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The effect of Cu on phase transformation kinetics in low-carbon steels Dilney, Shaun 1999

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The Effect of Cu on Phase Transformation Kinetics in Low-Carbon Steels BY SHAUN DILNEY B.Eng., Technical University of Nova Scotia, Canada, 1997 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (DEPARTMENT OF METALS AND MATERIALS ENGINEERING) We accept this thesis as conforming To the required standard THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER, 1999 ©Shaun Dilney, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Y l/Uls J" Hflj^ F/fi/lk EvvjI^ggT^ The University of British Columbia Vancouver, Canada Date ft jll ICil-DE-6 (2/88) ii ABSTRACT The production of steel through recycling is a global industry dependent upon available scrap steel from a variety of sources including automobiles and steel structures. The constant recycling of steel has resulted in an increase in levels of residual elements, Sn, As, Cu, etc., that cannot be removed by economical means. To avoid processing difficulties associated with steel scrap containing high residuals electric arc furnace (EAF) steelmakers pay a high price for low residual scrap. The ability to process scrap containing high levels of residual elements, specifically Cu, would be very advantageous. In addition to the economic feasibility of processing scrap with high Cu content, there are also improvements in properties to be had by alloying with Cu. Currently, high strength low alloy (HSLA) steels containing Cu are used for specific applications, e.g. shipbuilding, and pipelines in Arctic environments, due to their high strength and corrosion resistance as compared to ordinary HSLA steels. Processing of Cu-bearing steels to produce steel strip and plate requires extensive knowledge on the effect of Cu content, cooling rate, and austenite grain size will have on phase transformation kinetics, resulting microstructure, and mechanical properties. This work investigates the role that each of these variables plays in the processing of low-carbon steel strip and plate under simulated industrial conditions. Further, the role of Cu iii on phase transformation kinetics is investigated using semi-empirical and fundamentally based models. IV TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF FIGURES vi LIST OF TABLES viii NOMENCLATURE ix ACKNOWLEDGEMENTS xiv 1 INTRODUCTION . 1 2 Literature Review 8 2.1 Effect of Cu on Microstructure 8 2.1.1 Precipitation 8 2.1.2 Phase transformation 14 2.2 Transformation Modeling 21 2.2.2 Austenite Decomposition 24 2.2.3 Ferrite Nucleation and Growth 25 2.2.4 Acicular Ferrite Growth 31 2.2.5 Bainitic Growth 33 2.2.6 Avrami Equation 34 2.2.7 Grain Size Modified Avrami Equation 35 2.2.8 Umemoto Equation 36 2.2.9 Application of Isothermal Kinetic Equation to CCT 37 3 Objectives and Scope 40 4 Experimental 41 4.1 Materials 41 4.2 Experimental Techniques 42 4.2.1 Preliminary Grain Growth Experiments 42 4.2.2 Gleeble Grain Growth Experiments 44 4.2.3 CCT Experiments 46 4.2.4 Micro structural Techniques 51 4.2.5 Hardness Measurements 54 5 Results 55 5.1 Austenite Grain Growth 55 5.1.1 Preliminary Grain Growth Experiments 55 5.1.2 Gleeble Grain Growth 56 5.2 CCT Experiments 57 5.2.1 Phase Transformation Kinetics 57 5.2.2 Microstructure 60 5.2.3 Hardness 66 6 Modeling 74 6.1 Prediction of T A e 3 74 6.2 AISI Model 74 6.2.1 Transformation Start 76 V 6.2.2 Ferrite Growth 8 2 6.2.3 Ferrite Grain Size 92 6.3 Diffusion Model 9 6 7 Conclusions 8 Future Work 1 0 5 9 References 1^ 6 APPENDIX 1 0 9 v i LIST OF FIGURES Figure 1.1. Prediction of copper concentration for obsolete scrap [2] 2 Figure 1.2. Schematic diagram of a hot strip mill 5 Figure 2.1. Effect of cooling conditions on the relation between Cu content and hardness in Fe-Cu alloys for furnace cooling (•), air cooling (O), and water quenching (•) [16] 11 Figure 2.2. Precipitation strengthening in Fe-0.9wt%Cu alloy [9] 13 Figure 2.3. Aging curve at 500°C for the solutionized condition [8] 13 Figure 2.4. TTT diagram for Owt%Cu (open marks and dashed lines) and 1.5wt%Cu (solid marks and solid lines) steels [13] 15 Figure 2.5. Illustration of a calculated equilibrium phase diagram of Fe-Cu binary system. The To line for BCC (a) / FCC (y) is also shown on the figure [16] 18 Figure 2.6. Continuous cooling transformation diagram for a HSLA-80 steel [18] 20 Figure 2.7. Hall-Petch plot for HSLA-80 steel studied by Speich and Scoonover [15]... 21 Figure 2.8. Portion of the Fe-Fe3C equilibrium phase diagram [18] 22 Figure 2.9. Set of constant Mn sections through the Fe-C-Mn phase diagram showing the change in position of the T A e 3 line with increasing Mn content [21] 24 Figure 2.10. The pillbox nucleus model [25] 26 Figure 2.11. The rate of nucleation and growth with respect to temperature [27] 28 Figure 2.12. Carbon concentration profile normal to the advancing a/y interface [17]. .. 29 Figure 2.13. Growth of ferrite plates in a Fe-0.22wt%C alloy at 710°C [12] 32 Figure 2.14. Schematic of the isothermal stepping of continuous cooling transformation curves 38 Figure 4.1. Apparatus for preliminary grain growth experiments 43 Figure 4.2. The specimen chamber and basic components of the Gleeble 1500 thermomechanical simulator 45 Figure 4.3. Sample design used in Gleeble grain growth experiments 45 Figure 4.4. Specimen design for CCT experiments using the Gleeble 47 Figure 4.5. Heating and cooling schedule of CCT experiments 48 Figure 4.6. The diametric response of the 0.05wt%Cu steel for the air cooling condition with austenite grain size of 22pm 49 Figure 4.7. Example of prior austenite microstructure produced by furnace and Gleeble grain growth experiments 51 Figure 5.1. Results of furnace grain growth experiments showing temperature and time combinations that cause abnormal grain growth 56 Figure 5.2. Fraction vs. temperature plot for various cooling rates using the 0.05wt%Cu steel with dY = 22 pm 58 Figure 5.3. The effect of austenite grain size on phase transformation (0.05wt%Cu cooled at 16°C/s) 59 Figure 5.4. Effect of Cu on phase transformation kinetics (air-cooled condition) 60 Figure 5.5. Polygonal ferritic microstructures produced for a 0.05wt%Cu steel having an austenite grain size of 22pm 61 vii Figure 5.6. The effect of austenite grain size on polygonal ferrite formation. Micrographs shown are for the 0.05wt%Cu steel and 9 = l°C/s. Caption shows austenite grain size 63 Figure 5.7. Microstructural evolution for large austenite grain size and various cooling rates. Micrographs shown are that of 0.4wt%Cu steel with 170pm y grain size 64 Figure 5.8. Effect of Cu and cooling rate on final ferrite grain size for an austenite grain size of 20pm 66 Figure 5.9. Hall-Petch plot for polygonal ferrite micro structures produced using an austenite grain size of 20pm 67 Figure 5.10. Hall-Petch relationship with additional data for polygonal microstructures formed utilizing higher reheat temperatures of 1100 and 1150°C 70 Figure 5.11. Hardness vs. cooling rate for (a) 1100°C and (b) 1150°C for three steel compositions 72 Figure 5.12. The effect of y grain size on hardness for all three steel grades cooled at 6°C/s where the symbols are the experimental data and the solid line is the data trend. 73 Figure 6.1. Comparison of experimental results (symbols) and the prediction (solid line) for the undercooling, required to initiate transformation, as a combined function of austenite grain size and cooling rate 80 Figure 6.2. Comparison of experimental results (symbols) and the prediction (solid line) for the undercooling, required to initiate transformation, as a combined function of austenite grain size and cooling rate for the 0.8wt%Cu steel 81 Figure 6.3. Plot of lnb vs. undercooling, (TAe3-T), for the 0.8wt%Cu steel with an austenite grain size of 145 pm 84 Figure 6.4. Modeling fraction transformed for 0.8wt%Cu steel with dY of 20pm 86 Figure 6.5. Modeling fraction transformed for 0.4wt%Cu with dT of 75pm 86 Figure 6.6. Modeling fraction transformed for 0.05wt%Cu steel with dY of 121pm 87 Figure 6.7. Avrami model fit for the normalized ferrite fraction of all three steels at various cooling rates 88 Figure 6.8. Experimental data compared to grain size modified Avrami equation for small grain sizes 90 Figure 6.9. Experimental data compared to grain size modified Avrami equation for medium grain sizes 91 Figure 6.10. Experimental data compared to grain size modified Avrami equation for large grain sizes 91 Figure 6.12. Comparison of experimental results (symbols) and predictions (lines) for the final ferrite grain size compared with transformation start temperature for the 0.8wt%Cu steel 95 Figure 6.13. Comparison between experimental and predicted values using the ferrite grain size model 96 Figure 6.14. Results of carbon diffusion model for (a) 0.05wt%Cu steel and (b) 0.4wt%Cu steel 100 Figure 6.15. Results of carbon diffusion model for (a) 0.8wt%Cu steel and (b) 0.8wt%Cu steel with correction for Cu content 101 V l l l LIST OF TABLES Table 2.1. Chemical composition in wt% of HSLA-80 steel [15,18] 19 Table 2.2. Comparison of n values used in Avrami equations by various researchers 35 Table 4.1. Chemical compositions of steels investigated (in wt%) 41 Table 4.2. Temperatures and times used in preliminary grain growth experiments 43 Table 4.3. Experimental conditions of temperature and time used in Gleeble grain growth experiments 44 Table 5.1. Results of Gleeble grain growth experiments 57 Table 5.2. Parameters A and mA used in Equation 21 65 Table 6.1. T A e 3 temperatures (°C) calculated for each steel using methods developed by Andrews [20] and Kirkaldy and Baganis [21] 74 Table 6.2. Comparison of chemical compositions, in wt%, of DQSK steel and the 0.05wt%Cu steel grade used in this study 78 Table 6.3. Fitting parameters c, e, and d used in Equation 28 for all three steel grades. ..81 Table 6.4. Parameters F and G used in Equation 30 for all three steel grades 84 Table 6.5. Fit parameters used for polygonal ferrite microstructures and normalized Avrami model 87 Table 6.6. Fit parameters used for the grain size modified Avrami model and entire transformation curve for all three steels and cooling rates 90 Table 6.7. The fitting parameters J an, r| used in Equation 32 for all three steel grades.. 93 Table 6.8. Values of E 0 and E, used in Equation 34 describing the effective segregation energy for a variety of steel alloy compositions 98 ix NOMENCLATURE b fitting parameter for Avrami equation c fitting parameter in equation describing C* as a function of temperature and grain size C 0 initial carbon concentration C a equilibrium carbon concentration in the ferrite phase C r equilibrium carbon concentration in the austenite phase C"r carbon concentration in ferrite at the oc/y interface Cr" carbon concentration in austenite at the oc/y interface C* limiting carbon concentration d fitting parameter in equation describing C* as a function of temperature and grain size d a ferrite grain size dy austenite grain size D a ferrite diametric response extrapolated into two phase region DT austenite diametric response extrapolated into two-phase region D(T) diametric response at temperature T Dyc diffusion coefficient of carbon in austenite e fitting parameter in equation describing C* as a function of temperature and grain size E(T) effective segregation energy at temperature T E 0 fitting parameter for effective segregation energy E, fitting parameter for effective segregation energy F slope of linear relationship describing temperature dependence of b value in Avrami equation Ff fraction of ferrite FG slope of linear relationship describing temperature dependence of b value in grain size modified Avrami equation F x fraction of austenite transformed G intercept of linear relationship describing temperature dependence of b value in Avrami equation G B growth rate of bainite GG intercept of linear relationship describing temperature dependence of b value in grain size modified Avrami equation AG* free energy of formation of a critical nucleus HV hardness measured using Vickers scale HV0 hardness constant in Hall-Petch relationship J* nucleation rate of ferrite at austenite grain boundaries k Boltzmann's constant ky constant in Hall-Petch equation kH constant in modified Hall-Petch equation kA fitting parameter for grain size modified Avrami equation xi m exponential fitting parameter for grain size modified Avrami equation mA fitting parameter in grain size equation Mneq Equivalent Mn concentration M p number of ferrite grains nucleated per austenite grain at corner sites n Avrami exponent N density of viable nucleation sites p exponential value for Umemoto equation r radial distance rc radius of curvature r* critical limiting radius R universal gas constant Rp planar half thickness of the ferrite Rf radius of corner nucleated ferrite ss steady-state segregation factor t time T temperature T A e 3 Equilibrium temperature of the proeutectoid ferrite transformation corresponding to the Ae3 line on the Fe-C equilibrium phase diagram TF transformation finish temperature T s transformation start temperature TN Nucleation temperature of corner ferrite T a o selected temperature in the ferrite region for analysis of dilation data TY0 selected temperature in the austenite region for analysis of dilation data X fraction transformed XB volume fraction of bainite Xf(t) ferrite fraction at time t Z Zeldovich nonequilibrium factor a ferrite ap parabolic rate constant a a thermal expansion coefficient of ferrite ciy thermal expansion coefficient of austenite ocmix thermal expansion coefficient during the y—»a transformation oc/y interface between ferrite and austenite P* frequency factor r\ fitting parameter in ferrite grain size equation q> cooling rate y austenite y—»a austenite to ferrite transformation a0 inherent strength of material in the Hall-Petch equation cjy yield strength at 0.02% offset aay interfacial energy of the high energy incoherent face in pill-box model <jcay interfacial energy of low energy coherent face in pill-box model x incubation time sothermal time step required to reach the specified fraction transformed xiv ACKNOWLEDGEMENTS First and foremost I would like to thank my supervisor Dr. Matthias Militzer without whose guidance this thesis could not have been finished. I would also like to thank him for his understanding and assistance in helping me achieve my academic and professional goals especially towards the end of this work. Further I would like to thank all of the staff and faculty who have contributed in many large and small ways to this work. Special thanks go to Mr. B. Chau, Mr. R Cardeno, and Mr. P. Wenman for their technical assistance and expertise. Finally I would thank all of my family and friends for their support and understanding throughout my studies. They have always encouraged me to follow my ambitions and have offered sound advice to help me achieve my goals. 