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Kinetics of nucleation and growth in a eutectoid plain carbon steel Kuban, Mehmet Baha 1983-04-22

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KINETICS OF NUCLEATION AND GROWTH IN A EUTECTOID PLAIN CARBON STEEL by MEHMET BAHA KUBAN B.Sc, University of Manchester, Institute of Science and Technology,,: 1981 THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Metallurgical Engineering We accept this thesis as conforming to the.required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1983 © Mehmet Bah.a Kuban, 1983 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 (3/81) ABSTRACT An accurate prediction of the continuous cooling trans formation (CCT) history of steels, obtained using isothermal transformation data has been of considerable academic and industrial importance for many years. The Additivity Principle, which is required to permit this calculation, has been defined but in general not completely satisfied. In this thesis the kinetics of nucleation and growth of the austenite-to-pearlite transformation in eutectoid, plain-carbon steels have been measured with the aim of clarifying the limits of applicability of this additivity principle. As a result, a new satisfactory condition, termed "effective site saturation", is proposed. The pearlite nucleation and growth rates were obtained for a range of austenite grain sizes and transformation temperatures. This data has also been used to develop a grain size parameter which could be included in the empiri cal transformation equation. The significance of the measured grain size exponent, 'm1, in terms of the opera tional pearlite nucleation sites has been examined. The relationship between the thermal history of the austenite phase and the resulting austenite grain size has i i i also been examined. The applicability of an available empirical expression for predicting the austenite grain size as a function of peak temperature and time at tempera ture has been confirmed. i v TABLE OF CONTENTS Page Abstract . ii Table of Contents; v List of Tables vList of Figures viii' List^of..Symbols xiAcknowledgement xvi Chapter 1 AN EXAMINATION OF THE AUSTENITE DECOMPOSITION REACTION AND THE PREDICTION OF CONTINUOUS COOLING BEHAVIOUR FROM CONSTANT TEMPERATURE DATA 1 2 THE INFLUENCE OF GRAIN SIZE ON THE KINETICS OF THE AUSTENITE DECOMPOSITION REACTION IN EUTECTOID CARBON STEEL 20 2.1 General Introduction 22.1.1 Grain Size Versus: Reaction Kinetics 20 2.1.2 Grain Size Versus Thermal History 34 2.2 Experimental Procedures 39 2.2.1 Dilatometric Isothermal Kinetics Measure-^ ments 40 2.2.2 Salt Pot Isothermal Kinetics Measurements. 44 2.2.3 Salt Preparation 42.2.4 Specimen Inhomogeneity 45 2.2.5 Decarburization 49 2.3 Results and Discussion 50 2.3.1 Effect of Grain Size on Transformation Kinetics, 52.3.2 Grain Size Versus; Thermal History 61 3 NUCLEATION AND GROWTH. KINETICS AND THE ADDITIVITY PRINCIPLE 63 3.1 General Introduction 63.1.1 Nucleation of Pearlite 63 3.1.2. Growth, of Pearlite 74 3.1.3 Additivity 81 3.2 Experimental Procedures 92 V Chapter Page 3.3 Results, and Dlscusisaon . '. 95 3.3.1 Nucleation Rates; 93.3.2 Growth Rates. . 106 3.3.3 Additivity and Site Saturation 115 3.3.4 Effective Site Saturation 121 4 4.1 Summary ; 136 4.2 Recommendations for Future Work 138 BIBLIOGRAPHY 140 APPENDICES 146 1 Volume Contributions 1 AO, 2 The Effective Site Saturation Criterion vi LIST OF TABLES Table Page 1.1 Composition, thermal history and grain size of S.A.E. 4340 steel used in the study by Grange and Kiefer (Ref. 9) 8 1.2 Steel Containing 0.5% C, 1 ..1% Cr, 0.25% Mo. Austenitized 30 minutes at 850°C 16 2.1 The value of the grain size exponent 'm' for different nucleation sites 35 2.2 Composition of eutectoid plain-carbon steel (wt.%) 41 2.3 Austenite grain size (A.S.T.M.), as a function of ........ 51 2.4 Dependence of the grain size exponent 'm' on the fraction transformed of pearlite 58 2.5 Comparison of grain size exponent, 'm', values 60 3.1 Approximation of rate of nucleation in eutectoid steel. Grain size A.S.'T.M. 4-5 70 3.2 Comparison of nucleation rates determined by using three different methods .., 75 3.3 Comparison of growth rates obtained by using two different methods 80 3.4 Correction procedure to determine the number of modules per unit volume from number of nodules observed on a polished surface. Reaction temperature, 640°C, austenitising temperature 950°C 94 vi i Table Page 3.5 Pearlite nucleation rate data...... 99 3.6 Comparison of nucleation rates obtained by 105 using metal!ographic and graphical methods ... 3.7 Pearlite growth rate data 109 3.8 Comparison of growth rates obtained by using metal 1ographic and graphical methods 112 3.9 Test of isokinetic condition 117 3.10 Cahn: Nucleation rate criterion 113.11 Initial nucleation rate in terms of n°^j^s. . . 120 3.12 Cahn: Early site saturation criterion 120 3.13 Calculated values of the time exponent in the Johnson-Mehl equation 123 3.14 The effect of grain size and isothermal reaction temperature on volume contributions.. 131 3.15 The "Effe.ctive Site.Saturation" criterion, ton > 0.38, values calculated for experi-z90 mental results determined for the 1080 steel used in this study 134 3.16 Calculated values of > 0.38, the "Effec-^90 tive Site Saturation" criterion, for iso thermal reactions reported in literature 135 v i i i LIST OF FIGURES Fi gure Page 1.1 Schematic representation of the heat treat ing operations involved in following the pro gress of isothermal pearlite transformation, using the metal 1ographic method (Ref. 6) 3 1.2 Typical early transformation diagram, with the ranges of temperatures for the formation of lamellar and acicular products indicated (Ref. 7) 3 1.3 Schematic representation of the relationship between cooling rate and temperature of initial transformation on cooling (Ref. 9) ... 5 1.4 The relationship between the continuous-cooling diagram and the isothermal diagram for a eutectoid steel (Ref. 8) 5 1.5 Isothermal transformation diagram for S.A.E. 4340 steel (Ref. 9) 8 1.6 CCT diagram for S.A.E. 4340 steel. Based on experimental data (Ref. 9) 9 1.7 CCT diagram for S.A.E. 4340 steel . Derived from isothermal data (Ref. 9) 10 i x Fi gure Page 1.8 Comparison of experimental and calculated curves for the initiation of the ferrite reaction in a 4340 steel (Ref. 13) 11 1.9. Schematic representation of the additivity principl e 14 1 -1:Q The shape factor as a function of tempera ture (Ref. 22) 16 2.1 Comparison of A.S.T.M. grain size numbers with the corresponding fracture rating for a range of austenitic grain sizes (Ref. 28) .... 22 2.2 Differences in hardenabi1ity caused by changes in austenite grain size in a 0.75% C steel (Ref. 29) 22 2.3 Comparison of the austenite decomposition curve with that of a first order chemical reaction (Ref. 30) 25 2.4 Effect of grain size on the reaction curve (Ref. 30) 29 2.5 Schematic diagram of the space filling tetra-kaidecahedra 32 2.6 Schematic drawing of the apparatus employed for measurement of transformation kinetics ... 41 2.7 Effect of austenitising time at 840°C on the austenite-to-pearlite transformation kinetics for an eutectoid plain-carbon steel..; 43 Fi gure 2.8 Different levels of transformation on the edges and the middles of salt pot specimens .. 2.9 Mn content versus position on the salt pot specimen 2.10 Salt pot specimen demonstrating homogeneity after homogenising treatment 2.11 Effect of austenite grain size on the iso thermal transformation kinetics; the"; 10% pearlite transformation line has been shown for each grain size 2.12 The lnln yl— versus In t graph for isothermal pearlite reaction at 640QC; austenitised at 800°C 2.13 Fit obtained when 't ' is used for reaction a v initiation time for 0.82 C steel 2.14 The n ln t-j^ versus In d for t = 0 at tQV graph showing a slope 'm' equal to 2.3 3.1 Effect of the nucleation rate on the iso thermal reaction curve of pearlite (Ref. 30).. 3.2 Schematic representation of the effect of varying rates of nucleation on the rate of reaction with grain size and growth rate constant (Ref. 30) Number of nuclei " reaction time fop unit volume different grain sizes (Ref. 60) xi Figure Page 3.4 Typical inverted cumulative distribution graph (Ref. 62) 73 3.5 Nodule diameter(d) versus transformation time (t) (Ref. 62)3.6 Number of nodules (EN) per unit volume versus reaction time (Ref. 62) 73 3.7 Nodule diameter versus reaction time for different grain sizes (Ref. 60) 78 3.8 Nodule radius versus reaction time (Ref. 56).. ^9 3.9 Nodule radius versus reaction time (Ref. 37)..( ^9 3.10 Effect of growth rate on the shape of the reaction curve.(Ref. 19) 82 3.11 Schematic representation of the principle of additivity 83 3.12 Graph showing fraction of grain boundaries occupied by pearlite as a function of volume-fraction transformed in a Fe-9Cr-lC alloy austenitised for 12 hrs. at 1200°C (Ref.36)... 88 3.13a Nod"les versus reaction time for isothermal mm pearlite reaction at 640°C 96 3.13b N.od!^es versus reaction time for isothermal mm pearlite reaction at 690°C 97 3.14a Pearlite nodules in specimen partially trans formed to approximately 10% gransformation at the isothermal reaction temperature of 640°C. Grain size, A.S.T.M. 7.3 Magnification X160 .. 100 Fi gure Page 3.14b Pearlite nodules in specimen partially trans formed to approximately 10% transformation at the isothermal raaction temperature of' 640eC. Grain size A.S.T.M. 3 Magnification XI60 100 3.15 Inverse cumulative distribution graph for isothermal transformation at 640°C 3.16 Inverse cumulative distribution graph for isothermal transformation at 690°C 3.17a Number of nodules per unit volume versus reaction time, obtained by constructing verticals to the inverse cumulative distri bution graph. Reaction temperature 640°C. Grain size A.S.T.M. 7.3 3.17b Number of nodulesper unit volume versus reaction time. Reaction temperature 690°C. Grain size A.S.T.M. 7.3 3.18a Largest diameter versus reaction time. The slope of each curve gives the growth rate (mm/s) for different grain;sizes. Reaction temperature, 640°C 3.18b Largest diameter versus reaction time. Reaction temperature, 690°C 103 104 107 108 Fi gure 3.19a Nodule diameter(d) versus reaction time(t), obtained by constructing horizontals to the inverse cumulative distribution graph. Slopes of each curve gives growth rate (mm/s). Reaction temperature, 640°C. Grain size, A.S.T.M. 73 3.19b Nodule diameter(d) versus reaction time(t). Reaction temperature, 690°C. Grain size, A.S.T.M. 73 3.20a Pearlite nucleation in~small grain size specimen (A.S.T.M. 9.1) 3.20b Pearlite nucleation in large grain size specimen (A.S.T.M. 3) 3.21 Initial nucleation rate in terms of number^nodulesl metallograpnically in specimen transformed partially to approxi mately 15% transformation 3.22 Schematic representation of homogeneous and heterogeneous reaction kinetics 3.23 Predicted variation of the "Inhomogeneity Factor", ;.I, with percent transformed of pearlite 3.24a Experimental variation of 'I', for the iso thermal reaction temperature of 640°C 3.24b Experimental variation of 'I1, for the iso thermal reaction temperature of 690°C X 1 V LIST OF SYMBOLS : Volumetric nucleation rate in the Johnson and Mehl equation (Equation 2.4) in number of nodules per mm3 per second. : Growth rate in mm per second : Reaction time : Radius of Pearlite Nodule : Extended volume transformed : True volume after subtracting impinged volume : Fraction transformed of pearlite : Temperature dependent parameter in the Avrami equation (Equation2.5). : time exponent in the Avrami equation : Austenite grain diameter : time exponent for high temperature nucleation equation (Equation 2.7). : grain size exponent in Equation 2.8. : Grain diameter at zero time at temperature.(Eqn.2.16) : Final grain diameter. : Grain diameter exponent for the grain growth equation. Heat of activation for the transformation process Grain growth equation constant Diffusivity of carbon in austenite Concentration gradient Pearlite spacing Grain diameter in the shape factor (Equation 3.1) and the time scale factor (Equation 3.3). Measured nucleation rate in number of nodules per unit volume per unit time Peak temperature independent initial grain size in equation 2.15 ACKNOWLEDGEMENTS I would like to thank Professor E. B. Hawbolt for the advice and encouragement as my thesis supervisor. Thanks are also extended to Professor 0. K, Brimacombe, the other members of the Phase Transformations Study Group and Professor R. G. Butters. Financial assistance was received in the form of a research grant from the American Iron and Steel Institute. Urumel i hi sanna oturmus, um, Oturmusda bir turku tutturmusum; Istanbul'un mermer ta§:lan. ;• Ba§rma da konuyor, konuyor aman martT kusjart... Istanbul Turkusunden Orhan Veil Kamk 1 CHAPTER 1 AN EXAMINATION OF THE AUSTENITE DECOMPOSITION REACTION AND THE PREDICTION OF CONTINUOUS COOLING BEHAVIOUR FROM CONSTANT TEMPERATURE DATA "To make yron or Steele hard, take the iuyce of varuen, cold in latine, verbana, and strayne it into a glasse, and ye wil quenche any yron., take thereof, and put to of men's pisse, and the distilde water of wormes so mixe together, and quenche there in so farre as ye will have it hard, but heede it be not too harde, there of take it forth soone after, and let it coole of itself, for when it is well seasoned ye shall see golden spottes on your yron. Also the common hardning of yron or Steele is in cold water and snow water, so when the edge shall seeme blue after this hardning, signifieth a good sign , and a right hardning."1 This was the standard procedure for heat treating steel 2 in the 16th century and probably long before that. Our knowledge of the hardening mec.hanisms has been increasing since then, but not without protracted, agonizing research and probing, sometimes in the wrong directions. However, the importance of furthering our fundamental understanding 2 of the steel decomposition processes is clear for the material progress of human society. An enormous amount of research effort has been expended in this direction and more is required. Early studies employed the metal!ographic methods to analyze the austenite decomposition at constant temperatures (Fig. 1.1); the classical work of Davenport and 3 Bain is a leading example. From information on the decomposition reaction at dif ferent temperatures, diagrams of a very important and practi cal nature were obtained. These familiar diagrams, called isothermal transformation or Time-Temperature Transformation (TTT) diagrams, gave valuable information on the start, end and duration of the austenite decomposition reaction, thus making it possible to predict final microstructure and con stituents^ for processes carried out at constant tempera tures (Fig. 1.2). A large number of isothermal transformation diagrams 4 5 were constructed by Bain and Davenport, and others. ' A variety of steels of different composition and grain size were included. However, the practical application of TTT diagrams to the heat treatment of steel is limited to those processes 3 et Hcst/np term BH rt}C In Solution /OOHM ?S%H SO KM ?S%M 100KF+C PStif'C SO'Af'C PSHFtC 0 Time et Tcmpensh/ne Lett/ Tt for Transformation Fig. 1.1 Schematic representation of the heat treating operations involved in following the progress of isothermal pearlite transformation, using the metallographic method (Ref. 6). Tnontforvnation Time flog. Soole )• Fig. 1.2 Typical early transformation diagram, with the ranges of temperatures for the formation of lamellar and acicular products indicated (Ref. 7). 