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Modelling the carbide composition changes in 12 Cr12 Mo14 V steel during long-term tempering
Materials Science and Engineering, A 155 (1992) 197-205
197
Modelling the carbide composition changes in 1Cr1 MoW steel during long-term tempering X. D u a n d J. A . W h i t e m a n
University of Sheffield, Department of Metallurgy, Mappin Street, Sheffield (UK) R. C. Thomson and H. K. D. H. Bhadeshia University of Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge CB2 3QZ (UK) (Received December 17, 1991 )
Abstract The composition of pearlitic cementite in a ½Cr½Mo¼Vsteel has been extensively studied for long tempering times at a number of different temperatures. The chromium content of the cementite is found to increase steadily with time as the microstructure is tempered, at the expense of the iron content. Transformation of the cementite to alloy carbides occurs at long tempering times. The composition changes in the cementite have been modelled theoretically using numerical methods. There is excellent agreement between the predictions of the model and the experimental results. The dependence of composition on particle size has been studied and has been shown not to be significant because of the relatively large size and low chromium concentration of the pearlitic cementite. It is therefore possible to estimate an effective service temperature of components of ½Cr½MolVsteel in power plant for use in prediction of their remanent life.
1. Introduction steels In the power generation industry ~Cr~MoW 1 1 are used extensively for high pressure (up to 180 bar) and high temperature (about 565 °C) applications such as boiler headers and steam pipes. The exact operating temperature of each individual component is difficult to estimate because of fluctuations in steam temperatures and differences between the metal and steam temperatures. This uncertainty can lead to conservative estimates of residual life and wastage due to premature plant closure. It has been proposed that determination of indirect parameters, such as carbide size, shape and composition, which are functions of temperature and time can be used to estimate the thermal history of a component. In bainitic microstructures in which cementite grows without partitioning of the substitutional alloying elements, the initial composition of bainitic cementite can be readily estimated. This work, however, focusses on 1 1 1 the ferritic-pearlitic microstructures in a ~Cr~MoW steel. Investigations by Carruthers and Collins [1] on this material have shown that changes in the substitutional solute concentration of cementite may be a viable technique for the estimation of an effective service temperature. 0921-5093/92/$5.00
The pearlite reaction is fundamentally different from that of bainite in that it is a reconstructive 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 [2, 3] for all transformation conditions. Paraequilibrium growth of pearlite does not occur, nor does the cementite have an equilibrium composition. Therefore there is an uncertainty 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 dimensions [4]. Consequently it is of considerable interest, from both an industrial and an academic point of view, to investigate any changes in carbide characteristics with tempering heat treatments.
2. Experimental details
2.1. Materialsand heat treatment The material used in these experiments was a standard ~Cr2Mo~V 1 1 steel supplied by National Power and © 1992 - Elsevier Sequoia. All rights reserved
198
x. Du et al.
/ Modelling carbide composition changes
designated as cast M1. The chemical composition is given in Table 1. The samples were normalized from an austenitizing temperature of 950 °C and then tempered at 690 °C for 1 h in order to simulate the commercial stress-relief heat treatment for this steel. Specimens were then machined to 10 x 20 mm 2 followed by tempering at a variety of temperatures between 640 and 525 °C in a specially designed furnace [5] 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 _+2 °C. There was no significant oxidation of decarburization 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 cementite compositions of samples tempered continuously and discontinuously were, as expected, the same within experimental error. 