1 1 INTRODUCTION Over the past 40 years the business of producing steel by recycling has revolutionized the steel industry. The process utilizes an electric arc furnace (EAP) to melt steel scrap, mainly from cars and steel structures, to produce new products. It is not only a very effective way of producing steel but also protecting the global environment through recycling. One disadvantage of this process is global competition for quality scrap to be used in EAF steelmaking. This high quality scrap usually contains very low levels of impurity elements, such as Cu, Sn, Sb, Ni, and As, and is usually termed low residual scrap. The reason why this type of scrap is coveted by steelmakers is most of these residual elements cannot be removed by economical means during processing. The processing of low residual scrap typically results in fewer problems during steelmaking and higher quality finished products. The competition for low residual scrap has led companies to the necessity of utilizing lower priced scrap, containing high residuals, in order to remain competitive. In addition, having to use this high residual scrap today it is expected that the levels of these elements present in the steel will increase in the future as more electronics are used in the automobile industry and steel is continuously recycled. For example, current Cu levels in 2 scrap range from 0.1-0.35wt%; however, by the year 2015 the level of Cu is expected to rise up to 0.4wt%Cu [1]. This phenomenon is displayed in Figure 1.1. Cu levels could rise as high as 1.2-1.5 times the present levels by the year 2020 [2]. This analysis may be a conservative estimate because presently some EAF steelmakers produce steel containing 0.4wt%Cu. In order to process steel scrap containing these higher impurity levels companies will have to know the effects of Cu on the thermomechanical processing (TMP), microstructure, and mechanical properties of these steels. In fact the companies that can process steel scrap containing this high level of Cu will have a distinct advantage over their competitors as they will be able to buy lower cost steel scrap on the world market thus reducing their feed costs and increasing their marginal profits. 0.5 0.4 High Residual Low Residual U 0.1 Q i 1 1 1 1 1 1 1 1985 1990 1995 2000 2005 2010 2015 2020 Fiscal Year Figure 1.1. Predictions of copper concentration for obsolete scrap [2]. 3 Historically Cu has been viewed as a detrimental element in steel because it promotes hot shortness. Hot shortness occurs when steel is hot worked above the melting point of Cu (1083°C), Cu separates from solid solution and segregates at austenite grain boundaries that subsequently are subjected to failure under the tensile stresses developed during hot rolling [3]. The problem of hot shortness is very complex and does not only depend on alloy composition but also the oxidizing atmospheres to which the steel is exposed. Nicholson and Murray showed that furnace oxygen content greatly affected the level of surface oxidation [4]. The problem of hot shortness is controlled through two main means: by altering the chemistry of the alloy and through sophisticated TMP techniques. Nickel reduces susceptibility to surface hot shortness by increasing the solubility of Cu in austenite thus decreasing segregation to the austenite grain boundaries and by increasing the melting point of the Cu-enriched phase [5]. Faster cooling rates and longer soaking times have been found to be beneficial in preventing hot shortness. The main advantage of Cu addition to steel is its age hardening capabilities. The Fe-Cu system, similar to the Al-Cu system, is one of decreasing solid solubility of Cu with decreasing temperature. With proper heat treatment Cu will precipitate from supersaturated solid solution and strengthen the steel through age hardening. Currently, research is underway to develop new Cu-bearing interstitial free (IF) and low-carbon steels. These steels would be processed in the normal fashion and then, once formed into their final shape, they are heat treated to strengthen the steel through age hardening. 4 This advantage has already been utilized in developing modified high strength low alloy (HSLA) steel grades containing significant levels of Cu. These modified steels are used in the construction of natural gas pipelines, ships, and offshore platforms in Arctic environments [6,7]. HSLA steels are a class of steels that have superior strength, toughness, and weldability as compared to common mild steel grades. Minor alloying elements, such as Ti, Nb, and V, and special hot-mill processing methods are used to control the microstructure and mechanical properties of these steels. In addition Cu is added to improve corrosion resistance. Cu additions of 0.05 to 0.2wt% can show improvements in corrosion resistance 2 to 3 times better than ordinary mild steel [3]. Steels referred to as weathering grades have been developed using small additions of copper, phosphorous, nickel, and chromium. These steels rust at a lower rate than plain carbon steels and, under favorable climatic conditions, can develop a relatively stable layer of hydrated iron oxide that retards further attack [3]. In order to use Cu-bearing steels for specialized applications one must first produce steel strip or plate by TMP that is subsequently shaped to form the required products. The production of steel strip and plate, specifically as it pertains to cooling conditions, is highly sensitive to a number of factors including chemical composition. The chemistry of the steel is an important factor in determining the cooling conditions required for steel strip and plate. Elements such as Ni, Mn, and Cu are austenizing agents that stabilize the austenite phase field. The stabilization of the austenite phase field will change the 5 austenite to ferrite (y-»ct) phase transformation kinetics thus changing the microstructure and final mechanical properties. Therefore it is important to understand the effect of C u on phase transformation kinetics in order to be able to achieve the desired properties of the final product. Hot strip rolling is a thermomechanical process used to produce steel in the form of thin sheet. A schematic of the process is shown Figure 1.2. This process consists of five basic steps: reheating, rough rolling, finish rolling, run-out table cooling, and coiling. After the steel is cast it is cut into slabs that are sent into a reheating furnace. In the furnace the slabs are reheated to approximately 1200°C for 2-3 hours thereby homogenizing the slab and redisolvlng solubles. The slab with a thickness of approximately 250mm enters the roughing mi l l at approximately 1200°C; this temperature allows for comparatively large reductions per pass. After completion of rough rolling the temperature of the steel is in the range of 1050-1150°C and the thickness is reduced to 25-30mm. m Reheat Furnace Roughing M i l l Finishing M i l l Run-out Table Coi le r Figure 1.2. Schematic diagram of a hot strip mill. 6 Following the roughing mill, the steel enters the finishing mill. This process usually consists of 5 to 7 tandem rolling mills that reduce the thickness of the steel to 1.5-8mm. Finish rolling is scheduled so that the maximum roll reductions occur in first stands and lower reductions in the later stands to ensure uniformity of thickness and surface quality throughout the strip. The steel leaves the finishing mill usually at a temperature between 850-900°C. The run-out table was originally developed to shorten the length of the hot strip mill. Today it is understood to be a very important part of the hot strip rolling process because the cooling rates on the run-out table will dictate to a large degree the final microstructure of the steel that is coiled. A typical run-out table consists of water spray banks that are situated above and below the strip. The steel strip passes through the cooling banks and experiences average cooling rates in the range of 10-150°C/s. Steel plate is produced in a similar but slightly different manner. Steel slabs are continuously cast and typically reduced to cross-sections of 15-20mm and widths of up to 3m. The plates are then allowed to cool at ambient temperatures. The large thermal volume associated with these thick plates creates slow cooling rates of 20°C/s or less. Although there have been studies performed on the effects of Cu on transformation, a systematic study is still lacking where a range of copper compositions is investigated and a transformation model is developed incorporating the effect of Cu. This work is focused on determining the effect of Cu content, cooling rate, and austenite grain size on the 7 transformation kinetics and resulting microstructure and mechanical properties of low-carbon steels. 8 2 Literature Review 2.1 Effect of Cu on Microstructure Copper is found in steels primarily as a residual element from the steelmaking process but can also be added to improve corrosion resistance and/or improve strength through precipitation hardening. The study of the Fe-Cu system has been ongoing for many years with one of the main focus being Cu precipitation in the Fe matrix. Another area that has found recent interest is the effect Cu may have on the phase transformation kinetics and resulting microstructure of low and ultra-low-carbon steels. Because the combination of precipitation hardening and microstructure will dictate the mechanical properties it is important to understand their respective roles in order to produce Cu-bearing steel grades with the desired microstructure and mechanical properties. 2.1.1 Precipitation The Fe-Cu system is one of decreasing solid solubility with temperature. From its maximum of 1.8wt% at 850°C the solid solubility substantially decreases at room temperature. Minor alloying additions of Cu, from 0.6-6.0wt%, have been found to dramatically effect the strength of steel alloys [8,9,10]. Thompson and Grauss [11] studied the precipitation sequence of Cu in Fe. Precipitates begin as body centered cubic (BCC) coherent precipitates having high copper content, which then transform into semi-9 coherent or incoherent face centered cubic (FCC) particles known as epsilon or s-Cu precipitates. These s-Cu precipitates have an orientational relationship between precipitate and matrix similar to the Kurdjumov-Sachs relationship [12]. The Kurdjumov-Sachs relationship describes the orientation between an austenite grain and the ferrite grains formed during the y-»a transformation [13]. Ferrite nucleation from one austenite grain follows the relationship: {lll}y II {110}a;(110)y || (lll)a In the case of s-Cu precipitates the nucleation direction [110]e is parallel to the growth direction of ferrite [11 l]a. Cu can precipitate from Fe, either during the cooling process or during subsequent isothermal age hardening heat treatment. The first type of precipitation has been referred to as 'cooling precipitation' or 'autoaging' [14,15] and refers to precipitation occurring on the run-out table or in the coiler. The second type refers to isothermal precipitation during postproduction heat treatment. 2.1.1.1 Cooling Precipitation During their investigation, Kimura and Takaki [16] had discovered that the hardness of Cu-bearing steels depended greatly on the cooling rate used. Figure 2.1 shows the effect 10 of cooling condition and Cu content on hardness. It can be seen that furnace cooled specimens, being fully ferritic, are, as expected, softer than the water-quenched specimens for all Cu compositions. However, there appears to be a transition point where the air-cooled specimens tend to be significantly harder than the water-quenched ones. This point occurs when the Cu contents reaches 3wt%Cu. Because this specimen is fully ferritic it is expected to be softer than the water quenched specimens at all compositions but Cu precipitation hardens the steel during air-cooling. TEM studies of these precipitates found that their size increased with decreasing cooling rate. Air-cooled precipitate sizes were an average of 10-20nm while the furnace-cooled precipitates were of the order of 50nm. • Obviously the furnace cooling condition behaves more like an equilibrium cooling condition thus promoting larger precipitates and a larger mean spacing between them. As a result, no significant increase in hardness was observed in the furnace-cooled specimens associated with precipitation. Because the precipitates in the air-cooled specimens were formed at a relatively faster cooling rate they are more finely dispersed with lower mean spacing thus increasing hardness as shown in Figure 2.1. A similar relationship between water-quenched and air cooled specimens was found by Wada et al. [14] for yield strength, but air cooled specimens were stronger for Cu contents greater than approximately l.lwt%Cu. One reason for this more pronounced effect of Cu may be the Mn content. Wada et al. used specimens containing 0.64-0.8wt%Mn while Kimura and Takaki used steels with a Mn content of 0.35wt%. 11 0 1 2 3 4 Cu content (mass%) Figure 2.1. Effect of cooling conditions on the relation between Cu content and hardness in Fe-Cu alloys for furnace cooling (•), air cooling (O), and water quenching (•) [16]. 2.1.1.2 Isothermal Precipitation One of the earliest researchers on precipitation in copper bearing steels was Hornbogen [9], who investigated aging behaviors of Fe-0.9wt%Cu alloys at various aging temperatures ranging from 400 to 700°C. Figure 2.2 displays the aging curves for this 12 temperature range. It can be seen that as aging temperature is increased, the time to reach peak strength decreases. Further, the magnitude of strengthening increases with decreasing aging temperature, the lowest aging temperatures giving the highest amount of precipitation hardening. In a later study, Hornbogen and Glenn [10] further investigated the character of s-Cu precipitates and the rate of particle growth. For a Fe-1.23wt%Cu alloy aged at 600°C for 15h the particles were spherical with an average size of 9nm. Further, it was found that particles grew and elongated as time progressed. After 24h at 700°C, spherical precipitates transformed into rod-like shapes of FCC structure with almost pure Cu composition. These rod shaped particles were found to grow in a preferred direction [110]e and displayed an orientational relationship similar to that described by Kurdjumov-Sachs. A recent study of Cu precipitation by Deschamps et al. [8] investigated precipitation behavior in low-carbon steels with copper contents ranging from 0.25wt% to 0.8wt%. This study involved steels in three states: (a) as hot rolled, (b) solutionized, and (c) solutionized and cold worked. Figure 2-3 shows precipitation hardening at 500°C for Cu-bearing steels ranging from 0.25 to 0.8wt%Cu in the solutionized condition. It can be seen from this diagram that significant hardening occurs for the 0.6 and 0.8wt%Cu steels. Aging time (hours) Figure 2.2. Precipitation strengthening in Fe-0.9wt%Cu alloy [9]. 70 60 50 40 ^ 30 20 10 0 -10 0.1 1 10 100 1000 Time at 500°C (h) Figure 2.3. Aging curve at 500°C for the solutionized condition [8]. I i II 11 II | II 1111111 i i 1111111 i i 111111 -e-0.25% i i 1111111 i i 111 II 11 i i 1111111 i i 111111 14 2.1.2 Phase transformation 2.1.2.1 Effect of Cu on Isothermal Transformation Isothermal transformation behavior for Cu-bearing plain carbon steels has recently been investigated by Ohtsuka et al. [13]. The steels investigated had a base composition of 1.48wt%Mn-0.48wt%Si-0.10wt%C and contained up to 1.5wt%Cu. The. final; microstructures of these steels were primarily ferritic in nature. Copper contents of 1.5wt% has been found to have a substantial effect on the transformation behavior of the steels studied, specifically the transformation kinetics, nucleation rates of ferrite, and growth of ferrite grains. Figure 2.4 shows a partial time-temperature-transformation (TTT) diagram, which illustrates that Cu retards the transformation for the steels examined. The time to reach 10, 50, and 90% transformation have all been delayed by an order of magnitude in the steel containing 1.5wt%Cu. This delay time can be attributed to Cu being a mild austenite stabilizer. Ohtsuka et al, continued their investigation to see why the transformation rates of the steel were decreased when Cu was present. They examined the nucleation rates for both steels and found that in the 1.5%Cu bearing steel the nucleation rate was halved in comparison to the 0%Cu steel. The nucleation rate is most likely affected by two 15 parameters: (1) segregation of Cu to the austenite grain boundaries and (2) the formation of fine Cu clusters or precipitates at ferrite nucleation sites [13]. tu 1 S-l a , 1000 950 § 900 I — a CO 850 800 i i i i I 11 o 10% • A 50% • 90% I I I I I 11 i I I I I 11 i Open symbols - without copper Closed symbols - with copper I I I I I M l I I I I I I I I I I I I I I I I I I I I I M M M " 10 100 Time (s) 103 104 Figure 2.4. TTT diagram for 0wt%Cu (open marks and dashed lines) and 1.5wt%Cu (solid marks and solid lines) steels [13]. When Cu segregates to the austenite boundaries it may reduce the available ferrite nucleation sites and thus lower nucleation rates. Further, if e-Cu precipitates are present in the microstructure they may have a pinning effect on the moving oc/y interface and thus reducing the ferrite grain size. Wada et al. [14] showed that the inverse square root of the mean grain diameter increases linearly 16 with copper content, both for water-quenched and air-cooled specimens. Ohtsuka et al reasoned that this decrease in mean grain size was due to a solute drag-like effect of the Cu but did not elaborate. Cu refines ferrite grain size in plain carbon steels and thereby increases the yield stress of the material according to the Hall-Petch relationship: S = ( T o + M « " 2 ( i ) where a0 and ky are constants, ay is the lower yield strength and da is the average ferrite grain size [17]. A similar relationship can be used for hardness: HV = HV0+kHd-aV2 (2) where HV is the hardness measured on the Vickers's scale and HV0 and kH are constants similar to those of Equation 1. 