4 which are essentially isothermal in nature. If a steel is cooled rapidly from the austenitising temperature to some intermediate temperature and held there for a certain length of time, the TTT diagram will indicate what the final structure will be. But very few commercial heat treatments occur in this manner. In most heat treatment processes, the metal is heated up to the austenite region and continu ously cooled to room temperature. Davenport and Bain, in addition to generating data on isothermal transformations in steels, also pointed out the need for correlating the transformation characteristics obtained during continuous-cooling with those obtained during isothermal treatment. Bain in fact produced a schematic continuous cooling diagram for a 0.85%e steel (Fig. 1.3).6'7 A demonstration of the difference between isothermal and continuous-cooling diagrams can best be made by.comparing similar treatments for a eutectoid steel. Fig. 1.4 shows, imposed on an isothermal transformation diagram, the altered reaction start and completion times for the designated o continuous-cooling curve. After six seconds, the cooling curve crosses the line representing the start of the pearlite transformation for an isothermal reaction at 650°C. A con tinuously cooled specimen would have been at temperatures above 650°C for the total lapsed time of 6 seconds and would Time in Seconds flog. Scale). Fig. 1.3 Schematic representation of the relationship between cooling rate and temperature of initial transformation on cooling (Ref.9). 800 I I 1 1 1 ' Eulecloid lemperolure 700 6 sec 600 _650'C \ / A / ' \/ i Y i A ' ' \ s \ * \ / \ ' Xc \ • / \ \ /VI \ """^L End of peoriile tronslor— ^•motion on continuous _ cooling ~ Siorl of peorlite Ironsformotion on continuous cooling 500 \ / \ \ \ \l \ ^ / \ ^\j— V \ N \ 1 400 \ \ v X \s ^ \ N X \ V \ *. \ *v v \ \ \ N. \ 300 \ vv V s\ \ \. \ V \ \ \ . \ N. \ V. 200 \ 100 M90 \2 N 1 0 I 1 1 1 0.1 1 10 100. 101 10*" 10s 5»10s Time, in seconds Fig. 1.4 The relationship between the continuous-cooling diagram and the isothermal diagram for an eutectoid steel.(Ref. 8). 6 only have reached 65Q°C at the end of 6 seconds. Since the time to start the pearlite reaction, the incubation time, is longer at higher temperatures, a continuously cooled specimen requires a longer incubation time than does an isothermally treated sample. Hence in a continuous cooling process, the reaction start will be depressed to a lower temperature and pushed to a longer time. The most important characteristic of a specimen being allowed to transform over a range of temperatures is the mixed microstructure that results. In the first attempt to describe experimentally deter mined Continuous Cooling Transformation (CCT), diagrams, Grange and Kiefer stated, "It is to be noted that in the isothermal ease the structure formed at any single tempera ture level is uniform whereas; on continuous cooling, transformation proceeds over a range of temperatures, and the final structure is therefore a mixture or a series of products, each product being substantially indistinguish-g able from what forms isothermally at the same temperature." They also noted that it would be far more convenient to derive a continuous-cooling diagram from isothermal data, if a satisfactory method of derivation could be developed. To allow for the experimental determination of a 7 continuous-^cool ing transformation diagram, Grange and Kiefer selected a S.A.E. 4340 steel (Table 1.1), whose isothermal diagram indicated sluggish transformation be haviour (Fig. 1.5). A total of 104 specimens, representing seven different constant cooling rates had to be employed to metal 1ographically follow the transformation during cooling. The experimentally constructed CCT diagram can be seen in Fig. 1.6. Grange and Kiefer also developed an empirical method for deriving a cooling diagram from an isothermal diagram. The essence of their method consisted.of respresenting any stage of the cooling by a point on the isothermal diagram which indicates, by its position, the equivalent amount of transformation that has occurred on cooling to that tempera ture at the specified rate. They carried out a fairly complex construction procedure on semi-log paper, the details g of which can be found in their paper, to produce the CCT diagram in Fig. 1.7. In further tests on several grades of low-alloy steels, experimental determinations were found to check satisfactorily with empirical determinations of CCT diagrams. Comparison of experimental and calculated curves for the initiation of the ferrite reaction in 4340 steel can be seen in Fig. 1.8. One important discrepancy with the empirically 8 C Mn Si Ni Cr Mo Comno»ilion 0.«2 0.78 0.24 1.79 0.80 0.3.1 Preliminary Treatment— llol-rollril 1H inches round, normaliied from IMO degrees 1:»hr. Specimen Sir.e—1J4 incite* diameter, hull dink* inch lliick Aiislenilir.ini; Treatment—1550 desrrcs Kahr. for IS minutes Anslenile Grain Sire No. 7-8 A.S.T.M. Enitilibrmm Transformation Aci Acs Temperatures 1.100 degrees Falir. 1J75 degrees Fnhr. Tab~le. 1..1 Composition, thermal history and grain size of S.A.E. 4340 steel used in the study by Grange and Kiefer (Ref.9). Trent formation Lmc, SoonJs Fig. 1.5' Isothermal Transformation Diagram for S.A.E. 4340 steel (Ref.9). 9 Fig. 1.6 CCT diagram for S.A.E. 4340 steel. Based on experimental data (Ref. 9). 10 Transformation Time, Second1! Fig. 1.7, CCT diagram for S.A.E. 4340 steel. Derived from isothermal data (Ref.9). 11 • «00, • It • ISO / J 1 t EXPERIMENT OF ORAfCE I «L VALUF KIEFER io.' io5 «34 io* io* TIME IBCLOW A|l IN SECONDS \ Fig. 1.8 Comparison of experimental and calculated curves for the initiation of the ferrite reaction in a 4340 steel (Ref.13). 12 determined CCT diagram lay in the location of the curve representing the completion of the pearlite reaction. Grange and Kiefer attributed this to the errors in the determina tion of the end portion of the transformation (isothermal data for this end of the transformation). In the case of eutectoid plain-carbon steel Bain had earlier proposed that only pearlite and martensite would be produced because transformation to bainite would be sheltered by the higher temperature transformation to pearlite. Grange and Kiefer, by adopting Bain's argument, could produce somewhat incomplete CCT diagrams.^ The suggestion to study the non-isothermal decomposi-tion reactions in the form of combined constant temperature reactions was initial1y made by Scheil,11 and later by 1 2 Steinberg. The TTT to CCT transformation was considered to be possible if the transformation obeyed an additivity rule. If the additivity principle held for a specific non'-i so-thermal austenite decomposition reaction, the con tinuous cooling reaction events could then be treated as a series of constant temperature reactions. The question then becomes one of determining the effect of partial decomposition at any given temperature upon the subsequent decomposition at a different temperature. In general, the 13 additivity principle requires, that the transformation at any temperature be a function only of the amount already present and the transformation temperature, i.e. Fx = Ufx,T) ...(1.1) Hence if we consider a phase initially brought to one temperature where it is unstable and partially transforms, and is then bxoiujgih';t to a second temperature to tranform further by the same reaction, the additivity principle would require that the reaction at the second temperature 1 3 be unaffected by that at the initial temperature. This principle can be seen schematically in Fig. 1.9.. Experimental investigations to test the additivity principle for different steel compositions, were carried out by various workers.1^'^'^'17 These included in vestigating the conditions for and limitations of applying the additivity rule for nucleation and growth reactions. 1 p Avrami defined an isokinetic range of temperatures as one within which the nucleation and growth rates of the transformation reactions are proportional.and stated that a reaction that is isokinetic is additive. Krainer measured the time for initiation of the 14 Fig.:1.9 Schematic representation of the additivity principle. 15 transformation in specimens, of SAE 4150 steel (0.5% C, 1.1% Cr, 0.25% Mo) held at single temperatures within the range 59Q°C to 68Q°C and at two successive temperatures within this range. His results can be seen in Table il.2, and show that the initiation of transformation is additive throughout the temperature range investigated. Lange^ and Lange and Hansel^ pointed out that the shape of the curve for percent transformation versus time for the isothermal transformation of pearlite in plain carbon steels varies little with transformation tempera ture . A change in temperature simply multiplies all times by a factor. This similarity of shape they argued, indi cated that the reaction is approximately isokinetic and so, necessarily additive. 22 Dorn, de Garmo and Flanigan on the other hand, tested the isokinetic condition with a steel of composition 0.92% C, 1.53% Mn, 0.20% Si.and 0.26%Mo and found that the pearlite transformation was not isokinetic in the temperature range 620°C to 710°C (Fig. 1.10). 20 Cahn later added a less restrictive condition for addi ti vi ty b.a.sed Jonj site saturation . He observed that for the pearlite reaction at most temperatures, the rate of nucleation becomes irrelevant and the rate of growth 16 Table 1 .2 Slcel Containing 0.5 Per Cent C, 1.1 Per Cent Cr, 0.35 Per Cent Mo. Austenitizcd 30 Minutes at 850*^. Pint Temperature Second Temperature Sum Min of Deg. C. Min utes llcltl Frnc-tinnal Time Deg. C. utes to Initiate Trans forma Frac tional Time Frac tional Times tion 0 0.00 640 8 1 00 t .00 6 Bo 0 0 0. 35 640 6 IS 0 77 I .03 660 18 0 0.50 640 4 10 0 S> 1.01 680 37 0 0.75 640 I PS 0 34 0.99 660 36 • • .00 0 00 1.00 0 0.00 500 38 1 00 1.00 640 3 0 0.35 590 30 • 5 0 73 0.97 640 4 0 0.50 590 • 3 50 0 48 0.98 640 6 0 0.75 590 7 70 0 38 1.03 640 8 • 1.00 0 00 1.00 0 0.00 500 38 1 OO .1.00 680 0 0 0.35 590 31 50 0 77 1 .03 CKo 18 0 0.50 590 14 30 0 51 1 .OI O80 37 0 0.75 590 6 70 0 34 0.99 680 36 1 .00 0 00 1 .OO 0.6 i i 0.6 \ 0.4 D.?\ 0 WO IHO 1150 IPPO IPSO BOO Temperature, "£ Fig. 1.10 The shape factor as a function of temperature (Ref. 22). 17 dominates the transformation due to the early exhaustion 21 of available nucleation sites. Tamura et al., found Cahn's observations to be generally true. In a recent study conducted in this department by 23 Agarwal and Brimacombe, a mathematical model was formula ted to predict the kinetics of the austenite-to-pearlite transformation and the transient temperature distribution in a eutectoid, carbon steel rods during continuous-cooling processes such as Stelmor or Schloemann. ': .. This study used isothermal kinetics and assumed that the additivity principle was valid for the austenite-to-pearlite trans formation, but showed relatively poor agreement with experi mental determinations of continuous-cooling kinetics. The main factors that were believed to be contributing to this discrepancy were: 1. the inaccuracies in the start and end times in existing isothermal transformation curves; and 2. the validity of using the additivity principle to describe the incubation, nucleation and growth processes. Hence a more extensive research programme was initiated at the University of British Columbia. This M.A.Sc. thesis 18 was generated as one part of this research, project. The general objectives of the programme were to be: 1. To accurately characterize the kinetics of the austenite decomposition reaction under carefully controlled isothermal as; well as continuous cooling conditions. 2. To predict the continuous-cooling behaviour using the additivity rule while clarifying the limitations for use of this principle. The following variables were to be investigated in the studies; grain size, thermal history, cooling rate, composition and section size. The Tatter incorporates changes in the cooling rate in a single specimen. To simplify the transformation behaviour, the initial studies examined the austenite to pearlite reaction in eutectoid plain-carbon steels. This particular component of the study concentrated on characterizing the effect of grain size and thermal history on the isothermal austenite to pearlite decomposition and then investigating the con ditions for the application of the additivity rule. Hence the experimental work consisted of: 1. Examining specimens that were given varying thermal 19 treatment to produce different grain sizes and sub sequently reacted at constant subcritical tempera tures. A comparison of the transformation rate for the austenite to pearlite reaction was made for dif ferent grain sizes. 2. Determining the pearlite nucleation and growth rates employing a series of specimens reacted to a maximum of 20 percent transformation. The data is used to test the present understanding of the additivity rule and to generate another sufficient condition for its use in predicting continuous-cooling kinetics from isothermal kinetic data. 20 CHAPTER 2 THE INFLUENCE OF GRAIN SIZE ON THE KINETICS OF THE AUSTENITE DECOMPOSITION REACTION IN EUTECTOID PLAIN CARBON STEEL 2.1 GENERAL INTRODUCTION 2.1.1 Grain Size versus Reaction Kinetics The metal 1ographic features of the constituents present in steel coo.l.ed from austenite were observed and 24 fairly well understood as early as the 1890 s, despite the confusion in terminologies. Austenite grain size was recognized by Davenport and Bain as having an important influence on the rates of the isothermal austenite decomposi tion reactions. Bain investigated this subject soon after-25 26 wards, ' and contributed to the understanding of the transformation by developing an improved means of revealing 2 7 2 8 and measuring austenite grain size. * The role of austenite grain size in affecting the hardening of steel is one of ancient recognition. The French metallurgist Reaumur had in 1722 devised for his blister steel a grain growth test in association with the performance of hardened tool steels and. even had a crude 21 29 scale for designating the austenite grain size. Bain made the following comment: It seems inescapable, that the ancients who hardened steel must have made two important observations: 1. That steel which, after hardening revealed a coarse fracture surface hardened more deeply than that having a fine texture. 