatures transformation products, acicular ferrite, pearlite or bainite. 2.5.4 Effect of Pre-strain During finish rolling, deformation of austenite below T n r causes retained strain in the lattice, producing a pancaked austenite having irregular grain boundaries and containing internal deformation bands (or localized regions with high dislocation density) [95]. These regions act as ferrite nucleation sites and enhance the nucleation rate resulting in a higher A r 3 temperature [37]. The increase in nucleation rate is attributed to the three factors [96] schematically illustrated in Fig. 2.11, which shows the early stage of transformation for (a) the initial or strain free condition, (b) the deformed condition in which the austenite grains are elongated but the nucleation rate per unit area of grain Chapter 2 LITERATURE REVIEW 36 boundary is not altered significantly, (c) the deformed condition in which the austenite grains are elongated and the nucleation rate per unit area of grain boundary is increased due to the "roughening" of the grain boundaries, and (d) the heavily deformed condition where the austenite grains are elongated and the nucleation rate is increased at the grain boundaries and internally at deformation bands. The surface area of austenite per unit volume increases with increasing elongation of the grains, i.e., increasing retained strain. For simplicity, Umemoto et al. [96] assumed that the initial austenite grains are spherical with unit radius, as shown in Fig. 2.12a. By applying the rolling reduction p, the sphere becomes ellipsoidal, as shown in Fig. 2.12b. The surface area of the grain before rolling is given as: S°g h =4/r(l) 2 =4TT (2.22) The surface area of the grain after rolling with a reduction, p, is given as [96]: S^=L-P {4xfVl-(2^-y)sin2c9^}xjI x\i-py -x\\-p)2 \dx (2.23) The ratio of the surface area per unit volume before rolling to that after, Sg 1-,/SOg b, is plotted in Fig. 2.13 as a function of the rolling reduction, p, and the true strain, s [4]. Increasing the rolling reduction increases the ratio of surface area. However, the increase in grain surface area per unit volume is less than 2 times for a rolling reduction of 0.7. Chapter 2 LITERA TURE REVIEW 3 7 The effect of retained strain on the austenite decomposition has also been studied by DeArdo et al. [97]. They proposed that in controlled rolling S v , the total effective area per unit volume in mm^/mm^, can be expressed as the grain boundary area per unit volume and the surface area of the deformation bands and twins contained within the elongated grains as follows: SV=SV(GB) + SV(IPD) (2.24) where S V(GB) is the grain boundary contribution to S v and SV(IPD) is the intragranular planar defect contribution to S v . The quantity S v has been expressed by an empirical equation as follows [97]: S=0A29NIK +2.5717V/7 +NIT (2.25) where N L R , Nyj£ and N L T are the grain boundary intercept number per unit length along the rolling, thickness and transverse directions, respectively; N p g is the number of intragranular planar defects (IPD) per unit area, mm/mm^; and 8 is the angle between the intragranular planar defect and the plate thickness direction. Although the variation in S v with alloying and processing parameters has not been defined completely, the most important parameters have been shown to be the extent of deformation below the recrystallization temperature and the grain size of the austenite Chapter 2 LITERATURE REVIEW 38 prior to pancaking [98-100] j n e effect of rolling reduction on the S v has been summarized by Speich et al. [ 9 8 ] and is illustrated in Figs. 2.14 and 2.15. They calculated the variation of S v for a hypothetical array of cube-shaped grains of variable initial size which were subjected to various plane strain deformations, all to simulate the behaviour of grains during controlled rolling [ 9 8 ] . A major contributor to S v is the grain boundary area per unit volume. Under the assumptions of a cubical grain shape and plane strain deformation, the contribution of the grain boundary area to the total S v will vary with reduction as follow [ 9 8 ] : rrGfi L S- ~ D (2.26) where D is the cube edge length and R is the rolling reduction ratio. The variation of the contribution of the initial grain boundaries and deformation bands to S v are shown in Fig. 2.15. Ouchi et al. [101] have shown that the intragranular defects, such as deformation bands and twin boundaries, contribute to the S v as follows: S f = 0.63(% Re duction - 30) mm'' (2.27) Equation (2.27) indicates that no deformation bands form during controlled rolling until a reduction of 30% has been reached, and then the band density increases linearly with additional strain. It is clear form Figs. 2.14 and 2.15 that decreasing the grain size prior Chapter 2 LITERATURE REVIEW 39 to pancaking and increasing the amount of reduction below the recrystallization temperature increases the magnitude of S v . Tamura 178, 94] confirmed that the number of ferrite grains nucleated on austenite grain boundaries is substantially increased by deformation. Specimens of an Fe-0.12C-0.04Nb-0.04V steel were austenitized at 1200 °C for 30 minutes, rolled 30 or 50% in reduction by a single pass at 840 °C (in the unrecrystallized temperature range) and held at 680 °C in the intercritical region for 30 seconds and then quenched to room temperature. The number of ferrite grains intersected per mm of austenite grain boundary was reported as 41, 214, and 330 for 0, 30, and 50% rolled specimens, respectively. The observed substantial increase in nucleation in deformed austenite (41 for strain free and 330 for 50% deformation) is much greater than that related to the increased grain boundary surface area due to pancaking of austenite [102-105] a f t e r 50% deformation, as shown in Figs. 2.13, 2.14 and 2.15. Thus, the considerable augmentation in nucleation in the deformed material is contributed by crystallographic defects; i) at the austenite grain corners, edges and boundaries, particularly the roughening the austenite grain boundaries and ii) inside the austenite grains as deformation bands. 2.6 FERRITE GRAIN SIZE For ferritic steels, the relationship between ferrite grain size and yield strength, which reflect the mechanical properties of the final product, is given by the Hall-Petch equation [70]: Chapter 2 LITERA TURE REVIEW 40 cry=k0+ky.da-U2 (2.28) where ay is the yield strength, k g and k y are material constants and d a is the ferrite grain size. Ultrafine-grained ferrite with higher strength and lower ductile-to-brittle transition temperatures can be produced by careful control of the time-temperature-deformation sequence during hot rolling. It should be noted that for a given grain size, the O y of the material is a function of the dislocation density [106, 107] In the hot strip mill process, in addition to the ferrite volume fraction which can be predicted by fundamental (carbon diffusion) or empirical equations, quantification and modeling of ferrite grain size is very important. Generally, the ferrite grain size is modified by one or all of the following processing techniques: (i) reducing the austenite grain size [85-87, 88-90]- (ii) addition of microalloying elements [108-109]. (jjj) increasing the retained strain in the austenite prior to transformation [108-110]- (j v) lowering the ferrite transformation temperature by increasing the cooling rate [111"! 15]. For a given chemistry, the factors that affect the ferrite grain size, d a , (in urn) have been shown to be: - the initial austenite grain size, dy, (in um) - the magnitude of retained strain, s - and the cooling rate, cp, (between A e 3 and approximately 500 °C) Chapter 2 LITERATURE REVIEW 41 Several approaches have been made to predict the ferrite grain size using simple empirical equations based on these three factors. A summary of some of these equations is given in Table 2.2. Table 2.2: Empirical equations for predicting ferrite grain size. Steel Equation Ref. H S L A da =3.75 +0.1 SWr +\A<p~m [116] C-Mn da = U.7 + 0A4dr + 37.7<p-m [85] C-Mn da=da0(\-0A5eU2) da0 =2.5 + 3#f 1 / 2+20{l-exp(-0.015^)} [86] C-Mn dao = (Po + Pfeq ) + (Pl +Pfeq )(P~V2 eX P(-^ 7)} Ccq < 0 . 3 5 : / ? 0 = -0 .4 , /? , = 6 . 3 7 , $ = 2 4 . 2 , $ = - 5 9 , $ = 2 2 , $ = 0 . 0 1 5 0.45 >Ceq > 0 . 3 5 : $ = 2 2 . 6 , / ? , = - 5 7 , $ = 3 , $ =0,p4 = 2 2 , $ = 0.015 [117] ferritic-pearlitic ^ = ^ 0 4 { l - e x p ( 0 . 0 7 5 ^ ) } ^ 0 0 1 4 d,, = 1 0 ( 1 - X ) 0 3 3 exp(-e)dr X : fraction austenite recrystallized, K=8.9 for C-Mn-Nb [118] C-Mn-Nb da = 84 . 3 S ^ 4 7 V - 1 6 9 S = {l67(s - 0.1) +1.0}2000 / dy + 63(f - 0.3) [119] C-Mn-Nb da = ( l - 0 . 8 £ 0 1 5 ) [ 2 9 - 5 ^ - ' / 2 + 20{l-exp(-0.015^)}] [70, 87] C-Mn r / \ n l / 3 I 714301 da= 5.51 x l 0 , 0 < 7 5 exp / i 4 J U XF |_ ^ ^0.05 J J [120] The first predictive ferrite grain size relationship was given for Ti, V , and Nb steels when ferrite was formed from recrystallized austenite H16]. The next equation by Chapter 2 LITERATURE REVIEW 42 Sellars [85] proposed an alternate equation for hot rolled C-Mn steels and emphasized the importance of the retained strain in controlled rolled Nb microalloyed steels. Later, Sellars and Beynon [86] proposed a more general expression which was further modified by Hodgson and Gibbs [H7] for plain-carbon steels based on the carbon equivalent, Ceq=C+Mn/6. Anelli [H8] a n f j Abe et al. [H9] a i s o defined relations to describe the ferrite grain size as a function of hot rolling processing parameters for 0.07-0.09 C, 1.4-1.5 Mn and 0.005-0.03 Nb, and ferritic-pearlitic steels respectively. Most of the empirical relations describe the ferrite grain size as a function of cooling rate. Recently, Gibbs et al. U®> 8 7] studied the ferrite grain size in controlled rolled Nb microalloyed steels using torsion testing technique and confirmed the dominant effect of the retained strain, 8 , on d a for such steels. However, Suehiro et al. [120] proposed a model to correlate the ferrite grain size with the transformation start temperature, To.05 i n °K- Therefore, the calculation of cooling rate during transformation is not required to predict the final ferrite grain size. Figures 2.16 and 2.17 compares the experimental results and model predictions of the ferrite grain size using the equations of Gibbs et al. [70, 87] a n c j Suehiro et al. D20]5 respectively. As can be seen in Fig. 2.16, the measured ferrite grain size is in a good agreement with model predictions. Figure 2.17 shows the difference in the calculated ferrite grain size, d c a j , from the values observed, d 0 b s , as a function of dislocation density before the start of transformation. It is clear that the model can reasonably predict the ferrite grain size at low dislocation density where the austenite grains are restored (Fig. 2.17). Chapter 2 LITERATURE REVIEW 43 DeArdo [121] and Ouchi et al. [101] a i s o proposed models to predict the ferrite grain size describing the applied strain as a function of effective austenite interfacial area, S v , (grain boundary area plus deformation bands). Their models include deformation bands as well as boundaries and near planar defects in quantifying the total S v . In these models, the applied strains are independent of the initial austenite grain size. Since their proposed models have not described the applied retained strain as a function of initial austenite grain size, they can not be applied to the relatively wide range of initial austenite grain sizes comparable to the industrial process conditions. The drawback of such models has been reported in other works [122, 123, 124] where a big discrepancy between experimental results and the model predictions has been observed. Since the influence of retained strain on the ferrite grain refinement is a strong function of the initial austenite grain size, it seems that the proposed models may only be applicable to the narrow range of austenite grain sizes examined. Chapter 2 LITERA TURE REVIEW 44 Figure 2.1: The ratio of the driving force for heterogeneous nucleation of grain corners (AG*r7AG*h o r r i ) , grain edges (AG*£/AG*h o m ) and grain boundaries ( A G * Q / A G * n o m ) to that for homogenous nucleation and as a function of the cosine of the contact angle, 9 [8]. Chapter 2 LITERA TURE REVIEW 45 Figure 2.2: Schematic representation of fraction transformed as a function of time for a typical isothermal nucleation and growth phase transformation. Chapter 2 LITERA TURE REVIEW CQ- CQ Cy Wt% Carbon igure2.3: Fe-Fe^C phase diagram depicting equilibrium concentration for the formation of proeutectoid ferrite from austenite at Temperature T] . Chapter 2 LITERATURE REVIEW Figure 2.4: A proeutectoid portion of the Fe-Fe3C phase diagram showing the equilibrium, the critical cooling (r) and the critical heating (c) phase field boundaries for a rate of heating and cooling at 0.125 °C/min [11]. Chapter 2 LITERA TURE REVIEW 48 Figure 2.5: Diagram showing the approximation of continuous cooling as the sum of a series of short time of isothermal increments W. Chapter 2 LITERA TURE REVIEW 49 Figure 2.6: Schematic diagram of the formation process of a new phase during continuous cooli ng W. Chapter 2 LIT ERA TV RE REVIEW Figure 2.7: Isothermal transformation diagram for a 1019 steel [ 6 6 I Chapter 2 LITERATURE REVIEW 51 Figure 2.8: Modified CCT transformation diagram for 1017-1022 steels i 6 1 l Chapter 2 LITERATURE REVIEW 2000 r 6.0 7.0 8.0 iovr,°K-' 10.0 J L _ L _L 1300 1100 900 800 TEMPERATURE, °C. Figure 2.9: The Solubility products of aluminum, niobium, vanadium an titanium nitrides and carbides [ 8 ° ] . Chapter 2 LITERA TURE REVIEW 53 1,000r O o LU 800 - 600 400 200 10 t V C C T Diagram " 1 10° "IO1 10 2 10 3 TIME, sec. T R H T ( ° C ) 900 1,300 J I 10 4 10{ Figure 2.10: C C T diagram for three steels which contain 0.2% wt.% C , 1.2% wt.% M n and 0.11 wt.% N b showing the effect of reheat temperatures of 1300 or 900 ° C [ 9 2 J . Chapter 2 LITERA TURE REVIEW 54 Figure 2.11: An early stage of ferrite transformation in 4 different austenite conditions; (a) undeformed condition; (b) a deformed condition in which the grains are elongated only; (c) a deformed condition in which grains are elongated and the rate of nucleation on grain boundaries is increased and (d) a deformed condition in which grains are elongated, the rate of nucleation on grain boundaries is increased and nucleation also occurs on deformation bands within the deformed grains [96]. Chapter 2 LITERA TURE REVIEW 55 Figure 2.12: The shape change of a spherical austenite grain by rolling with reduction p; (a) before rolling and (b) after rolling t 9 6 ] . Chapter 2 LITERA TURE REVIEW 56 Strain e (=-ln(l-p)) 0 0.5 1.0 Rolling reduction p Figure 2.13: The ratio of austenite grain boundary surface area per unit volume before and after rolling, as a function of rolling reduction, p [4]. Chapter 2 LITERATURE REVIEW c i_ a> CL (0 o> CO .3 "o co **— w c CD « "E (A < 400 £ e co e -2 200 o > Rolling reduction (/?) ratio 1.1:1 1.25:1 1.66:1 2.5:1 5:1 10:1 100 50 25 I Cube plane d-shap ; strain >ed gra ins I / I 20 um / / 50 um / ~100 recr grai um ystalli2 n size ed 0 20 40 60 80 100 Rolling reduction^/?), % Figure 2.14: Effect of rolling reduction on the total effective nucleating area/vol., S v , for cube-shaped austenite grains of 20, 50 and 100 urn [ 9 8 1 . Chapter 2 LITERA TURE REVIEW Figure 2.15: Contribution of the increase in grain boundary area/vol., S(v'tt, and internal deformation band area/vol., S'?B, to the total nucleation area/vol., S'J""', for an initial austenite grain size of 100 um [98]. Chapter 2 LITERATURE REVIEW Figure 2.16: Comparison of measured ferrite grain size and model prediction Chapter 2 LITERA TURE REVIEW 60 <A 2 T J A 0 S TJ -1 Deformation temperature: 800-c Cooling rate: 5°C/s 9 5 0 ° C • * - i — ' i 1 1 1 1 , i 1 — i i i 11111 i • i i i • t • 10' 10" 10" Dislocation density (cm" 2 ) Figure 2.17: Difference of the calculated ferrite grain size, d c a i , from the value observed, d 0t, s , as a function of dislocation density before the start of transformation [120] CHAPTER 3 O B J E C T I V E S In process modelling of microstructure evolution during the thermomechanical processing of low carbon plain-carbon and H S L A steels, the accurate prediction of the austenite-to-ferrite decomposition kinetics and quantification of the resulting microstructure is essential for linking microstructure to mechanical properties. Despite the extensive research which has been conducted to model the phase transformation and the resulting microstructure, the application of these models to industrial thermomechanical processing on the hot strip mill i.e., as it occurs on the run-out table during controlled cooling and/or later during coiling, is limited. For a given chemistry, an appropriate model should reflect the range of austenite grain sizes present at the exit of the last stand of the finishing mill, the wide range of cooling rates attainable on the run-out table and the potential retained strain at the entrance of the run-out table. Thus, the objective of this study is to develop a mathematical model describing the austenite decomposition kinetics and resulting ferrite microstructure obtained for two low carbon plain-carbon and two microalloyed steels obtained during cooling on the run-out table of a hot strip mill. The model has to incorporate the effect of initial austenite grain size and retained strain. To develop such a model, the following research steps are required: 61 Chapter 3 OBJECTIVES 62 i) Experimental quantification of austenite decomposition kinetics as a function of cooling rate and initial austenite grain size simulating hot strip mill processing conditions for each of the candidate steels. ii) Quantification of the resulting microstructure. iii) Experimental measurement of the retained strain effect on the phase transformation kinetics and the resulting microstructure for the HSLA-Nb steel. iv) Validation of the model predictions using the available industrial and/or published data. CHAPTER 4 EXPERIMENTAL TECHNIQUES 4.1 MATERIALS Two low carbon plain-carbon steels, drawing quality special A l killed, DQSK, and structural, A36, and two single microalloyed steels, HSLA-V and HSLA-Nb, the composition of each being given in Table 4.1, have been investigated in this work. The steels were obtained from the Gary Works of US Steel, being candidate steels for the AISI/DOE project. Both transfer bar (product at the end of the roughing mill) and coiled sheet (product after hot strip mill processing) samples were obtained, along with the mill data pertinent to each sample. Table 4.1: Chemical compositions (in wt.