2.1.2.2 Effect of Cu on Continuos Cooling Transformation Although isothermal studies are important to gain understanding of transformation kinetics and microstructural evolution in practice most steels are produced under continuous cooling conditions. Kimura and Takaki [16], studied the effects of Cu on continuous cooling transformation (CCT) in Fe-0.35%Mn-0.003%C-(0.5-4%Cu) steels. 17 Steel specimens in this research were subjected to water quenching, air cooling, and furnace cooling, after solution treatment at 1523K for one hour. Air and furnace cooling produced microstructures consisting of irregular shaped ferrite grains. The size of the ferrite grains was observed to decrease with increasing cooling rate and Cu content. This reduction in grain size correlates well with the results obtained for isothermal heat treatment [13]. In water-quenched alloys the microstructure is also ferritic for alloys with Cu less than lwt%, but has been reported to be substantially martensitic for alloys with 2-4wt%Cu [16]. Kimura and Takaki calculated an equilibrium phase diagram of the Fe-Cu binary system, shown in Figure 2.5, that was used to investigate transformation reactions occurring for various Cu contents. Lines (1) and (2) in this diagram are metastable extension of the phase boundaries between (a+y)/y and y/(y+s-Cu), respectively. The T0 line for the (FCC) y-> (BCC) a transformation of the Fe-Cu system is also shown in the diagram. Kimura and Takaki proposed that between lines (1) and (2) and above the T0 line the alloy undergoes an eutectoid reaction where ferrite and e-Cu are formed simultaneously. The eutectoid reaction of the Fe-Cu alloy is thought to be essentially similar to the pearlitic reaction of the Fe-C system, but the microstructure obtained is of a globular type because diffusion of Cu is not so fast as compared to grain boundary mobility [16]. Below the T0 line it has been proposed that austenite undergoes a massive transformation to ferrite, which does not require diffusion of Cu atoms. After this massive 18 transformation s-Cu would precipitate from solution. If the steel is further cooled below the T0 line a martensitic transformation will occur. 1300 0 1 2 3 4 5 Cu content (mass%) Figure 2.5. Illustration of a calculated equilibrium phase diagram of Fe-Cu binary system. The To line for BCC (a) / FCC (y) is also shown on the figure [16]. Cu-bearing HSLA steels that have undergone significant investigation are two HSLA-80 steels. The chemistries of these steels are very similar as shown in Table 2.1. Speich and Scoonover [15] investigated the continuous cooling behavior for HSLA-80 plate with an initial austenite grain size of 10pm. Figure 2.6 shows the CCT diagram generated from 19 their dilatometry experiments. With a 10pm austenite grain size, austenite transforms to low-carbon martensite at a cooling rate of 4300°C/s. At a cooling rate of 1000°C/s, the microstructure referred to as acicular ferrite forms. At cooling rates lower than approximately 100°C/s the majority of austenite transforms to polygonal ferrite, the remainder being acicular ferrite and pearlite. For cooling rates lower than approximately 20°C/s over 90% of the austenite transforms to polygonal ferrite, the remainder being small pearlite colonies [18]. Ref. C Mn Ni Cu Nb P s Cr Mo Al N [15] [18] 0 . 0 3 6 0 . 0 5 0 0 .51 0 . 5 0 0 . 9 5 0 . 8 8 1 . 2 5 1 .12 0 . 0 4 0 . 0 4 0 . 0 0 4 5 0 . 0 0 9 0 0 . 0 0 8 5 0 . 0 0 2 0 0 . 6 6 0 .71 0 .21 0 . 2 0 0 . 0 3 7 0 . 0 2 0 0 . 0 0 9 2 0 . 0 0 9 0 Table 2.1. Chemical composition in wt% of HSLA-80 steel [15,18]. In the temperature range of 700-650 °C small changes in hardness during the formation of polygonal ferrite (PF) were determined to be the result of s-Cu precipitation. This resulted in the designation of the PF + s-Cu zone in the continuous cooling transformation diagram. No evidence of Cu precipitation was found for cooling rates prior to polygonal ferrite formation. S.W. Thompson et al. [18], found similar results in investigating the austenite decomposition of HSLA-80 plates containing 1.12wt%Cu. Their research produced a CCT diagram similar to that of Speich and Scoonover except they differentiated between many different forms of ferrite and identified the appropriate phase fields for each. 20 Speich and Scoonover reported a hardness plateau for cooling rates between 1.0 to 0.05°C7s, that may be a result of precipitation. However, if one constructs a Hall-Petch plot using data from the research of Speich and Scoonover, as shown in Figure 2.7, it is evident the effect of Cu must be very modest in comparison to the effect of ferrite grain size. 1.0C0 800 U 600 ui GC 3 < CC tz±± t i t Z COMPOSITION. WT. %: - 7\ ' I I - 0.036 C. 0.51 M n . 0.34 Si . 0.66 Cr. 0.95 Ni - 0.21 Mo . 1 25 C u . 0.04 Nb. 0.04 Al. 0.009 N 400 200 AUSTENIT1ZED FOR 30 min AT 898X AUSTENITE GRAIN SIZE: 10 1.600 1.200 0.01 J i_U A c , : 720 C -A c , : 890X -A a , : 828°C : 10 100 TIME. S E C (below A* , ) 1.000 10.000 100.000 Figure 2.6. Continuous cooling transformation diagram for a HSLA-80 steel [18]. 21 Figure 2.7. Hall-Petch plot for HSLA-80 steel studied by Speich and Scoonover [15]. 2.2 Transformation Modeling 2.2.1.1 Fe-C System In order to study the phase transformation kinetics of low-carbon steels one must understand the underlying principles controlling this process. Consider the portion of the Fe-Fe3C phase diagram shown in Figure 2.8. Low-carbon steels have a carbon composition of 0-0.25wt%C. This is a hypoeutectoid composition and proeutectoid ferrite forms prior to the pearlitic transformation. 22 1000 u 800 ki <u Cu 6 H 600 400 912°C y / 1 3 / + Fe3C 1 a + 7 \ / 727°C " _ a + Fe3C 1 0 1 2 Carbon Concentration (wt%) Figure 2.8. Portion of the Fe-Fe3C equilibrium phase diagram [19]. 2.2.1.2 Fe-C-Cu-X Systems The low-carbon steels used in this study are Fe-C-Cu-X multicomponent systems with a complex equilibrium phase diagram, where X can be a combination of Ni, Mn, Cr, Al, etc. Although the phase diagram for such a system will be different from that shown in Figure 2.8 for the Fe-C system the latter is still of help to illustrate the principles of phase transformation in these complex systems. 23 Elements such as Ni, Mn, and Cu are austenite stabilizers that increase the size of the austenite phase field, thus lowering the Ae3 temperature, TA e 3. Ferretizing agents such as Cr and Al have the opposite effect, reducing the austenite phase field and raising the temperature where proeutectoid transformation begins. For example, Mn will change the position of the Ae3 line on the equilibrium Fe-C phase diagram, as shown in Figure 2.9. Many studies have been performed to determine the T A e 3 temperatures for low-carbon steels having complex compositional systems. Andrews [20] proposed an empirical approach based on experimental observation, TAe3 (° O = 912 - 203VC -15.2Ni + 44.7'Si +104V + 3\.5Mo + 13.IFF - 30M« (3) -1 lCr - 20Cw + 700P + 400,4/ + 120,4s + 40077 where all compositions are in weight percent. A somewhat different approach was taken by Kirkaldy and Baganis [21] where the T A e 3 temperature in multicomponent systems was calculated using thermodynamic data from a large amount of Fe-X and Fe-C-X systems. For a limited alloy compositional range this method was found to be highly successful in predicting T A e 3 for the purpose of constructing TTT and CCT diagrams. 24 1200 g 3 1100 . k i O H 6 H 1000 0.0 0.5 1.0 Carbon concentration (wt%) Figure 2.9. Set of constant Mn sections through the Fe-C-Mn phase diagram showing the change in position of the T A e 3 line with increasing Mn content [22]. 2 . 2 . 2 Austenite Decomposition The Fe-Fe3C phase diagram can be used to predict what phases will be present in the final microstructures of these steels. Low-carbon steels will have a high degree of proeutectoid ferrite formation and as such will be primarily polygonal ferrite with small cementite colonies. This microstructure will develop only when cooling rates are slow enough to encourage the formation of equilibrium phases. At higher cooling rates the ferrite will change from a polygonal structure to non-polygonal structures. Further increases in cooling rates may promote the formation of bainitic or martensitic structures. 1.0wt%Mn \ \ X 0wt%Mn 25 2.2.3 Ferrite Nucleation and Growth Austenite decomposition is a process of nucleation and growth. During nucleation small clusters of atoms will combine to form nuclei of the new phase at energetically favorable sites. For austenite decomposition these sites would consist of grain corners, edges, and boundaries. Cahn [23] proposed that grain corners are the most favorable sites for nucleation followed by grain edges and grain boundaries. Cahn's prediction was confirmed experimentally by Enomoto and Aaronson [24] for ferrite nucleation at prior austenite grain boundaries. Enomoto and Aaronson also investigated the thermodynamics describing ferrite nucleation at grain boundaries. Their study compared the use of bulk equilibrium composition and critical nucleus composition to calculate the free energy of activation for a ferrite nucleus at a grain boundary. Using classical nucleation theory they developed equations describing the nucleation of ferrite nuclei for paraequilibrium and orthoequilibrium conditions for Fe-C-X alloys [25]. In paraequilibrium it is assumed that carbon is in equilibrium in austenite and ferrite and the ratio of alloying element X and Fe in the Fe sublattice, is the same in both. In orthoequilibrium it is assumed that all elements are in equilibrium in both austenite and ferrite. These two approaches were studied using classical nucleation theory where the time-dependent nucleation rate is given by: 26 J* = Nfi*Zexp -( AG*} ( T) exp.— (4) I kT ) V t) where N is the density of viable nucleation sites, p* is the frequency factor, Z is the Zeldovich nonequilibrium factor, AG* is the free energy of activation for formation of a critical nucleus, T is the incubation time, t is the isothermal reaction time, and kT has its usual meaning. The minimum free energy of activation for formation of a nucleus can be found using a pillbox type model, with one coherent broad face, another broad face lying in the grain boundary plane and one small incoherent face. This type of nucleus shape, shown in Figure 2.10, is used to minimize interfacial energies. The interfacial energy crcr is for the low energy coherent broad face and <7ar is the interfacial energy of the high energy incoherent face. Using the pillbox model and Equation 5, classical nucleation theory was successfully used to describe isothermal nucleation of ferrite at austenite grain boundaries in some low-carbon steel grades examined. C ay c ay Figure 2.10. The pillbox nucleus model [25]. 27 Nucleation and growth occur simultaneously with new nuclei spawning at preferential nucleation sites even as old nuclei are growing. The relationship between nucleation and growth rates with respect to temperature is shown in Figure 2.11. Both, nucleation and growth rates, increase as temperature decreases and appear to reach their maximum value at 550°C. The shape of this curve will be dictated by the interplay between driving force and mobility. As temperature decreases the driving force, caused by undercooling, for nucleation and growth increases while the mobility, controlled by diffusion, decreases. Presumably if Figure 2.11 were extended below 550°C we would see a typical ' C shaped curve because mobility will continue to decrease even as driving force increases thus decreasing nucleation and growth rates. This interaction between driving force and mobility is also responsible for the classical ' C shaped curve of TTT diagrams. The growth of ferrite is controlled by long range carbon diffusion in austenite. The equilibrium fractions of ferrite and austenite at any point can be determined by using the Fe-Fe3C phase diagram and the lever rule. This can be expressed by: Xf(T) = - L - ^ (5) r a where C 0 is the initial carbon concentration, and C a and CY are the carbon equilibrium concentrations in the ferrite and austenite phases, respectively. To describe the ferrite growth kinetics, it is usually assumed that there is local equilibrium at the cc/y interface. Then, we can use the equilibrium carbon concentrations to construct a plot of carbon 28 concentration normal to the advancing interface, as shown in Figure 2.12. CJaand CaJ are the concentrations of carbon in austenite and ferrite at the a/y interface and C 0 is the bulk concentration. As ferrite grows the effective diffusion distance, L, changes from L,! to L 2 . Therefore carbon must diffuse a longer distance away from the interface for growth to continue. Since the effective diffusion distance is increasing with time the growth rate must decrease with time. u 3 ca i— u Ou g 725 700 650 600 550 RATE OF NUCLEATION « ^ RATE ^ \ \ \ . \ \ \ DF GROWTH \ \ \ \ j io-; 10^ io-3 Rate of Growth (mm/sec) io-: 10-' 10-4 10-2 10° 102 Rate of Nucleation (NUCLEImm2/sec) 104 Figure 2.11. The rate of nucleation and growth with respect to temperature [26]. The growth of ferrite is generally assumed to be one dimensional with thickening of ferrite plates starting from the austenite grain boundaries [24,25,27]. The growth rate of ferrite is parabolic with time and thus the growth rate of ferrite will be proportional to the inverse square root of growth time. This growth law is valid until impingement of the 29 product regions occurs. In the case of the y-»a phase transformation this impingement takes on two forms. The first, termed soft impingement, occurs when the diffusion fields ahead of the advancing a/y interface overlap thus reducing the rate of carbon diffusion because of carbon saturation. The second impingement is termed hard impingement. This occurs when the growing ferrite grains physically contact each other along newly formed ferrite grain boundaries. Figure 2.12. Carbon concentration profile normal td the advancing a/y interface [17]. Zener has studied the parabolic growth rate [28]. Assuming planar growth geometry and using Zener's linearized concentration gradient: 30 Rp=a/A (6) is obtained where R,, is the planar half thickness of the ferrite at time t and a,, is the parabolic rate constant that is given by: here Drc is the diffusion coefficient of carbon in austenite and CaJ and are the carbon concentrations in ferrite and austenite at the a/y interface respectively. Kamat et al [29] developed a model to describe ferrite growth, assuming nucleation site saturation at austenite grain boundaries and long-range carbon diffusion is rate controlling. This model adopts spherical growth geometry with the diameter of the sphere representing the austenite grain size; ferrite grows radially inwards from the outer surface to the center. Relationships describing the temperature and carbon concentration dependence of the carbon diffusion coefficient in austenite are incorporated into the model. Diffusion for spherical growth geometry is described by: ?