CARBIDE COMPOSITION CHANGES IN POWER PLANT STEELS AS A METHOD OF REMANENT CREEP LIFE PREDICTION By Rachel Clare Thomson Newnham College, Cambridge Department of Materials Science and Metallurgy Pembroke Street Cambridge CB23QZ A dissertation submitted for the degree of Doctor of Philosophy September 1992 Declare the past, diagnose the present, foretell the future. Epidemics, Book I, Section 11 Hippocrates of Cos, ca 460-ca 357 BC PREFACE This dissertation is submitted for the degree of Doctor of Philosophy at the University of Cambridge. It contains an account of research carried out between October 1989 and September 1992 in the Department of Materials Science and Metallurgy, Cambridge, under the supervision of Dr. H.K.D.H. Bhadeshia. Unless appropriately referenced, the work is original and is not the result of collaboration. No part of this dissertation has been, or is currently being, submitted for any degree or diploma at this, or any other, university. This dissertation contains less than 60,000 words. Rachel Thomson September 1992 IJ ACKNOWLEDGEMENTS I wish to thank Professor C. Humphreys for the provision of laboratory facilities in the Department of Materials Science and Metallurgy at the University of Cambridge. I am indebted to Dr H.K.D.H. Bhadeshia for his encouragement and enthusiasm during the course of this work. I would like to thank both National Power and the Science and Engineering Research Council for providing financial support for this project, and especially Dr D. Gooch of the National Power Technology and Environment Centre (NPTEC), Leatherhead, for the helpful discussions and interest he has shown in this work. I must also thank Mrs P. Dolbear at NPTEC for her assistance with X-ray diffraction studies. I am also grateful to the staff at the National Physical Laboratory, Teddington, particularly Mr H. Davies and Dr A. Dinsdale, for the provision of MTDATA, a program for the calculation of chemical equilibria in multicompollcnt systems, and their advice on its use. Thanks are also extended to the technical staff of the department who have contributed to this project; in particular, Mr D. Nicol for valuable advice on electron microscopy and carbon replica preparation, Mr J. Leader for his general ability to get equipment working, the photographic department - Mr B. Barber and Mrs C. Best for their generous help, and Mr G. Morgan and his staff in the workshop for making some of my specimens. I must also thank my friends and colleagues in the department, especially Dr R. Reed (now of Imperial College) for his early help with transmission electron microscopy, Dr C. Boothroyd for his help with scanning transmission electron microscopy, G. Rees, M. Gregg and J. Race. My thanks also go to the other members of the Phase Transformations group, with whom it has been very enjoyable to work. I am also grateful to 1. Redfern for his assistance with computing matters. Helpful discussions with Drs S. Babu, H. Harada, M. Miller, J. Whiteman and Professors C. Atkinson and G. Olson are acknowledged with pleasure. Finally, I wish to thank my family for their unfailing support and encouragement. III ABSTRACT The prediction of the remanent creep t life of a component requires a knowledge of both the service stresses and temperatures. Temperature data are subject to considerable scatter due to spatial variations around the components, and irregular fluctuations with time as a result of changes in the mode of plant operation. It has been shown that a change of about lOoe can lead to a corresponding change in the remanent life estimate by a factor of two. It is therefore desirable to be able to estimate the average thermal history of each component in order to accurately assess its remaining creep life, thereby avoiding premature replacement whilst maintaining safety standards. In this work, changes in the steel microstructure are related to the thermal history, thereby enabling the microstructure to be used as an in situ time-temperature recorder. When many of the conventional power plant steels entered service, their microstructures contained relatively fine particles of cementite whose substitutional solute concentration was initially similar to the solute content of the steel as a whole. These carbides were far from their equilibrium chemical composition, size and shape. During service at high temperatures the cementite tends to approach its equilibrium composition with respect to the substitutional elements, which can, in principle, be used to estimate the thermal history of the component. The purpose of this work is to determine the fundamental factors controlling the rate at which carbide compositions change, so that the extrapolation of experimental data can be made with greater confidence. Experimental studies have been made using energy-dispersive X-ray analysis in a transmis- sion electron microscope of the kinetics of cementite enrichment in steels which have pearlitic, bainitic or martensitic microstructures. Simultaneous measurement of particle size and compo- sition over a wide range of tempering times at various temperatures have established the fact that smaller particles enrich more quickly than larger ones. Power plant components can be very large, with the microstructure varying considerably within a given component. Since the formation of allotriomorphic ferrite causes an increase in the carbon concentration of the residual austenite, which subsequently transforms to bainite, the distribution and scale of cementite precipitation is also expected to vary significantly with the volume fraction of bainite. Theory indicates that the rate at which the cementite particles change composition will also differ as a consequence. For example, the cementite in regions t Creep deformation is the time-dependent plastic extension which a material undergoes when subject to a load at elevated temperature for a long period of time. IV containing less bainite is expected to enrich at a lower rate compared with those particles in regions with a large amount of bainite. The effect of typical variations in the microstructure on cementite enrichment kinetics is studied for different volume fractions of allotriomorphic ferrite and bainite in 2tCrlMo steel. A theoretical model has been developed of the diffusion of substitutiona.1 solute elements to cementite particles in microstructures typical of power plant steels, subject to the ther- modynamic constraints which determine the equilibrium composition of the two phases. The theoretical predictions have been compared with experimental observations in ~Cr~ Mot V and 2tCrlMo steels. The theoretical modelling of the diffusion fields around enriching particles has higlighted the need for the compositions of the substitutional solute elements at the fer- rite/cementite interface to be known accurately. The composition-distance profiles of alloying elements through a particle have therefore been studied using atom probe field ion microscopy and scanning transmission electron microscopy to establish whether in fact local equilibrium exists at the carbide/matrix interface. Extension of the model to treat enrichment and coarsening simultaneously has been con- sidered. In reality, both these processes contribute significantly in the approach towards equi- librium, especially at the later stages of service. It has been shown that the driving forces for the processes of enrichment and coarsening in fact compete against one another and that the coarsening process is defeated by enrichment process until the particles are close to their equilibrium composition. At long service times, all of the common power plant steels are expected to precipitate more stable alloy carbides, at the expense of cementite. Alloy carbide precipitation has been investigated in a 12CrlMol V steel in which the enrichment kinetics are much faster than in a low alloy steel. However, it has been found that the equilibrium alloy carbide precipitates during the commercial stress-relief heat treatment and does not change in composition during further tempering. This is an important result; indications are that once the cementite transforms to alloy carbides, any changes in their composition are not large enough for this method to be used as a quantitative estimation of remanent life. Low alloy steels, however, contain cementite for a considerable fraction of their useful service life. v CONTENTS Preface . . . . . Acknowledgements Abstract . . . . . Contents. . . . . Nomenclature and Abbreviations Chapter 1: Introduction to Remanent Life Prediction 1.1 Introduction . 1.2 Methods of remanent life prediction . . . . 1.3 Possible future indicators of thermal history . 1.4 Conclusions . . . . . . . . . . . . . . . Chapter 2: Physical Metallurgy Of Alloyed Steels 2.1 Introduction 2.2 Bainite . . . 2.3 Martensite 2.4 Summary of transformation mechanisms 2.5 Carbide precipitation. . . . . . . . . 2.6 Interphase precipitation . Chapter 3: Theoretical Studies - An Introduction 3.1 Introduction . 3.2 Partitioning in pearlitic and bainitic cementite 3.3 Equilibrium compositions of cementite and ferrite 3.4 Diffusion coefficients . . . . . . . . . 3.5 One dimensional modelling . . . . . . 3.6 Consideration of the effect of particle size Chapter 4: Experimental Procedure 4.1 Introduction 4.2 Materials . . 4.3 Heat treatments 4.4 Hardness measurements 4.5 Optical microscopy 4.6 Transmission electron microscopy 4.7 Energy dispersive X-ray analysis 4.8 Particle size measurements . . . 4.9 Bulk extraction of carbides and X-ray diffraction Chapter 5: 2iCr1Mo Steel 5.1 Introduction .... 5.2 Materials . . . . . . 5.3 Initial heat treatments 5.4 Tempering heat treatments 5.5 Results and discussion from bainitic microstructures 5.6 Results and discussion from mixed microstructures . 5.7 Comparison of experimental results and theoretical predictions 5.8 Conclusions . . . . . . . . . . . .. . VI 11 III IV vi viii 1 2 9 20 20 22 23 26 30 36 37 41 43 44 44 46 48 49 57 60 61 62 62 63 63 64 67 70 71 73 74 75 76 92 94 131 141 142 Chapter 6: !Cr!Mot V Steel. 6.1 Introduction . 6.2 Materials and heat treatment 6.3 Experimental results . . . . 6.4 Modelling of the diffusion process 6.5 Conclusions . . . . . . . . Chapter 7: l2CrlMoV Steel 7.1 Introduction . 7.2 Materials and heat treatment 7.3 Results . . 7.4 Discussion . 7.5 Conclusions . . . . . . . . Chapter 8: Atom Probe and STEM Investigations . 8.1 Introduction . 8.2 Atom probe field ion microscopy . . . . . . . . 8.3 Scanning transmission electron microscope studies 8.4 Conclusions . . . . . . . . . . . . . . Chapter 9: Further Theoretical Studies 9.1 Introduction .. 9.2 Experimental studies of particle coarsening 9.3 Particle size and solubility . 9.4 Approximations . . . . . . . . . . . . 9.5 Application to simultaneous coarsening and enrichment of cementite 9.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 10: Conclusions and Suggestions for Future Work . APPENDIX I APPENDIX Il APPENDIX III REFERENCES vu 146 147 147 148 152 160 161 162 162 163 177 177 179 180 182 190 192 193 194 194 196 199 200 202 204 207 209 214 219 a at.% A A Ae1 Ae3 b.c.c. B Bs c c c' COlB cBOI c~ cB 00 c~ cBr C C CA d D Do DOl DB e eV E EDX f f.c.c. 9 90 Gm h HP HV I lA ILS ISO IP IPS k kAB kz L LP NOMENCLATURE AND ABBREVIATIONS Lattice parameter Concentrations in atomic percent Constant Number of cavitating grain boundaries Temperature of the eutectoid reaction Temperature separating the ex + I and I phase fields for a specific alloy Body-centred cubic Constant Bainite start temperature Speed of light in vacuo Thickness of a plate Dimensionless concentration in the finite difference method Concentration in ferrite in equilibrium with cementite Concentration in cementite in equilibrium with ferrite Equilibrium concentration in ferrite Equilibrium concentration in cementite Equilibrium concentration in ferrite at the ferrite/ cementite interface Equilibrium concentration in cementite at the ferrite/cementite interface Avel'age concentration in the alloy Constant Weight fraction of element A Interatomic spacing along a specific crystallographic orientation Diffusion coefficient Pre-exponential factor for the diffusion coefficient Diffusivity in ferrite Diffusivity in cementite Electronic charge Electron volt Strain energy Energy-dispersive X-ray analysis Volume fraction of martensite Face-centered cubic Chemical potential Chemical potential of pure substance Molar Gibbs free energy Planck's constant High pressure Vickers Hardness units Integrated intensity per unit length of diffraction line Characteristic intensity of element A Invariant line strain International Standards Organisation Intermediate pressure Invariant plane strain Boltzmann constant Experimental constant Partition coefficient with respect to element z Camera length Low pressure V1IJ m Ms MU MTDATA n nex ne N NA NDT NP-LE NPL o P-LE q Q r r r R R s ss Sv STEM t' t tc ti tif T Ti To T'o TEM TTT us V Vb VmVex Ve Ws wt.% x Electronic mass Martensite start temperature Mean Linear Intercept Metallurgical and Thermodynamic Data Service Number of atoms Number of slices of ferrite Number of slices of cementite ..jh2 + k2 + [2 where h, k and [ are plane indices Avagadros number Non-destructive testing Negligible partitioning local equilibrium National Physical Laboratory Surface area Partitioning local equilibrium Half thickness Activation free energy per mole for diffusion Grid parameter in the finite difference method Radius of a spherical particle Length of a plate Universal gas constant Distance between transmitted and diffracted electron beams Shear component of a shape deformation strain Supersaturated Grain surface area per unit volume Scanning Transmission Electron Microscopy Dimensionless time in the finite difference method Time Time to reach a specific concentration Time Failure time Temperature Temperature Temperature at which austenite and ferrite of the same composition have the same free energy As To but accounting for the stored energy of ferrite Transmission Electron Microscopy Time-Tern perature- Transformation Unsaturated Volts Volume fraction of bainite Molar volume Volume fraction of ferrite Volume fraction of cementite Widmanstatten ferrite reaction start temperature Concentrations in weight percent Mean concentration in bulk alloy Mole fraction of element z Thickness of slice in finite difference method Carbon concentration in austenite at end of bainite reaction Dimensionless distance in the finite difference method Concentration in ferrite IX Yz ,, 'enr 6 ~T ( () () A A Ao J.L O'i 0' re! Half-thickness of ferrite in diffusion couple Thickness of cementite in diffusion couple Concentration (of carbon) in austenite in equilibrium with ferrite Concentration (of carbon) in ferrite in equilibrium with austenite Concentration of element z Ferrite One-dimensional parabolic thickening rate constant Martensite Lower baini te Upper bainite Widmanstiitten ferrite Austenite Interfacial free energy per unit area Enriched austenite Activity coefficient Dilational component of a shape deformation strain Metal-to-steam temperature differential Epsilon carbide Volume fraction of allotriomorphic ferrite Bragg angle Cementite Wavelength Absolute activity Absolute activity of pure substance Shear modulus Stress Reference stress Equilibrium volume fraction of ferrite x CHAPTER 1 INTRODUCTION TO REMANENT LIFE PREDICTION This chapter provides a general introduction to my research and contains a review of remanent life prediction procedures. 1 CHAPTER 1 INTRODUCTION TO REMANENT LIFE PREDICTION 1.1 Introd uction High temperature power and process plant components are designed to codes which define a conservative useful life. Therefore, it could be supposed that the plant will give satisfactory service up to, but not much beyond the design life. However, experience has shown that many power plant can operate safely for times significantly longer than their design lives. Therefore two distinct parts of service can be defined: (a) the original design life, and (b) the safe economic life (which is outside the influence of the design codes but may be a significant fraction of the total service life). Materials operating at high temperatures under creep conditions have a finite operating life and so consideration must be given to a 'beyond design' end-of-life criterion. The assessment of the remanent creep life t in carbon and low-alloy steel components operating at elevated temperatures has, in recent years, received increased attention from power generation authorities, petrochemical companies and government inspection and certification agencies throughout the world. In England and Wales there are at least 54,000 MW of electricity generating capacity, including 12 power stations which between them contain a total of 41 highly efficient 500 MW coal fired units. These stations have comparatively low operating costs and are therefore used for every day (base-load) generation. However, these stations were built in the 1960s and 1970s, individual units having now reached total operating times in the range 90,000-120,000 hours. It has been established that it is economically desirable and technically possible to extend the lives of these stations to periods in excess of 250,000 hours. 1.1.1 Replacement strategy In order to implement this policy, the criteria which determine whether or not a component should be replaced need to be considered. Two possible options have been investigated: (a) After 150,000 hours service to replace all major components which can be shown to survive 150,000 hours, but which cannot be guaranteed to survive beyond 250,000 hours, and t The remanent creep life is the service time remaining for a partially creep damaged component before creep-induced failure occurs, and relates to components operating under high temperature con- ditions where creep is the main mode of failure. 2 (b) to replace each major component only when remanent life assessment techniques indicate that this is necessary. The first criterion is certainly the simplest and would ease the problem of planning for refurbishment programmes since several years notification of the need for replacement could be given. This would, however, in many cases lead to the premature or completely unnecessary replacement of components which would not have been established to have an 'end-of-life' condition in terms of degradation and damage. It may also increase the periods during which the plant is not operational which would result in substantial cost penalties. The second possibility is the one adopted by the generating companies as it avoids these disadvantages and is financially beneficial. Components are not generally replaced prior to need and hence refurbishment work can be spread over the complete operating life of the units, thereby reducing the time for which the plant is not operational. However, for this strategy to be implemented it is clearly necessary to develop an accurate and reliable procedure for remanent creep life assessment, a procedure based on sound physical principles so that extrapolation over long periods of time can be carried out with confidence. 1.1.2 The need for life assessment The reasons why remanent life appraisal is necessary can be summarised as follows: • Safety: To meet safety regulations specified by legislative bodies and the utility insurers, and therefore to preserve the safety of personnel and plant integrity. • Operation: To avoid costly, unscheduled plant shutdowns by preventing high temperature failures. • Strategy: To plan for component replacement and to allow time for the manufacture of replacements and therefore to allow operation of high temperature plant beyond the original design life. 1.1.3 Procedure documents In order to develop a life assessment procedure for a particular component, it is necessary to consider the operating regimes, the type of component and the materials from which it is manufactured, the potential failure mechanisms and the available failure statistics, and also the difficulties in repairing the component and the cost of any shutdowns. Formal procedure documents have been or are being written to assess the safe and economic life of each component and the need for replacement. The procedures are based on a system of regular monitoring of operating parameters, systematic inspection, the procurement of samples for post-service testing and the calculation of remaining life by using relevant materials data in an established 3 relationship describing the degradation and life-limiting failure mechanisms. An important aspect of these formal procedure documents is that they link the 'science' of life prediction established within the laboratory with the 'engineering requirements' associated with continued operation, the need for repair, or in some cases replacement, and the requirements for non- destructive testing (NDT) inspection. 1.1.4 Power plant In a power station heat is produced by burning coal or oil (or from a nuclear pile) within a furnace. Water is supplied to the boiler from a common feed main by feed pumps. The feedwater first passes through the economiser and into the steam drum. (The economiser is situated next to the tubes containing the exit steam from the furnace walls and so it is used to preheat the feedwater before it enters the boiler.) The water is then drawn from the steam drum into the tubes lining the furnace walls, subsequently returning to the drum as a mixture of water and steam. Water and steam are separated within the steam drum, the water being returned to the furnace wall tubes by boiler circulating pumps. Hot gases from the combustion chamber flow across the boiler horizontally to heat the superheaters, reheaters and economiser elements, before flowing to the gas airheater (to heat the incoming air to the combustion chamber). Steam from the drum then passes through the superheater pendants to the high pressure (HP) cylinder where it is directed through nozzles on to the turbine blades to rotate the turbine. Exhaust steam from the HP cylinder returns to the boiler to pass through the reheater pendants so that its temperature is restored. The reheated steam is then passed to the intermediate pressure (IP) cylinder, the exhaust from which is then passed directly into the low pressure (LP) cylinder. The HP, IP and LP cylinders are coupled together to drive the rotor of the generator. The route for water and steam circulation is illustrated schematically in Figure 1.1. A diagram of a power station boiler and the associated steam plant (Littlebrook Power Station Guide, National Power Technical Publications) is given in Figure 1.2. Consideration must be given to the types of component and materials likely to require accurate life prediction. In general, these will depend on plant design and operational practice. However, other criteria include the severity of the operating regime, known failure statistics, the difficulty of repair and the cost of associated outages, the cause of failure and the potential benefits to be gained by developing an accurate life predictive capability. On the first of these criteria it is evident that boiler components offer a more pressing need than turbine components. This is because turbine components, although operating under extremely onerous conditions, nevertheless generally operate within the design parameters for 4 TURBINE CONOENSER SUPERHEATER ECONOMISER FURNACE WALLS 1- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - i 1 I I I I 1 I I I I 1 I I I I I 1 REHEATER II I 1 I I 1 I I I 1 I 1 I I I I I I I I I1 _ Figure 1.1: Water and steam circulation in power plant (Davison and Yeldham, 1975). temperature, pressure and cyclic loading. Boiler components such as tubing and steam head- ers, however, frequently operate outside the parameters used in their design, particularly with respect to temperature and corrosive environment. The main components which are critical are steam headers, superheater and reheater tubing in boilers, turbine valve chests, rotors and casings, main steam and reheat pipework, generator rotors and bolts used for high temperature applications. A summary of the components for which it would be possible to draw up a procedural document and their typical life limiting factor is shown in Table 1.1. The typical areas of attention for plant life extension on coal-fired power stations are illustrated in Figure 1.3. 5 Table 1.1: Typical life limiting factors for power station components. Component Typical Life Limiting Factor Boilers Headers-superheater ,reheater Creep, thermal fatigue Tubes-furnace wall Fireside corrosion Superheater, reheater Creep, fireside corrosion Pipework HP and RH pipework Weld cracking, creep Boiler and turbine valves Weld cracking, creep, bolt failures Thermal fatigue Turbines and generators Turbine valve chests Thermal fatigue, creep, bolt failures Turbine HP and Jp casing Thermal fatigue, creep Turbine HP and Jp rotors Creep, fatigue High temperature bolting Creep, stress erosion, thermal fatigue Generator rotors Fatigue 6 H H ft--1i H fI -H 11 11 T ~.• 30M SII ,~\ ORU\\ \I 11 ' .. .,,'" """ TO "P, -TURllII£54fe7' / AIRINTAKE FllGMH.P. TlIRIJIIf~,e / I '0 •+ n 25M y tt j I ~L ECO/llOMISER ~IZO/llTAL HEMEl'" '11I1"''''11I'1' IIUH"HII STEAM ENCLOSURE SIDEWAll TUBES SlCOND"'IIY FIN"'l SUl'fIlHUT(1I II(,,£"T(II "iIl"''''III~'' flN"'lSUf'(III~·., SUf'(III- "("HII H("'1(1I ,:..... 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Colour Key P~!·-?ntllll fir' b I Pr"flle £l1••••~~helllCl\l Coohno tower Generator lraJ\lformer 1'1, lli ROUlUlO lestlf)(l Improvf ok, J Stator Prt'rJ IIUlf' I.ll ,Ht Imb~~~~~~nd~~ ••••.ttdomq • J' If i,"'" 'f.11l • Rotor PIPl1ldftUf' 1.11 UI Improve wmdmq UlSUlalJon Fit non -corrosav ~ quId CII>Q pumps A1r extracuon Rotors Thl'rmal51ft 1.£lCal stress r,lL "rs E."mate thermal fatigue endurance Measure creep stram7 Temporary repa.rr Replacement HP and IP steam chests ThPrmal filll'lue crackmq Condenser tubes v 'Ii.; Steam and electnc dnven pumpa lA ,ff."·rf'JrmotflC't lJ:: 1~, 11 Tube replacement to optimum demgn Rettoflt certnd9" F'rt modem tuoh IP'!"d pump Turbine components Premature. fallulP Non -destructIve tests to assess component hCe -BP•••••••L......j- H,.ler tube. ·/illfdflm Corr'~__'n and erOl m Refubilh •••••• r Replace "'pes and han9ars WP.I( md :.u5l)O~ itflJC1lU,ll Ulftl"1Tlfy 11 j 11 ~ I: 11 MillI. ,,"'-liers andnm •• soe _dn•• \\,<", ~ t •t t e-oIllIld ••••••••••••nlanoneqUlp••••nt - ___ n ID I"OOI,'A_ AJip •• '-ters to.",,,,,, -;-;----. -"",.- Impr' ~,.~ ~,.pIace eIcrne',',":==~_1lI 'I\lbe a_tunen •• ~.",,-,.£.I:p&nIIOn )OInla -'1libIDQ I ~d<,!Ic=: I~£q:irl RedesIgn ""l.I;;::; •• ;;;;;;;;;- •., 1-..:-= 1.2 Methods of remanent life prediction The useful life of power plant components can be limited by various damage mechanisms including creep, fatigue, wear and corrosion. This work focusses on the prediction of remanent life by estimation of the thermal history of low alloy ferritic and bainitic steels, tCrt Mol V and 2lCr1Mo, and martensitic 12Cr1M01 V steels, which ultimately fail under creep conditions. Creep strength arises from the addition of substitutional alloying elements, (Mo, Cl', V and Mn), to the base steel composition. There are two contributions to the creep strength. The first arises from solid solution strengthening, the added alloying elements making cross slip and dislocation climb more difficult (Argent et al., 1970) by distorting the solvent lattice. Molybdenum, the largest of the substitutional alloying elements, is the most effective addition in solid solution strengthening. The second contribution to creep strength, which is particularly important in the later stages of service, is the ability of the alloying elements to form a stable dispersion of precipitates which hinder dislocation motion and prevent the migration of boundaries and sub- boundaries during creep. Creep resistance is attenuated as the more stable carbides coarsen, spheroidise and agglomerate (Sellars, 1974). Creep damage itself can be said to occur by two different methods; the development of intergranular cavities leading to cracking, and secondly an acceleration of the creep rate directly related to microstructural changes such as the coarsening of initially creep resistant precipitate dispersions, changes in precipitate identity, increasing grain size or a change in the number density of dislocations. These two processes occur simultaneously and will depend on the initial heat treatment conditions, the applied stress and the temperature. For high temperature plant investigations a wide variety of complementary techniques to estimate the remaining life of components are employed, several of which are being used under service conditions. These have been reviewed extensively (Cane and Townsend, 1984; Wilson, 1986; Cane, 1986; Cane and Williams, 1987) and the various techniques are summarised below: (1) Post-exposure creep testing of components. (2) Metallography to assess the extent of microstructural degradation, with particular emphasis on cavity nucleation and cracking. (3) Examination of plant operational records, e.g. temperature and pressure records taken daily, the use of standard materials data and the life fraction rule. (4) Estimation of the average thermal history of a component by detailed investigation of carbide composition, identity and size within the microstructure. 9 1.2.1 Post exposure creep testing Creep life has most commonly been estimated using parametric relationships to extrap- olate short term creep data obtained at elevated stresses and/or temperatures. Post-service evaluation techniques can clearly be classed as mostly destructive methods of assessment, to the extent that a weld repair may be needed due to the volume of material required. To obtain results in a reasonable time, the tests have to be performed under accelerated conditions by increasing stress or temperature or both. If tests are performed by accelerating the temperature at constant stress care must be taken to avoid excessive oxidation of the test piece. Tests may have to be performed under a non-oxidising environment, either in a vacuum or argon. Both creep and rupture testing have been well documented (Hart, 1976; Woodford, 1974) therefore only a brief example of the use of creep testing is presented here. Samples were cut from a ~Cr~Mot V reheater drum after 70,000 hours service and ma- chined into specimens for creep testing (Cane and Townsend, 1984). The drum was known to be overheating and thermocouple measurements revealed a maximum operating temperature of 592°C. Creep rupture tests were performed at the operational stress, 43 MPa, and at tempera- tures between 640 and 680°C. The data were extrapolated linearly at a slope parallel to that of the mean data for unused material to predict the remanent life at the service temperature, and an estimation of the life which would be gained by a reduction in the operating temperature. This is illustrated in Figure 1.4. It should be noted that such extrapolation will not take fully into account the microstructural changes during service and therefore the results should be treated with caution. 1.2.2 Metallographic examination of damage Increasing effort has been put into the assessment of remanent life by direct observation of the steel microstructure. It is therefore necessary to identify what features in the microstruc- ture indicate a departure from the steady strain rate and the onset of tertiary creep. If creep cavitation can be identified as a failure mechanism in a particular component, then quantifica- tion of the number density of cavities can be a useful indicator of the remanent life. Some low alloy steels are susceptible to low ductility creep failures in certain microstructural conditions, particularly the coarse grained structures which occur in weld heat affected zones. Others have low ductility in their standard condition. Eventual failure results from the nucleation, growth, and coalescence of cavities on grain boundaries (especially prior austenite grain boundaries). Cavities are often associated with the larger grain boundary alloy carbides, and oxide and sulphide particles. The cavities provide nuclei for micro crack initiation, can locally alter the 10 680 ~, UNUSED 660 .~ MATERIAL. , 43 MPa\, 640 AFTER ., u , 0 •••• 70.000 h "SERVICE620 ,,, 600 , --- 592°C 580 ---- 580°C 102 103 104 105 LIFE. h Figure 1.4: Remanent life assessment of iCri Mot V steel reheater drum material by iso-stress post- exposure testing (Cane and Townsend, 1984). nature of the fracture path and may change the balance of the elements in the solid solution. Experimental studies have been made (Shammas, 1987) in which the number fraction of cavitated grain boundaries has been measured at various stages throughout a creep test. This fraction is usually termed the 'A' parameter. Assessment of the 'A' parameter is made by taking plastic replicas from a metallographically prepared surface which is subsequently examined with an optical microscope. A sequence of micrographs illustrating the accumulation of creep damage in a 1CriMo steel is shown in Figure 1.5. Initially isolated cavities (A=O.102) gradually orientate parallel to the stress axis (A=O.204), and then develop into microcracks (A=O.289). Macrocracks correspond to a value of A::::::::O.5at which point the component should clearly be removed from service. In steels of high creep ductility, from which most high temperature components are con- structed, significant cavitation does not occur until late in life and is not therefore a useful indicator of remaining life. Effective use of this method of cavitation damage quantification is therefore restricted to weld heat affected zones rather than bulk material. 11 20llm (c) 200llm (b) (d) 560°C 84 MPII ARGON ~ \( ) I.\ (e) UNETCHED 1 mm (a) tI\ - 0.233 (b) tI\ - 0.468 (c) tI\ - 0.718 (d) tI\ - 0.8SM (a) tI\ - 1 TEMPERATURE: STRESS: ENVI RONMENT: A- 0.102 A- 0.204 A- 0.289 A- 0.313 A- 0.468 ISOLATED ORIENTED MICROCRACKED MACROCRACKED MACROCRACKED Figure 1.5: Accumulation of creep damage through life of a 1Cr~ Mo steel specimen (Shammas, 1987). 