%) of the steels investigated. Grade C Mn P s Si Mo V Ti Nb A l N DQSK 0.038 0.30 0.010 0.008 0.009 - - - - 0.040 .0047 A36 0.17 0.74 0.009 0.008 0.012 - - - - 0.040 .0047 HSLA-V 0.045 0.45 0.012 0.005 0.069 <.005 0.080 0.002 <.005 0.078 .0072 HSLA-Nb 0.082 0.48 0.012 0.005 0.045 <.005 <.002 <.002 0.036 0.024 .0054 63 Chapter 4 EXPERIMENTAL TECHNIQUES 4.2 EXPERIMENTAL EQUIPMENT 4.2.1 Gleeblel 1500 Thermomechanical Simulator 64 The Gleeble 1500 thermomechanical simulator has been used to perform controlled heating, hot deformation, controlled cooling and phase transformation tests. In industrial hot strip mill processing, the austenite decomposition occurs following finishing rolling, usually during controlled cooling on the run-out table where the temperature decreases continuously via controlled cooling regimes. The cooling rates of the bulk material on the run-out table are between air cooling and 150 °C/s [125]. To simulate the industrial cooling conditions and achieve the maximum cooling rate on the run-out table, CCT measurements were made employing tubular specimens, 20 mm in length with an 8 mm outer diameter and a 1 mm wall thickness. The schematic diagram of a tubular specimen held in place by tubular stainless steel support anvils and the helium quenching system is shown in Fig. 4.1. Employing the experimental setup shown in Fig. 4.1, the cooling rates were extended to approximately 300 °C/s for the tubular specimen by using the maximum flow rate of helium gas. The temperature of the specimen was controlled and monitored using an intrinsic Chromel-Alumel thermocouple which was spot welded onto the outer surface of the specimen at mid-length, as shown in Fig. 4.1. The resistive heating design, together with the temperature feed-back control system of the Gleeble machine, provides rapid response for precise control of specimen temperature during the heating, isothermal holding and "Gleeble" is a trademark of Dynamic Systems, Inc. Chapter 4 EXPERIMENTAL TECHNIQUES 65 cooling cycles of each test schedule. The force to ensure electrical contact between the tubular sample and the hollow anvils is provided by the spring. The mid-plane diametral dilation of the specimen due to thermal expansion or contraction during heating or cooling and the volume changes occurring during transformation of the y—»a and y—»a+p was monitored by a Linear Variable Differential Transformer (LVDT) crosswise strain device, as shown in Fig. 4.1. Since all the compression tests were carried out at high temperatures, the resistive heating system was utilized to attain and control the testing temperatures. Both the dilation and temperature measurements were monitored in the same cross sectional plane in the middle of the specimen and acquired continuously. To minimize oxidation during the experiment, the test chamber was evacuated to a pressure of less than 3 mTorr, then back filled with high purity argon gas. This procedure was repeated before each test commenced. The compression tests employed for introducing retained strain into the HSLA-Nb steel samples were also carried out using the Gleeble 1500 thermal/deformation testing system (Fig. 4.2). Solid cylindrical specimens with two different sizes were employed. Specimens with 15 mm in length and 10 mm were used during controlled cooling (1 °C/s), and specimens with 6 mm in length and 4 mm in diameter were employed in accelerated cooling conditions to simulate the cooling rates on the run-out table. The compression mode was used because it avoids heterogeneous flow due to necking, as would occur in the case of tension tests making it possible to introduce relatively large strains. During deformation, the linear displacement of the anvils was controlled and programmed (stroke control) and the applied force and diametral strain were measured Chapter 4 EXPERIMENTAL TECHNIQUES 66 using an axial load cell and a crosswise strain (C-strain) device, respectively. As for strain free CCT tests, the temperature measurement was performed using a Chromel-Alumel thermocouple spot welded at the mid-length of the specimen in the plane that the C-strain device was located. A l l the test parameters, i.e., force, stroke displacement, C-strain and temperature were recorded using the computer data acquisition system interfaced with the Gleeble 1500. Electrical contact between the specimen and the sample holder was obtained initially by manually applying a small amount of compressive force; subsequent contact during the test cycle is maintained with the aid of a constant pressure air ram. 4.2.2 Torsion Test Apparatus Several torsion tests were also performed on the HSLA-Nb steel using the materials testing system (MTS) closed loop hydraulic torsion machine at McGil l University. The significance of using the torsion tests is as follows. Firstly, deformation with higher strain can be applied to simulate the hot strip mill processing conditions; this is limited in compression. Secondly, the thermocouple spot (at the surface) and the deformation area (surface layer) are in the same position; in compression, the thermocouple is located at the surface while the maximum deformation is at the center of the sample. Figure 4.3 shows a schematic diagram of the employed torsion apparatus. On the left-hand side, a hydraulic servovalve (1) controls the flow of oil to a hydraulic motor (2), which transmits rotational force to the rotating bar (3). The rotational displacement is Chapter 4 EXPERIMENTAL TECHNIQUES 67 measured by a 50 turn potentiometer (4). In the center, the specimen (5) is screwed into the stationary grip (6) and the torque during rotational deformation is measured by a torque cell (7). The ensemble on the right side can be translated in order to permit the installation and removal of the specimen, which is only fitted into a slot in the rotating grip. A computer interface system was used for the purpose of running the tests and data acquisition. The torsion specimen with a 21 mm gage length and 6.4 mm diameter were used to perform single pass retained strain tests. At one end, a thread was machined to permit the specimen to be screwed into the grip. At the other end, a flat was machined on the test sample to fit into a slot in the grip. The temperature controlling thermocouple was spot welded on the mid-length of the specimen surface. Both twist rate and angle of rotation were programmed to simulate single or multi-stages of deformation. The resulting torque and twist were converted to stress and strain data. To minimize oxidation, the specimen and anvils were kept within a quartz tube of 57 mm internal diameter with a continuous flow of pure argon gas. 4.2.3 Microstructural Investigation After each thermal/mechanical experiment, a specimen for metallographic examination was cut from the mid-length where the thermocouple was spot welded, using an AI2O3 cut-off wheel. A directed spray coolant was used to protect the specimens from overheating during cutting. After cutting, one half of the specimen from the thermocouple position was cold mounted in a resin polymer and then ground Chapter 4 EXPERIMENTAL TECHNIQUES 68 progressively using 120 through 600 grit silicon carbide papers and finally polished employing a 6 um and a 1 um diamond solution. Quantitative analysis of the resulting microstructure was carried out utilizing a C-Imaging System image analyzer, the ferrite fraction and grain size being quantified. Etching techniques that are adequate for qualitative structural assessment or manual measurements are not always suitable for image analysis. Thus, the etching time using 2% nital solution [126] w a s modified to give higher contrast between the phases. The ferrite grain size was quantified using Jeffries' method [127] m m i s method, each whole grain was counted once and each partial grain, cut by the edge of the field of measurement, was counted as a half grain, as described by A S T M standards, ASTM El 12-88 [127] From the ferritic microstructure, the mean grain area was determined and from the mean area, the mean equivalent area diameter, EQAD, was determined. To obtain statistically relevant results, an automated stage pattern facility was utilized. For each sample at least 50 fields were quantified for the measured ferrite fraction and at least 500 ferrite grains were analyzed for the reported ferrite grain size. The measurement of austenite grain size was more complicated than that for the ferrite grain size. To measure the austenite grain size, the specimens were water quenched from austenitizing temperatures. After polishing the specimens, a picral based etchant solution (2 mg picric acid, 1 mg HC1, 1 mg dodecylben zenesulfonic acid in 100 mL water) was found to give the best contrast between martensite and prior austenite grain boundaries. It should be mentioned that in most cases the prior austenite grain boundaries are outlined by the ferrite phase. Polished and etched specimens were photographed using black and white film at magnifications, from X80 to X900, Chapter 4 EXPERIMENTAL TECHNIQUES 69 depending on the austenite grain size. The revealed prior austenite grain boundaries, outlined by ferrite in most cases, were traced on transparent plastic film using a felt tipped pen for subsequent quantitative image analysis. Figure 4.4 illustrates an example of the described technique for a water quenched microstructure and the related traced film of the prior austenite grain boundaries. Depending on the microstructure, it was sometimes difficult to determine the location of the austenite grain boundaries. The following assumptions were made to interpret the microstructure [128]-(1) A grain does not exist within the boundary of another grain. (2) Grain edges are at the intersection of three boundaries. (3) The grain shape is equiaxed. The austenite grain size was also quantified, based on the equivalent area diameter, EQAD. Since for the diffusion model the volumetric diameter was required for the initial austenite grain size, the measured mean EQAD was subsequently converted to volumetric diameter by d v oi=1.2 dp;QAD Thus, all reported austenite grain sizes are in volumetric diameter. 4.3 EXPERIMENTAL PROCEDURES 4.3.1 CCT Tests Because of the low carbon level of the steels, it was impossible to perform isothermal tests with sufficient accuracy to develop isothermal transformation diagrams, TTT curves. The low carbon content encouraged the initiation of the rapid Chapter 4 EXPERIMENTAL TECHNIQUES 70 transformation to ferrite during cooling from the austenitizing temperature to the desired isothermal test temperature. To overcome this problem, the cooling rate from the austenitic region to the isothermal testing temperature was enhanced. However, under these conditions the temperature control is adversely affected. In particular, the high cooling rate leads to extensive "under cooling" prior to attaining the desired isothermal testing temperature and this markedly affects the nucleation behaviour. In order to determine the austenite-to-ferrite/pearlite transformation kinetics, diametral dilatometric CCT tests were performed on the Gleeble 1500 thermomechanical simulator using tubular specimens. The specimens were initially heated up to different austenitizing temperatures to produce the desired austenite grain size [128]. After stabilizing at the austenite temperature, the specimens were air cooled at approximately 20 °C/s to 900 °C and held for 30 seconds to homogenize the temperature. In order to study the effect of accelerated cooling on the austenite decomposition, three types of cooling procedures were employed: resistive heating controlled cooling (<10 °C/s), air cooling («20 °C/s) and a range of helium gas cooling conditions (>30 °C/s). The cooling rates were measured prior to transformation, at approximately 850 °C. During each test, the temperature and mid-plane diameter of the specimen was recorded as a function of time. Figure 4.5 shows an example of dilation measurements as a function of temperature for air cooling of the A36 steel with an austenite grain size of 18 um. At high temperatures, in the austenitic region (above 750 °C), the diameter of the specimen decreases approximately linearly with temperature. The slope of the curve corresponds to the thermal contraction coefficient of austenite (ay). For this cooling rate and austenite grain size, at temperatures below 600 °C, the austenite decomposition Chapter 4 EXPERIMENTAL TECHNIQUES 71 reaction is complete and the diameter of the specimen decreases linearly with temperature. The slope of this region corresponds to the thermal contraction coefficient of the product phases, a combination of ferrite and pearlite, oip. During austenite decomposition, the dilation curve shows an increase due to the increasing atomic volume of the ferrite and pearlite phases produced [6]. The volume fraction of transformed austenite, F X(T), was determined from the dilation response, D(T), as follows [129, 130]-D(T) - D (T) F (T\ = A Dp(T)-Dy(T) ( 4 1 ) where Dy=Dr(Ty0) + ay(T-Ty0) ( 4 2 ) and Dp=Dp(Tp0) + ap(T-Tp0) ( 4 3 ) are the extrapolated dilations from the untransformed and fully transformed regions, with TyQ, and TpQ being limiting temperatures within these two regions, and Oy and cip are the thermal expansion coefficients of austenite and produced phases, respectively. Equation (4.1) is consistent with the assumption of a law of mixtures for the thermal expansion coefficient, a m j x , during the transformation, i.e.: «»« =apFx + ar(\-Fx) (4.4) Chapter 4 EXPERIMENTAL TECHNIQUES 72 where F x is the volume fraction transformed. When the austenite-to-ferrite transformation is completed, the austenite-to-pearlite transformation is initiated. For the lower cooling rates, both transformations can be separately observed from the dilatometric response as indicated in Fig. 4.5. However, at high cooling rates, it is impossible to distinguish the completion of the austenite-to-ferrite and the initiation of the austenite-to-pearlite (or austenite-to-bainite) transformations. Thus, a microstructure analysis of the quenched samples was performed to quantify the volume fraction of each phase. 4.3.2 Double Hit Compression Tests The isothermal double hit compression testing is a technique used to evaluate the static restoration, i.e. recrystallization and recovery phenomena, following a rolling simulation. This method is based on the principle that the yield strength at high temperatures is a sensitive measure of the structural state of the material. The sample of known austenite grain size and temperature is deformed to a prescribed strain, immediately unloaded and, after a specified time, simulating the interpass time, deformed again at the same strain rate. The degree of softening (fractional softening) taking place during the unloading period can be estimated as follows: (4.5) Chapter 4 EXPERIMENTAL TECHNIQUES 73 where a m is the flow stress immediately before unloading, and OQ and o r are the yield stresses pertaining to the first and the second deformations, respectively, as shown in Fig. 4.6. Since retained strain has a major effect on the austenite decomposition kinetics and the resulting microstructure, quantification of the degree of softening between the passes of the finishing mill is necessary to simulate the hot strip mill process. To have the maximum retained strain in double hit test, the deformation was applied at temperatures as low as approximately 20 °C above the calculated Ae3 temperatures [79, 131] m pjg 4.6 the A36 steel was initially austenitized at 950 °C for 2 minutes to produce a mean austenite grain size of 18 um. It was then air cooled to 850 °C (deformation temperature) and kept for 3 minutes to equilibrate the temperature. The double hit deformation tests involved two different interpass times. In the shorter interhit time, 1 second, the degree of softening is reduced and the resulting flow stress, a r , approaches a m , the initial unloaded level. However, when the interpass time is longer, 10 seconds, the reloading curve shows a flow stress of a r2, which approaches that observed for the first deformation, indicating that recovery and recrystallization has occurred during the interpass time. Chapter 4 EXPERIMENTAL TECHNIQUES 4.3.3 Pre-strain Tests 4.3.3.1 Compression 74 Nb is the microalloy addition made to H S L A steels to enable controlled rolling, i.e., retaining strain during the final finishing passes, prior to the austenite decomposition. Compression tests were utilized to investigate the influence of retained strain on the austenite decomposition kinetics and the resulting microstructure of the HSLA-Nb grade. To reflect the industrial process conditions in the laboratory tests, different austenite grain sizes, degrees of retained strain and cooling conditions were employed. Two types of compression experiments were performed; axisymmetric compression tests were performed on both 6 mm and 4 mm diameter samples. A 6 mm diameter by 8 mm length sample was used to examine the effect of deformation in the austenitic region and the subsequent austenite decomposition by diametral dilation measurements. However, to avoid the development of any surface-centerline temperature gradients, all the specimens were control cooled to room temperature at 1 °C/s. In this series of experiments, first, the specimens were reheated to one of these temperatures, 950, 1100 or 1150 °C, to produce the desired initial austenite grain sizes, 18, 44 or 84 um, respectively. Next, they were air cooled to 880 °C and kept for 3 minutes to stabilize the temperature throughout the specimens. Then, they were deformed to different levels of strain at a constant strain rate of 0.1 s"1. Following deformation, the samples were continuously cooled to room temperature at 1 °C/s and the diametral dilation was recorded to monitor the austenite decomposition kinetics. Chapter 4 EXPERIMENTAL TECHNIQUES 75 To better simulate accelerated cooling conditions, pre-strain compression tests have been performed using the smaller cylindrical specimen, 4 mm in diameter by 6 mm in length. By reducing the diameter of the axisymmetry compression specimen, higher cooling rates could be employed resulting in smaller surface-center thermal gradients during accelerated cooling, simulating the run-out table cooling conditions. By employing these specimens and using air or helium gas quenching, various cooling rates up to 150 °C/s were achieved. 