2. That steel which broke easily after hardening had a coarser fracture surface than that which broke only with the application of heavier blows. In Sweden, as early as 1926, the fineness or coarseness of the fracture surfaces of hardened tool steel was regular ly employed as a quantitative measure of certain qualities, the actual rating being made by comparison with five stan dard fracture surfaces; evenly distributed over the ful 1 range usually encountered. Shortly afterwards, a ten-step standard scale was adopted and as can be seen in Fig. 2.1, it agreed exceedingly well with the standard ASTM austenite grain size scale. The influence of austenite grain size on the hardness of a steel section, 1 inch in diameter is demonstrated in Fig. 2.2. Since hardenabi1ity is the capacity of a steel to transform to martensite, increasing the austenite grain size can be seen to retard the formation of pearlite, or enhance the formation of martensite. Bain correctly 22 Fracture Oram St}e-Fig. 2.1 Comparison of A.S.T.M. grain size numbers with the corresponding fracture rating for a range of austenitic grain sizes (Ref. 28). 3 Temp. (Mean) 1800 °/T p 380 °C. jB I700"F=. , 3Z5°C. Ci 1575 °F 855 °C. 3-5 JD 785°C. E_ 7-4-5 °C ^ "So Carbon O • 74 Manganese O-^l Silicon 0\4-Fig. 2.2 Differences in hardenability caused by changes in austenite grain size in a 0.75%. C steel (Ref. 29). suggests that the real factor at work in controlling hardenability was the pearlite nucleation rate, i.e. the relative number of nuclei appearing per unit time, per unit volume of austenite. In describing the effect of nucleation rate Bain states, "It is comparable to a great number of equally skilled painters scattered over a wall as compared with only a few. The wall is painted sooner by many workmen than by a few." Metal 1ographic evidence confirmed that both the pearlite nucleation rate and the grain size affected the austenite to pearlite transformation rate", and that in a vast majority of steels, pearlite nuclei were located at the grain boundaries of the austenite. Thus the smaller the grains, the greater was the grain boundary area; the greater the grain boundary area per unit volume, the more numerous the nuclei. Based on the available isothermal data (TTT diagrams, sometimes called S-curves) and the known major character istics of the austenite decomposition reaction, Bain and Davenport made the first attempt at explaining the shape of the S-curve and effect of austenite grain size. The austenite decomposition curve, being a rate curve, 24 was first compared to rate curves obtained for chemical reactions that occur in gases and liquids. The major dif ference between two sets of curves was noted at the begin ning and end of the transformation plots (Fig. 2.3). Whereas a first order chemical reaction curve started with a maximum velocity, the S-curve did not. In addition, on approaching the end of the transformation curve, the chemical reaction curve approached the 100% transformed line asymptotically, Whereas the S-curve appeared to finish in a finite time. The discrepancies were readily explainable in terms of the nature of the two reactions. The first order chemical reaction rate was determined by assuming the probability of formation of activated molecules had an energy redistribution arising from favourable collision throughout the system; typical of a homogeneous reaction process, whereas the decomposition of austenite is deter mined by a nucleation and growth process, occurring at .inter-30 faces, i.e.; a heterogeneous reaction process. Since metal 1ographic evidence established that for pearlite formation, the reaction was nucleation and growth controlled, Mehl pointed out the; need to derive a 25 Time Theoretical Curve Hours 0 2 4 6 8 10 12 14 16 Id 20 22 24 26 26 I 1—i—i—i—i—i—i—i—i—i—i—i—i—i—r— Log Scale Fig. 2.3 Comparison of the austenite decomposition curve with that of a first order chemical reaction (Ref. 30). 26 quantitative expression in terms: of the real physical para-31 meters, the nucleation rate and the growth rate. Thus the familiar Johnson and Mehl equation which characterizes the reaction rate in terms, of nucleation and growth pro cesses emerged. In deriving this: kinetic equation for the transformation Johnson and Mehl made the following assumpti ons: 1. The reaction proceeds by nucleation and growth. 2. The rate of nucleation, Nv, expressed in number of nuclei per unit of time, per unit of volume, and the rate of radial growth, 6, expressed in units of length per unit of time are both constant throughout the reaction. 3. Nucleation is random, without regard for matrix structure. 4. The reaction products form as spheres except when impingement occurs during growth. They derived an expression for the extent of reaction versus time in terms of Ny and G using the following ap proach; the rate of growth of a sphere nucleated at some arbitrary time is calculated; the rate of growth of an actual nodule of pearlite - a sphere that has suffered impingement and thus is no longer spherical - is a fraction of the rate of growth of the sphere; this fraction 27 is equal to the fraction of untransformed matrix. This determines the rate of growth, of one nodule, which when multiplied by the number of nodules nucleated at the same time, gives the rate of growth of all nodules nucle ated at this arbitrary time; integrating this expression gives an equation for the volume transformed as. a function of time; t.= t /N £TT R3dt ... (2.1 ) 3 t=o where for the austenite to pearlite reaction,R is the radius of the pearlite nodule and R = Gt ...(212) where G is the growth rate of the pearlite sphere. This equation will give what was later termed by Avrami, the extended volume, and includes that volume which arises from impingement of nodules. Both Johnson and Mehl and later Avrami calculated the true volume fraction in the following way; Vtrue ' l-»xp(-V„> ...12.3) where V is the extended volume as determined by the ex J integral given above. 28 Hence the Johnson and Mehl equation becomes;; X = l-exp(-|NvG3t4) ...(2.4) This equation as stated previously, defines fraction transformed versus time for random nucleation. To 1 9 characterize the pearlite reaction Johnson and Mehl had to make the following additional assumptions fior grain boundary nucleation:, 1. Nucleation occurs exclusively at grain boundaries. 2. The matrix is composed of spherical grains of equal size. 3. The nuclei grow only into the grain in which they originate and do not cross grain boundaries. 4. The rate of transformation is retarded by impingement of growing nodules and growth to the adjacent grain boundaries. Including these additional assumptions enables 19 Johnson and Mehl to quantitatively determine the effect of grain size on the shape and position of the isothermal transformation curve of the pearlite reaction (Fig. 2.4). The increased grain size produces fewer grain boundary nucleation sites per unit volume and requires longer Fig. 2.4 Effect of grain size on the reaction curve (Ref.30). 30 growth times for the nodules; to traverse the austenite grain, i.e. increasing time for completion of the reaction. This primarily geometrical problem of characterizing a transformation process which includes both nucleation and growth, was given a general treatment by Avrami. Avrami also makes the assumption that nucleation occurs only at certain preferred sites; which are gradually exhausted. For a three-dimensional nucleation and growth process, he developed the more general relationship between fraction transformed, X, and isothermal /reaction time, t: X = l-exp(-btn) ... (2.5) where 3 <_.n <_ 4 and b is a constant. 32 Christian, in his analysis of the Avrami equation, suggests that the general expression for the volume trans formed remains valid for two-dimensional and one-dimensional growth with 2. <_.n<_3 respectively. The Avrami equation varies in the same way with dif ferent grain size as does the Johnson and Mehl equation; any changes in the volumetric nucleation rate, Ny, will result in a variation of the empirical constant 'b' in the Avrami equation. 31 One of the important assumptions, made by Johnson and Mehl was that nodules, of the reaction product v.woul d grow only into the grain in which they nucleated.' Rothenau and 33 Boas .in their exhaustive work with the electron emission microscope, showed that the reverse of this was true for the pearlite reaction in eutectoid plain carbon steels. They observed that pearlite nodules readily - cross austenite grain boundaries. Cahn also attempted to calculate an isothermal reaction rate but excluded the effects of grain boundary growth restraints. Using Clemm and.Fisher's analysis of the energetics of p;ar.t;i-'cjj;l-a;r s i tes,34 he included the pos sibility of nuclei being localized at grain surfaces, 20 35 grain edges or grain corners. ' Assuming for a grain shape, that of aspace-f i 11 i ng tetrakaidecahedron (Fig..2.5) and determining the numbers of corners, edges and surfaces in terms of the grain diameter, Cahn derived a transforma tion rate equation assuming that the grain boundaries offer no resistance to a growing nodule. Cahn, analysing the nucleation and growth kinetics measurements of several workers, such as Parcel and Mehl, Lyman and Triano and 37 Hull, Colton and Mehl, came to the conclusion that in most steels, pearlite nucleation was. fast enough to cause early site saturation (this concept is to be examined in more 32 edge Fig. 2.5 Schematic diagram of the space filling tetrakai decahedra. 33 detail in the 3rd chapter) even at fairly high temperatures which resulted in the nucleation event being unimportant to the transformation. The reaction "finish time" was related to the growth rate, G, and the grain diameter, d, z f ". °' Q ^ ...(2.6) Hence, increasing or decreasing the grain size would have a direct effect on the duration of the reaction. Cahn however, did derive an expression for trans formation at very high termperatures where low nucleation rates predominate and where site saturation may not occur. In such a case a Johnson-Mehl type expression in which the volumetric nucleation rate, Nv = k tni ...(2.7) k, nj : constants t was deri ved by Cahn t : reaction time 20 Using Cahn's analysis and the dependence of reaction 40 and nucleation rates on the grain size, Tamura et al., developed a relationship which incorporated into Avrami's empirical rate equation the austenite grain size, d: 'i X = l-exp[-b^-] ...(2.8) d" It is important to note that the 'b' contained in equa tion 2J8YLS not the same as that contained in the Avrami equation (EquAtidn).2.5) due to the introduction of the grain size factor. From their studies of pearlite and bainite transforma-39 40 tions, Tamura et al. ' suggested that the exponent 'm' signifies the type of site active in the nucleation pro cess as shown in Table 2.1.. It is one objective of this project to test their analysis, to determine the exponents n, and m for a eutectoid plain carbon steel and to investi gate by means of metal 1ographic observation the signifi cance attached to 1m1. • •' 2.1.2 Grain Size Versus Thermal History The austenite grain size of any steel is a result of the prior thermal history and factors such as the composition, peak.temperature and duration of heat treatment, etc. It is therefore important to establish a relationship between prior thermal history and grain size, not only for industrial cooling processes, but also for predicting heat affected zone microstructures in weld materials. It is therefore necessary to characterize the resulting grain size of a material in terms of the peak temperature and-holding timeatppealk temperature. 35 TABLE 2.1 The Value of 'm' for Different Nucleation Sites Nucleation Site Surface Edge Corner m 1 2 3 36 The uniform coarsening of the grains in a stress free material held at an elevated temperature is known as grain growth. One can experimentally follow the growth of a single grain on a polished surface, in. situ, on a heated stage of a microscope. However, the resulting growth is inhibited by the free surface and so the phenomena may not be characteristic of that of bulk grain growth. 41 Carpenter and Elam, investigated grain growth in a 1.5% antimony, tin alloy with the following results being noted; 1. Growth occurs by grain boundary migration and not by coalescence of neighbouring grains. 2. Boundary migration is discontinuous; the rate of migration of a boundary is not constant in sub sequent heating periods and the direction of migration may change. 3. A given grain may grow into a neighbour on one side and be simultaneously consumed by a neighbour on another side. 4. The consumption of a grain by its neighbours is frequently more rapid just as the grain is about to di sappear. Using the same material, Sutoki added; 37 5. A curved grain boundary usually migrates towards its centre of curvature. 43 In addition, Harker and Parker observed: 6. Where boundaries in a single phase metal meet at angles different from 120 degrees, the grain included by the more acute angle will be consumed. Different mechanisms and different sources for the driving force of grain growth have been proposed. Exten-44 sive reviews have been published by Burke and Turnbull , 45 and Nielsen. It is generally recognized that in a completely recrystal1ized material, the driving force for grain growth is the reduction of the surface energy of the grain boundaries. As the number of grains per unit volume decreases and their size increases, the grain boun dary area per unit volume becomes less, and the overall surface energy is lowered. Many authors have pointed out the similarities between growth of cells in a froth of soap and grain growth in metals that are recrystal!ized. For the simple model of cells in a soap foam, using the surface energy of the boundaries as a driving force, a simple formulation of o grain growth kinetics can be established; 38 where D2 - = K't . .. (2.9) D = cell size at t = o o D = f i nal eel 1 si ze K1 = constant of proportionality t = time Although it has been shown that the kinetics of growth of cells in a -soap froth agrees well with this expression,4 experimental studies of metallic grain growth have failed to confirm an extension of this equation based on the activation energy for grain boundary migration, D? - D2 = A exp t ... (2.10) 0 R - T where Q : empirical heat of activation for the process R : gas constant T : degrees Kelvin A : constant Instead, most of the isothermal grain growth, data in metallic systems corresponds, to an empirical equation of the form; Dn" - Dl]" = K't ... (2.11 ) 39 where K', is a material dependent proportionality constant. Hannerz and Kazinczy studied grain growth in austenite in steels with varying alloy contents, and found that carbides and nitrides of Nb, V, Ti drastically re duced the growth rate of the austenite grains and this cor responded to a value of the exponent!;. n"=~ 20, in grain refined steels. They also determined n"? 