£. = L[,yc?£\m.?£. ( 8 ) dt dr\ dr) r dr 31 where r is the radial distance. The effect soft impingement was incorporated by assuming that the center of the austenite grain is a point of zero mass transfer at which the carbon content increases as ferrite grows. The ferrite growth velocity was derived by applying a mass balance at the a/y interface, taking into account the diffusion gradient at the interface: increasing the gradient at the interface increases the flux across the interface and, thus, the growth velocity [29]. This original growth model was modified by Militzer et al. [30], to include the effects of a Mn solute drag-like effect. Because the solid solubility of Mn is higher in austenite than in ferrite one can assume that there will be Mn solute redistribution at the a/y interface. As a result, a Mn spike may form at the interface which will slow carbon diffusion and the movement of the ct/y interface. 2.2.4 Acicular Ferrite Growth Increasing cooling rates and/or large austenite grain sizes produce non-polygonal ferritic structures by shifting the transformation to lower temperatures. These ferritic structures can take many forms including acicular ferrite or Widmanstatten ferrite. Widmanstatten ferrite grows directionally normal to the austenite grain boundaries and has an orientational relationship with the prior austenite grains as described by the Kurdjumov-Sachs relationship [17]. In this work all forms of ferrite that are not equiaxed will be referred to as irregular ferrite. 32 Many different mechanisms have been proposed to have an effect in ferrite plate growth. The growth rate of these ferrite plates does not precisely follow a parabolic rate law, as shown in Figure 2.13. Growth of these ferrite plates may be a result of a ledge mechanism where ferrite plates grow by the migration of multiple ledges [31]. The effect of ledge migration can account for the deviations seen in Figure 2.14 from a parabolic rate law. However, There are indications that diffusion still plays an important role in this transformation. Indeed, some attempts to mathematically express the growth of ferrite plates have followed a diffusion-controlled approach. 3 'JH — 0 0 ° c > Fe-0.22%C 1 1 710°C 1 1 1 0 1 2 3 4 5 6 Growth time (s) Figure 2.13. Growth of ferrite plates in a Fe-0.22wt%C alloy at 710°C [12]. 33 2.2.5 Bainitic Growth A combination of very high cooling rates and large austenite grain size will promote the formation of bainite colonies in the microstructure of low-carbon steels. Bainite consists of ferrite and cementite phases in the form of needles or plates [19]. The morphology of bainite is affected by temperature with upper bainite forming in the temperature range of 550-400°C and lower bainite at 400-250°C [12]. There has been some controversy as to the mechanism of bainite growth. Bainitic growth is very similar to the growth of acicular ferrite in that it is irregular with respect to time and is directional with a Kurdjumov-Sachs relationship with the prior austenite grains. Many theories have been prepared for the transformation mechanism of bainite varying from displacive, diffusionless transformation mechanism to ledgewise diffusional growth [32]. There is evidence for both mechanisms but because ferrite and cementite are both present in bainite; however, more weight is usually given to the theory of diffusional controlled growth when at higher temperatures. Zener and Hillert [33] proposed a model for the growth of bainite for which carbon diffusion from the tip of the lath is rate controlling. When the tip of the bainite lath has a curvature of radius rc, carbon content Crra in austenite at the cc/y interface changes depending on interfacial energy and becomes lower than Cy determined by the Ae3 line in the phase diagram. The growth rate G B of the bainite lath can be calculated by determining r and CY" in such a way that G B is maximized as follows, 34 2rc I Cr ~ C« (9) Volume fraction of bainite is calculated by the following equation. dX. B = kBGB{\-X) (10) dt The parameter kB can be determined from kB=1.278xl0"2exp(3431.5/T) for low-carbon steels having composition Fe-0.l~0.2wt%C-l.0wt%Mn [32]. 2.2.6 Avrami Equation Empirical equations have been used to describe many time-temperature dependent solid-state processes. The isothermal austenite decomposition can be described using Johnson-Mehl [34]-Avrami [35,36,37]-Kolmogorov [38] (JMAK) model, popularly known as Avrami equation: X = l-exp(-bt") (11) 35 where b and n are fitting parameters. This empirical relationship has been successfully applied to various phase transformation processes. The value of the exponent n is geometrically significant. For 3<n<4 the growth is three-dimensional. Similarly for 3<n<2 and 2<n<l the growth is assumed to be two-dimensional and 1-dimensional respectively. Some typical n values for ferrite growth in low-carbon steels are shown in Table 2.2. Steel Designation n 1010 [39] 1.00 1020 [40] 1.17 1025 [41] 1.33 DQSK [54] 0.90 A36 [54] 0.90 Table 2.2. Comparison of n values used in Avrami equations by various researchers. 2.2.7 Grain Size Modified Avrami Equation In an effort to further link the empirical Avrami equation to the y—»cc transformation it has been attempted to modify the Avrami equation to account for prior austenite grain size [42]. This grain size modified Avrami equation is expressed as, 36 X = 1 - exp V dr J ; 6 = - ^ - or \nb = \nkA-m\ndr (12) dr where dy is the austenite grain size, and kA now holds the temperature dependence of the equation. 2.2.8 Umemoto Equation A similar empirical approach was taken by Umemoto et al. [43] who investigated phase transformation kinetics in 0.2 and 0.43wt%C low-carbon steels. Experimentally it was found that the Avrami equation predicted faster transformation rates than those observed. It was proposed this was due to soft impingement. The Umemoto equation takes this impingement into account by multiplying the Avrami equation by (1-X)P, as follows: — = {nbt"-x\\-XY (13) dt where experimentally it was found p=0.5. 37 2.2.9 Application of Isothermal Kinetic Equation to CCT The Avrami equation has been applied successfully to many isothermal processes; however, many heat treating and quenching processes used in steelmaking are performed under continuous cooling conditions. Under these conditions the phase transformation kinetics will not only depend on steel alloy composition and prior austenite grain size but also the cooling path. Sheil [44] proposed that the amount of undercooling and the incubation time of nucleation are related. He assumed that the incubation time could be divided into isothermal steps during which a fraction of the total isothermal incubation time is consumed. When the sum of all of these fractions reaches unity the transformation begins. Thus, if t, is the time spent at a given isothermal stage and x, in the isothermal incubation time corresponding to that temperature, the fraction consumed isothermally is given by: Summing this relationship over the entire incubation time and taking the limit where AT—»0 yields the additivity rule or Sheil Equation: t, (14) (15) 38 This additivity rule can also be applied to describe the transformation behavior during continuous cooling conditions. The application of the additivity rule to continuous cooling conditions requires that for each isothermal step the rate of transformation is a function of the current temperature and fraction transformed, and not of the thermal history. This creates a concept that the evolution of microstructure has no 'memory' and thus is only a function of the current temperature and fraction transformed. This concept known as the additivity principle is displayed visually in Figure 2.14 where the line represents a continuously decreasing temperature gradient and the boxes represent isothermal fractions. The first time step At, is the time between 0 and t, and T, is the isothermal temperature in the time step. The fraction transformed during At, is AX,. The new AX2 for the next time step at temperature T2 is calculated using kinetic information corresponding to At2. T=hvJi Atj At2 At3 At4 Figure 2.14. Schematic of the isothermal stepping of continuous cooling transformation curves. 39 In order to utilize the additivity principle for this specific application one must determine whether or not the process being modeled is additive. One method for this analysis was proposed by Christian [45]. Christian postulated that the additivity principle can be applied when the transformation can be described by two separable functions, one in terms of fraction transformed and the other in terms of temperature, <K = LW1 (i6) dt G(X) where G(X) and H(T) are separable parts of the equation describing the functions of transformation and temperature. In the Avrami equation this leads to n being a constant and the equation being applicable to non-isothermal conditions. If the transformation is separable according to Equation 16 the total time to reach a specified fraction transformed under continuous cooling conditions is obtained by adding the fractions of time to reach this stage isothermally until the sum reaches unity [29]. 40 3 Objectives and Scope There are two main objectives of this work: (1) to understand the role Cu plays for the phase transformation kinetics, resulting microstructure, and mechanical properties of low-carbon steels, (2) to develop empirical and fundamentally based models to describe the microstructural development during austenite decomposition of these steels. Steel chemistries have been chosen to be equivalent to the residual level of Cu in today's steel scrap as well as the level that may be present in a heat treatable steel alloy. The study emphasizes the simulation of industrial processing conditions. Due to the low carbon levels of the steel used it is impossible to perform isothermal experiments to determine the phase transformation behavior of these steels. Therefore steel alloys containing 0.05 to 0.8wt%Cu are subjected to continuous cooling experiments only. The final microstructure of these steels is examined to determine the role of Cu content on microstructure. Results are used to apply models to predict T A e 3 , transformation start temperature, ferrite growth, and ferrite grain size. Hardness measurements are used to determine the mechanical properties of these Cu-bearing steels. Hall-Petch relationships will be used to explain the effect of Cu on mechanical properties. 41 4 Experimental 4.1 Materials The compositions of the three aluminum killed low-carbon steels investigated are shown in Table 4.1. Dofasco (Hamilton, Ontario) provided all steels as forged bars from laboratory heats. tirade u win 5 UU Nl H — N #1 0.005 0.I&0 0.00B (3.80 u.oyb o.ooy 0.057 0.0060 #2 0.065 0.307 0.006 0.40 0.098 0.010 0.035 0.0037 #3 0.061 0.320 0.007 0.05 0.130 0.009 0.046 0.0043 Table 4.1. Chemical compositions of steels investigated (in wt%). The third grade has the chemistry of a commercially product which is used in basic consumer goods such as refrigerators and stoves. The first and second grade were o produced by adding 0.8wt% and 0.4wt% copper, respectively. The 0.4wt%Cu grade is representative of a high copper steel produced by an EAF facility. The 0.8wt%Cu grade steel was made to determine the effects of higher copper levels in low-carbon steels. 42 4.2 Experimental Techniques 4.2.1 Preliminary Grain Growth Experiments In order to determine the effect of prior austenite grain size it was important to determine reheating conditions to produce a variety of homogeneous austenite microstructures which can be represented by their mean grain size; bimodal (non-homogeneous) microstructure resulting from abnormal grain growth would not be suitable. At least three different grain sizes are required for each composition to investigate the effect of prior austenite grain size. A basic metallurgical furnace was used to determine the combinations of temperature and time needed to produce the necessary austenite microstructures. The experimental set-up is shown in Figure 4.1. The samples used were 3mm x 5mm x 6mm. A type K thermocouple, NiCr-NiAl, was spot welded onto the specimen to record measurement data. The tube was purged with He for 5 minutes before inserting into the furnace and the start of heating. The He atmosphere was maintained during the experiment to prevent oxidation. 43 Furnace H Figure 4.1. Apparatus for preliminary grain growth experiments. Heating rates are approximately 2-3°C/s. Because the heating of the specimen followed a natural heating curve it was important to determine at what temperature the time of reheating would begin. For these preliminary experiments the reheat start time was determined to be the time at which the sample was within ±5°C of the reheat temperature. Conditions of time and temperature used in these experiments are shown in Table 4.2. Temperature Time (°C) (s) 950 0,120,300 1000 0,120,240,420 1050 0,120,240,420 1100 0,120,240,420 Table 4.2. Temperatures and times used in preliminary grain growth experiments. 44 After holding at the specified temperature and time the specimens were water quenched to preserve the prior austenite microstructure for analysis of austenite grain size. 4.2.2 Gleeble Grain Growth Experiments Although it was possible to determine reheat conditions to produce homogeneous austenite microstructures from the furnace tests, confirmation of these results using the Gleeble 1500 Thermomechanical Simulator was necessary due to different heating rates to holding temperature. The Gleeble uses resistive heating with a constant heating rate of 5°C/s whereas furnace tests w i l l not have a constant heating rate. Using the results of the preliminary grain growth experiments it was possible to minimize the amount of work required in the Gleeble. Figure 4.2 displays the specimen chamber of the Gleeble and the basic components of the chamber. The experimental conditions of time and temperature used in the Gleeble are shown in Table 4.3. Temperature Time (°C) (s) 950 120 1100 300 1150 120 Table 4.3. Experimental conditions of temperature and time used in Gleeble grain growth experiments. 45 Figure 4.2. The specimen chamber and basic components of the Gleeble 1500 thermomechanical simulator. The samples used in these experiments were of dimensions 3mm x 5mm x 15mm. Sample design is shown in Figure 4.3. A Pt-PtRh thermocouple was spot welded on the center of the outer surface of the specimen. Samples were reheated at 5°C/s to the specified temperature, held for the required time, and water quenched. mid-plane Figure 4.3. Sample design used in Gleeble grain growth experiments. 