4.3.3.2 Torsion To reproduce the retained strain realized in the hot strip mill during processing of the HSLA-Nb steel and the subsequent run-out table accelerated cooling, torsion tests were employed. In torsion tests, cylindrical specimens with a gage length of 21 mm and 6.4 mm in diameter were employed. The torsion tests were performed with a thermocouple spot welded onto the specimen surface at the mid-length of the gage, the area with the maximum strain. Loose thermocouple wires were used to keep them on the samples during deformation. To simulate the accelerated cooling conditions on the run-out table, the surface of the specimen was cooled by He gas applied to the area of maximum strain where the thermocouple is also located. Such an experimental set up permits the combined simulation of pre-strain and run-out table cooling conditions. The thermal recalescence developed during austenite decomposition was analyzed to interpret the transformation behaviour. Since the austenite decomposition is an exothermic reaction, the generated heat is proportional to the amount of new phase Chapter 4 EXPERIMENTAL TECHNIQUES 76 formed. Thus, quantification of the heat of transformation permits to obtain information on the transformation kinetics. Debray [132] has given more details of the application of this method for quantification of the continuous cooling transformation (CCT) kinetics following torsion testing. It should be noted that in equipment controlled cooling tests, i.e., cooling rates lower than during air cooling, the generated heat of the phase transformation is compensated by the equipment, which makes it impossible to calculate the transformation kinetics. Therefore, air cooling is the minimum cooling rate which can be applied to obtained interpretable recalescence/transformation kinetics. Similar to compression, in torsion tests, the HSLA-Nb specimens were heated to 950 °C soaked for 2 minutes to produce 18 um initial austenite grain size, then cooled to the deformation temperature of 880 °C and held for 3 minutes to homogenize the temperature throughout the specimen. They were then deformed to a selected strain level and immediately continuously cooled to room temperature at a selected cooling rate, varying from air cooling («10 °C/s) to helium quench of 150 °C/s. Chapter 4 EXPERIMENTAL TECHNIQUES 77 Specimen Spring Helium gas used to quench Cu electrical contacts Thermocouple Crosswise strain measurement Helium gas out Anvil Figure 4.1: Schematic diagram of the tubular specimen support in the Gleeble test chamber. Chapter 4 EXPERIMENTAL TECHNIQUES 78 Figure 4.2: Schematic diagram of axisymmetric compression testing in the Gleeble test chamber. Chapter 4 EXPERIMENTAL TECHNIQUES 79 Figure 4.3: General overview of the MTS torsion machine at McGil l University; (1) hydraulic servovalve; (2) hydraulic motor; (3) rotating torsion bar; (4) turn potentiometer; (5) specimen; (6) stationary grip and (7) torque cell. Chapter 4 EXPERIMENTAL TECHNIQUES SO Figure 4.4: The (a) water quenched sample of HSLA-Nb steel showing ferrite outlining the original austenite grain boundaries and the (b) transparent tracing of the prior austenite grain boundaries for the HSLA-Nb steel. Chapter 4 EXPERIMENTAL TECHNIQUES 81 8 400 500 600 700 800 900 Temperature (°C) Figure 4.5: Experimental dilation versus temperature results for the A36 steel after austenitizing at 950 °C. The solid lines indicate the extrapolations from the pre- and post-transformation regions (dv=18 um). (' ) T Chapter 4 EXPERIMENTAL TECHNIQUES 82 350 50 - 0 0 "I r 0.0 0.1 0.2 0.3 0.4 0.5 Strain Figure 4.6: Typical double hit compression test performed at 850 °C for interpass times of 1 and 10 seconds for the A36 steel having an austenite grain size of 18 um and deformed at a strain rate of 0.1/s. CHAPTER 5 C C T R E S U L T S The experimental results of the austenite decomposition behaviour and their corresponding empirical models are presented in chapter 5 and chapter 6. In this chapter, the effect of cooling rate on the strain free austenite decomposition kinetics and the resulting microstructure for the four candidate steels is examined with the initial grain sizes approximating that realized at the exit of the finishing mill. In the next chapter, the effect of retained strain in the HSLA-Nb steel on the continuous cooling transformation behaviour and the resulting microstructure is investigated for a range of y grain sizes from 18 to 84 um. 5.1 HEAT TREATMENT SIMULATION TO DEVELOP DESIRED AUSTENITE GRAIN SIZE The typical recrystallized austenite grain sizes resulting at the exit of the finishing mill are in the range of 20-50 um [133]; this assumes that recrystallization has occurred after each rolling pass. To obtain a suitable initial austenite microstructure for CCT tests, it was necessary to produce the desired average grain size combined with a normal grain 83 Chapter 5 CCT RESULTS 84 size distribution. The heating rate, reheating temperature and holding time at the reheating temperature are the important experimental parameters. Giumelli [128] quantified the austenite grain growth kinetics and the resulting grain size distributions for the two plain-carbon steels, A36 and DQSK, included in this study. He also provided the simulation heat treatments to develop different austenite grain sizes for subsequent CCT tests for the two plain-carbon steels. Based on this work, a number of heat treatment cycles were also developed for the two H S L A steels to obtain an appropriate range of initial austenite grain sizes and normal grain size distributions. These heat treatment schedules are summarized in Table 5.1. As indicated in Table 5.1, the same simple thermal cycle shown in Fig. 5.1 was adopted for each steel to produce the smaller austenite grains, typical of the austenite at the end of the finishing mill. The specimens were heated to 950 °C at 5 °C/s and held for 2 minutes to stabilize the temperature throughout the specimen. This heat treatment provided a uniform austenite grain structure having a mean volumetric grain size of 38, 18, 36 and 18 um for DQSK, A36, H S L A - V and HSLA-Nb, respectively. For the plain-carbon A36 and DQSK steels, increasing the reheating temperature and the reheating time yielded larger austenite grain sizes; increasing temperature was found to be more effective for enlargement of austenite grains [128] However, at reheating temperature from 1000 to 1150 °C, rapid and non-uniform grain coarsening, abnormal grain growth, was often observed. This has been attributed to coarsening and dissolution of A1N particles [134]. The resulting non-homogeneous grain size Chapter 5 CCT RESULTS 85 distribution exhibited fine grains embedded in regions of substantially larger grains [134] No heat treatments were employed which resulted in abnormal grain growth. Table 5.1: Heat treatment schedules to develop the specified mean, volumetric austenite grain sizes. 1 Heat. Hold Hold Cooling Hold Hold y Grain Grade rate Temp. \ *1 Rate Temp. 2 *2 Size °C/s °C sec. °C/s °C sec. um 5 950 120 - - - 38 DQSK 5 1100 120 «20 900 30 136 [128] 5 1150 60 «20 900 30 190 A36 5 900 120 - - - 15 [128] 5 950 120 - - - 18 5 950 120 - - - 36 HSLA-V 100 1150 0 «20 900 30 85 5 1150 30 «20 900 30 120 5 950 120 - - - 18 HSLA-Nb 100 1100 0 *20 900 30 44 5 1150 30 «20 900 30 84 To develop the 46 um austenite grain size for the A3 6 steel, a special heat treatment cycle was employed [128] First, the specimens were heated to 1200 °C, held Chapters CCT RESULTS 86 for 3 hours, then water quenched to room temperature and subsequently given stepped thermal cycles as illustrated in Fig. 5.2. The grain growth in the HSLA steels was similar to that obtained for the plain-carbon steels. A number of laboratory heat treatment tests were performed using the temperature controlling capabilities of the Gleeble 1500 as well as air furnace tests, the results being shown in Fig. 5.3 [135]. It is evident that below approximately 1050 °C, pinning by A1N (and/or microalloyed precipitates) prevents a rapid grain growth, whereas at temperatures above approximately 1125 °C, the pinning force rapidly decreases allowing for substantial uniform grain growth. This is more pronounced for HSLA-Nb steel; the presence of undissolved Nb(C, N) precipitates prevents the austenite grain growth. Although the heat treatment schedules employed for the HSLA steels are different (controlled heating and 5 min. reheating time for the HSLA-Nb steel versus furnace heating and 60 min. holding time for the H S L A - V steel) the transition from grain growth inhibition to grain coarsening is characterized in both grades by abnormal grain growth, a non-homogeneous microstructure developing with areas of small grains embedded in a network of larger grains. For most industrial processing conditions i.e., as experienced during hot strip mill processing, polygonal ferrite is the desired and produced transformation product. It is well known that increasing the austenite grain size and/or cooling rate enhances the tendency to form a non-polygonal ferrite microstructure. Thus, the maximum desired initial austenite grain size is that grain size that produces polygonal ferrite for a minimum cooling rate (air cooling) on the run-out table. This was the basis of employing heat treatment schedules to produce different initial austenite grain sizes. Chapter 5 CCT RESULTS 87 As illustrated in Table 5.1, in H S L A steels, by keeping the heating rate constant at 5 °C/s and changing the reheating temperature from 950 to 1150 °C, the relatively small and large grain sizes were produced. However, a number of heat treatment procedures were employed to produce a homogeneous intermediate grain size. These procedures included a change in heating rate, reheating temperature, reheating time and cooling rate. It is evident that increasing the heating rate increases the number of austenite nuclei during the austenite reversion process consistent with literature findings t'36] n w a s found that a combination of a higher heating rate of 100 °C/s, no holding time and reheating temperatures of 1150 and 1100 °C were effective procedures to produce homogeneous intermediate grain sizes for H S L A - V and HSLA-Nb steels, respectively. 5.2 CCT RESPONSE To investigate the austenite decomposition kinetics as a function of steel grade and austenite grain size, a series of diametral dilation measurements were performed during CCT testing. The continuous cooling phase transformation kinetics for the DQSK steel having 38, 136 and 190 um austenite grain sizes are shown in Fig. 5.4. In DQSK steel, the ferrite is approximately 95% of the austenite decomposition products while the produced ferrite is polygonal. A l l of the CCT tests show a relatively rapid rate of transformation up to a transformed volume fraction of about 70%, depending on the initial austenite grain size, followed by a decreasing transformation rate to completion of the austenite decomposition (Fig. 5.4). The dominant transformation kinetics result from a combination of nucleation and growth of the ferrite phase for the low carbon steels in Chapter 5 CCT RESULTS 88 this study. At the beginning of the transformation, nucleation dominates leading to early site saturation with an increasing transformation rate. The growth rate of the resulting ferrite grains is rapid reflecting the steep carbon gradient in the austenite at the transforming interface. However, after about 70% austenite decomposition, the combination of site saturation, the reduced carbon gradient at the austenite interface and soft and hard impingement leads to a reduced transformation rate. This transformation sequence exhibits the sigmoidal-shaped curves shown in Fig. 5.4. As shown in Fig. 5.4, accelerating the cooling rate from the austenite region, reduces the transformation start temperature. Since the austenite-to-ferrite transformation is a diffusional transformation, it needs a finite amount of time to nucleate and grow. By increasing the cooling rate, the available time at any temperature decreases and consequently the transformation start and finish temperatures are decreased, a trend which can be seen for each of the austenite grain sizes. To clearly show the effect of austenite grain size, the austenite decomposition kinetics in Fig. 5.4 for air cooling, «20 °C/s, have been replotted in Fig. 5.5. It is obvious that as the original austenite grain size increases, both the transformation start and finish temperatures decrease. In fact, increasing the austenite grain size decreases the grain boundary surface area per unit volume, thereby reducing the number of available sites for the heterogeneous nucleation of ferrite, and consequently reducing the transformation temperatures. This is consistent with the results presented by DeArdo et al. [92] who found that an increase in the initial austenite grain size shifts the CCT diagram to longer times, lowering the transformation temperature for a given accelerated cooling condition. It is evident that because of the larger grain boundary area per unit volume (more Chapter 5 CCT RESULTS 89 nucleation sites) and the shorter carbon diffusion distance, the relatively smaller austenite grain sized austenite (38 um) exhibits a higher transformation rate (Fig. 5.5). The austenite-to-ferrite transformation in the A36, H S L A - V and HSLA-Nb steels shows a similar behaviour to that exhibited by the DQSK steel, as shown in the Appendix (Figs. App. 1, App. 2 and App. 3, respectively). 5.2.1 Quantification of Transformation Start Temperature (Ar3) To specify the effect of austenite grain size and cooling rate on the transformation start temperature, Ar3, the temperature for 5% transformation [129] is plotted versus the cooling rate for three different austenitizing conditions for the DQSK steel in Fig. 5.6. As can be seen, increasing the cooling rate suppresses the Ar3_ For a given cooling rate, a smaller austenite grain size results in an increase in the number of potential nucleation sites. This accelerates the transformation rate and yields a higher Ar3 temperature. Increasing the alloying elements, in particular the carbon level, decreases the equilibrium Ae3 [79] temperature and thus, also, the A r 3 temperature, while exhibiting a similar response to the effect of cooling rate and austenite grain size (see Appendix, Figs. App. 4, App. 5 and App. 6). This will be described in more detail where the transformation behaviour of the four candidate steels is compared. Chapter 5 CCT RESULTS 5.2.2 Microstructural Evolution During CCT Testing 5.2.2.1 The Ferrite Grain Size and Volume Fraction 90 In addition to the dilation measurements made during the CCT tests, the resulting microstructures were also investigated with the ferrite grain size and ferrite fraction being quantified. The plot of the polygonal ferrite grain size and ferrite volume fraction for the DQSK steel as a function of cooling rate for three austenite grain sizes, 38, 136 and 190 um, is shown in Fig. 5.7. As can be seen, the initial austenite grain size has a major impact on the final microstructure, particularly on the ferrite grain size, whereas, the polygonal ferrite fraction is almost independent of the austenite grain size. For a given cooling rate, decreasing the austenite grain size yields a finer ferrite grain size. However, this effect is diminished as the cooling rate increases. Decreasing the austenite grain size increases the grain boundary surface area per unit volume and consequently increases the number of available nucleation sites for ferrite. This is the reason for the dependency of the ferrite grain size on the initial austenite grain size. Almost the same behaviour as for the DQSK grade was seen for the A36, HSLA-V and HSLA-Nb steels when the produced ferrite grains were polygonal (see Appendix, Figs. App. 7, App. 8 and App. 9, respectively). Figure 5.8 illustrates the resulting microstructures obtained from CCT tests with different cooling rates ranging from 1 to 290 °C for the DQSK steel having a 38 um initial austenite grain size. Each micrograph shows a microstructure containing a mixture of polygonal ferrite (about 95%) and pearlite. As can be seen, the increase in cooling rate Chapter 5 CCT RESULTS 91 reduces the ferrite grain size. The dramatic reduction of ferrite grain size as a function of accelerated cooling can be explained by classical nucleation theory; the concept which can be extended to heterogeneous nucleation. For classical, composition invariant, homogeneous nucleation, at equilibrium (Tg), the changes in enthalpy (AH V ) and entropy (ASV) are as follows AH AGV =GP -Ga = AGa^p = 0 = AHV - TEASV or ASV = —- (5.1) For a given amount of supercooling, AT below Tg, the volume free energy change, A G V , associated with the transformation is given as: AGV=AHV-TASV (5.2) since A H V and A S V are relatively insensitive to small changes in temperature near equilibrium, combining the above equations gives: AH AT AGv=AHv-T-rL = AH— (5.3) 1li 1E where AT is the amount of undercooling which increases with accelerated cooling. The total free energy change, AG,.associated with the formation of the new embryo can be written as: Chapter 5 CCT RESULTS 92 AG^VAGv+JJiAji+VAG£ (5.4) where V is the volume of the produced embryo, A} is the area of the embryo/matrix boundary with the constant interface energy yj, and Zi denotes the summation over all surfaces of the embryo and A G S is the strain energy per unit volume. In classical homogeneous nucleation theory, the probability of observing any embryo with a given size having n atoms in the equilibrium state is shown to be proportional to exp(-AG/kT). The number of embryos containing n atoms, N n , can be expressed by the relation [6]: where N is the total number sites per unit volume, k is the Boltzman constant. Since increasing the cooling rate increases the supercooling, AT, this leads to an increase in the magnitude of |AG V | , Eq. (5.3). The increase in | A G V | gives more potential for the formation of the new phase by decreasing AG in Eq. (5.4). Finally, the decrease in AG increases the number of nuclei dramatically, Eq. (5.5). This is the reason that the nucleation density can be enhanced with accelerated cooling [94, 137]. The higher the nucleation density the larger the number of ferrite grains yielding a finer resulting ferrite grain size. (5.5) Chapter 5 CCT RESULTS 93 Accelerated cooling is a suitable technique to enhance the nucleation rate resulting in a refined polygonal ferrite microstructure. For the steels examined in this study, the nucleation rate increased as the cooling rate increased up to maximum which was valid from approximately 20-300 °C/s, depending on the steel grade and the initial austenite grain size. At higher cooling rates, the ferrite morphology changes from polygonal to non-polygonal structures; this effect was amplified by increasing the austenite grain size. Further increase in the cooling rate (increased supercooling) caused an increase in the acicular ferrite followed by refinement of the needle-shape ferrite structure [138] 5.2.2.2 Transition From Polygonal to Non-Polygonal Microstructure The final microstructures obtained in CCT tests performed at 1, 19, 65 and 122 °C/s for the A36 steel having an initial austenite grain size of 18 urn are illustrated in Fig. 5.9. For specimens cooled at rates of 1, 19 and 65 °C/s, the microstructures contain a mixture of polygonal ferrite (about 80%) and pearlite. However, a non-polygonal structure was obtained in the specimen cooled at 122 °C/s. The transition boundary for the polygonal to non-polygonal microstructures for the employed steels for a range of initial austenite grain sizes and cooling rates is illustrated in Fig. 5.10. For example, for the A36 steel with an 18 um initial austenite grain size, a transition from a polygonal to non-polygonal structure was observed for the cooling rate higher than about 100 °C/s. Under identical cooling conditions, increasing the austenite grain size can change the ferrite morphology from polygonal to a non-polygonal structure. For example, for cooling rates up to 290 °C/s, no transition to non-Chapter 5 CCT RESULTS 94 polygonal structure is revealed for the DQSK steel with an austenite grain size of 38 um. However, for a cooling rate of approximately 20 °C/s, a transition to a non-polygonal microstructure is obtained for an austenite grain size of 190 urn. The increase in the initial austenite grain size increases the diffusion distance between the ferrite nucleating sites, which are located preferably at the grain boundary, and the center of the austenite grain. Since the austenite-to-ferrite transformation occurs by long-range carbon diffusion, more time is required to redistribute the carbon in the remaining austenite for a larger austenite grain. Thus, under the same cooling conditions, a greater degree of supercooling is attained before the carbon is redistributed, encouraging the formation of a non-polygonal structure in the interior of the grains. For a given initial austenite grain size, increasing the cooling rate lowers the transformation temperature and enhances the formation of a non-polygonal microstructure (Fig. 5.10). Increasing the alloying elements, in particular the carbon content, also lowers the transformation temperature and enhances the formation of an acicular microstructure. Although the carbon equivalent content, C e q U j v a i e n t=C+Mn/6 t 7 ° ] , of the H S L A - V steel is comparable to that of the DQSK grade (0.12% for the HSLA-V steel and about 0.09% for the DQSK grade), surprisingly, the transition temperature of this steel grade is much lower than that of the DQSK steel. This will be examined in detail later in this chapter when the phase transformation characteristics of the DQSK and HSLA-V steels are compared. Chapters CCT RESULTS 5.3 MODELING OF y-xx TRANSFORMATION KINETICS 5.3.1 Transformation Start Temperature (Ar3) 95 The 5% transformed volume fraction, To.fj5> obtained from the dilatometric response was used to characterize the transformation start temperature D29]5 AT3. A plot of Ar3 as a function of cooling rate for the DQSK steel is shown in Fig. 5.6. It can be seen that Ar3 decreases rapidly with initial increasing cooling rate; however, the rate of decrease of the Ar3 temperature is reduced at higher cooling rates. The Ar3 temperature is a strong function of chemical composition and austenite grain size. The following empirical relation was found to describe the transformation start temperature, TQ,.05> m °C as a function of cooling rate for each austenite grain size of the four steel grades: T0 05 = TAei-A<p» (5.6) where cp is the cooling rate in °C/s and A and B are fitting parameters. The parameters A and B for the different steel grades and grain sizes are summarized in Table 5.2. Further, assuming that the exponent B of Eq. (5.6) is constant and the parameter A is a grain size-dependent term for each grade, the Ar3 for each steel grade can be described by the following relation: \ m = T ^ - { C + Ddf)<pE (5.7) Chapters CCT RESULTS 96 where C, D and E are fitting parameters. The parameters C, D and E for each steel are given in Table 5.3. Table 5.2: Parameters A and B for Eq. (5.6). Grade y G . S. (urn) A B D Q S K 38 36 0.23 136 68 0.13 190 64 0.17 A36 15 63 0.15 18 70 0.13 46 85 0.14 H S L A - V 36 41 0.18 85 57 0.15 120 66 0.17 H S L A - N b 18 59 0.14 44 66 0.14 84 86 0.16 Chapters CCT RESULTS Table 5.3: Parameters C, D and E for Eq. (5.7). 