12 1.2.3 Assessment based on plant operational records An analysis of the past operating history of a component is one of the most important steps in any remanent life assessment procedure. In practice, data taken during plant operation include pressure and temperature measurements, these being logged continuously or taken at fixed times during the day. To calculate a preliminary assessment of the exhausted creep life fraction, the life fraction rule (Robinson, 1938) is used. This states that (1.1) where ti is the time spent at stress O'i and temperature Ti, and tiJ is the failure time at stress O'i and temperature Ti• It was proposed that for any series of stress and temperature conditions, the life fractions could be linearly summed with final failure denoted by unity. This is a very simple procedure and thus can be used as a first stage of remanent life assessments to establish components requiring further monitoring. For many years the life fraction rule has been used without much consideration of the potential errors. The failure time, tiJ, at a particular stress, O'i' is taken from the International Standards Organisation (ISO) stress rupture data. For any class of material upper and lower bounds have to be placed on the rupture life due to the range of variables such as specimen size and composition variations involved in collecting ISO data. This immediately introduces pessimism into remanent life estimates because it is usually necessary to use the lower bound of the data because it is not possible to identify the actual position of the material within the band without additional creep testing and/or knowledge of virgin material properties. If archive material is no longer available it would be necessary to reheat-treat the service exposed material to recreate the starting microstructure, although it should be noted that for some materials simply repeating the original heat treatment may not restore the material to its original condition. This bandwidth is illustrated for 2tCr1Mo steel at 560°C (based on the stress to give failure in 100,000 hours), the bandwidths being given as a percentage change in the applied stress, in Table 1.2. Table 1.2: The variation in failure time as a function of the percentage change in the applied stress. % Change -20% -10% -5% 0 5% 10% 20% III stress Failure 38000 62000 78000 100000 110000 130000 200000 time, hours 13 Another problem with the use of standard data is that often they only exist for times of approximately 80,000 hours and so extrapolation to times approaching 150,000 hours is uncertain. This is because during tests the load carrying area is reduced as the specimen extends and by oxidation. Current extrapolation procedures do not take this into account and therefore errors in life estimates occur. The life fraction rule is often used in conjunction with post-exposure testing to determine the failure times at specific stresses, rather than using standard materials data. The earliest difficulty to be recognised was that when smaller specimens were machined from failed uniaxial creep samples, they had a finite life on retesting, inferring that the life fraction rule is conservative. Alternatively, such results could be interpreted to mean that creep damage is not distributed uniformly within a specimen, being primarily at the point of failure, and thus sampling errors are always present. To be able to apply the life fraction rule it is necessary to know the representative rupture stress for the component concerned. The key point is that the majority of creep-rupture data are generated under simple uniaxial conditions, whereas in reality components are subject to much more complex loading. It is necessary, therefore, to be able to define a representative stress which, when applied to uniaxial data, adequately characterises the component deformation and failure. The idea of using a reference stress, O"ref' has received much attention in recent years. O"ref for a particular component is defined as that stress which would fail a simple tensile specimen at the same temperature in the same time as the component. When the temperature also varies with time, a reference temperature can be similarly defined at which the comparative specimen test should be performed. Determination of reference stresses and temperatures for irregularly shaped components can now be accomplished by theoretical and experimental work involving computer techniques such as finite element stress analysis together with model and full size component testing. A typical finite element mesh used to calculate the reference stress for a complex pipe geometry is shown in Figure 1.6. It has been shown that operational stresses and times can be determined accurately and therefore the only unknown for input into the life fraction rule is the exact operating tem- perature of a particular component. The accuracy of remanent creep life estimates using the life fraction rule depends critically upon the sensitivity of the component material to varia- tions in temperatures. Therefore, careful attention is required when establishing component metal temperatures from operating records. Depending on the direction of heat flow, the metal temperatures may be higher or lower than the steam and may vary significantly with plant op- eration. The importance of accurate service temperature assessments was emphasized by Cane 14 ".NOZZLE 2 •• N1607 N162S N"02 ,.. 500 1000 1500 1000 2500 TIME (h) WELD N16~U~6074J; N1402 Figure 1.6: A typical finite tllement mesh used to calculate the reference stress for a complex pipe geometry (Gooch, 1988). The inset shows typical results of a finite element analysis plotted as stress as a function of time at certain critical locations. and Townsend (1984). They considered in particular the measurement of the temperature of steam headers, and found that errors in the measurement of operating temperature and of the accumulated time-temperature behaviour arose from: (1) instrumentation errors, (2) spatial variations in the temperature along the header, (3) and irregular temperature fluctuations with time as a result of changes III the mode of boiler operation. The inlet stub tube variation around an 18 tube element on a 500 MW reheater drum is shown in Figure 1.7. It is clear that determination of the metal temperature by measurement of the steam temperature can lead to large errors. For conservatism in the life estimate calculation it is necessary to assume a large ~ T for the metal-to-steam temperature differential, and consequently considerable pessimism is observed in the creep life estimate. The uncertainty may be as high as ±5°C. The effect of temperature on rupture life is illustrated in Table 1.3. This is based on the 15 650 45413937 53035 630 TUBES (T) 610 u° w ( 5)Cl::::;) 590I- C=::> 0 x 2 at.% C conc. Figure 2.5: Bainite growth mechanisms. If growth involves diffusionless transformation then any excess carbon in bainitic ferrite can partition into the retained austenite within a fraction of a second after the transformation because of the high diffusivity of interstitial carbon. It is not possible to determine directly the carbon concentration of the ferrite during its growth. The bainite reaction is found to stop before the carbon concentration of the retained austenite reaches that of the equilibrium or paraequilibrium phase boundary, Le. when diffusionless transformation of carbon-enriched 29 austenite becomes thermodynamically impossible. The extent of the reaction is a function of temperature, increasing as the temperature is reduced. It is possible to extrapolate to find a bainite start temperature, Bs' above which bainite is not observed to form. This is known as the incomplete reaction phenomenon, in which the degree of transformation to bainite is always far less than that demanded by equilibrium. Bhadeshia (1987) summarises the bainite reaction as a displacive transformation in which there is no diffusion of substitutional or iron atoms across the transformation interface. The excess carbon trapped in bainitic ferrite is removed by a combination of diffusion into the resid- ual austenite, and by the precipitation of carbides between the ferrite. The retained austenite eventually decomposes by a diffusional transformation into a mixture of more carbides and ferrite. The plate morphology of bainite is explained by the minimisation of strain energy due to the IPS shape change associated with the displacive mechanism of the transformation. The kinetics of bainite are also shown to be consistent with the proposed diffusionless, displacive transformation mechanism. 2.3 Martensite Martensite forms at the highest undercoolings, when the free energy change for the trans- formation is very large. Hence, rapid quenching of austenite to room temperature results in martensite, a very hard brittle structure in which carbon, originally in solid solution in austen- ite, remains in solution. Unlike the formation of ferrite or pearlite, the marten site reaction is a diffusionless shear transformation which is highly crystallographic in character and leads to a characteristic lath or lenticular microstructure. The addition of alloying elements to a steel can affect the temperature, Ms' at which the martensite reaction can begin on cooling the parent phase. The extent to which the reaction proceeds depends on the undercooling below this temperature. Note that martensite can form at very low temperatures where atomic mobility is almost negligible because the transformation is diffusionless. The growth rate can be very high, limited by the speed of sound in the material concerned. The fact that martensite can form at very low temperatures also means that any process which occurs during its formation also cannot depend on thermal activation, e.g. the interface between marten site and the parent phase must be able to move easily at very low temperatures. For the interface to have high mobility and velocity at low temperatures, it must be semi- coherent or fully incoherent (Christian and Knowles, 1981). It should be noted that fully coherent interfaces are only possible when the two lattices can be related by an IPS. In the I/O: 30 transformation the austenite lattice cannot transform to a b.c.c. martensite lattice by an IPS only (it occurs by the so-called Bain strain combined with a suitable rigid body rotation and a lattice invariant deformation which is either twinning or slip) and, therefore, the lattices are joined by semi-coherent interfaces. For the 1/ a' interface to be glissile it must contain at least one invariant line along which interface dislocations lie. The interface between the martensite and the parent plate is usually called the 'habit plane'. If the transformation is unconstrained, the habit plane is macroscopically flat, whereas in a constrained transformation it grows in the shape of a thin lenticular plate or lath, resulting in the interface being curved on a macroscopic scale. This is illustrated in Figure 2.6. y- a. y I<===~~-.............a. y y uncons trained transformation constrained transformation Figure 2.6: Unconstrained and constrained growth of martensite. There are two kinds of martensite, a plate and a lath morphology. The extent of the martensite reaction has been found to be virtually independent of time. The volume fraction of martensite, f, formed as a function of undercooling below Ms is given by 1 - f = exp[-O.Ol1(Ms - T)J , (2.1) where T is the temperature to which the sample has been cooled below Ms. Since there is no diffusion during the martensite transformation, there will be reproducible orientation relationships between the parent and product lattices. The orientation relationship usually consists of approximately close-packed planes, and with corresponding close-packed directions also being approximately parallel e.g. Kurdjumov-Sachs (2.2) 31 2.3.1 The shape deformation due to the martensitic transformation When martensite grows there must be a change in shape because the pattern of atomic arrangement changes on transformation and the transformation is diffusionless, the change of shape being caused by the migration of interface dislocations. This is illustrated in Figure 2.7. bc Shear Transformation Atomic correspondence JPS shape change with a significant shear component Dlffusool ess dad 00000 0, I I ! 00-0 0··0 0 2J ~ 6 0 0 : :~ I·o .cp..- -0 --0:' I Io -~ I --Q -8 I I I 1-6 -0 O·-0 0 I I· c 0 -0 0 0 Oh"" d c;>--- .... : '1'e--, , , I , , I ,5, 1l / I ,, , / ', / ,, , a) proximately hexagonal close-packed arrangement of metal atoms with localized distortions to accommodate the carbon atoms. Each carbon atom is surrounded by a triangular prism con- taining 6 iron atoms. This is illustrated in Figure 2.11 a). The prisms are then joined by corners and edges to form sheets stacked perpendicular to the c-axis, leading to the 'pleated' structure illustrated in Figure 2.11 b). Figure 2.11: a) The triangular prism environment of iron atoms around carbon in Fe3C (after Jack and Jack, 1973), and b) View of the atomic arrangement in cementite (after Yakel, 1985). Within each ellipse there is a 99.9% probability of finding the atom. The sizes of the ellipses depend on thermal vibration parameters, and hence the larger ellipses represent the carbon atoms. M3C is predominantly an iron-rich carbide with the same orthorhombic structure as Fe3C, however several alloying elements can partition to this carbide in significant quantities. The unit cell dimensions are affected by partial substitution of alloying elements. Woodhead and Quarrell (1965) have found that Mn can dissolve in large quantities, as can Cr, with up to one fifth of the Fe atoms being replaced by Cr (specific to low alloy steels). Ni and Co can also dissolve as they form metastable orthorhombic carbides, although they usually partition to ferrite. Mo, Wand V have also been found to have limited solubilities in M3C. In general M3C carbides can be referred to using the general formula (Fe,Cr,Mn,MohC. This is a Cr-rich carbide with the trigonal structure of Cr7C3, having a solubility of Fe up to 60% (although Titchmarsh (1978) has found that the Cr:Fe ratio can be greater than 1 in 2iCrlMo steel). Mn, V and Mo can also dissolve, with decreasing probabilities respectively. 39 Baker and Nutting (1959) state that nucleation of M7C3 can only occur in the vicinity of cementite or at the cementite/ferrite interface, which is supported by Kuo (1953) who states that separate nucleation is improbable because there is not enough Cr in the matrix. Beech and Warrington (1966) state that cementite particles on the point of dissolving may leave areas sufficiently rich in chromium in which M7C3 could precipitate since these will be the most favourable sites. An interesting feature of M7C3 is that electron diffraction patterns show characteristic streaks, making it easily distinguishable from other carbides. The streaks have been attributed to faults lying on {10.0} planes, with the fault vector being approximately half the unit cell repeat distance (Beech and Warrington, 1966). 2.5.3 M23C6 This is usually a Cr-rich carbide having the complex Lc.c. structure of Cr23C6, however, in steels containing significant amounts of Mo it can have the formula Fe21Mo2C6• In steels containing both Cr and Mo its composition can be anywhere between the above. Mn has also been found to partition to M23C6 in small quantities. Baker and Nutting (1959) and others observe that M23C6 has never been found in the vicinity of M7C3 colonies. Beech and Warrington (1966) also support this view, finding no evidence supporting an 'in-situ' mechanism for the transformation M7C3~M23C6' 2.5.4 M6C M6C is essentially a Mo-rich carbide with a f.c.c. structure. In a simple ternary system of Fe-Mo-C, it exists in the range Fe2Mo4C or Fe3Mo3C depending on the Mo content (Kuo, 1956). M6C may also take small quantities of Cr and V into solution. It forms at grain boundaries, growing rapidly at the expense of all surrounding carbides, nucleating at existing particles. The transformation M02 C to M6C occurs more rapidly in bainite than in ferrite. 2.5.5 M2C As with M6C, M2C is also a Mo-rich carbide with an Lc.c. structure and is usually denoted simply by Mo2C. Cr and V have been found to be soluble in significant quantities, with a much smaller amount of Fe also dissolving. It commonly precipitates as fine needles parallel to the < 110 > Cl' direction in ferrite. The orientation relationship is that of Pitsch-Schrader (1958):- The precipitation of Mo2C is usually said to be the major factor in conferring creep resistance on low alloy ferritic steels. 40 Table 2.1: A summary of data for the common alloy carbides found in steels, (Andrews et al, 1967). Carbide Structure Lattice Parameter / A Formula Units /Cell Density /g cm-3 M3C Orthorhombic a=4.5241 4 7.704 b=5.0883 c=6.7416 M7C3 Trigonal a=13.982 8 6.965 c=4.506 M23C6 Cubic F a=10.638 4 6.996 M6C Cubic F a=11.082 16 6.325 M2C Hexagonal a=3.002 1 9.188 c=4.724 Data for the various alloy carbides discussed above are summarised in Table 2.1. 2.6 Interphase precipitation A number of studies (Berry and Honeycombe, 1970; Edmonds and Honeycombe, 1973; Tillman and Edmonds, 1974; Honeycombe, 1976; Dunlop and Honeycombe, 1976) have been made of the so-called interphase precipitation in isothermally transformed alloy steels. It was shown that direct decomposition of alloyed austenite containing a substantial amount of strong carbide-forming elements (e.g. V, Mo, Ti, Cr) can lead to a distribution of alloy carbide in the ferrite. Berry and Honeycombe (1970) investigated a number of alloys containing different amounts of Fe, Mo and C isothermally transformed in the range 600-900°C. They found two different morphologies of the carbide M2C in the allotriomorphic ferrite; long, straight fibres growing from the prior austenite grain boundaries and sheets of smaller, needle-like, particles in a Widmanstatten ferrite array. It is these sheets of smaller particles which are termed 'inter- phase precipitation'. It was found that the fibrous form of M2C was favoured when the growth of allotriomorphic ferrite is slow, i.e. below the nose of the time-temperature transformation curve in the range 600-700°C, whereas the interphase precipitation was found at higher trans- formation temperatures. The orientation relationship derived between the M2C fibres and the ferrite matrix was (Oll)a 11 (0001)Mo2C (101)a 11 (1I01)Mo2c [1I1]a 11 [1210]Mo2C' 41 a relationship commonly observed for hexagonal phases precipitating within a b.c.c. matrix. The Widmanstatten ferrite type M2C carbides were found to have the orientation relationship (Ol1)a 11 (0001 )Mo2C (100)a 11 (2IIO)Mo2c [lOO]a 11 [2110]Mo2c, which is also that describing the precipitation of M2C in tempered martensite. Edmonds and Honeycombe (1973) compared the microstructure and mechanical properties of a Fe-4Mo-0.2C steel both in the quenched and tempered and the isothermally transformed conditions. The isothermally transformed specimens showed elongation and high ductility when fractured, whereas the quenched and tempered specimens showed no elongation and there was evidence of cracking along the prior austenite grain boundaries. The ductile-brittle transition was found to be 30-40°C lower for the isothermally transformed alloy. These observations can be explained by the fact that the formation of alloy carbide in fibre or sheet form at the grain boundaries prevents the passage of dislocations, resulting in strong dispersion strengthening. Honeycombe (1976) discusses the mechanism for the growth of the interphase precipitates. Early ideas for the mechanism of interphase precipitation were that the precipitates had nu- cleated on dislocations, known to be favourable sites for carbide nucleation. However, this would not explain the very regular precipitate arrays observed. Ferritejaustenite interfaces vary from high energy random boundaries to low energy planar boundaries which grow by step-by-step propagation. The nature of the interface itself is very important in determining the morphologies of the different carbide dispersions. The ferrite interfaces associated with interphase precipitation grow mainly by a ledge mechanism. Nucleation occurs on the planar boundary whereas the ledge itself is free from precipitates because of its higher mobility. The planar boundary is of low energy with limited mobility and therefore the growth of ferrite oc- curs by movement of a series of incoherent high energy steps. The fibrous carbides nucleate at the austenite boundary and then grow into the ferrite where the interface is more irregular with local curvature. Diffusivity along a disordered boundary is greater than on a coherent or semi-coherent one and therefore fibrous carbides are associated with lower temperatures and incoherent interfaces where there are enhanced diffusion paths. 42 CHAPTER 3 THEORETICAL STUDIES - AN INTRODUCTION In this chapter a theoretical model for the diffusion of substitutional alloying elements to cementite particles is developed. Symmetric and asymmetric particle distributions are consid- ered. The method of calculation of the equilibrium concentrations in the phases involved and choice of diffusion coefficients are discussed. 43 CHAPTER 3 THEORETICAL STUDIES - AN INTRODUCTION 3.1 Introduction A large amount of experimental data has been collected over the years concerning the chem- ical composition of various carbides as a function of different tempering treatments. The aim of this work is to develop a sound theoretical basis for the assessment of these data. Carruthers and Collins (1981) and Afrouz et al. (1983) have attempted to explain the mechanism of com- position changes in pearlitic and bainitic cementite in terms of diffusion-controlled coarsening theory (Wagner, 1961; Lifshitz and Slyozov, 1961). They therefore plotted composition changes as a function of d, where t is the time at the tempering temperature, and, finding approxi- mately linear relationships, inferred that the changes occurred in the context of a coarsening reaction. However, it is well established (see for example Greenwood, 1969 and Christian, 1975) that coarsening reactions in alloys are dependent on the fact that the equilibrium composition of the matrix in contact with a particle is a function of the principal radii of curvature of the particle/matrix interface. For example, the matrix adjacent to smaller spherical particles would be expected to have a higher equilibrium concentration of solute than that adjacent to larger particles. Hence, a diffusion flux is stimulated from the smaller to the larger particles resulting in the larger particles growing at the expense of the smaller ones. The driving force for this process is the reduction in total interface energy. However, the changes in cementite composition are fundamentally different from a coars- ening reaction. The matrix is supersaturated in solute with respect to nearly all the particles and so the concentration of solute will at first increase in all particles irrespective of size. The flux of interest is that of solute into a particle from the surrounding matrix for both large and small particles. It is not correct therefore to explain the changes in particle composition in terms of coarsening theory. The enrichment behaviour only of cementite particles is discussed in this chapter. It should be noted, however, that coarsening in the true sense may occur at very long service times and also needs to be considered in the development of the model. The possibility that simultaneous coarsening and enrichment may occur is discussed in Chapter 9. 3.2 Partitioning in pearlitic and bainitic cementite The precipitation of carbides during the bainite transformation has already been discussed in Chapter 2. After the formation of carbides, bainitic microstructures are a long way from 44 equilibrium. Hultgren (1947, 1951) established that upper bainitic cementite has a substitu- tional alloy content close to (or slightly higher than) that of the steel as a whole rather than its equilibrium concentration. Chance and Ridley (1981) investigated chromium partitioning during isothermal transformation for bainitic and pearlitic microstructures using analytical elec- tron microscopy on carbon extraction replicas. They found that in upper bainite the partition coefficient, defined to be the ratio of chromium in cementite to that in ferrite, kCr' was close to unity. In the case of pearlitic cementite, the amount of partitioning increases with transfor- mation temperature. At low temperatures (500-600°C) kCr remained approximately constant at ~ 4, and rose to a value of ~ 15 at 730°C. This is illustrated in Figure 3.1. 40 20 .•.•.. .•.•..•equilibrium .... 600 700 Transformation Temperature;C Figure 3.1: Partition coefficient between cementite and ferrite as a function of transformation tem- perature (Chance and Ridley, 1981). The carbon concentration of cementite is substantially larger than that of austenite or ferrite, cementite (M3C) containing 25 at.% of carbon to maintain the stoichiometry. A trans- formation to cementite, which has the same Fe/Cr ratio as the parent phase, should give a partition coefficient which is greater than unity. It can be concluded that the formation of cementite during transformation to upper bainite involves only a small degree of redistribution of elements such as chromium. This is consistent with the fact that upper bainitic cementite forms from carbon-enriched austenite, and so the driving force for cementite formation is higher allowing greater departure from the equilibrium composition. 45 For pearlitic cementite, however, it is found that its composition directly after transfor- mation is always between equilibrium and paraequilibrium for alloy steels (Chance and Ridley, 1981; Al-Salman et al., 1979; Williams et al., 1979). Transformation to pearlite involves the co-operative growth of ferrite and cementite, with the reaction front providing a boundary along which the chromium can redistribute providing the reaction is not too rapid. There is at present no theory to predict the starting composition of pearlitic cementite from austenite, consequently modelling of the composition changes in carbides has so far focussed on bainitic cementite. If the starting composition of pearlitic cementite is known from experimental data, then the enrichment behaviour can be modelled. This is illustrated in Chapter 6. 3.3 Equilibrium compositions of cementite and ferrite For many years the equilibrium compositions of the various carbides in alloyed steels were not known. Vengopalan and Kirkaldy (1978) determined expressions for the partition coefficient, kz, of alloying elements between cementite and ferrite using empirical constants defined by the expression (A + ET)k ~exp---- z RT' for dilute alloys. The values of the constants A and B are given in Table 3.1. (3.1) Table 3.1: Parameters used for the calculation of partition coefficients (Vengopalan and Kirkaldy, 1978). Element Z A, J mol-1 B, J mol-1 K-1 Cr 47028 -17.45 Mn 42844 -20.21 Mo 27363 -5.86 Ni -2619 -2.80 Si 0 -25.10 The partition coefficient k z is defined to equal c(Jo/ cod}, therefore using the condition for mass-balance at equilibrium (the Lever rule) (3.2) with respect to the carbon concentrations in the cementite and ferrite, c(Jo and c°(J, respectively the volume fraction of cementite in the alloy, V(J, can be determined. c is the average carbon concentration in the bulk alloy. Using the definition of the partition coefficient and the above 46 expression, the equilibrium compositions of the two phases can be calculated as a function of temperature using the equation: cCOOl = _ Vo - YL +,Lk. K. (3.3) where C801 and C0I8 are now the concentrations of the substitutional alloying elements in the cementite and ferrite respectively. However, implicit in this expression is the assumption that the solution is dilute, and it is not valid for steels with more than a few percent of the alloying elements. This method was used to find the equilibrium concentration of the various alloying elements between cementite and ferrite in the 12Cr1MoV steel discussed in Chapter 7, and was found to break down, predicting more than 100 at.% of chromium in the cementite! It is now possible to calculate the equilibria in multicomponent alloys using experimentally determined thermodynamic data without using any dilute solution approximations and taking into account the effects of all the alloying elements in the steel. Phases other than cementite and ferrite can also be taken into account. In this work equilibrium calculations were performed using the National Physical Laboratory's Metallurgical and Thermodynamic Data Bank (MT- DATA), a computer package containing critically assessed thermodynamic data for a number of alloy systems. MTDATA allows the equilibria in multicomponent, multiphase systems to be calculated from a knowledge of the thermodynamic data for the subsystems. It is possible to calculate for a given temperature, pressure or volume, the phases present and the amounts of species within each phase by minimising the Gibbs free energy of the system for specified com- ponent amounts. Further details are given by Hodson (1989). The main database used for the calculations in this work is the solution database created by the Scientific Group Thermodata Europe. For a specific steel composition and temperature the equilibrium phases can first be de- termined. The calculation yields information on the alloy content of the phases in question, their relative proportions and the Gibbs free energy of the system. If the equilibrium carbide phase is then suppressed and the calculation repeated, the new equilibria will contain the sec- ond most stable carbide. By repeating this process it is possible to predict the sequence of carbide formation on tempering steels alloyed with chromium and molybdenum. The results of specific calculations to determine the composition of the ferrite and carbide phases and pre- cipitation sequences are presented in Chapters 5, 6 and 7 for the 2tCr1Mo, !Cr!Mot V and 12Cr1MoV steels respectively. 47 (3.4) 3.4 Diffusion coefficients In a binary alloy an empirically defined diffusion coefficient is simply the proportional- ity constant relating the rate of transfer of diffusing substance through a unit area of section and the concentration gradient measured normal to the section. A tracer diffusion coefficient represents the diffusivity of radioactively labelled isotopes in an otherwise chemically homoge- neous solution. When the radioactive tracer atoms are of the same species as the atoms of the medium, the tracer diffusion coefficient is called the tracer self-diffusion coefficient. However, these two coefficients are not applicable if the diffusion is taking place In a concentration gradient. In the presence of a chemical composition gradient, an additional virtual force acts on the diffusing species due to the chemical potential gradient associated with the composition gradient. In order to take this into account and therefore represent the flux of one component, A, of a binary solid solution A-B in a concentration gradient of A, an intrinsic diffusion coefficient should be used. In this work intrinsic chemical diffusion coefficients are used from the work of Fridberg et al. (1969). In order to calculate the overall diffusion coefficient, the expression QD = Doexp(- RT)' is used, where Q is the activation energy, R is the universal gas constant, T is the temperature in Kelvin and Do is the pre-exponential factor for diffusion. Fridberg states that the values for the self-diffusion of iron in austenite and ferromagnetic ferrite are given by Do = 1.6 cm2s-1 and Q = 240,000 J mol-1 Do = 0.5 cm2s-1 and Q = 240,000 J mol-1 respectively. The intrinsic diffusion coefficients of the various alloying elements in ferrite are then determined by comparison with the self-diffusion of iron, the difference being described by a factor independent of temperature. These diffusion coefficients refer to the interdiffusion of the alloying element in a binary system, i.e. of chromium in ferrite, molybdenum in ferrite, and therefore do not strictly relate to diffusion in a multicomponent system. The values of interdiffusion coefficents used in this work are given in Table 3.2. Table 3.2: Chemical interdiffusion coefficients (Fridberg et al., 1969). Element Do/m2s-1 Q /J mol-1 er 1.5x 10-4 240,000 Mn 1.0x10-4 240,000 Mo 1.0x 10-4 240,000 48 It is important to note that in this work it is assumed that the diffusion of the interstitial carbon is significantly faster than the diffusion of the substitutional alloying elements and that the flux of the latter will not be influenced by the former. Carbon diffusion in ferrite has been shown not to follow a simple Arrhenius-type relationship because of the possibility of carbon occupying both octahedral and tetrahedral sites in the lattice. Using the method due to MCLellan et al. (1965) a value of 1.5x10-11m2s-1 is obtained for the diffusivity of carbon in ferrite at a temperature of 565°C. This is approximately eight orders of magnitude faster than the diffusion of chromium in ferrite. Diffusion of the alloying element only is therefore considered to be the rate-controlling step. In a more sophisticated treatment ternary diffusion, e.g. Fe-Cr-C, would need to be considered, although it should be noted that the interdiffusion coefficients allow for a flux of the alloying element within a flux of iron. There is little information available in the literature on the diffusivity of the alloying elements in carbides. Torndahl (1968 - cited by Fridberg et al., 1969) studied the rate of diffusion of manganese in cementite. His results seemed to indicate that the value of this diffusion coefficient lies between the values in ferrite and austenite. Recent work (Barnard et al., 1987) using an atom probe has attempted to measure the chromium diffusivity in bainite and cementite. They found that the value in cementite was two orders of magnitude lower than corresponding measurements in ferrite. The diffusivity of chromium in ferrite measured was, however, different by an order of magnitude from that measured previously by Bowen and Leak (1970) and the value for the interdiffusion coefficient given above. The diffusion coefficient of chromium in cementite is discussed further in Chapter 8. 3.5 One dimensional modelling A method to enable modelling of the diffusion of substitutional solute elements to cemen- tite, for the case of a symmetric carbide distribution, was developed by Bhadeshia (1989). It is presented here in full in order that comparisons may be drawn with the improvements in the model discussed in the following sections. The problem of cementite enrichment is not easy to solve analytically because of the need to consider soft impingement t. The approach used in this work is to find solutions to the governing diffusion equations using numerical methods because they can easily take into account soft impingement. 3.5.1 Symmetric case - Definition of the problem Cementite particles within a ferrite matrix are treated as a composite one dimensional t Soft impingement is the overlap of the diffusion or temperature fields, or from active regions of the same particle. Hard impingement implies physical contact between the particles. 49 diffusion couple in which a slab of cementite, thickness x(J' is sandwiched between two slabs of ferrite, thickness xa' such that X(J--- = V(J, (3.5) (2xa + x(J) where V(J is the equilibrium volume fraction of cementite in the alloy. This analysis is based on the idea that if all the cementite particles were to be massed together in a slab of width x(J, they would occupy the same volume fraction as a number of individual carbides in a section of ferrite of length x(J + 2xa. This approximation will be a good one if the spatial distribution of plate-like carbide particles in the steel is appropriate. The thickness of the cementite is a parameter in the program chosen to represent an actual particle size in a steel at long ageing times, ~100 nm. The equilibrium volume fraction of cementite in the alloy, V(J, can be found by two alternative methods. Firstly, application of the Lever rule to the binary Fe-C phase (3.7) diagram gives (c - ca(J) V(J = ( (J (J) , (3.6)c a - ca where c is the average carbon concentration in the alloy, ca(J and c(Ja are the equilibrium carbon concentrations in the ferrite and cementite respectively. It is assumed that ca(J = 0 and c(Ja=6.67 wt.