46 4.2.3 CCT Experiments Continuous cooling transformation (CCT) experiments were performed using the Gleeble 1500 Thermomechanical Simulator. These experiments simulate the cooling conditions present in the production of both steel strip, on a hot strip mill run-out table, and steel plate, with natural cooling. Cooling rates ranged from l-250°C/s. These cooling rates were produced by using a combination of resistive cooling (<10°C/s), air or natural cooling («20°C/s), and helium quenching (>20°C/s). Specimen design for the continuous cooling experiments is shown in Figure 4.4. The combination of a thin walled specimen and tubular design is very advantageous because the passing of helium through the center of the specimen can produce high cooling rates and the thin wall ensures that thermal gradient will be minimized, thus producing no microstructural gradients. A similar specimen design has been proven to obey Newtonian cooling conditions according to the Biot number (Bi < 0.1) [29]. A Pt-PtRh thermocouple was spot welded at mid length on the outer surface of the specimen. The experimental design for the CCT experiments is very similar to the one shown in Figure 4.2. Resistive heating is provided through the grips of the Gleeble to the specimen. Temperature is continuously recorded and controlled using the thermocouple spot welded in the center of the specimen. A dilatometer is positioned on the mid-plane 47 of the specimen to continuously record the volume change in the same cross sectional plane as the thermocouple. The experimental design incorporates a spring mechanism to avoid specimen deformation. If the specimen were held rigid between the grips heating the specimen and associated volumetric expansion would create deformation along the length of the specimen. This deformation would be recorded by the dilatometer and could be misinterpreted as the diametric response caused by phase transformation. The spring design ensures that the specimen can expand without deformation to the specimen. The data recorded through use of the dilatometer is then only associated with thermal expansion of the specimen and phase transformation but not deformation. 1mm wall thickness mid-plane Figure 4.4. Specimen design for CCT experiments using the Gleeble. The mid-plane diametral dilation of the specimen due to thermal expansion or contraction during heating or cooling and the volume changes occurring during the y - » a transformation were monitored by a Linear Variable Differential Transformer ( L V D T ) crosswise strain device. To minimize oxidation during the experiment, the test chamber was evacuated to a pressure of less than 3Torr, and then back filled with high purity argon gas. This procedure was repeated before each test commenced [46]. 48 The specimen reheat and cooling schedule is shown in Figure 4.5. Specimens were reheated at 5°C/s to the reheat temperature where they were held for the specified time to obtain the desired austenite grain size. After each reheat condition the specimens were air-cooled at approximately 20°C/s to 900°C and held for 30s. This 30s time period was used to ensure that all specimens, regardless of reheat time and temperature, were at one homogenization temperature before continuous cooling. Figure 4.5. Heating and cooling schedule of C C T experiments. Figure 4.6 displays an example of the diametric response for the 0.05wt%Cu steel. The bold curved dark line is the diametric response recorded during the experiment. The slope of the linear extensions regions above 810°C and below 650°C correspond to the austenite and ferrite linear thermal expansion coefficients, respectively. The region between these two linear sections reflects the volume expansion associated with the y—>a transformation. For the thermal expansion in this two-phase region, a law of mixtures is assumed: Time 49 aMix=aaFx+ar{\-Fx) (17) where F x is the fraction of austenite transformed and c c a and Oy are the thermal expansion coefficients of ferrite and austenite respectively. 0 . 0 3 5 0 . 0 3 c o 0 . 0 2 5 J S Q 0 . 0 2 0 . 0 1 5 0 .01 5 5 0 6 5 0 7 5 0 8 5 0 Temperature (°G) Figure 4.6. The diametric response of the 0.05wt%Cu steel for the air cooling condition with austenite grain size of 22pm. Then, the diametric response D(T) displayed in Figure 4.6 can be used to determine the fraction transformed of austenite F X (T) as follows: FX{T) = D{T)-Dr(T) Da(T)-D(T) (18) 50 where Dr=Dr(TrQ) + ar(T-Tr0) (19) and Da=Da(Ta0) + aa(T-Ta0) (20) are the extrapolated linear dilations from the untransformed and fully transformed regions, with TY0 and T a o being selected temperatures within these two regions. The transformation start and finish time and temperatures were taken to be the points of 5% and 95% transformed respectively. Because the cooling rate will change during the transformation of austenite to ferrite, due to recalescence, it is important to define a consistent method for measuring the cooling rate for each experiment: For the experiments performed the cooling rate was measured by finding the slope of time vs. temperature at ±20°C of the T A e 3 temperature. 5 1 4.2.4 Microstructural Techniques Austenite grain growth specimens were cut on the mid-plane and the microstructure was examined in cross-section. The samples were mounted in a resin polymer and ground progressively using 60 to 600 grit grinding media. The samples were then polished to a lpm finish. In order to determine the prior austenite grain size an etchant is used consisting of 2mg of picric acid, lmg of HC1 and lmg of dodecylben zenesulfonic acid in Figure 4.7. Example of prior austenite microstructure produced by furnace and Gleeble grain growth experiments. 52 100ml of water. Samples were etched for a period of 3-6 minutes to reveal the prior austenite grain boundaries. The etchant reacts with the steel to display the proeutectoid ferrite on the prior austenite grain boundaries in white and the prior austenite grains, in the form of bainite and martensite, as dark gray. An example of the austenite microstructures revealed by this etchant is shown in Figure 4.7. Microstructures were examined for grain size using a C-Imaging System image analyzer. Polished and etched specimens were photographed either using the CCD camera of the imaging system or a basic metallographic microscope and black and white film. The microstructures were traced using transparency film for examination of austenite grain size. Depending on the microstructure produced it was sometimes difficult to determine the location of austenite grain boundaries. The following assumptions were used to interpret the austenite microstructure [47]. (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 method used for measuring austenite grain size was the Jeffries method. Using this method all grains wholly contained in the field of measurement are counted as one grain and those grains cut by the border of the field of interest are counted as Vi of a grain. This is in accordance with ASTM specification El 12-88 [48]. Knowing the number of grains for each field of interest it was possible to determine the average equivalent area diameter 53 (EQAD) grain size, in um, by dividing the total area of the field of interest by the number of austenite grains. In order to ensure statistical relevance at least 300 grains were examined for austenite microstructures. The measured EQAD was converted to a volumetric grain size for use in diffusion modeling by employing the relationship dV0l=1.2dEQAD [47]. All reported grain sizes have been converted to volumetric diameter measurements unless otherwise specified. Ferritic microstructures produced by the CCT experiments were examined using similar methods as those used to analyze austenite grain growth specimens. Samples were cut along the cross section within 1mm to the mid-plane of the specimen. The samples were mounted in a polymer resin and ground and polished. The 1mm of extra material was removed during the grinding and polishing process in order to examine the cross-section for which diametric and thermal data were recorded. Samples were etched using a 2%nital etching solution for approximately 10-15s. Because these microstructures contain small colonies of cementite it is necessary to determine the fraction of the microstructure that is ferrite. Ferrite fraction was measured by averaging the ferrite fraction of 50 fields for each specimen. Knowing what fraction of the microstructure is ferrite it is then possible to determine ferrite grain size. This was measured for at least 500 grains using the C-Imaging System and tracings on transparency film of the ferrite grain boundaries. The Jeffries method was used but the EQAD was determined by dividing the area of the field of interest by the number of grains and then multiplying the quotient by the ferrite fraction. 54 4.2.5 Hardness Measurements In order to link microstructure characteristics to mechanical properties microhardness measurements for CCT specimens were performed. A Beuhler Microhardness tester was used with a diamond Vickers indentor, lOOg load, and 15s dwell time. At least ten measurements were taken for each sample and averaged to determine the hardness of the specimen and the hardness variability (standard deviation) throughout the specimen. All measurements are given according to the Vickers (HV) scale. 55 5 Results 5.1 Austenite Grain Growth 5.1.1 Preliminary Grain Growth Experiments In the steels examined abnormal grain growth may occur due to dissolution or coarsening of A1N particles. These particles pin the grain boundaries thereby inhibiting grain growth. During dissolution some grain boundaries become unpinned earlier than others causing selected grains to grow. As a' result bimodal microstructures with large grains and colonies of significantly smaller grains develop temporarily until the larger grains have consumed all the small grains. In order to produce homogeneous microstructures one must determine the combinations of time and temperature for which abnormal grain growth occurs and avoid them. Figure 5.1 displays the austenite grain sizes (EQAD) for the 0.05wt%Cu steel for all reheat condition indicating the regions of abnormal grain growth. The grain growth behavior of all three steels was very similar. It can be seen from this figure that abnormal grain growth regions occur after approximately 6min holding at 1000°C, after 2min of holding at 1050°C and for the first 4min at 1100°C. Based on this data it was determined that a reheat condition of 2 minutes at 950°C would produce a homogeneous austenite grain size of approximately 56 20pm with all A1N precipitated. Reheating at 1100°C for 5 minutes would produce a homogeneous austenite grain size of approximately 60-75 um. From the results at 1100°C it was inferred that reheating at 1150°C for 2minutes would produce a homogeneous austenite grain size greater than 100pm. Complete data for preliminary grain growth experiments can be found in the Appendix. 0 2 . 4 6 8 10 Time (minutes) Figure 5.1. Results of furnace grain growth experiments showing temperature and time combinations that cause abnormal grain growth. 5.1.2 Gleeble Grain Growth Reheat conditions, as specified by preliminary tests, were verified by performing grain growth tests in the Gleeble. The results of these grain growth experiments are summarized in Table 5.1. The three reheat conditions produced three different classes of austenite grain sizes; a small austenite grain size of average 21pm, a medium austenite grain size of average 72pm, and a large grain size of average 148pm. These three reheat 57 conditions were selected for subsequent CCT tests. Hereafter the three grain size classes will be referred to as small, medium, and large austenite grain sizes. It is possible that the differences in austenite grain size between the three copper grades may be caused by the differences in Al, N, and C contents but further work would be necessary to verify this. The error in austenite grain size measurements is approximately 25-30%. Steel Reheat Condition (wt%Cu) 2min@950°C 5min@1100°C 2min@1150°C 0.8 20(um) 75(um) 152(um) 0.4 20(um) 77(um) 170(um) 0.05 22(um) 65(um) 121(um) Table 5.1. Results of Gleeble grain growth experiments. 5.2 CCT Experiments 5.2.1 Phase Transformation Kinetics 5.2.1.1 Effect of Cooling Rate The cooling rate can have a pronounced effect on the phase transformation kinetics of these steels because increasing the cooling rate requires higher undercooling for the transformation to occur. Figure 5.2 displays the fraction transformed vs. temperature plot for the 0.05wt%Cu steel with an austenite grain size of 22pm. This plot shows that as 58 cooling rate increases the transformation start and finish temperatures, T s and TF, decrease. The steels produced from the small austenite grain size for all cooling rates are approximately 93% polygonal ferrite, the remainder being pearlite. This result is as expected and similar trends have also been found for the other two steels using this combination of cooling rate and y grain size. Complete listings of transformation start and finish times and temperatures can be found in the Appendix. For the experiments performed the error in transformation start and finish temperatures is approximately ±5°C. 600 700 800 900 Temperature (°C) Figure 5.2. Fraction vs. temperature plot for various cooling rates using the 0.05wt%Cu steel with d y = 22pm. 59 5.2.1.2 Effect of Austenite Grain Size Figure 5.3 displays the effect of austenite grain size on phase transformation kinetics for the 0.05wt%Cu steel in the air-cooled condition. From this diagram it can be seen, that the detected dilation change of the specimen is reduced to lower temperatures as austenite grain size increases. The larger austenite grain size lowers the nucleation rate by reducing the austenite grain boundary area per unit volume thus promoting lower measured T s temperatures. Further, ferrite growth requires more time because of longer growth distances. T3 O E (A C c o u (0 625 675 725 775 Temperature (°C) 825 Figure 5.3. The effect of austenite grain size on phase transformation (0.05wt%Cu cooled at 16°C/s). 60 5.2.1.3 Effect of Cu Copper content has been found to have an effect on the phase transformation even at these relatively low levels. Figure 5.4 displays the effect of Cu on phase transformation kinetics for steels with small y grain sizes in the air-cooled condition. Increasing the Cu content from 0.05wt% to 0.8wt% decreases the Ts by an average of 19°C. This reduction in Ts is consistent with the reduction in Ae3 temperature expected for increasing Cu content. The result that transformation start temperature is a function of Cu content is in good agreement with the literature [13,16]. Temperature (°C) Figure 5.4. Effect of Cu on phase transformation kinetics (air-cooled condition). 5.2.2 Microstructure 61 5.2.2.1 Effect of Cooling Rate As illustrated in Figure 5.5 for the 0.05wt%Cu steel, with a starting austenite grain size of 22pm, increasing the cooling rate causes a ferrite grain size refinement of the polygonal microstructure. Cooling rates of 1, 16 (air-cooling), 69, and 215°C/s produce ferrite Figure 5.5. Polygonal ferritic microstructures produced for a 0.05wt%Cu steel having an austenite grain size of 22pm. grain sizes of 25, 19, 11, and 8pm, respectively. This trend was also confirmed for the two Cu-bearing steels. Increasing the cooling rate requires higher undercooling to initiate 62 the transformation. A higher driving force for phase transformation is associated with higher undercooling which leads to more ferrite nuclei promoting ferrite grain refinement. 