97 Grade C D E D Q S K 38 0.14 0.18 A36 56 0.62 0.14 H S L A - V 23 0.29 0.17 H S L A - N b 22 0.30 0.15 A comparison of the experimental data for the H S L A - V grade and the predictions using Eq. (5.7) is given in Fig 5.11. Equation (5.7) can be seen to provide reasonable description of the experimental data. 5.3.2 Ferrite Growth Kinetics 5.3.2.1 Avrami Equation Equation (5.7) can be used to predict the transformation start temperature, Trj.05> for the four steels as a function of cooling rate and initial austenite grain size. In order to predict the phase transformation kinetics during continuous cooling, another model should be linked to Eq. (5.7) to describe the austenite-to-ferrite 5% to 95% transformation. The isothermal Avrami equation, utilizing the additivity rule, was employed to characterize the ferrite growth kinetics, as follows: X = \-exp(-bt") (5.8) Chapter 5 CCT RESULTS 98 where X is the normalized ferrite fraction transformed, b is a temperature-dependent parameter, n is constant and t is the time of transformation. In this study, the normalized ferrite fraction transformed was calculated by dividing each increment of transformed fraction of austenite by the ferrite portion of the resulting microstructure. Thus, the analysis was applied to the ferrite portion of the transformation for cases which resulted in polygonal microstructures with ferrite fraction of approximately 80% for the relatively high carbon A36 steel and 95%, 95% and 90% for the low carbon DQSK, HSLA-V and HSLA-Nb steels, respectively. As mentioned in the literature review, the theory of transformation kinetics has been largely confined to the isothermal reaction. This is because in isothermal studies, one of the variables, temperature, is kept constant which makes it easier to describe the transformation phenomena. However, the low carbon content of the steels, particularly the DQSK, HSLA-V and HSLA-Nb steels, makes it impossible to obtain valid isothermal test data for transformation temperatures representative of the run-out table. The transformations initiate prior to reaching the isothermal test temperature. However, in industrial steel processing, i.e., on the run-out table of the hot strip mill, the austenite decomposition initiates and proceeds under accelerated cooling conditions. Instead, continuous cooling results have been used to determine an effective isothermal transformation rate equation. Considering continuous cooling to be a series of isothermal steps and the transformation to be additive, the temperature dependence of b can be determined from the experimental CCT results by assuming that the exponent n is constant, independent of temperature [36]. It should be emphasized that this analysis was Chapters CCT RESULTS 99 applied only on those CCT tests which produced a pre-dominantly polygonal ferritic microstructure. As mentioned in the literature review, by rearranging Eq. (5.8), the isothermal ferrite transformation rate can be expressed as follows: A direct analysis of the CCT test results was performed in which n was varied over the range of 0.8-1.2; this being the range reported in the literature for the austenite-to-ferrite transformation [49]. The parameter b was then calculated and plotted as a function of temperature for various values of n. Clearly, changing the exponent n significantly affects the b value. For example, the behaviour of the parameter b as a function of temperature for the 38 um austenite grain size of the DQSK steel is shown in Fig. 5.12. It is evident that the b values for each CCT test as a function of temperature for n=l.l and n=0.7 are quite different (Figs. 5.12a and 5.12c) making it impossible to have a unified b relationship independent of cooling rate. However, a reasonably consistent fit for n=0.9 for all the steel grades was obtained, which permits the parameter b to be expressed as a function of temperature for all cooling rates examined for the four steels (Fig. 5.12b). Adopting n=0.9, the calculated In b values as a function of supercooling ( T A ^ - T ) for the CCT tests performed on the DQSK, HSLA-V, A36 and HSLA-Nb steels reheated to 950 °C, which produced 38, 36, 18 and 18 jam initial austenite grain sizes respectively, are shown in Figs. 5.13 and 5.14, and in the Appendix (see Figs. App. 10 and App. 11), dX dt (5.9) Chapter 5 CCT RESULTS 100 respectively. At smaller supercoolings (lower cooling rates), the transformation starts with smaller In b values. As the supercooling increases, the In b shifts to larger values. This systematic increase of In b as a function of supercooling is a consistent trend for all four steels (Figs. 5.13, 5.14, App. 10 and App. 11). For slow cooling rates, the In b increases almost linearly with increasing supercooling. However, at larger supercooling, this parameter levels off and the austenite decomposition proceeds with a slower In b rate. This behaviour is much more pronounced for the HSLA steels, in particular, for the HSLA-V steel. While CCT tests with lower cooling rates exhibit a non-linear In b response (e.g., Fig. 5.14), at higher cooling rates the In b parameter increases almost linearly as the supercooling increases. As a first approximation, a linear curve was fitted to the In b values as a function of the supercooling for different initial austenite grain sizes of each grade, given by the following equation: lnb = F(TAe2-T) + G ( 5 1 0 ) where F and G are fitting parameters. Table 5.4 summarizes the parameters F and G for the four candidate steels for the range of initial austenite grain sizes examined. A comparison of the experimental transformation kinetics with predictions based on the Avrami equation using n=0.9 and Eq. (5.10) for the 38 um DQSK steel is given in Fig 5.15; a similar comparison for the A36, H S L A - V and HSLA-Nb grades with 18, 36 and 18 um initial austenite grain sizes is presented in Appendix, see Figs. App. 12, App. Chapters CCT RESULTS 101 13 and App. 14, respectively. This semi-empirical approach can reasonably predict the phase transformation kinetics for a wide range of cooling rates, encompassing the cooling conditions realized on the run-out table and for initial austenite grain sizes comparable to those obtained in the last stand of the finishing mill (-20-50 um) [133] Table 5.4: Parameters F and G for Eq. (5.10). Grade y G. S. (urn) F G D Q S K 38 0.028 -3.08 136 0.033 -5.59 190 0.038 -6.67 A36 15 0.044 -6.54 18 0.039 -5.95 46 0.047 -8.09 H S L A - V 36 0.022 -2.38 85 0.023 -3.85 120 0.021 -4.62 H S L A - N b 18 0.031 -4.19 44 0.030 -5.55 84 0.030 -6.99 Chapter 5 CCT RESULTS 5.3.2.2 Umemoto Equation 102 As an alternative, another empirical equation (the Umemoto equation, = (nbtn~*)(\- X)Up) [58] was used to describe the austenite-to-ferrite portion of the dt continuous cooling transformation obtained for the four steels assuming additivity. Two step procedures have been investigated to utilize the Umemoto equation. In the first approach, to be consistent with the finding of Umemoto et al. [58], the parameter p was kept constant at 0.5 for all four candidate steels and the fitting parameters were calculated including the time exponent, n, assuming that In b is a linear function of suppercooling. It was found that for the 38, 18, 36 and 18 um DQSK, A36, HSLA-V and HSLA-Nb steels the best fit was obtained with n values of 1.2, 1.1, 1.2 and 0.9, respectively. In the second approach, all the parameters were varied to find the best fitting parameters, including the time exponent, n, and parameter p, to describe the ferrite growth kinetics. Surprisingly, for three steels, DQSK, A36 and HSLA-V, the best value for the parameter p was almost zero, p=0.001, and the best time exponent, n, was 0.9 indicating that the Avrami equation is indeed sufficient to model the austenite-to-ferrite transformation kinetics for these steels. Figure 5.16 compares the CCT experimental results and model predictions employing the Avrami and the Umemoto equations, the latter using p=0.5 or a variable (best fit) value. As can be seen, all of the employed equations are appropriate models to characterize the ferrite growth kinetics. The. same trend was observed for the other steel grades (see Appendix, Figs. App! 15, App. 16 and App. 17 for the A36, HSLA-V and Chapter 5 CCT RESULTS 103 HSLA-Nb, respectively). It seems that the application of the Umemoto equation does not offer any advantage compared to the Avrami equation. Firstly, the Umemoto equation has one more fitting parameter, the parameter p. Secondly, when using the Umemoto equation, the best n value for describing the CCT tests varied from steel grade to steel grade (n=1.2, 1.1, 1.2 and 0.9 for the DQSK, A36, H S L A - V and HSLA-Nb steels, respectively). Whereas, when the Avrami analysis was used, the time exponent n, was constant for all four steels at 0.9. In summary, the additional complexity resulting from the use of the Umemoto equation does not improve the prediction of the austenite-to-ferrite transformation kinetics. 5.3.2.3 Grain Size-Modified Avrami Equation in< As a first approximation, the parameter F in Eq. (5.10) can be taken as dependent of the austenite grain size. Using the grain size-modified Avrami equation [54], Eq. (2.12), the effect of austenite grain size, d, was included in the model as follows: X = 1 - exp ; b = 7m or \nb = Ink-mind (5.11) where k is a temperature-dependent factor as follows: Ink = F(TA^-T) + H (5.12) Chapter 5 CCT RESULTS 104 The grain-size modified Avrami equation has been used to characterize the kinetics of the austenite-to-ferrite transformation for each of the four steel grades. The plot of In d versus In b values for the four steel grades for a specific undercooling (100 °C; this undercooling is suitable and applicable to all steel grades and produced austenite grain sizes) is illustrated in Fig. 5.17. In general, the In b value for the four steels systematically increases as the In d value decreases; an exception is noted for two small austenite grain sizes, 15 and 18 um, in the A36 steel. This may be related to the fact that a very small difference exists between the two austenite grain sizes, 15 and 18 um. The exponent m, as well as the parameters F and H, for each of the steels are given in Table 5.5. Table 5.5: Exponent m and parameters F and H for Eqs. (5.11) and (5.12). Grade m F H D Q S K 2.16 0.033 4.81 A36 1.68 0.043 -1.59 H S L A - V 1.60 0.022 3.30 H S L A - N b 1.80 0.030 1.08 The comparison between the experimental data and the grain size-modified model predictions for the DQSK, A36, H S L A - V and HSLA-Nb grades are illustrated in Figs. 5.18, App. 18, App. 19 and App. 20, respectively. As can be seen, there is good Chapters CCT RESULTS 105 agreement between the experimental data and the model predictions for different accelerated cooling conditions and for the austenite grain sizes examined in this study. As can be seen in Fig 5.17, the grain size exponent, m, for the four steels is close to 2 which is consistent with the data reported in the literature [54, 55, 58]. T h U s , the possibility of adopting a constant grain size exponent, m=2, was assessed for all the steel grades. Using m=2, a new set of fitting parameters, F and H was found for each steel using Eq. (5.12). These parameters are shown in Table 5.6. Table 5.6: Parameters F and H for Eq. (5.12). Grade F H D Q S K 0.033 4.09 A36 0.043 -0.58 H S L A - V 0.022 5.05 H S L A - N b 0.030 1.83 The comparison between the experimental data and that predicted using the grain size-modified Avrami equation for the DQSK, A36, H S L A - V and HSLA-Nb steels using m=2 is given in Figs. 5.19, App.21, App .22 and App. 23, respectively. As can be seen, the equation predicted and experimental data are in a reasonable agreement. Chapters CCT RESULTS 106 5.4 COMPARISON OF THE TRANSFORMATION BEHAVIOUR OF THE FOUR STEELS 5.4.1 CCT Tests The transformation kinetics obtained for the four candidate steels, each having a similar austenite grain size (38, 46, 36, 44 um for DQSK, A36, H S L A - V and HSLA-Nb, respectively), and each subjected to a cooling rate of l°C/s, are shown in Fig 5.20. The most obvious difference in the CCT test results is the difference in the transformation temperature of each steel. Clearly, the transformation temperature strongly depends on the alloying elements H 39]? m particular the carbon level [140, 141] A.S m e carbon level increases, the hardenability increases [140, 141] shifting the CCT curve to longer time resulting in a lower transformation temperature. The other concern in CCT tests is the difference in the phase transformation kinetics. For the same cooling conditions, as the carbon level increases, the transformation rate decreases. For instance, while the time for 50% of the austenite decomposition for the DQSK grade is less than 10 s, approximately 20 s is required for the A36 steel. The higher transformation rate in the DQSK steel is related to the higher diffusion rate. As the carbon level increases, the transformation occurs at lower temperature resulting in a reduced carbon diffusivity and thus a lower austenite decomposition rate. The other difference between, the transformation curves is related to the production of the pearlite phase, which is the minor phase resulting from the eutectoid Chapters CCT RESULTS 707 austenite decomposition after the completion of the ferrite formation. As can be seen in Fig. 5.20, for the A36 steel, after the completion of the y—»a («80% transformed) the y-»p transformation initiates with a smooth increase in the transformation rate. Since, in the other three steels, the amount of pearlite phase is very low (<10%), and the pearlite is produced in the last stage of austenite decomposition, the transition points are not as clearly defined as they are for the A36 steel. 5.4.2 Comparison Between DQSK and HSLA-V Steels Since the DQSK and HSLA-V steels have almost the same levels of C, 0.038 and 0.045 wt.%, and Mn, 0.30 and 0.45 wt.%, respectively, it is informative to compare the transformation characteristics of these two grades and to study the effect of V on the phase transformation kinetics and the resulting microstructure. The transformation kinetics of the two steels with comparable austenite grain sizes and different cooling rates is shown in Fig. 5.21. It can be seen that the two steels behave almost identically. This is consistent with the findings of Singh et al. [30] who have found that the effect of V , in amounts present in the HSLA steels, on the phase transformation kinetics is very limited. Although, under the same accelerated cooling conditions, the transformation kinetics of these steels is similar, the H S L A - V steel is more prone to produce an acicular microstructure. The resulting microstructures of CCT tests for the DQSK and HSLA-V steels having 38 um and 36 um austenite grain sizes and cooled at 290 and 238 °C/s cooling rates are shown in Fig. 5.22a and 5.22b, respectively. Both specimens contain in Chapter 5 CCT RESULTS 108 excess of 95% ferrite. Although the cooling rate in the DQSK sample is higher than that in the HSLA-V specimen, which encourages the formation of non-polygonal structure, the DQSK specimen has more polygonal ferrite with smooth ferrite grain boundaries. Whereas, the ferrite grain boundaries in the H S L A - V specimen are more irregular approaching the acicular microstructure. The same trend was observed for industrial processed DQSK and H S L A - V coil samples shown in Fig. 5.22c and 5.22d. Again, in the DQSK grade, the grain boundaries of the ferrite are smooth but, in the HSLA-V steel the grain boundaries of the ferrite are more irregular. The irregularity of the ferrite grain boundaries must be related to the presence of vanadium; the vanadium is in solution as a SDLE and/or as vanadium precipitates, V(C, N). It is likely that the segregation of the solute at the y/oc boundaries (SDLE) is dominant [142, 143]? because the time available before the phase transformation is not enough to form the V(C, N) [144] This is also confirmed by Sun et al. [142] who have performed an electron microscopy investigation of precipitation in the HSLA-V steel. Further, there was no evidence for interface precipitation of V(C, N) in particular at the existing vanadium level in this H S L A - V steel and for the imposed accelerated cooling conditions of the CCT tests. 5.5 FERRITE GRAIN SIZE The ferrite grain size in the final microstructure is essentially determined at the start of transformation, assuming nucleation site saturation. However, some ferrite Chapters CCT RESULTS 109 coarsening may occur during the transformation [145] To determine i f ferrite grain growth occurs after completion of the austenite decomposition, a number of heat treatment tests in the ferritic region for the A3 6 steel were performed. After transformation, the specimens were heated to different temperatures up to 700 °C and held for different times up to 3 hours, but no ferrite grain enlargement was observed. The number of ferrite grains, and thus the ferrite grain size, depends mainly on the amount of nucleation at grain corners, edges and boundaries area. A normal ferrite grain size distribution was found for the undeformed condition of the employed steels. The width of the grain size distribution changes little as cooling rate increases [146]. Therefore, the ferrite grain size distribution can be characterized by the mean grain size. Since details of this nucleation process are not known with sufficient accuracy, it is virtually impossible to deduce the ferrite grain size from the above nucleation and early growth model, or from a similar fundamental approach. Empirical or semi-empirical relations were used to describe the ferrite grain size produced during the phase transformation. Commonly, such relations exhibit a pronounced cooling rate dependence [85-87, 117] However, in view of the actual nucleation process, it is consistent to predict the ferrite grain size as a function of the transformation start temperature, as proposed by Suehiro et al. [120]. Their proposed model, slightly modified by Militzer et al. [147]s and applied to the experimental measurements to predict the ferrite grain size as a function of transformation start temperature, and austenite grain size and ferrite fraction is as follows: Chapter 5 CCT RESULTS 110 da = 1 . 