%. This method tended to overestimate V(J by a small amount. A second, and more accurate method, is to use the volume fraction of cementite predicted by MTDATA for the ferrite/cementite equilibria. The advantage of this method is that it takes into account all the minor alloying element additions to the bulk alloy. It is important to set the thicknesses of the ferrite and cementite to be consistent with the calculated volume fraction of cementite present at equilibrium. To this end, the size of the ferrite slice is calculated within the program for the chosen cementite particle size. The diffusion equation must be obeyed separately in the cementite and ferrite phases: ac(J (J02 c(J -=D-at ax2 aca a2ca7ft = Da ax2 . (3.8) The particle is of a fixed size and therefore the mass balance at the cementite/ferrite interface is given by D(J ac(J = Da aca ,ox ox where the gradients in this case are evaluated at the interface. (3.9) 3.5.2 Symmetric case - Numerical solution In the analysis non-dimensional variables are used. The advantage of this is that numbers occurring in the calculations cover roughly the same ranges for all calculations. Concentrations 50 are normalised with respect to the average concentration in the alloy and distances with respect to the thickness of the cementite, hence I X X =- X9 I C C =-C I Dt t = -2' X9 (3.10) (3.11) (3.12) where D is the diffusion coefficient. For the analysis the cementite and ferrite are divided up into a number of slices, n, of equal thickness, x s such that, (3.13) (3.14) This means that the x'-t' region IS covered with a grid of rectangles of sides hx' and ht' respectively, hence the coordinates of a grid point (X',t') can be written (ihx',jht'), where i and j are integers. The normalised concentration at that point (in ferrite) is denoted by c~~i' The use of finite-difference methods to obtain numerical solutions to the diffusion equation is discussed in detail by Crank (1975). The idea is that some, or all, of the derivatives in the diffusion equation are replaced by finite-difference approximations. The explicit t finite difference approximation for diffusion in the ferrite matrix is given by where 101 101 + ( 101 2 101 + 101 )Cl '+1 = c·· r C· 1 . - C·· C·+1·,J , ,J ,- ,J ',J ',J' (3.15) (3.16) ht'r---- (hx,)2 ' and is taken to be 0.4. The value of r determines the accuracy of the method and also the computation time. A compromise value has been chosen by trial and error. The finite difference method can be readily visualised using a graphical construction. If the value of r is taken to be 1 for example, then equation 3.15 reduces to '01 1('01 + '01 )c1,i+1 = "2 Ci-1,i ci+1,i' t There are two methods of using finite difference approximations. Explicit formulae, as the name implies, express an unknown directly in terms of known values, whereas implicit formulae contain more than one unknown in each equation, necessitating the solution of a number of simultaneous equations. The latter method is usually considered to be more accurate but at the same time is very expensive in terms of computer time. The finite difference approximations are derived in Appendix I. 51 Hence, the concentration at a particular point after one time interval has passed is simply the arithmetic mean of the concentrations at the two adjacent points in the previous time interval. This is illustrated in Figure 3.2. C i,j+l C i-l,j C i,j Ci+ l,j Figure 3.2: Graphical method to illustrate the finite difference model. The normalised concentration c~o: in the a at the alB interface was initially set at c0:8 le, although the computer algorithm was designed to allow this to vary as soon as the flux matching condition at the interface necessitated changes. Then equation 3.15 was used to calculate the value of c at all points along successive time rows of the grid, for the initial conditions that c~~o= c0:8 le, and c~~o= 1 for all i > O. A similar analysis is applied to diffusion in the cementite. Finite difference approximations applied to the mass balance condition at the interface mean that c~~iare determined by the equation D ( 18 18) D ( 10: 10:)8 CO,i - C1,i = 0: C1,i - CO,i ' (3.17) where c~~o= 1 for all i > O. It should be noted that the value of the concentration in cementite at the interface was not fixed by local equilibrium considerations, but increased gradually with time towards the equilibrium level. It is assumed that the diffusion coefficients in cementite and ferrite are equal for this work. This is discussed further in Chapter 8. In general c80: > > c0:8, therefore this condition ensures that the surface concentration of cementite at the BIa interface, c~~i'is for a considerable period of time, less than c80: le. 52 For both phases, soft impingement will eventually occur. This means that the concen- trations at the maximum values of i for both (J and Cl' are eventually affected by the fluxes originating at the (J / Cl' interface. The concentrations in the slices with i = imax (Le. the extent of the ferrite and at the centre of the cementite particle) are therefore given by reflecting the concentration profile across an imaginary boundary located at imax' hence c~9 '+1 = C~9 , + 2r(c~9 l' - C~9 ,). tmG% ,J 'ma.l: ,J 'ma% - ,3 lmGS' ,J The diffusion couple and notation used are illustrated in Figure 3.3. (3.18) Symmetry Cementite plane Ferrite S C Calculate i------' I,,-----------------t·.- concentration byas 'reflection' at the C boundary Calculate concentration by 'reflection' at the boundary Mass balance at the interface Figure 3.3: The diffusion couple and notation used for calculation of the enrichment rate of cementite in the symmetric case. As the diffusion proceeds, C~~j eventually reaches c9Ci /e (at very long times). When this has occurred, it is diffusion in the cementite which begins to control the equilibration process, and the program switches to adjusting C~~j to a value consistent with the condition for conservation of mass at the interface. The value of C~~j then begins to increase to a value greater than cCi9/e. lt has already been stated that the diffusion coefficients of substitutional alloying elements in cementite are not known accurately. The sensitivity of the computer model to the value of the diffusion coefficient of er in cementite, D9, has been investigated. As the magnitude of the diffusion coefficient in cementite is reduced there are two main effects. The first is that the concentration in cementite at the particle/matrix interface rises more quickly as D 9 becomes 53 lower than D because of the need to satisfy the condition for mass balance at the interface Cl (Equation 3.17). The second effect is an increase in the concentration gradient within the cementite particle because more time is necessary to redistribute the alloying element from the interface. For smaller particles, this will result in the overall enrichment rate being quicker because, although the diffusion coefficient is smaller, the diffusion distance is still comparable to the particle size and the increased concentration at the interface is able to redistribute across the particle. Larger particles, for which the diffusion distance is smaller than the size of the particle, are not affected significantly. (The diffusion distance, x, of a given element in a specific length of time,t, can be estimated using the formula x2 = Dt where D is an appropriate diffusion coefficient. ) Low-alloy steels used in the power generation industry, having been continuously cooled from the austenising temperature, are usually given a high temperature (~700°C) stress-relief heat treatment before entering service at the lower temperature of ~565°C. Consequently, two computer programs have been developed, the first one (FINITE) is used for modelling the changes which take place during the stress-relief heat treatment, and the second (FINN), for which the input is the data generated by FINITE, to simulate the composition changes which occur during service after the stress-relief heat treatment. The computer program FINITE is is presented in Appendix H. The effect of temperature on the enrichment rate is illustrated in Chapter 5, the tempera- ture dependence coming from the temperature dependence of the diffusion coefficient (equation 3.4) and the temperature variation of the equilibrium calculated level of substitutional alloying elements in cementite. Calculations are performed for a cementite particle in a 2!Cr1Mo steel, with a size of 60 nm at temperatures of 510, 565 and 620°C. The effect of particle size on the enrichment rate is discussed in Chapters 5 and 6 for 2!Cr1Mo and !Cr!Mo! V steels respectively. 3.5.3 Asymmetric case - Definition of the problem For the case in which the amount of ferrite on either side of the carbide plate is different, the central plane of the carbide is no longer a mirror plane and it becomes necessary to consider an asymmetric carbide distribution. The method of solution of the diffusion equations for an asymmetic carbide distribution is essentially the same as that for the symmetric case. Only the significant differences are highlighted below. The problem is initially set up with a slice of cementite of thickness Xli inbetween two slices of ferrite (identified by the labels a and b) of 54 different thicknesses, xoa and xob such that (3.19) The input parameters for the calculation are the chosen particle size and volume fraction and a constant which represents the degree of inhomogeneity in the microstructure, the ratio of the thickness offerrite (a) to ferrite (b). Hence, the program automatically calculates the thick- ness of the two ferrite slices to be consistent with the desired volume fraction and distribution of carbide. The diffusion equation must be satisfied independently in both slices of ferrite and the cementite: (3.20) (3.21) (3.22) 3.5.4 Asymmetric case - Numerical solution The number of slices in the cementite and ferrite are given by (3.23) (3.24) (3.25) The finite difference approximations to the diffusion equation are the same as in the sym- metric case (equation 3.15) with an additional equation being added for the second ferrite slice. The boundary conditions are the same as for the symmetric case, although in the asymmetric case there are four, rather than two, boundaries to be considered. Soft impingement is taken into account at the extremes of the two ferrite slices in the same manner as equation 3.18. This allows the different f1.uxes originating from the two ferrite/ cementite interfaces to be taken into account. The condition for mass balance (equation 3.17) is applied separately at the interfaces between cementite and ferrite (a), and between cementite and ferrite (b). Both coBa and coBb are initially set to coB /e, but are then allowed to vary independently because of the asymmet- ric carbide distribution. The numerical calculation of the level of substitutional solute in the cementite takes into account the differences in the interface values. The asymmetric diffusion 55 Ferrite a Cementite Ferrite b 9aaC C9ab I--------- I~'---) " Va9a a9bC C Calculate concentration by 'reflection' at the boundary Mass balance at the interface Mass balance at the interface Calculate concentration by 'reflection' at the boundary Figure 3.4: The diffusion couple and notation used for calculation of the enrichment rate of cementite in the asymmetric case. couple and the notation used in the calculation of enrichment rate are illustrated in Figure 3.4. The computer program used in the asymmetric case (INHOMOG) is presented in Appendix Ill. Figure 3.5 illustrates the effect of varying degrees of inhomogeneity in the microstructure. The chromium content of a cementite particle of size 60 nm is plotted as a function of the square root of time for a symmetric distribution, and for one ferrite slice being twice and five times as big as the other. The calculations were done at a temperature of 565°C for a 2tCr1Mo steel. It can be seen that there is a marked reduction in the enrichment rate as the microstructure becomes more inhomogeneous. This is due to soft impingement in the smaller ferrite slice happening earlier than in the symmetric case and slowing down the rate of diffusion. Figure 3.6 shows the actual chromium concentration profiles through the diffusion couple, one ferrite slice being twice the size of the other. The cementite particle size was chosen to be 50 nm and the calculations were again performed at 565°C for a 2tCr1Mo steel. Four curves are shown on the graph representing intermediate times of 40, 100, 200 and 3,500 hours in the diffusion process. The average chromium concentration in the cementite particle can be seen to be gradually increasing as a function of time as it approaches equilibrium. After 3,500 hours the profiles are flat in both the cementite and ferrite, indicating that saturation has been reached. 56 50 ............ .. • • • • IDhomoi5 - Symmetric - -IDhomoi2 o o 10 20 30 40 50 R . /H V2oot hme ours 60 Figure 3.5: Chromium concentration in a cementite particle as a function of the square root of time for varying degrees of inhomogeneity in the microstructure. Soft impingement can also be seen to be occurring more rapidly in the shorter ferrite slice; the concentration at the extent of the ferrite drops as it begins to be affected by fluxes originating at the interface. The chromium profile inside the cementite particle used in Figure 3.6 is illustrated in Figure 3.7. The profile corresponds to a diffusion time of 100 hours. The slightly asymmetric profile in the cementite particle reflects the fact that soft impingement has occurred in the smaller ferrite slice. Comparison of the prediction of the asymmetric model with experimental results are made in Chapter 5. 3.6 Consideration of the effect of particle size The use of the finite-difference model has highlighted the strong effect of particle thickness on its average composition during ageing. For a given flux across the ()/ a interface, smaller particles will be sinks for solute and will enrich at a higher rate. Output from the model has indicated that the time tc to reach a given composition varies as (xe)2, although this is only the case if soft impingement has not occurred in the ferrite (corresponding to approximately 8,000 hours of service life). It is possible to account for this analytically; however, the analysis 57 40 N ~ 20 "g 10.....•.. cd 7 "".•..c:l~ Co) 4=o Co)••(.) 2 1 -- Hrs40 ......... HrslOO ---_. Hrs200 -'--" Hrs3500 nI'.1I!I1 1500o 500 1000 .1O~ Distance /m 2000 Figure 3.6: Chromium concentration profiles through a diffusion couple at times of 40, 100, 200 and 3500 hours during the diffusion process. The cementit'l puticle size is 50 nm and the temperature 146014501410 15.9 1400 16.0 N ~ 15.98 "~U 15.96••••.•.. ""cd~.s 15.94 Co) c:lo Co) "" 15.92 (.) 1420 1430 1440 .1O~ Particle size / m Figure 3.7: Schematic illustration of the chromium concentration profile within a cementite particle after 100 hours at 565°C. 58 cannot allow for the coupling of fluxes between the cementite and ferrite and so will tend to overestimate the time required to reach a given concentration. Consider a slab of thickness X(J embedded in an infinite matrix of ferrite (and no soft impingement in the ferrite). If the time required for the cementite to reach a concentration c(J is te, then a standard mass balance procedure can be used (e.g. Crank, 1975) to show that where 00 0.5x(J(c(J - c) = J cO'(x, te) dx , o (3.26) (3.27) This equation can be solved to show that 1l"X(J2(C _ C(J)2 t ------ e - 16D 0'( cO'(J _ C)2 (3.28) It can be seen that, within the validity of the equation, the composition of cementite should vary with d rather than with d. It should also be noted that, since cO'(J is a relatively weak function of temperature, most of the temperature dependence of the ageing process comes from DO'. This means that for experiments carried out at various temperatures a plot of In te against 1fT should give a positive slope corresponding to the activation energy for diffusion divided by the universal gas constant. A similar analysis can be carried out for spherical particles, following Crank (1975). If the particle radius is a and the distance ahead of the particle is noted by r, then the solute distribution ahead of the particle is given by 0' _ [a(c - cO'(J)] ( x ) c (s,tJ - (a + s) erfc 2.;n;;t; Using the same procedure as above, it can be shown that (3.29) (3.30) In this case an initial enrichment proportional to d is indicated, with a subsequent reduction in the time exponent. In both cases the enrichment also varies with the square of the particle radius in agreement with the numerical model. However, it is more difficult to interpret an activation energy for the spherical particles as the equation is no longer linear in DO'. 59 CHAPTER 4 EXPERIMENTAL PROCEDURE The various techniques employed in the experimental studies of precipitation characteristics in 2tCrlMo, !Cr!Mot V and 12CrlMoV steels are described in this chapter. 60 CHAPTER 4 EXPERIMENTAL PROCEDURE 4.1 Introduction This chapter includes a description of the experimental programme and the techniques employed, as summarised in Figure 4.1. Particle size measurements Optical Microscopy Hardness Atom probe & STEM (Chapter 8) STEEL Heat treatment to produce starting microstructure Tempering heat treatments TEM on thin foils and extraction replicas Quantitative EDX microanalysis Corn parison with 'ex-service' material X-Ray diffractio of extracted carbides Electron diffraction Figure 4.1: Flow chart illustrating the detailed experimental programme for three steels with different chromium contents. 61 4.2 Materials The precipitation of cementite and other alloy carbide phases was examined for three typical power plant steels of varying chromium concentrations. The first was a !Cr! Mol V steel with a pearlitic microstructure which was expected to contain cementite as the dominant carbide phase at the temperatures of interest for several hundred years. The second contained slightly more chromium, 21Cr1Mo, the starting microstructure consisting of a mixture of bainite and martensite. Alloy carbides began to precipitate at the expense of cementite after a few hundred hours in this steel. The third steel was heavily alloyed with chromium, 12Cr1MoV, resulting in the equilibrium alloy carbide precipitating within a few minutes on tempering at elevated temperatures. The chemical compositions of the steels used are given in Table 4.1. Further details of the materials supplied and heat treatments employed are given in Chapters 5, 6 and 7 for the 2iCr1Mo, !Cr!Moi V and 12Cr1MoV steels respectively. The !Cr!Moi V steel was supplied as prepared carbon extraction replicas from previous work by Du (1986). Details of the original method of preparation of the replicas are included below for completeness. Additional measurements were made on these specimens in order to relate particle size and chemical composition. Table 4.1: Chemical composition of the steels used in wt. % Steel C Si Mn P S Cr Mo V Ni Cu Co Nb+Ta As Sn !Cr!Mo!V 0.14 0.23 0.61 0.007 0.023 0.36 0.66 0.26 0.21 0.13 - - - -2 2 4 2iCr1Mo 0.15 0.29 0.49 0.01 0.025 2.20 0.96 0.01 0.14 0.18 0.02 - 0.03 0.02 12Cr1MoV 0.21 0.25 0.46 0.009 0.012 10.9 1.03 0.30 0.52 0.02 0.02 0.06 - - Ex-service 0.18 0.22 0.58 0.01 0.007 12.4 1.07 0.28 0.64 0.13 0.03 <0.01 - - 'X20CrMoV12' 4.3 Heat treatments 4.3.1 Furnace heat treatments Prior to the tempering heat treatments, the samples were sealed in silica tubes under a partial pressure of argon (150 mm Hg) to prevent any decarburisation or oxidation. The quartz tubes were then placed on ceramic boats inside furnaces to prevent any contamination by contact with the base of the furnace. The furnace temperatures were checked at regular intervals during the long term heat treatments with a PtfPt-13 wt.% Rh thermocouple. 62 4.3.2 Thermomechanical simulator heat treatments A thermomechanical simulator ('Thermecmastor' manufactured by Fuji Electronic Indus- trial Co. Ltd.) was used in order to control and follow the initial heat treatments of the 2tCr1Mo steel more accurately than could be achieved in a furnace. The Thermecmastor in- corporates a sophisticated dilatometer, although is usually used for investigations of the effects of stress on transformation because the strains can be monitored in two orthogonal directions. It has a high frequency induction heating system, allowing homogeneous heating of the specimen to within ±5°C, and is computer controlled enabling the heat treatment cycle to be programmed and monitored with ease. Heating can be done under a vacuum or with a gas atmosphere (Ar, N2). Rapid heating and cooling at specified rates are also possible, with the gases Ar, He or N2 being used for quenching. In this work heating was performed in an argon atmosphere and quenching was done with nitrogen gas. Temperature is measured using a PtJPt-13 wt.% Rh thermocouple resistance welded to the specimen. The dilation of the specimen in a radial direction during transformation is measured using a laser beam. Specimens for tests (under compression or with no applied load) are cylinders of 8 mm diameter and 12 mm long. In order to prevent surface oxidation and nucleation effects (Strangwood and Bhadeshia, 1987), the specimens were nickel plated before use in the Thermecmastor. The nickel plating was carried out in two stages. Firstly, an adherent but rough layer of Ni was plated onto the surface by a 'striking' treatment in a solution of 250 g of nickel sulphate, 27 ml of concentrated sulphuric acid and 1 litre of water, with an applied current density of 7.75 mA mm-2, for 6 minutes. After striking the samples were plated in a solution containing 140 g nickel sulphate, 140 g anhydrous sodium sulphate, 15 g of ammonium chloride and 20 g boric acid made up to a litre with distilled water. The applied current density was 0.4 mA mm-2, and plating was carried out for 30 mins resulting in a nickel layer thickness of approximately 0.1 mm. 4.4 Hardness measurements Macrohardness measurements were made using a Vickers pyramid hardness testing machine using a load of 30 kg and an f' objective. Five measurements were taken over the whole sample area. Microhardness measurements were made with a Leitz miniload machine using a load of 0.981 N, and loading and dwell times of 15 seconds each. Twenty measurements were taken over the whole area of the specimen and the mean value calculated. 4.5 Optical microscopy Samples were prepared for microstructural characterisation by hot mounting in acrylic moulding powder, followed by grinding on SiC paper to 1200 grit and polishing with 1 J.lm cloth 63 coated with diamond paste. Specimens of 2tCr1Mo steel were etched in 2% nital (nitric acid in methanol) and specimens of the 12Cr1MoV steel were etched using Bain-Villela's reagent (5 ml hydrochloric acid, 1 g picric acid in 100 ml of methanol) for times of up to 3 minutes. Samples of the ~Cr~ Mot V steel were received already in the form of carbon extraction replicas; however, these were originally etched in 4% nital for cementite extraction from the shorter time heat treatments, and in Villela's reagent for extraction of the larger alloy carbides from the longer term heat treatments. Optical micrographs were taken with an Olympus microscope with a camera attached using llford Pan F film. 4.6 Transmission electron microscopy Specimens for transmission electron microscopy (TEM) were prepared by both by the twin-jet electropolishing of thin foils and the carbon extraction replica technique. 4.6.1 Thin foil preparation Thin 3 mm discs are required as the starting point for thin foil preparation. These were cut directly from the heat-treated 3 mm rods of the 12Cr1Mo V steel using a SiC slitting wheel, whereas 3 mm discs were mechanically punched out of thin slices cut from the larger rectangular specimens of 2t Cr 1Mo steel using a high-speed saw. The discs were then mechanically ground by hand to 50 /lm and then twin-jet electropolished to electron transparency at 50 V, with the solution being cooled to O°C using liquid nitrogen. The polishing solution used for the 12Cr1MoV steel contained 10% perchloric acid, 15% glycerol and 75% industrial methylated spirits, and that for the 2tCr1Mo steel, 5% perchloric acid, 20% glycerol and 75% industrial methylated spirits. The thinned samples were examined in a Phillips 400T TEM operated at 120 kV. 4.6.2 Extraction replica preparation The extraction replica technique is very useful for the identification or counting of carbide or precipitate phases in a metallic system. The main advantages of replicas over foils are that they eliminate any effects due to the steel matrix and thus enable the chemical composition of the carbides to be measured more accurately, and working with a magnetic specimen in the electron microscope is avoided. The replica is also very thin ~ 100 A, has no self-structure and will not burn in an electron beam. Single-stage carbon extraction replicas were prepared using the method described by Smith and Nutting (1956) from surfaces prepared as for optical microscopy using a lighter etch. Shad- owing of the carbon replica with gold (Mukherjee et al., 1968) was not considered necessary 64 because only the particle sizes were measured, rather than volume fractions. The presence of gold on the replica would also have interfered with the electron diffraction and quantitative EDX measurements used to identify the second phase particles. A carbon coating of 200-300 A (colour blue-brown) was deposited in a vacuum of 10-5 torr on to the etched specimens. The carbon film was scored using a sharp blade to enable removal of several small sections covering the whole area of the sample. The film was then removed by electrolytic etching in a solution containing 5% hydrochloric acid in methanol at +1.5 V. The film was then washed in industrial methylated spirits and floated off in distilled water and collected on 400 square mesh copper grids for examination in the TEM. Replicas from the !Cr! Mot V steel specimens were originally prepared using 4% nital for specimens previously etched in 4% nital, and 10% nital for those previously etched in Villela's reagent. 4.6.3 Calibration of the camera constant The settings of the various magnetic lenses within the column of a TEM affect the mag- nification of diffraction patterns. Usually the microscope is operated with the lenses at fixed settings and so the magnification of the diffraction pattern is a constant. This magnification factor is expressed in terms of an equivalent camera length necessary to produce the same magnification in a diffraction camera without the lenses. This is illustrated schematically in Figure 4.2. Incident Electron Beam Camera length L Specimen Transmitted-~---~- Diffracted Spot R Spot Figure 4.2: Schematic illustration of the magnification of a diffraction pattern by the microscope lenses. 65 The camera constant is denoted by the expression, corrected for relativistic effects, Rd{hkl} = LA = camera constant (4.1) where R is the real distance measured on the diffraction pattern between the transmitted and the diffracted spot, L is the camera length (usually 575 mm or 800 mm in the Philips 400T TEM operated at 120 kV), d{hkl} is the spacing of the {hkl} crystallographic planes and A is the electron wavelength. A is given by the following expression which is corrected for relativistic effects:- hA = ( v ) = 0.0335A, (4.2)2meV 1+ 2~C2 where h is Planck's constant, m and e are the electron mass and charge respectively, V is the accelerating voltage of the electrons and c is the speed of light in vacuum. It was very important for the identification of the various carbide phases which have similar lattice parameters to determine the camera constant accurately. This was done by examination of the diffraction pattern from a gold film sputtered onto a copper grid. A film produced by chemical vapour deposition consists of very fine grain size polycrystals. For a given electron beam direction a number of particles are oriented so as to satisfy the Bragg equation hence each plane gives rise to a number of reflections lying in a cone of angle 40. The resulting diffraction pattern therefore consists of a set of concentric rings corresponding to the {hkl} planes which are diffracting. To calculate the camera constant the diameters of the rings in the diffraction pattern were first measured. Then the ratios of the squares of the radii of the outer rings to those of the first or second low-index ring were determined. This enabled the N values corresponding to each of the rings to be found; N is given by the usual expression for cubic systems (4.3) where {hkl} are the plane indices. The N values were then converted to d spacings using the formula d= _a_..;N (4.4 ) for cubic systems. The accurate lattice parameter, a, for gold has been measured as 4.0780A (Barrett and Massalski, 1968). Multiplication of the calculated d spacings by the radius of each individual ring gives a constant value. The average of all the values for the individual rings was used for the best accuracy. This method is illustrated in Table 4.2, which evaluates the camera constant for a current of 6.40 A through the objective lens at the eu- centric specimen height. The diffraction pattern from the sputtered gold film is illustrated in 66 Figure 4.3. The calculated camera constants for a number of different nominal camera lengths and currents through the objective lens used in the characterisation of second phases are given in Table 4.3. The various carbides were identified using both selected area electron diffraction and convergent beam electron diffraction when the carbides were very small compared with the size of the selected area diffraction aperture. Table 4.3: Calculated camera constants for a number of different nominal camera lengths and currents through the objective lens. Nominal camera Objective lens Calculated camera length fmm current fA constant fxlO12m2 800 6.40 2.66 800 6.20 2.71 575 6.20 1.86 4.7 Energy dispersive X-ray analysis (EDX) For the detailed experimental results of particle size and composition on the !Cr!MoiV, 2iCr1Mo and 12Cr1MoV steels, detailed microanalyses were carried out on particles using carbon extraction replicas. At least 30 isolated particles on each specimen were analysed, depending on the particular measured composition variation, covering an area of several grid squares. In the early stages of tempering the cementite composition was found to vary so greatly between different particles that up to 100 analyses were needed to get a good estimation of the variation and a reasonable estimate of the average concentration. A LINK series 860 energy dispersive X-ray spectrometer attached to a Phillips 400T 120 kV TEM was used for all the analyses. X-ray spectra were recorded at a specimen tilt of 35°, and live times of at least 200 seconds were used to ensure statistically significant results, depending on the count rate from individual particles. The dead time was not allowed to exceed 25%. The data were analysed using the LINK RTS2-FLS software. The original measurements on the !Cr!MoiV specimens made by Du (1986) were on extraction replicas in both a 100kV Philips 400T and a 200kV Hitachi H-700T transmission electron microscope, each equipped with an EDAX 9100 energy dispersive X-ray analysis fa- cility. 50,000, 25,000 and 25,000 counts were preset in the Fe KO', Mo KO' and V KO' windows respectively to keep a constant statistical error. Counts from the carbon replica background were kept at 200±50 counts per second in the Hitachi H-700T and 100±50 cpts in the Philips 67 400T microscopes to ensure a constant intensity beam. The incident spot size was 1000 A and all the analyses were done with the spot covering the whole particle. Chromium is chosen as an indicator of composition change because of its large concentration and partition coefficient; the iron content simply mirrors the changes in chromium content. The total manganese content is relatively small and therefore any errors will be relatively large. Molybdenum has a much larger atomic mass compared with iron, chromium or manganese. Since the microanalytic measurements are carried out assuming that all elements absorb the X-rays to a similar degree, the molybdenum data are likely to be flawed, the extent of the error depending on the thickness of the particle along the electron beam direction (a parameter which is very difficult to determine for each individual particle). Typical EDX spectra for the various carbides in the three steels are presented in detail in the experimental chapters 5, 6 and 7. 4.7.1 Basis for quantification of EDX Quantitative microanalysis involves the comparison of the intensities of an unknown peak with that from a measured or calculated standard, removal of the background, peak integration and correction for peak overlap. The intensity of a peak is proportional to the composition of the material being analysed. In order to avoid determination of various constants depending on mass, specimen thickness and diffraction conditions, ratios of the integrated characteristic intensities are related to the composition of the specimen using the equation due to Goldstein et al. (1986) for a binary system CA = kABIACB IB (4.5) where CA and CB are the weight fractions of elements A and B in the analysed volume, lA and 1B are the characteristic intensities of elements A and B (after subtraction of the background), and k AB is an experimental constant. The number of similar equations for all the elements being analysed is necessarily less than the number of elements, therefore in order to solve these equations it is assumed that all the elements are detected and that the sum of the concentrations is 100%. It should be noted that due to the presence of a beryllium window on the front of the EDX detector, the carbon content of carbides cannot be allowed for. The results of the EDX analyses can be normalised to allow for the appropriate stoichiometric carbon content in the various carbides. The factors k AB' k AC' kc B etc. can be determined experimentally using pure elements or homogeneous compounds containing the desired element and the element chosen as a standard (Si in this case), e.g. chromium silicide, or by calculation from first principles. Experimental 69 determination is better due to difficulties into taking account of the detector response and other minor factors. The peak intensities and shapes from the standard compounds are used to determine the k-factors for every element to be analysed normalised with respect to Si. Pure compounds containing Si were used to determine the k-factors experimentally for the elements of interest when the EDX system was set up. The overall intrinsic system error is ~0.5-1.0%. The characteristic energies for the X-ray peaks of interest and the k-factors with respect to Si are given in Table 4.4. Table 4.4: Characteristic X-ray peak energies for EDX. The average energy is given for the Kal and Ka2 peaks because, unlike X-ray diffraction, EDX is not usually able to resolve these peaks. The k-factors determined from standard compounds are included for the more intense a peaks only. Element Peak Energy /keV kSi Mo LO'l,2 2.293 1.766 Mo L.a1 2.394 - V K 4.948 1.1970'1,2 Cr K 5.410 1.2130'1,2 V L.a1 5.427 - Mn KO'l,2 5.898 1.291 Cr K.a1 5.946 - Fe KO'12 6.397 1.322 Mn K.a1 6.490 - Fe K.a1 7.057 - Cu KO'l,2 8.037 1.595 Cu K.a1 8.940 - Mo KO'l,2 17.426 4.830 Mo K.a1 19.786 - Correction for the absorption of characteristic X-rays in the particle analysed have been ignored, being close to unity for the average size of carbide present « 100 nm). Characteristic X-ray fluorescence is of second order in magnitude to absorption and is therefore also ignored. 4.8 Particle size measurements The size of each carbide particle was determined by measuring a number of random in- tercepts across it on the photographic negative. Hence, particle size is expressed in terms of a 70 mean linear intercept. This measure was chosen as it is closely related to the diffusion distance across the particle and can be used for irregular geometries. The particles are in the form of thin plates, so that most of the enrichment should be from diffusion in a direction normal to the plate plane. The linear intercept as measured above, should give a good description of the particle size along this diffusion direction. 