5,6 for as-cast coarse grained steels. 48 Hu and Roth, reported a variety of n" values between 4Q 2 and 4, Alberry, Chew and Jones found 'n;'" to be 2.73 for 50 their 0.5 Cr, Mo-V steel and Ikawa et al. determined n" - 4 for a commercial purity Ni steel. Most of these studies were undertaken to determine the prior austenite grain size in the heat affected zones of welds. In this thesis,this same method has been used to determine the grain growth kinetics in oar eutectoid plain carbon steel and hence can be used to establish the relationship between peak temperature, heating time and final grain size for eutectoid steel. 2.2 EXPERIMENTAL PROCEDURES Experiments were performed to investigate the isothermal reaction kinetics for different grain sizes and for different 40 reaction temperatures. 2.2.1 Pi 1atometric Isothermal Ki neti cs Measurements For an accurate control of temperature and a precise measurement of transformation kinetics, the appara tus shown on Fig. 2.6 was used for all isothermal and con tinuous cooling tests. The progress of the austenite de composition was measured continuously with a dilatometer consisting of a water cooled, quartz tipped extensometer. Diametral" rather than axial dimensional changes were monitored in the middle of the test specimen to prevent errors assoe-iated with axial temperature gradients^ The specimen temperature was monitored and controlled using a chromel-alumel intrinsic thermocouple spot welded to the outside surface of the tubular specimen on the same diameter plane as that measured by the diametral dilatometer. A voltage feedback system was attached to the thermocouple and was used to preselect test temperatures. Signals from the extensometer and thermocouple were continuously re corded with a common time base. The overall dimensions of the tubular steel specimens used in this apparatus were; length = 100 .mm, Q.D: = 8 mm., and wall thickness; =• 0.8 mm. All samples were machined from a 1080, eutectoid carbon steel rod, having the composition shown in Table 2.2. Si PHASE SH 1FTER TEMPERATURE CONTROL TEMPERATURE 8 DIAMETER RECORDER A Diometrol Dilotomeler B Inlet for internol gos -flow C Outlet for internol gos flow D Inlet for externol gos flow E Thermocouple on somple F Support Structure 2.6 Schematic drawing of the apparatus employed for measurement of transformation kinetics. Table 2.2 COMPOSITION OF EUTECTOID  PLAIN-CARBON STEEL (ut%) c Mn Si S P Al 0.79 0.91 . 0.49 0.029 0.018 0.084 Cu Cr Sn Ni Mo 0.049 0.062 0.003 0.014 0.002 42 The austenitising treatment, i.e. time and temperature were preselected and the resultant austenite grain size 51 measured metal 1 on water quenched, partially transformed samples. Before selecting a specific austenitis-ing condition, it was decided to investigate the effect of time at austenitising temperature. The austenite to pearlite kinetic results for 1, 5 and 15 minutes austenitising time at 840°C, demonstrated similar transformation kinetics for the 5 and 15 minute treatments and slightly faster kinetics for the 1 minute, as shown in Fig. .2.2. A 5 minutes austenitising treatment was chosen to minimize decarburization while ensuring a homogeneous austenite structure. Although different austenitising temperatures were used to produce a range of austenite grain sizes, the test sample was always returned to 740°C prior to cooling to the transformation temperature to ensure identical cooling conditions in each test sample. The maximum available cooling rate of 108°C/sec combined with the approximate 1 second TTT nose at 6Q0QC, restricted'valid TTT tests to temperatures above 600°C. Two isothermal test temperatures were selected, 690°C to reflect high temperature nucleation and growth conditions and 64Q°C to depict Tow temperature pearlite nucleation and growth conditions. 43 700 o o O OJ E 650 .OJ 600 l 1 1 - • -— 0 i o -- OA o -- -- Austenitising Treatment — f * y^ / . y 840 °C 1 min 5, 15 min - ( 0 A Of - M 11 OA V'O sforrru fAV • o -- 1 § Tran 1 % • A -- . f i iction 99% # O -i i 1 i it -i i 100 1000 Time (s) Fig. 2.7 Effect of austenitising time at 840°C on the austenite-to-pearlite transformation kinetics for an eutectoid plain-carbon steel. 44 2.2.2 Salt Pot Isothermal Kinetics Measurements Traditional isothermal transformation tests were also performed to compare the measured metal!ographic transformation results with, the dilatometric data. The traditional procedure of transferring relatively thin samples from one salt pot to another and quenching samples after increments of isothermal holding time provides a larger sample area for examination of nucleation and growth rates. This method is also much more suitable for nuclea tion and growth measurements, due to the large number of specimens required. The test samples, 10 mm diameter x 1-2 mm thickness were austenitised for 5 minutes at temperatures identical to dilatometric tests with the exception of the 1100°C austenitising condition. The grain size was determined metal 1ographically from partially transformed, water quenched specimens.^ 2.2.3 Salt Preparation The lowest temperature selected for isothermal tests was to be 640°C. A salt having a melting point of approximately 60.0°C was required for a working temperature of 640°C. The available high, temperature salt was a neutral salt (L.H. 1550} which, contained 85% BaCl 2, 15% NaCl and had a melting point of approximately 640°C which 45 was not suitable. To lower the melting point, additions of KC1 and NaCl were used. After several trials, the desired melting conditions were obtained using a salt of composition; 10.0 L.H. 1 550 , 1 5 NaCl, 40 KC1 . The composi tion of the component chlori des was, 55% BaCl^. 25% KC1 , 20% NaCl. This salt had a melting point of approximately 590°C. The temperature control for all salt pots was approxi mately + 2°C and the transfer time from pot to pot was less than one second. After-heat treatment which, involved austenitising for 5 minutes, transferring the sample to the 740°C salt for 1 minute,then transferring the specimen to the salt maintained at the desired isothermal test temperature, the specimen was quenched in water, cold mounted in bakelite, polished and etched using 2% Nital. The fraction of pearlite was measured directly using a Quantimet 720. The high contrast between the pearlite and martensite ensured that a valid area fraction of pearlite was measured for each field of view. 2.2.4 S p e c i. m e n I n h o m o g e n e i t y Initial isothermal transformation tests, con ducted in the salt pots yielded the result shown in Fig. 2.8. Fig. 2.8 Different levels of transformation on the edges and the middles of salt pot specimens. Mag. X 7. The figure in the middle is the photograph of a disc specimen ground down to half its diameter. The middle of the specimen therefore, corresponds to the centerline of the wire rod. 47 Wt % Mn v.s Position EDGE MIDDLE EDGE POSITION of SPECIMEN Fig. 2.9 Mn content versus position on the salt pot specimen. N.B. It must be noted that the average Mn content as can be seen in Fig. 2.9, is lower than the Mn content on Table 2.2 that shows the composition of this steel . 48 Fig. 2.10 Salt pot specimen demonstrating homogeneity after homogenising treatment. Mag. X 7. Specimens shown correspond to the diametral cross-section of disc specimens. 49 The disc specimens demonstrated an enhanced transformation rate at the edges, and a slower transformation rate at the center of the specimen. The center corresponds to the center!ine of the rod used in the study. The variation in transformation kinetics was attributed to macrosegregation in the original steel rod. Although Mn was thought to be the segregating .element,' an electron probe examination of the Mn content did not confirm this suspicion (Fig. .2.9). A homogenising treatment of the specimen as recommended CO CO in the literature ' was then performed. Specimens were sealed in quartz tubes under vacuum and kept at 1200°C for 15 hours. Tests performed after such a treatment did not show the previously noted inhomogeneity of pearlite transformation (Fig. 2.10). This homogeni sing treatment was applied to all specimens. 2.2.5 Decarburi zation The extent of decarburization on the disc specimens resulting from the austenitising heat treatment in the neutral salts was also determined. Specimens cut from the 108Q rod were treated 5 minutes at 850°C, followed by 1 minute at 740°C, a total of 6 minutes to determine the resulting decarburi zati on . The mi.crostructure containing the decarburized layer was then photographed and the depth, of decarburi zati on was determined. Using 50 a maximum al 1 owable decarbur.ized layer of 10% of the speci men thickness, the austenitising at 850°C was found to be acceptable. 2.3 RESULTS AND DISCUSSION 2.3.1 Effect of Grain Size on Transformation Kinetics The grain sizes obtained with the given austeni tising conditions for both the dilatometric and salt pot tests are given in Table 2.3. The effect of grain size on isothermal transformation kinetics can, be seen on Fig. 2.1:1. Also included on this figure is the kinetic data obtained from the salt pot, confirming that the nucleation and growth measurements from bulk specimens treated in the salt pot correspond to that obtained using the dilatometric data. That higher isothermal reaction temperatures decrease the pearlite reaction rate due to slower nucleation and growth kinetics can be seen in Fig. 2.IT. The underlying reasons for the temperature dependence of nucleation and growth is well researched,50'31 .38,55 and can be•summarized as follows: The nucleation event is usually concerned with the overcoming of thermodynamical barriers before a new phase can grow with steadily decreasing free energy. The criti cal particle size beyond which particles become growth nuclei decreases with undercoolingffram the equilibrium temperature, i.e. the lower the isothermal transformation TABLE 2.3 Austenite Grain Size Austenitising Temperature °c A..S.T.M. Grai n Size 740 10.8 800 . 9.1 840 7.8 900 7.4 950 7.3 1100 3.0 52 Fig. 2.11 Effect of austenite grain size on the isothermal trans-formationrknne'tlcs; the 10% pearlite transformation line has been shown for each grain size. 53 fi 1 temperature, the higher the nucleation rate of pearlite. The temperature dependence of the growth rate is; more complicated and is determined by the spacing (the diffusion distance), the diffusion rate and the Concentra te tion difference. As the temperature falls, the reduction in the diffusion rate is more than compensated by the de creasing pearlite spacing and increasing concentration gradient. The growth rate therefore increases rapidly to a maximum at a particular temperature, below which the dif fusion rate becomes very small, and then decreases. For the pearlite reaction at a specific isothermal transformation temperature,increasing grain size can be seen to increase the incubation•time and to increase the time to complete the transformation. Since the growth rate is essentially structure insensitive and a function only of transformation temperature, the difference in transforma tion rate with increasing grain size is accountable only by a drop in the nucleation rate, as confirmed by the measurement of this quantity. Work done earlier on this material has shown that the pearlite reaction can be well characterized by the Avrami equation (Equation 2.5). The kinetic data for each iso thermal test was plotted in terms of In In y^-— versus In t (Fig. 2.12). The exact initiation time for the transformation 1.0 54 0.0 x i 1.0 -2.Oh t = 0 ot tAV=3,0€s n= 2,143 In b = -3,0305 n'= 4,252 In b'= -8,4304 Austenitising Temperature •  800 °C Reaction Temperature 640 °C ' • L 1.5 2.0 In t Fig. 2.12 The Inln y^- versus In t graph for'isothermal pearlite reaction at 640QC; austenitised at 8009C. 55 was difficult to determine because the transformation start was estimated by first fitting a least squares line to a mini mum of eight points on the In In y-^- versus Int plot with t = o, based on an approximate start temperature. Then the transformation initiation time was increased by a small increment and again the least squares analysis was performed. This procedure was repeated until a best fit line was obtained for the data points. The resultant initiation time was termed ' t„wv,„ .'. The resulting 1 n' and 'In b' were deter-avrami 3 mined on the basisof t,„. The extremely good fit obtained a v when t = o at t .. is used as the reaction initiation time a v i.e. excluding the incubation time, can be seen in Fig. 2.13 for a eutectoid plain-carbon steel. Although the Avrami equation characterizes well the pearlite reaction at constant subcritieal temperatures it does not include the grain size as a parameter. This was done by Tamura et al. who incorporated a grain size para meter and studied the pearlite transformation in terms of a more generalized transformation equation (Equation 2.8). Equation 2.8 can be re-written as; n' In t = m In d + In In Ink (2.12) Thus by plotting n' Int versus Ind : the value of the grain size exponent 'm' can be determined. 56 Fig. 2.13 Fit obtained when 't 3 av time for 0.82 C steel. is used for reaction initiation 57 To determine whether 'm.' is dependent on the fraction trans-formed, the data was also plotted as n' In tQ £g versus Ind, n'ln tQ 5 versus Ind and n'ln tQ 75 versus Ind; it was found to be independent of fraction transformed (Table 2.4). The plot for 50% transformation is given in Fig. 2.14;., A value of approximately 2.2 was determined. A comparison of 'm' values determined by using two similar composition eutectoid plain-carbon steels with Tamura et al's 'm' values for the pearlite reaction can be seen on Table 2.5. It must be noted however that Tamura et al. used times calculated from t = 0 at T „ and found the value ofm= 1.8 A] for the pearlite reaction. Fig. 2.14 is based on t = 9 at . taw, the start of measurable transformation. If the time a V was calculated based on t = 0 at T^, the value of 'm' obtained is approximately 3.0 and is higher than that obtained in the study by Tamura et al. Tamura et al. attached significance to the value of this number as a probable indication of pearlite nuclea tion sites as summarized in Table 2.J. As will be seen later in the metal 1ographic studies,corner and edge nucleation would seem to be dominant and probably corner is more important,, consistent with m = 2.2. 