2 ( F / e x p ( j j ; - K / T s ) ) m (5.13) where T s is the transformation start temperature (in °K), d a is ferrite grain size, dy is the austenite grain size in um, Ff is the ferrite volume fraction, and J, K and r\ are the fitting parameters. The ferrite volume fraction, Ff, and fitting parameters, J, K and n, are summarized in Table 5.7 for all four steel grades. Table 5.7: The ferrite volume fraction, Ff, and J, K and n fitting parameters for Eq. (5.13) [147]. Grade Ff J K TI D Q S K 0.96 50.7 51000 0.0238 A36 0.80 52.3 51000 0.0286 H S L A - V 0.95 47.8 51000 0.0356 H S L A - N b 0.90 49.6 51000 0.0355 Figure 5.23 compares the calculated results based on the parameters in Table 5.6 with the measured grain sizes obtained for the HSLA-Nb grade. The agreement is good, particularly for the small ferrite grain size (da<10 um) of interest for the industrial conditions. Chapters CCTRESUTS 111 Figure 5.1: Schematic diagram for producing a small austenite grain size characteristic of that realized at the end o f the finishing mil l . Chapters CCT RES UTS 112 Figure 5.2: Schematic diagram for producing a 46 um austenite grain size for the A36 steel. Chapter 5 CCT RESULTS 113 200 180 < Q! 1 2 0 8 ioo •a so n 60 0 40 L 2 0 -H S L A - V H S L A - N b 850 9 0 0 950 1000 1050 1100 1150 1200 1250 Temperature, °C Figure 5.3: Austenite grain growth behavior for the HSLA-Nb steel obtained by Gleeble tests at a 5 °C/s heating rate and a 5 min. holding time, and HSLA-V steel, air furnace heated to the designated temperature and held for 60 min. [135]. Chapters CCTRESUTS 114 s _o % - i o cs ns s C 03 H 1.0 0.8 0.6 -| 0.4 0.2 0.0 ~ A ~ A 7 ° ° qg o A A A A A ° ° D ° n O A D • A D ' O O , (a) o o o. o„ A • • o o A A A O o o 5 °C/s • 87 °C/s A 290 °C/s A 0 A A • • X L o o o 640 680 720 760 Temperature (°C) 800 1.0 s u cs ns CJ £ a C C3 U H 0.8 H 0.6 0.4 0.2 0.0 o >A ~ • n ° ° n O 5 °C/s • 81 °C/s A 144 °C/s A A A a a a o, o a - O L O -600 640 680 720 760 Temperature (°C) 800 s u CS i -s I * ) s cs H 1.0 0.8 0.6 0.4 0.2 H 0.0 o 5 °C/s • 40 °C/s A 81 °C/s -o-840 ( b ) 840 620 640 660 680 700 720 740 760 780 800 820 Temperature (°C) Figure 5.4: Continuous cooling transformation kinetics for the D Q S K steel tor initial austenite grain sizes of; (a) 38 um; (b) 136 um and (c) 190 urn. Chapters CCTRESUTS IIS 1.0 0.8 0.6 0.4 0.2 0.0 A • O O o A D o A3 A • A • O O O A • A • A A A • • O O o • A • A • A • A • A • A • O O O O O O o dy=38 Lim • dy= 136 fim A dy=190 Lim • • A A • A • A A A • A • • • O O O O O O O o o 640 660 680 700 720 740 760 780 800 820 840 Temperature (°C) Figure 5.5: Transformation kinetics for the air cooled («20 °C/s) DQSK steel for the range of initial austenite grain sizes, 38, 136 and 190 (am. Chapter 5 CCT RES UTS 116 860 840 820 H ° 800 t3. 780 | 760 H 740 720 700 dy=38 urn dy=136 Lim d =190 jam 0 20 40 60 80 100 120 140 160 180 200 Cooling rate (°C/s) Figure 5.6: Transformation start temperature, A r 3 , taken at the temperature for 5% transformation versus c o o l i n g rate for three different grain sizes o f 36, 136 and 190 u m for the D Q S K steel. Chapter 5 CCT RESULTS 117 0 20 40 60 80 100 Cooling rate (°C/s) Figure 5.7: Polygonal ferrite grain size and ferrite volume fraction for the DQSK steel obtained from CCT tests for three different initial austenite grain sizes of 38, 136 and 190 um. Chapters CCTRESUTS 118 Figure 5 .8 : Microstructure obtained after continuous cooling tests on the DQSK steel having a 38 um initial austenite grain size and subjected to different cooling rates; (a) 1 °C/s; (b) 87 °C/s and (c) 290 °C/s. Chapter 5 CCT RESUTS 119 Figure 5.9: Microstructure obtained after continuous cooling tests on the A36 steel having an 18 um initial austenite grain size and subjected to different cooling rates; (a) 1 °C/s; (b) 19 °C/s; (c) 65 °C/s and (d) 122 TVs. Chapter 5 CCT RESUTS 120 350 300 250 U V 200 a u OX) e 150 o o U 100 50 0 • DQSK • A36 A HSLA-V • HSLA-Nb • \ • \ Non-polygonal polygonal \ \ \ A 0 20 40 60 80 100 120 140 160 180 200 Austenite grain size (yan) Figure 5.10: The transition boundary for the polygonal to non-polygonal microstructure for each of the four steel grades for a range of initial austenite grain sizes and cooling rates. Chapters CCTRESUTS 121 20 0 dy=120 Lim Predictions 0 30 60 90 120 150 180 210 240 Cooling rate (°C/s) Figure 5.11: Comparison between experimental data and predictions o f A r 3 for the HSLA-V steel for different accelerated cooling conditions and initial austenite grain sizes. Chapter 5 CCT RES UTS 122 10 8 6 4 2 0 10 8 A 6 4 2 H 0 10 8 6 4 2 H 0 n=l.l (a) 290 °C/s 87 °C/s 61 °C/s 14 °C/s 680 700 720 740 760 780 800 820 840 Temperature (°C) n=0.9 (b) 290 °C/s 87 °C/s 61 °C/s 14 °C/s 680 700 720 740 760 780 800 820 840 Temperature (°C) 290 °C/s n=0.7 87 °C/s (c) 6i;c / s 1 4 o C / s 680 700 720 740 760 780 800 820 840 Temperature (°C) Figure 5.12: Behavior of the Avrami parameter b versus temperature for different CCT tests for the DQSK steel with a 38 um initial austenite grain size, showing the effect of varying the time exponent n; (a) n=l .1; (b) n=0.9 and (c) n=0.7. Chapter 5 CCT RESUTS 123 3 40 o p o • A O 0 14 °C/s 38 °C/s 61 °C/s 87 °C/s 290 °C/s Regression 60 80 — i 1 1 i 120 140 160 180 200 100 (TAej-T) ( O Q Figure 5.13: Behavior of In b values versus supercooling for the DQSK steel with 38 um initial austenite grain size and n=0.9. Chapter 5 CCT RESUTS 124 60 80 100 120 140 160 (TA -T) (°C) 180 200 220 Figure 5.14: Behavior of In b values versus supercooling for the HSLA-V steel with 36 um initial austenite grain size and n=0.9. Chapters CCT RES UTS 125 Temperature (°C) Figure 5.15: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the DQSK steel having a 38 um initial austenite grain size. Chapter 5 CCT RESUTS 126 640 660 680 700 720 740 760 780 800 820 Temperature (°C) Figure 5.16: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the DQSK steel having a 38 um initial austenite grain size. Chapter 5 CCT RESUTS Chapter 5 CCT RESUTS E28 Temperature (°C) Figure 5.18: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 136 urn austenite in the DQSK. steel using the grain size-modified Avrami model predictions. Chapters CCT RESUTS 129 Temperature (°C) Figure 5.19: Comparison of the experimental results with the predictions obtained using the grain size-modified Avrami equation for the DQSK steel having a 38 um initial austenite grain size and m=2. Chapters CCT RESUTS 130 600 640 680 720 760 800 840 Temperature (°C) Figure 5.20: Comparison of the y decomposition kinetics obtained for the four candidate steels, each having a similar austenite grain size (38 um DQSK, 46 um A36, 36 um HSLA-V and 44 um HSLA-Nb) and the same cooling conditions, 1 °C/s. Chapter 5 CCT RESUTS 131 c £ 13 E e H 1.0 0.8 J 0.6 0.4 -0.2 0.0 ' A ™ o o • o< • A . A A * A A A A A . m m • A A A A o DQSK, 1 °G/s (38 L i m ) A • DQSK, 87 °C/s A A A DQSK, 290 °C/s A * A • HSLA-V, 1 °C/s (36 L i m ) A A • HSLA-V, 68 °C/s A A A HSLA-V, 238 °C/s A A A • • g 1 1 • • n « s : o 9 580 620 660 700 740 780 Temperature (°C) 820 860 Figure 5.21: Comparison of the austenite decomposition kinetics for the DQSK and HSLA-V steels showing the effect of cooling rate for similar initial austenite grain sizes of 38 um for the DQSK and 36 um for the : HSLA-V. Chapter 5 CCT RESUTS 132 Figure 5.22: Microstructures obtained after CCT tests for; (a) DQSK steel having 38 urn austenite grain size and subjected to 290 °C/s cooling rate: (b) HSLA-V steel having 36 um austenite grain size and subjected to 238 °C/s cooling rate, and industrial processed coil samples; (c) DQSK and (d) HSLA-V steels. Chapters CCT RESUTS 133 730 740 750 760 770 780 790 800 810 820 Transformation start temperature (°C) Figure 5.23: Comparison of the experimental ferrite grain size and predictions based on Eq. (5.13) for the HSLA-Nb steel as a function of the transformation start temperature. CHAPTER 6 R E T A I N E D S T R A I N R E S U L T S 6.1 DOUBLE HIT COMPRESSION TESTS Double hit compression tests provide appropriate information about the relationship between flow stress and softening kinetics of steels at high temperature. In this technique, by the application of two sequential deformations and a delay time between the deformations, the temperature and interpass times obtained during two passes of hot strip rolling can be simulated. The degree of softening associated with the interpass time can be related to the softening processes occurring between the two deformations i.e., between the rolling stands. In this study, however, the attention was directed towards determining the conditions for obtaining retained strain in the last stands of a finishing mill and the usage of these conditions to determine the effect of retained strain on the phase transformation kinetics and resulting microstructure. To introduce retained strain, a deformation temperature between T n r and Ae3 is needed. Double hit compression tests were conducted on the Gleeble 1500 thermomechanical simulator at 900, 850, 900 and 880 °C for the DQSK, A36, HSLA-V and HSLA-Nb steels, respectively. These temperatures are approximately 20 °C above 134 Chapter 6 RETAINED STRAIN RESULTS 135 the corresponding Ae3 temperatures and are comparable to the temperatures of the last one or two stands of the finishing mill where the maximum retained strain can be accumulated prior to the austenite decomposition on the run-out table. As mentioned in chapter 4, the specimens were initially heated up to 950 °C, soaked for 2 minutes to obtained a known austenite grain size, then air cooled to the desired deformation temperatures and kept for 3 minutes to homogenize the temperature throughout the specimens. Each specimen was then deformed to a strain of approximately 0.2, unloaded, held for the desired interpass time and reloaded to a total strain of about 0.5. Figure 6.1 shows the stress-strain curves obtained from double hit compression tests on the H S L A - V and HSLA-Nb steels which are more susceptible for introducing retained strain. The strain rate and interpass time for both tests were 0.1 s"1 and 10 seconds, respectively. For the H S L A - V steel, in the first pass, the yield stress and the maximum stress after about 0.25 strain are about 60 and 180 MPa, respectively. These values for the HSLA-Nb are approximately 90 and 210 MPa, respectively. During the interpass time, while the HSLA-V steel exhibits more than 70% softening, the HSLA-Nb grade shows about 20% softening which could be attributed to recovery. The higher work hardening during straining and lower softening kinetics during unloading in the HSLA-Nb steel has been attributed to the presence of niobium carbonitrides. These precipitates pin the austenite grain boundaries yielding the recrystallization retardation during the unloading and the interhit time [148] However, in the H S L A - V steel, the V(C, N) precipitates are considered to form primarily in the ferrite so that static recrystallization in austenite is not affected [142]. Therefore, this chapter examines the Chapter 6 RETAINED STRAIN RESULTS 136 effect of retained strain on the phase transformation behaviour and the resulting microstructure of the HSLA-Nb steel. 6.2 EFFECT OF RETAINED STRAIN ON THE AUSTENITE DECOMPOSITION BEHAVIOUR FOR THE HSLA-Nb STEEL 6.2.1 Test Matrix Unlike the plain-carbon (A36 and DQSK) and the microalloyed HSLA-V steels, in the double hit tests, the deformation above Ae3 left the HSLA-Nb grade unrecrystallized for interpass time of 10 seconds. Thus, for this grades, it is necessary to examine the effect of the retained strain in addition to that of the austenite grain size and the cooling rate on the transformation behaviour. To isolate the effect of retained strain and cooling conditions on the austenite decomposition kinetics and resulting microstructure, two test series were conducted. In both series, deformation was carried out at 880 °C i.e., under no-recrystallization conditions in the austenite region. In the first series, different levels of deformation (0.2, 0.3, 0.4 and 0.6 strain) were employed to quantify the effect of retained strain on the austenite decomposition behaviour and the resulting microstructure, the cooling rate after deformation being constant at 1 °C/s. In the next series, the amount of applied strain was kept constant, at either 0.2 or 0.5, and for each deformation condition the cooling rate was varied up to approximately 150 °C/s to investigate the combined effect of deformation and accelerated cooling on the subsequent Chapter 6 RETAINED STRAIN RESUL TS 137 austenite decomposition kinetics and the resulting microstructure. The experimental conditions are summarized in Table 6.1. Table 6.1: The experimental conditions for quantification of the effect of retained strain on the austenite decomposition kinetics and resulting microstructure for the HSLA-Nb steel. Pre-strain Specimen strain cooling rate y grain size tests geometry (mm) (°C/s) (lim) series 1 8x6 0.2, 0.3, 0.4 0.6 1 18, 44, 84 series 2 6x4 0.2, 0.5 «20-150 18, 44, 84 6.2.2 Effect of Retained Strain During Controlled Cooling In the first test series, the effect of retained strain was simulated by deformation of the specimen at 880 °C followed by controlled cooling to room temperature at 1 °C/s. The continuous cooling austenite decomposition kinetics as a function of temperature for three initial austenite grain sizes of 18, 44 and 84 urn are illustrated in Fig. 6.2. Although the phase transformation kinetics for the smallest austenite grain size (18 um) is almost independent of the amount of retained strain (Fig. 6.2a), and the applied deformation marginally affected the austenite decomposition behaviour in the 44 um austenite grain (Fig. 6.2b), the deformation did significantly affect the austenite decomposition kinetics for the steel having an 84 um initial austenite grain size (Fig. 6.2c). Chapter 6 RETAINED STRAIN RESULTS 138 In the coarser grains, the Ar3 is enhanced by deformation and the transformation rate, which is proportional to the slope of the transformed fraction versus temperature curve (because the cooling rate is constant at 1 °C/s), is accelerated with retained strain. For example, for an 84 um austenite grain size deformed to 0.6 strain, the Ar3 is enhanced by approximately 50 °C compared with the strain free test, a result which is consistent with the literature [48, 138, 149] Further, the transformation rate is increased, as evidenced by the observation that the strain free test required 125 seconds to complete the y—»a phase transformation (5% to 95%), whereas, less than 110 seconds is required for the highly deformed (s=0.6) sample. Ouchi et al. [101] a nd Roberts et al. [124] suggested that the retained strain substantially increases the Ar3 temperature of the Nb-containing steels by removing Nb from solid solution by strain induced precipitation. They proposed that the Nb in solid solution actually lowers the A13, by segregating to the y/a grain boundaries which reduces the y/a interface mobility. After deformation in the austenitic region, the soluble Nb element is removed as Nb(C, N) precipitates leading to a higher transformation temperature. Their proposed theory however, can not explain the observed effect on the phase transformation kinetics of the different initial austenite grain sizes shown in Fig. 6.2. Firstly, the addition of Nb to the HSLA-Nb steel can not lower the transformation start temperature by about 50 °C, which can be seen in Fig. 6.2c. Secondly, the transformation temperature did not change after the application of deformation for the 18 um austenite grain size, as seen in Fig. 6.2a. Finally, Sun et al. [148] have shown that by keeping the specimen at the deformation temperature, 880 °C, the majority of the Nb is Chapter 6 RETAINED STRAIN RESULTS 139 already out of solid solution as Nb(C, N) precipitates on the austenite grain boundaries which prevent the boundary movement. Therefore, the degree of increase in the Ar3 of the HSLA-Nb steel shown in Fig. 6.2c can not be related to the strain induced precipitation. Mano et al. P^O] a j s o studied the effect of retained strain on CCT behaviour. They found that the retained strain shifted the CCT diagram to the left or shorter times. The degree of shifting of the diagram to the shorter time depends on the initial austenite grain size; it is more pronounced for a larger austenite grain size. Since the CCT diagram has a C-shape, this also increases the transformation temperature for a given cooling rate, consistent with the results obtained in the present work (Fig. 6.2c). However, in the smaller grain size, the effect of retained strain on the CCT diagram is limited; this implies that the effect of retained strain on the transformation temperature is insignificant consistent with the test results shown in Fig. 6.2a. The resulting microstructures obtained from the strain free and deformed (s=0.6) samples after controlled cooling at 1 °C/s for 18 and 84 jam initial austenite grain sizes are illustrated in Fig. 6.3. The micrographs of all the specimens contain a mixture of approximately 90% ferrite and 10% pearlite. Since the ferrite portion of the microstructure is the dominant phase, the ferrite grain size is the most important parameter for controlling the mechanical properties of the final product. As can be seen for the 18 um austenite grain sized samples (Fig. 6.3a and 6.3b), the ferrite grain size of both specimens is similar, being 13 um for the undeformed sample and 10 um for the 0.6 strained sample. The effect of retained strain on the ferrite grain refinement in the larger Chapter 6 RETAINED STRAIN RESULTS 140 austenite grain size (84 urn) material is clearly visible; the ferrite grain sizes in the strain free and 0.6 strained samples are approximately 23 um and 13 (am, respectively (Fig. 6.3c and 6.3d). This indicates that the effect of retained strain on the final microstructure is grain size-dependent and increases with increasing austenite grain size. The marked grain refinement in the deformed specimen is due to additional ferrite nucleation at the irregular pancaked austenite grain boundaries and at crystallographic defects (deformation bands and dislocations) in the grain interior. This grain refinement will improve both the yield strength and the toughness of the final product. Most of the literature on deformation enhanced ferrite grain refinement is based on fairly large initial austenite grain sizes which clearly show the effect of retained strain on the ferrite grain refinement [48, 78, 138, 151] consistent with the 84 um austenite results obtain in the current work. Limited research has been reported on the effect of retained strain in fine grain sized austenite [94, 117] As mentioned before, three phenomena are involved in ferrite grain refinement when deformation is employed; (1) pancaking the austenite grains by deformation increases the grain boundary surface area per unit volume of austenite, (2) deformation increases the irregularity of the grain boundaries and (3) deformation introduces crystallographic defects (dislocations, deformation bands) inside the austenite grains. Among these, the first factor (the increase in grain boundary surface area per unit volume) is similar for both large and small initial austenite grains. Since in the smaller initial austenite grain sized material the ferrite grain size in the highly deformed and strain free samples was almost the same (Fig. 6.3a and 6.3b), therefore, the increase of irregularity at the austenite grain boundaries and the Chapter 6 RETAINED STRAIN RESULTS 141 presence of the crystallographic defects inside the grains must be responsible for the extra ferrite nucleation and resulting ferrite grain refinement. The coarser austenite has been shown to develop visible deformation bands inside the grains [78, 151] w h i c h are preferred sites for ferrite nucleation. The reason for such a behaviour may be related to the interaction of dislocations generated during deformation