4.9 Bulk extraction of carbides and X-ray diffraction It is possible to isolate the carbide precipitates in steels by the electrochemical dissolution of the matrix. X-ray diffraction of the extracted particles can then be used for identification and quantitative analysis, including accurate lattice parameter measurements and volume fraction data for the various carbides formed in the steel during tempering. This technique is discussed in detail by Andrews and Hughes (1958), and more recently by Stuart and llidley (1966), Leitnaker et al. (1975), Pilling and Ridley (1982) and Stevens and Lonsdale (1987). In particular Stevens and Lonsdale (1987) investigated the experimental conditions nec- essary for optimum carbide extraction. The composition and strength of the electrolyte and the conditions of voltage or current density determine the efficiency with which dissolution of the matrix occurs whilst leaving the carbide precipitates intact. Chemical dissolution of the extracted precipitates in the electrolyte can occur. This is dependent on the electrolyte and the temperature and time of the extraction. The use of high volt ages and associated high current densities results in large amounts of carbides being extracted in a short time; however, the likelihood of chemical dissolution of the precipitates may be increased by resistance heating of the electrolyte. The precipitates are more likely to separate from the specimen and fall into the solution thus increasing their risk of loss. The literature suggests that 5% aqueous hydrochloric acid is suitable for the extraction of low alloy steels, whereas 10% alcoholic hydrochloric acid is usually used for high alloy steels. The disadvantages of the alcohol as a base are that the lower associated current densities result in a higher acid concentration and longer extraction times having to be used, enhancing chemical dissolution of extracted carbides. Stevens and Lonsdale (1987) also suggest that for steels containing the carbide M3C using alcohol as a base may mean that few of these carbides are extracted. The specimen was anodically dissolved in a cell with a platinum cathode and a solution of 5% hydrochloric acid in water for the 2t CrlMo steel and 10% hydrochloric acid in methanol for the 12CrlMoV steel as the electrolyte at a voltage of 1.5 V. Typical extraction times were 6-8 hours. The electrolyte was then decanted off and the precipitate thoroughly dried in an oven at approximately 60°C. Careful weighing at all stages of the extraction to an accuracy of 10 J1g 71 was performed to find the exact amount of precipitate extracted. An internal standard, Ce02, was added to the precipitates. This was accurately weighed to approximately 25% of the total mass of the precipitate. A Siemens D500 diffractometer (CuKa radiation) was used to scan between 30° and 65° 28 at a step size of 1 second duration, corresponding to 0.004° 28, where 8 is the Bragg angle. The diffraction peak positions were located using Siemens DIFFRAC 500 software, also used to calculate the associated integrated intensities of the peaks. 72 CHAPTER 5 2tCrlMo STEEL Extensive studies of cementite composition changes in bainitic and mixed microstructures of bainite and allotriomorphic ferrite are discussed in this chapter. The observed composi- tion changes are found to be highly dependent on the position of the carbides within the microstructure and on the particle size. The transformation of the cementite to alloy carbides is also studied. It is found that alloy carbides precipitate with a composition very close to their equilibrium composition and therefore subsequent enrichment is negligible. 73 CHAPTER 5 2iCrlMo STEEL 5.1 Introduction 2iCrlMo steel is widely used for superheater tubing in power plant, and as filler ma- terials for joining ~Cr~ Mot V steam piping. Its creep properties, and their correlation with microstructural changes, have been studied widely (e.g. Baker and Nutting, 1959; Hale, 1975; Klueh, 1978). It is well established that the creep properties improve with subsequent tem- pering and then eventually degrade after the precipitation of the larger equilibrium alloy car- bides. 2tCrlMo steel is usually given a stress-relief heat treatment at 700°C before going into service at a temperature of approximately 565°C. Klueh (1978) states that the creep rate is controlled initially by the motion of dislocations which contain atmospheres of carbon and pos- sibly molybdenum clusters, and subsequently by atmosphere-free dislocations moving through M2C precipitates. The high temperature mechanical properties of the material are affected strongly by the metallurgical instability of the alloy involving carbide precipitation reactions. The tempering process results initially in the formation of iron carbides, which are subsequently replaced by more stable alloy carbides. Many studies of the precipitation sequences in 2iCrlMo steels have been made. Baker and Nutting (1959) discuss precipitation sequences in a commercial alloy in both quenched and normalised conditions in the temperature range 673-1023K. Andrews et al. (1972) have produced a comprehensive set of 'near-equilibrium' experimental diagrams relating to carbide stability. They used many steels in the composition ranges 0-6 wt.% Cr, 0-2 wt.% Mo and 0-1 wt. % V, and tempered as-quenched microstructures for up to 1000 hours at 923 and 973K. Titchmarsh (1978) studied carbide precipitation in samples tempered at 933K for up to 200 hours in order to demonstrate the identification of various carbides using EDX analysis techniques. Hippsley (1981) also studied 2tCrlMo steel, although this was in the context of cracking during the stress-relief heat treatment in the bainitic Heat-Affected-Zone (HAZ) of welds. Pilling and llidley (1982) investigated the effect of carbon content in three low carbon 2tCrlMo alloys, tempering at 700°C. Baker and Nutting (1959) found that the sequences of carbide precipitation in the nor- malised (ferritic/bainitic) and quenched (autotempered martensite) microstructures were al- most identical. The only difference being that precipitation of M2 C occurred in the early stages of tempering the normalised steel, and persisted in the ferrite phase, forming well-defined fiat- 74 tened needles. They also found that bainitic carbides spheroidised quickly during tempering at 600°C. After 50 hours Cr7C3 was found in the bainite near the bainite/ferrite interface, M23C6 then being found in the bainitic regions, and only in the regions which were free from Cr7C3· The experimental results of Baker and Nutting are presented in Figure 5.1. 700 0° iller 600:JI- e::(er illa..~ 500 illI- 400 10 100 1000 TEMPERING TIME / hrs Figure 5.1: Carbide stability diagram for a 2tCrlMo steel. (Modified from Baker and Nutting, 1959) There is evidence to suggest that small changes in chemical composition can alter the pre- cipitation behaviour of the alloy. Yu (1989) has shown that increasing the silicon concentration stabilises M6C, and accelerates the precipitation of M2C. Similarly an increase in the man- ganese concentration was found to accelerate the precipitation of M7C3• An analysis based on the thermodynamic stability as a function of chemistry and temperature could in principle be used to explain these results. However, no information can be obtained on the rate of precipi- tation from such calculations. In stating such precipitation sequences, it is important to relate them to the part of the microstructure in which they occur. Lee (1989) has recently confirmed that the starting microstructure can have a profound effect on the tempering sequence. In a Fe-1Cr-0.5Mo-0.15C wt.% steel detailed differences between pearlitic, bainitic and ferritic microstructures were demonstrated, and it was also shown that the carbide type was sensitive to position within the microstructure. The predicted equilibrium carbides in the steel utilised in this work using MTDATA were M6C and M23C6 in the temperature range 500-650°C. 5.2 Materials The 2tCr1Mo steel was supplied in the form of a cylindrical bar approximately 100 mm in diameter and 300 mm long. Rectangular specimens of size 10x10x60 mm were machined from 75 the bar for furnace heat-treatment, and smaller cylindrical specimens of 8 mm diameter and 12 mm length were also machined for use in the thermomechanical simulator. The chemical composition of the steel (in wt. %) is given in Table 5.1. Table 5.1: Chemical composition of 2lCrlMo steel in wt. % C Si Mn P S Cr Mo V Ni Cu Al Co As Sn 0.15 0.29 0.49 0.01 0.025 2.20 0.96 0.01 0.14 0.18 < 0.01 0.02 0.03 0.02 5.3 Initial heat treatments The initial microstructure for use in power plant is formed by continuously cooling a thick section of material, resulting in a mixture of allotriomorphic ferrite and bainite (with some martensite). In this work it was decided to investigate both a predominantly bainitic microstruc- ture (also containing some areas of martensite) and a mixed microstructure of approximately 50% allotriomorphic ferrite and bainite. [The former microstructure is henceforth referred to as 'fully bainitic' for brevity, although it should always be understood that it consists of a mixture of bainitic ferrite and martensite.] The bainite in the specimens containing 50% allotriomor- phic ferrite forms from carbon-enriched austenite and therefore the enrichment kinetics of the cementite are expected to be different from those in the fully bainitic microstructure. In order to determine the heat treatments required to produce these two starting microstructures it is necessary to calculate the time-temperature-transformation (TTT) diagram for the steel. 5.3.1 Calculation of the TTT curve and phase diagram A model developed by Bhadeshia (1982) was used to calculate the TTT curve and phase diagram for the 2lCr1Mo steel; the results are presented in Figure 5.2 and Figure 5.3. (The 'kinks' in the dot-dashed line in Figure 5.2 and in the Ae; line in Figure 5.3 are artefacts of the compu ter program.) The phase diagram shows three distinct lines: the line To is the locus of points where ferrite and austenite of identical composition have equal free energy and the T~ line is a modification of this which allows for the strain energy involved in the transformation (400 J mol-I). The line Ae3' is the paraequilibrium phase boundary indicating equilibrium between ferrite and austenite when the ratio of iron to substitutional solute atoms is constant everywhere, i.e. when there is no substitutional alloying element partitioning during transformation. The start temperatures Bs and Ms for the bainite and martensite reactions respectively are also marked on the TTT curve. The TTT curve was then used to determine a suitable heat treatment cycle. To produce a mixed microstructure of allotriomorphic ferrite and bainite it can be seen 76 that holding the specimen at 700°C will allow the growth of allotriomorphic ferrite and further transformation at 480°C, within the bainite phase field, will produce bainite. A fully bainitic microstructure can be produced by simply holding the specimen at 480°C. 5.3.2 Calculations to determine the volume fraction of allotriomorphic ferrite A model has been developed by Bhadeshia et al. (1987) to calculate the volume frac- tion of allotriomorphic ferrite formed in steel weld deposits. This theory was applied to the 2tCrlMo steel to estimate the volume fraction of allotriomorphic ferrite in a sample after a given time for transformation at 700°C. The calculation of the growth rate of allotriomorphic ferrite uses the methods discussed by Avrami (1939) and Cahn (1956) to calculate the isothermal reaction kinetics for ferrite allotriomorphs forming at grain boundaries, modified to incorporate parabolic growth kinetics. The allotriomorphs are modelled as discs parallel to grain boundary planes with a half-thickness, q. Geometrical considerations lead to the following approximate expressIOn when the austenite boundary is decorated with uniform layers of allotriomorphic ferrite ( ) 2Sv 1 ( )-in 1 - ( = Tal t~ , 5.1 where Sv is the austenite grain surface area per unit volume, al is the one-dimensional parabolic thickening rate constant and t IS the reaction time in seconds. is the equilibrium volume fraction of ferrite, given by = (5.2) where x"!cx, XCX,,! and "if are the carbon concentrations in the austenite, ferrite and the bulk alloy respectively. ( is the calculated volume fraction of allotriomorphic ferrite divided by . The values of X"!CX, XCX,,! and al were determined using the same computer model as that for calculating the TTT curve. At 700°C these were 2.28 at. %, 0.0669 at% and 0.1014x 10-3 cm s- i respectively. "if was 0.69 at. %. Assuming an initial austenite grain size of approximately 150 j.lm, estimated from the prior austenite grain size in the bainitic specimens, gives a value of Sv equal to 13.33x 103 m-I. Therefore, for transformation at 700°C for 1 hour, theory predicts a volume fraction of allotriomorphic ferrite of ~0.6. It can also be shown using the approximation q = al d, that a tempering time of 1 hour at 700°C is consistent with the above calculation. It was therefore decided that the transformation to allotriomorphic ferrite should be carried out initially for 1 hour at 700°C. 5.3.3 Starting bainitic microstructure The rectangular specimens were first dip-coated in a commercial application (containing a dispersion of clays and refactory solids in a solution of an organic resin in solvent) whose 77 900 ...... _ _. _ ~~.3 _.0 . •• o. 0 ••••••• ~.e.~l_ .600 u 0 700 W....•...•• ~~~Eo-< 600<~ B.~0.. ~~Eo-< 500 ! I M.I 400 ...... - - ... 1- 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 TIME / secs Figure 5.2: Calculated Time-Temperature-Transformation curve for 2tCrlMo steel. ~. 25 MOLE FRACTJOJ\ OF CARBON Figure 5.3: Calculated section of the phase diagram for 2tCrlMo steel. 78 function was to limit any decarburisation which might occur during heat treatment. They were then austenitised at 1050°C for 15 minutes in a furnace before transfer to an adjacent fluidised bed at 480°C for 30 minutes. Optical and scanning electron micrographs illustrating the predominantly bainitic microstructure with small islands of martensite are presented in Figure 5.4a) and b). It is well known that the bainite reaction does not go to completion when cementite formation does not accompany the growth of bainite. It is then possible to calculate the expected volume fraction of bainite at 480°C using the equation (5.3) where xTo is the mole fraction of carbon remaining in austenite when the reaction stops, x is the average carbon concentration in the alloy and x et is the carbon concentration in bainitic ferrite (assumed to be zero). The phase diagram in Figure 5.3 predicts a value for xTo of ~0.026 at 480°C and x is 0.0069, giving a volume fraction of ~0.7 at 480°C. This is in good agreement with the observed volume fractions in Figure 5.4. As the transformation temperature is lowered the volume fraction of bainite will increase. The initial microstructure was also characterised in the TEM using thin foil speCImens. The micrograph in Figure 5.5 illustrates the bainitic and martensitic areas, the martensite being heavily dislocated. There is also a small amount of retained austenite present at the edges of the bainite sheaves; the electron diffraction pattern in Figure 5.6 shows reflections attributable to the retained austenite. A carbon extraction replica taken from the as-transformed fully bainitic specimen is pre- sented in Figure 5.7. It is interesting to note that there are no cementite particles in the bainitic regions immediately after isothermal transformation. This implies that it is upper bainite which forms at 480°C because lower bainite would contain carbides as a consequence of the trans- formation mechanism. The bainite reaction has been discussed extensively in Chapter 2. The formation of upper bainite results in the rejection of carbon into the austenite surrounding the bainite plates. Some of this enriched austenite is retained on quenching after isothermal transformation. Immediately tempering begins, the austenite starts to decompose to a mixture of ferrite and cementite. This cementite will initially have a composition consistent with for- mation by a para.equilibrium mechanism owing to the large differences in the diffusion rates of carbon and substitutional solute elements. Whether it is upper or lower bainite which can be found in the microstructure following isothermal transformation above Ms has been investigated widely for plain Fe-C steels. aka and Okamoto (1986) proved that steels with more than 0.8 wt.% of carbon do not contain any upper 79 bainite, observing only lower bainite at all transformation temperatures above Ms' In addition, Ohmori and Honeycombe (1971) found only upper bainite in plain carbon steels containing less than 0.4 wt.% carbon. Few similar studies have been made for alloy steels. The steel used in this work has a carbon concentration of 0.15 wt.%. It is of great interest, therefore, to investigate whether or not lower bainite can be formed by isothermal transformation near Ms. To this end, the value of Ms was first determined by austenitising a specimen in a thermomechanical simulator at 1050°C for 15 mins, followed by quenching to room temperature using nitrogen gas. Graphs in which the relative length change is plotted against temperature and time are presented in Figure 5.8a) and b) respectively. The Ms temperature was found to be 420°C. This is in good agreement with the value of 390°C predicted by the model described in section 5.3.1. Two similar isothermal transformations experiments to those used to create the starting bainitic microstructure used in the majority of this work were then carried out, again in the thermomechanical simulator. In both cases specimens were austenitised at 1050°C for 15 mins and then one specimen was isothermally transformed at 450°C, and the other at 400°C, each for 30 mins. It is important to note that although 400°C is slightly below Ms, a considerable volume fraction of bainite is to be expected on isothermal transformation so near Ms' Graphs showing plots of temperature against time and relative length change against time for the transformation at 450°C are presented in Figures 5.8c) and d), and at 400°C in Figures 5.8e) and f). The specimen isothermally transformed at 400°C was then examined in the TEM to determine if there was any lower bainite present in the microstructure. A low magnification transmission electron micrograph is presented in Figure 5.9. Careful examination of the picture reveals that there are large areas of both lower and upper bainite. A higher magnification image of the upper bainitic region presented in Figure 5.10 clearly shows plates of upper bainite separated by films of retained austenite. Low and high magnification images of the lower bainitic region are presented in Figure 5.11 and Figure 5.12 respectively. The most striking feature of these images is that the cementite precipitates are in one orientation only with respect to the lower bainitic ferrite. There is also evidence of some films of retained austenite in the lower bainitic regions, but it is not as extensive as in the upper bainitic regions. The microstructure contained approximately 45% lower bainite, 45% upper bainite and also 10% martensite. A martensite lath is illustrated in Figure 5.13. The cementite within the lath is found in three different orientations, in contrast to that in the lower bainite. It should be noted that this martensite has formed during isothermal transformation just below Ms and has tempered on continued holding at 400°C. This is still consistent with the fact that there are no 80 carbides found in the specimens transformed at 480°C which contained a mixture of martensite and bainite. In that case the martensite formed on quenching and therefore no tempering occurred allowing cementite precipitation, and the bainite was all upper bainite and therefore did not contain any carbides. The differences in scale of both the laths and the carbide precipitation in the lower bainite and the martensite are clearly illustrated in Figure 5.14. The martensite lath is much coarser than the bainite, whereas cementite precipitation is on a much finer scale in the martensite due to the increased carbon concentration and occurs in more than one orientation. Chapter 2 discussed the rejection of carbon from plates of upper bainite during growth. As a consequence of this, the austenite matrix will become richer in carbon. In the later stages of transformation the bainite growing from the enriched austenite may then decompose to lower bainite. This explains why the mixture of upper and lower bainite is observed in this case. 5.3.4 Starting mixed allotriomorphic ferrite and bainitic microstructure The necessary heat treatment cycle to produce a mixed microstructure is austenitisation at 1050°C for 15 minutes, followed by holding at 700°C for 1 hour, then further transformation at 480°C for 30 minutes, then finally quenching to room temperature. It proved extremely dif- ficult to control the amount of decarburisation in the specimens using a furnace at 1050°C and two fluidised beds at 700 and 480°C respectively. The heat treatments were therefore performed on the smaller 8 x 12 mm cylindrical specimens in a thermomechanical simulator. This enabled the exact heating cycle and cooling rates to be accurately programmed. The experiments were essentially performed in vacuum, however, nitrogen gas was introduced into the chamber to quench the specimen between the tra.nsformation temperatures. The vacuum pumps were then switched back on to pump out the gas once the specimen had reached the next required trans- formation temperature. Three test experiments were performed in which the only difference was the speed with which the vacuum pumps were activated after the introduction of the N2 gas to quench the specimen from 1050°C to 700°C. The heat treatment cycle and graphs showing the relative length change versus time for three of the test specimens are presented in Figure 5.15a)-d). It can be seen from Figure 5.15b) that speCImen 1 shows the maximum relative length change of ~0.01, with specimens 2 and 3 showing relative length changes of ~0.008 and ~0.007 respectively. The relative length change corresponds to the amount of growth of allotriomorphic ferrite and therefore specimen 1 should contain the highest volume fraction of ferrite, with spec- imens 2 and 3 having progressively lower volume fractions. Optical micrographs of specimens 1, 2 and 3 are presented in Figure 5.16, Figure 5.17 and Figure 5.18 respectively. It can seen that 81 a) b) Figure 5.'1: a) Optical alld h) HCil.lllling ('I('ctroll IlIicrograpllH of 11)(' starlillg haillitic IllicroHtrllctllr(' AlIst('nilis('d 1050°(; 15 rnillllt('s, 480°(; :10 millut('s alld tll(,1I walN qll(,lIclI('d. 82 Figure 5.5: Tr~lIslllissioll ('le('lroll 1Ilicrogr~pll showillg a 11Iixlllr(' of haillil(' ~lId lIlart(,lIsit(', the IlI~rt(,lIsit(' heillg h('~vily c1islocal('d. 'I'hN(, is also a sllIall ~1Il01lnl of r('taillecl ~1Ist('nit(' A1Ist(,lIi- tis('d 10:;0°(' 15 llIi1l1l1('s, ,180°(' :10 Illi1lllt('S alld 111('11walN qll(,lIril(,(1. Figur 5.6: S('I( cl ('d ar('a p\('cl rOil d if!"ract iOIl pall Nil showi "1-\ rdl('cl iOlls clIll' 10 rl'l il i IlI'd alist ('11it (' wilhill Ih(' 11Iicroslr1lctllr('. n.s I"ll Figure 5.7: Carbon extra(·tioll r<'plir;L t.ak{'n frolll the i\.011< OIl > (x, • After 238.5 hours the microstructure consists predominantly of M7C3 and M2C. The ce- mentite in the bainitic regions has been completely replaced by M2C with some larger M7C3 par- ticles on the boundaries between sheaves. Some cementite with the higher chromium remains in the martensite, although there is also precipitation of M7C3 on the edges of these regions. This is illustrated in Figure 5.35a). A selected area electron diffraction pattern from an M7C3 par- ticle is presented in Figure 5.35b); characteristic streaks from the presence of stacking faults in the structure (discussed in Chapter 2) are clearly visible. The specimens tempered for 512 and 1048 hours (Figure 5.36 and Figure 5.37 respectively) showed further precipitation of M7C3 at the expense of the martensitic cementite. All the cementite had dissolved in the specimen tem- pered for 1048 hours. There was a slight enrichment of the M7C3 with respect to the chromium concentration with increasing tempering time; this is discussed in section 5.5.4. After 2072 hours the M7C3 precipitates have coarsened slightly (Figure 5.38). The carbide M6C has also begun to precipitate at the expense of some of the M2C needles which have dissolved. This is illustrated in Figure 5.39a) which shows aligned M2C carbides together with some smaller, squarer particles which have been identified by selected area electron diffraction as M6 C (Figure 5.39b). A selected area diffraction pattern from the M2C needles is also presented in Figure 5.39c). The needles of M2C were too fine to take selected area electron diffraction patterns, except from a cluster, prior to this tempering time. It has been shown above that the carbide type is very sensitive to position within a given microstructure. After a short period of tempering M2C dominates within the bainitic plates, whereas mixtures of M2C, M7C3 and M3C are to be found at the bainite plate boundaries and predominantly M3C in the martensitic regions. This is probably because far less carbon is available within the upper bainitic plates, whereas the plate boundaries are the sites for cementite precipitation during the growth of upper bainite. More carbon is available (in the form of cementite, or dissolved in carbon-enriched retained austenite) in the vicinity of the plate boundaries which can stimulate the formation of a variety of alloy carbides. 97 380 360 > 340=" 320enen ~ 300-a ""~ 180o ""~ 260::e 240 220 0. o 200 400 600 800 1000 Tempering Time /Hours Figure 5.21: Macrohardn('ss IlWasltr(,IllC'llts as a fUllction of tillw for SP('CiIlWIlS t.('mp<'r('d at. .')I0, 56.5 Figure 5.22: Opt ical Illicrost.ructurp frolll th(' fully bainit ic sl)('cilll(,1l t(,lIlp<'r('d for 2072 hours at. 565°(;. •.. I , \. .. , " , .. . , , f Figure 5.23: Car non cxl raction replica from the fully bainitic spccimen tempered for 10 minutes at 565°C showing that ccrncntitc has bcgun to precipitatc, in particular in between and parallel to the platcs of uppcr bainitc. Figure 5.24: Transmission elcctron micrograph from a thin foil spc("irncn from thc fully bainitic spcc- illwn tcmpNcd for IQ JIlinutcs at 565°C showing a platc of tcmpNcd martcnsite containing cemcntite in thre distinct oricntations. 99 'r ,,/ . ,.i, -i', ",' t " ~ ~'I- f It ••. ,.",( ,I,')-.......' x·t;,~,. Figure 5.25: 565°C. arboll C'xtractioll rC'plira from thC' fully bilinitic SPC'CiIlWIltC'lTIpNC'dfor 64 hours at 100 Figure 5.26: Low magnification transmi sion electron micrograph showing carbide particles delineating lath boundaries in the bainitic and martensitic regions after tempNing at 565°C for J28 hours. The grid bars across the image are the COppN grid on which the replica is supported. Figure 5.27: ementite precipitatiou ill thc martcn. itic regions of a specimen tempNed for 12 hours at 565°C in a Widmanstattcn array. 101 a) b) ~.~---' "'.~ . . ,.. ""*' -< r..- ::-:Y,7,.' • Figure 5.28: a) Low alld b) high rnagllificatioll carboll ('xtract.ion r('plicas frorn tll(, sp('cirnen t('rnpNcd at .565 QC for 128 hours showi IIg c('nwlltit(' pr('cipitation 011the bOllllc!ari('s of th(' bainitic r('giom; which contain cxtcllsive prC'cipitittioll of M2C 1)('('<11(',,; ill a Wic!lIlallstii,tt('n array. 102 .~ . ,. -''* ;. 1.0 Itlll ~ 'I, •- ,( c) d),0.25 11ll) L--J / I a) b) Figure 5.29: Low a) allfl high b) magnification translllis:>ioll e('ctroll micrographs illllstrating d('nse cementite pr('('ipitatioll ill Wi<,clrncnt('mpN('d for 1048 hours at 565°C showing that t1l<'microstructur(' consists pr('dolllinantly of largc M7C3 and fill(, M2C particles. Figure 5.38: Carhon ('xtractioll r('plica frorn sp('C1rn(,1It(,lIll><,r('d for 2072 hours at 565°C showillg that th(' rnicrostrllrtur(' consists pr<'dolllinantly of larg<' M7C3 alld fin<, M2C particles. 108 a) I h) c) Figure 5.39: ,,) ('Mholl ('XI racl 1011rI'pllca frolll "IH'cilll('1I 1('lIlperecl for :207:2 hours "I ;)()~)o('sho\\'ill~ aliglled \IL(' parlicle" wllh "11lid I, "IJlliH('r \1(,(' cMhidps ill Iwl\\'('('II. Splect('d iHPa Pieclroll difrraclioll pallprlls frolll 1\1(;<' carhiclps h) allcl a clllsIN of 1\1/' c). I O~) 5.5.3 EDX measurements of the Cr content of cementite at 565°C The composition of isolated cementite particles was measured using EDX. A photograph was taken of each individual particle analysed in order to correlate the particle size with com- position. Graphs are presented in Figure 5AOa)-g) showing the measured Cr concentration in cementite plotted as a function of the reciprocal particle size for the specimens tempered up to 128 hours at 565°C. The calculated regression line has been plotted on each graph. The correlation coefficient for each plot, the average particle size and the average Cr concentration are presented in Table 5.5. Table 5.5: Summary of experimental measurements of Cr concentration and particle size for specimens tempered up to 178 hours at 565°C. Tempering Correlation Average Cr Average particle time /Hours coefficient conc. /wt.% size /nm 1 0.57 6.70 52"6 1 0.65 15.04 56 4 0.82 14.96 68 7 0.43 17.85 58 32 0.27 18.06 56 64 0.36 26.91 65 128 -0.05 25.30 65 178 (Martensitic) - 24.57 72 178 (Bainitic) - 16.34 75 It can be seen from the graphs that there is a definite trend for the smaller particles to be richer in Cr, although there is some scatter about the regression line. The correlation coefficient is observed to steadily increase with tempering time initially and then to decrease. This is to be expected because initially all the particles are formed under paraequilibrium conditions and have the same concentration as the matrix, then as tempering proceeds the smaller particles will enrich at a faster rate than large particles. This will initially result in an increase in the correlation coefficient, however, at increasing tempering times other effects dominate over the size dependence of the enrichment rate. These include the precipitation of alloy carbides with the subsequent dissolution of cementite in the bainitic regions of the specimens and soft impingement of the cementite particles as they approach the equilibrium concentration. The very poor correlation coefficient and scatter in the measured Cr concentrations for the 128 hour 110 specimen correspond with the precipitation of the Cr rich M7C3• The measured Cr content of the cementite in the specimen tempered for 178 hours is pre- sented separately in Figure 5.41a)-c). It has already been noted that two separate populations of cementite were observed in the bainitic and martensitic regions of the microstructure. Figure 5.41c) clearly shows the dichotomy of the cementite compositions; the upper points (marked with triangles) are from martensitic regions of the microstructure free from alloy carbide precip- itation whereas the lower points (marked with circles) are from cementite particles in bainitic regions in which extensive alloy carbide precipitation has occurred. The two distributions are shown separately in Figure 5.41a) and b). The average Cr level in the martensitic and the bainitic regions are included in Table 5.5. It has been shown that the Cr content of a cementite particle is dependent on its size. It is therefore important when finding the average Cr content after a given tempering time of a distribution of cementite particles to take an unbiased sample of particle sizes. To this end histograms have been plotted in Figure 5.42a)-f) showing the number of carbides analysed of different sizes for the specimens tempered for 10 minutes, 1, 4, 7, 32, and 64 hours at 565°C. Although the size distributions are not all identical, it is important to note that there is no significant bias for any of the tempering times towards smaller or larger particles. 5.5.4 Enrichment of M7C3 with tempering time The carbide M7C3 was found to precipitate after tempering at 565°C for approximately 128 hours and then to coexist with cementite for some time before the cementite dissolves. The composition of the M7C3 was monitored along with the cementite by EDX. The average com- position (measured from at least 10 particles per specimen and not taking into account carbon content) of the M7C3 is presented in Table 5.6. It was found that there was a gradual increase in the Cr concentration with tempering time from 58 to 65.5 wt.%. The Mn concentration was found to correspondingly decrease with tempering time. The Mo data as a function of tempering time were scattered. Some of the scatter can be attributed to the inherent difficulty in measuring the Mo content accurately with EDX because of the failure to account for ab- sorption errors. It seems that the absolute level also depends on the particles surrounding the M7C3 particles. A similar effect to that already described for cementite particles in the vicinity of M2C particles was observed; a few M7C3 carbides within clusters of M2C needles contained very little molybdenum. No significant dependence of the composition on the particle size was observed for the M7C3 carbides for each tempering time. Thermodynamic calculations were performed using MTDATA to investigate the equilib- rium chromium levels of both M7C3 and M23C6 in equilibrium separately with ferrite. It was 111 a) b) 2.25CrlMo Steel-IO mlns at 565°C 2.25CrlMo Steel-l hour at 565°C 40 • • •• • •• ••••• ••.,... •• 10 15 10 15 30 35 a10' l/Mean linear intercept / m-t 40 35 N•••~ 30 ...•.••. c:l 15 0...... ~ 10•..c:l8 15 c:l0 Col 10~U 5 0 40 5 •• • 10 15 10 15 30 35 a10' l/Mean linear intercept / m-t 40 5 35 o 5 N•••~ 30 ...•.••. c:l 15o...... ~ 10...c:l8 15 c:lo Col 10~U c) cl) 2.25CrIMo Steel-4 hours at 565°C 2.25CrIMo Steel-7 hours at 565°C 40 35 N•••~ 30 ...•.••. c:l 15o...... ~ 10...c:l8 15 c:lo Col 10~U 5 o 5 ID ~ w ~ ~ ~ al0' l/Mean linear intercept / m-t 40 35 N•••~ 30 ...•.••. c:l 15 0...... ~ 10•..c:l8 15 c:l 0 Col 10~U 5 0 40 5 •• 10 15 20 15 30 35 a10' l/Mean linear intercept / m-t 40 Figure 5.40: a)-g) Chromium concentration in cementite plotted as a function of reciprocal particle size for various tempering times at 565°C for fully bainitic microstructures. 112 e) f) 2.25CrlMo Steel-64 hours at 565°C 40 • e.•• • • ••• •• 10 15 20 25 30 35 -JO' t/Mean linear intercept / m-I 40 35 ~ ••••~ 30 ....... c:l 25 0...... ~ 20•..c:l8 15 c:l 0 Co) 10 '"(.) 5 0 40 5 • 10 15 20 25 30 35 -10' t/Mean linear intercept / m-I 2.25CrIMo Steel - 32 hours - 565°C 40 35 ~ ••••~ 30 ....... c:l 25 0...••.. ~ 20•..c:l8 15 c:l •0 Co) 10 '"(.) 5 0 5 g) 2.25CrIMo Steel-128 hours at 565°C 40 35 ~ ••••~ 30 ....... c:l 25o...•.. ~ 20•..c:l8 15 c:lo Co) 10 '"(.) • • • •• •• • • • • ••• •• • 5 o 5 10 15 20 25 30 35 -10' t/Mean linear intercept / m-I 40 113 a) 2.25Cr IMo Steel 40 b) 178 hours at 565°C Ca) 40 178 hours at 565°C Cb) 35 ~••••~ 30 "Cl 25o..•.. ~ 20•.. Cl ~ 15c:Io Co) 10 •••Co) 5 - - .\..- - - .. I • ,,-- - - • 35 ~ ~ 30 "Cl 25o'.•.. ~ 20•..Cl ~ 15c:Io Co) 10 •••Co) 5 • ---.~ --. • o 5 c) 10 15 20 25 30 35 e10' l/Mean linear intercept / m-I o 40 5 10 15 20 25 30 35 el0' l/Mean linear intercept / m-I 40 2.25CrlMo Steel - 178 hours at 565°C 40 35 ~ ~ 30 "Cl 25o'.•.. ~ 20•..Cl ~ 15c:Io Co) 10 •••Co) 5 o 5 10 15 20 25 30 35 el0' l/Mean linear intercept /m-I 40 Figure 5.41: a)-c) Chromium concentration in cementite plotted as a function of reciprocal particle size for specimen tempered for 178 hours at 565°C for fully bainitic microstructures. 114 o 15 25 35 45 55 65 15 15 95 W lIS W Particle size / DD1 2 • 10 f) 64 hours o 15 25 35 45 55 65 15 15 95 W lIS W Particle size / DD1 • 2 o 15 25 35 45 55 65 15 15 95 W lIS 125 Particle size / DD1 b) 1 hour 10 2 10 cl) 7 hours • •-a-::6..•t:lo...o 4o:z: •-ai 6•t:lo...o 4o:z: a) 10 mins 10 ••.! .~ 61:•t:lo... 0 4 0:z: 2 0 15 25 35 45 55 65 15 15 95 105 lIS 125 Particle me / DD1 c) 4 hours 10 ••-a-::6..•t:lo...o 4 0:z: 2 0 15 25 35 45 55 65 15 15 95 105 115 125 Particle size / DD1 e) 32 hours 10 ••-a:= 6..•t:lo...o 4 0:z: 2 0 15 25 35 45 55 65 15 15 95 105 lIS 125 Particle size / DD1 Figure 5.42: Histograms showing the distribution of particles sizes measured after a) 10 mins, b) 1 hour, c) 4 hours, d) 7 hours, e) 32 hours, f) 64 hours tempering at 565°C for the fully bainitic specimens. 115 Table 5.6: Composition of M7C3 with tempering time at 565°C measured by EDX. Time /Hours Cr /wt.% Mn/wt.% Mo /wt.% Fe /wt.% 128 58 8 11 23 178 59 6 9 26 238.5 61 4.5 9 25.5 512 62 6.5 3 28.5 1048 63.5 5 7 24.5 2072 65.5 5 5 24.5 not possible to allow M7C3 and M2C, and M23C6 and M2C to coexist with ferrite. The cal- culations therefore give an idea of the chromium level only in each carbide because much of the molybdenum would be tied up in M2C in the real situation. The calculated equilibrium chromium levels in M7C3 and M23C6 as a function of temperature are presented in Table 5.7. The predicted equilibrium level of ~59 wt.% Cr in M7C3 at 565°C is in reasonable agreement with the measured concentrations using EDX. The slightly lower value predicted compared with the observed value can be explained by the fact that some of the Mo predicted to be in the M7C3 would actually be in M2C, leading to an increase in the predicted Cr level in the M7C3• Table 5.7: Calculated equilibrium Cr levels in M7C3 and M23C6 as a function of temperature using MTDATA scaled to remove the stoichiometric carbon concentration to enable direct comparison with EDX measurements. Temperature rC M7C3 Cr level /wt.