5.2.2.2 Effect of Austenite Grain Size Austenite grain size plays an important role in the formation of microstructural phases because it dictates the amount of grain boundary area available for the preferential nucleation of ferrite [24]. Thus, with smaller austenite grain sizes we will have more ferrite grains form per unit volume, a trend that can be seen in Figure 5.6. A combination of large austenite grain size and high cooling rate may result in the formation of microstructural phases other than polygonal ferrite. Consider the microstructures shown in Figure 5.7. These microstructures were created using the 0.4wt%Cu steel and an austenite grain size of 170pm. Higher cooling rates promote the formation of ferrite colonies or branches with directional properties. These non-polygonal ferrite colonies will have different mechanical properties than a polygonal ferrite microstructure. At the highest undercoolings it may be possible to form bainite colonies. The polygonal structures formed at cooling rates <20°C/s were observed to have an average ferrite fraction of 90% and slightly irregular structure. The ferrite grains formed were not all equiaxed. This indicates that the microstructures formed during controlled cooling of an initial austenite microstructure with medium or large grain sizes are different than those formed from the small grain size, which led to highly equiaxed 63 ferrite grains. Although visually they appear very similar, polygonal ferrite grains formed from larger austenite grain sizes may have non-polygonal characteristics. Figure 5.6. The effect of austenite grain size on polygonal ferrite formation. Micrographs shown are for the 0.05wt%Cu steel and 9 = l°C/s. Caption shows austenite grain size. 64 Figure 5.7. Microstructural evolution for large austenite grain size and various cooling rates. Micrographs shown are that of 0.4wt%Cu steel with 170pm y grain size. 5.2.2.3 Effect of Cu Copper has been known to cause ferrite grain size refinement [14]. The degree of refinement is dependent upon the copper content, as shown in Figure 5.8. This diagram displays the effect of Cu and cooling rate on final ferrite grain size for all three steel grades with and average austenite grain size of 20pm. From this diagram it is evident 65 that an increase from 0.05wt% to 0.4wt% produces essentially no ferrite grain size refinement in the steel. Only when the Cu content is raised to 0.8wt% does a refinement effect of Cu on ferrite grain size appear. The grain size shifts by approximately l-2pm for cooling rates greater than 20°C/s. Complete data for all polygonal ferrite structures can be found in the Appendix. The fit lines shown in Figure 5.8 are power law equations described by, da = A ^ ( 2 1 ) where cp is the cooling rate, and A and mA are fitting parameters. These parameters are shown for all three steels in Table 5.2. The change in the A and mA parameters show the modest effect Cu has on grain size. Cu (wt%) A m A 0.8 24.0 -0.23 0.4 24.0 -0.19 0.05 24.0 -0.19 Table 5.2. Parameters A and mA used in Equation 21. 66 Cool ing Rate (°C/s) Figure 5.8. Effect of Cu and cooling rate on final ferrite grain size for an austenite grain size of 20pm. 5.2.3 Hardness The hardness of Cu-bearing low-carbon steel will depend on a variety of microstructural features including, Cu precipitation, A1N precipitation, polygonal ferrite grain size (where applicable), and microstructural composition. Hardness data for all experimental conditions are given in the Appendix. 67 5.2.3.1 Polygonal Ferrite The microstructures produced using a small austenite grain size are almost fully ferritic («93%) with a polygonal ferrite microstructure. The error in measuring the hardness of polygonal microstructures is approximately ±8%. A Hall-Petch plot is shown in Figure 5.9 to display the effect of ferrite grain size on hardness. As grain size increases, the hardness decreases, and therefore the yield strength of the alloy will also decrease. Examining this graph one can see that there is no discernible effect of Cu on 170 T • , Figure 5.9. Hall-Petch plot for polygonal ferrite microstructures produced using an austenite grain size of 20pm. 68 the hardness of these steels. The higher hardness of the 0.8wt%Cu steel of 121HV at l°C/s as compared to 110HV and 109HV for the 0.4wt%Cu and 0.05wt%Cu steels can be accounted for by the finer ferrite grain size. There is no measurable strengthening effect of Cu precipitation. For larger austenite grain sizes (>20pm) it was possible to create polygonal grain structures only at slow cooling rates. The error in measuring the hardness of these microstructures is less than ±11%. Consider what happens when data for non-polygonal structures is compared to the linear Hall-Petch relationship developed in Figure 5.9 as shown in Figure 5.10. These steels do not follow this linear relationship and as such hardness is not a function of ferrite grain size. The reason for this deviation from the Hall-Petch relationship can be traced back to the effects of precipitation and dissolution of second phases and transformation hardening. One could also argue that Cu precipitation could be strengthening the steel at slow cooling rates but from the previous polygonal data it is evident that this effect would be very minor. One major effect on hardening arises from A1N dissolution during reheating and precipitation during cooling. The dissolution and precipitation of A1N particles are time and temperature dependent processes and therefore changing experimental conditions will alter their character in the Fe matrix. When steel is cooled from a high austenizing 69 temperature, 1150°C, all of the A1N particles are dissolved. The particles will reprecipitate at ferrite grain boundaries after phase transformation and thus will not create hardening effects in the matrix. When the steel is reheated to 950°C for 2min it does not allow for dissolution of A1N particles and as such they will remain as coarse particles at the austenite grain boundaries causing no additional strengthening effects. If the steel is reheated to 1100°C for 5min it has just passed the area of abnormal grain growth and as such there may not be sufficient time for all A1N particles to go into solution. Some rather fine particles may survive and can be present inside the ferrite grains. These A1N particles may create hardening effects in these steels. This is one reason for the higher hardness observed in Figure 5.10 for polygonal specimens at higher reheat temperatures. The precipitation of A1N particles during or after the y-»ct transformation can also have an effect on hardness. The precipitation of A1N in solid steel is particularly sensitive to cooling rate and can be suppressed entirely at cooling rates greater than about 65K/min (approximately l°C/s) [49]. The hardening effect of cooling rate and A1N precipitation can be seen in Figure 5.11(a) where hardness values for all three steels at l°C/s are higher than those at slightly faster cooling rates (6-20°C/s). 70 Figure 5.10. Hall-Petch relationship with additional data for polygonal microstructures formed utilizing higher reheat temperatures of 1100 and 1150°C. The second component of this hardness increase is transformation hardening. Even though ferrite grain sizes can be measured at slow cooling rates there is some degree of non-polygonal character to these grains, as shown in Figure 5.6. These non-polygonal ferrite microstructures may cause an increase in hardness. 5.2.3.2 Non-Polygonal Phases The formation of non-polygonal ferrite and bainite does not permit the measuring of ferrite grain sizes. These highly irregular structures will contribute however to the strengthening of the steel. Figure 5.11 displays the effects of cooling rate on hardness for 71 two reheating conditions. At cooling rates greater than air cooling the microstructure is non-polygonal and is increasing in hardness as cooling rate increases. From Figure 5.11(a) it is apparent that austenite grain size and A1N precipitation is affecting the experimental results where the 0.4wt%Cu steel is harder than the 0.8wt%Cu steel at cooling rates greater than air-cooling. The 0.4wt%Cu steel, having an y grain size of 77pm, is slightly harder than the 0.8wt%Cu steel, with an y grain size of 75pm. The smallest y grain size, 65pm of the 0.05wt%Cu steel, has the lowest hardness at every cooling rate. The effect of austenite grain size on hardness is displayed in Figure 5.12. In Figure 5.11(b) where A1N precipitation is less of a factor hardness increases with increasing Cu content. The thermodynamic effect of Cu is lowering T s and TF thus creating more transformation hardening. Another point of interest in Figure 5.11 is the degree of deviation in hardness measurements. Microstructures formed using higher cooling rates have a microstructural composition consisting of varying levels of polygonal ferrite, pearlite, acicular ferrite, and bainite. These structures are not uniformly positioned throughout the specimen and as such hardness measurements will be prone to variability. The standard deviation of hardness measurements is a function of dY. This explains why the variability in hardness measurements is ±8% for polygonal microstructures and ±11% for non-polygonal. 72 Figure 5.11. Hardness vs. cooling rate for (a) 1100°C and (b) 1150°C for three steel compositions. 73 150 i i i i i 0 50 100 150 200 Austenite Grain Size (Mm) Figure 5.12. The effect of y grain size on hardness for all three steel grades cooled at 6°C/s where the symbols are the experimental data and the solid line is the data trend. 74 6 Modeling 6.1 Prediction of TAe3 The transformation start temperatures for proeutectoid transformation, T A e 3 , were calculated using the methods of Andrews [20] and Kirkaldy and Baganis [21]. The results of this analysis are shown in Table 6.1. this table shows that both methods give reasonable T A e 3 temperatures with increases of 13-16°C/s for an addition of 0.8wt%Cu. In this study the T A e 3 temperatures given by the Kirkaldy and Baganis method were used in subsequent analysis since this method employs basic thermodynamic data. Cu (wt%) Andrews Kirkaldy 0.8 852 864 0.4 859 869 0.05 868 877 Table 6.1. T A e 3 temperatures (°C) calculated for each steel using methods developed by Andrews [20] and Kirkaldy and Baganis [21]. 6 .2 AISI Model The work performed in this study has been based on physical parameters found in industrial steel strip and plate production. Modeling the cooling conditions of the run-out 75 table and combining it with the microstructural evolution of the strip is very complex. Recently a model was developed at UBC in partnership with the American Iron and Steel Institute (AISI) and the US Department of Energy (DOE). This model was designed to take into account for all of the processes used during the hot-strip rolling of low-carbon steels in one model that can predict the final properties of the steel strip. One portion of this model is dedicated to predicting the microstructural evolution of the strip while it is travelling on the run-out table. The run-out table of a hot strip mill is the last processing step before coiling of the steel. When the hot band enters the run-out table, from the finishing stands, its temperature is above the transformation start temperature (Ts) for the phase transformation of y -» a. As the strip moves along the run-out table it is cooled by water in the form of water sprays, laminar water banks, or water curtains. These sprays accelerate the cooling rate of the strip. By the time the strip reaches the coiler it is assumed that the steel has completely transformed to a. The run-out table model incorporates three sub-models for microstructural evolution of the steel strip along its thermal history. The first model is used to determine the transformation start temperature of the steel. The second model utilizes Avrami type equations to predict ferrite growth as well as TF. The third part of the model determines the final ferrite grain size. 76 6.2.1 Transformation Start In order to utilize the Avrami equation one must determine the starting point of phase transformation. The Avrami model is used to describe ferrite growth starting from austenite grain boundaries when nucleation site saturation is achieved. The number of nuclei dictates the number of ferrite grains that grow. Nucleation and early growth of ferrite at grain boundaries determines the starting point of the Avrami model, i.e. the measurable transformation start. Militzer et al. [30] have described the model used to predict the start of ferrite growth. The transformation start model of Militzer et al. [30] can be summarized as follows. The start of transformation is the temperature at which 5% of the austenite structure is transformed to ferrite. At 5% transformed no more nucleation occurs and site saturation on the austenite grain boundaries is attained. Ferrite nucleates preferentially at grain corners. Early growth of corner nucleated ferrite determines how much additional nucleation can occur at remaining austenite grain boundary area. Growth of ferrite is controlled by carbon diffusion in austenite. A simple diffusion model is assumed adopting spherical geometry and steady state. The growth rate of corner nucleated ferrite with a radius R/ is given by: dR Car-C0 1 Car~CaRj (22) dt 77 where Drc is the diffusion coefficient of carbon, Cay is the carbon concentration at the a/y interface, C 0 is the bulk carbon concentration and C a is the carbon concentration in ferrite. For constant cooling rate, q>, the integration of this equation for continuous cooling, yields: R , = _ f £ L C -C°dT> < ^ } c ^ _ c a (23) where TN is the nucleation temperature of corner ferrite. There is no ferrite nucleation where ferrite already covers the austenite grain boundaries. But also in the vicinity of the growing ferrite no nucleation takes place because of the higher carbon concentration there. The carbon concentration profile around the growing ferrite grain is given by [58]: C(r) = (C»r _C0) (Rf\ v r J + C0 (24) A limiting carbon concentration, C*, above which nucleation is inhibited is introduced. Consequently, C* defines the radius, r*, around the growing ferrite where no nucleation takes place such that: Car-C, C*-Cn (25) 78 The nucleation site saturation condition is reached when: M/2 = d) (26) where M p is the number of ferrite grain nucleated on grain corners per austenite grain. Combining Equations 23, 25, and 26 yields the equation that can be used to determine the transformation start temperature Ts: 0 j2Mp(car -C°) h Car - C ° , , (27) where usually MP=2 can be assumed. The transformation start model previously developed for a DQSK steel was applied with modifications made for C and Mn composition. This could be done because the DQSK steel used in the previous study is very similar to the current steels under study as shown in Table 6.2. The nucleation temperature used was the transformation start temperature for the slowest cooling rate, l°C/s. G r a d e C Mn S C u Ni A l N DQSK #3 0.038 0.061 0.740 0.320 0.008 0.007 0.02 0.05 0.010 0.130 0.040 0.046 0.0047 0.0043 Table 6.2. Comparison of chemical compositions, in wt%, of DQSK steel and the 0.05wt%Cu steel grade used in this study. 79 Figure 6.1 displays the undercooling to obtain transformation start as a function of cpd1 as suggested by the model. The experimental results for all three steel grades are shown together with the model prediction assuming C*/C0=1.3. From this plot it is evident that no discernable effect of Cu can be detected. The decrease of the transformation start temperature with Cu can then solely be attributed to be a thermodynamic effect; i.e. lowering the TA e 3; no kinetic effect is apparent. The model fit is satisfactory at lower undercoolings but with higher undercoolings there appears to be some deviation. This deviation may be a result of the formation of non-polygonal phases in the microstructure of these steels at high cooling rates. These phases may nucleate and grow via a ledge mechanism rather than by carbon diffusion [31]. To better fit the data a C* value which slightly depends on temperature and y grain size can be introduced. Militzer et al [50] improved the accuracy of grain size predictions for a DQSK steel by using a C* value expressed by C* c + — + d exp - 0.0003(7;-r)2 2 (28) where c, e, and d are fitting parameters unique for each steel studied. Using this equation improvement in T s prediction was achieved. Figure 6.2. displays the predictions for the 0.8wt%Cu steel. Table 6.3. displays the fitting parameters used in Equation 27 for all three steel grades. From this table it can be seen that there is no apparent Cu dependence and this agrees well with the results shown in Figure 6.1. 2 0 - H 1 — i 1 1 1 102 1 03 1 04 1 05 1 0E 107 9dY2, ° C s ' V m 2 Figure 6.1. Comparison of experimental results (symbols) and the prediction (solid line) for the undercooling, required to initiate transformation, as a combined function of austenite grain size and cooling rate. 81 Cu (wt%) c e d 0.8 1.18 5.9 0.16 0.4 1.15 5.45 0.3 0.05 1.18 6.9 0.24 ' Table 6.3. Fitting parameters c, e, and d used in Equation 28 for all three steel grades. Figure 6.2. Comparison of experimental results (symbols) and the prediction (solid line) for the undercooling, required to initiate transformation, as a combined function of austenite grain size and cooling rate for the 0.8wt%Cu steel. 