in the no-recrystallization region. In the relatively large austenite grains, the distance between the generated dislocations and the grain boundaries is relatively large. This suggests that the chances of interaction and pileup of the dislocations inside the grains before reaching the grain boundary should be enhanced. The pileup of the dislocations increases the free energy of the system and can act as sites for nucleation of the ferrite by accommodating the parent/product misfit strain by the strain field of the dislocations, thereby decreasing the activation energy for the formation of a nucleus [152, 153] This decreases the required free energy change for the nucleation resulting in smaller undercooling and leading to a higher transformation temperature. The degree of increase in the nucleation rate depends on the type of dislocations [6]. In contrast, in the relatively small austenite grains, the distance between the dislocations generated inside the austenite grains and the grain boundaries is relatively small. It is thus easier for the crystallographic defects to move to the grain boundaries, reducing the potential for formation of deformation bands. Therefore, the number of sites for the nucleation of the ferrite is less influenced by the retained strain in the small austenite grained material. Chapter 6 RETAINED STRAIN RESULTS 142 6.2.3 Effect of Combined Retained Strain and Accelerated Cooling on The Phase Transformation Behaviour and The Resulting Microstructure Quantification of the effect of retained strain on the CCT behaviour and the resulting microstructure for the HSLA-Nb steel is important for characterizing microstructure evolution during hot strip mill processing of these steels. To permit deformation and reduce thermal gradients in the sample during accelerated cooling, smaller compression specimens, 6 mm in length and 4 mm in diameter, were employed. The smaller sized samples reduced the sensitivity of the dilation measuring equipment. However, by carefully controlling the experimental conditions, it was possible to quantify the phase transformation kinetics and characterize the resulting microstructure. The effect of cooling rate on the austenite decomposition kinetics obtained for the HSLA-Nb steel having 18 and 84 um austenite grain sizes deformed to 0.2 and 0.5 strain is illustrated in Figs. 6.4 and 6.5, respectively. These results further confirm that the transformation is shifted to lower temperatures with increasing cooling rate. In the 18 um austenite grain size material, the transformation start temperatures for retained strain of 0.2 and 0.5 show a significant decrease with increasing cooling rate (Fig. 6.4). The transformation start temperature for both 0.2 and 0.5 strained samples for a cooling rate equivalent to air cooling («20 °C/s) is approximately 800 °C. In other words, there is no significant effect of retained strain on the austenite decomposition kinetics for the 18 um initial austenite grain size. Chapter 6 RETAINED STRAIN RESULTS 143 Figure 6.5 shows that for the 84 um initial austenite grain sized material subjected to the same cooling conditions (»20 °C/s), the transformation start temperature for the 0.5 strained specimen is about 780 °C, 30 °C higher than the 750 °C obtained for the 0.2 strained one. The results also confirms that in accelerated cooling conditions the austenite decomposition kinetics are influenced by retained strain. It should be noted that as for the 18 jam deformed material (Fig. 6.4), the transformation temperature of the 84 um strained material (Fig. 6.5) is a strong function of cooling rate; the transformation temperature decreases with increasing cooling rate. In other words, under deformation condition, the accelerated cooling can still have a significant effect on the transformation temperature. The strain free and pre-strained austenite decomposition kinetics for the 18 and 84 um specimens for two different cooling rates are shown in Fig. 6.6. Figure 6.6a for the 18 um initial austenite, cooled at 100 °C/s, shows that straining the specimen has very little effect on the transformation temperature, consistent with controlled cooled (1 °C/s) CCT test results reported in Fig. 6.2a. For the larger 84 um austenite samples cooled at 20 °C/s, the retained strain is more effective in raising the transformation temperature, consistent with the results presented in Fig. 6.2c. Thus, in the industrial processes where the initial austenite grain sizes are relatively large and the cooling rates are relatively slow, the effect of retained strain on the phase transformation behaviour should also be considered. The microstructure obtained in the CCT tests with retained strain simulating the controlled rolling for the HSLA-Nb steel on a hot strip mill and the microstructure of an industrially processed HSLA-Nb coil sample are illustrated in Fig. 6.7. Both Chapter 6 RETAINED STRAIN RESULTS 144 microstructures contain fine polygonal ferrite close to 5 um. However, the coil sample does show smaller ferrite grain size with localized elongated ferrite grains in the rolling direction. Thus, an appropriate laboratory simulation of the controlled rolling process using appropriate initial austenite grain size, retained strain and accelerated cooling can produce a similar ferrite grain size as that obtained in the industrial coil sample. To further verify the compression test results and investigate the effect of higher levels of retained strain (up to a strain of 1) on the austenite decomposition, a number of single hit torsion tests were also conducted. As describe in chapter 4, the pre-heat conditions before the application of torsional deformation produced an austenite grain size of 18 um (heating to 950 °C at 5 °C/s and holding for 2 minutes) prior to air cooling to the 880 °C deformation temperature. Following torsion deformation at 880 °C, the samples were cooled to room temperature by air cooling («20 °C/s) and by helium quenching up to approximately 150 °C/s. No effect of retained strain on the transformation start temperature, as revealed by thermal recalescence, was apparent, consistent with the Gleeble testing results for the 18 (am austenite grain size. The ferrite grain size obtained in the deformed torsion samples also showed little effect of applied strain on the ferrite grain refinement. Under cooling conditions comparable to that obtained on the run-out table (cp«100 °C/s), a small ferrite grain size of approximately 4 pm was obtained in the helium quenched strain free and deformed torsion specimens with initial austenite grain size of 18 pm. This was consistent with the resulting microstructure obtained in the compression samples. This supports the Gleeble compression test results indicating little effect of retained strain on the resulting microstructure for the small, 18 pm, initial austenite grain size. Chapter 6 RETAINED STRAIN RESULTS 145 In addition to ferrite grain refinement, the other important effect of retained strain, particularly for the relatively larger austenite grain sized material, is that it encourages the formation of an equilibrium microstructure. The ferrite fraction (combined polygonal and non-polygonal, Widmanstatten or acicular) as a function of cooling rate for 0, 0.2 and 0.5 strain in the 84 um initial austenite grain size material is shown in Fig. 6.8. It is quite clear that increasing the cooling rate reduces the formation of the ferrite phase. Whereas, the retained strain pushes the transformation to higher temperatures and encourages the formation of polygonal ferrite. The effect of austenite grain size and cooling rate on the transition from polygonal to non-polygonal structures for strain free and 0.5 strain is illustrated in Fig. 6.9. As can be seen, this boundary shifts to higher cooling rates and larger austenite grain sizes as retained strain is applied; the retained strain stabilizes the polygonal structure. Therefore, under industrial accelerated cooling conditions on the run-out table, the fraction of polygonal ferrite microstructure increases with increasing retained strain; in other words, the critical cooling rate for maintaining polygonal ferrite morphology is increased with retained strain. It should be noted that for each grain size of austenite there is a saturation level of retained strain beyond which the ferrite fraction approaches a steady state condition. Chapter 6 RETAINED STRAIN RESULTS 146 6.3 EMPIRICAL MODELLING OF AUSTENITE-TO-FERRITE TRANSFORMATION KINETICS 6.3.1 Transformation Start Temperature The transformation start temperature, AIT,, is the first parameter which should be quantified to model the transformation kinetics. The Ar3 temperature corresponding to 5% transformation is plotted in Fig. 6.10 as a function of cooling rate for different initial austenite grain sizes and levels of retained strains for the HSLA-Nb steel. It is clear that enlargement of the initial austenite grain size, combined with accelerated cooling, lowers the Ar3, whereas the retained strain enhances the Ar3 for the coarse austenite grains. It is evident that the effect of retained strain on the phase transformation behaviour is a austenite grain size-dependent parameter and is more effective for the larger austenite grain sized material. Thus, the empirical model should therefore include the three parameters, cooling rate, initial austenite grain size and retained strain and reflect the interaction among them. As described above, two series of deformation tests were performed to verify the effect of retained strain on the transformation behaviour. In the first series, all experiments were carried out under controlled cooling at 1 °C/s cooling rate. Although this condition is not relevant to the cooling rates experienced during accelerated cooling on the run-out table of the hot strip mill, it is relevant to the cooling in a plate mill. Based on controlled cooling experimental results, an appropriate mathematical algorithm was Chapter 6 RETAINED STRAIN RESULTS 147 developed to describe the Ar3 temperature as a function of austenite grain size and retained strain as follows: TAli =T0,05(°K) = TAe3 + 1 1.5xlO~V, -0.021 - + (0.0058f)J 2.2 (6.1) where dy is the initial austenite grain size in pm and s is the retained strain. Good agreement between experimental data and predictions from Eq. (6.1) is obtained, as shown in Fig. 6.11, where the cooling rate is 1 °C/s and the initial austenite grain size and retained strain are varied between 18-84 pm and 0-0.6, respectively. The trend of the transformation start temperature as a function of cooling rate for different levels of applied strain is clear. Similar to the controlled cooling at 1 °C/s, the application of deformation has almost no effect on the Ar3 for the smaller austenite grain sized material [ 1 6 3 ] A maximum increase in the Ar3 for the larger austenite grain sized material is seen (Fig. 6.10). While the smaller austenite grain size shows the same behaviour at accelerated cooling conditions as that for the slower controlled cooled (q>=l °C/s) conditions, the increase in the Ar3 of the larger grain size is reduced as the cooling rate increases. In other words, the effect of retained strain on the Ar3 for the accelerated cooling conditions is negligible. To provide an appropriate model to describe the Ar3 as a function of cooling rate and retained strain, more data would have been required in the transition range for the larger austenite grain sizes. The transition range is the cooling Chapter 6 RETAINED STRAIN RESULTS 148 rate between 1 °C/s and air cooling where the effect of retained strain on the Ar3 for the relatively large austenite grains is reduced dramatically. 6.3.2 Ferrite Growth Kinetics In order to predict the austenite-to-ferrite transformation kinetics for 1 °C/s controlled cooling an empirical model was developed. As a first approximation, it was assumed that the Avrami equation, X = \- exp(-bt") , utilizing the additivity principle could describe the austenite-to-ferrite transformation kinetics with the time exponent, n, assumed to be constant. It was found that the value of 2.1 gives the best fit for the time exponent, n. This value for the time exponent is different from that obtained for the accelerated cooling CCT tests. The solute drag-like effect of Mn which is more effective for the slow cooling rate (1 °C/s), might be the reason for the difference of the time exponents. Using n=2.1, the parameter b was described as a function of supercooling, TAe3"T the initial austenite grain size in jam, dy, and retained strain, s, as follows: In b = 0.0008(7^ - T) - 0.015 In dy + A e - 4.3 where A is an austenite grain size-dependent parameter as follows: A = 0.0008^ + 0.0034 Chapter 6 RETAINED STRAIN RESULTS 149 The experimental results and predictions based on Eq. (6.2) are plotted in Fig. 6.12 and show good agreement. For the accelerated cooling conditions, air cooling at 20 °C/s and higher cooling rates, the grain size-modified Avrami equation was also used to describe the phase transformation kinetics. To be consistent with the analysis of the strain free continuous cooling tests on the HSLA-Nb grade with different initial austenite grain sizes, the time exponent n was kept constant at 0.9. Using this approach, two alternative empirical equations are proposed to describe the parameter b. In the first, the parameter b was described as a function of supercooling, initial austenite grain size in pm and retained strain as following: ln6 = 0.015(7^ - T)- f i l i n g +As+ 1.18 ( 6 3 ) where A = 0.0\5dr -0.23 The retained strain term, A , of the equation is a grain size-dependent parameter, as it was in Eq. (6.2), and its effect being more pronounced as the austenite grain size increases. It should be noted that cooling rates of «20-150 °C/s, s=0-0.5 and dy=18-84 pm were used as the boundary conditions for developing Eq. (6.3). The experimental data versus Eq. (6.3) model predictions are shown in Fig. 6.13. The agreement between experimental data and the predictions is quite reasonable. Chapter 6 RETAINED STRAIN RESULTS 150 The second method to model the CCT tests including retained strain is also based on a grain size-modified Avrami equation. In this model, the parameter b was described as a function of supercooling and an effective austenite grain size. The concept of an effective grain size, or effective interfacial area, has also been used by other researchers [101, 120, 154] Employing two parameters from the strain free CCT tests (Table 5.5), the initial austenite grain size is now assumed to be an effective grain size for the tests with retained strain. The following relations have been obtained to describe the parameter b and the effective austenite grain size in um, which is a function of retained strain: ln& = 1.80+ 0.030(7^ -7) -1 .9Ind , effective (6.4) where Ind. effective (l-Ae))ndr and A = 0.006dy +0.010 The experimental data and predictions based on Eq. (6.4) are illustrated in Fig. 6.14; they are in reasonable agreement. Thus, both alternative models can explain the phase transformation kinetics when retained strain is involved. Chapter 6 RETAINED STRAIN RESULTS -6.3.3 Modelling of Final Microstructure 151 The microstructure in the coil of the HSLA-Nb steel resulting from industrial processing combines approximately 95% polygonal ferrite and the rest pearlite (Fig. 6.7b). Since the pearlite colonies are widely separated, the ferrite grain size is the most important microstructural parameter affecting the mechanical properties, particularly the yield strength. The ferrite grain size as a function of cooling rate for different levels of retained strain and different initial austenite grain sizes is shown in Fig. 6.15. Limited data is available, particularly for the larger initial grain sizes, simply because the accelerated cooling increases the supercooling, encouraging the formation of non-polygonal microstructures. However, straining the specimen prior to transformation (retained strain) encourages the formation of polygonal ferrite. This is clear in Fig. 6.15c where it was possible to quantify the polygonal ferrite grain size at higher cooling rates in the heavily deformed sample. As can be seen in Fig. 6.15, increasing the initial austenite grain size results in a larger ferrite grain size. For a given austenite grain size of the deformed and strain free materials, the ferrite grain size decreases as the cooling rate increases. However, for both deformed and undeformed samples, the ferrite grain size approaches a steady state conditions at higher cooling rates. In other words, the application of deformation under accelerated cooling is less effective. For example, under controlled cooling conditions at l°C/s, for the 18 pm austenite grain size, the retained strain of 0.5 reduces the ferrite grain size by about 3 pm. This reduction for 44 pm austenite is about 10 pm and for 84 pm austenite is about 15 pm. However, for higher cooling rates, e.g., for a cooling rate of Chapter 6 RETAINED STRAIN RESULTS — 152 20 °C/s, the 18 um austenite grain size with 0.5 strain results in a ferrite grain size reduction of about 3 urn and for the 44 jam austenite of only about 4 um. Based on the literature, several algorithms were adopted to describe the relationship between ferrite grain size, initial austenite grain size, retained strain and cooling rate t^7, 118, 119, 155] n W as found that a modification of the mathematical form given by Gibbs et al. [87, 155] j s ^ appropriate model to relate the ferrite and initial austenite grain size, incorporating the previously described processing parameters as: da = (l - 0.8^°8) - 1.2 - 11.9^-° 3 + 16.3{l - exp(- 0.015^) (6.5) where cp is the cooling rate in °C/s and dy is the austenite grain size in um. The experimental data versus ferrite grain size predictions based on Eq. (6.5) is shown in Fig. 6.16. As can be seen, there is a reasonable agreement between experimental data and model predictions. Chapter 6 RETAINED STRAIN RESUL TS 153 (a) 350 ^ 250 cs Pu §, 2 0 0 1 150 5 100 50 0 0.0 Figure 6.1: 0.1 0.2 0.3 Strain HSLA-V dy=36 pim Tdef=900 °C ds/dt=0.1s 1 0.6 (b) HSLA-Nb 1 d =18 [im - Tdef=880 °C i i ds/dt=0.1s"' 0.4 0.5 Double hit compression test for an interpass time of 10 seconds for the; (a) HSLA-V steel at 900 °C having a 36 pm initial austenite grain size and for the (b) HSLA-Nb steel at 880 °C having an 18 pm initial austenite grain size (ds/dt=0.1 s"'). Chapter 6 RETAINED STRAIN RESULTS 154 1.0 -I 0.8 -0.6 -0.4 - o 0.2 - • A 0.0 --aTA" d = 18 f i m o 600 o • A r O - & -600 640 680 720 760 Temperature (°C) 800 1.0 -j 0.8 -0.6 -0.4 -o 0.2 - • A 0.0 -O A d.=44 j i m 640 680 720 Temperature (°C) 1.0 -i U O ° o 0 U ° o 0.8 -d =84 j_im 0.6 -0.4 -o 0.0 strain 0.2 - • 0.3 strain A 0.6 strain 0.0 -o • o • . A O • O • O • • A o • o • o • o o (a) 840 (b) 840-(c) • A • • A O n o Ha A _ 600 640 680 720 760 Temperature (°C) 800 840 Figure 6.2: Austenite decomposition kinetics for the HSLA-Nb steel control cooled at 1 °C/s cooling rate after 0, 0.3 and 0.6 applied strain for; (a) 18, (b) 44 and (c) 84 urn initial austenite grain sizes. Chapter 6 RETAINED STRAIN RESUL TS 155 Figure 6.3: Microstructure of controlled cooled ((p=l °C/s) compression specimens of HSLA-Nb steel after deformation at 880 °C; (a) dy=18 pm and s=0, (b) dy=18 pm £=0.6, (c), dy=84 pm and s=0 and (d) dy=84 pm e=0.6. Chapter 6 RETAINED STRAIN RESUL TS 156 1.0 o.8 ^ 0.6 0.4 0.2 0.0 0.8 H 0.6 0.4 0.2 0.0 A • • U?) A O A • O (a) A O A • A • A • o 0 O A • O d.