% M23C6 Cr level /wt.% 750 52.2 30.4 700 54.5 34.5 650 56.5 39.2 600 58.0 44.4 565 58.7 48.2 550 58.8 49.8 5.5.5 Enrichment of Mo2C with tempering time It has been observed (Pilling and Ridley, 1982) that the carbides M2C and M6C become richer in molybdenum as a function of tempering time in a 2tCr1Mo steel. These tempering heat treatments were carried out at 700°C. In this study, the M2C carbide needles formed at 116 565°C are very fine and therefore attempts at measuring their composition by EDX are subject to considerable error, especially with respect to the concentration of molybdenum. M6 C was found to precipitate after 1048 hours tempering and contained ~ 60 wt.% molybdenum. This is in good agreement with the equilibrium composition calculated using MTDATA at 565°C, which suggests that there would be no further enrichment on prolonged tempering. At the higher temperatures used by Pilling and Ridley (1982) the molybdenum-based alloy carbides will precipitate quickly and therefore may not quite be at their equilibrium composition, whereas at lower temperatures they do not precipitate until much later tempering times. In this case the carbides appear to precipitate very close to their equilibrium compositions. 5.5.6 Consideration of the precipitation of M23C6 It was important to exclude completely the possibility that the cementite observed in the bainitic regions coexisting with M2C could in fact be some other carbide, such as M23C6, because conclusive proof with selected area electron diffraction was difficult. Therefore, a fully bainitic specimen was tempered at 750°C for 48 hours in order to accelerate the precipitation of M23C6• The microstructure after this heat treatment presented in Figure 5.43a) consisted of two different carbide dispersions. The larger carbides were identified as M23C6 by both EDX and selected area electron diffraction (Figure 5.43b), and the smaller carbides as M7C3. The average composition of the M23C6 was 31 wt.% Cr,2 wt.% Mn, 9 wt.% Mo, and 58 wt.% Fe, and that of the M7C3 as 51 wt.% Cr, 2.5 wt.% Mn, 7 wt.% Mo, and 39.5 wt.% Fe. These Cr levels are in excellent agreement with those predicted by MTDATA (see Table 5.7 above) for tempering at 750°C, and confirm that the amount of Cr each carbide can support increases as the tempering temperature decreases. The predicted Cr level in M23C6 at the lower temperature of 565°C of 48 wt.% can therefore be assumed to be accurate. This means that were M23C6 to be present in the specimens tempered at 565°C it should contain 48 wt.% Cr, ruling out any possibility that the cementite with reduced Mo content and lower Cr levels in the bainitic regions could be M23C6• M23C6 was not observed in the bainitic microstructure for tempering times up to 3000 hours at 565°C. 5.5.7 Microstructural evolution during tempering at 510°C The microstructural changes in specimens tempered at 510°C were considerably slower than at 565°C. The optical microstructure after tempering for 256 hours is presented in Figure 5.44. 117 a.) h) Figllr 5.43: ;,) ('arholl l'xtractioll r('plica frotll a flllly haillili(' HP(,("ffll('1I 1l'lffJ)('rl'd for ,11'1hOllrH at. 7!'j(}°C; Hhowing larw' parlil'!l'H of M /'1('" alld HllIalll'r partil'!('H of r",l'(" h) S(,k("t"d an'a (,I('('lroll.. , ) ) diffractioll p;llkrll front all M2:ICG rarhid(, IIH There are no observable differences compared with the starting microstructure. Figure 5045 is a transmission electron micrograph from a replica taken from a specimen tempered for 1 hour; comparison with Figure 5.23 shows that the initial precipitation of cementite is much slower at the lower temperatures, as expected. Tempering for up to 256 hours allowed cementite to precipitate and enrich as in the specimens tempered at 565°C. The enrichment rate of the cementite was found to be a lot slower and no M2 C precipitation was found after 256 hours, compared with M2C being found after 32 hours in the specimens tempered at 565°C. 5.5.8 EDX measurements of the Cr content of cementite at 510°C The plots of Cr concentration against the reciprocal of particle size are presented in Fig- ure 5A6a)-c) for the specimens tempered at 510°C. There is considerable scatter in the compo- sitions measured after tempering for 1 hour, however, the slope of the regression line increases after tempering for 128 and 256 hours as the effect of the smaller particles enriching more quickly than the larger particles becomes more prominent. The results of these analyses are summarised in Table 5.8. Table 5.8: Summary of experimental measurements of Cr concentration in cementite and particle size for specimens tempered up to 256 hours at 510°C. Tempering Correlation Average Cr Average particle time /Hours coefficient cone. /wt.% size /nm 1 -0043 11.8 45 128 0.13 15.9 62 256 DAD 20.1 64 5.5.9 Microstructural evolution during tempering at 620°C Microstructural changes at 620°C were rapid compared to those at 565°C. This is illustrated in Figure 5047 which shows extensive cementite precipitation after tempering for only 1 hour taken from a carbon extraction replica. A MnS inclusion is also marked in the figure. The steel contains quite a number of MnS particles as a result of the manufacturing process, however, these are distributed evenly throughout the microstructure and therefore have no influence on the changes which occur. After 10 hours tempering there is extensive precipitation of M7C3 together with fine M2C needles. After 25 hours the M7C3 is widespread, illustrated in Figure 5048. M7C3 did not appear until after tempering for 128 hours at 565°C. It was clear that there were two different types of cementite, one richer in Cr and Mo, and one containing 119 less Cr and virtually no Mo, in the specimens tempered for only 25 hours at 620°C. This is illustrated in Figure 5.49. The two cementite particles marked with arrows at the boundary between two sheaves and in regions in which there is extensive MzC precipitation both have the composition 15 wt.% Cr,3 wt.% Mn,O wt.% Mo, and 82 wt.% Fe, whereas the cementite particles in the martensitic regions have an average composition 23 wt.% Cr, 4.5 wt.% Mn, 5.0 wt.% Mo, and 67.5 wt.% Fe. 5.5.10 EDX measurements of the Cr content of cementite at 620°C The plots of Cr concentration against the reciprocal of particle size are presented in Fig- ure 5.50a)-c) for the specimens tempered at 510°C for 1, 10 and 25 hours respectively. These results exhibit considerably more scatter than do those at 510 and 565°C. The explanation of this is that microstructural changes are accelerated at the higher temperature with alloy carbide precipitation being present to some extent in all the specimens. The results are summarised in Table 5.9. The cementite has started to dissolve (corresponding to a drop in the experimentally measured cementite concentrations) after only 25 hours at 565°C. Table 5.9: Summary of experimental measurements of Cr concentration and particle size for specimens tempered up to 25 hours at 620°C. Tempering Correlation Average Cr Average particle time /Hours coefficient cone. /wt.% size /nm 1 0.35 17.6 73 10 0.13 25.5 81 25 0.14 23.2 79 5.5.11 Coexistence of M7C3 with cementite It has been noted that M7C3 precipitated whilst cementite was still present in the mi- crostructure, and then the two coexisted for some time. The cementite in the immediate vicinity of M7C3 particles was found to have a lower Cr content than the average measured for an isolated cementite particle. It was thought that in the same way as the precipitation of MzC appears to draw Mo from the cementite, precipitation of the Cr-rich M7C3 drew Cr away from any cementite particles nearby. This is illustrated in Figure 5.51 which shows a cementite 120 Figure 5.44: Optical micrograph for a fully bailliti sp CII11(,1Itcmpcr('d at 510° for 256 hours, I , , I , ,,' 1,0 1'111 Figure 5.45: Carholl l'xtradioll rl'plil"il takf'1I fro 11I a haillitil" sl)(,l"illlf'1I U'IIIPN('d at !"iIO°C for I hour sllOwillg that ('1'11 It'll I ilf' prl'l"ipitatioll IS VI'rY slow at this t('lIqH'rat IHI', 1'21 a) 2.2SCr1Mo Steel-1 hr at S10GC b) 2.2SCrlMo Steel-128 hrs at 510GC 40 35 ~ ~ 30 "= 250....•.. ~ 20•..=~ 15c:l 0 u 10 '"U 5 0 5 c) • • 10 15 20 25 30 35 el0' t/Mean linear intercept /m-1 40 40 35 ~ ~ 30 "= 25o....•.. ~ 20•..=~ 15c:lo u 10 '"U 5 o 5 • • •• • •", •• •• •••• • •• •• •• • •• • 10 15 20 25 30 35 el0' t/Mean linear intercept /m-I 40 2.25CrlMo Steel - 256 hrs at SlOGC 40 35 ~ ~ 30 "c:l 25o....•.. ~ 20•..=~ 15c:lou 10 '"U 5 o 5 10 15 20 25 30 35 el0' t/Mean linear intercept / m-t 40 Figure 5.46: a)-c) Chromium concentration in cementite plotted as a function of reciprocal particle size for specimens tempered for various times at 510°C for fully bainitic microstructures. 122 " ", , 0.2 fJ-lTl L-.-..J Figure 5.49: Carbon extractioll replica from the fully bainitic specimen tempered for 25 hours at 620°C showing cement.ite particles with redllced Mo cont.ent ill a region of extensive M2C precipitation. 121\ a) b) 2.25Cr1Mo Steel - I hr at 620°C 2.25Cr1Mo Steel - 10 hrs at 620°C 40 40 40 ••••• 10 15 20 25 30 35 elO' l/Mean linear intercept /m-I 35 ~ ~ 30 "c:l250.•...•..e 20••c:l8 15c:l0 Co) 10 '"'U 5 0 40 5 • 10 15 20 25 30 35 el0' l/Mean linear intercept / m-I o 5 5 35 ~ ~ 30 "c:l 25o.....•..e 20••c:l8 15c:lo Co) 10 '"'U c) 2.25CrIMo Steel - 25 hrs at 620°C 40 35 ~ ~ 30 "c:l 25o.•...•..e 20••c:l8 15c:lo Co) 10 '"'U •• • ••• • •. .- 5 o 5 10 15 20 25 30 35 e10' l/Mean linear intercept / m-I 40 Figure 5.50: a)-c) Chromium concentration in cementite plotted as a function of reciprocal particle size for specimens tempered for various times at 620°C for fully bainitic microstructures. 125 particle next to an M7C3 particle in a fully bainitic specimen tempered for 10 hours at 620°C. The cementite has a composition 19 wt.% Cr,4 wt.% Mn, 1 wt.% Mo, and 76 wt.% Fe, compared with the Cr level in an isolated cementite particle of comparable size of 24 wt.% Cr,4 wt.% Mn,6 wt.% Mo, and 66 wt.% Fe. The M7C3 particle contains 51 wt.% Cr. By considering the equilibrium Cr levels in cementite and ferrite and in M7C3 and ferrite using MTDATA it can be established whether there is a flux of Cr through the ferrite from cementite towards an M7C3 particle. It was not possible to allow both cementite and M7C3 to exist at 565°C for the composition of the 2}CrlMo steel used because MTDATA calculates the carbides present at equilibrium. When the three phases cementite, ferrite and M7C3 were allowed to coexist MTDATA cor- rectly calculates the microstructure to consist of M7C3 and ferrite only. In order to investigate the possibility of a Cl' flux from cementite to M7C3 when the two coexist as a consequence of kinetic factors, the bulk carbon concentration was increased until the cementite became thermodynamically stable again and coexists with the M7C3• This is a somewhat artificial procedure in that the calculated absolute equilibrium values in the three phases will not relate to the real situation, but it will allow the possibility of a Cr flux from cementite to M7C3 to be studied. Care was taken that as the bulk carbon concentration was increased to force the three phases to exist, the Fe/Cl' ratio in the alloy overall was kept constant. Figure 5.52 shows the calculated equilibrium Cr level in cementite as a function of the bulk carbon concentration. It can be seen that for high carbon concentrations only cementite is the stable carbide, and for low carbon concentrations M7C3 is stable; for intermediate compositions M7C3 and cementite coexist. The lowest carbon concentration at which M7C3 and cementite were in equilibrium with ferrite, 0.75 wt.%, was chosen to perform further calculations because this point would be most closely related to the composition of the 2}Cr1Mo steel. The equilibria between cementite and ferrite and between M7C3 and ferrite were then investigated separately at this overall con- centration to find the Cr level in the ferrite at the interface between each of the particle types. The results of these calculations are presented in Figure 5.53. It can be seen that because the Cl' level in the ferrite matrix surrounding a cementite particle is higher than that surrounding an M7C3 particle, a flux of Cl' is stimulated from the cementite to the M7C3, hence explaining the drop in Cl' level in a cementite particle in the vicinity of an M7C3 particle. 126 5.5.12 Coexistence of Mo2C with cementite A similar calculation was performed to that described in the previous section to study the coexistence of M2C and cementite. Once again, in order to force MTDATA to allow M2C and cementite to coexist in ferrite, the carbon concentration in the bulk alloy was increased, keeping the Fe/Cr ratio constant. Below 0.5 wt.% C only M2C was stable, but further increasing the carbon concentration allowed M2C and cementite to coexist. As the carbon concentration increased, the volume fraction of cementite was predicted to increase at the expense of the M2C. The results of the calculation for an overall concentration of 0.5 wt.% C are presented in Figure 5.54. It can be seen that the increase in the matrix concentration of Cr and Mo around a cementite particle would result in a flux of both to the M2C. This is consistent with the experimentally observed fact that once there is extensive M2C precipitation within the bainitic plates, the cementite between the plates begins to 'lose' both chromium and molybdenum. 5.5.13 Calculation of the diffusion constants from experimental results The enrichment kinetics of cementite particles were studied for various times at three different temperatures in order that the diffusion coefficient and the activation energy could be calculated for the diffusion of chromium in ferrite. The dependence of the diffusion coefficient of chromium in ferrite, DO', is given by the analytical equation (3.28) 7l"X/(C - c8)2t ------ c - 16Da(ca8 _ c)2 The most accurate way of performing this calculation is to use all the experimental data gathered in the TEM and evaluate the quantity lI"XB2(C _ CB)2 16( caB _ c)2 (5.4) for each individual particle analysed at each of the different tempering temperatures and times. Regression of the tempering time, tc' against the expression 5.3 should then give a straight line passing through the origin with a gradient equal to the reciprocal of the diffusion coefficient. The tempering times and temperatures used in this analysis only included those specimens in which enrichment of the cementite was taking place rather than the dissolution due to the precipitation of Cr-based alloy carbides. This therefore included tempering times up to 64 hours at 565°C, all the specimens tempered at 510°C and excluded the 25 hour specimen tempered at 620°C. The value of caB, the equilibrium concentration of Cr in the ferrite, varies with temperature. The values used for the calculations of the diffusion coefficient were calculated using MTDATA 127 Cr in Matrix =0.279 Wt. % 23 Wt.% Cr ,...--- 17 Wt. % Cr Cr FLUX ---•••• Cr in Matrix 0.052 Wt.% Figure 5.53: Schematic illustation of a cementite particle next to an M7C3 particle showing calculated equilibrium concentrations in the particles and the matrix using MTDATA. Cr 53 Wt.% Mo 24 Wt.% Cr 0.03 Wt.% Mo 0.001 Wt.% Cr flux - flux Cr 24 Wt.% Mo 6 Wt.% Cr 0.44 Wt.% Mo 0.57 Wt.% Figure 5.54: Schematic illustation of a cementite particle next to an M2C particle showing calculated equilibrium concentrations in the particles and the matrix using MTDATA. 129 allowing only the phases cementite and ferrite to exist. These data have been presented in Table 5.2. The predicted chromium level in the cementite is higher than that observed in the particles experimentally (because of the precipitation of Cr-based alloy carbides discussed above) and therefore the predicted of ca6 should be slightly higher than that used in the calculations. The effect of this difference will be very small because it will not change the value of the regression constant, and hence the value of D a' at anyone temperature because it would simply be changing the absolute value of the constant in the denominator of expression 5.3. The volume fraction of cementite is small compared to the ferrite and therefore any changes in the overall concentration in the matrix due to changes in the cementite composition will also be small. The equilibrium values also take into account the carbon content of the cementite, which the EDX data do not. The EDX measurements were therefore scaled to allow for 6.67 wt.% of C to be contained in the cementite (the stoichiometric carbon content for M3C). A computer program was written to calculate the regression coefficient, and therefore the diffusion constant, at each of the three tempering temperatures. The results of the calculations are presented in Table 5.10. Table 5.10: Calculated diffusion coefficient as a function of temperature for the fully bainitic speci- mens. Temp rC Da /m2s-1 510 3.5±0.2 X 10-19 565 2.5±0.1 X 10-18 620 2.7±0.3 X 10-17 The calculated value of the diffusion coefficients at the three temperatures were then used to calculate the activation energy for the diffusion of Cr in ferrite using the Arhenius relationship D = Do exp ( - R~ ) , (5.5) where Q is the activation energy, R is the universal gas constant, T is the temperature in Kelvin and Do is the pre-exponential factor. Taking the natural logarithm of equation 5.5 results in the expression, Q 1In D = - R T + In Do (5.6) from which it can be seen that plotting a graph of the logarithm of D a against reciprocal temperature yields a slope equal to - ~. Such a graph is plotted in Figure 5.55; a regression line is plotted through the experimental points. The correlation coefficient for these three data 130 points was found to be 0.99. The value for the activation energy of diffusion, Q, was found to be 230,000±10,000 J mol-I, and the pre-exponential factor was found to be 7.0±0.3x 10-4m2s-1• The values given by Fridberg et al. (1969) for the inter-diffusion of Cr in ferrite are an activation energy of 240,000 J mol-I, and a pre-exponential factor of 1.5x 1O-4m2s-1. 5.6 Results and discussion from mixed microstructures 5.6.1 Precipitation within the allotriomorphic ferrite A carbon extraction replica from the isothermally transformed mixed microstructure be- fore tempering showed that although there was no precipitation in the bainitic regions of the microstructure, extensive precipitation had occurred in the ferrite. Fibrous carbides were found to exist in the allotriomorphic ferrite, both at grain boundaries with other ferrite grains (Fig- ure 5.56 and Figure 5.57) and at the ferritic/bainitic grain boundaries (Figure 5.58). The fibres were approximately 30 nm thick and up to 2 pm long. Selected area electron diffraction (Figure 5.58c) from a cluster of such fibres (Figure 5.58a) showed that a unique spot diffraction pattern could be obtained from the cluster suggesting all the fibres had the same orientation. A dark field electron micrograph from one such spot is presented in Figure 5.58b), again illustrating that parallel fibres can be illuminated from a single diffraction spot. The selected area electron diffraction pattern is attributable to hexagonal M2C. EDX analyses were possible on clusters of fibres and they were found to have a chemical composition of 50 wt.% Mo, 40 wt.% Cr with small amounts of Fe and Mn, consistent with the electron diffraction results. A second morphology of M2 C clusters was also observed in the ferrite. These particles, illustrated in Figure 5.59, were much smaller than the fibres (length~60 nm, ~20 nm thick), precipitating in a WidmansUitten array usually parallel to the prior austenite grain boundaries. The M2C fibres and small particles present in the as-transformed microstructure persisted throughout temper- ing, also being observed in the specimens tempered for 180 hours at 565°C. This interphase precipitation of M2C has been discussed in Chapter 2. Larger precipitates, identified by EDX as both M2C and M6C, were also found on ferrite-ferrite grain boundaries. Precipitation of this type is illustrated at a triple point in Figure 5.60. The M6C precipitates become larger during tempering at the expense of some of the smaller M2C particles. 5.6.2 Precipitation within the bainitic regions The characteristics of precipitation in the bainitic regions of the mixed microstructures are broadly the same as in the fully bainitic specimens. However, cementite precipitation in the bainitic regions of the mixed microstructure specimens is very dense compared with the 131 -37.0 ~ -38.0-....~~~e- -39.0 c:l.... :::: -40.0~oCJ c:l -41.0o.... I/J ~ -42.0 e-.... "'d c:l -43.0- -44.0 1.1 1.15 1.2 1.25 -10-) Reciprocal temperature /K-1 1.3 Figure 5.55: Plot of the logarithm of the calculated diffusion coefficient in ferrite as a function of temperature showing the regression line through the points 132 fully bainitic specimens. This is to be expected because of the increased carbon concentration in the bainitic regions due to the rejection of carbon into the austenite as the allotriomorphic ferrite forms. The carbon extraction replica taken from a specimen tempered for 47 hours at 565°C presented in Figure 5.61 illustrates this point. The contrast between the dense cementite precipitation in the bainitic regions and the empty ferritic regions is illustrated in Figure 5.62. Large M6C particles are also visible on the ferrite grain boundaries. Figure 5.63 shows a replica from a specimen tempered for 180 hours. Widmanstatten type cementite is clearly visible within a martensite lath. It has been shown that the bainitic and martensitic regions contain extensive cementite precipitation, whereas the ferritic regions contain M2C (which is replaced by M6C on prolonged tempering). This difference must be related to the mechanism of transformation. The ferrite forms reconstructively and therefore the atomic mobility inherent in this process could also permit the simultaneous precipitation of alloy carbides. The growth of bainite and martensite is displacive, precluding the formation of alloy carbides during transformation. 5.6.3 EDX measurements of the er content of cementite in mixed microstructures The plots of Cr concentration against the reciprocal of particle size are presented in Fig- ure 5.64a)-e) for the mixed microstructure specimens tempered at 565°C for 1, 47, 80, 128 and 180 hours respectively. The calculated regression lines are plotted on the first four plots, how- ever the results for the 180 hour specimen were beginning to show a division of the cementite particles into those associated with bainitic and martensitic regions, and therefore it was not thought appropriate to find a single regression line for two different distributions. The results of these analyses are summarised in Table 5.11. Table 5.11: Summary of experimental measurements of Cr concentration in cementite and particle size for mixed microstructure specimens tempered at 565°C. Tempering Correlation Average Cr Average particle time fHours coefficient cone. fwt.% size fum 1 0.74 9.1 76 47 0.44 15.9 68 80 0.55 20.2 59 128 0.41 21.9 71 180 - 26.2 63 133 1.0'.lID '---' Figure 5.56: Carbon extraction replica from th as-transformed mixed microstructure showing fibrous M2C carbides at ferritic/ferritic grain boundaries. Figure 5.57: arbon extraction replica from the as trausformN1 mixed microstruC'tuf(' showiu fibrous M2C carbides at r. rritic/bainitic graiu boundaries. 134 a) b) c) Figure 5.58: Carbon ('xtraction replica frolll th(' mixed lllinostrllctll r(' aft,N t(,lTlpNing for 180 hOll r ' at [j(j!)oC. a) Bright fi('ld and h) dark fi('ld irnag('s of fihrolls M2C partici('s showing that all the' fibres have' th(' sam(' ori('n1.a1.ion. c) Sl'!('c1.('d ar('a ('I('ctron diff'raction pat.t.Nn frorll a c1l1s1.Nof th(' fihr('s showing that a singil' spot pattNn is ohtain('d. I:j,I') 0.5 pm Figure 5.59: Carbon extraction replica from the as-transformed mixed microstructure showing a second morphology of M2C clusters precipitating in a Widmanstatten array. 0.5 Illll Figure 5.60: Carhon extraction replica from the as-transforllled mixed micro. truct.ure illustrating precipitation of M6C at a triple point het.wee-n ferrite- grains. 136 Figure 5.61: Carbon extraction rf'plica from a mixed microstructure specimen tempered for 47 hours at 565°C showing df'nsf' cf'mcntite prf'cipitatioll. ",•.....•• " Figure 5.62: Carbon f'X t.raction r('pl iCi\ frolll a IlIi x('d III icrostrllctlJrf' sp('ci 1I1f'1ItPII1perf'd for '17 hOll rs at 56:>°(; showillg I hp 1'0111ra.'it llC'twPf'1I till' dplISf' CPIIlC'lIt.itf' prf'cipit.at.ioll ill thf' baillitic rf'giolls alld th(' Pill pty allotrior llOrph ic fprri 1.(' rpgiolls. U7 Figure 5.63: Car bOil extractioll replica frolll a llIixed IlIicrostructure specimen tempered for 180hours at. 5G5°C "howillg Widlllall"t.iit.t.ell Iyp(' pr('cipitat.ion of celllc'nt.it.cwit.hin a mart.ensit.c lath. a) b) 1 hour at 565°C 47 hours at 565°C 40 40 35 35 N N ~30 ~ 30 •...•.. •...•.. • c:l2S c:l 25 0 0... ...~ ~f 20 f 20~ ••c:l c:lu 15 8 15uc:l c:l 0 0u 10 u 10 • ••'" ""U U 5 • 5• 0 0 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 el0' elO' t/Mean linear intercept / m-1 l/Mean linear intercept / m-1 c) cl) 80 hours at 565°C 128 hours at 565°C 40 40 35 35 N N.,l .,l ~ 30 • ~ 30 •...•.. •...•.. •c:l 25 c:l 25 ••0 0 •... ...~ ~f 20 f 20 -- •• •.- •• •c:l c:l8 15 8 15c:l c:l 0 0 u 10 u 10 "" '"U U 5 5 0 0 5 10 15 20 25 30 3S 40 5 10 15 20 25 30 35 40 elO' elO' t/Mean linear intercept / m-1 l/Mean linear intercept / m-1 Figure 5.64: a)-e) Chromium concentration in cementite plotted as a function of reciprocal particle size for various tempering times at 565°C for mixed microstructure specimens. 139 e) 40 180 hours at 565°C 35 ~ ~30 ......•• c:l 25o...••.. ~ 20•..c:l8 15c:lo u 10 '"(.) 5 • •• • • •••• •• • • • • • • • o 5 10 15 20 25 30 35 el0' t/Mean linear intercept / m-I 40 140 5.7 Comparison of experimental results and theoretical predictions The experimental measurements of Cr concentration in cementite in the fully bainitic and mixed microstructure specimens are summarised in Figure 5.65. It can be seen that the cementite in the fully bainitic specimens enriches more quickly than in the specimens containing only 50% bainite. This is to be expected because the formation of a.llotriomorphic ferrite in the mixed microstructure specimens causes an increase in the carbon concentration of the bainitic regions. The carbon concentration in the two different regions can be determined from a simple mass balance equation:- (5.7) where x is the average carbon concentration in the a.lloy, VC\' is the volume fraction of allotri- omorphic ferrite, and XC\' and x-y are the carbon concentrations in the ferrite and the austenite respectively. x is 0.15wt.%, VC\' is 0.5 in the specimens used, XC\' (determined from the program used to calculate the TTT curve in section 5.3.1) =0.0228 wt. % and hence x-y is calculated to be 0.277 wt. %. This is by definition the carbon concentration in the bainite which forms from the carbon-enriched austenite. There is therefore approximately twice as much carbon available for carbide precipitation initia.lly in the mixed microstructure specimens than in the fully bainitic specimens. The symmetric and asymmetric finite difference methods discussed III Chapter 3 can be used to predict the enrichment rate of cementite in the fully bainitic and mixed microstructures respectively. Both calculations were carried out at 565°C, and for average particle sizes of 60 nm in the bainitic and 70 nm in the mixed microstructures. These are consistent with the particle sizes measured experimentally. The two curves are shown in Figure 5.66, plotted as a function of time. Experimentally it is observed that the bainite in the mixed microstructure specimens, which has formed from enriched austenite, contains cementite which enriches more slowly than that in the fully bainitic specimens. This is consistent with the predictions of the model. Figure 5.67 and Figure 5.68 show the predicted curves for the bainitic and mixed mi- crostructures respectively, for short times only, plotted against the experimental results. The deviation of the experimental points tempered for more than 64 hours in the fully bainitic spec- imens corresponds to the precipitation of M7C3 and the subsequent dissolution of the cementite particles. It can be seen that the model is consistently underpredicting the value of chromium in cementite after a given time compared with the experimental results. The most probable explanation for this is that the value of the diffusion coefficient of chromium in cementite is a little high. A lower value would cause the predicted enrichment rate to be higher, increasing the 141 predicted concentration for a given tempering time. The relatively small size of the particles (~60 nm) increases the sensitivity of the model to the values of the diffusion constants used. This point is discussed further in Chapters 3 and 8. However, it is important to note that the experimental results clearly show a linear dependence of enrichment rate on the square root of tempering time, as predicted by the model. The experimental results have highlighted the dependence of enrichment on particle size, smaller particles enriching more quickly than larger ones. Figure 5.69 shows the results of a calculation using the finite difference model of the enrichment rate at 565°C for three different particle sizes, 50 nm, 75 nm and 100 nm. The model predicts a difference of ~20 wt.% Cr between the 50 and 100 nm particles after tempering for 100 hours. This is consistent with the measured variation of composition with size, and illustrates the importance of making the two measurements simultaneously. 5.8 Conclusions Detailed experimental studies of cementite composition changes in fully bainitic and mixed ferritic/bainitic microstructures have been made. The enrichment rate has found to be slower in the bainitic regions of the mixed microstructures than in the fully bainitic specimens. A strong dependence of enrichment on particle size has been observed, the smaller particles enriching more quickly than the larger ones. Both of these observations are consistent with the predictions of the computer model. Differences in precipitation behaviour between bainitic, martensitic and ferritic regions of the microstructure have been established. This has important consequences for remanent life assessment in that a simple measurement of cementite composition is not sufficient; the size and position in the microstructure must be simultaneously determined. The calculated value for the activation energy of chromium diffusion in ferrite, and hence the diffusion coefficient, show good agreement with previously measured values. The need for a measurement of the diffusivity of chromium in cementite has been highlighted. The usefulness of equilibrium thermodynamic calculations in predicting the microstructural changes which occur has also been demonstrated. No significant dependence of the composition of the chromium-rich alloy carbide, M7C3, on size or tempering time has been found. Indications are that once alloy carbides have precip- itated any further enrichment is too small to be useful in estimating the average temperature experienced by the microstructure. This is discussed further in Chapter 7. 142 50 100 150 200 Tempering Time at 565°C/Hours Microstructure ••.••• Bainitic .. ~. Mixed ~ 30 ~ " 25 U:i20 ~••= 15o••~ctS~ 10~=4,) ~ 5o (.) ~ 0U o Precipitation of er rich alloy carbides, .... ••••••........T......•If ..~ Figure 5.65: Comparison of the average chromium content in cementite in fully bainitic and mixed microstructure specimens as a function 01 tempermg time at 565°C. 20 ~..,; ~ " 15=o•••.•.• cd~.•.. ~ 10c.>=oc.> ~ U 5 - Bainitic --- Mixed o 50 100 150 200 Tempering time at 565°C /Hours Figure 5.66: Predicted rate of enrichment in cementite in the bainitic and mixed microstructure specimens using the asymmetric finite difference model described in Chapter 3. 143 30 ~ 25 ..,; ~.........20 c:so.....•.. cd 15~.•..c:suuc:s 10ou ~ U 5 o Precipitation of M,CJt• • • o 2 4 6 8 W U ~ Root tempering time at 565°C /Hours1/2 Figure 5.67: Comparison of the experimentally measured Cr concentration in cementite in the bainitic specimens with the predicted rate of ell.id:I.1~a,; using the asymmetric model described in Chapter 3. 30 ~ 25 ~.........20 c:so...•.•.. cd 15~.•..c:suuc:l 10ou ~U 5 o • •• o 2 4 6 8 W U ~ Root tempering time at 565°C /Hoursl/2 Figure 5.68: Comparison of the experimentally measured Cr concentration in cementite in the bainitic regions of the mixed microstructure specimens with the predicted rate of enrichment using the asymmetric model described in Chapter 3. 144 50 - S50nm S75nm --- SlOOnm o o 5 W ~ W ~ ~ Root tempering time at 565DC /Hoursl/2 Figure 5.69: Illustration of the dependence of the enrichment of cementite on the particle size calculated at 565°C using the finite difference model. 145 CHAPTER 6 !Cr!Mo! V STEEL2 2 4 Measurements of composition changes in cementite over long periods of time in a pearlitic !Cr!MotV steel have been carried out at a variety of tempering temperatures. The original measurements were made by Du (1986), although only empirical expressions describing the results were found. In this chapter additional measurements made by myself on the original specimens to determine the variation of cementite concentration with particle size are discussed. Having obtained the particle size data, the composition changes are modelled theoretically. Very good agreement is found between theory and experiment. The material described in this chapter has been published in Materials Science and Engi- neering A, 155, 1992, p. 197-205. 146 CHAPTER 6 !Cr!Mo! V STEEL2 2 4 6.1 Introduction In bainitic microstructures in which cementite grows without partitioning of the substitu- tional alloying elements, the initial composition of bainitic cementite can be readily estimated. This work, however, focusses on the ferritic/pearlitic microstructures in a !Cr!Mo{- V steel. Investigations by Carruthers and Collins (1980) on this material have shown that changes in the substitutional solute concentration of cementite may be a viable technique for the estima- tion of an effective service temperature. ~Cr~ Mo{-V steel is probably the most widely used low alloy steel in power plant. The pearlite reaction is fundamentally different from that of bainite in that it is a re- constructive transformation in which growth occurs at an incoherent interface with the parent austenite. Diffusion of all the elements is therefore an integral part of the reaction, and the partitioning of substitutional elements has been reported (Al-Salman et al., 1979; Chance and Ridley, 1981) for all transformation conditions. Paraequilibrium growth of pearlite does not occur, nor does the cementite have an equilibrium composition. Therefore, there is an uncer- tainty about the starting chemistry of pearlitic cementite. In addition, the cementite is rather coarse compared with that associated with bainite. In fact, each pearlite colony is a bicrystal of cementite and ferrite, the so-called cementite lamellae being interconnected in three dimen- sions (Hillert, 1962). Consequently it is of considerable interest, both from an industrial and an academic point of view, to investigate any changes in carbide characteristics with tempering heat treatments. 