58 TABLE 2.4 Dependence of the Grain Size Exponent 'm' on the Fraction Transformed of Pearlite. Pearlite Transprmation [%) 'm' 25 2.2 50 2.3 75 2.2 14 12 10 8 • i • ~m=2-6l t = 0 at tov O Reaction at 640°C O 650°C A II II 670°C • H II 690°C m = 2l7 40 Fig. 2.14 The nTnt-^ versus ln d for .t = 0 at t graph showing a slope 'm' equal to 2.3. TABLE 2.5 Comparison of 'm' Values Source 'm' ( 1080 steel This ( work ( 0.77 C steel Tamura et al. (Eutectoid plain carbon steel ) 2.2 2.0 1.8 61 2.3.2 Grain Size Versus; Thermal History The determination of the grain size versus 49 thermal history relationship developed by Alberry et al., was based on an examination of the prior austenite grain growth in heat affected zones of welds. After determining grain size for different holding times at constant peak tempera ture and using the relationship D" - D£ = K(t1-t2) ...(2.12) where DN and D2 are grain sizes obtained after holding at temperature for-time&i^ andtt2 respecti vely, they determined |!n'" using a series of least squares plots, selected using a maximum correlationJ coefficient. They found n" = 2.73. The original relationship47 i.e. Equation 2.11; II N II DN - D = Kt o where K^= A exp(-C-|r), ...(2.13) and Dq is the grain size at t « 0, can be also used, however. Assuming that the time for the specimen to reach the peak temperature is negligible, i.e. grain size 6Q at t = 0 is similar for all temperatures; then, 62 D^" - D"" = A exp(.-Q/R(T1-T2))t ...(.2.14a) = A exp(-Q/R(T3-T4))t ...(2.14b) Using -the activation energy of austenite grain growth 53 as Q = 460,000 J/mol/K, • from;.•. Bastien et al . , and' g'ra i n diameter in mm and the appropriate time, t = 5 minutes,the equations can be solved numerically to determine the value of 'A' and l;n!"; the result is: n" = 3.57 A = 2.98 x 1012 min3,57/s The specific grain growth equation therefore becomes; 3.57 _.*3.57 = 2>98x ^^iexpT460'00;/ 100°)]t ..(2.15) Z 0 Kl For this 1080 steel, compared with D2.73 . D2.73 = K41 x 1013[exp(-460,00R0 + 33 ,000) } t ^ (2< ] fi) determined by Alberry et al. for a 0.11 C alloy steel. * N.B. It must be noted that DQ in equation 2.15 is different from DQ in equation 2.15 because DQ is not a function of peak temperature. 63 CHAPTER 3 NUCLEATION, GROWTH KINETICS AND THE ADDITIVITY PRINCIPLE 3.1 INTRODUCTION 75 The pearly constituent observed in 1864 by Sorby and later named pearlite is probably the metal structure that has been studied in *most detail. A great deal of confusion existed in the morphological terminology defining the eutec toid transformation products. Globular, rod-like degene rate, fine, coarse, bearded, massive, banded, reefy, blocky, sorbitic, troostitic pearlites and many other terms were often used. This situation gradually became more logical as the nature of the formation of pearlite was in vestigated and became- better understood The nucleation and growth character of pearlite was 54 examined as early as 1905 by Arnold and McWilliam •-) (and ,-by '55 -.- •-. Benedics 'and i described clearly in the works of Bain 3 and Davenport. 3.1.1 Nucleation of Pearlite A correct theory for the formation of pearlite was necessary if quantitative relationships for harden-64 ability.; in steels were to be determined. Theories: for the formation of pearlite existed almost as soon as the con stituent was observed under the microscope. An excellent review of the theories for formation of 56 pearlite is given by Hull and Mehl. From experimental evidence accumulated up to the time of their review, they summarized the then current understanding of the genesis of pearlite as follows: "...Pearlite forms directly from austenite by a process of nucleation and growth and colonies of pearlite originate as a result of edgewise growth and sidewise nucleation and growth. Ferrite, cementite or both ferrite and cementite simultaneously may serve to nucleate pearli te." The question of which constituent served as the active nucleus of pearlite remained a controversial one due to the 56 57 somewhat contradictory available evidence. ' However it was generally accepted, based on studies of orientation relationships with pro-eutectoid cementite, that cementite 30 was the most probable active nucleus for pearlite. This generally accepted interpretation had to be modi fied in the light of new evidence provided by Hillert,58 Hultgren and Ohlin.^'4 Through, some cr.itical experiments, they 65 found that ferrite was an equal partner with cementite in nucleating pearlite and that the growth of colonies took place not by repeated sidewise nucleation and growth but by the branching of existing ferrite and/or cementite plates. Hence during the random composition fluctuations that occur in the metastable body of austenite, there is a point, structurally and energetically, of no return. The main barrier, i.e. the creation of surface energy acts as a restraining force for nucleation and is inversely proportional to the size of the particle. Therefore there exists a critical size beyond which the thermodynamic driving force favouring the formation of a new phase, dominates. Based on his observations, Hillert envisioned that the ferrite and cementite of pearlite were initially competing with each other and only gradually: was cooperation developed. Depending on the 1evel of cooperation, the degree of lamel-larity was determined. Hillert argued that all the observed forms of pearlite, lamellar through spheroidal, could be explained by this concept of "level of cooperation". In such a si-.tua.tion, the nucleation rate, can be inter preted as the rate with, which these 'embryo1, of either ferrite or cementite fluctuate to critical size,beyond which they become stable. 66 Pearlite nucleation uses essentially pre-existing sur faces such as grain corners, grain edges and grain boundaries, due to the contribution to the driving force of such sur faces, and is therefore heterogeneous.. 19 Johnson and Mehl analyzed the effect of changing nucleation rate using the J.M equation based on the assump tions summarized in the previous chapter. They defined a shape factor 'X' where: By selecting different values for this constant by keeping 'a1, the grain size and G, the growth rate, constant they determined the effect of different values tin the nucleation rate, N, on the isothermal reaction. The result of this can be seen in Fig. 3.1 where the shape factor varies between 1 and °°, this representing an extreme variation tn N. The interesting result of this analysis is that the time of the reaction is changed only by 60%, although N changes from 1 to °°. The effect of low and high nucleation rates on the rate of the pearlite reaction when the growth rate and grain size are constant can be demonstrated schemati cally as shown in Fig. 3.2. To test their equations, real nucleation rates were Fig. 3.2 Schematic representation of the effect of varying rates of nucleation on the rate of reaction with grain size and growth rate constant (Ref. 30). 68 needed; in fact measurements of nucleation rate for the austenite-to-pearlite reaction were made before Johnson and Mehl formulated their equation. The inherent difficulty in trying to observe the initia tion of a transformation is that, invariably the nucleation event occurs on too localized a scale in both space and time to be detected with available techniques. Hence, there is little hope of making direct measurements on the nuclei as they are being created or to ascertain the exact nature of the process. We can at best examine the details of nucleation using models whose predicted behaviour seems to agree well with the observed rate of nucleation and its dependence on known parameters, The earliest nucleation measurements are reported by Mirkin and Blanter,59 a .! Scheil and Lange-Wei se.f 0 and oftater 37 a more systematic investigation by Hull, Col tori..arid Mehl. There are two accepted methods for measuring nucleation rate; 1. Determining the nucleation rate by metal!ographical ly observing the number of pearlite nodules per unit volume in a series of specimens reacted for different times at one isothermal reaction temperature. The nucleation rate is the time derivative of the number 69 of nodules;. Th.e. assumption in this, approach, is; the. nodules; are of spherical shape. Scheil and Lange-60 Wei se using this method, measured th.e. rate at which new nodules, reached a measurable size in the specimen, i.e. measured the nucleation rate. 2. Determining the nucleation rate by measuring the size distribution of pearlite nodules in a single sample. In addition to assuming spherical nodules, this method also assumes that G is a constant with time and is uniform from nodule to nodule. In their review of the various methods of measuning 61 the nucleation rate Cahn and Hagel stated that the assump tions necessary for the simple specimen method to work are not valid and that the multi specimen method is the best suited for examining the pearlite nucleation rate. The nucleation rate is known to be influenced by the austenitising time and temperature, the grain size, and the homogeneity of the austenite. Early nucleation measure-ments suffer from the lack of specification of information and therefore are difficult to interpret (Table 3.1 and Fig. 3.3). As can be seen in Table. 3.1 and Fig. 3.3, the. nuclea tion rate is usually reported as the number of nodules; per 70 TABLE 3.1 Approxijnation of N ucleati on in Eutect o i d Steel, „ P c 60 Grann Size 4-5. Temperature of Formation °e No. of Nuclei per cm3 per sec No,, of Nuclei :per cm2, of grain surface area per sec. 717 5xl02 1.6 704 7x10 4 2. 2xl02 662 2xl06 6.3xl03 620 6x1 07 1.9x105 580 3xl08 9.4xl06 71 Fig. 3.3 Number of nuclei versus Reaction Time for different unit volume grain sizes (Ref. 60). 72 3 2 mm .st . and sometimes as the number of nodules per mm .s: .. The main variables affecting the nucleation rate per unit volume can be seen to be grain size and isothermal reaction temperature. The lower the reaction temperature, the larger the driving force for nucleation and the smaller the grains, the more sites available for nucleation at grain corners, edges and surfaces. One shortcoming of the metal 1ographic determination of the nucleation rate is that it can be car ried out only until approximately dZ0%.t 6f<% the . i ; sample is transformed, after which impingement of the pearlite nodules makes this method inaccurate. Recently, measurements of the nucleation rate on a 62 6 3 number of steels were carried out by Brown and Ridley. ' They determined the nucleation rates by a number of methods, all employing data from the inverse cumulative distribution' curve (Fig. 3.4). Their method (!) uses the d versus t plot (Fig. 3.5) constructed by drawing horizontals to the inverse cumulative distribution curve (Fig. 3.4). By extrapolating graphs of d versus t for different ENV (total number of nodules/unit volume) to zero, the positive intercepts with the time axis gives the time at which there is a corresponding £NV value at d « o. The second method,2[2) uses data generated by constructing verticals on the inverse cumulative distribution curve (Fig. 3.6). Finally, the Johnson-Mehl equation (Equation 2.4) is used to determine 0 i Q z o z 3 10" Troniformotion tcmperotuft 643 TrontformoTion \ \ \ *\ time, mm \ \ \* \ * 35 \ • \ \ \ o <5 - • 55 • 65 i i_ Fig. NODULE DIAMETER d«IO,mm 3.4 Typical Inverted Cumulative Distribution graph (Ref.62). < a io 73 Tr on 1 fO fin o r ion remperorurr 645 C / // X IN, / // / / • 10 o 50 /// / A • 10' , /// s s » 5 " KT My. • K)J 1 —L 1 20 JO 40 50 60 TRANSFORMATION TIME t, 70 Fig. 3.5 Nodule Diameter (d) versus Transformation Time (t) (Ref.62) A 60 ~T1 Steel AjO-SiC Tronsformotion i i 1 temperoture, 720*C i -60 -40 -20 - -dx lo'mm 1 0 40 50 60 70 TIME (t), s 90 Fig. 3.6 Number of nodules (&N) per unit volume versus Reaction Time (Ref. 62). 74 nucleation rates. The results of all three procedures can be seen on Table 3.2 and demonstrate good agreement. Increas ing undercodl be seen to increase the nucleation rate.; Also the nucleation rate seems to exhibit a time dependence at isothermal transformation temperature (Fig. 3.6). 3.1.2 Growth of Pearlite Any theory to explain the growth of pearlite structures had to take into account: 1) the lamellar structure of the cementite-ferrite aggregate and the de pendence of the carbide spacing on the transformation temperature; 2) the magnitude of the growth rate of pearlite colonies and the increase in growth rate at lower temperatures; and 3) the inhibition of growth with alloy additions. The kinetics of pearlite growth has been examined both theoretically and experimentally by many workers and signifi cant calculations have been carried out by Scheil,68 Brandt,69, Zener70 and Hillert.71 Apart from its techno logical importance, the uniformity and reprodueabi1ity of the lamellar structure has been an area of interest. The main factors influencing the pearlite growth rate can be demonstrated by using the approximate growth, equation 5 that was derived by Mehl and Hagel based on diffusion 75 TABLE 3.2 Comparison of Nucleation Rates Determined by Using 3 Different Methods.62,63 Temperature °C - 3 -1 Nucleation Rates [nuclei, mm s ) Method 1 Method 2 Johnson-Mehl Equation 720 2.7xl0_1 9.4xl0"2 -2 712 4.2xl0_1 5.0xl0_1 5.0xl0"2 702 5.0 1.0 1.8xl0_1 685 33 18 2.8 667 110 20 9 76 geometry, diffusion of carbon and concentration gradients across the pearlite interface. At.any given temperature, D AC 6 a — ...(3.2) S P where S is the interlamellar spacing of pearlite, AC is the concentration gradient- and -D is the diffusivity of carbon in austenite. This equation does not agree very well with experimental data but produces the same shape as experimental data and therefore makes possible certain deductions. The growth rate as can be seen from Equation 3.2 is not dependent on grain size or any other structural factor. Since a 1.1. of the quantities on the right-hand side of Equation 3.2 are temperature dependent, clearly one would expect the growth rate of pearlite to be tempera ture dependent as well. With decreasing temperature the gradient term AC increases and D and S decreases. But c p Dc decreases relatively rapidly and tends to dominate the growth. The usual way of measuring the growth rate of pearlite has been to metallographically measure the largest nodules on specimens reacted for a series of times at constant temperature. The time rate of change of the nodule size 77 is taken as the growth, rate. This method can only measure growth until impingement occurs, which is usually at approxi mately 20% transformation. Growth, rates measured by Scheil 60 56 and Lange-Weise (Fig. 3.7), Hull and Mehl (Fig. 3.8) and 37 Hull, Colton and Mehl (Fig. 3.9) all demonstrate a con stant growth rate at an isothermal transformation tempera ture . Growth rate can also be determined indirectly from inverse cumulative distribution curves (Fig. 3.4). From the same graph of d versus t (Fig. 3.5) drawn by construct ing horizontals to the inverse cumulative distribution curvegrowth, rates can also be obtained by determining the time derivative of these plots. Growth rates deter mined in this way (1 );, again compare well with growth rates determined, in the traditional maximum nodule size method (2), as can be seen in Table 3.3. However an apparent paradox exi sts ti.n the graphical determination such that only the growth rate of nodules of constant size can be determined. The effect of growth rate on the isothermal transforma tion can be seen by examining the Johnson-Mehl curves. The growth rate will, influence both the shape factor (Equation 3.1 ). and. the time seal e factor, Z where 78 Fig. 3.7 Nodule Diameter versus Reaction Time grain sizes (Ref. 60). for different 79 C / t it i* te TlMC IU HCONDS Fig. 3.8 Nodule Radius versus Reaction Time (Ref. 56). 