2.2 Extraction replica preparation Samples were ground on SiC paper to 1200 grit and then polished using 1 / t m diamond-coated cloth. They were then lightly etched in 4% nital for cementite extraction from the shorter time heat treatments, and in Villela's reagent (saturated picral and 5% HC1 solution) for extraction of the larger alloy carbides from the longer-term heat treatments. A carbon coating of 2 0 0 - 3 0 0 A (colour blue-brown) was deposited in a vacuum of 10 -s Torr onto the etched specimens. This was then removed electrolytically using 4% nital for specimens previously etched in 4% nital, and 10% nital for those previously etched in Villela's reagent. The replicas were left in industrial methylated spirits for some hours to remove any impurities before being floated off in distilled water and collected on 100 mesh copper support grids. 2.3. Microanalysis Microanalysis was performed on extraction replicas in both a 100 kV Philips 400T and a 200 kV Hitachi H - 7 0 0 H transmission electron microscope, each equipped with an E D A X 9100 energy-dispersive X-ray analysis facility. 50000, 25000 and 25000 counts were preset in the Fe K a , Mo K a and V K a windows respectively to keep a constant statistical error. Counts from the carbon replica background were kept at 200_+50 counts s -1 in the Hitachi H - 7 0 0 H microscope and 100_+ 50 counts s -1 in the Philips 400T microscope to ensure a constant-intensity beam. The incident spot size was 1 0 0 0 / k and all the analyses were done with the spot covering the whole particle. At least 20 separate analyses were performed
TABLE 1. Chemical composition of the ½Cr½Mo¼Vsteel (wt.%) Element
Content in cast M 1
C Si Mn P S Cr Mo V Ni Cu
0.14 0.23 0.61 O.0O7 0.023 0.36 0.66 0.26 0.21 0.13
on each different carbide per heat treatment. 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 an accurate measurement of the average concentration. 2.4. Particle size measurements The size of each carbide particle was determined by measuring a number of random intercepts across it on a transmission electron microscope photographic negative. Hence particle size is expressed in terms of a mean linear intercept. This particular 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.
3. Experimental results 3.1. Microstructure and carbide morphologies The microstructures after the normalization heat treatment at 950 °C were mixtures of ferrite, pearlite and bainite. The development of the microstructure as tempering proceeds is illustrated in Fig. 1; the transmission electron micrographs were taken from carbon extraction replicas and are therefore specific to the carbide distribution. After the stress-relief heat treatment at 690 °C for 1 h the main ferritic and pearlitic regions were still clearly defined; however, it can be seen from Fig. l(b) that the pearlitic cementite had already begun to spheroidize. Further coarsening occurs during prolonged tempering. Figures 1(c) and l(d) illustrate this in specimens tempered at 640 °C for 483 h and 2996 h respectively. Cementite particles located at the ferrite grain boundaries were generally found to be coarser
X. Du et al. /
Modellingcarbide composition changes
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, M23C~, 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. M23C~, is found after 5 8 5 0 h at 640°C and M~,C after 9353 h, whereas after 9381 h at 565 °C only M23C ~ is found, and cementite remains the stable carbide after 12 887 h tempering at 525 °C. In addition to the chromium-rich M3C, M23C6and MvC 3 carbides, a fine dispersion of molybdenum- and vanadium-based carbides, M2C and MC respectively,
199
also precipitated during the stress-relief heat treatment and persisted throughout the tempering process. 3.2. Composition of the carbides The representative energy-dispersive X-ray spectra of the various carbides are presented in Fig. 2. M3C is characterized by low vanadium and molybdenum concentrations, whereas M23C~, has much higher chromium and molybdenum contents. M~,C contains a slightly smaller chromium content than M23C~,, but can be identified by its high molybdenum and silicon contents. Figure 2(d) illustrates the characteristic spectra from MC, a vanadium-based carbide which can dissolve some molybdenum, and Fig. 2(e) that from M2C, which is molybdenum rich, although it contains a signi-
Fig. 1. The development of the carbide distribution during long-term tempering at 640 °C: (a) after normalizing at 950 °C; (b) as (a), but additionally tempered at 690 °C for 1 h; (c) tempered at 640 °C for 483 h; (d) tempered at 640 °C for 1996 h.