6.2 Materials and heat treatment The material used in these experiments was a standard ~Cr~ Mo{-V steel supplied by Na- tional Power designated as cast M1. The chemical composition is given in Table 6.1. The samples were normalized from an austenitising temperature of 950°C and then tempered at 690°C for one hour in order to simulate the commercial stress-relief heat treatment for this steel. Specimens were then machined to 10x20 mm and tempered at a variety of tempera- tures between 640 and 525°C in a specially designed furnace (Carruthers and Collins, 1980) for varying times. Within the furnace, the samples were screwed into a nimonic 80a bar to ensure an even temperature distribution. The temperature error at any specimen position was 147 ±2°C. There was no significant oxidation or decarburisation of the threaded test pieces during tempering. Tempering was discontinuous because the specimens were removed at various time intervals to prepare samples for examination in the transmission electron microscope, and then put back for further heat treatment. It was confirmed in a separate experiment that the ce- mentite compositions of samples tempered continuously and discontinuously were, as expected, the same within experimental error. Table 6.1: Chemical composition of the ~Cr~Mot V steel in wt.% Cast C Si Mn P S Cr Mo V Ni Cu M1 0.14 0.23 0.61 0.007 0.023 0.36 0.66 0.26 0.21 0.13 6.3 Experimental results 6.3.1 Microstructure and carbide morphologies The microstructures after the normalisation heat treatment at 950°C were mixtures of ferrite, pearlite and bainite. The development of the microstructure as tempering proceeds is illustrated in Figure 6.1; the transmission electron micrographs were taken from carbon ex- traction replicas and are therefore specific to the carbide distribution. After the stress-relief heat treatment at 690°C for one hour the main ferritic and pearlitic regions were still clearly defined, however, it can be seen from Figure 6.1b) that the pearlitic cementite had already begun to spheroidise. Further coarsening occurs during prolonged tempering. Figures 6.1c) and d) illustrate this in specimens tempered at 640° for 483 and 2996 hours respectively. Ce- mentite particles located at the ferrite grain boundaries were generally found to be coarser than those within the grains. The coarsening process ultimately dissolved most of the intragranular cementite particles, leaving relatively few large particles on the boundaries. It is found that eventually very much larger alloy carbides, M23C6 and M6C, precipitate at the expense of the cementite which dissolves completely. The transformation to alloy carbides was found to be much faster at the higher tempering temperatures. M23C6 is found after 5,850 hours at 640°C and M6C after 9,353 hours, whereas after 9,381 hours at 565°C only M23C6 is found, and cementite remains the stable carbide after 12,887 hours tempering at 525°C. In addition to the chromium-rich M3C, M23C6 and M7C3 carbides, a fine dispersion of molybdenum and vanadium based carbides, M2C and MC respectively, also precipitated during the stress-relief heat treatment and persisted throughout the tempering process. 148 6.3.2 Composition of the carbides The representative energy dispersive X-ray spectra of the various carbides are presented in Figure 6.2. M3C is characterised by a low vanadium and molybdenum concentration, whereas M23C6 has a much higher chromium and molybdenum content. M6C contains a slightly smaller chromium content than M23C6, but can be identified by its high molybdenum and silicon contents. Figure 6.2d) illustrates the charcteristic spectra from MC, a vanadium based carbide which can dissolve some molybdenum, and Figure 6.2e) that from M2C, which is molybdenum- rich, although it contains a significant amount of vanadium, and traces of chromium, manganese and iron. The experimentally determined composition bands spanning the ranges of temperatures studied of the alloying elements in the carbides in atomic % , allowing for the stoichiometric car- bon content in each alloy carbide (for example, 25 at.% of carbon in cementite) are summarised in Table 6.2. Table 6.2: Chemical composition ranges of the carbides M3C, M23C6 and M6C in at. % Carbide V Cr Mn Mo C M3C 0.7-1.1 2.0-7.6 2.0-10.0 0.6-1.0 25.0 M23C6 0.3-0.6 9.0-15.0 6.0-8.0 3.0-5.0 20.7 M6C 2.0-3.0 5.5-8.0 6.0-8.0 16.0-20.0 14.3 The chromium content of the cementite was found to increase steadily with time at the tem- pering temperature, the rate of enrichment being higher at the higher tempering temperatures. Manganese was found to diffuse into the cementite faster than the chromium, and saturated at a higher concentration. At the lower tempering temperatures saturation was not observed within the time periods studied. The saturation levels of chromium and manganese were also found to increase with decreasing tempering temperature. In the M23C6 the chromium content also appeared to increase slightly with tempering time, whereas the manganese content decreased. However, much longer service times are needed before the enrichment kinetics of M23 C6 can be established with confidence. The vanadium content of the M23 C6 was much lower than that in the other carbides. M6C was found to have an almost constant composition at all stages of tempering. The dissolution of cementite and precipitation of M23C6 occurred after the cementite had reached saturation. The literature suggests that the alloy carbide sequence usually involves first a transformation to M7C3 prior to M23C6, but this sequence was not observed experimentally. 149 11 • • • a) c) • .. 1 JtIn ., " ( J b) d) i_.. .~ 2 Jtm Figure 6.1: 'I'll(' dl'vl'loPIII(,lIt of th(' carhid(' diHtributioll during IOllg t('rnl t('rnpNillg at 6/IO°C:; a) ilftl'r lIorlllalizillg at. !J:;OoC, h) as a), hilt. addit.iollally t.('mp('r('d at 690°C for hour, c) furt.hN t.(,IlIl)('r('d aI, (i~O°C for ~8:1 hOllrH illld d) t('rnpN('d at. (;10°(; for 19!16 hours. 1:'0 d) V K(l a) >-,.,...;......• Fe~t '.f)~ C,) ~ ~....•~ •....•......• r--;r:n....••....• C,) VK[3~ CuKa....••....• MoKa~ CuK,GMnKa Fe fuKaCrK(} Energy b) ::: c) •....• () Cr~ Energy ....•....• e) Energy Figure 6.2: Characteristic energy dispersive X-ray spectra for the various alloy carbides found to precipitate during the tempering heat treatments: a) M3C, b) M23C6, c) M6C, d) MC and e) M2C. 151 A possible explanation for this is that the chromium content of the steel, and its ratio to molybdenum was too low for M7C3 to form. It is also probable that the small molybdenum- based carbides in the matrix limited the molybdenum content of the larger M23C6 and M6C carbides, and stabilized the M23C6 to longer times. 6.4 Modelling of the diffusion process 6.4.1 Thermodynamic calculations Thermodynamic calculations were performed to calculate the equilibrium carbides expected in M1 steel as a function of temperature, and to study the metastable equilibrium between ferrite and cementite. The calculations allowed for the elements Fe, Cr, Mn, Mo, C, V, Si, Ni, Sn, Cu, P and S and the phases M3C, M7C3, M6C, M23C6, M2C, VC, austenite and ferrite. The equilibrium carbides at all temperatures were found to be M23C6, M6C and VC which is in good agreement with the carbides observed after long ageing times in all the specimens (Mo2C is assumed to have all transformed to M6C under equilibrium conditions). Calculations were then performed by suppressing all carbides except cementite, thereby allowing the equi- libria between the metastable cementite and the ferrite matrix to be studied. The calculated chromium levels in the ferrite and cementite are presented in Table 6.3. These data are also plotted in Figure 6.3. It can be seen that the maximum permitted concentration of chromium in cementite increases with decreasing temperature, as observed experimentally. Table 6.3: Equilibrium concentration (at.%) of chromium in ferrite and cementite calculated using MTDATA as a function of temperature in steel Ml. Phase 690°C 640°C 630°C 620°C 610°C 590°C 575°C 565°C 525°C Ferrite 0.25 0.23 0.22 0.22 0.21 0.20 0.19 0.18 0.16 Cementite 5.53 6.35 6.53 6.72 6.91 7.31 7.63 7.85 8.77 The equilibria between ferrite/M23C6 and ferrite/M6C can also be calculated. The calcu- lated equilibrium chromium concentration in M23C6 varies between 7-9 at.% from 690-525°C respectively, and that in M6C from 2-4 at.% over the same temperature range. These equilib- rium calculations also predict that the level of molybdenum at equilibrium is 10 at.% in M23C6 and 45 at.% in M6C. 6.4.2 Finite difference modelling Calculations were performed using the model described in Chapter 3 to predict the enrich- ment rate of cementite for comparison with the experimental results. The initial compostitions 152 in the cementite and ferrite are obtained by assuming that there is no partitioning of the substi- tutional solute elements during transformation. The particle size used in the model was 175nmj this represented the mean value obtained from particle size measurements over many specimens. The effect of the chosen particle size on the enrichment rate is illustrated in Figure 6.4 for particles of 150, 175 and 200nm at 590°C. Obviously there is no effect on the saturation level of chromium which is determined by equilibrium thermodynamics, but the enrichment rate is slightly faster for a smaller particle. In order to simulate the industrial heat treatment, calculations were carried out in which the composition changes in cementite resulting from a stress-relief heat treatment at 690°C for one hour were evaluated prior to the modelling of long term tempering at the lower service temperatures. As an initial approximation it is assumed that there is no redistribution of substitutional solute elements during the formation of pearlite. The starting concentrations were therefore set to be the bulk chromium composition of the alloy in both the ferrite and cementite. The interface concentrations used were the equilibrium concentrations of chromium in the cementite and ferrite respectively, calculated using MTDATA as described in the previous section. The measured chromium concentrations are compared with the theoretical predictions in Figure 6.5a)-h), for specimens tempered at 640, 630, 620, 610, 590, 575, 565, and 525°C. It should be noted that the saturation level in cementite predicted by MTDATA is slightly different from that measured experimentally. This is thought to be due to the presence of the fine M2C in the steel, precipitated during the stress-relief heat treatment, which reduces the molybdenum content in the cementite and raises the chromium content above that predicted if only cementite and ferrite are allowed to exist. The experimentally determined chromium contents of M23C6 and M6C are also plotted to illustrate the time at which the cementite transforms to alloy carbides at the various tempering temperatures. The absolute chromium levels in the alloy carbides are higher than those predicted by thermodynamic calculations. The high molybdenum concentrations predicted in M23C6 and M6C are not observed experimentally, resulting in larger chromium concentrations being measured in the alloy carbides than their predicted values. Again this can be attributed to the fact that molybdnum is tied up in fine M2C precipitates, reducing the amount of molybdenum available for inclusion in M23C6 and M6C. The effect of the M2C precipitation altering the absolute chromium levels predicted in carbides is very small in the case of cementite, where the predicted level is 2-3 at. % and the measured level is approximately 1 at. %. It has already been mentioned in the introduction that the chemical composition of cemen- tite in pearlitic steels is found to be somewhere in between equilibrium and para.equilibrium 153 12 ~..,; Id•••.•••10 G).•...-.•.. ~ 8G)a G) Co) R 6••• Ro',= 4Id•••.•.. R G) ~ 2 o (.) o 500 - er Mn --- Mo •.- .......---.•.•.•.._-- ..--- ..---.._---- 550 600 650 Temperature fOc 700 Figure 6.3: Equilibrium substitutional alloying content of cementite as a function of temperature calculated using MTDATA. 10 o o .'~ ......' -----,,""/"". "..- /.' " 20 40 60 80 Time1/2 /Hoursl/2 •••• SI50nm - S115nm -- S200nm 100 Figure 6.4: The effect of particle size on the enrichment kinetics of cementite. 154 ++ ••• 20 40 60 80 100 120 TimeV2 /HoursV2 b) 15 ~...;as "- Cl 10 0•••-as~-Cl~ to) 5Cl 0 to) ~U 0 120 0 cl) a) 640°C 15 ~...;as "- Cl 10 +0•••-as~ •- •Cl~ •to) 5Cl 0 to) ~U 0 0 20 40 60 80 100 TimeV2 /Hours V2 c) 620°C 15 IS 120 + •+•• 20 40 60 80 100 T· V2 /H 1/2lme ours • . ,,'t' ' o o ~...;as "- Cl 10o•••-asA '--Cl~ ~ 5o to) '-U 120 + • • 20 40 60 80 100 T· V2 /H 1/2lme ours ~.... "~,,, o o ~...;as "- Cl 10o•••-as~-Cl~ ~ 5o to) '-U Figure 6.5: a)-h) A comparison of experimental measurements of chromium concentration in cemen- tite, ., with the finite difference model (solid line). The dotted line represents the predictions of the model in the case where partitioning of some chromium is allowed for. The chromium concentration of the alloy carbides occurring at long service times is plotted for comparison: + M23C6, 6 M6C. 155 e) f) 15 15 120 • + • 20 40 60 80 100 " 1/2 /H 1/2Time ours o 120 0 ~...,;="-+ g 10".-=~-c:lQ,) ~ 5o (,) ~U 20 40 60 80 100 T" 1/2 /H 1/2lme ours o o ~...,;="- c:l 10o".-ClS~-c:lQ,) ~ 5o (,) ~U g) h) 15 15 120 • 20 40 60 80 100 T" 1/2 /H 1/2lme ours o 120 0 ~...,;="- c:l 10o".+=~-• c:lQ,) ~ 5o (,) ~U 20 40 60 80 100 T" 1/2 /H 1/2lme ours o o ~...,;="- c:l 10o".-=~-c:lQ,) ~ 5o (,) ~U 156 a) b) Normalised 950°C + 690°C 1 hour Tempered at 640°C 51 hours 15 15 •• •• 100 200 300 400 Particle size / nm 500 ••••••••••• • •• ••• • •• •• 100 200 300 400 Particle size / nm ~ ~"= 10o•••••••QS'-•••=8 5=o t) '-u o 500 0 •• •• o o ~ ~"= 10o•••••••QS'-•••=8 5=o t) '-u c) Tempered at 640°C 483 hours cl) Tempered at 640°C 1482 hours 15 15 •• ~ • • •• ••• ~ ~"= 10o....•••QS'-•••=8 5=o t) '-u • •••• • I ••.:... • •• I· •• • • •• •• ~...,; ~"= 10o• ••••••QS'-•••=8 5=o t) '-u ••• • • • o o 100 200 300 400 Particle size / nm o 500 0 100 200 300 400 Particle size / nm 500 Figure 6.6: a)-f) Chromium concentration in cementite plotted against particle size for specimens tempered for varying times at 640°C. 157 15 e) Tempered at 640°C 1824 hours 15 f) Tempered at 640°C 2996 hours • N ~"=10o••••-='--=8 5=oCJ '-U ••• •••••• •••• ••• •• • N ~"= 10o• •••-='--=8 5=oCJ '-U • •• • • •• ••• • ••• •• • • o o 100 200 300 400 Particle size / nm o 500 0 158 100 200 300 400 Particle size / nm 500 after transformation, and there is as yet no theory to predict the starting composition of the cementite. This is in contrast to bainitic cementite in which it can be assumed that there is negligible partioning of substitutional solute elements during transformation. It can be seen in Figure 6.5 that there is an error in the predicted starting composition of the pearlitic cemen- tite after the stress-relief heat treatment because any partitioning occurring on transformation is not taken into account. To allow for this problem with the inital stage of modelling, the simulation of the stress-relief heat treatment was allowed to run until the composition of the cementite had reached that measured experimentally. This corresponded to a period of temper- ing at 690°C for 18 hours rather than the one hour experienced in the practical situation. This is an artificial procedure because it considers partitioning to occur during the stress-relief heat treatment rather than on transformation, but it simply allows the use of the correct starting composition of the pearlitic cementite. The improvement in the agreement between the pre- dicted and measured values is shown by the dotted line superimposed on the graphs in Figure 6.5. This problem will be overcome when a theoretical basis for the precipitation of pearlitic cementite during transformation can be established. 6.4.3 Particle size The size and concentration of a series of particles were examined in specimens tempered at 640°C. Plots of chromium concentration against particle size are presented in Figure 6.6a)-f). The situation is complicated by the fact that the initial cementite lamellae appear to spheroidise and coarsen during tempering. The physical explanation of the SIze effect is that the total amount of solute that any particle can hold scales with particle size. A smaller particle will therefore reach its equilibrium concentration at an earlier stage in the tempering process. Therefore, size effects are unlikely to be easily detected during the early stages of tempering when most of the particles are below their saturation concentration and capable of accumulating solute. It is expected therefore that the size effect becomes more prominent during the later stages of ageing. A second point to note is that at any given ageing time, the average concentration of the solute in the particle, cB, varies inversely with particle size, xB• Thus cB will only be sensitive to xB when the latter is small. This is illustrated in Figure 6.4, where variations in xB within the expected range for the present study do not cause very large changes in cB when compared with experimental error. Nevertheless it is evident from the data presented in Figure 6.6 that the dependence of cB on xB begins to emerge with statistical significance only at the longest tempering time studied. Longer times could not be studied because of the onset of alloy carbide formation. 159 6.5 Conclusions In a ! Cr! Mot V steel after normalisation at 950°C followed by a stress-relief heat treat- ment at 690°C for an hour, the cementite composition varies on further tempering at tempera- tures in the range 640-525°C. The chromium and manganese content of the cementite increase with tempering time at the expense of the ferrite content. After the equilibrium composition of the cementite has been reached, transformation to the alloy carbides M23C6 and M6C occurs. The diffusion of the substitutional solute elements to cementite has been modelled and very good agreement has been found with the experimentally determined compositions. Further theoretical work is necessary to model the formation of cementite from austenite so that the starting composition of pearlitic carbides can be predicted. The dependence of composition on particle size was found not to be significant due to the relatively large size of the pearlitic cementite, and the fact that the calculated equilibrium concentration of chromium in cementite in this steel was relatively low, approximately 8 at.%. This is contrast to the particle size dependence of alloy element concentration discussed in the previous chapter for bainitic ce- mentite. Comparison of the experimentally determined chromium concentration in cementite, after a particular operating time, with the predictions of the numerical model of the diffusion process can therefore be used to estimate the service temperature of !Cr! Mot V steel power plant components. 160 CHAPTER 7 12CrlMo STEEL Carbide precipitation studies in 12Cr1MoV steel are discussed in this chapter. As a result of the very high chromium concentration of 12Cr1MoV steel, the reaction kinetics are rapid compared to those in low alloy steels. It is found that the equilibrium alloy carbide precipitates during the commercial stress-relief heat treatment and does not change in composition during further tempering. This is an important result; indications are that once the cementite trans- forms to alloy carbides, any changes in their composition are not large enough for this method to be used as a quantitative estimation of remanent life. (Low alloy steels, however, contain cementite for a considerable fraction of their useful service life.) The material described in this chapter has been published in Metallurgical Transactions A, 23A, 1992, p. 1171-1179. 161 CHAPTER 7 12CrlMo STEEL 7.1 Introduction The vast majority of creep-resisting steels used in power plant or in the petrochemical industry are based on low-carbon, low-alloy steels containing carbide forming elements such as chromium, molybdenum and vanadium as deliberate additions. In addition to creep resistance, prolonged service at elevated temperatures also requires good oxidation and hot-corrosion re- sistance, possibly in environments containing hydrogen and sulphur. In the United Kingdom, the steels are often used within the temperature range 480-565°C, the service stresses being of the order of 15-30 MPa over time periods of some thirty years. There is currently con- siderable research in progress to implement higher alloy steels with the aim of improving the creep strength so that the service temperature can be increased (Alberry and Gooch, 1983; Middleton, 1986). Alternatively, the higher strength can be exploited by reducing section size, which can be beneficial from the viewpoint of welding, thermal fatigue and the reduced cost of support structures. A lot of the effort to date has focussed on 12CrlMoV steel. The purpose of this work was to examine the effect of representative heat-treatments on the chemistry and some other characteristics of the carbides to be found in 12Cr1MoV type steels. 7.2 Materials and heat treatment The material used in this work was a 12Cr1MoV steel supplied by National Power Tech- nology and Environment Centre, Leatherhead, from heat 60348. The steel was supplied in the form of a rod of diameter 4 cm X 1 m long. Thinner rods of 3 mm diameter and bars 1X 1X 4 cm were machined from the original sample. Experimental results were compared with 'ex- service' material (i.e. steel which has been in service in a power station), courtesy of Laborelec, Belgium. The service history of this latter pipe was 68,646 hours at 592°C followed by 146,000 hours at 587°C, both at a pressure of 175 bar. The compositions of both steels, which are both within British Standard, BS3604, and the German standard X20 for 12Cr1MoV steels, are given in Table 7.1. In spite of this, it is worth noting that the chromium concentration of the ex-service steel is significantly higher. Heat treatments were carried out in order to recreate the microstructures used in the commercial condition when the steels are first implemented for service. The material is metal- lurgically complex and requires careful control of the heat treatment to ensure that the starting 162 Table 7.1: Chemical compositions of the 12CrlMoV steels in wt. % C Si Mn P S Cr Mo V Ni Cu Al Co Nb+Ta 12CrlMoV 0.21 0.25 0.46 0.009 0.012 10.9 1.03 0.30 0.52 0.02 <0.005 0.02 0.06 Ex-service 0.18 0.22 0.58 0.01 0.007 12.4 1.07 0.28 0.64 0.13 0.01 0.03 <0.01 X20CrMoV12l microstructure is 100% martensitic. The specimens were sealed in silica tubes containing a par- tial pressure of argon of 150 mm Hg. Austenitisation was carried out at 1060°C for 15 minutes. It has been shown by Barraclough and Gooch (1985) that the austenitising temperature for 12CrlMoV steels is crucial in determining the microstructure and mechanical properties. Too Iowa temperature will cause heavily spheroidised microstructures with dramatically reduced creep resistance, and too high a temperature can result in the formation of 0 ferrite and a large austenite grain size, which is undesirable. Yet the temperature must be high enough to ensure the complete dissolution of carbides. After austenitisation the specimens were air-cooled, and re-sealed in silica tubes and tempered for up to 2 hours at 700°C, in order to simulate the com- mercial stress-relief heat treatment, and then further tempered at 565°C to simulate service conditions. 7.3 Results 7.3.1 Microstruet ural changes A typical optical micrograph is shown in Figure 7.1. It can be seen that the microstructure is 100% martensite and does not contain any 0 ferrite. TEM micrographs of the as-quenched microstructure are presented in Figure 7.2. Figure 7.2a) shows martensite platelets containing some internal twins, confirmed by selected area electron diffraction. Figure 7.2b) demonstrates the fact that there are no carbides in the as-quenched microstructure, Le. that no autotempering has occurred. Gooch (1982) reported that the microstructure obtained by cooling from 1l00°C contained a fine dispersion of cementite particles. This difference is attributed to the relatively slower speed of the quench. Figure 7.3a) and b) illustrate the carbides beginning to form at prior austenite grain and lath boundaries, and also intra-lath, in a specimen which has been tempered at 700°C for 15 minutes. The carbides were identified by selected area electron diffraction as both M7C3 and M23C6• The carbide M7C3 was also found in specimens aged for up to 30 minutes at 700°C, but these had all dissolved at the end of the stress-relief heat treatment. Figure 7.4 shows that 163 M7C3 was mainly found within the martensite laths and distant from the clustered M23C6 precipitates. This is in agreement with Beech and Warrington (1966) who found that M23C6 and M7C3 were both present from an early stage of tempering, and that on spheroidisation the particles within the martensite laths disappeared. The diffraction pattern in Figure 7.4 illustrates the characteristic streaks of M7C3 resulting from its faulted structure compared with that of pure Cr7C3 (Westgren et ai, 1928). No difference in morphology was found between M7C3 and M23C6, apart from a tendency for the former carbides to be much finer. A typical carbon extraction replica from a sample which had been given the commercial stress-relief heat treatment, Le. tempering at 700°C for 2 hours, is shown in Figure 7.5. The distribution of the carbides in relation to the martensite boundaries is clearly illustrated. The carbides at the end of the stress-relief heat treatment were found to consist chiefly of a dispersion of M23C6 particles concentrated on the austenite grain and lath boundaries. A comparison between the distribution of coarse M23C6 carbides in the ex-service material and in a specimen isothermally heat treated at 700°C for 1173 hours is presented in Figure 7.6. The empirical Larson-Miller (Larson and Miller, 1952) parameter, defined as T(20 + logt), where T is the temperature in Kelvin and t is the time in hours, indicates that these two different heat treatment conditions are comparable. The carbide size and distribution is similar in the two materials, although for reasons which are not clear there appears to be a tendency for increased clustering of the carbides in the ex-service material. Macrohardness measurements were made on all the specimens using a 30 kg load. These results are presented in Table 7.2. Each data point is the average of three measurements on each sample, with the total scatter being no more than 10 RV. The macrohardness data confirms that the microstructure of the ex-service material and the 12CrlMoV steel are similar, and that little change in carbide precipitation occurs on tempering. Table 7.2: Macrohardness measurements Specimen Macrohardness fRV Pre-tem pering 622 700 °C-15 mins 315 700 °C-30 mins 309 700 °C-60 mins 296 700 °C-120 mins 315 700 °C-1173 hours 293 Ex-service material 302 164 The appearance of additional phases, such as Laves phase, on tempering a 12Cr1MoV steel depends critically upon the base composition of the steel. In the steels used in this work no additional phases were found during tempering which is consistent with the work of Briggs and Parker (1965). 7.3.2 Thermodynamic calculations Thermodynamic calculations were performed using MTDATA in order to calculate the equilibrium phases in the 12Cr1MoV steel. The carbide M23C6 was found to be the stable carbide, coexisting with ferrite, at all temperatures in the range of interest, 400-800°C. The equilibrium solution temperature of the carbides was found to be 950°C. Barraclough and Gooch (1985) found that 30 minutes at 950°C was not an adequate solution heat treatment, although 30 minutes at 1000°C was satisfactory. The temperature at which delta ferrite became stable on heating was calculated as 1220°C in the 12Cr1MoV steel, and as lllOoC in the ex-service material, which contained an additional 1.5 wt.% chromium. This difference is consistent with the work of Irvine et al. (1960) who found that an increase in chromium content of 1 wt.% led to an increase in b-ferrite content of ~14%. This confirms that the commercial austenisation temperature range of 1020-1070°C is adequate to completely dissolve carbides and will not produce large amounts of b-ferrite. M2JC6 was found to be the most stable carbide, then M7C3, followed by cementite. A precipitation sequence of M3C ---* M7C3 ---* M23C6 is therefore possible. The results of the thermodynamic calculations for 7000G (the stress-relief heat treatment) and for 565°C (the service temperature) are presented in Table 7.3. The alloying element content of the two carbides of interest, M7C3 and M2JC6, is presented as a function of temperature in Figure 7.7a) and b). Table 7.3: Chemical compositions of the carbides in both the 12CrlMoV steels used in wt.%. The calculations were performed using MTDATA at 700°C and 565°C respectively. 12CrlMoV Steel 'Ex-service' 12Cr1MoV steel 700°C Fe Cr Mo Mn C Fe Cr Mo Mn C M7C3 5.2 82.2 3.1 0.6 8.9 4.6 83.2 2.7 0.7 8.8 M23C6 10.7 65.1 19.1 - 5.1 9.0 66.4 19.5 - 5.1 565°C Fe Cr Mo Mn C Fe Cr Mo Mn C M7C3 1.6 84.4 4.5 0.7 8.8 1.4 85.1 4.0 0.7 8.8 M2JC6 4.2 70.3 20.4 - 5.1 3.6 70.9 20.4 - 5.1 165 Figure 7.1: Opticalmicrograpli for SPC'imcn aust nitiscd at 1060° for 2 liours at 700°C. 166 15mins, air cool d, and tcmpC'red a.) h) 0.1 1/111 l-J 0.1 1/111 I F igur 7.2: Tri1I1Slllissioll ('I('cl rOil IlIicrogri1phs fro 11I t h(' ,LSqll(,lIdl('d IlIicrosl rllct IIr('. a) illllstral,('s 11)(' Iwilllled IIIi1rtc'lIsite IIlicrostrllctllrl'; thc' ills(,l, is it s('lecl('d ar('a diffractiOIl pattl'r11 showillg thl' twill (I) ,lIld IlIalrix (Ill) rC'f1('ctiolls. The twill plilll(, is 211. Il) is a highN IIIi1gllificatioll illlag(' showillg I hat 110alllo tC'IIIPl'fillg has on'lIrn'd. IG7 a) b) • ., -,. 0.3 /"11 L---! Figure 7.3: Trallslllissioll ('I('droll rllicrographti illustrat illg ca.rbidc forlllat.ion at both th(' gralll a) alld lath h) i>ollllci"ri('s ill a sp('cimcu t(,lllpNcd for l!i millut('s at 700°(:. I(jX Figure 7.4: (',trboll ('xl ractioll rc'plica showillg slllall M7C:l particl('s distihllt('d wit.hill th(' mart(,lIsite lat hs alld dist - ::a) .- ~(f) Le'u, z lG ~ c..o.;.(200: M2JCa M2JC6 (422)~ (420)~ M on M7CJ~ (2021 <:eo.;. (2201 TWO - ntET A lDEGREES) cee;, (Jll) 61.5 &5.0 b) • SIEMENS·.0 I FFRAC 500 11••• _ (f) lLu >-•... ~.;;:;;~zw•...z 120: - 110 DE' C - 1 HOI..It SUIUt' OfFSET. 1.10 TIO - THETA (DEGREES) Figure 7.10: X ray diH'raction ratt<'l'ns for SIH'cilll('ns t<'lllrf'r<,d at 700°(; for 10 rnills a.)and I hour h) rcsr<,ctivcly illustrating that M7CJ initially IH('s('nt along with M2:JC6 ha.sdissolved aftf'r t<,rnpNing for I hour. 170 in good agreement with the calculated value. The calculated lattice parameters differed by no more than 0.02A, indicating again no significant differences in the composition of the M23C6 after tempering. 7.4 Discussion The carbides precipitating during the stress-relief heat treatment in 12CrlMoV steel have been identified by X-ray diffraction and selected area electron diffraction as M7C3 and M23C6. Therefore, before entering service at approximately 565°C, the steel contains a distribution of M23 C6 particles. The initial composition of the carbides is close to that predicted using equilibrium thermodynamics, and it has been established by EDX that there is no further change in the composition of the carbides with tempering. No significant dependence of chromium concentration on particle size was found. Lattice parameter measurements and comparison with ex-service material confirm that there is no change in composition of the M23C6 on tempering, especially with respect to molybdenum, which might have been expected from the thermodynamic calculations. The fact that there is no enrichment occurring on tempering in 12CrlMoV steel is in contrast to the low alloy steels reported in the previous chapter. Du (1986) found that the chromium content in M23C6 precipitating in a !Cr!Mot V steel increased with time. Whether or not alloy carbides precipitate at their equilibrium composition is therefore dependent on the concentration of alloying elements available in the base composition of a steel. Recent work by Bjarbo (1991) (for an alloy with a higher chromium content than that used in this work) has shown that M23 C6 which precipitates during the stress-relief heat treatment is enriched in chromium by less than 5 wt.% during a creep test for 20,000 hours at 600°C. 7.5 Conclusions The kinetics of carbide precipitation in 12CrlMoV steels are rapid when compared with other low-alloy steels of the type commonly used in power plant. This is attributed to the fact that the steel studied has relatively large concentrations of carbide-forming substitutional solutes. Thus, unlike the low-alloy steels, relatively stable alloy carbides have been found to dominate in the microstructure immediately after the stress-relief heat treatment. Since this heat treatment is always necessary before implementing the alloy in service, there seems little prospect of estimating the thermal history of a component from the chemical composition of its carbides. In fact, both the thermodynamic analysis and the experimental data show that the chromium concentration of the M23 C6 carbide is very sensitive to the average chromium concentration of the steel. It is found that variations in the chromium concentration within 177 the accepted industrial specifications, can lead to larger corresponding variations in carbide compositions, than would be caused during service. It has been established that there is no significant change in the carbide identity or com- position during service after the stress-relief heat treatment. Therefore, the question arises as to which other microstructural changes could be fruitfully investigated. It seems from a com- parison of figures 7.9d) and e), which show an increase in particle size from about 125-300 nm, that carbide coarsening could potentially be used as a microstructural parameter. 178 CHAPTER 8 ATOM PROBE AND STEM INVESTIGATIONS The atom probe studies discussed in this chapter provide a link between the experimental measurements of mean concentration levels in cementite using energy dispersive X-ray analysis in a transmission electron microscope, and the theoretical modelling of the diffusion process discussed in Chapter 3. Consistent with theoretical predictions, the enrichment of substitutional solutes in the carbide at the carbide/matrix interface is not observed to reach the levels required for local equilibrium at the interface. The material described in this chapter has been accepted for publication in Surface Science. 179 CHAPTER 8 ATOM PROBE AND STEM INVESTIGATIONS 8.1 Introduction It was shown in Chapter 3 that the cementite associated with upper bainite forms with no redistribution of the substitutional alloying elements, by paraequilibrium transformation. The modelling of the subsequent approach towards equilibrium, involving the diffusion of substitu- tional elements is central to this work. It is often assumed in problems of diffusion that local equilibrium exists at an interface. t A calculation was performed using MTDATA (see Chapter 3) to determine the equilibrium concentration of chromium in cementite and ferrite for the 2lCrlMo steel at 565°C. Alloy carbide formation was suppressed; only the phases cementite and ferrite were allowed to exist. The results of the calculation are given in Table 8.1. The predicted volume fraction of cementite at this temperature was 0.022, which is consistent with mass balance considerations. The partitioning ratio indicated by the calculations is consistent with the values of ~50 measured by AI-Salman et aI (1979) at 600°C for pearlitic cementite in an Fe-Cr-Mn-C steel, although this comparison is not strictly valid because of the difference in steel chemistry. Local equilibrium therefore would require a very large increase in chromium concentration in cementite at the interface, compared with the 2.2 wt.% that exists in the bulk alloy. Table 8.1: Calculated equilibrium concentration in cementite and ferrite at 565°C. Calculated equilibrium concentration of Cr /wt.% Ferrite 1.05 Cementite 54.00 Modelling of the enrichment behaviour of cementite to date assumes only that local equib- rium exists in the matrix at the carbide/matrix interface. The concentration in cementite at the interface is determined by mass balance considerations in the diffusion equations. During the earlier stages of enrichment (e.g. 10 mins) the model predicts a small increase in the con- centration of chromium at the edges of a cementite particle with respect to its core. At the t Local equilibrium requires that the concentrations of the solute in both the carbide and the matrix at a carbide/matrix interface are given by the tie-line of the equilibrium phase diagram. 