25 SO 75 100 125 150 SECONDS Fig. 3.9 Nodule Radius versus' Reaction Time (Ref. 37). 80 TABLE 3.3 Comparison of Growth Rates Obtained by Using Two Different Methods.62'63 Temperature Growth Rates (mm/s) °C Method 1 Method 2 712 l.lxlO"4 l.OxlO"4 702 4. 3xl0~4 5.0xl0"4 685 1.6x10"3 2.2xl0"3 675 2. 2x10"3' 3.8xl0"3 667 2.5xl0"3 5.4xl0"3 655 2.7xT0~3 8.5xl0"3 648 3.3xl0"3 1.lxlO"2 81 A change in G that will result in a variation of the shape factor from 0.3 to 00 can be seen to change the shape of the reaction curve from 'c' to 'a' (Fig. 3.10). It can be seen from Equation 3.3 that increasing the growth rate has a similar effect on the overall transformation kinetics as decreasing the grain size. In reality though,the growth rate is a far more important variable, for it can be varied over a much greater range than grain size, by alloy addi tions. 3.1.3 Additivity Due to the independent variation of nucleation and growth rates, to mathematically describe non-isothermal reactions it is necessary to show that the instantaneous reaction rate is only a function of the amount of transforma tion product present and the reaction temperature. This is the additivity requirement. 32 To define the concept of additivity Christian. con siders the simplest type of non-isothermal reaction that is obtained by combining two isothermal treatments,as shown in Fig. 3.11. The assembly is transformed at temperature T1 where the kinetic law is f - f^ (t) for a time t-j, where f is the fraction transformed. It is then very quickly transferred to a second temperature T^. If the reaction is additive, the course of the transformation at 10 will be 83 100 0 j* 501 o2 REACTION TIME (sec) 100 Fig. 3.11 Schematic representation of the principle of additivity. 84 exactly the same as if the fraction transformed at T-| , f-, (t»j ) had all been transformed at T,,. Therefore if t2 is the time taken at to produce the same amount of transformation as produced in time t^ at , W = fz(tz) ...(3.4). and the course of the whole reaction f = f^t) t><<t] = f2(t+t2-t]) t > t] ...(3.5) For example, if ta-| is the time taken to produce a fixed amount of transformation 'fa' at and t^2 is the cor responding time to produce the same amount of transformation at T2, then in the composite process above, an amount 'f ' of transformation will be produced in a time, t = ta2, - t2 + t1 if the reaction is additive If t1/t2 ...(3.6) *a2 !JL + ^hl - ! ...(3.7) tal ta2 An additive reaction thus implies that the total time to reach a specified amount of transformation is obtained by adding the fractions of the time to reach this stage i sothermal ly until the sum reaches: unity. The generaliza tion of the last equation to any time temperature path is:; t dt 1 ...(3.8) where t(T) is the isothermal time to stage 'fa' , and t is the time to 'fa' for the non-isothermal reaction. This equation can only be derived if Equation 3.6 is true and this relationship will hold only if the reaction rate is dependent only upon: 1. Fraction transformed 2. Temperature Christian suggests that any transformation for which the instantaneous reaction rate may be written: 41 = H±X (3 9) dt g(TT where h(T) is a function of temperature only and g(f) is a function only of volume fraction transformed, can be expected to be additive. Both the Avrami equation and the Johnson-Mehl equa-72 tion can be shown to be of this type. Consider the X Avrami equation, = l-exp(-btn) .Equation 2.5 86 where n ~ constant b =. function of temperature only Rearrangi ng log (1-x) =• -btn t = n/'°gp^ Differentiating with respect to 't' (i.e. Equation 2.5) n - e v- n b. t J n-1 (l-x)c-bn) [lQgn-x)] " 1/n n"1 (l-x)(n).(-b) .[log(l-x)] rt n:(-b)1/n n-1 ^1-x) hog(l-x)^ (3.10) = MT) g(x):. In the Johnson-Mehl equation: X = 1 - exp(-| NG3t4) where n = 4 and b = -| NG , ;hence the J M. equation is expected to be additive if N and G are functions of temperature alone 87 1 8 Avrami suggested that non-isothermal transformation kinetics could be predicted using isothermal kinetic data N if the ratio of the nucleation rate to the growth rate, g, remained a constant over the temperature range of the reaction (i.e. that they have the same temperature varia tion). This condition was. termed the "isokinetic condi-' tion". p p OC Early nucleation and growth observations ' showed that the isokinetic condition did not hold. Cahn recogniz-r ing that this condition was too restrictive proposed the 35 concept of early site saturation; He observed that, the pearlite reaction,*, exclusively a grain boundary reaction,"! exhausted the available nucleation sites very early in the reaction (Fig. 3.12). Growth was thus the dominant factor and the transformation consisted essentially of widening of grain boundary slabs of pearlite. Growth being only a function of temperature ensured that the reaction was a function only of temperature and instantaneous fraction transformed and therefore satisfied the additivity criter ion . Cahn went on to propose a series; of criteria that would test the site saturation condition. Metal, 1ographically he suggested that with .a partially transformed"•specimen,": iif it .is 88 o o s ' i I I • L_ 0 0.2 0.4 0.6 0.B VOLUME-FRACTION TRANSFORMED Fig. 3.12 Graph showing fraction of grain boundaries occupied by pearlite as a function of volume-fraction transformed in a Fe-9Cr-lC alloy austenitised for 12 hrs. at 1200°C (Ref. 36). 89 possible to see one pearlite nodule per grain, site satura tion was; beginning to occur. Based on at^least';one~nodul e ; , per grain, if G tn ,-^ ± Q.5 ... (3.11 ) d where d is the grain size, G is the growth rate and § is the time to complete 50% of the transformation. This implies a condition of site saturation. Cahn's second criteria for site saturation, based on nucleation rates for specific sites was calculated on the basis of a grain shape model and energetics of available 34 nucleation sites as developed by Clemm and Fisher. The grains of parent austenite were assumed to be equally large tetrakaidecahedra arranged so that they fill space. A tetrakaidecah.edra-i.-s a body centered-cubic array oriented so that the square faces are on the (100) planes,, and hexagonal faces are on the (111) planes. The distance between square faces is designated D, the grain diameter of the austenite (.Fig. 3215). On the basis of a unit volume, Cahn, calculated the number of grain corners, length of grain edges and area of grain surfaces as follows: 90 c[number of grain corners] , l|/mm3 ...(3.12) mm DJ L[length of grain edges,-, R 8^ m/mm3 ...(3.13) mm- D crsurface arean _ 3.35M 2/MM3 /- , S|_ 3- J " —g—mm /mm ...(3.14) mm The site saturation criteria for specific sites become N > 2.5 \- ...(3.15) c D for corner i site" saturation. N > 1 03 6 ...(3.16) 4 D for edge site saturation N > 6xl03 _G_ ... (3.1 7) 4 D for surface site saturation. After establishing that the reaction was site saturated, the kinetic: laws were easily obtained depending on whether the active growth sites, are grain boundary surfaces, X ,= l-exp(.-2SGt) . (3.18) 91 or grain edges, X> l-exp(.-TrLG2t2) ...(3.19) or grain corners, .. .(3.20) Cahn did derive a reaction equation for transforma tions with very low nucleation rates, e.g. at high tempera tures, based on Johnson and Mehl's analysis of time depen-1 9 dent nucleation rates, but h,e stated that even for this condition there was the possibility of local site saturation. Thus the current state of understanding on the nuclea tion and growth of pearlite, their relationship to the additivity principle and the ability to predict continuous behaviour from constant temperature data is as follows: 1) The isokinetic condition (N/6 = constant) is not a generally observed phenomenon., 2) For the pearlite reaction in the majority of steels, site saturation is a general phenomenon, thereby permitting the application of the additivity principle. In this thesis metal 1 ograpb.i c work was undertaken to investigate the nucleation and growth, aspects of the pearlite reaction for a eutectoid plain carbon steel and 92 to test the various criteria for establishing the applic ability of the additivity principle for the pearlite reaction. 3.2 EXPERIMENTAL PROCEDURES Experimental determination of the pearlite nucleation and growth rates was: done on samples heat treated in salt pots using the same equipment and heat treatment procedure as previously described in Chapter 2. A series of 10 mm diameter, 1-2 mm thick, disc-shaped samples were reacted at constant temperatures for different times to obtain a number of specimens covering th.e transformation range up to 20% pearlite. These samples could then be examined metallo-graphically and use made of the method employed by Scheil and rn O "7 CO Lange-Weise, Hull, Colton and Mehl and Ridley and Brown for establishing the nucleation rate N, and the growth rate G Two reaction temperatures 640°C and 690°C were used, these corresponding to, the high temperature, low driving force, flat portion of th.e TTT diagram (690°C), and high driving force., nose portion of the TTT diagram (640°C). Tfie austenitising treatment was 5 minutes at peak temperature. The austenitising temperatures, isothermal reaction temperatures and the resulting range of grain 93 sizes, obtained can be seen in Table 2.3. A 2% nital etching procedure was- employed for reveal ing the microstructural details;, the same as that used to determine the reaction kinetics described in Chapter 2. The following prefetching treatment was required for revealing both prior austenite grain size and the pearlite. After being cold mounted, the specimens were treated in a boiling solution of 2 g picric acid, 25 g NaOH and 100 ml water for 15 minutes. A swab etch with 2% nital was then carried out to reveal the pearlite nodules. A pearlite nodule counting procedure was performed manually on representative photo-micrographs, .of ; .each specimen using the Zeiss optical microscope. A particle size distribution was carried out for each specimen per unit area, and these were corrected using the Sch.eil.-and, Schwartz procedure, to obtain the number of 3 nodules/mm . An example of the correction procedure can be seen on Table 3.4 for the reaction temperature 64;Q°C and austenitising at 950°C. Corresponding nucleation rates 3 were obtained from graphs of the number of nodules/mm versus reaction time. The slopes of these curves gave N nodules 3 mm .sc ; CAverage slope was taken for reactions with increasing nucleation rate.) TABLE 3.4 Correction Procedure to Determine Number of Nodules Per Unit Volume From Number of Nodules Observed on Polished Surface. Reaction Temperature 640°C, Austenitising Temperature 950°C. Diameter(mm) 12.5xl0"2 25xl0"2 37.7xl0"2 50xl0"2 62.5xl0"2 Number of particles per mm2 135 110 95 55 15 Number of particles with actual 9 d = 62;$xlO mm 25 Corrected no. 135 108 91 50 Number of particles with actual d = 50x10~z mm 75 Corrected no. 133 101 76 Number of particles with actual -d = 37.5x10"^ mm 102 Corrected no. 127 81 Number of particles with actual d = 25x10"^ mm 93 Corrected no. 115 Measured distribution 135 110 95 55 15 Corrected distribution . 115 93 102 75 25 Number of particles per unit volume 9200 3720 2720 1500 400 Total number of , particles per mm 17,540 1 U3 -1^ 95 The pearlite growth rate was: determined from similar salt pot heat treated specimens that had been reacted for times of up to approximately 20-30% of the total trans-37 formation. The standard method of measuring the diameter of the largest individual pearlite nodule as a function of isothermal transformation time was used. The alternative measuring procedures of nucleation and C p CO growth rates used by Brown and Ridley ' were also examined, as a check on the magnitudes of the values obtained by the two techniques. This involved construction of inverse cumulative distribution curves for each isothermal trans formation reaction. These curves were used for the con struction of the plots of nodule diameter versus isothermal reaction time and the number of nodules versus isothermal mm reaction time. 3.3 RESULTS AND DISCUSSION 3.3.1 Nucleation Rates The main method of obtaining the nucleation rate from plots of number of^oduTes versus is:othermal trans. mm formation time can be seen on Fig. 3.13. The slope of the individual isothermal transformation curves gives number of nodules . ... , , TL . im-i^.— ^ —- i.e. the nucleation rate. The influence mm . s. of the reaction temperature and the grain size on the 96 10* ICf to. 1 ,o5 to X) o 10' 10 oo o O A °8A A Reaction Temperature: 640°C Austenitising Treatment O 800°C O 840°C A 950°C • II00°C • ± 10 20 Time (s) • t± • • 30 Fig. 3.13a Nodul e-- versus Reaction Time for isothermal pearlite 1 ran t, reation at 640°C. I05h 10 IO E E i 10 o z 10 10 o o 200 Nodules Number of Nodules v.s Time mm REACTION TEMPERATURE : 690°C AUSTENITISING TREATMENT O 800 °C U 840 *C A 900 °C O 950 °C • A 400 600 TIME ( Sec ) 800 1000 rig. J.UD - versus Reaction'Time for isothermal pearlite reaction at 690°C mm 1200 98 resulting nucleation rate can be seen by examining Table 3.5. Increasing the pearlite grain size reduces the nuclea tion rate dramatically. This can also be observed metallo-graphically on the photomicrographs shown in Fig. 3.14 where the initial stages of the reaction are compared for small and large grain size specimens. The alternative method of determining the nucleation rate requires drawing vertical lines on the inverse cumula tive distribution curves (Figs. 3.15, 3.16) at values of constant 'd'. This approach yields the reaction time re quired for obtaining an equivalent size distribution for a given grain size; the resultant graph can be seen on Fig. 3.17. The time derivative of each line on Fig. 3.17 gives the number of nodules^ |e> the nucleation rate. Tne mm comparison of nucleation rates obtained by both methods can be seen in Table 3.6 and agree reasonably well. With increasing grain size from A.S.T.M. 9.1 to A.S.T.M. 3, the number of grain corners, the grain edge length and the grain surface area, on a unit volume basis, are dramatically reduced. This explains the decrease in the nucleation rate. Also it can be seen that with greater undercooling and larger driving force for 99 TABLE 3.5 Pearlite Nucleation Rate Data Austenitising Temperature °C A.S.T.M. Grain Size Average Grain Diameter (mm) Nucleation Nodules Rate = 3, mm /s 640°C 1 690°C 800 9.1 15 10,400 995 840 7.8 27 18,000 382 900 7.4 30 — 7xl0"2 950 7.3 32 3,800 16xl0"2 1100 3.0 200 6 -Fig. 3.14a Pearlite nodules in specimen partially transformed to approximately 10% transformation at the isothermal reaction temperature of 640°C. Grain size, A.S.T.M. 7.3 Magnification X160. Fig. 3.14b Pearlite nodules in specimen partially transformed to approximately 10% transformation at the isothermal reaction temperature of 640°C. Grain size A.S.T.M. 3 Magnification X160. 