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Modellingcarbide composition changes
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Fig. 2. Characteristic energy-dispersive X-ray spvctra for the various alloy carbides found to precipitate during the tempering heat treatments: (a) M3C; (b) M23C6; (c) M6C; (d) MC; (e) M2C.
ficant 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 per cent, allowing for the stoichiometric carbon content in each alloy carbide (for example, 25 at.% C in cementite), are summarized in Table 2. The chromium content of the cementite was found to increase steadily with time at the tempering 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 M23C 6 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 M23C 6 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 M23C 6 occurred after the cementite had reached satu-
TABLE 2. Chemical composition ranges of the carbides M3C, M23C6 and M6C (at.%) Carbide
V
Cr
Mn
Mo
C
M3C Mz3C6 M6C
0.7-1.1 0.3-0.6 2.0-3.0
2.0-7.6 9.0-15.0 5.5-8.0
2.0-10.0 6.0-8.0 6.0-8.0
0.6-1.0 3.0-5.0 16.0-20.0
25.0 20.7 14.3
ration. The literature suggestst that the alloy carbide sequence usually involves first a transformation to M7C 3 prior to M2aC 6, but this sequence was not observed experimentally. A possible explanation for this is that the chromium content of the steel, and its ratio to the molybdenum content, was too low for MvC 3 to form. It is also probable that the small molybdenum-based carbides in the matrix limited the molybdenum content of the larger M23C 6 and M6C carbides, and stabilized the M23 C 6 to longer times.
4. Modelling of the diffusion process 4.1. Thermodynamic calculations Phase diagram calculations were performed using a computer package (called MTDATA) developed by the
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Modelling carbide composition changes
National Physical Laboratory, in which the equilibria in multicomponent multiphase systems are determined using critically assessed thermodynamic data [6]. The calculations are based on the minimization of the total Gibbs free energy for the system, and yield the chemistries and quantities of the phases in equilibrium at any temperature for the specified average composition (in this instance, steel M1). The calculations allowed for the elements iron, chromium, manganese, molybdenum, carbon, vanadium, silicon, nickel, tin, copper, phosphorus and sulphur and the phases M3C , M7C3, M 6C, M23 C6, Mo 2C, 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 (MozC is assumed to have all transformed to M6C under equilibrium conditions). Calculations were then performed by suppressing all carbides except cementite, thereby allowing the equilibria between the metastable cementite and the ferrite matrix to be studied. The calculated chromium levels in the ferrite and cementite are presented in Table 3. These data are also plotted in Fig. 3. It can be seen that the maximum permitted concentration of chromium in cementite increases with decreasing temperature, as observed experimentally. The equilibria between ferrite and M23C6 and between ferrite and M6C can also be calculated. The calculated equilibrium chromium concentration in M23C 6 varies between 7 and 9 at.% from 690 to 525 °C respectively, and that in M6C from 2 to 4 at.% over the same temperature range. These equilibrium calculations also predict that the level of molybdenum at equi-' librium is 10 at.% in M23C 6 and 45 at.% in M6C.
4.2. Finite difference modelling Of all the substitutional solute elements, chromium is ideal as an indicator of composition change; the iror~ content mostly mirrors the changes in chromium content. It can be seen in Fig. 3 that the absolute levels of chromium and manganese in cementite are similar at the temperatures of interest; however, chromium is of greater importance when transformation to chromiumbased alloy carbides occurs. Molybdenum has a much larger atomic mass compared with iron, chromium or manganese. Since the microanalytical 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). A computer model has been developed [7] to study the kinetics of changes in cementite composition during tempering. This uses a finite difference method
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TABLE 3. Equilibriumconcentration(at.%) of chromiumin ferrite and cementite calculated using MTDATAas a function of temperature in steel M1 Temperature (°C)
Chromium content
690 640 630 620 610 590 575 565 525
N \
Ferrite
Cementite
0.25 0.23 0.22 0.22 0.21 0.20 0.19 0.18 0.16
5.53 6.35 6.53 6.72 6.91 7.31 7.63 7.85 8.77
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Temperature /'C Fig. 3. Equilibrium substitutional alloying content of cementite as a function of temperature, calcuated using MTDATA: manganese; ..... , chromium;- - -, molybdenum.