180 longer tempering times, after soft impingement of the diffusion fields from the extremities of the particle, the model predicts a more even distribution of chromium across the particle rising slowly to the equilibrium level. Measurements of cementite composition using energy-dispersive X-ray analysis (EDX) in a TEM are only able to determine the average particle concentration. The maximum measured Cr concentration in cementite by EDX in the specimens tempered at 565°C was ~ 35 wt.%. It is not possible to measure the equilibrium Cr content in the cementite in this steel at this temperature because the alloy carbide M7C3 precipitates at the expense of the cementite before it has reached saturation. The model assumes that the diffusion coefficients, DO'and D8, in the matrix and cementite respectively are the same; this assumption is justified to some extent by the good agreement between kinetic theory and experiment demonstrated in Chapters 5, 6 and 7. DO'is obtained as 1.65x 1O-19m2s-1 according to Fridberg et al (1969), whose assessed data are in good agreement with those of Bowen and Leak (1970). Barnard et al (1987) have used atom probe techniques to measure DO' and D8• The data for 486°C are presented in Table 8.2. The value of DO' measured by Barnard et al is an order of magnitude less than the other two values, and of D8 approximately two orders of magnitude less than the measured value of DO'. Table 8.2: Measurements of the diffusion of chromium in ferrite and cementite at 486°C. DO'/m2s-1 D8/m2s-1 Bowen and Leak (1970) 4.9xlO-21 - Fridberg et al (1969) 4.6x 10-21 - Barnard et al (1987) (1) 2.6x10-22 - (2) 4.9x 10-22 0.02x 10-22 The effect of varying the value of D8 with respect to the value of DO' on the cementite enrichment rate was therefore investigated using the model described in Chapter 3. Three different values of D8 were chosen and two different tempering times, 10 mins and 178 hours. The resulting composition profiles and predicted concentrations are presented in Figure 8.1 and Table 8.3. The most important result is that for De= 510 DO'the predicted average level of Cr in cementite is 16 wt.% for a 10 min ageing period, whereas if DO'=De this level is 2.5 wt.%. The average concentration of chromium in cementite after 10 mins tempering measured using EDX is ~6 wt.%. This result is therefore inconsistent with the value of De measured by Barnard et al (1987). It is possible that De is slightly less than DO', but not by a factor of 50. The purpose of this work was therefore to investigate to what extent local equilibrium exists at the particle/matrix interface during the enrichment of cementite. 181 Table 8.3: Average Cr concentration and the interface concentration in cementite as a function of De and tempering time. Concentrations are given in wt.%. De 10 mins 178 hours Av. conc. Interface conc. Av. conc. Interface conc. =Da 2.48 3.14 13.09 13.11 =0.3Da 3.14 5.23 38.51 38.59 =0.02Da 16.06 47.74 53.99 53.99 .. 40 ···..... 35 178 hours ....." ..D_=D'•...............~.:4s .... .... .. c-·_- D••••=O.3Drer D••••=O.02Dr ••. 10 15 20 25 30 Cementite slice no. 5 ..... .. ---- --=.o o 60 ~ 50 ~ " 40Clo...••••~ 30•••Cl~ Co)Cl 20o Co) •••U 10 Figure 8.1: Predicted chromium concentration in a cementite particle of size 100 nm in a 2iCr1Mo steel after 10 mins and 178 hrs tempering at 565°C as a function of the diffusion coef- ficient in cementite. Slices 1 and 40 represent the surfaces of a plate-shaped cementite particle in the finite difference model, the core being located at slice 20. 8.2 Atom probe field ion microscopy 8.2.1 Principle of operation of atom probe An atom probe consists of a field ion microscope with an ultrahigh-resolution mass spec- trometer attached. The field ion microscope produces images of the specimen in which there is one-to-one correspondence with atomic positions. The mass spectrometer is then used to 182 perform very accurate chemical analysis. A brief summary of the principle of operation of an atom probe is presented below. Extensive discussion concerning the operation of atom probes can be found in the book by Miller and Smith (1989), and details of the atom probe used in this work in the paper by Waugh et al. (1992). A field ion specimen is a very sharp needle of tip radius approximately 100 nm. The specimen is cooled down to cryogenic temperatures using a closed-cycle helium refrigerator and held in a vacuum chamber with a background pressure of 10-11 mbar. For producing a field ion image (field ionisation), a background pressure of neon gas of 10-5 mbar is introduced into the chamber and a large positive voltage is applied to the specimen. The inert gas atoms become polarised in the high electric field near the tip and are attracted towards it. Ionisation of the polarised gas atom can then occur by quantum mechanical tunnelling of an electron to the tip. The remaining positively charged gas ion is then repelled from the tip towards the channel plate. On striking the channel plate, a cascade of electrons is produced which strike a phosphor screen resulting in a bright image spot. The number of ions will be greatest where the local field is highest, for example, above prominent surface atoms. A picture of the Cambridge atom probe is presented in Figure 8.2, and the corresponding schematic diagram in Figure 8.3. Limited information can be obtained from the field ion image. The image is usually used to recognise features of interest such as second phases or boundaries. Phase contrast can arise where there are differences in the ionisation probabilities of the elements in the two phases. Ferrite is usually imaged as sets of concentric rings showing the b.c.c. symmetry of the phase, whereas austenite, martensite and carbides usually image darkly. The elements molybdenum and silicon, to a lesser extent, image brightly because the evaporation field for these elements from an iron-based matrix is higher than that for iron itself, and so they remain at prominent surface positions. The second stage involves the removal of atoms from the surface of the specimen by the process of field evaporation as the voltage applied to the specimen is increased further. The background pressure of neon gas is reduced for atom probe analysis. The atoms are field- evaporated at a well-defined moment in time by the application of an additional voltage pulse. The mass to charge ratio of the atom can then be determined from the time taken to reach the detector, which can be measured to an accuracy of 1 ns. There is a hole in the channel plate which enables the selection of atoms from a specific area. The lateral resolution is the size of this hole projected onto the tip, which is approximately 5 nm. The accuracy with which small scale composition variations can be determined depends on their relative orientation to the axis of the analysis cylinder. Repeated pulsing of the sample is used to build up a layer by layer 183 Figure 8.2: The atom probe field ion microscope (APFIM 200) used in this work. Retlectron Detector and ViewIng MIrror Prot>e Hole Channel Plate ViewIng Mirror Lens Stage Controls and High Voltage Feedthrough Carousel Transfer Mechanism Schematic Cross Section Of Instrument Figure 8.3: A schematic cross section of the APFIM 200. 184 I PROBEHOl.£-OMNELPlATE--_ .... ----~SORPED IONSFROM SAMPLE~~------------------_.------ IJl ------------r- +HV PJlSE SAMPlE +HV Figure 8.4: Schematic diagram illustrating the operation of the atom probe field ion microscope. MATERIAL ANALYSED COMPOSITION PROFILE / //// ///// ///// ////. '//// //// ////. /' SPECIMEN TIP Figure 8.5: Diagram illustrating the ideal precipitate analysis geometry. 185 atomic composition profile from the specimen. A schematic diagram illustrating the operation of the atom probe field ion microscope is presented in Figure 8.4. A diagram illustrating the ideal precipitate analysis geometry is illustrated in Figure 8.5. 8.2.2 Experimental details The 2tCr1Mo steel discussed in chapter 5 was used for the atom probe studies. Blanks were cut from the heat treated specimens of size 0.5xO.5x20 mm using a diamond saw. These were initially thinned electrochemically using the same conditions as for the preparation of the TEM foils of this material discussed in chapter 4. Needles for examination in the atom probe were then prepared using a two stage electropolishing technique; stage 1 producing a necked specimen profile using a thin layer of the electropolishing solution above floated on an inert solution at ~30 V, and stage 2 producing a needle by electropolishing in a solution of 2% perchloric acid in butoxyethanol at ~25 V. Both solutions were cooled to O°C using liquid nitrogen. Specimens were resharpened by dipping the tips in a lacquer resist and electropolishing in the two solutions. Atom probe analyses were performed at 100 K with background pressures of neon gas of 1X 10-5 mbar and 1X 10-8 mbar for imaging and analysis respectively. The voltage pulse fraction used was 20%. 8.2.3 Results and discussion The specimens tempered for relatively short times (up to 2 hrs) were examined in the atom probe, and those for longer times in the STEM, which was able to accommodate the larger particle sizes. A typical TEM micrograph from a thin foil tempered for 10 mins at 565°C is shown in Figure 8.6, showing plate-shaped carbides, identified as cementite using selected area electron diffraction. The cementite plates typically measured 125x30 nm. Analysis in the atom probe is easier if the particles are aligned with the long dimension parallel to the length of the needle. As observed by Wada et al. (1982), the cementite particles were found to be very unstable under the action of the applied electric field, leading to frequent specimen fracture. It was observed in the STEM that the cementite particles charged in the electron beam indicating poor conductivity. Field ion micrographs from the matrix and cementite phases are presented in Figure 8.7. The image from the matrix was often found to contain small clusters of very bright atoms; sub- sequent atom probe analysis showed that these might be attributed to very small molybdenum carbides. The cementite phase is observed to have little structure in the image and to contain relatively large diffuse spots. Mass spectra from specimens tempered for 10 mins and 2 hrs are presented in Figure 8.8. 186 Figure 8.6: A transmission electron micrograph from a specimen tempered at 565°C for 10 mins illustrating plate-shaped cementite particles. a) b) Figure 8.7: Field ion images from the matrix (a) and the cementite (b) phases. The calculated composition within the matrix, distant from the cementite particles, correspond- ing to each of these spectra is presented in Table 8.4. It can be seen that there is a reduction in the chromium level in the matrix after tempering for 2 hrs. This corresponds to the en- richment of cementite with respect to chromium, resulting in a drop in the chromium level in the matrix. After 2 hrs tempering, the concentration of chromium measured in cementite by energy-dispersive X-ray analysis on carbon extraction replicas in the TEM is approximately 11 wt.%. It is interesting to note that the molybdenum and carbon contents in the matrix are a little higher than might be expected, particularly in the specimen tempered for 10 mins. Close examination of the composition profile corresponding to the mass spectrum in Figure 8.9a) reveals small clusters containing both molybdenum and carbon atoms. This is illustrated in Figure 8.9a). This suggests there are very small particles of molybdenum carbide in the early stages of formation within the matrix. A Markov chain analysis for the the molybdenum atoms indicates that there are more Mo-Mo bonds than would be expected in a homogeneous solid 187 Table 8.4: Composition of the matrix measured in the atom probe for samples tempered for 10 mins and 2 hrs in wt. %. Time C Si Mn P S Cr Mo V Ni Cu Fe 10 mins 0.16 0.49 0.48 0.01 0.04 2.38 1.87 0.09 0.09 0.03 94.36 ±0.02 ±0.06 ±0.08 ±0.01 ±0.01 ±0.15 ±0.20 ±0.03 ±0.02 ±0.03 ±0.60 2 hrs 0.13 0.37 0.60 0.05 - 1.34 1.04 - 0.04 - 96.44 ±0.03 ±0.07 ±0.14 ±0.03 ±0.20 ±0.25 ±0.04 ±0.75 (a) MASS SPECTRUM (b) ~ 1Q' MASS SPt:=CTAUM Figure 8.8: Mass spectra taken from the matrix in specimens tempered for 10 mins (a) and 2 hrs (b) containing 7,000 and 3,000 ions respectively. solution, although many more ions are needed to establish the significance of this result. Further work is therefore needed to establish any correlation between the carbon and molybdenum concentrations, and to examine the development of clusters as a function of ageing time. Similar 188 observations have been made by Olson et al. (1991). Dark field imaging in the STEM at high magnification, which is especially good for showing high atomic number contrast, is able to resolve small particles which probably correspond to the molybdenum and carbon clusters observed in the atom probe. This is illustrated in Figure 8.9b). M02C particles had not been observed in previous TEM investigations until the specimens had been tempered for 32 hrs. 1000 1100 1400 1600 1800 3000 Total number of ions I .... ~o I ~Clusters of Mo and C ~ il ; I ~ § .~.. -'.'.'.'. b) I I ~-. ::.. ::'.'.. :. ; ; · ., I ·, I ·.. I ,.. ~ ,.. .' ..'. .: '.'. '.'. '.'. '.'. '.'. : '.'. '. 10a) Figure 8.9: a) Composition profile (15 ions per block) corresponding to part of the mass spectrum in Figure 8.9a) for the specimen tempered for 10 mins showing small clusters of molybdenum and carbon atoms and b) dark field STEM micrograph from a carbon extraction replica taken from a specimen tempered for 10 mins illustrating very small particles exhibiting high atomic number contrast. The measured content of silicon in the matrix is observed to be slightly higher than the composition of the steel as a whole. Silicon, usually observed as Si2+, has a mass to charge ratio of 14, which is the same as that for N+. However, the concentration of nitrogen in the steel is expected to be less than 40 ppm. High levels of Si is a common observation, and is usually attributed to the preferential evaporation of the matrix because Si is refactory and hard to evaporate. Preferential evaporation occurs because the iron evaporates more easily, so that during the time when the specimen is not being pulsed (i.e. is at the set d.c. voltage) the iron continues to evaporate whereas the Si only evaporates during the pulsing. Therefore, the Si appears to have a larger concentration than expected. A typical mass spectrum from a cementite particle after 10 mins tempering is illustrated In Figure 8.10. The corresponding concentration for the major alloying elements of interest is approximately 20 at.% C, 3 at.% Cr, 2 at.% Mo and the balance, Fe. The chromium and molybdenum levels are slightly lower than those measured by energy-dispersive X-ray analysis (~5 at.% Cr), possibly because there is expected to be a variation with particle size. However, 189 the carbon content is clearly less than the 25 at% required by the stoichiometry of cementite, M3C. It is possible that the probe hole did not completely overlap the cementite particle, but is more likely that the carbon detection efficiency has been reduced by the relatively high analysis temperature used to try to reduce the fracture rate of the samples. Carinci et al. (1988) found that a specimen temperature of 80 K reduced the observation of carbon clusters and led to a corresponding reduction in the overall carbon content. Sha et al (1992) have recently shown that there is an ambiguity in the assignment of the peaks due to carbon clusters ct and ct+ and that careful reassignment of these peaks can increase the total amount of carbon in the atom probe analysis by as much as 10%. :5 10 MASS SPECTRUM Figure 8.10: A typical mass spectrum from a cementite particle in a specimen tempered for 10 mins. The composition profiles of carbon, chromium and silicon along a cementite/matrix inter- face for a specimen tempered for 5 mins are presented in Figure 8.11. The carbon concentration here is only 10 at.%, consistent with the probe hole being half way across the carbide and the matrix. The inclination of the probe hole to the interface was approximately 80°C. It is im- portant to note that the concentration of chromium in the cementite at the interface is far less than the 54 wt. % expected from local equilibrium. This result therefore verifies the theoretical model in which local equilibrium does not exist in the cementite during the early stages of enrichment. There is also some evidence of an increase in the silicon content of the matrix outside the cementite particle. Silicon is known to partition from cementite. 8.3 Scanning transmission electron microscope studies It has already been noted that atom probe analyses were difficult because of the size of the carbides relative to the size of the specimen tip. After the precipitation of the larger M7C3 carbides atom probe analyses proved nearly impossible. Therefore a scanning transmission 190 a) b) c) 40 40 40 CARBIDE CARBIDE CARBIDE Interface ~ 1000 1500 1000 Total number of ions o lSOO Interface \ 1000 1500 1000 Total number of ions o lSOO Interlace ~ 1000 lSOO 1000 Total number of ions o Figure 8.11: Composition profiles for carbon (a), chromium (b) and silicon (c) along a cemen- tite/matrix interface in a specimen tempered for 5 mins. electron microscope (STEM) was used to look at the composition profile through some of the larger cementite particles. Analyses were performed using a VGHB501 STEM operated at 100 kV on thin foils made from the specimens tempered for 178 hours. A little caution needs to be exercised in the interpretation of these results for two reasons. Firstly, the resolution of the STEM was at its poorest due to a strong astigmatism produced by the ferromagnetic specimen. (Attempts to use carbon extraction replicas proved unsuccess~ul because the specimen drifted within the time needed to perform accurate microanalysis.) In addition the particle is 3- dimensional; any surface enrichment will be averaged to some extent because the particle is probed by the electron beam in a 2-dimensional section. 8.3.1 Results and discussion Figure 8.12 shows the chromium concentration profile across a cementite particle and into the matrix measured using energy-dispersive X-ray analysis in a STEM. This particle is contained in a specimen which has been tempered for 178 hours at 565°C. Care has been taken only to include the section of the particle having parallel sides in the analysis in order to remove any interference from the matrix at the ends of the particle. The analysis was performed in a direction exactly normal to the carbide/matrix interfaces. The absolute level of chromium measured in the matrix was lower than that measured on a carbon extraction replica (Chapter 5) due to interference from the predominantly iron-containing matrix. Thus, it is not possible 191 to determine an absolute level of chromium in the cementite. However, the relative difference between the chromium concentration at the centre and the edge of the particle was found to be approximately 3 wt. %. This result is significant because it would appear to preclude the possibility that the chromium concentration in the cementite at the carbide/matrix interface has reached the predicted equilibrium level, implying local equilibrium has not yet been attained at the interface. MATRIX 60nm MATRIX Figure 8.12: The concentration profile of chromium across a carbide and into the surrounding matrix measured using energy-dispersive X-ray analysis in a STEM from a specimen which has been tempered for 178 hours at 565°C. 8.4 Conclusions The most important result is that, consistent with theoretical predictions the concentration of cementite at the cementite/ferrite interface is found to be far below that expected from equilibrium considerations. This is in samples which are annealed at elevated temperatures in order to permit the initially non-equilibrium cementite to enrich in chromium concentration. The apparent clusters of molybdenum and carbon atoms found in the ferrite matrix of specimens tempered for only 10 mins at 565°C using atom probe analysis, could indicate the early stages of Mo2C formation, although much further work is needed to establish this quantitatively. The diffusion coefficient of chromium in cementite needs to be established accurately, al- though this would be easier in a steel of slightly different composition in which the precipitates were more conducive to atom probe analysis. STEM analyses have proved difficult for the magnetic specimens and the large interference from the predominantly iron containing matrix means that quantitative analyses are difficult, although used in conjunction with TEM on carbon extraction replicas they can provide useful information. 192 CHAPTER 9 FURTHER THEORETICAL STUDIES In this chapter the question of whether simultaneous particle coarsening and enrichment can occur is addressed. It is shown quantitatively that the driving forces for the two processes are of opposite sign, and that the enrichment process appears to defeat coarsening until the bainitic carbides have reached their equilibrium compositions. 193 CHAPTER 9 FURTHER THEORETICAL STUDIES 9.1 Introduction Particle coarsening is the dissolution of small precipitates and the simultaneous growth of larger particles at a fixed volume fraction. Ultimately a system will tend towards only one large particle. The driving force for the process is a decrease in the total interfacial energy. Factors which need to be considered in the development of a full theory of particle coarsening include the size and shape of the particles, the relationship between size and solubility, and whether the reaction is diffusion or interface controlled. A distribution of particle sizes within a matrix causes concentration gradients, and therefore, in order for these to be maintained, atoms have to transfer across the interface between the particle and the matrix. If diffusion of atoms within the matrix is the rate-controlling step then the growth is said to be diffusion controlled, whereas if it is more difficult for an atom to cross the interface into the matrix, then growth is said to be interface controlled. Theoretical growth rate equations for individual particles for both diffusion and interface controlled reactions have been derived by Greenwood (1956) and (1969), and then these have been incorporated into analyses ofthe dispersion as a whole by Wagner (1961) and Lifshitz and Slyozov (1961). A brief review of experimental studies of particle coarsening is presented in the next section. The equations governing the coarsening process are then discussed in detail together with the necesssary modifications to allow for the coarsening of particles in a solid matrix. The application of the theory to simultaneous particle coarsening and enrichment is then outlined. 9.2 Experimental studies of particle coarsening Early experiments were performed under the conditions for which the Wagner, Lifshitz and Slyozov theories were developed, Le. virtually pure particles in a liquid. This work has been reviewed by Greenwood (1969). Recent interest has, however, concentrated on extending the theory to account for precipitates in a solid matrix. In most cases, this has been studied successfully using thin foils and extraction replicas in a transmission electron microscope. The main area of interest in this work is the coarsening of carbide particles in steels, and so the previous work on the Fe-C system only will be reviewed here, although it shoud be noted that there have been considerable advances in studies on the Ni-AI system by Ardell (1969). 194 There have been many theories proposed in the literature for the mechanism of cementite coarsening. Hyam and Nutting (1956) measured the carbide particle size distribution during the tempering of four plain carbon steels in the temperature range 500-700°C. They then related the changes in the particle diameters on tempering to hardness measurements, from which they calculated the activation energy for the softening process, following the assumption that particle size and separation are directly responsible for changes in hardness. The value which they obtained led them to conclude that cementite coarsening is controlled by the self-diffusion of iron, rather than the diffusion of carbon. Mukherjee et al. (1969) have pointed out that these measurements are unreliable because changes in the matrix structure during tempering are not taken into consideration. Oriani (1964) then considered that both the diffusion of carbon and the diffusion of iron should be taken into account. His argument was that the growth of a cementite precipitate requires a change in volume according to the equation which must be accommodated at both the growing and dissolving precipitates which necessitates coupled diffusion of iron and carbon. There was limited agreement of this theory with the experimental data due to approximations having to be made for the values of various constants. Oriani's theory of coupled diffusion was then challenged by Bj6rkland et al. (1972) who studied the effect of alloying elements on the rate of Ostwald ripening of cementite. They used a sophisticated treatment of the thermodynamics of the problem, but a rather basic treatment of the diffusion. They suggested that the diffusion coefficient may be reduced by elements dissolved in the cementite which diffuse very slowly and are therefore rate-controlling. They predicted that a Mn content of 0.001 wt.% in an Fe-C alloy would decrease the growth rate by a factor of 10. This idea is supported by Mukherjee et al. (1969), who studied the effect of chromium on carbide coarsening. They found that increasing the chromium content retarded the growth of cementite particles, and that the coarsening rate of the various chromium-based alloy carbides decreased in the order Fe3C, M3C, M23C6, M7C3. It is interesting to note that they found that M3C and M7C3 coarsened at a rate consistent with the diffusion of chromium being rate-controlling, whereas the coarsening of Fe3C is too rapid for the equivalent diffusion of iron to be rate-controlling. An alternative interface controlled coarsening mechanism was proposed by Heckel and De Gregorio (1965). They studied a spheroidised eutectoid steel containing 0.75 wt.% C, and with other elements, such as Si and Ni, being present at levels ofless than 0.005 wt.%. They 195 concluded that interface controlled kinetics were applicable having obtained coarsening rates two or three times lower than those predicted by carbon diffusion being rate-controlling. One possible explanation, however, is that even the small amounts of impurities present are retarding the coarsening. Heckel and De Gregorio proposed that the coarsening rate is limited by the rate of formation of cementite at the growing interfaces where the interfacial reaction is proportional to the solute thermodynamic activity gradient across the interface. Another important factor considered by Mukherjee et al. (1969) is the influence of the matrix structure on coarsening rates. They found that the fine grain size and dislocation substructure in a martensitic microstructure caused a significant increase in the coarsening rate. They also noted that irregularities in particle size distribution curves could be resolved by the superposition of two different distributions, one from particles within the matrix and one from particles situated on the grain boundaries, caused by a transfer of material from the matrix to grain boundaries during tempering. 9.3 Particle size and solubility The starting point for a theory of coarsening must be to relate the size of a particle to its solubility. The simplest relationship is the Gibbs-Thomson or Thomson-Freundlich equation for spherical particles of radius r, with an interfacial energy per unit area,. The complete theory is given in Christian (1975) from which the following synopsis is taken. Consider an assembly in which 0 (cementite) particles of surface area 0 and surface free energy per unit area, are in equilibrium with the 0' (ferrite) matrix. It can be shown that the energy of the interfaces displaces the equilibrium condition, and may be considered to contribute an additional thermodynamic potential, resulting in the fact that the solubility limit, cOt8, and the equilibrium composition, c8Ot, of the cementite may both vary with the radius of the particle. The quantities relating to interface curvature are denoted by c~ and c~, where r is the particle radius, and those referring to the equilibrium compositions for infinite planar interfaces by c~ and c~. (N.B. Concentrations are used here rather than atomic fractions which are valid only when there is a negligible volume change on transformation. However, this assumption is implicit here because no strain energy terms due to the transformation are included in the treatment.) The effect can be illustrated as follows. If a virtual change is considered in which dn atoms are transferred from the 0' phase to the 0 phase, there will be an increase in the surface area of the 0 particles, and therefore a corresponding increase in energy of ,dO. This may be 196 Gibb's free energy •••• ••• •• ••• •• •••• •• •••• •• •• ge 00 ce ce Concentration00 r •Figure 9.1: Free energy curves versus composition to illustrate the Gibbs-Thom~on effect, (based on Christian, 1975). represented as a displacement of the free energy per atom from g(J to g~ where (9.1) The new equilibrium compositions are given by the common tangent construction to the free energy curves, as illustrated in Figure 9.l. The effective chemical potentials per atom for curved interfaces are denoted by gt and g~r, and the new equilibrium conditions are g~r = gAr and g~r = g8r. From the geometry of the diagram, it can be seen that ~c~ = c~ - c~ which is of the same order of magnitude as and also that the approximation, can be made. The chemical potentials per atom of an ideal solution can be expressed as gA - g~ = kT In (1 - x) and gB - g~ = kTlnx , 197 (9.2) (9.3) (9.4) (9.5) (9.6) where gO refers to the chemical potential of the pure substance. The absolute activity, A, is defined in terms of the chemical potential as Equations 9.5 and 9.6 can then be written in terms of absolute activities as AA~ = In (1 - x) and A (9.7) (9.8) ABIO = In x , (9.9) B where AO refers again to the pure substance. Equations 9.8 and 9.9 can then be modified to take into account non-ideal solutions by multiplying their right hand sides by the appropriate experimentally measured activity coefficients, such that (9.10) (9.11)ABIO = fBln x . B Therefore, by substitution of the activity coefficients, fEr and fEoo' it can be shown that ( fCl' COO ) gCI' _ gCI' = kT In Br rBr Boo fCl' CCI' 'Boo 00 (9.12) and then, using the dilute solution approximation that fE=constant and equating equations 9.4 and 9.12 gives ~c~ ~ In ( c~ ) = ~ (dO) ( 1 - c~ ) cCI' cCI' kT dn c8 - cCI' 00 00 00 00 Using the approximation that the particles are spherical, for which 41l"r3o = 41l"r2 and n = -V '3 m (9.13) (9.14) where Vm is the molar volume and n is the number of atoms per mole, and then using the properties of partial derivatives, 00 00 or on - {f;'on - equation 9.13 is simplified to the form usually used as the basis of coarsening theory, In ( c~ ) = 2, Vm ( 1 - c~ ) , cCI' kTr c8 - cCI'00 00 00 198 (9.15) (9.16) Gibbs free energyt Matrix Particle Smaller particle cr!:Q dn Increased Cr cone ---.-- Cr concentration Figure 9.2: Schematic illustration of the increase in free energy due to particle curvature and the decrease in free energy due to increased thermodynamic stability. equilibrium level, and that there is a constant volume fraction of precipitate. Oriani (1964) also points out that Wagner (1961) assumes that the atoms in the matrix offer no resistance to the motion of an interface, Le. that the matrix atoms move at a much greater rate than the diffusion of the solute, and can therefore be neglected. 9.5 Application to simultaneous coarsening and enrichment of cementite In order to address the question of whether or not particle coarsening (in the strictest sense) can occur whilst the process of enrichment is occurring the driving forces for the two reactions need to be investigated. It has been shown in the previous section that the driving force for coarsening originates from an increase in free energy due to particle curvature of a smaller particle. However, diffusion of chromium, for example, to cementite particles is driven by a reduction in free energy as thermodynamic equilibrium is approached. The driving forces for enrichment and coarsening will therefore tend to oppose each other. It has also been shown that smaller particles will enrich more quickly than larger particles and therefore the reduction in free energy due to an increased chromium content will be most marked for the smaller particles, thus cancelling out, to a certain extent, any increase in free energy due to an increased radius of curvature. This is illustrated schematically in Figure 9.2. These two opposing processes are quantified in the following sections. 200 (9.20) 9.5.1 Increase in free energy due to particle curvature The increase in concentration of solute in the matrix surrounding a small particle has been discussed in section 9.3. An alternative approach is to consider the increase in free energy due to interface curvature. The expression for the increase in free energy due to interface curvature is given by the expression ao 2Vml I an = -r-' For cementite, a value of I given by PuIs and Kirkaldy (1972) is 0.6 Jm-2• The molar volume can be estimated from the unit cell dimensions and the number of atoms contain in one unit cell: cementite is orthorhombic with lattice parameters a=4.523A, b=5.089A and c=6. 743A, and there are 12 atoms contained in one unit cell. Vm is therefore given by v _ (4.523 x 5.089 x 6.743 x 10-3°) N m - 12 x A' (9.21) where NA is Avagadro's number. The increases in free energy for particle sizes of 10, 100 and 10000 nm are presented in Table 9.1. As expected the largest increase corresponds to the smallest particle size. Table 9.1: Increase in free energy as a function of particle size. Particle size /nm Inc. in free energy / J mol-1 10 934 100 93.4 10000 0.934 9.5.2 Decrease in free energy due to increased thermodynamic stability In order to quantify the decrease in free energy due to an increase in thermodynamic stability because of an increase in chromium content of the cementite, an expression for the free energy of cementite is required. Lundberg et al. (1977) state that the molar Gibbs free energy os cementite is given by (9.22) where YFe and YCr are concentration parameters related to the ordinary mole fractions, x, by XCrYCr = 1- YFe = ---I- Xc 201 (9.23) Other data are GFec, =74,113 J mol-I, GCrC~ =-13,578 J mol-I and Ao=1,790 J mol-I. Ce- mentite is virtually stoichiometric with respect to carbon content and therefore it contains 0.0067 mole fraction carbon. Evaluating this expression for particles containing various pro- portions of chromium and iron indicates that addition of 1 at. % Cr lowers the free energy of the cementite by approximately 1 kJ mol-I. These results are summarised in Figure 9.3. It has been shown in previous chapters that chromium concentration varies linearly with reciprocal particle size. Calculations were per- formed using the finite difference model to determine the chromium concentration as a function of tempering time for typical sizes and concentrations of the cementite particles found in the 2iCr1Mo steel. The predicted value of chromium concentration was then converted into a value of Gibbs free energy (using equation 9.22). An additional contribution to the free energy due to the capillarity effect was then added to give the total free energy. It can be seen from the plots of total free energy as a function of reciprocal size in Figure 9.3, for three different tempering times, that smaller particles become increasingly more stable than the larger ones. The contribution to the free energy from the capillarity term is also plotted for comparison. It is clear that capillarity is a very small effect compared with the fact that the larger particles enrich more slowly than the smaller ones. 9.6 Conclusions The above results suggest that coarsening is defeated by the fact that in a distribution of particle sizes, the smaller particles will be richer in chromium and will not be able to give up chromium to the larger particles, as is the case in a true coarsening reaction, due to the opposite driving forces for the two reactions. Coarsening, in the true sense, will not therefore become important until the very late stages of ageing. This argument explains why coarsening is not observed for the bainitic cementite discussed In Chapter 5. It has already been shown in Chapter 6 that pearlitic cementite particles are much larger than bainitic cementite and therefore the sensitivity to particle size effects is much reduced. However, for pearlitic cementite the lamellae are observed to spheroidise during the enrichment process (Figure 6.1). This can be thought of as a shape change from the initally coarse plate-shaped lamellae, rather than coarsening itself. In the absence of enrichment with respect to substitutional alloying elements, the spheroidisation rate would presumably be much faster. 