101 Fig. 3.15 Inverse Cumulative Distribution graph for isothermal transformation at 640°C. Fig. 3.16 Inverse Cumulative Distribution graph for isothermal transformation at 690°C. TD ,3 A 10 10' 10 1 i i 1 1 • • — A — • A O • A O o O A O O Austenitising Temp:950°C - O Reoction Temp:640°C --2 Dia. • 1X10 mm nodule A 2xio"2 n O 3XI0~2 H » H O O 4XI0"2 II M H i i 1 1 1 8 9 Time (s) 10 3.17a Number of nodules per unit volume versus Reaction Time obtained by constructing verticals to the Inverse Cumulative Distribution graph. Reaction temperature 640°C, Grain Size ASTM 7.3. i 1 i O -60 Austenitising Temperature : 950°C Reaction Temperature : 690° C 50 O 2 XI0 2mm O 4XlO~2mm nodules diameter -E to a> 40 A 8XlO~2mm • l2XI0-2mm O l6XI0"2mm II II II H o -• i \J O T3 A Z W 30 20 -o o o o" A 10 o 0 A A n D» A 0 • o n i A i LL—=u ^ 1 300 400 500 600 700 Time (s) 3.17b Number of nodules per unit volume versus Reaction time. Reaction temperature 690°C, Grain Size ASTM 7.3. TABLE 3.6 Comparison of Nucleation Rates Obtained Using Graphical  and Metallographic Methods A.S.T.M. Grain Size Isothermal Reaction Temperature °C Nucleation Rate -nodulesx K 3 ; mm .s Method Source 7.3 640 3800 Metallographic 7.3 690 16xl0"2 Metallographic 1080 steel used in this work 7.3 640 3000 Graphical (For the smallest size distribution) 7.3 690 8xl0~2 Graphical Literature Values 5% 640 47 Metallographic 0.78 C Plain Carbon Steel37 5Js 690 5.9xl0"2 Metallographic 650 36 Metallographic 0.80 C Plain Carbon Steel37 4Ji 689 6.2xl0"2 Metallographic 0-1 685 18 Graphical 0.81CPlain Carbon Steel37 o nucleation,the nucleation rate at 640°C is at least an order of magnitude larger than that obtained at the 690°C isothermal reaction temperature. Also on Table 3.6 are results of nucleation rate measurements made by different workers using the different methods. 3.3.2 Growth Rates. Growth rates were determined from plots of the largest single pearlite nodule diameter versus isothermal transformation time (Fig. 3.18). The influence of grain size and reaction temperature on the pearlite growth rate can be seen in Table 3.7. The alternate way of determining the pearlite growth rate is to construct horizontals to the inverse cumulative distribution curve, (Figs. 3.15, 3.16), at constant values Qf number of nodules; Thfs yields & re1 ationS:hip between mm reaction time and nodule diameter for specific nodule size distributions; (Fig. 3.19). The time derivative of these curves give the pearlite growth rate. The resulting growth rates are more scattered than those obtained by direct measurement of the largest pearlite diameter as can be seen in Table 3.8; this; table also contains the pearlite growth rates measured by various; other workers using both methods of measurement. 28 24 h 20 I 16 CM I 2 12 8 0 1 1 1 • Reaction Temperature.- 640°C — Austenitising Treatment -O 800°C O 840°C • A 950°C • II00°C -- • -° A -CP0 AA — o 1 I 1 10 Time (s) 40 o Fig. 318a Largest Diameter versus Reaction Time. The slope of each curve gives the growth rate (mm/s) for different grain1sizes. Reaction temperature, 640°C. 25 _ 20 6 E CM o X Q o _l 15 CD I 10 o b to cn 0 10 Reaction Temperature-. 690°C Austenitising Treatment O 800°C A 840°C • 900°C • 950°C • J • A O o o o A & A A • 100 Time (s) 1000 Fig. 3.18b Largest Diameter versus Reaction Time. Reaction temperature, 690°C. o co 109 TABLE 3.7 Pearlite Growth Rate Data Austenitising Temperature °C A.S.T.M. Grain Size Pearlite Growth Rate(mm/s) 640°C 690°C 800 9.1 10.6xl0"3 5.4xl0"4 840 7.8 8xl0"3 9.8xl0"4 900 7.4 2.9xl0~4 950 7.3 6.7xl0"3 3.3xl0~4 1100 3.0 10.7xl0"3 no E E CM « 4 O X •o 0 Austenitising Temp: 950°C Reoction Temp:640°C O I04 nodules/mm3 ^N>d O I03 A 500 • I02 .A o 0 • A o • A o O o 7 8 Time (s) • A o O 10. Fig. 3.19a Nodule diameter(d) versus Reaction time (t),obtained by constructing horizontals to the Inverse Cumulative Distribution graph. Slopes of each curve gives growth rate (mm/s). Reaction temperature, 640°C. Grain Size, A.S.T.M. 7.3. Austenitising Temperature:950°C Reaction Temperature : 69Q°C | O 50 nodules/mm3 £N>d O 10 A 5 • 2 • • 1 A ~ 300 • A O • A O O _L 400 500 Time (s) A O O i 600 O o 7( 3.19b Nodule diameter(d) versus Reaction time (t). Reaction temperature, 690°C. Grain Size, A.S.T.M. 7.3. TABLE 3.8 Comparison of Growth Rates Obtained by Using Metallographic and  Graphical Methods. A.S.T.M.:. " .Grain..::. Size Reaction Temperature °c Growth Rate (mm/s) Method Source 7.3 640 6.7xl0"3 Largest Diameter 7.3 690 3.3xl0~4 Largest Diameter 7.8 640 8.0xl0"3 Largest Diameter 1080 steel used 7.8 690 9.8xl0"4 Largest Diameter in this work 7.3 & 7.8 640 5-45x10"3 Graphical 7.3 & 7.8 690 l-20xl0"4 Graphical Literature Values 5 640 6.2xl0~3 Largest Diameter 0.78 C Plain Carbon 5 690 8.5xl0~4 Largest Diameter Steel37 4 650 3.6xl0~3 Largest Diameter 0.80 C Plain Carbon 4 689 4x10"4 Largest Diameter Steel37 0-1 685 1.6xl0"3 Largest Diameter 0.81 C Plain Carbon c* T62 Steel OTI 685 2.2xl0"3 Graphical ro 113 An important conclusion from the growth rate measure ments is the relative independence of growth rate cfrom austenite grain size. For the large range of austenite grain sizes exaroi ned,little if any effect is seen on the growth rate of the pearlite. The growth rate is largely determined by the isothermal reaction temperature. This 2 result is consistent with, the previous work of Dorn, et al., Hull, et al .37 and Sch.eil et al .60 The following observations can be made after an examination of the photomicrographs of the small and large grain size samples shown in Fig. 3.20: 1. Pearlite nodules in the small grain size sample tend to be located at 3 or 4 grain intersections and have an approximately equi-directional growth (spherical), growing into all surrounding grains (Fig. 3.20a). 2. Pearlite nodules in the large grain size sample have a greater tendency to nucleate at 2 grain inter sections, grow only into 1 of the adjacent grains and therefore to have non-spherical shapes (Fig. 3.20b). The possible reasons for these different growth morphologies can be summarized as; fol 1 ows: 1. Pearlite nodules will nucleate at the high energy, multi-grain intersections available in the small grain-sized material. Fewer of these high energy sites per unit volume are avai1able in the Fig. 3.20b Pearlite nucleation in large grain size specimen (A.S.T.M. 3). Mag. X 230. 115 coarse grained sample, requiring the nodules to nucleate at two grain intersections in the large grained material. 2. The one-sided Chemi-spherical) growth of pearlite nodules nucleating on the grain boundaries that could be due to lower interface mobility in one direction, suggests the existence of a special orientation relationship*as observed for nodules on the flat grain boundaries of the larger grain size (Fig. 3.20b). On the other hand for nodules nucleating at multi-grain intersections (i.e. either corner or edge) in the smaller grain-sized sample, a special orientation relationship would be highly unlikely, resulting in predominantly spheri cal growth (Fig. 3.20a).58'64'74 The effect this difference in nucleation and growth morphologies would have on the kinetics of the isothermal pearlite reaction for small and large grain sizes cannot be separated from the effect of differing nucleation rates for the two reactions. Roth, the lower nucleation rate and the non-spherical nature of growth in the large grained samples will result in a slower isothermal reaction rate. 3.3.3 Additiyity and Si te Saturation It Has been demonstrated consistently that the 116 Avrami'.; equation is able to express the kinetics of non-isothermal pearlite transformations, assuming the adch'ti-38 39 49 72 73 vity principle to be valid. »>•>., pQr thiS'Same data the isokinetic condition as' defined by Avrami, i.e. N the proportionality of over a given reaction temperature range, has been found not to be valid as shown in Table 3.9, consistent with earlier observations (Fig. 1.11). This is a consequence of the more rapid increase in the nucleation rate with increasing temperature as compared with the smaller change in the growth rate. The site saturation concept as described by J. W. 20 3 5 Cahn ' was also examined to explain the applicability of the additivity principle. The number of available 3 nucleation sites/mm for any austenite grain size can be determined using Cahn's austenite grain shape model of a space filling tetrakaidecahedra. An assessment of the site saturation, criteria derived by Cahn, based on the nucleation rate for specific sites can be seen in Table 3.10 for corner site saturation. Since it is experimentally impossible to measure nucleation rates for each individual nucleation site, the comparison was made using the corner nucleation rate. As can be seen, the experimentally determined total nucleation rate, 117 TABLE 3.9 Test of Isokinetic Condition N - Constant £ -Austenitising Temperature °c A.S.T.M. Grain Size 3 N Nodules/mm E mm/s 640°C 690°C 800 9.1 98xl04 184xl04 840 7.8 225X104 39xl04 950 7.3 57xl04 0.05X104 TABLE 3.10 Cahn : Nucleation Rate Criteria Ns > 6xl03 G/D' Ne > 103 G/D Nc > 2.5 G/D Austenitising Temperature °c Reaction Temperature °c 2.5 G/D4 o (1/mm .s) Total Nucleation Rate /nodules \ 1 3 mm . s 690 26,675 995 800 640 528,000 10,400 690 4,610 382 840 640 37,500 18,000 900 690 895 0.07 950 690 787 0.2 640 15,900 3,800 1100 640 16.7 5.6 118 2 n 3 R fi l which is Nc + Ne + Ns ' ' is consistently lower than those required for corner site saturation and therefore much lower than is required for edge or boundary nucleation. Cahn's other criterion for determination of early site saturation was based on a consideration of attaining one pearlite nodule per grain. In a photomicrograph of speci mens partially reacted to approximately 15% transformation (Fig.3.21), it can be seen that one pearlite nodule per grain is metal 1ographically far from true. This was con firmed by a calculation based on determining the number of austenite grains per unit volume from the grain diameter and the experimentally measured number of pearlite nodules per unit volume. The results of this calculation done for specimens reacted partially up to approximately 15% transformation is given on Table 3.11. It can be seen that, without exception, for all of the cases examined, the condition of one nodule per grain is likely never attained. Cahn also derived the mathematical expression for this metal 1ographic consideration based on the time it would take one nodule, to consume half of one grain: ^-2. <_ 0.5 . . .(3.11) d This would hold if site saturation was taking place. The results of this calculation can be seen to suggest that 3.21 Initial nucleation rate in terms of number °f nodu1es> grain metallographically in specimen transformed partially to approximately 15% transformation. Mag. X 600. TA BLE 3.11 Initial Nu cleat ion Rate in Terms of 120 Nodules;/Grain Austenitizing Temperature °C C.5 min) I.s,oth.e.rmal Transformation Temperature A.S.T.M. Grain Size Initial Nucleation Rate 3 (no/mm ) Initial Number Nodules, Grain 8Q0 640 690 9.1 9.1 10,400 995 1/0-88 1/141 840 640 690 7.8 7.8 18,000 382 1/32 1/44 950 640 7.3 3,800 1/19 1100 640 3 6 1/6 TABLE 3.12 Cahn : Early Site Saturation Criterion Austenitizing Temperature °C C5 min) 640°C Gt0.5 d 690°C 800 4.5 3.0 840 2.5 5.4 9Q0. - 11.0 950, 2.1 12.4 11Q0. 2.4 -this condition 3.12). for site saturation is not realized 121 (Table In the light of these calculations one would have to conclude that since the isokinetic condition does not hold and site saturation has not taken place, the additivity principle should not be applicable. Yet there is direct evidence that the additivity principle can be applied 38 39 40 72 successfully to predict continuous cooling behaviour. ' ' ' ' It is important to recognize the fact that both Avrami's "isokinetic condition" and Cahn's "site saturation model" were a sufficient condition for the additivity principle to work but were not a necessary condition. An alternative requirement for applying the additivity principle, termed "effective site saturation" was thus investigated. 3.3.4 Effective Site Saturation An experimentally determined nucleation rate is a measure of the rate at which new centres of trans formation product appear. As long as there are avai1able sites, this experimental nucleation rate need not decrease. However, as the transformation approaches completion, one would expect the available sites to be decreasing in numbers, if not exhausted. The question is; what is the contri bution to the total volume fraction transformed of the late-coming centres of growth? If an overwhelming fraction of 122 the transformed phase is the result of growth of the very early nuclei, although the experimentally measured nuclea tion rate may be a constant, the late nuclei contribute very little to the total volume fraction transformed and "effective site saturation" will have taken place. To calculate the volume contribution from nodules nucleating at different times during the course of the transformation, it is necessary to characterize the trans formation in terms of the nucleation and growth rates. The Johnson-Mehl (J.M) equation (Equation 2.4) includes these quantities to express the progress of the transformation. A calculation was; carried out using the Johnson and Mehl equation (Equation 2.4), the experimentally determined nucleation and growth rates and the appropriate isothermal reaction times corresponding to approximately 5 and 10% volume fraction transformed. A determination of the re sulting time exponent (originally 4 in the J.M equation) was made. The results for the isothermal reaction temperatures of 640°C and 690°C can be seen on Table 3.13. The time exponent values determined confirm that the Johnson-Mehl equation with its n - 4, does not characterize the pearlite reaction for the isothermal reaction tempera tures examined. 