=18 fim 8=0.2 o 20 °C/s • 103 °C/s A 170 °C/s • o A • • O o A • A • A A D o o o -Or 1 1 1 i 620 640 660 680 700 720 740 760 780 800 820 Temperature (°C) 1.0 -fs—-o- • o o A - • A • A • A • A • A • O O O (b) O O A o A • d=lS (j,m s=0.5 O 17°C/s • 101 °C/s A 152 °C/s O A • o A • A • A A A A • • • • • O O o o. O - o o-1 1 1 1 r 620 640 660 680 700 720 740 760 780 800 820 Temperature (°C) Figure 6.4: Effect of cooling rate on the austenite decomposition kinetics obtained from the HSLA-Nb steel with an 18 um austenite grain size and with; (a) 0.2 and (b) 0.5 retained strain. Chapter 6 RETAINED STRAIN RESULTS 157 -a s C C5 U H 1.0 0.8 0.6 0.4 0.2 0.0 • Cr A • A • A O O o A • o o A • o A • d =84 urn Y A n o o o 8=0.2 O 21 °C/s • 96 °C/s A 165 °C/s A • A • O • O • o A • O A • O A • O . A a 500 550 = H 1.0 0.8 0.6 0.4 0.2 0.0 i 1—— i — 600 650 700 Temperature (°C) o A • O A • O O A O • • o A O A • d =84 um A • o Y 8=0.5 o 22 °C/s • 87 °C/s A 108 °C/s • o A • O • A • O A • A • O (a) 750 800 (b) A • O A • O A A • M O A , • , i 500 550 600 650 700 Temperature (°C) 750 800 Figure 6.5: Effect of cooling rate on the austenite decomposition kinetics obtained from the HSLA-Nb steel with an 84 pm austenite grain size and with; (a) 0.2 and (b) 0.5 retained strain. Chapter 6 RETAINED STRAIN RESUL TS 158 1.0 0.8 0.6 0.4 0.2 0.0 o (a) • O • ^ • c d = 18 jim O 0.0 strain • 0.2 strain A 0.5 strain • % O 0 • • • • o A _ 1.0 0.8 0.6 0.4 0.2 0.0 580 600 620 640 660 680 700 720 740 760 Temperature (°C) A . O ° A (b) A d.=84 (im o n A o o • o • °o • o • o o o A • • • o • O 0.0 strain • 0.2 strain A 0.5 strain O O o o o A A • A • A • A CL -A-1—•—i i i i i r~ 560 580 600 620 640 660 680 700 720 740 760 780 800 Temperature (°C) Figure 6.6: Effect of retained strain and cooling rate on the austenite decomposition kinetics obtained for the HSLA-Nb steel; (a) 18 um austenite cooled at ^100 °C/s and (b) 84 um austenite cooled at ~20 °C/s. Chapter 6 RETAINED STRAIN RESUL TS 159 Figure 6.7: Comparison of the microstructure of HSLA-Nb steels obtained in laboratory test with that of a industrially processed hot rolled coil; (a) continuous cooling test (dv=18 pm, retained s=0.5, (p^lOO °C/s) and (b) industrial processed coil sample. Chapter 6 RETAINED STRAIN RESUL TS 160 100 8=0 0 50 100 150 200 250 Cooling rate (°C/s) Figure 6.8: The effect of retained strain and cooling rate on the ferrite fraction produced during the decomposition of 84 um austenite. Chapter 6 RETAINED STRAIN RESUL TS 161 tt 0 o 0> 100 v 5 70 u Of) a o o 'at o 50 U 30 30 40 50 60 70 Austenite grain size ( j a m ) 80 90 Figure 6.9: The effect of retained strain on the austenite grain size dependence of the critical cooling rate for polygonal or non-polygonal ferrite formation. Chapter 6 RETAINED STRAIN RESUL TS 162 820 U o 4> U 3 03 U a E U < 780 740 700 660 620 0 dy=l 8 jum, 8=0 dy=18|am, s=0.5 dy=84 jum, 8=0 dv=84 |am, 8=0.5 40 80 120 Cooling rate (°C/s) 160 200 Figure 6.10: Effect of austenite grain size, cooling rate and retained strain on the transformation start temperature, Ar3, (taken at the temperature of 5% transformation) for the HSLA-Nb steel with an 18 or 84 pm austenite grain size. Chapter 6 RETAINED STRAIN RESUL TS 163 840 820 U o <u u 1 800 u <u D M E cu H 780 760 0/ -o / 0/ o Experimental data Predictions 760 Figure 6.11: 780 800 820 Temperature (°C) 840 Comparison of the experimental T005, Ar3 temperature for the HSLA-Nb steel versus equation (6.1) predictions for retained strain up to 0.6, austenite grain sizes varying between 18 and 84 um and a cooling rate of 1 °C/s. Chapter 6 RETAINED STRAIN RESUL TS 164 Temperature (°C) Figure 6.12: Comparison of the experimental ferrite transformation kinetics for three different levels of applied strain (0, 0.3 and 0.6) with equation (6.2) predictions for the HSLA-Nb steel having an austenite grain size of 84 pm cooled at 1 °C/s. Chapter 6 RETAINED STRAIN RESUL TS 165 580 620 660 700 740 780 820 Temperature (°C) Figure 6.13: Comparison of the HSLA-Nb experimental ferrite transformation kinetics for different initial austenite grain sizes, cooling rates and levels of retained strain with model predictions based on equation (6.3). Chapter 6 RETAINED STRAIN RESUL TS 166 580 620 660 700 740 780 820 Temperature (°C) Figure 6.14: Comparison of the HSLA-Nb experimental ferrite transformation kinetics for different initial austenite grain sizes, cooling rates and levels of retained strain with model predictions based on equation (6.4). Chapter 6 RETAINED STRAIN RESUL TS 15 767 20 40 60 80 100 120 140 Cooling rate (°C/s) 180 200 £ zL cj *(*> a "« im WD CJ tm CJ 10 15 20 Cooling rate (°C/s) 30 3 25 a> .H 20 ? 10 i- 5 cj d ==84 | i m -O- 8=0 -•— s=0.2 1 f A _ _ _ _ 8=0.5 1 1 A 1 l|°C/s 25 30 0 5 10 15 20 Cooling rate (°C/s) Figure 6.15: Ferrite grain size as a function of cooling rate for different levels of applied strain and; (a) 18, (b) 44 and (b) 84 pm initial austenite grain sizes. Chapter 6 RETAINED STRAINRESUL TS 0 0 20 40 60 80 100 120 140 160 Cooling rate (°C/s) Figure 6.16: A comparison of experimental data and Eq. (6.5) predictions, showing the effect of cooling rate on the ferrite grain size for different austenite grain sizes of 18 urn, 44 um and 84 um (e=0.5). CHAPTER 7 C A R B O N D I F F U S I O N R E S U L T S 7.1 CARBON DIFFUSION MODEL Ferrite nucleates at the austenite grain boundaries and metallographic observation confirmed that approximately 5% of the ferrite can satisfy the site saturation condition [47, 138] i f s i t e saturation occurs early in the transformation, the subsequent phase transformation kinetics are solely characterized by ferrite growth until the final ferrite fraction is attained and pearlite forms in the remaining austenite. A fundamental model for isothermal decomposition of austenite to ferrite based on carbon diffusion was developed by Kamat P^ , 156]- [\ u a s b e e n modified by Militzer et al. 51, 157] f 0 include SDLE and continuous cooling conditions. The model is focused on low carbon steels having a polygonal (equiaxed) ferrite morphology. In isothermal conditions, once the temperature of a hypo-eutectoid steel is below the Ae3 temperature (Fig. 7.1), ferrite will nucleate and grow at the austenite grain boundaries. Since the equilibrium carbon content of the ferrite, Ca\, is much lower than that of the parent phase, C Q , the excess carbon is rejected into the remaining austenite. 169 Chapter 7 CARBON DIFFUSION RESULTS 170 Local equilibrium is assumed at the austenite/ferrite interface. Carbon diffusion in the remaining austenite is considered to be the primary factor controlling the rate of austenite decomposition. The carbon redistribution in the austenite is a long-range diffusion controlled phenomenon. As a result, a non-uniform carbon distribution is obtained throughout the austenite matrix with the highest level of carbon at the a/y interface. As can be seen in Fig. 7.1, at Ti, the ferrite growth stops when the remaining austenite reaches the equilibrium composition, C y i . The equilibrium carbon content of the produced ferrite, C a , and the remaining austenite, Cy, are strongly temperature dependent (Fig. 7.1). For a constant temperature, the carbon gradient at the a/y interface is initially steep and becomes shallower with increasing time. The instantaneous ferrite growth rate depends on the carbon diffusion flux in the austenite phase as follows [158]: where Drc is the carbon diffusion coefficient in the austenite, which is temperature-composition dependent, and cC I dx. is the carbon gradient in the austenite at the a/y interface ahead of the growing ferrite. The carbon diffusion coefficient, D[., in austenite has been quantified by Agren [159]; DYC = 4.53 x 10 7 1+-C M C M \-C M 1-C M J 8339.9 T expi- -2.2x 10" 17767 -V ^ - 2 6 4 3 6 ^ -CM j (7.2) Chapter 7 CARBON DIFFUSION RESULTS 171 where T is temperature in °K and Cjyj is carbon content in mole fraction. As the ferrite fraction increases with time, the gradient and therefore the flux decrease at a given temperature. To obtain the same ferrite thickness at two different temperatures (e.g., Ti and T 2 in Fig. 7.1), different holding times are required; the associated carbon gradient ahead of the ferrite being different for each temperature, as is the carbon diffusion coefficient, Drc . The shaded areas at each temperature in Figure 7.1 result from the carbon mass balance in which the carbon rejected from the ferrite equals that enriched in the austenite. Modelling the austenite-to-ferrite transformation involves stereological complications related to the geometry (i.e. grain size and grain size distribution) and the special arrangement of the grains in three dimensional space. The austenite grains must be space filling with a minimum surface area per unit volume. The optimum space-filling shape with a minimum of surface area is the tetrakaidecahedron which is a polyhedron with 14 faces. The surface tension requirements are fulfilled with three grains meeting at an edge and four edges meeting at a corner. To simplify the diffusion problem, Kamat [12] has adopted the geometry of grains having a boundary which is either planar or spherical, as he assumed that the growth rate of a tetrakaidecahedron would be between these two geometries. Since he found a much better agreement between the experimental results and the spherical model predictions, in this work, the model with spherical geometry has been chosen. The average volumetric austenite grain size was adopted to represent the diameter of the spheres. Chapter 7 CARBON DIFFUSION RESULTS 172 7.1.1 Model Assumptions Kamat [156] m ade the following assumptions to develop the original model: 1) For a given temperature, the equilibrium carbon contents of the y and a phases at the phase interface, Cy and C a , are dictated by the iron-carbon phase diagram and are attained instantaneously. 2) The variation of carbon concentration within the ferrite phase has been considered negligible (because of Dyc « D"), the composition being represented by c a . 3) Zero mass transfer has been assumed at the center of the sphere (grain). 4) Nucleation has been neglected by assuming that early site saturation occurs and the ferrite grain grows into the grain interior as a spherical shell. 5) The densities of both phases, a and y, are assumed to be equal, independent of the temperature and carbon concentration. To predict the ferrite growth kinetics under the industrial cooling conditions, the model has been modified by Militzer et al. p i , 51, 157] a n ( j extended to include non-isothermal conditions. The modified model incorporates the changing equilibrium concentration of ferrite and austenite at the phase boundary due to the temperature change and the temperature- and concentration-dependence of the carbon diffusion coefficient in austenite [10, 160] As mentioned above, for a given temperature, a constant value of the carbon content in the ferrite has been used, as dictated by the Fe-C-X equilibrium diagram [77]. Chapter 7 CARBON DIFFUSION RESULTS 173 Since ferrite grows radially inwards from the surface toward the center of the sphere, the model constitutes radial diffusion in a sphere coupled with the moving a/y interface (Fig. 7.2). The diffusion equation for spherical geometry is: where C is the carbon content in the austenite, r is the radial distance and t is the time. As an initial condition, a homogeneous carbon concentration, C Q , is assumed in the austenite. As the ferrite grows, the carbon content in austenite builds up. The growth of ferrite results in soft impingement i.e., overlapping diffusion field at the center of the spherical grain. The model takes into account this soft impingement effect by treating the center of the spherical austenite grain as a point of zero mass transfer at which the carbon content builds up as ferrite grows [ 156] The relevant initial and boundary conditions are shown in Fig. 7.3. The details of the model formulation, including the finite-difference numerical techniques utilized, are given elsewhere [156] (7.3) 7.2 MODEL PREDICTIONS 7.2.1 Continuous Cooling Conditions Kamat's model predictions gave reasonable agreement with isothermal transformation kinetics in 1010 and 1020 steels [12]. In this work, the model was applied Chapter 7 CARBON DIFFUSION RESULTS 174 to describe continuous cooling conditions by subdividing the cooling path into appropriate isothermal steps. It was found that for lower cooling rates or higher transformation start temperatures, much more rapid growth rates are predicted compare to the experimental results. For example, for the A36 steel, longer experimental growth times are observed at the higher transformation temperatures, as illustrated in Fig. 7.4. However, at lower transformation temperatures, i.e., for increasing supercooling, the agreement between the experimental results and the carbon diffusion controlled model predictions improves. For plain-carbon steel, the magnitude of the difference between the predicted and the experimental results suggests an intermediate growth regime between Mn-diffusion control at higher temperatures and C-diffusion at lower temperatures. This suggests a growth rate between orthoequilibriumt^l] and C-diffusion control at lower temperatures - paraequilibrium growth. This is in agreement with earlier findings that Mn slows the transformation rate down, presumably by solute drag [20, 162] T h u S j present approach incorporates the substitutional Mn solute drag-like effect (SDLE) into the carbon diffusion model. The solute drag-like effect of Mn is included by selecting the appropriate local equilibrium condition for carbon at the a/y interface, accounting for the higher interfacial Mn concentration. The steady state segregation factor is given by P l ] : ss = e\p(E(T)/RT) (7.4) Chapter 7 CARBON DIFFUSION RESULTS 175 where E(T) is the effective segregation energy; this temperature-dependent energy accounts for an increasing amount of Mn being able to follow the interface movement with increasing temperature. Solute drag can effectively be taken into account in the C-diffusion model by assuming solute segregation to the a/y interface with a segregation energy, E, which decreases as undercooling increases: E = E,-E,(TA^-T), E>0 where EQ and E^ were determined from fitting the diffusion model with the experimental findings. In this way, the gradual transition to C-diffusion controlled ferrite growth is accommodated with increased undercooling. Therefore, for accelerated cooling with high undercooling, the solute-drag factor approaches zero; i.e., the transformation kinetics will be carbon diffusion controlled. In plain-carbon steels, under solute drag conditions, a steady-state Mn enrichment is formed at the moving interface. Assuming local equilibrium, the higher interfacial Mn concentration reduces the interfacial C concentration, as illustrated in Fig. 7.5. This may result in a decreasing gradient for C diffusion and hence a reduced growth rate. The same approach was adopted for the HSLA steels, to incorporate the SDLE factor in the C-diffusion model. The solute segregation parameters are considered to be independent of cooling rate and y grain size, but depend on the steel chemistry, as indicated in Table 7.1 for the steels included in this study. Chapter 7 CARBON DIFFUSION RESULTS 176 Table 7.1: Parameters EQ, E\ of Eq. (7.5). Grade E 0 E l DQSK 0.22 0.0010 A36 0.22 0.0012 H S L A - V 0.15 0.0010 HSLA-Nb 0.21 0.0010 Figures 7.6, 7.7, 7.8 and 7.9 illustrate comparisons of the experimental austenite decomposition kinetics and the model predictions for the austenite-to-ferrite transformation as a function of temperature for different cooling rates and relatively small austenite grain sizes for the DQSK, A36, H S L A - V and HSLA-Nb steels, respectively. The results show that the modified carbon diffusion model, incorporating SDLE, can adequately predict the austenite-to-ferrite portion of the phase transformation kinetics («80-95% of austenite decomposition, depending on the grade) in all four candidate steels. In the A36 steel with lower cooling rates (Fig. 7.7), the model appears to under predict the transformation rate. This could be attributed to the onset of soft impingement, when the rate of interface movement decreases, enabling more Mn to desegregate and thereby reducing its solute drag-like effect [21]. Later on, the C enrichment in the remaining austenite is high enough for the formation of pearlite. The results indicate that for the low cooling rate (1 °C/s), where the transformation takes place at comparatively high temperatures, the reduction of the solute drag force in the later stages of ferrite Chapter 7 CARBON DIFFUSION RESULTS 177 growth is significant. For higher cooling rates, which are typical of the run-out table in the finishing mill, the solute drag-like effect is rather small because of the high undercooling and a more accurate description of the reduced solute drag-like effect in the final stage of ferrite growth is less important (Fig. 7.4). In fact, the original carbon diffusion model gives a fairly accurate description of ferrite growth after site saturation at sufficiently high undercooling. 