202 70.0 'j 60.0-oa 50.0 ~"~ 40.0~ + 30.0 i ~ 20.0 10.0 0.0 1 hr '\0::::·::'·":.7. :---------------- _' ....., ..... 32 h............ ........ rs.... , .•.•.... . .....•..•.......... . ..•..•..•..•..•..•..•.128 hrs.•..•..•..•..•..•..•..•. .•..•..•. o 5 10 15 20 25 30 35 40 Reciprocal particle sIze /_106 m-I Figure 9.3: Total Gibbs free energy as a function of particle size after different enrichment times for cementite particles in 2tCrlMo steel. 203 CHAPTER 10 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 204 CHAPTER 10 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK It is now possible to interpret fundamentally carbide enrichment kinetics of the kind asso- ciated with remanent life prediction in power plant steels. Thus it is, in principle, possible to extrapolate carbide chemistries with confidence over the sort of time scales typical of elevated temperature applications. Specifically, the precipitation characteristics of three power plant steels containing different chromium concentrations, !Cr!MotV, 2tCrlMo and 12CrlMoV, have been studied in detail. ! Cr! Mot V steel, being pearlitic, was found to contain relatively large cementite particles. As a consequence of this, the substitutional alloy content of the cementite is not particularly sensitive to particle size. The low chromium content in the steel means that the equilibrium concentration of chromium in the cementite is low. This results in a much smaller degree of enrichment during ageing, thereby reducing the sensitivity to the particle size. The agreement between the theoretical model and the experimentally measured enrichment data is found to be very good. For this steel, measurement of cementite composition change can prove a valuable indicator of the average thermal history, and therefore of the remanent creep life. Power plant components are very large, and therefore the microstructure can vary consid- erably through the section of a given component. Studies of the precipitation characteristics in the 2tCrlMo steel have highlighted the importance of cementite composition being related to the position in the microstructure. Significantly different enrichment rates have been observed in fully bainitic and mixed ferritic/bainitic microstructures. The much larger equilibrium con- centration of chromium in cementite and the smaller size of bainitic carbides in this steel result in the measured chromium concentration being very sensitive to particle size, the smaller parti- cles enriching more quickly than the larger ones. It has also been shown that when alloy carbides co-exist in the microstructure with cementite, the cementite composition no longer changes in a simple manner. The precipitation of chromium-rich alloy carbides can substantially reduce the chromium level in the cementite. The kinetics of precipitation have been found to be extremely rapid in the 12CrlMoV steel. The equilibrium alloy carbide precipitates during the stress-relief heat treatment and subsequently does not change in composition. It is perhaps not surprising that changes in alloy carbide chemistries, induced by tempering, are found to be less striking than those observed for cementite. The growth of alloy carbides involves considerable long range diffusion and there is therefore greater opportunity for the carbide to be closer to equilibrium when it first forms. 205 The derivation of this approximation is given below. The Taylor expansions on the (j + 1)th time row are:- (8c) 1 2 (8 2c)ci-1,i+1 = ci,i+1 - Or F + 2(or) 8 2 + '" .r i,i+l r i,i+1 (1. 7) (1.8) Subtraction and addition of these two equations lead respectively to the following equations:- (~~) i,i+1 ci+1,i+1 - ci-1,i+1 20r (1.9) (8 2c) 8r2 i,i+1 Then, using the approximation that Ci+1,i+1 - 2ci,i+1 + ci-1,i+1 or2 (1.10) (:~) ~ ~ [(:~) ;,;+1 + (:~) J ' (8 2 c) 1 [(8 2 C) (8 2 c)]8r2 = 2 8r2 i,i+1 + 8r2 i,i ' the following expressions can be obtained:- (1.11) (1.12) (1.13) (1.14)( 82c) 1 [C'+1 '+1 - 2c, '+1 + C'_1 '+1 C'+l' - 2c, '+ c'_1 ,]_ = _ ',J ',J ',J +' ,J ',J ',J 8r2 2 (or)2 (or)2 This is termed the implicit finite difference method because unknowns on the time level (j + 1) are expressed in terms of known values on the time level j. Therefore, N grid points result in N simultaneous equations to solve in order to obtain the unknown values. More computation is required at each step than with the explicit finite difference method, but this calculation remains stable for all values of Oi, whereas the explicit method is only stable for ot ~ 0.50r2 and therefore it is possible to use larger and therefore fewer time steps. 208 APPENDIX 11 FINITE.FOR C Program using finite difference method for the solution of the problem C of X enrichment of cementite during the ageing of bainitic steels C C EQFER = Equilibrium at.% of X in ferrite at ageing temperature C EQCEM = Equilibrium at.% of X in cementite at ageing temperature C EBAR = Average X at.% in alloy C FERS = normalised concentration of X at ferrite surface C CEMS = normalised concentration of X at cementite surface C TIMH = time in hours C KTEMP = Absolute temperature C TCEM = Thickness of cementite in meters C TFER = Half-thickness of ferrite in meters C N.B. This is calculated from the volume fraction of chromium C in the alloy in the program C C DFER = Diffusivity of X in ferrite C DCEM = Diffusivity of X in cementite C Q = Activation free energy for diffusion C FREQ = Pre-exponential factor for diffusion C The mean size of a cementite particle is usually taken to be 100nm C (This is based on experimental experience) C C Concentrations normalized relative to average alloy concentration C Dimension normalize relative to carbide particle thickness C ICEM, IFER, J1 are the number of finite slices C for dimension and time respectively C (N.B. ICEM is read into this program but IF ER is calculated: both C values must be transferred to FINN via the dataset) C TIM = Time, in seconds C A3 controls the amount of information that is printed out C SETIME controls the time in hours that the experiment runs. C JTEST modifies the mass balance condition when the CEMS reaches C the equilibrium concentration. Hence mass is conserved. C C Typical data C 838.15 0.5D-03 39.0D+00 2.5D+00 1.0D-07 0.1 5 C 0.0003D+00 2.0D+00 1.0 1.0 C 2.53D-04 240580.0 (DIFFUSION DATA, JOULES ETC.) C End of data C IMPLICIT REAL*8(A-H,K-Z), INTEGER(I,J) DOUBLE PRECISION CFER(1500,2), CCEM(20,2) J4 = 0 J5 = 0 JTEST = 0 READ( 5, *) KTEMP,EQFER,EQCEM,EBAR, TCEM, VOL UME,ICEM 209 READ(5,*) CFER(1,1),CCEM(1,1),A3,SETIME READ(5,*) FREQ,Q RFER = OAOD+OO RCEM = RFER TFER = (TCEM*(l.OD+OO- VOLUME))j(2*VOLUME) DFER = DIFF(KTEMP,Q,FREQ) DCEM = DIFF(KTEMP,Q,FREQ) STCEM = 0.5D+00*TCEMjICEM IFER = DINT(TFERjSTCEM) STFER = TFERjIFER TIME = RFER*STFER*STFERjDFER J1 = DINT(3600*SETIMEjTIME) WRITE( 6,100) DFER,DCEM, VOLUME,TFER, TCEM,EQFER,EQCEM,KTEMP,ICEM + ,IFER,STCEM,STFER DO 1 I = 2,ICEM CCEM(I,l) = 1.0D+00 1 CONTINUE DO 2 I = 2,IFER CFER(I,l) = 1.0D+00 2 CONTINUE C FERS = EQFERjEBAR DR = DFERjDCEM WRITE(6,101) CCEM(l,l),CFER(l,l) C C Finite difference analysis C TIM = O.OD+OO WRITE(6,102) DO 50 J = 2,J1 TIM = TIM +TIME TIMH = TIMj3600.0D+00 IF (TIMH .GT. SETIME) GOTO 51 CEMM = O.OD+OO FERR = O.OD+OO C C C ****** Ferrite ****** DO 10 II = 1,IFER IF (II .EQ. 1) THEN C Note: surface concentration in ferrite is at equilibrium C until CEMS reaches the equilibrium concentration IF (JTEST .EQ. 0) THEN CFER(1,2) = CFER(l,l) + RFER*(FERS - 2.0D+00*CFER(1,1) + + CFER(2,1)) ELSE FERS = ((CCEM(l,l)-CEMS)jDR) + CFER(l,l) ENDIF C Ensure reflection at last slice ELSEIF (II .EQ. IFER) THEN CFER(IFER,2) = CFER(IFER,l)+ RFER *(CFER(IFER-1,1) 210 + -2.0D+00*CFER(IFER,1)+CFER(IFER-1,1)) CALL SOFT(CFER(IFER,2),1,J4,TIMH) ELSE CFER(II,2) = CFER(II,1)+RFER*(CFER(II-1,1) + -2.0D+00*CFER(II,1 )+CFER(II+ 1,1)) ENDIF FER = CFER(II,2)*EBAR XTFER = STFER *II FERR = FER+ FERR CFER(II,l) = CFER(II,2) 10 CONTINUE C C ******** Cementite ******** C DO 20 1= 1,ICEM C Calculate surface concentration in cementite C appropriate for mass balance IF (I .EQ. 1) THEN CEMS = DR*(CFER(l,l)-FERS)+CCEM(l,l) C Reflect at position of symmetry IF (CEMS .GT. (EQCEMjEBAR)) THEN CEMS = EQCEMjEBAR JTEST = 1 ELSE CCEM(1,2) = CCEM(l,l) + RCEM*(CEMS-2.0D+00*CCEM(1,1) + + CCEM(2,1)) ENDIF ELSEIF (I .EQ. ICEM) THEN CCEM(ICEM,2) = CCEM(ICEM,1)+RCEM*(CCEM(ICEM-1,1) + -2.0D+00*CCEM(ICEM,1 )+CCEM(ICEM -1,1)) CALL SOFT (CCEM(ICEM,2),2,J5,TIMH) ELSE CCEM(I,2) = CCEM(I,1)+RCEM*(CCEM(I-1,1) + -2.0D+00*CCEM(I,1)+CCEM(I+1,1)) ENDIF CEM = CCEM(I,2)*EBAR XTCEM = I*STCEM CEMM = CEM+CEMM CCEM(I,l )=CCEM(I,2) 20 CONTINUE C 50 51 CEMM = CEMMjICEM FERR = FERRjIFER DUMMY = JjA3 DUMMY = DINT(DUMMY)-DUMMY IF (DUMMY .EQ. 0.0) THEN AVER = (FERR*TFER + CEMM*0.5D+00*TCEM)j(TFER+0.5D+00*TC WRITE( 6,103) TIMH,CEMM,FERR,AVER,FERS*EBAR,CEMS*EBAR ENDIF CONTINUE WRITE(6,104) 211 60 61 70 71 C 100 + + + + + + + + 101 + 102 103 104 105 106 DO 60 I = 1,ICEM IF (CCEM(I,2) .LT. 1.0001) GOTO 61 WRITE(6,105) I,CCEM(I,2),CCEM(I,2)*EBAR CONTINUE WRITE(6,106) DO 70 J = 1,IFER IF (CFER(J,2) .GT. 0.999) GOTO 71 WRITE(6,105) J,CFER(J,2),CFER(J,2)*EBAR CONTINUE CONTINUE FORMATC Diffusion coefficient in ferrite, m**2/s = " D12.4/' Diffusion coefficient in cementite, m**2/s, = ',D12.4/ , Volume fraction of cementite (MTDATA) = ',D12.4/ , Half thickness offerrite, m =',D12.4/ , Thickness of cementite, m =',D12.4/ , Eq. cone. of X at interface, in ferrite, at.% = ',D12.4/ , Eq. cone. of X at interface, in cementite, at.% = ',D12.4/ , Absolute Temperature = " F8.2, , ICEM, IFER = ',219/ , STCEM (m) = ',D12.4, , STFER (m) = ',D12.4/ /) FORMATC Time 0, slice 1, cementite and ferrite norm cone " 2F12.4/) FORMATC HOURS CEM FERRITE AVERAGE X FERS CEMS') FORMAT(D10.2,F9.4, F9.4,F9.4,F9.4,2F9.4) FORMAT(' No Norm. Cone. at.%X in Cementite') FORMAT(I8,D 12.4,2F10.4) FORMATC No Norm. Cone. at.%X in Ferrite') STOP END DOUBLE PRECISION FUNCTION DIFF(KTEMP,Q,FREQ) DOUBLE PRECISION KTEMP, R, Q, FREQ R = 8.3143 DIFF = FREQ*DEXP(-Q/(R*KTEMP)) C R = Universal Gas Constant, J/mol/K C KTEMP = Absolute Temperature C Data for X inter diffusion in alpha iron, from Fridberg (1969) paper RETURN END SUBROUTINE SOFT (A,I,J,TIMH) DOUBLE PRECISION A,TIMH IF (J .GT. 1) RETURN IF (I .NE. 1) THEN IF (A .GT. 1.01D+00) THEN WRITE(6,1l) TIMH J = 3 ENDIF ELSEIF (A .LT. 0.99) THEN WRITE(6,10) TIMH J = 3 212 ELSE RETURN ENDIF RETURN 10 FORMATC SOFT IMPINGEMENT IN FERRITE', Fl1.5,' hours') 11 FORMATC SOFT IMPINGEMENT IN CEMENTITE',Fl1.5,' hours') END 213 APPENDIX III INHOMOG.FOR C Program using finite difference method for the solution of the problem C of X enrichment of cementite during the ageing of bainitic steels C for an inhomogeneous carbon distribution. C C TIMH time in hours C KTEMP=Absolute temperature C TCEM=Thickness of cementite in meters C EQFER=Equilibrium wt.% of X in ferrite at ageing temperature C EQCEM=Equilibrium wt.% of X in cementite at ageing temperature C EBAR=A verage X wt. % in alloy C DFER=Diffusivity of X in ferrite C DCEM=Diffusivity of X in cementite C Q = ACTIVATION FREE ENERGY FOR DIFFUSION C FREQ = PRE-EXPONENTIAL FACTOR FOR DIFFUSION COEFFICIENT C Concentrations normalized relative to average alloy concentration C Dimension normalize relative to carbide particle thickness C TIM = Time, in seconds C A3 controls the amount of information that is printed out C SETIME controls the time in hours that the experiment runs. C JTEST modifies the mass balance condition when the CEMS reaches C the equilibrium concentration. Hence mass conserved C RATIO is the ratio of TFERA to TFERB (the relative sizes of the C inhomogeneous ferrite distribution) C C IMPLICIT DOUBLE PRECISION(A-H,K-Z) INTEGER I,J DOUBLE PRECISION CFERA(1500,2), CFERB(1500,2), CCEM(1500,2) READ( 5,*) KTEMP,EQFER,EQCEM,EBAR, TCEM, VOLFRAC,ICEM,RATIO READ(5,*) A3,SETIME,FREQ,Q J4=O J5=O J6=O JTESTA=O JTESTB=O C Set up the initial conditions TFERB=(TCEM*(l- VOLFRAC) )j(VOLFRAC*(l + RATIO)) TFERA=TFERB *RATIO DFER=DIFF(KTEMP,Q,FREQ) DCEM=DIFF(KTEMP,Q,FREQ) RFER=OAD+OO RCEM=RFER DR=DFERjDCEM STCEM=TCEMj(ICEM+1) IFERA=D INT(TFERA jSTCEM) IFERB=DINT(TFERB /STCEM) 214 STFERA=TFERA/IFERA STFERB=TFERB/IFERB C Set up time loop TIME=(RFER *STFERA *STFERA)/DFER J 1=DINT( 3600D+00*SETIME /TIME) C Write out the initial program parameters WRITE( 6,100) DFER,DCEM,VO LFRAC,TFERA,TFERB,TCEM,EQFER,EQCEM, + KTEMP,ICEM,IFERA,IFERB,STCEM,STFERA,STFERB C Set up the initial conditions everywhere DO 10I=1,IFERA CFERA(I,l)= 1.0D+00 10 CONTINUE DO 20I=1,ICEM CCEM(I,l)= 1.0D+00 20 CONTINUE DO 30I=1,IFERB CFERB(I,l)=l.OD+OO 30 CONTINUE IMID=INT(ICEM-1)/2 FERSA=EQFER/EBAR FERSB=EQFER/EBAR TIM=O.OD+OO DO 40 J=2,J1 TIM=TIM +TIME TIMH=TIM/3600D+00 C For the calculation of the average composition in the phases CEMM=O.OD+OO FERRA=O.OD+OO FERRB=O.OD+OO C C *************************FerriteA************************** C + + + DO 50 II=l,IFERA IF (II .EQ. 1) THEN IF (JTESTA .EQ. 0) THEN CFERA(1,2)=CFERA(1,1 )+RFER * (FERSA-2.0D+00*CFERA(1,1 )+CFERA(2,1» ELSE FERSA=( (CCEM( 1,1)-CEMSA) /DR)+CFERA( 1,1) ENDIF ELSEIF (II .EQ. IFERA) THEN CFERA(IFERA,2)=CFERA(IFERA,1)+ RFER *(CFERA(IFERA-1,1) -2.0D+00*CFERA(IFERA,1 )+CFERA(IFERA-1,1» CALL SOFT(CFERA(IFERA,2),1,J4,TIMH) ELSE CFERA(II,2)=CFERA(II,1)+ RFER *(CFERA(II-1,1) -2.0D+00*CFERA(II,1 )+CFERA(II+ 1,1» ENDIF FERA=CFERA(II,2)*EBAR XTFERA=STFERA*II FERRA=FERA+FERRA 215 CFERA(II,I) =CFERA(II,2) 50 CONTINUE C C *************************FerriteB*************************** C DO 60 II=I,IFERB IF (II .EQ. 1) THEN IF (JTESTB .EQ. 0) THEN CFERB( 1,2)=CFERB( 1,1)+ RFER *(FERSB-2.0D+00*CFERB( 1,1: +CFERB(2,1)) ELSE FERSB=( (CCEM( 1,1)-CEMSB) /DR )+CFERB( 1,1) ENDIF ELSEIF (II .EQ. IFERB) THEN CFERB(IFERB,2)=CFERB(IFERB,I)+ RFER *(CFERB(IFERB-l,l) -2.0D+00*CFERB(IFERB,1 )+CFERB(IFERB-l,I)) CALL SOFT(CFERB(IFERB,2),2,J5,TIMH) ELSE CFERB(II,2)=CFERB(II,I)+ RFER *(CFERB(II-l,l) -2.0D+00*CFERB(II,1 )+CFERB(II + 1,1)) ENDIF FERB=CFERB(II,2)*EBAR XTFERB=STFERB*II FERRB=FERB+FERRB CFERB(II,1 )=CFERB(II,2) CONTINUE + + + 60 C C *************************Cementite************************** C DO 701=1,ICEM C Calculate the surface concentration in cementite on border C with ferrite A appropriate for mass balance IF (I .EQ. 1) THEN CEMSA=D R*(CFERA( 1,1)-FERSA )+CCEM( 1,1) IF (CEMSA .GT. (EQCEM/EBAR)) THEN CEMSA=EQCEM/EBAR JTESTA=1 ELSE CCEM( 1,2)=CCEM( 1,1)+ RCEM*( CEMSA-2.0D+00*CCEM( 1,1) + +CCEM(2,1)) ENDIF ELSEIF (I .EQ. ICEM) THEN C Calculate the surface concentration in cementite on border C with ferrite B appropriate for mass balance CEMSB=DR *(CFERB( 1,1)-FERSB )+CCEM(ICEM,I) IF (CEMSB .GT. (EQCEM/EBAR)) THEN CEMSB=EQCEM/EBAR JTESTB=1 ELSE CCEM(ICEM,2)=CCEM(ICEM,I)+ RCEM*( CCEM(ICEM-l,l) + -2.0D+00*CCEM(ICEM,I)+CEMSB) 216 ENDIF ELSE CCEM(I,2)=CCEM(I,1)+ RCEM*( CCEM(I-1,1)- + 2.0D+00*CCEM(I,1)+CCEM(I+1,1)) ENDIF IF (I .EQ. IMID) THEN CALL SOFT(CCEM(IMID,2),3,J6,TIMH) ENDIF CEM=CCEM(I,2)*EBAR XTCEM=I*STCEM CEMM=CEM +CEMM CCEM(I,l )=CCEM(I,2) 70 CONTINUE C Write out the results CEMM=CEMM/ICEM FERRA=FERRA/IFERA FERRB=FERRB /IFERB DUMMY=J/A3 DUMMY =DINT(DUMMY)-DUMMY IF (DUMMY .EQ. 0) THEN AVER=(FERRA *TFERA +CEMM*TCEM + FERRB*TFERB) / + (TFERA+TCEM+TFERB) WRITE(6,101) TIMH, CEMM, FERRA, FERRB + ,AVER, FERSA*EBAR, CEMSA*EBAR, CEMSB*EBAR, FERSB*EBAR ENDIF 40 CONTINUE WRITE(6,*) , No wt.%X in FerriteA' DO 80 I = IFERA,l,-l WRITE( 6,102) ((I-(IFERA + 1))*-1)*STFERA,CFERA(I,2)*EBAR 80 CONTINUE WRITE(6,*) , No wt.%X in Cementite' DO 90 I = 1,ICEM WRITE( 6,102) (1+IFERA-1 )*STCEM,CCEM(I,2)*EBAR 90 CONTINUE WRITE(6,*) , No wt.%X in FerriteB' DO 95 I = 1,IFERB WRITE( 6,102) (1+IFERA + ICEM-2)*STFERB,CFERB(I,2)*EBAR 95 CONTINUE 100 FORMATC' Diffusion coefficient in ferrite, m**2/s = ',D12.4/ + ' Diffusion coefficient in cementite, m**2/s, = ',D12.4/ + ' Volume fraction of cementite (MTDATA) = ',D12.4/ + ' Thickness of ferriteA, m =',D12.4/ + ' Thickness of ferriteB, m =',D12.4/ + ' Thickness of cementite, m =',D12.4/ + ' Eq. conc. of X at interface, in ferrite, wt.% = ',D12.4/ + ' Eq. conc. of X at interface, in cementite, wt.% = ',D12.4/ + ' Absolute Temperature = " F8.2/ + ' ICEM, IFERA, IFERB = ',319/ + ' STCEM (m) = ',D12.4/ + ' STFERA (m) = ',D12.4, , STFERB (m) = ',D12.4/ /) 101 FORMAT(D10.4,3F8.3) 217 102 FORMAT(2DI4.4) STOP END DOUBLE PRECISION FUNCTION DIFF(KTEMP,Q,FREQ) DOUBLE PRECISION KTEMP, R, Q, FREQ R=8.3143 DIFF=FREQ*DEXP( -Q/ (R*KTEMP)) C R = Universal Gas Constant, J/mol/K C KTEMP = Absolute Temperature C Data for X tracer diffusion in alpha iron, from XC Handbook 57 RETURN END SUBROUTINE SOFT(A,I,J,TIMH) DOUBLE PRECISION A,TIMH IF (J .GT. 1) GOTO 99 IF (I .EQ. 1) THEN IF (A .LT. 0.99D+00) THEN WRITE(6,110) TIMH J=3 ENDIF ELSEIF (I .EQ. 2) THEN IF (A .LT. 0.99D+00) THEN WRITE(6,111) TIMH J=3 ENDIF ELSEIF (I .EQ. 3) THEN IF (A .GT. 1.0ID+00) THEN WRITE(6,112) TIMH J=3 ENDIF ENDIF 110 FORMATC SOFT IMPINGEMENT IN FERRITEA', Fl1.5,' hours') 111 FORMATC SOFT IMPINGEMENT IN FERRITEB', Fl1.5,' hours') 112 FORMATC SOFT IMPINGEMENT IN CEMENTITE', Fl1.5,' hours') 99 RETURN END 218 REFERENCES AARONSON, H. I., (1986) 'Bainite Reaction', Encyclopedia of Materials Science and Technology, Pergamon Press, Oxford. p. 263-266. AFROUZ, A., COLLINS, M. J. and PILKINGTON, R., (1983) 'Microstructural Examination of 1CrO.5Mo Steel during Creep', Metals Technology, 10, p. 461- 463. ALBERRY, P. J. and GOOCH, D. J., (1983) '12CrMoV-A status review', Central Electricity Generating Board Report TRPD/L/2506/N83. AL-SALMAN, S. A., LORIMER, G. W. and RIDLEY, N., (1979) 'Pearlite Growth Kinetics and Partitioning in a Cr-Mn Eutectoid Steel', Metallurgical Trans- actions A, lOA, p. 1703-1709. ANDREWS, K. W. and HUGHES, H., (1958) 'Micro-constituents in Steels; Their Electrolytic Isolation and X-ray Study', Iron and Steel, 30, p. 43-50. ANDREWS, K. W., DYSON, D. J., and KEOWN, S. R., (1967) 'Interpretation of electron diffraction patterns', Publ. Hilger and Watts, London. ANDREWS, K. W., HUGHES, H. and DYSON, D. J., (1972) 'Constitution diagrams for Cr-Mo-V steels', Journal of the Iron and Steel Institute, 191, p. 337-350. ARDELL, A. J., (1969) 'Experimental confirmation of the Lifshitz- Wagner theory of particle coarsening', in 'The mech- anism of phase transformations in crystalline solids', Institute of Metals Monograph No. 33, p. 111-116. ARGENT, B. B., VAN NIEKERK, M. N. and REDFERN, G. A., (1970) 'Creep of ferritic steels', Journal of the Iron and Steel Institute, 208, p. 830-843. AVRAMI, M., (1939) 'Kinetics of Phase Changes 1', Journal of Chemical Physics, 7, p. 1103. BAKER, R. G. and NUTTING, J., (1959) 'The tempering of 2.25Cr1Mo Steel after Quenching and Normalizing', Journal of the Iron and Steel Institute, 191, p. 257-268. BARNARD, S. J., SMITH, G. D. W., GARRETT-REED, A. J. and VANDER SANDE, J., (1987) 'Atom Probe Studies (2) Low Temperature Chromium Diffusivity in Bainite', Proceedings of International Conference on Solid State Phase Transformations, Pittsburgh, USA. BARRACLOUGH, D. R. and GOOCH, D. J., (1985) 'Effect of inadequate heat treatment on creep strength of 12CrMoV steel', Materials Science and Technology, 1, p. 961-967. BARRETT, C. S. and MASSALSKI, T. B., (1968) 'Structure of Metals and Alloys', McGraw-Hill, New York. 219 BATTAINI, P., D' ANGELO, D., MARINO, G. and HALD, J., (1990) 'Interparticle Distance Evolution on Steam Pipes of 12Cr1Mo1V Steel during Power Plant Service Times', in 'Proceedings of the 4th International Conference of the Creep and Fracture of Engineering Materials', Swansea, Eds. B. Wilshire and R. W. Evans. BEECH, J. and WARRINGTON, D. H., (1966) 'M7C3 to MZ3C6 transformation in chromium containing alloys', Journal of the Iron and Steel Institute, 204, p. 460-468. BERRY, F. G. and HONEYCOMBE, R. W. K., (1970) 'The Isothermal Decomposition of Austenite in Fe-Mo-C alloys', Metallurgical Transactions, 1, p. 3279-3286. BHADESHIA, H. K. D. H., (1981) 'Bainite: The Incomplete-Reaction phenomenon and the approach to equilibrium', Proceedings of the International Solid-Solid Phase Transformation Conference, Pittsburgh. p. 1041-1048. BHADESHIA, H. K. D. H., (1982) 'A Thermodynamic Analysis of Isothermal Transformation Diagrams', Metal Science, 16, p. 159-165. BHADESHIA, H. K. D. H., (1985) 'Diffusional Formation of Ferrite in Iron and its Alloys', Progress in Materials Science, Perga- mon Press, Oxford, 29, p. 321-386. BHADESHIA, H. K. D. H., (1987) 'Worked Examples in the Geometry of Crystals', The Institute of Metals, London. BHADESHIA, H. K. D. H., (1988) 'Bainite in Steels', Phase Transformations '87, Institute of Metals, London, ed. G. W. Lorimer, p. 309-314. BHADESHIA, H. K. D. H., (1989) 'Theoretical Analysis of Changes in Cementite Composition During Tempering of Bainite', Materials Science and Technology, 5, p. 131-137. BHADESHIA, H. K. D. H., (1992) 'Bainite in Steels', The Institute of Materials, London. BHADESHIA, H.K.D.B. and EDMONDS, D. V., (1979) 'The Bainite Transformation in a Silicon Steel', Metallurgical Transactions A, lOA, p. 895-907. BHADESHIA, H. K. D. H. and WAUGH, A. R., (1982) 'Bainite: An atom probe study of the Incomplete-Reaction phenomenon', Acta Metallurgica, 30, p. 775-784. BHADESHIA, H. K. D. H., SWENSSON, L.-E. and GRETOFT, B., (1987) 'Theory for allotriomorphic ferrite formation in steel weld deposits', Welding metallurgy of structural steels, ed. J. Y. Koo, TMS-AIME, Warrendale, Penn., USA. p. 517-530. BHADESHIA, H. K. D. H. and CHRISTIAN, J. W., (1990) 'Bainite in Steels', Metallurgical Transactions A, 21A, p. 767-797. BJARBO, A., (1991) Ph.D. Thesis, Royal Institute of Technology, Sweden. BJORKLAND, S., DONAGHEY, L. F. and HILLERT, M., (1972) 'The effect of alloying elements on the rate of Ostwald ripening of cementite in steel', Acta Me tallurgica, 20, p.867-874. 220 BOWEN, A. W. and LEAK, G. M., (1970) 'Diffusion in Bee Iron Base Alloys', Metallurgical Transactions, 1, p. 2767-2773. BRIGGS, J. Z. and PARKER, T. D., (1965) 'The Super 12%Cr Steels', Climax Molybdenum Company. CAHN, J. W., (1956) 'Transformation kinetics during continuous cooling', Acta Metallurgica, 4, p. 572. CANE, B. J., (1986) 'Present Status of Predictive Methods for Remanent Life Assessment and Future Developments', Materials Forum, 9, p. 5-33. CANE, B. J. and TOWNSEND, R. D., (1984) 'Prediction of Remaining Life in LowAlloy Steels', Central Electricity Generating Board Report TPRD /L/267 4/N84. CANE, B. J. and WILLIAMS, J. A., (1987) 'Remaining Life Prediction of High Temperature Materials', International Metals Reviews, 32 (5), p. 241-262. CARINCI, G. M., HETHERINGTON, M. G. and OLSON, G. B., (1988) 'M2C precipitation in AP1410 steel', Journal de Physique (Paris) C6, 49, p. 311-316. CARRUTHERS, R. B. and DAY, R. V., (1968) 'The Spheroidization of Some Ferritic Superheater Steels', Central Electricity Generating Board Report SSD/NE/R 138. CARRUTHERS, R. B. and COLLINS, M. J., (1980) Central Electricity Generating Board Report, NER/SSD/M/80/327. CARRUTHERS, R. B. and COLLINS, M. J., (1981) 'Quantitative Microanalysis with High Spatial Resolution,' (Conf. Proc.), London, The Metals Society. p. 108-11I. CHANCE, J. and RIDLEY, N., (1981) 'Chromium Partitioning During Isothermal Transformation of a Eutectoid Steel', Metallurgical Transactions, 12A, p. 1205-1213. CHRISTIAN, J. W., (1975) 'Theory of transformations in metals and alloys', Part I, 2nd Edition, Oxford, Pergamon Press. CHRISTIAN, J. W. and KNOWLES, K. M., (1981) 'Solid-solid phase Transformations', Eds. H.I.Aaronson et al., TMS-AIME, Warrendale, Penn- sylvania. p. 1175. CHRISTIAN, J. W. and EDMONDS, D. V., (1984) 'The Bainite Transformation', Phase Transformations in Ferrous Alloys, ASM, Metals Park, Ohio. p. 293-326. CRANK, J., (1975) 'The mathematics of Diffusion', 2nd Edition, Oxford, Clarendon Press. DAVISON, J. K. and YELDHAM, D. E., (1975) 'Boiler Tube Failures and their Causes', Materials in Power Plant, Series 3, Number 3. DU, X., (1986) Ph.D. Thesis, Sheffield University, England. 221 DUNLOP, G. 1. and HONEYCOMBE, R. W. K., (1976) 'Ferrite morphologies and carbide precipitation in a Cr-Mo-V creep-resisting steel', Metal Science, 10, p. 124-132. EDMONDS, D. V. and HONEYCOMBE, R. W. K., (1973) 'Structure and properties of an isothermally transformed Fe-4Mo-O.2C alloy', Journal of the Iron and Steel Institute, 211, p. 209-216. FRANCK, F. J., TAMBUYSER, P. and ZUBANI, 1., (1982) 'X-ray powder diffraction evidence for the incorporation of Wand Mo into M23C6 extracted from high temperature alloys', Journal of Materials Science, 17, p. 3057-3065. FRIDBERG, J., TORNDAHL, L-E, and HILLERT, M., (1969) 'Diffusion in Iron', Jernkont. Ann, 153, p. 263-276. GOLDSCHMIDT, H. J., (1948) 'The Structure of Carbides in Alloy Steels', Journal of the Iron and Steel Institute, 160, p. 345-362. GOLDSTEIN, J. 1., WILLIAMS, D. B. and CLIFF, G., (1986) 'Quantitative X-ray analysis' in 'Principles of Analytical Electron Microscopy', Ed. Joy et al. p. 155-183. GOOCH, D. J., (1982) 'Creep Fracture of 12CrMoV steel', Metal Science, 16, p. 79-88. GOOCH, D. J., (1988) 'How much longer? - Remanent life assessment of high temperature components', in 'Central Electricity Generating Board Research', Special Issue, 21, p. 60-67. GREENWOOD, G. W., (1956) 'The growth of dispersed precipitates in solutions', Acta metallurgica, 4, p. 243-248. GREENWOOD, G. W., (1969) 'Particle Coarsening', in 'The mechanism of phase transformations in crystalline solids', Institute of Metals Monograph No. 33 p. 103-110. GULLBERG, R., (1971) 'Comparison of chromium content in (Fe, Cr)23C6 carbides by electron microprobe and X-ray diffraction', Journal of the Iron and Steel Institute, 209, p. 71-72. HALE, K. F., (1975) 'Creep Failure Prediction from Observation of Microstructure in 2.25Cr1Mo Steel', in 'Physical Metallurgy of Reactor Fuel Elements', The Metals Society, London. p. 193-201. HART, R. V., (1976) 'Assessment of Remaining Creep Life Using Accelerated Stress-Rupture Tests', Metals Tech- nology, 3, p. 1-7. HECKEL, R. W. and DE GREGORIO, R. L., (1965) 'The growth and shrinkage rates of second-phase particles of various size distributions', Trans- actions of the Metallurgical Society of the A.I.M.E., 233, p. 2001-2011. HEHEMANN, R. F., (1970) 'The bainite transformation', Phase Transformations in Ferrous Alloys, ASM, Metals Park, Ohio. p. 293-326. 222 HILLERT, M., (1962) 'The formation of pearlite', in 'The Decomposition of austenite by diffusional processes', Eds. V. F. Zackay and H. Aaronson, Interscience, New York, NY. HIPPSLEY, C. A., (1981) 'Precipitation sequences in the Heat-Affected-Zone of 2.25Cr1Mo steel during stress-relief heat treatment', Metal Science, 15, p. 137-147. HODSON, S. M., (1989) MTDATA-Metallurgical and Thermochemical Databank, National Physical Laboratory, Ted- dington, Middlesex, U.K. HONEYCOMBE, R. W. K., (1976) 'Transformation from Austenite in Alloy Steels', Metallurgical Transactions A, 7A, p. 915-936. HULTGREN, A., (1947) Transactions of the American Society of Metals, 39, p. 415. HULTGREN, A., (1951) Kungl. Svenska Vetenskapsakademius Handlingar, 135, p. 403. HYAM, E. D. and NUTTING, J., (1956) 'The tempering of plain carbon steels', Journal of the Iron and Steel Institute, 184, p. 148-184. IRVINE, K. J., CROWE, D. J. and PICKERING, F. B., (1960) 'The physical metallurgy of 12% chromium steels', Journal of the Iron and Steel Institute, 195, p. 386-405. JACK, D. H. and JACK, K. H., (1973) 'Carbides and Nitrides in Steel', Materials Science and Engineering, 11, p. 1-27. KINSMAN, K. R., EICHEN, E. and AARONSON, H. I., (1975) 'Thickening Kinetics of proeutectoid ferrite plates in Fe-C alloys', Metallurgical Transactions A, 6A, p. 303-317. KLUEH, R. 1., (1978) 'Interaction solid solution hardeing in 2.25Cr1Mo steel', Materials Science and Engineering, 35, p. 239-253. KO, T. and COTTRELL, S. A., (1952) 'The formation of bainite', Journal of the Iron and Steel Institute, 175, p. 307-313. KUO, K., (1953) 'Carbides in Chromium, Molybdenum and Tungsten Steels', Journal of the Iron and Steel Institute, 173, p. 363-375. LAI, J. K. 1., CHAN, S. T. and DUGGAN, B. J., (1990) 'The development of a novel temperature indicator', High Temperature Technology, 8, p. 18. LARSON, F. R. and MILLER, J., (1952) Trans. ASME, 74, p. 765. LEE, Y. J., (1989) Ph.D. Thesis, Monash University, Australia. LEITNAKER, J. M., KLUEH, R. 1., and LAING, W. R., (1975) 'The composition of eta carbide phase in 2lCrlMo steel', Metallurgical Transactions, 6A, p. 1949-1955. 223 LIFSHIFTZ, J. M. and SLYOZOV, V. V., (1961) 'The kinetics of precipitation from supersaturated solid solutions', Journal of Physics and Chemistry of Solids, 19, p. 35-50. LUNDBERG, R., WALDENSTROM, M. and UHRENIUS, B., (1977) 'Isothermal Sections of the Fe-Cr-C system in the Temperature Range of 873-1373K', CAL- PHAD, 1, p. 159-199. MCLELLAN, R. B., RUDEE, M. L. and ISCHIBACHI, T., (1965) 'Thermodynamics of dilute interstitial solid solutions with dual site occupancy and its applica- tions to the diffusion of carbon in a-iron', Trans. Met. Soc. A.I.M.E., 233, p.1938-1948. MIDDLETON, C. J., (1986) Central Electricity Generating Board Report TPRD/L/MT0380/M86. MILLER, M. K. and SMITH, G. D. W., (1989) 'Atom probe microanalysisj Principles and applications to materials problems', Materials Re- search Society. MUKHERJEE, T., STUMPF, W. E., and SELLARS, C. M., (1968) 'Quantitative assessment of extraction replicas for particle analysis', Journal of Materials Sci- ence, 3, p. 127-135. MUKHERJEE, T., STUMPF, W. E., SELLARS, C. M. and TEGART, W. J. MCG., (1969) 'Kinetics of coarsening of carbides in chromium steels at 700°C " Journal of the Iron and Steel Institute, p. 621-631 OHMORI, Y. and HONEYCOMBE, R. W. K., (1971) 'The isothermal transformation of plain carbon steels', Proceedings ICSTIS Supplementary transactions of the Iron and Steel Institute of Japan, 11, p. 1160-1164. OKA, M. and OKAMOTO, H., (1986) 'Isothermal transformations in hypereutectoid steels', in Proceedings of International Confer- ence on martensitic transformations, ICOMAT '86, Japan Institute of Metals, p. 271-275. OLSON, G. B., KINKUS, T. J. and MONTGOMERY, J. S., (1991) 'APFIM study of multi component M2C carbide precipitation in AF1410 steel', Surface Science, 246, p. 238-245. ORIANI, R. A., (1964) 'Ostwald ripening of precipitates in solid matrices', Acta Metallurgica, 12, p. 1399-1409. PILLING, J. and RIDLEY, N., (1982) 'Tempering of 2.25 Pct Cr-1 Pct Mo Low Carbon Steels', Metallurgical Transactions, 13A, p. 557-563. PITSCH, W. and SCHRADER, A., (1958) Arch. Eisenhuettenw., 29, p. 715 PULS, M. P. and KIRKALDY, J. S., (1972) 'The Pearlite Reaction', Metallurgical Transactions A, 3A, p.2777-2796. ROBINSON, E. L., (1938) Trans. ASME, 60, p. 253. SELLARS, C. M., (1974) 'Creep Strength in Steel and High Temperature Alloys', The Metals Society, London. p. 20-30. 224 SHA, W., CHANG, L., SMITH, G. D. W., LUI CHENG and MITTEMEIJER, E. J., (1992) 'Some aspects of atom probe analysis of Fe-C and Fe-N systems', Surface Science, 266, p. 416-423. SHAMMAS, M. S., (1987) 'Remanent Life Assessment of the Ferritic Weld Heat Affected Zones by a Metallographic Mea- surement of Cavitation Damage-The 'A' Parameter', Central Electricity Generating Board Report, TPRDfLf3200fR87. SHAW, S. W. K. and QUARRELL, A. G., (1957) 'The Formation of Carbides in Low-Carbon Chromium-Vanadium Steels at 700°C " Journal of the Iron and Steel Institute, 185, p. 10-22. SMITH, R. and NUTTING, J., (1957) British Journal of Applied Physics, 7, p. 214-217. SMITH, R. and NUTTING, J., (1957) 'The Tempering of Low-Alloy Creep-Resistant Steels containing Chromium, Molybdenum, and Vanadium', Journal of the Iron and Steel Institute, 187, p. 314-329. STARK, 1., SMITH, G. D. W., and BHADESHIA, H. K. D. B., (1987) 'The element redistribution associated with the Incomplete-Reaction Phenomenon in Bainitic Steels: An atom probe investigation', Proceedings of an International Conference, 'Phase trans- formations 1987', Institute of Metals, London, Edited by G.W. Lorimer. p. 211-215. STEVENS, R. A. and LONSDALE, D., (1987) 'Electrolytic Extraction of Carbide Precipitates from Low Alloy Ferritic Steel Power Plant Components', Central Electricity Generating Board Report OED fSTB(S)f87 f0028fR. STRANGWOOD, M. and BHADESHIA, H. K. D. H., (1987) 'Solute segregation, oxygen content, and the transformation start temperature of steel welds', Proceedings of International Conference on Welding Metallurgy of Structural Steels, AIME, Warrendale, Pennslyvania, Edited by J.Y. Koo p. 495-504. STUART, H. and RIDLEY, N., (1966) 'Thermal Expansion of Cementite and Other Phases', Journal of the Iron and Steel Institute, 204, p. 711-717. TILLMAN, C. J. and EDMONDS, D. V., (1974) 'Alloy carbide precipitation and aging during high-temperature isothermal decomposition of an Fe-4Mo-0.2C alloy steel', Metals Technology, 1, p. 456-461. TITCHMARSH, J. M., (1978) 'The Identification of Second-Phase Particles in Steels using an Analytical Transmission Elec- tron Microscope', in Proc. 9th Inst. Congress on Electron Microscopy, J .M. Sturgess, ed., Microscopical Society of Canada, Toronto. 1 p. 618-619. TOFT,1. H. and MARSDEN, R. A., (1961) 'The Structure and Properties of 1CrO.5MoSteel After Service in Central Electricity Generating Board Power Stations', Journal of the Iron and Steel Institute, Special Report 70, p. 276-294. VENGOPULAN, D. and KIRKALDY, J. S., (1978) 'Hardenability Concepts with Applications to Steels', Conference Proceedings, 249, New York, AIME. WADA, M., HOSOI, K. and NISHIKAWA, 0., (1982) 'FIM observation of 2.25Cr1Mo steel', Acta Metallurgica, 30, p. 1013-1018. 225 WAGNER, C., (1961) 'Theorie der Alterung von NiederschHigendurch Umlosen', Z. Elektrochem, 65, p. 581-59l. WAUGH, A. R., RICHARDSON, C. H. and JENKINS, R., (1992) 'APFIM 200 - A refiectron-based atom probe', Surface Science, 266, p. 501-505. WESTGREN, A., PHRAGMEN G. and NEGRESCO, T. R., (1928) 'On the structure of the iron-chromium-carbon system', Journal of the Iron and Steel Institute, 117(1), p. 383-400. WILLIAMS, P. R., MILLER, M. K., BEAVEN, P. A. and SMITH, G. D. W., (1979) 'Fine scale analysis of partitioning in pearlitic steels,' in Proceedings of the York phase trans- formations meeting, 2, p. 11-98. WILSON, M., (1986) 'The Assessment of the Remaining Creep Life of Carbon and Low Alloy Steel Power Plant Components', Materials Forum, 9, p. 53-66. WOODFORD, D. A., (1974) Proc. International conference on Creep and Fatigue in Elevated Temperature Applications, Philadelphia, 1973. Sheffield 1974. WOODHEAD, J. H. and QUARRELL, A. G., (1965) 'Role of Carbides in Low-alloy creep Resisting Steels', Journal of the Iron and Steel Institute, 203, p. 605-620. YAKEL, H. L., (1985) 'Crystal structures of stable and metastable iron-containing carbides', International Metals Reviews, 30(1), p. 17-40. YU, J., (1989) 'Carbide stability diagrams in 2.25Cr1Mo steels', Metallurgical Transactions A, 20A, p. 1561- 1564. 226