to provide numerical solutions to the equations governing the diffusion processes. Soft impingement, i.e. the overlap of the diffusion fields between adjacent particles, is also taken into account. The input parameters required by the model are the starting concentrations in the cementite and the ferrite, the concentrations at the interface, the temperature, the diffusion coefficients of chromium in cementite and ferrite (which are assumed to be the same due to there being no reliable data on the diffusion of chromium in cementite itself) and the size of the particle. The initial compositions in the cementite and ferrite are obtained by assuming that there is no partitioning of the substitutional solute elements during transformation. Interface concentrations are determined by the requirement that there should be no build-up of solute at the interface, and they therefore gradually approach the equilibrium values. The diffusion coefficients used in the model are chemical interdiffusion coefficients
X. Duet al. /
202
Modelling carbide composition changes
[8]. The value for the interdiffusion coefficient D of chromium in iron is given by D = D 0 exp ( - ~ - T ) where D Ois 1.5 × 10-4 m 2 s- l, Q is 240 000 J mol- 1, R is the gas constant and T is the temperature in Kelvins. The particle size used in the model was 175 nm; 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 Fig. 4 for particles of 150, 175 and 200 nm 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 1 h 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 Figs. 5(a)-5(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 Mo2 C in the steel, precipitated during the stress-relief heat treat-
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ment, 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 M23C 6 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 M23C 6 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 molybdenum is tied up in fine Mo2C precipitates, reducing the amount of molybdenum available for inclusion in M23C 6 and M 6C. The effect of the Mo2C 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 cementite in pearlitic steels is found to be somewhere between equilibrium and paraequilibrium 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 partitioning of substitutional solute elements during transformation. It can be seen in Fig. 5 that there is an error in the predicted starting composition of the pearlitic cementite after the stress-relief heat treatment because any partitioning occurring on transformation is not taken into account. To allow for this problem with the initial 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 tempering at 690 °C for 18 h rather than the 1 h 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 predicted and measured values is shown by the dotted curves superimposed on the graphs in Fig. 5. This problem will be overcome when a theoretical basis for the precipitation of pearlitic cementite during transformation can be established. 4.3. Particle size
It has been demonstrated [7] that for the early stages of carbide enrichment (in the absence of soft impingement in the matrix) the kinetics of composition
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Fig. 5. A comparison of experimental measurements of chromium concentration in cementite with computer modelling, at (a) 640 °C, (b) 630 °C, (c) 620 °C, (d) 610 °C, (e) 590 °C, (f) 575 °C, (g) 565 °C and (h) 525 °C: e, M3C; + , M23C6; z~, M6C; , model; ..... , fixed (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.
change are given by
t~ -
16Da(c~O
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where tc is the time required for the carbide to reach a concentration c ° x ° is the thickness of the carbide
plate, D a is the diffusion coefficient for the substitutional alloying element in ferrite (assumed to also represent diffusion in the carbide), ca 0 is the concentration of the substitutional solute element of interest and ~ is the corresponding bulk concentration in the alloy. This equation shows clearly that the degree of enrichment to be found after any specified heat treatment will depend
X. Duet al. /
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Particle size / n m (f) Particle size / n m (el Fig. 6. Chromium concentration in cementite plotted against particle size for specimens tempered for various times: (a) normalized at 950 °C and tempered at 690 *C for 1 h; (b)-(f) tempered at 640 °C for (b) 51 h, (c) 483 h, (d) 1482 h, (e) 1842 h and (f) 2996 h.
on the particle size. Consequently, measurements of carbide compositions should be presented alongside the corresponding particle sizes, the latter measured in a way related to the problem. 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 Figs. 6(a)-6(f). The situation is compli-
cated by the fact that the initial cementite lamellae appe/tr to spheroidize 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
x. Duet al.
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Modelling carbide composition changes
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 c o varies inversely with particle size x °. Thus c o will only be sensitive to x ° when the latter is small. This is illustrated in Fig. 4, where variations in x ° within the expected range for the present study do not cause very large changes in c o when compared with experimental error. Nevertheless it is evident from the data presented in Fig. 6 that the dependence of c o on x 0 begins to emerge with statistical significance only at the longest tempering time studied. It should be noted that even longer times could not be studied because of the onset of alloy carbide formation.