82 6.2.2 Ferrite Growth Many researchers have incorporated phase transformation models in thermal models for run-out table cooling [51,52,53]. Kumar et al. [53] have used a thermal model combined with an Avrami model to describe the thermal history of steel strip using finite difference methods. This Avrami model is used to incorporate the transformation heat generated during the austenite to ferrite transformation into the thermal model. If this heat were neglected in the model the final T f and finish times would be in error. Therefore modeling ferrite growth is not only important from a microstructural stand point but also as it relates to thermal modeling. A similar approach is taken in the AISI model with the ferrite growth being described by Avrami relationships. 6.2.2.1 Differential Form of Avrami Equation In order to apply the Avrami equation it must be modified to account for continuous cooling conditions. Pandi et al. [54] described how this could be done applying the Avrami equation in the differential form: ^ = bY"n[-\n{\-X)p{\-X) (29) 83 Based on Equation 29 and using the experimental transformation data b is calculated as a function of dX/dt and X assuming a constant value for n. Specifically a linear relationship for the natural logarithm of b vs. the degree of undercooling, (TAe3-T) was assumed. This relationship can be used to describe the entire transformation curve or only the ferrite portion. Experimental data plotted using the entire transformation curve using a value of n =0.9 are shown in Figure 6.3. The value of n is chosen so that the data converges in one function of b vs. T for all CCT tests. In the given case, a function of lnb vs. (TAe3-T) can be found, similar to the results reported by Pandi et al [46]. The b parameter will contain the temperature dependence of the Avrami equation and increases with decreasing transformation temperature, following the relationship, \nb = F{TAei-T)+G (30) where F and G are the slope and intercept of the linear relationship respectively. The straight line shown is the linear fit to the data according to Equation 30. CCT data ranging from 6-250°C/s were fit to the differential form of the Avrami equation for austenite decomposition. The cooling rate of l°C/s was removed from this analysis because the experimental data may contain not only growth but also nucleation leading to different fit parameters in the Avrami equation. At high cooling rates site saturation will be achieved quickly resulting in only ferrite growth occurring after measurable transformation start. At slow cooling rates measurable ferrite growth may be detected 84 before nucleation site saturation is achieved. The fit parameters F and G for the higher cooling rates are shown in Table 6.4. for all three steels. 3 o 41°C/s OA • 70°C/s A 83°C/s o 194°C/s , fit / f l -I 1 1 1 1 0 100 200 300 400 Undercooling (T^-T) Figure 6.3. Plot of lnb vs. undercooling, (TA e 3-T), for the 0.8wt%Cu steel with an austenite grain size of 145pm. wt%Cu Reheat F G 0.8 2min@950°C 0.026 3.68 0.4 2min@950°C 0.029 3.67 0.05 2min@950°C 0.029 3.98 0.8 5min@1100°C 0.026 5.60 0.4 5min@1100°C 0.029 6.20 0.05 5min@1100°C 0.029 5.72 0.8 2min@1150°C 0.026 5.98 0.4 2min@1150°C 0.029 6.26 0.05 2min@1150°C 0.029 6.22 Table 6.4. Parameters F and G used in Equation 30 for all three steel grades. From Table 6.4. it can be seen that F is relatively constant and G is changing slightly with austenite grain size. Modeling results for three steel grades and reheat conditions are 85 shown in Figure 6.4 to Figure 6.6. From these diagrams it is evident that for the 0.8wt%Cu steel the model fit is good for 6, 34, and 75°C/s with deviations occurring at later stages in transformation. For this steel, with a dY of 20pm, deviations occurred in the air-cooled condition and at high cooling rates, >140°C/s. Similar results were found for all three steel grades with small y grain sizes. It is assumed that this deviation may be a result of trying to fit the entire transformation curve, not just the ferrite fraction. It should be noted that it was necessary to fit only a portion of the curve, up to 80% transformed, in order to achieve a satisfactory fit. The entire transformation curve contains a large tail that lowers the F and G values to a point where they are not comparable with the other y grain sizes. The cause of this large tail must be the 8-10% pearlite that forms at the end of the transformation with smaller austenite grain sizes. For the 0.8wt%Cu steel with a grain size of 75pm the model fit is satisfactory from 6-188°C/s with only minor deviations at the fastest cooling rate. Similarly for medium and large grain sizes the model fit seems satisfactory for a wide range of cooling rates. The model seems to work well for all experiments that produced non-polygonal structures. Because we cannot easily determine the microstructural composition of these steels it is satisfactory to model these experiments using the Avrami model for the entire transformation curve. Although models have been developed to model these non-polygonal phases [32,33] they cannot easily be applied without knowledge of the amount 86 of each phase in the microstructure. Fitting the entire transformation causes deviation for polygonal structures but fortunately the model can be modified to better fit this data. T3 E 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 o 6°C/s \ >0 ^4y-o 34°C/s A 75°C/s Model Predictions 650 700 750 Temperature (°C) 800 Figure 6.4. Modeling fraction transformed for 0.8wt%Cu steel with dY of 20pm. T J CD E a c ro c o o 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 525 A 188°C/s Model Predictions 575 625 675 Temperature (°C) 775 Figure 6.5. Modeling fraction transformed for 0.4wt%Cu with dY of 75pm. 87 T3 CD E 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 • 6°C/s \ o 52°C/s K \ \ A 205°C/s \ \ \ Model Prediction 525 575 625 675 725 Temperature (°C) 775 Figure 6.6. Modeling fraction transformed for 0.05wt%Cu steel with d y of 121pm. Modification of the Avrami equation is a simple procedure for polygonal ferritic microstructures, containing 90-93% ferrite, the remainder being pearlite. Because almost the entire microstructure is ferritic one can ignore the small pearlite portion of the transformation and normalize the fraction transformed to ferrite. Not only does this link the Avrami equation to microstructural properties but it also corrects the Avrami equation so as to more accurately fit to the experimental data. For polygonal structures of the smallest grain size class an average ferrite fraction of 93% was used. This is reasonable because the range of values is 92-94% ferrite are within experimental error that could be as high as ±2%. The fit parameters used for all steels and cooling rates are shown in Table 6.5. wt%Cu Reheat F G 0.8 2min@950°C 0.031 -4.23 0.4 2min@950°C 0.034 -4.18 0.05 2min@950°C 0.032 -4.33 Table 6.5. Fit parameters used for polygonal ferrite microstructures and normalized Avrami model. 88 z 650 700 750 800 Temperature (°C) Figure 6.7. Avrami model fit for the normalized ferrite fraction of all three steels at various cooling rates. Figure 6.7 illustrates that the model fit is satisfactory for all compositions and all cooling rates shown with the model predicting the ferrite fraction transformed within 10°C up to 90% transformed. Similar results for each cooling rate have been found for all three steels with the model deviating slightly at higher cooling rates. Therefore, when a polygonal microstructure is formed, it is better to fit the ferrite portion (>90% transformed) with a separate Avrami equation. This procedure has eliminated the problem that happened when attempting to fit the entire transformation curve. 89 6.2.2.2 Grain Size Modified Avrami Equation The effect of austenite grain size can be introduced by expressing b as kA Id™ [46]. The grain size modified Avrami equation was fit to the data in a similar fashion except this time it was the kA term that holds the temperature dependence of the equation according to, \akA=F0{TM-T)+G0 (30) where FG = F and G = GG-m\ndr (31) The fit parameters used for all steels and cooling rates are shown in Table 6.6. Figure 6.8, Figure 6.9, and Figure 6.10. display the model fits for the entire transformation curve for small, medium, and large grain sizes, respectively. The model fit is not as good as by the original Avrami Equation because the G values determined from GG and m are slightly different than the original G values. Deviations have been found at high cooling rates (>100°C/s) and low cooling rates (6°C/s). 90 Cu (wt%) F G G G m 0.8 0.026 -0.26 1.18 0.4 0.029 -0.048 1.28 0.05 0.029 0.11 1.35 Table 6.6. Fit parameters used for the grain size modified Avrami model and entire transformation curve for all three steels and cooling rates. Figure 6.8. Experimental data compared to grain size modified Avrami equation for small grain sizes. 91 Figure 6.9. Experimental data compared to grain size modified Avrami equation for medium grain sizes. T J CD E o CO 1 0.8 0.6 0.4 0.2 LL 0 o 0.8wt%Cu 1 • 0.4wt%Cu 6' A 0.05wt%Cu Predictions 475 525 575 625 675 Temperature (°C) 725 775 Figure 6.10. Experimental data compared to grain size modified Avrami equation for large grain sizes. 92 6.2.2.3 Umemoto Equation The Umemoto equation was fit to experimental data using its differential form: M - l dX = nb dt n (l-Xj (32) P where n and p are constants [46]. It has been found that the Umemoto equation does not fit the equation as well as the Avrami or grain size modified Avrami equation. Many different values of p ranging from 0.1 to 0.9 were used but the best fit was found to be a value of 0.5. 6.2.3 Ferrite Grain Size The Avrami model can be used to determine the final thermal properties of the steel strip before coiling but it does not predict the microstructural state and mechanical properties of the strip. For low-carbon steels one could estimate the final yield strength of the steel if the grain size was known by using the Hall-Petch relationship [17]. Therefore, predicting final ferrite grain size is important to estimate the mechanical properties. Many researchers have proposed equations to predict the ferrite grain size for low-carbon steels [55,56,57]. In this work a slightly modified form of the model proposed by 93 Suehiro [57] was used. This model, modified my Militzer et al. [58], is described by the equation: f r F{ exp Jdl 51000 (33) where Ff is the ferrite fraction, J and n are fitting parameters, and Ts is the transformation start temperature in °K. The grain sizes for ferrite and austenite, da and dy are in units of pm. The parameters J and r\ used in this study are shown in Table 6.7. for all three steel grades. A ferrite fraction of 93% was used in Equation 32. Cu (wt%) J r\ 0.8 52 0.029 0.4 52 0.0274 0.05 52 0.0278 Table 6.7. The fitting parameters J an, n used in Equation 32 for all three steel grades. Equations 27 and 32 clearly display the link between the models in this study because the transformation start model prediction from Equation 27 is used as a variable in Equation 32. It is assumed that the number of ferrite grains is dictated by the number of ferrite 94 nuclei formed at preferential sites at austenite grain boundaries. Priestner and Hodgson [59] confirmed with more detailed studies that the ferrite grain size is determined in the early stages of transformation. This model was fit to experimental data for polygonal ferritic microstructures with various austenite grain sizes. Figure 6.11 is a comparison of experimental data with model predictions for the 0.8wt%Cu steel. The model fit is good for all data of the 950°C reheating condition but some deviations occur at higher reheat temperatures. For all three steels the model was able to predict ferrite grain sizes for the small and large y grain sizes. However, for the medium grain sizes, with a reheat condition of 1100°C, the model performed poorly. It is believed this occurred due to wider initial austenite grain size distribution as a result of previous abnormal grain growth at this reheating temperature. The ferrite grain size produced would also be slightly abnormal and the model does not compensate for this. 95 720 740 760 780 800 820 Temperature (°C) Figure 6.11. Comparison of experimental results (symbols) and predictions (lines) for the final ferrite grain size compared with transformation start temperature for the 0.8wt%Cu steel. A comparison of experimental results and model predictions is shown in Figure 6.12. There is good agreement between experimental observations and the model with minor deviations at medium ferrite grain sizes, possible as a result of abnormalities in medium austenite grain sizes as discussed earlier. 96 60.0 Experimental Measurement (pm) Figure 6.12. Comparison between experimental and predicted values using the ferrite grain size model. 6.3 Diffusion Model A more fundamental approach of modeling ferrite growth is through the use of diffusion models. One such model was developed by Kamat et al [39] for isothermal ferrite growth. The model assumes that nucleation site saturation at austenite grain boundaries is achieved before substantial ferrite growth takes place. The transformation kinetics are then characterized by ferrite growth only and carbon diffusion in remaining austenite is rate controlling. Further, a/y interfacial equilibrium is assumed. The geometry of the austenite grain is spherical with no carbon flux at the center of the grain. The model is 97 solved using a finite difference method. This model has been modified by Militzer et al [30], to be used in continuous cooling conditions and to take into account solute drag-like effects of Mn. Nucleation of ferrite requires redistribution of both C and Mn. Since the equilibrium Mn concentration in ferrite is lower than that in austenite and Mn diffusion in austenite is a comparatively slow process, enrichment of Mn can initially be expected at the interfaces of the growing ferrite. The Mn atoms, originally segregated to the prior austenite grain boundary where nucleation occurs, further enhance the initial Mn enrichment at the oc/y interface thus decreasing the gradient for carbon diffusion. Therefore, C diffusion and Mn solute drag control the ferrite growth rate. The solute drag-like effect is incorporated into the model by selecting the appropriate local equilibrium condition for C at the interface, accounting for the higher interfacial Mn concentration. A steady-state segregation factor of Mn is given by 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 [30]. The effective segregation energy is used as a fitting parameter as described by 5 S = exp{E{T)/RT) (34) E(T) = E0-Ex{TAei-T) (35) 98 where E 0 and E, are fitting parameters distinct for each steel chemistry studied. Tabulated values of E 0 and E, reported in the literature are shown in Table 6.8. Grade E 0 (eV) Ei (eV/K) Ref. DQSK 0.22 0.0010 [30] A36 0.22 0.0012 [30] HSLA-V 0.15 0.0010 [46] HSLA-Nb 0.21 0.0010 [46] Table 6.8. Values of E 0 and E, used in Equation 34 describing the effective segregation energy for a variety of steel alloy compositions. The modified ferrite growth model of Militzer et al. was used for all three steels of this study. Effective segregation energy fitting parameters, E 0 and E„ were 0.22eV and 0.007eV/K for all three steels. Results for the 0.05wt%Cu and 0.4wt%Cu steel are shown in Figure 6.13. From these diagrams it is clear that the model fit is satisfactory. Results for the 0.8wt%Cu steel are shown in Figure 6.14. The model deviates substantially from the experimental data for low cooling rates, as shown in Figure 6.14(a). This deviation is a result of the Cu content of this steel and its thermodynamic effects. They are not considered in the model that is based on the ternary system Fe-C-Mn. Indeed, examination of the deviations between the model predictions and experimental observation for all three steels, it can be observed that the deviation is a function of Cu content. 