123 TABLE 3.13 Calculated Values* of the Time Exponent  in the Johnson-Mehl Equation. Austeni ti si ng Temperature °C Time Exponent for 640°C Isothermal Reaction Temperature Time Exponent for 69Q°C Isothermal Reaction Temperature 800 1.4 3.2 840 1.4 2.2 900 - 3.9 950 2.4 3.5 1100 2.8 -Calculations based on t = 0 at t 124 The • i nabi 1 i.ty " , of.- the • J.M equation to predict the volume fraction transformed was due to certain non-satisfactory assumptions. The assumptions made in the derivation of the J.M. equation are: 1. The rate of nucleation and the rate of growth are constant. 2. The growth of pearlite nodules is spherical and constant. 3. The nucleation is random (homogeneous nucleation). Although the first two assumptions are reasonable, the last assumption, in the ease of the pearlite nucleation, is definitely incorrect. Pearlite nucleates preferentially at grain corners, grain edges and/or .grain boundaries and is therefore a heterogeneous transformation product. To be able to use the J.M equation that includes nucleation and growth rates and to better simulate the actual transformation, an "inhomogeneity factor" defined as: T ^homogeneous V heterogeneous has been calculated. The schematic comparison of homogen eous versus heterogeneous reactions is made in Fig. 3.22. 125 HOMOGENEOUS NUCLEATION HETEROGENEOUS NUCLEATION ( Unit Volume ) ( Unit Volume ) ° o o After 1 sec. ^ex = ^real o ° o o°° After 2 sec. ®» <S ^ex = ^real Fig. 3.22 Schematic representation of homogeneous and heterogeneous reaction kinetics. 126 As can be seen, the rate of the inhomogeneous reaction will be slower than that of a homogeneous reaction due to greater impingement in the inhomogeneous reaction. The time dependent variation of 'I' for an isothermal reaction would be expected to have the form shown in Fig. 3.23. Because extensive 'impingement would not take place at the earlier stages of the transformation, the rates of the homogeneous and the heterogeneous reactions should not be very different. Similarly towards the completion of the reaction where the reaction rates would be very slow and.where there would not be much volume untrans-formed for nucleation and/or growth to take place in.: The difference between the rates of homogeneous and heterogen eous reactions would diminish. Both homogeneous and inhomogeneous reaction kinetics were determined using isothermal kinetic, data generated with the salt pot. The experimentally determined nuclea tion and growth rates were used in the Johnson and Mehl equation (Equation . 2.4), with n = 4, to determine the progress of the homogeneous reaction. (As assumed by J.M when deriving their rate equation.) The Avrami equation (Equation 2.5), in terms of the empirical constants 'n' and 'b' was used to follow the kinetics of the inhomogeneous (i.e. real) reacti on . Fig. 3.23 Predicted variation of the "Inhomogeneity Factor", I, with percent transformed of pearlite. 128 The effect of grain size on the "inhomogeneity factor" at different isothermal reaction temperatures can be seen in Fig. 3.24. The observed departures from the predicted behaviour could be due to twq possible considerations; 1. ' The nucleation effect; For the total range of grain sizes the possibility of a larger number of nodules located at high energy sites such as multi-grain intersections increases due to the greater availability of these sites in the fine grained material. This in turn increases the overall number of nodules that exhibit approximately spherical growth (as explained .i : earl i er in relati oh to Fig., 3. 20). 2. The impingement effect: Duetto the relative proxi mity of nucleation sites in small grained specimens, the pearlite nodules will start impinging more rapidly than in large grained samples where nuclea tion sites are far apart. Greater impingement of the pearlite nodules will give rise to relatively larger deviations from spherical growth. These two competing effects may be used to explain some of the abnormal behaviour seen on Fig. 3.24. In the 640°C graph (Fig. 3.24 a), the largest grain size samples are seen to deviate significantly from the expected be^ haviour. This could be explained by the nucleation effect 0 50 100 Volume Fraction Transformed (%) Fig. 3.24a Experimental variation of T, for the isothermal reaction temperature of 640°C. 0 50 100 Volume Froction Transformed (%) Fig. 3.24b Experimental variation of-,'I.1, for the isothermal reaction temperature of 690°C. 130 which would give rise to non-spherical growth that would increase the inhomogeneity factor. The contribution to the total volume transformed of nodules nucleating in the first 201 of the reaction was calculated by using the equation; (For the derivation of this equation see Appendix 1.) 4 ^ Vo/20 _ Z90 - U90 * W ...3.12 Zf V90 t90 where ^o/20 := Volume nodules nucleating in the first 20% at 90% transformation. Vgg .= Total volume transformed at 90% transformation. By using the time to 90% transformation for,V'gQ„ a calcula tion was carried out to determine the contribution to the total volume of nodules nucleating in the first 20% of the isothermal pearl i te transformation (i.e. t^Q - time to transformation). The results of this calculation can be seen on Table 3.14. for the range of grain sizes and isothermal reaction temperatures investigated. 131 TABLE 3.14 The Influence of Grain Size and Isothermal Reaction Temperature on Volume Contributions. ( 1 [ Contribution to the Total /olume Transformed, by Modules which Nucleated in the First 20% of the. "ransformation, at 9Q% rotal Volume Transformed (%) Austenitising Temperature f°C). Reaction Temperature (°C) 85 950 690 93 840 690 94 800 690 88 900 690 97 11QQ 640 % 950 640 82 840 640 86 800 640 132 In all instances the nodules nucleating in the first 20% of the reaction contribute to at least 80% of the total volume transformed at 90% transformation. The results clearly support the description of the experimental be haviour as "effective site saturation". This means that, the temperature dependent growth process dominates the transformation event. This observation can be coupled with an important thermodynamic consideration of the transformation process. Due to the greater volume of the pearlite phase a positive pressure would develop in the structure with increasing percent transformation. Le Chatelie'r.'s principle states that the system should move to minimize this effect, i.e. to reduce the amount transformed in areas adjacent to the growing nodules. In this case, the increased pressure should reduce the transformation temperature, thereby stabilizing the austenite to lower temperatures. The result would be to reduce the effectiveness of nucleation sites adjacent to existing nodules. Therefore this con dition would also encourage "effective site saturation". An "effective-site saturation" criterion can be formulated to test its validity for other grades of steel. By using 85% for the contribution to total volume at 90% 133 transformation, of nodules nucleating in the first 20% of the transformation in equation 3.12 the following relation ship can be obtained (Appendix A2): 12 0 — 0 •' 3 8- t g Q • ...3.13 where t2Q .. time to 20% transformation tg0 : time to 90% transformation This "effective site saturation" criterion has been tested for all experimental results of this study (Table 3.15) and for isothermal kinetic data reported in the literature for different grades of steel (Ja'bl.e 33.; 1 6').. The results show that for the total range of grain sizes, isothermal reaction temperatures and steel compositions investigated, the "effective site saturation" criterion is a sufficient condition for the applicability of the additivity principle. 134 TABLE 3.15 The "Effective Site Saturation" Criterion, t?n •-• x^J:0-38' Values Calculated for Experimental  r90 Results Determined for the 1080 Steel Used  in this Study. Reaction Temperature °C Grain Size A.S.T.M. *20 t90 *20 t90 Source 640 9.1 3.22 8.38 0.38 640 7.8 3.08 8.93 0.34 640 7.3 6.8 12.7 0. 53 640 3 31 . 76 55.14 0.58 1080 690 9.1 51 .1 1 01 . 4 0. 51 Steel 690 7.8 119.0 243.0 0.49 690 7.4 918 2275 0.40 690 7.3 847 2301 0. 37 135 TABLE 3.16 Calculated values of ^ >_ 0.38, the "Effective tgo  Site Saturation: Criterion, for Isothermal Reactions Reported in Literature. Reaction Temperature °c Grain Size A.S.T.M. t20 t9Q t20 t90 Source 500 51s 4.2 5.5 0.76 0.78XC plain 540 5% 4.8 6.5 0.74 carbon steel37 600 5k 6.4 10 0.64 630 5k 8 20 0.40 650 4% 23 42 0.54 0.80%C plain 37 carbon steel 660 B,k 70 92 0.76 690 4*s 700 1100 0.63 662 5 4.7 6.5 0.72 1.10XC steel37 691 5 80 200 0.40 0.57%C steel37 689 1 35 46 0.75 0.932X steel37 715 - 95 200 0.48 SKD-6 steel38 670 - 34Q 830 0.41 615 5-7 3.25 5^4 0.62 0.82XC plain 72 carbon steel 630 5r7 5.6 9*8 0.57 660 5-7 32.4 72 0.45 670 5-7 58 163 0.36 136 Chapter 4 4.1 SUMMARY ; The following conclusions summarize the resultsj discussion and interpretation of experiments performed to examine the kinetics of nucleation and growth of pearlite in eutectoid plain-carbon steels; a wide range of austenite grain sizes and transformation temperatures were included in this study: 1. The Avrami equation (Equation 2.5), as modified by 39 40 Tamura et al, ' to include a grain size parameter, can be used to characterize the pearlite transforma tion tn X = 1 - exp(-b ——) ...Equation.2.8 dm 2. The measured magnitude of the grain size exponent 'm' in Equation 2.8, indicates that edge nucleation of pearlite should dominate. Metal 1ographic observa tions confirm that the predominant pearlite nuclea tion site is austenite grain corners and/or grain edges; it is difficult to separate these two nuclea tion sites by metallographic observation, 137 The austenite grain growth kinetics of this 1080. steel can be characterized by using the relationship 49 developed by Alberry et al., to predict micro-structure in the HAZ of weldmentsv (Equation 2.16). This expresses the final grain size in terms of the peak temperature and holding time at peak temperature. D3' 57 - I)3/ 57 = 2.98xl012 exp /-460,000 + 1000 N ^ c„lia + 4„„ o ic ( -^j ;t ...Equation 2.15 The existing criteria that define the conditions under which the additivity principle is applicable, an 1 9 isokinetic temperature range, as defined by Avrami and saturation of aval 1ablelhucleation sites of pearlite, as outlined by Cahn, ' ' were shown to be ;tnsufficient in explaining the austenite-to-pearlite transformati on. An alternative,sufficient condition for the applic ability of the additivity principle to predict con tinuous cooling data from isothermal transformation data has been proposed. This condition was termed "effective site saturation" to express the essentially growth dominated nature of the pearlite reaction and the relative insignificance of the pearlite nucleation 138 event after the early stages of the transformation. Calculations based on the measured pearlite nuclea tion and growth rates have shown that the relative contribution of pearlite nodules nucleating in the first 20% of the transformation to the total volume transformed at the end of the transformation is very high; at least 80% of the total volume trans formed. The "effective site saturation" criterion (Equation 3.13) has been shown to be .a sufficient, condition for per mitting the use of the additivity principle, for a range of grain sizes, isothermal transformation i temperatures and steel grades. It can be summarized as follows: t^Q > 0.38 tng ...Equation 3.13 4.2 RECOMMENDATIONS FOR FUTURE WORK 1. Although salt pots have been used as the most suit able equipment for the accurate determination of nucleation and growth kinetics due to the large number of specimens involved, they have been shown to provide a very limited cooling rate. The very slow cooling rates (in the order of 25-30 QC/s), obtained on transferring a specimen from one salt 139 pot to another salt pot makes isothermal tests near the nose of the TTT curve, impossible; the trans formation initiates during cooling to the isothermal temperature. Therefore,for the satisfactory cor relation of nucleation and growth kinetics with isothermal kinetic data near and below the TTT nose and a complete fundamental, understanding of the whole range of transformation, an experimental technique which can achieve significantly higher cooling rates is a necessity. If Idisc-shaped flat specimens could be heated rapidly by using electrical resistance heating, two-directional water spraying or water jets could achieve faster cooling rates. 2. 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Hawbolt, E.B., et al., "The Characterization of .Trans formation Kinetics of Carbon Steels under Industrial Pro cess Conditions" Progress Reports 2-4 to prepared Ifor the A; US, I. T98Q-1983. 74. Aaron son, H.I. ,"Rro-Eutectoi1 Ferrite and Cementite Reactions" Decomposition of Austenite by Diffusional Processes. Ed. V.F. Zackay, H.I. Aaronson, Publ. A.I.M.E. 1962. 75. Sorby, H.C., J.I.S.I., No. 1, 1886, p.140. 76. Hawbolt, E.B., Chau, B., Brimacombe, J.K. "Kinetics of Austeni te.-Pearl ite Transformation in Eutectoid Carbon Steel", Accepted for publication in Met. Trans. 1983. Appendix 1 VOLUME CONTRIBUTIONS 147 APPENDIX 1 dx -i • ——i— —-—' i t = o t =• x t = t-j t = t2 Number of nuclei nucleating * N dx during a time dx .where-! .'• Nis the.; volume trie onti»e lea t ion, rate. The extended volume of growth of these nuclei at time t = is: a.^ Ndx . G3(t2-x)3 where a = shape factor 4 = y f°r spherical growth G = growth rate (mm/s) Therefore the extended volume (V_v) of growth of nuclei nucleating between t = o and t = t-j at time t = i s : t, *1 Vp2 = la . G3(t?-x)3Ndx exo/t1 ' L o ^ lx\ - (t2-tl)4] ...Al.l 148 The total extended volume (i.e. from t - o to t - t2), t 3 4 V 2 = NG1 *2 ' ..,AT . 2 ex The fractional volume contributed by the nuclei, nucleating between t ~ o and t « t^, to the total transformed volume at t = t2 is;1 t2 V exo/t1 t? - (t?-t )4 —z - = ——: ...AT. 3 2 4 Vex z2 (Ref 72) *2 It must be noted that V is not the extended volume transformed at t=t|, rather it is the extended volume at t = t2 of pearlite nodules nucleating between t = 0 and t = 1 and growing up to t = t2. Thus t2 V 0 e><0/tl Vt ft ) is considered to be equivalent to rue^ 1' , vt2 t2 ex v/ true since both extended volumes are corrected to true volume at t2. Appendix 2 THE EFFECTIVE SITE SATURATION CRITERION 150 APPENDIX 2 ex o/t- t\ - (t2-tT)4 A2.1 'ex when and *1 " t20 z2 = t90 *2 V ex^,. o/t 1 *2 V ex 0.85 The ^effective site saturation" criterion is '90 90. •90 •t2Q) > 0.85 A 2.2 Therefore ^0 °-38 % . A 2 , 3 


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