5. Conclusions 1 1 l In a :Cr~MoaV steel after normalization at 950 °C followed by a stress-relief heat treatment at 690 °C for I h, the cementite composition varies on further tempering at temperatures in the range 640-525 °C. The chromium and manganese contents of the cementite increase with tempering time at the expense of the ferrite content. After the equilibrium composition ot the cementite has been reached, transformation to the alloy carbides M23C ~ 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. Comparison of the experimentally determined chromium concentration in cementite, after a particular operating time, with the
205
predictions of the numerical model of the diffusion process can therefore be used to estimate the service temperature of power plant components.
Acknowledgments Financial support is acknowledged from the Chinese Government by X. Du, and from the Science and Engineering Research Council and National Power by R. C. Thomson. H. K. D. H. Bhadeshia's contribution was made under the auspices of the Atomic Arrangement, Design and Control project, which is a collaborative venture between the University of Cambridge and the Japan Research and Development Corporation. Special thanks are due to Dr. M. J. Collins of the Scientific Services Department of the former Central Electricity Generating Board, North Eastern Region (X. Du). R. C. Thomson is grateful to Professor C. Humphreys for the provision of laboratory facilities at the University of Cambridge.
References 1 R.B. Carruthers and M. J. Collins, Quantitative Microanalysis with High Spatial Resolution, Metals Society, London, 1981, pp. 108-111. 2 S.A. Al-Salman, G. W. Lorimer and N. Ridley, Metall. Trans. A, 10(1979)1703-1709. 3 J. Chance and N. Ridley, Metall. Trans. A, 12 (1981) 1205-1213. 4 M. Hillert, The Formation of Pearlite, in V. F. Zackay and H. Aaronson (eds.), The Decomposition of Austenite by Diffusional Processes, Interscience, New York, NY, 1962, pp. 197-247. 5 R. B. Carruthers and M. J. Collins, CEGB Rep. NER/SSD/M/ 80/327, 1980. 6 MTDA TA -- Metallurgical and Thermochemical Databank,
National Physical Laboratory, Teddington, 1989. 7 H. K. D. H. Bhadeshia, Mater. Sci. TeehnoL, 5 (1989) 131-137. 8 J. Fridberg, L.-E. T6rndahl and M. Hillert, Jernkontorets Ann., 153 (1969) 263-276.
197
Modelling the carbide composition changes in 1Cr1 MoW steel during long-term tempering X. D u a n d J. A . W h i t e m a n
University of Sheffield, Department of Metallurgy, Mappin Street, Sheffield (UK) R. C. Thomson and H. K. D. H. Bhadeshia University of Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge CB2 3QZ (UK) (Received December 17, 1991 )
Abstract The composition of pearlitic cementite in a ½Cr½Mo¼Vsteel has been extensively studied for long tempering times at a number of different temperatures. The chromium content of the cementite is found to increase steadily with time as the microstructure is tempered, at the expense of the iron content. Transformation of the cementite to alloy carbides occurs at long tempering times. The composition changes in the cementite have been modelled theoretically using numerical methods. There is excellent agreement between the predictions of the model and the experimental results. The dependence of composition on particle size has been studied and has been shown not to be significant because of the relatively large size and low chromium concentration of the pearlitic cementite. It is therefore possible to estimate an effective service temperature of components of ½Cr½MolVsteel in power plant for use in prediction of their remanent life.
1. Introduction steels In the power generation industry ~Cr~MoW 1 1 are used extensively for high pressure (up to 180 bar) and high temperature (about 565 °C) applications such as boiler headers and steam pipes. The exact operating temperature of each individual component is difficult to estimate because of fluctuations in steam temperatures and differences between the metal and steam temperatures. This uncertainty can lead to conservative estimates of residual life and wastage due to premature plant closure. It has been proposed that determination of indirect parameters, such as carbide size, shape and composition, which are functions of temperature and time can be used to estimate the thermal history of a component. In bainitic microstructures in which cementite grows without partitioning of the substitutional alloying elements, the initial composition of bainitic cementite can be readily estimated. This work, however, focusses on 1 1 1 the ferritic-pearlitic microstructures in a ~Cr~MoW steel. Investigations by Carruthers and Collins [1] on this material have shown that changes in the substitutional solute concentration of cementite may be a viable technique for the estimation of an effective service temperature. 0921-5093/92/$5.00
The pearlite reaction is fundamentally different from that of bainite in that it is a reconstructive 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 [2, 3] for all transformation conditions. Paraequilibrium growth of pearlite does not occur, nor does the cementite have an equilibrium composition. Therefore there is an uncertainty 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 dimensions [4]. Consequently it is of considerable interest, from both an industrial and an academic point of view, to investigate any changes in carbide characteristics with tempering heat treatments.