99 To account for the effect of Cu on ferrite growth rate it is proposed that a modified Mn content would be sufficient. This Mn equivalent, Mneq, is described by, Mneq = % Mn + 0.11 % Cu (36) where all compositions are in wt% and 0.11 is a correction factor for Cu alloying. The value of 0.11 was estimated from the error at 60% transformed for the 0.8wt%Cu steel at a cooling rate of l°C/s. Utilizing Equation 36 as input of the diffusion model, the predictions for the 0.8wt%Cu steel were much improved, as can be seen by comparing Figure 6.14(a) and Figure 6.14(b). This suggests that for these low-carbon steels, the effect of Cu on the y—>a transformation can be accounted for in a fundamental diffusion and solute drag model which is based on the Fe-C-Mn system by employing an effective Mn concentration. This correction reflects the increased y-stabilization due to Cu alloying as compared to Fe-C-Mn. There is no evidence of a solute drag-like effect of Cu which is consistent with the observations made for the transformation start, where Cu effects could also be related to thermodynamic aspects. Figure 6.13. Results of carbon diffusion model for (a) 0.05wt%Cu steel and (b) 0.4wt%Cu steel. Figure 6.14. Results of carbon diffusion model for (a) 0.8wt%Cu steel and (b) 0.8wt%Cu steel with correction for Cu content. 102 7 Conclusions Experimental results have confirmed that Cu is a mild austenite stabilizer that will cause changes in the thermodynamics of phase transformation. Comparison of experimental results for transformation start temperatures with calculated T A e 3 temperatures revealed that an addition of approximately lwt%Cu decreases the transformation start temperature by 20°C. This shift can be explained solely by thermodynamics and no further kinetic effects of Cu were derived from experimental observations. The shift in T A e 3 and transformation start temperatures explains the change in final ferrite grain size. As Cu content increases the y—»a transformation is shifted to lower temperatures thereby promoting ferrite grain refinement. Steels having an average austenite grain size of 20pm produce polygonal ferrite microstructures for all cooling rates. The Hall-Petch relationship gives an adequate description of hardness for these polygonal ferrite microstructures. Reheating conditions of 5min at 1100°C and 2min at 1150°C create polygonal ferrite for slow cooling rates (l-20°C/s) and non-polygonal irregular microstructures for higher cooling rates. These non-polygonal structures, consisting of acicular ferrite and bainite, increase the hardness of the steels examined. These irregular structures are non-homogeneous in microstructure causing large spreads in hardness measurements. A1N 103 precipitation has also been found to have an effect on hardness for steel specimens reheated at higher temperatures. The incomplete dissolution of A1N particles results in strengthening of polygonal and non-polygonal microstructures alike. A1N particles will also precipitate at cooling rates of l°C/s causing substantial hardness increases as shown by experimental observation. The modeling of phase transformation kinetics by empirical and semi-empirical methods has found satisfactory results for the steels examined. Semi-empirical equations have been fit to experimental data with positive results. The Avrami equation fits the data better than that of Umemoto. Models for transformation start and ferrite grain size have been applied to experimental data and fitting parameters have been derived for the steels examined. The transformation start model appears to work with no modifications for Cu required; however, some deviation has been observed at the largest undercoolings, possible due to the formation of non-polygonal microstructures. The ferrite grain size model works well for a variety of austenite grain sizes. A carbon diffusion model including a solute drag-like effect of Mn was applied successfully to the 0.05wt%Cu and 0.4wt%Cu steels with no modification for Cu alloying. It was found that the model must be modified for the 0.8wt%Cu steel. Because both Mn and Cu are austenite stabilizers, and Cu has been found to have no significant kinetic effects, the Mn content was changed in the carbon diffusion model to account for 104 the effect of Cu by introducing an equivalent Mn composition (Mneq). After this modification was made the carbon diffusion model gave satisfactory results for all steel compositions and cooling rates. 105 8 Future Work The steels examined in this work were derived from a commercial aluminum killed low-carbon steel grade and as such contained significant amounts of Mn, and other elements. Minor changes in Mn composition and residual elements could affect the phase transformation kinetics. This may be one reason why the solute drag-like effects of Cu observed by others [16] were not found in this study. Leaner steels, such as IF steels, with higher Cu contents would be better suited for a more detailed study on the effect of Cu and precipitation during continuous cooling. These steels would also be of more interest for developing post heat treatment steels. Hardness trends obtained for large austenite grain sizes (>20pm) were complex because of contributions from transformation hardening and precipitation. 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Grade time Temperature J(2D) Condition (#) (#) (min) (°C) (pm) 1A 1 u louu 2U normal 1B 1 2 1000 21 normal 1C 1 4 1000 21 normal 1D i 7 1000 22 abnormal 1E 1 0 1050 22 abnormal 1F 1 2 1050 22 abnormal 1G 1 4 1050 40 abnormal 1H 1 7 1050 53 abnormal 11 1 0 1100 25 abnormal 1J 1 2 1100 29 abnormal 1K 1 4 1100 61 abnormal 1L 1 7 1100 60 normal 2A 2 0 1000 27 normal 2B 2 2 1000 23 normal 2C 2 4 1000 32 normal 2D 2 7 1000 23 abnormal 2E 2 0 1050 25 normal 2F 2 2 1050 23 abnormal 2G 2 4 1050 53 abnormal 2H 2 7 1050 53 abnormal 21 2 0 1100 27 abnormal 2J 2 2 1100 25 abnormal 2K 2 4 1100 66 abnormal 2L 2 7 1100 57 normal 3A 3 0 1000 17 normal 3B 3 2 1000 22 normal 3C 3 4 1000 16 normal 3D 3 7 1000 16 abnormal 3E 3 0 1050 19 normal 3F 3 2 1050 18 abnormal 3G 3 4 1050 35 abnormal 3H 3 7 1050 46 abnormal 31 3 0 1100 18 abnormal 3J 3 2 1100 38 abnormal 3K 3 4 1100 51 normal 3L 3 7 1100 56 normal Table A. 1. Results of preliminary grain growth experiments. I l l Sample l emperature Time uooimg Kate Copper 15% t50% tS5% (#) (°C) (min) (°C/s) (%) (s) (s) (s) C1FC1 950 2 •1 O.cJu 69 89 H SH C1FC6 950 2 6 0.80 14 18 30 C1FAC 950 2 15 0.80 6 9 22 C1FH1 950 2 34 0.80 2 4 7 C1FH2 950 2 75 0.80 2 2 4 C1FH3 950 2 136 0.80 1 2 3 C1FH4 950 2 203 0.80 1 1 2 C2FC1 950 2 1 0.40 53 71 146 C2FC6 950 2 6 0.40 12 16 29 C2FAC 950 2 16 0.40 6 9 21 C2FH1 950 2 37 0.40 2 3 7 C2FH2 950 2 65 0.40 1 2 4 C2FH3 950 2 150 0.40 1 1 2 C2FH4 950 2 227 0.40 1 1 2 C3FC1 950 2 1 0.05 40 64 139 C3FC6 950 2 6 0.05 11 16 28 C3FAC 950 2 16 0.05 5 8 20 C3FH1 950 2 38 0.05 2 3 7 C3FH2 950 2 69 0.05 1 2 4 C3FH3 950 2 145 0.05 1 1 2 C3FH4 950 2 215 0.05 1 1 2 Table A.2. Transformation start and finish times for small austenite grain sizes. 112 sample l emperature 1 ime c o o l i n g Kate c o p p e r t5% t50% t§5% (#) (°C) (min) (°C/s) (%) (s) (s) (s) C1CC1 1100 5 \ MO •\U 183 C1CC6 1100 5 6 0.80 19 26 34 C1CAC 1100 5 23 0.80 5 10 17 C1CH1 1100 5 64 0.80 3 5 7 C1CH2 1100 5 102 0.80 2 3 5 C1CH3 1100 5 182 0.80 1 2 3 C1CH4 1100 5 217 0.80 1 2 3 C2CC1 1100 5 1 0.40 88 116 182 C2CC6 1100 5 6 0.40 20 28 35 C2CAC 1100 5 21 0.40 8 13 19 C2CH1 1100 5 51 0.40 3 5 7 C2CH2 1100 5 100 0.40 2 3 5 C2CH3 1100 5 188 0.40 1 2 3 C2CH4 1100 5 265 0.40 1 2 2 C3CC1 1100 5 1 0.05 82 112 174 C3CC6 1100 5 6 0.05 18 25 33 C3CAC 1100 5 18 0.05 6 11 18 C3CH1 1100 5 51 0.05 3 5 7 C3CH2 1100 5 112 0.05 2 3 4 C3CH3 1100 5 176 0.05 1 2 3 C3CH4 1100 5 246 0.05 1 2 2 Table A .3 . Transformation start and finish times for medium austenite grain sizes. 113 Sample l emperature i ime cooling Kate copper t5% t50% t95% (#) co (min) (°C/s) (%) . (s) (s) (s) clBcM H H 2 1 u.80 88.5 118.7 177.1 C1BC6 1150 2 6 0.80 21.4 29.7 39.1 C1BAC 1150 2 16 0.80 11.5 19.5 29 C1BH1 1150 2 41 0.80 4 6.3 8.8 C1BH2 1150 2 70 0.80 2.3 4.2 6.4 C1BH3 1150 2 83 0.80 2.2 3.2 4.6 C1BH4 1150 2 194 0.80 1.3 2 2.9 C2BC1 1150 2 1 0.40 82.5 116.7 175.1 C2BC6 1150 2 6 0.40 20.7 29.4 37.8 C2BAC 1150 2 16 0.40 12.9 20 28.4 C2BH1 1150 2 49 0.40 4.3 6.4 8.7 C2BH2 1150 2 72 0.40 2.7 4.3 6.3 C2BH3 1150 2 110 0.40 1.9 3 4.5 C2BH4 1150 2 202 0.40 1.3 1.9 2.8 C3BC1 1150 2 1 0.05 80.5 102.6 152.9 C3BC6 1150 2 6 0.05 18.7 27.4 39.1 C3BAC 1150 2 13 0.05 9.4 16.4 26.5 C3BH1 1150 2 52 0.05 3.7 5.9 8.4 C3BH2 1150 2 74 0.05 2.4 4 5.8 C3BH3 1150 2 111 0.05 1.6 2.6 3.8 C3BH4 1150 2 205, 0.05 1.1 1.7 2.4 Table A.4 >. Transformation start and finish times for large austenite grain sizes. 114 sample I emperature I ime cooling Rate copper T5% 150% T95% (#) (°C) (min) (°C/s) (%) (°C) (°C) (°C) (J1FC1 Ubu 2 -1 o.Urj . 797 77S 682 C1FC6 950 2 6 0.80 786 765 688 C1FAC 950 2 15 0.80 779 766 685 C1FH1 950 2 34 0.80 781 751 695 C1FH2 950 2 75 0.80 763 734 656 C1FH3 950 2 136 0.80 750 724 646 C1FH4 950 2 203 0.80 741 715 646 C2FC1 950 2 1 0.40 810 793 716 C2FC6 950 2 6 0.40 792 776 696 C2FAC 950 2 16 0.40 790 779 700 C2FH1 950 2 37 0.40 794 765 700 C2FH2 950 2 65 0.40 803 759 698 C2FH3 950 2 150 0.40 770 736 680 C2FH4 950 2 227 0.40 759 726 665 C3FC1 950 2 1 0.05 825 800 723 C3FC6 950 2 6 0.05 800 779 699 C3FAC 950 2 16 0.05 797 783 700 C3FH1 950 2 38 0.05 792 767 698 C3FH2 950 2 69 0.05 782 755 685 C3FH3 950 2 145 0.05 780 745 687 C3FH4 950 2 215 0.05 762 731 672 Table A.5. Transformation start and finish temperatures for small austenite grain sizes. 115 Sample Temperature Time cooling Kate copper 15% T50% T95% (#) (°C) (min) (°C/s) (%) (°C) (°C) (°C) C1CC1 MIM 5 1 0.80 782 752 681 C1CC6 1100 5 6 0.80 751 712 660 C1CAC 1100 5 23 0.80 756 717 651 C1CH1 1100 5 64 0.80 712 672 615 C1CH2 1100 5 102 0.80 713 669 618 C1CH3 1100 5 182 0.80 690 639 585 C1CH4 1100 5 217 0.80 679 622 538 C2CC1 1100 5 1 0.40 785 755 687 C2CC6 1100 5 6 0.40 750 706 661 C2CAC 1100 5 , 21 0.40 748 714 659 C2CH1 1100 5 51 0.40 712 674 627 C2CH2 1100 5 100 0.40 701 660 615 C2CH3 1100 5 188 0.40 688 646 600 C2CH4 1100 , 5 265 0.40 678 632 570 C3CC1 1100 5 1 0.05 793 764 700 C3CC6 1100 5 6 0.05 771 731 677 C3CAC 1100 5 18 0.05 774 738 680 C3CH1 1100 5 51 0.05 718 679 628 C3CH2 1100 5 112 0.05 718 680 637 C3CH3 1100 5 176 0.05 712 670 , 624 C3CH4 1100 5 246 0.05 705 655 599 Table A.6. Transformation start and finish temperatures for medium austenite grain sizes. 116 sample l emperature i ime cooling Kate copper T5% 150% 195% (#) (°C) (min) (°C/s) (%) (°C) CO CO <J1B(J1 •HSU 2 1 6\8u 7Vy 744 885 C1BC6 1150 2 6 0.80 743 704 652 C1BAC 1150 2 16 0.80 739 705 651 C1BH1 1150 2 41 0.80 703 664 614 C1BH2 1150 2 70 0.80 719 659 604 C1BH3 1150 2 83 0.80 690 644 595 C1BH4 1150 2 194 0.80 670 617 563 C2BC1 1150 2 1 0.40 786 750 694 C2BC6 1150 2 6 0.40 750 711 659 C2BAC 1150 2 16 0.40 737 708 659 C2BH1 1150 2 49 0.40 714 678 636 C2BH2 1150 2 72 0.40 716 672 620 C2BH3 1150 2 110 0.40 708 653 600 C2BH4 1150 2 202 0.40 687 635 589 C3BC1 1150 2 1 0.05 798 775 725 C3BC6 1150 2 6 0.05 769 727 662 C3BAC 1150 2 13 0.05 765 733 679 C3BH1 1150 2 52 0.05 726 688 640 C3BH2 1150 2 74 0.05 723 678 626 C3BH3 1150 2 111 0.05 721 667 627 C3BH4 1150 2 205 0.05 695 648 614 Table A.7. Transformation start and finish temperatures for large austenite grain sizes. sample Hardness Data (HV) (#) 1 2 3 4 5 6 7. 8 9 10 AVG STDEV U1I-C1 124 114 125 122 119 120 123 125 121 120 121 4 C1FC6 127 119 120 125 130 124 125 123 120 130 124 4 C1FAC 124 133 119 126 122 122 124 125 127 129 125 4 C1FH1 132 133 132 142 128 132 138 133 136 139 134 4 C1FH2 152 146 141 145 143 147 148 150 141 148 146 4 C1FH3 152 150 145 144 147 152 150 151 146 148 148 3 C1FH4 156 154 155 160 157 153 158 161 154 161 157 3 C2FC1 108 111 114 110 107 105 110 112 115 112 110 3 C2FC6 116 117 110 118 114 110 117 114 118 115 115 3 C2FAC 118 114 119 124 122 122 117 117 116 113 118 4 C2FH1 129 130 130 128 128 134 134 130 133 128 130 2 C2FH2 133 136 140 135 134 135 142 137 135 140 137 3 C2FH3 146 148 146 145 154 138 147 159 155 146 148 6 C2FH4 144 145 145 146 146 150 154 153 148 149 148 3 C3FC1 113 111 106 107 107 110 110 110 103 108 109 3 C3FC6 119 121 114 116 119 117 116 112 114 120 117 3 C3FAC 122 114 121 117 114 125 119 118 116 118 118 4 C3FH1 127 124 120 127 125 125 125 119 122 125 124 3 C3FH2 138 137 139 134 140 142 144 143 141 145 140 3 C3FH3 146 136 148 143 138 148 138 137 137 143 141 5 C3FH4 139 142 137 143 140 140 143 139 137 142 140 2 Table A.8. Hardness measurements for small austenite grain sizes. Sample Hardness Data (MV) (#) 1 2 3 4 5 6 7 8 9 10 AVG STDEV C1CC1 185 164 150 159 15b 157 152 152 15/ 155 153 4 C1CC6 139 139 128 141 132 132 132 140 136 130 135 5 C1CAC 142 137 134 130 142 136 134 142 137 137 137 4 C1CH1 148 151 150 156 143 144 146 156 143 149 148 5 C1CH2 157 157 156 163 159 164 171 157 164 171 162 6 C1CH3 174 183 186 166 187 165 168 189 170 168 176 9 C1CH4 193 197 197 181 206 203 196 186 189 181 193 9 C2CC1 162 168 166 160 169 167 163 157 158 167 164 4 C2CC6 136 145 145 142 137 136 148 147 140 147 142 5 C2CAC 146 142 147 137 142 141 142 142 140 141 142 3 C2CH1 177 177 158 174 158 162 158 167 172 171 167 8 C2CH2 157 184 177 185 164 164 178 169 177 174 173 9 C2CH3 187 165 171 178 166 176 186 186 170 182 177 8 C2CH4 190 171 199 174 199 169 183 195 166 178 182 12 C3CC1 138 135 146 144 146 146 136 143 142 143 142 4 C3CC6 132 128 124 131 127 132 129 124 127 125 128 3 C3CAC 130 128 129 122 132 130 125 128 132 134 129 3 C3CH1 162 148 159 161 157 150 163 148 163 156 157 6 C3CH2 161 158 159 161 156 154' 155 159 169 165 160 4 C3CH3 148 163 169 161 151 159 157 151 160 165 158 7 C3CH4 167 189 176 173 167 169 185 193 165 172 176 10 Table A.9. Hardness measurements for medium austenite grain sizes. s a m p l e H a r d n e s s D a t a ( H V ) (#) 1 2 3 4 5 6 7 8 9 10 A V G S T D E V C 1 B U 1 137 14U 141 14J> 142" 137 14/ 149 144 148 143 4 C 1 B C 6 1 4 5 1 4 2 1 4 3 141 1 4 9 1 4 3 1 4 5 1 3 5 1 4 5 1 5 0 1 4 4 4 C 1 B A C 1 4 0 1 5 0 1 4 5 1 4 2 1 4 2 1 3 6 1 3 7 1 3 7 1 3 8 1 4 8 141 5 C 1 B H 1 1 5 9 1 6 7 1 6 4 1 5 9 1 6 4 1 6 6 1 7 3 1 5 9 1 5 4 1 6 4 1 6 3 5 C 1 B H 2 1 7 4 171 1 7 3 1 6 2 1 6 7 1 7 3 1 6 9 1 6 3 1 7 8 1 6 7 1 7 0 5 C 1 B H 3 1 7 9 1 7 6 1 7 7 1 8 2 1 8 3 1 8 7 1 7 6 1 8 6 1 7 7 1 8 5 181 4 C 1 B H 4 1 9 7 1 9 4 1 9 0 2 0 3 2 0 8 2 0 7 1 8 7 2 0 5 1 8 9 1 8 9 1 9 7 8 C 2 B C 1 1 3 8 141 1 4 5 141 1 3 7 151 1 4 3 1 3 7 1 4 0 1 4 9 1 4 2 5 C 2 B C 6 1 3 9 1 3 9 1 3 7 1 3 8 1 3 8 141 1 4 3 141 131 1 4 2 1 3 9 3 C 2 B A C 141 1 3 8 1 4 5 1 4 7 1 5 2 1 4 7 1 5 3 1 3 7 1 4 0 1 3 5 1 4 4 6 C 2 B H 1 1 5 5 1 5 9 1 4 9 1 5 8 1 5 3 1 6 2 171 171 1 5 8 1 5 3 1 5 9 7 C 2 B H 2 1 8 6 1 5 7 1 7 8 1 8 5 1 7 3 1 7 0 1 6 7 1 6 5 1 5 9 1 6 2 1 7 0 1 0 C 2 B H 3 1 7 9 161 1 8 5 1 5 5 1 5 8 171 1 6 8 1 6 8 1 8 0 1 7 7 1 7 0 1 0 C 2 B H 4 1 8 5 181 1 9 0 1 8 8 1 7 3 1 8 4 1 9 5 1 7 3 1 7 7 1 7 5 1 8 2 8 C 3 B C 1 1 3 0 1 2 6 1 2 7 1 3 3 1 3 3 131 1 3 2 1 3 2 1 3 8 1 3 7 132r 4 C 3 B C 6 1 4 2 1 3 4 1 3 6 1 3 9 1 4 0 1 3 5 1 3 7 1 3 3 1 4 0 141 1 3 8 3 C 3 B A C 1 1 5 1 1 6 121 1 2 0 1 2 0 1 1 6 1 1 8 1 2 4 1 1 5 1 1 6 1 1 8 3 C 3 B H 1 1 3 6 1 4 3 1 3 4 1 4 4 1 4 4 1 3 7 1 3 5 1 4 6 141 1 3 9 1 4 0 4 C 3 B H 2 1 6 6 1 5 9 1 6 6 1 6 0 1 7 3 1 7 3 / 1 6 6 1 6 4 1 6 7 1 6 5 1 6 6 5 C 3 B H 3 1 5 7 1 5 6 1 6 0 1 7 8 1 5 7 1 7 2 1 6 9 1 6 8 1 5 9 1 6 8 1 6 4 8 C 3 B H 4 1 8 3 1 8 7 1 7 6 171 181 1 7 6 1 7 0 1 7 7 1 6 9 1 7 9 1 7 7 6 Table A . 10. Hardness measurements for large austenite grain sizes. 

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