7.2.2 Effect of Austenite Grain Size Distribution The model predictions for the relatively small initial austenite grain sizes depicted in Figs. 7.6, 7.7, 7.8 and 7.9 are in good agreement with the experimental data. However, as the austenite grain size increases, the discrepancy between the experimental results and the model predictions increases. For example, the comparison between the experimental data and the model predictions for an austenite grain size of 120 um for the HSLA-V steel is illustrated in Fig. 7.10. As can be seen, the model predicts a transformation which is more rapid than that experimentally observed. While in the first stage of the phase transformation, the model predictions illustrate a maximum austenite decomposition rate, the experimental results show a slower transformation rate. The reason for this discrepancy may be related to the complicated nature of the austenite grain size distribution of the coarser initial austenite microstructures. To produce the finer austenite grains for the continuous cooling tests, the specimens were reheated to 950 °C and held for 2 minutes which does not dissolve most of the existing precipitates i.e., A1N, V(C, N) and Nb(C, N). The presence of undissolved Chapter 7 CARBON DIFFUSION RESULTS 178 particles can pin the austenite grain boundaries limiting the austenite grain growth and keeping the width of the grain size distribution in a relatively narrow range, as shown in Fig. 7.1 la for the H S L A - V steel; this is consistent with the findings of Giumelli [128] f o r the plain-carbon steels. Therefore, an average grain size in the transformation model for the reheat conditions employed is a reasonable assumption. To produce a coarser austenite microstructure e.g., dy=120 pm, a higher reheating temperature (1150 °C), which is above the precipitate solution temperature, is required. Partial dissolution of the precipitates can result in abnormal grain growth. At the onset of abnormal grain growth, the dispersion of pinning particles changes. This gives more opportunity to the largest grains to grow by consuming smaller austenite grains having the greatest grain boundary energy per unit volume which causes the widening of the distribution and the appearance of a bimodal structure [128] Eventually, all the small grains are consumed and normal growth of the coarse grains commences. Even though reheating conditions were chosen to produce a fairly homogeneous microstructure by heating at the normal growth stage, a relatively broad grain size distribution, as a result of previous abnormal growth, can be seen in the coarser austenite shown in Fig. 7.1 lb for the HSLA-V steel. In this case, taking the average austenite grain size as the actual initial conditions for the subsequent phase transformation may not be a reasonable approximation. Therefore, to improve the model, the initial austenite grain sizes should be included. To illustrate this fact, the effect of initial austenite grain size on the phase transformation predictions is shown in Fig. 7.12 for a cooling rate of 1 °C/s. It is evident that increasing the austenite grain size lowers the transformation temperature (increases the degree of supercooling) but has little impact on the transformation rate. It should be Chapter 7 CARBON DIFFUSION RESULTS 179 noted that the difference between the transformation start temperatures of the small and larger grain sizes were calculated using Eq. (5.7) consistent with the results obtained using the phenomenological description given by Militzer et al. [21]. Quantitatively, the grain size distribution of austenite can be treated as an appropriate number of grain size classes. For example, the grain size distribution for the 120 um austenite for the HSLA-V steel (shown in Fig. 7.1 lb) has been partitioned in Fig. 7.13 into several size classes including the volume of each class. Figures 7.1 lb and 7.13 indicate that the larger grains account for a greater volume fraction of the microstructure. For example, the 160 um grains with 3% of the number fraction have 7% of the volume fraction, whereas, the 80 um grains with 32% of the number fraction have just 10% of the volume fraction. The combined 130 and 160 um sized grains which account for 19% of the grains make up 32% of the total volume. To predict the transformation kinetics, the austenite-to-ferrite transformation was assumed to be additive, starting with the smaller and proceeding to the larger austenite grains. Based on the C-diffusion model, the resulting ferrite fraction was calculated with the smallest austenite grain size and superimposed to the transformed ferrite volume fraction of the next class size. Thus, the total transformed ferrite volume fraction at temperature T, X(T), was calculated as following: X{T) = fJXl{T)f, ;=1 (7.6) Chapter 7 CARBON DIFFUSION RESULTS 180 where fj is the volume fraction of the grain size i and Xj(T) is the transformed ferrite fraction for the grain size i at temperature T. Figure 7.14 compares the experimental results and model predictions incorporating both an average austenite grain size and the austenite grain size distribution factor as initial conditions for subsequent phase transformation. As can be seen, incorporating the austenite grain size distribution into the carbon diffusion model provides an appropriate description for the initial stage of the transformation kinetics. This approach also improves the model prediction of the entire phase transformation kinetics as opposed to considering just an average grain size of austenite. Chapter 7 CARBON DIFFUSION RESUL TS 181 Figure 7.1: Schematic diagram o f the hypo-eutectoid section o f the iron-carbon equ i l ib r ium diagram showing the carbon diffusion gradients associated with the growth o f ferrite at two different temperatures [156]. Chapter 7 CARBON DIFFUSION RESUL TS 182 Tetrakaidecahedron Shape of Austenite Grain 1/2 Onln Stat Spherical Model Figure 7.2: Schematic diagram illustrating the tetrakaidecahedron shape attributed to an austenite grain and the spherical geometries used in the mathematical model [156] Chapter 7 CARBON DIFFUSION RESUL TS 183 a-y Irrtarfaca a k \ y c» ^ Zero mass transfer across boundary x.o l/2Gn*>Dta. Initial Condition: Att-O, 0<X<L C(I)-CQ (1-1, N) • Boundary Conditions: At t > 0, X-0 For First Nod* C(1 )-C y Att ^0, X-L For Last Nod* dC/dr-0 Figure 7.3: Schematic diagram illustrating the nodal arrangement and initial and boundary conditions for the spherical diffusion model [156] Chapter 7 CARBON DIFFUSION RESULTS 184 6 « 5 -0 -I 1 1 1 1 1 r~ 1 1 680 690 700 710 720 730 740 750 760 Transformation start temperature (°C) Figure 7.4: Comparison of the experimentally observed time to produce 50% ferrite with that predicted from the carbon diffusion model for the 0.17 wt %C with a dv=18 pm (simulating the A36 steel) t 2 1 ] . Chapter 7 CARBON DIFFUSION RESUL TS 185 0.0 -i 1 1 1 1 1 1 1 1 720 730 740 750 760 770 780 790 800 Temperature (°C) Figure 7.5: The effect of Mn segregation, quantified by the segregation energy, E , on the local equilibrium carbon concentration at the austenite/ferrite interface in the A36 steel; the broken line indicates the carbon bulk concentration, Chapter 7 CARBON DIFFUSION RESULTS 186 Temperature (°C) Figure 7 . 6 : Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.038 wt.% C, simulating the DQSK steel with 38 um initial austenite grain size. Chapter 7 CARBON DIFFUSION RESULTS 187 600 620 640 660 680 700 720 740 760 780 Temperature (°C) Figure 7.7: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.17 wt.% C, simulating the A36 steel with 18 um initial austenite grain size. Chapter 7 CARBON DIFFUSION RESULTS 188 640 680 720 760 800 840 Temperature (°C) Figure 7.8: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.045 wt.% C, simulating the H S L A - V steel with 36 um initial austenite grain size. Chapter 7 CARBON DIFFUSION RESULTS 189 600 640 680 720 760 800 Temperature (°C) Figure 7.9: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.082 wt.% C. simulating the HSLA-Nb steel with 18 pm initial austenite grain size. Chapter 7 CARBON DIFFUSION RESULTS 190 Temperature (°C) Figure 7.10: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.045 wt % C , simulating the H S L A - V steel with 120 pm initial austenite grain size ((p=l °C/s). Chapter 7 CARBON DIFFUSION RESULTS 191 0 20 40 60 80 100 120 140 160 180 Austenite grain size (jim) 60 80 100 120 140 Austenite grain size (|im) Figure 7.11: The three-dimensional austenite grain size distribution for the HSLA-V steel; (a) for a reheating temperature of 950 °C and holding time of 2 minutes (giving an average y grain size of 36 jam) and (b) for a reheating temperature of 1150 °C and holding time of 30 seconds (giving an average y grain size of 120 um). Chapter 7 CARBON DIFFUSION RESULTS 192 Temperature (°C) Figure 7.12: Comparison of the experimental results with the predictions from carbon diffusion controlled growth modified by SDLE for the 0.045 wt %C, simulating the H S L A - V steel using 80, 100, 120 and 140 pm as an average for the initial austenite grain size and a cooling rate of 1 °C/s. Chapter 7 CARBON DIFFUSION RESULTS 193 0.4 0.3 a o > 0.2 0.1 0.0 60 80 100 120 140 160 Austenite grain size (jim) 180 Figure 7.13: The volume fraction of each grain size class for the H S L A - V steel reheated to 1150 ° C and held for 3 0 seconds, giving an "average y grain size" of 120 urn. Chapter 7 CARBON DIFFUSION RESULTS 194 Temperature (°C) Figure 7.14: Comparison of the experimental results with the predictions employing 120 pm average austenite grain size and austenite grain size distribution for the 0.045 wt % C , simulating the HSLA-V steel (<p=l °C/s). CHAPTER 8 S U M M A R Y A N D C O N C L U S I O N S 8.1 SUMMARY The experimental measurement and modelling of the austenite-to-ferrite transformation kinetics and the resulting microstructure have been examined for conditions reflecting industrial processing. Two low carbon, plain-carbon steels and two HSLA single microalloyed steels were used in this study. In the absence of retained strain, a Gleeble 1500 machine using tubular specimens was adopted for the laboratory simulation, the test schedules reflecting the industrial processing conditions. Diametral dilation measurements were conducted on the tubular specimens to quantify the continuous cooling transformation kinetics. In these tests, the initial austenite grain size and cooling rate were varied in such a way as to span the austenite grain sizes and accelerated cooling conditions experienced on the run-out table of a hot strip mill. The effect of retained strain on the transformation behaviour for the HSLA-Nb steel was investigated employing axisymmetric compression and torsion testing because Nb(C, N) precipitates and/or Nb solute drag leads to a delay in austenite recrystallization and accumulation of retained strain during industrial processing. 195 Chapter 8 SUMMARY AND CONCLUSIONS 196 To model the austenite-to-ferrite transformation kinetics, the work was presented in two parts. The first part involved the development of empirical models of the austenite-to-ferrite transformation kinetics with the variables cooling rate, initial austenite grain size and degree of retained strain comparable to those of the industrial process. In this part, the continuous cooling transformation kinetics was characterized with the aid of the Avrami equation and additivity; the models included the effect of temperature, initial austenite grain size and retained strain. The second part involved describing the strain free ferrite growth kinetics for continuous cooling conditions using a carbon diffusion model developed originally by Kamat P ^ , 156] f o r isothermal cases and later modified by Militzer et al. [21, 51, 157] ^ 0 incorporate the solute drag-like effect and continuous cooling conditions. The model simplifications included a spherical geometry for the austenite grains with nucleation of ferrite occurring at the austenite grain boundary and nucleation site saturation. In this part, the effect of austenite grain size distribution on the subsequent phase transformation calculations was also examined. The microstructures resulting from the continuous cooling tests including ferrite grain size, volume fraction and morphology were quantitatively analyzed using a C-Imaging System image analyzer. A number of specimens from the four steels were also subjected to metallographic examination to obtain prior austenite grain size. The obtained results were used to develop an empirical model to relate the resulting microstructure to the processing parameters. Chapter 8 SUMMARY AND CONCLUSIONS 8.2 CONCLUSIONS 197 Based on the experimental results and model predictions of the phase transformation kinetics and resulting microstructure, the following conclusions can be drawn: 1) It has been shown that the thermal history plays a key role in producing the initial austenite grain size. For a given reheating temperature, the increase in heating rate increased the nucleation rate of austenite during the reversion to austenite and resulted in a finer austenite grain size. 2) The initial austenite grain size and accelerated cooling experienced on the run-out table have been shown to have major effects on the austenite decomposition kinetics and the resulting microstructure. It was shown in the CCT tests, the increase in the austenite grain size reduced the transformation temperature and yielded a more non-polygonal ferrite. For a given initial austenite grain size, increasing the cooling rates also suppressed the transformation temperature and resulted in a more non-equilibrium microstructure. 3) Although the austenite decomposition kinetics of the DQSK and HSLA-V steels were similar, the resulting microstructure of the latter steel showed more non-polygonal ferrite. It is suggested that the formation of non-polygonal ferrite in the resulting microstructure can be attributed to the vanadium solute drag-like effect. 4) For the HSLA-Nb steel, deformation between T ^ and Ae3 introduced retained strain in the austenite, increased the nucleation rate of the ferrite and resulted in a Chapter 8 SUMMARY AND CONCLUSIONS 198 refined ferrite grain size. It was shown that the degree of refinement is strongly affected by the prior austenite grain size and the cooling conditions; smaller austenite grains and higher cooling rates showed little refinement, whereas larger austenite grains and lower cooling rates showed an increasing degree of refinement with increasing strain. It was also shown that the retained strain, particularly for the larger austenite grain sized material, encouraged the formation of an equilibrium microstructure. The effect of processing variables on the phase transformation kinetics and the resulting microstructure are summarized on Table 8 . 1 . Table 8.1: Effect of processing variables on the phase transformation behaviour. Proc. Variables Tras. Temp. Tras. Rate Ferrite Grain Size Production Polygonal Ferrite tcp 1 t i I tdy I t I te Small dy - - -Large dy t t 1 t where cp is the cooling rate, dy is the austenite grain size and 8 is the retained strain. 5) The austenite-to-ferrite transformation start temperature was described with an empirical relationship incorporating cooling rate and austenite grain size. 6) The continuous cooling transformation model based on the isothermal Avrami equation and additivity was obtained using CCT data and showed reasonable Chapter 8 SUMMARY AND CONCLUSIONS 199 agreement with the experimental results obtained for run-out table cooling conditions. The model also included the austenite grain size factor and showed good agreement with CCT data for a range of austenite grain sizes spanning that obtained at the entrance of the run-out table. 7) For the HSLA-Nb steel containing retained strain, the model based on a grain size-modified Avrami equation incorporating an effective austenite grain size concept showed good agreement with the CCT data. 8) It was shown that a more fundamental carbon diffusion model H 2 , 156] incorporating a solute drag-like effect [21> 51, 157]^  C O u ld be used to describe the strain free CCT data. 9) Incorporating the austenite grain size as a number of size classes, instead of taking one average grain size as the initial condition for the carbon diffusion model calculations, improved the model predictions. This was more important for the larger austenite grain sizes which had a wider grain size distribution. 10) A good agreement between ferrite grain size predictions and experimental measured data was achieved for specimens subjected to a range of cooling rates and deformed at different levels for initial austenite grain sizes spanning that exiting the finishing mill. 8.3 FUTURE WORK 1) The strain free, grain size-modified Avrami equation has been effective for predicting the austenite-to-ferrite transformation kinetics for cooling conditions Chapter 8 SUMMARY AND CONCLUSIONS 200 experienced on the run-out table, the minimum cooling rate being that for air cooling, «20 °C/s. However, the model predictions were not as good for continuous cooling at slower cooling rates. 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A P P E N D I X 1 . 0 0.8 ] 0.6 0.4 0.2 0.0 - A -O • A A A A • o o A A • • o • o A A • o A A A cP A • O A A A dy=15 jLtm dy=18 L i m dy=46 L i m A A A A e 9 Q (9 C D a n 580 600 620 640 660 680 700 720 740 760 Temperature (°C) Fig. App. 1: Transformation kinetics for the air cooled (»20 °C/s) A36 steel for the range of initial austenite grain sizes, 15, 18 and 46 nm. 211 APPENDIX 212 1.0 0.8 0.6 0.4 0.2 0.0 620 660 700 740 780 Temperature (°C) 820 Fig. App. 2: Transformation kinetics for the air cooled («20 °C/s) H S L A - V steel for the range of initial austenite grain sizes, 36, 85 and 120 urn. APPENDIX 213 1.0 0.8 \ a o 03 E u a <*> c 03 H 0.6 0.4 0.2 0.0 540 580 620 660 700 740 Temperature (°C) Fig. App. 3: Transformation kinetics for the air cooled («20 °C/s) HSLA-Nb steel for the range of initial austenite grain sizes, 18, 44 and 84 pm. APPENDIX 214 660 640 dy=18 jim d =46 urn 0 20 40 60 80 100 120 Cooling rate (°C/s) 140 160 Fig. App. 4: Transformation start temperature, Ar3, taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 15, 18 and 46 pm for the A36 steel. APPENDIX 215 860 840 f 720 - B d 7 = 8 5 ^ m A dy=120 Lim 700 -I r - . 1 1 r - 1 0 20 40 60 80 100 120 140 Cooling rate (°C/s) Fig. App. 5: Transformation start temperature, Ar3, taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 36, 85 and 120 pm for the H S L A - V steel. APPENDIX 216 820 800 680 660 dy=44 Lim dy=84 Lim 0 20 40 60 80 100 120 140 Cooling rate (°C/s) 160 Fig. App. 6: Transformation start temperature, Ar3, taken at the temperature for 5% transformation versus cooling rate for three different grain sizes of 18, 44 and 84 um for the HSLA-Nb steel. APPENDIX 217 25 0 20 40 60 80 100 Cooling rate (°C/s) Fig. App. 7: Polygonal ferrite grain size and ferrite volume fraction for the A36 steel obtained from CCT tests for three different initial austenite grain sizes of 15, 18 and 46 um. APPENDIX 218 Cooling rate (°C/s) Fig. App. 8: Polygonal ferrite grain size and ferrite volume fraction for the HSLA-V steel obtained from CCT tests for three different initial austenite grain sizes of 36, 85 and 120 um. APPENDIX 219 0 10 20 30 40 50 60 70 Cooling rate (°C/s) Fig. App. 9: Polygonal ferrite grain size and ferrite volume fraction for the H S L A -Nb steel obtained from CCT tests for three different initial austenite grain sizes of 18, 44 and 84 urn. APPENDIX 220 80 100 120 140 160 180 200 (TA e ;T) (°C) Fig. App. 10: Behavior of In b values versus supercooling for the A 3 6 steel with 18 urn initial austenite grain size and n=0.9. APPENDIX 221 3 2 -t 0 -2 4 80 Fig. o 16°C/s • 50 °C/s A 60 °C/s O 105 °C/s 0 136°C/s 100 160 180 120 140 (TAej-T) (°C) App. 11 : Behavior of In b values versus supercooling for the HSLA-Nb steel with 18 pm initial austenite grain size and n=0.9. APPENDIX 222 Temperature (°C) Fig. App. 12: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the A36 steel having a 18 pm initial austenite grain size. APPENDIX 223 660 680 700 720 740 760 780 800 820 Temperature (°C) Fig. App. 13: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the H S L A - V steel having a 36 um initial austenite grain size. APPENDIX 224 Temperature (°C) Fig. App. 14: Comparison of the experimental ferrite transformation kinetics with Avrami model predictions for the HSLA-Nb steel having a 18 pm initial austenite grain size. APPENDIX 225 Temperature (°C) Fig. App. 15: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the A36 steel having a 18 um initial austenite grain size. APPENDIX 226 Temperature (°C) Fig. App. 16: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the H S L A - V steel having a 3 6 um initial austenite grain size. APPENDIX 227 640 660 680 700 720 740 760 780 800 Temperature (°C) Fig. App. 17: Comparison of the experimental ferrite transformation kinetics with Avrami and Umemoto model predictions for the HSLA-Nb steel having a 18 pm initial austenite grain size. APPENDIX 228 720 Temperature (°C) Fig. App. 18: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 18 pm austenite in the A36 steel with the grain size-modified Avrami model predictions. APPENDIX 229 660 680 700 720 740 760 780 800 820 Temperature (°C) Fig. App. 19: Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 36 urn austenite in the HSLA-V steel with the grain size-modified Avrami model predictions. APPENDIX 230 Temperature (°C) Fig. App. 2 0 : Comparison of the experimental ferrite transformation kinetics for different cooling rates for the 18 um austenite in the HSLA-Nb steel with the grain size-modified Avrami model predictions. APPENDIX 231 620 640 660 680 700 720 Temperature (°C) Fig. App. 2 1 : Comparison of the experimental y—»-a transformation results with the predictions obtained using the grain size-modified Avrami equation for the A36 steel having a 18 pm initial austenite grain size and m=2. APPENDIX 232 640 660 680 700 720 740 760 780 800 820 Temperature (°C) Fig. App. 2 2 : Comparison of the experimental y-»a transformation results with the predictions obtained using the grain size-modified Avrami equation for the HSLA-V steel having a 36 urn initial austenite grain size and m=2. APPENDIX 233 660 680 700 720 740 760 780 800 Temperature (°C) Fig. App. 23: Comparison of the experimental y-»a transformation results with the predictions obtained using the grain size-modified Avrami equation for the HSLA-Nb steel having a 18 pm initial austenite grain size and" m=2. 

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