2. Experimental details
2.1. Materialsand heat treatment The material used in these experiments was a standard ~Cr2Mo~V 1 1 steel supplied by National Power and © 1992 - Elsevier Sequoia. All rights reserved
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/ Modelling carbide composition changes
designated as cast M1. The chemical composition is given in Table 1. The samples were normalized from an austenitizing temperature of 950 °C and then tempered at 690 °C for 1 h in order to simulate the commercial stress-relief heat treatment for this steel. Specimens were then machined to 10 x 20 mm 2 followed by tempering at a variety of temperatures between 640 and 525 °C in a specially designed furnace [5] 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 _+2 °C. There was no significant oxidation of decarburization 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 cementite compositions of samples tempered continuously and discontinuously were, as expected, the same within experimental error. 2.2 Extraction replica preparation Samples were ground on SiC paper to 1200 grit and then polished using 1 / t m diamond-coated cloth. They were then lightly etched in 4% nital for cementite extraction from the shorter time heat treatments, and in Villela's reagent (saturated picral and 5% HC1 solution) for extraction of the larger alloy carbides from the longer-term heat treatments. A carbon coating of 2 0 0 - 3 0 0 A (colour blue-brown) was deposited in a vacuum of 10 -s Torr onto the etched specimens. This was then removed electrolytically using 4% nital for specimens previously etched in 4% nital, and 10% nital for those previously etched in Villela's reagent. The replicas were left in industrial methylated spirits for some hours to remove any impurities before being floated off in distilled water and collected on 100 mesh copper support grids. 2.3. Microanalysis Microanalysis was performed on extraction replicas in both a 100 kV Philips 400T and a 200 kV Hitachi H - 7 0 0 H transmission electron microscope, each equipped with an E D A X 9100 energy-dispersive X-ray analysis facility. 50000, 25000 and 25000 counts were preset in the Fe K a , Mo K a and V K a windows respectively to keep a constant statistical error. Counts from the carbon replica background were kept at 200_+50 counts s -1 in the Hitachi H - 7 0 0 H microscope and 100_+ 50 counts s -1 in the Philips 400T microscope to ensure a constant-intensity beam. The incident spot size was 1 0 0 0 / k and all the analyses were done with the spot covering the whole particle. At least 20 separate analyses were performed
TABLE 1. Chemical composition of the ½Cr½Mo¼Vsteel (wt.%) Element
Content in cast M 1
C Si Mn P S Cr Mo V Ni Cu
0.14 0.23 0.61 O.0O7 0.023 0.36 0.66 0.26 0.21 0.13
on each different carbide per heat treatment. 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 an accurate measurement of the average concentration. 2.4. Particle size measurements The size of each carbide particle was determined by measuring a number of random intercepts across it on a transmission electron microscope photographic negative. Hence particle size is expressed in terms of a mean linear intercept. This particular 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.
3. Experimental results 3.1. Microstructure and carbide morphologies The microstructures after the normalization heat treatment at 950 °C were mixtures of ferrite, pearlite and bainite. The development of the microstructure as tempering proceeds is illustrated in Fig. 1; the transmission electron micrographs were taken from carbon extraction replicas and are therefore specific to the carbide distribution. After the stress-relief heat treatment at 690 °C for 1 h the main ferritic and pearlitic regions were still clearly defined; however, it can be seen from Fig. l(b) that the pearlitic cementite had already begun to spheroidize. Further coarsening occurs during prolonged tempering. Figures 1(c) and l(d) illustrate this in specimens tempered at 640 °C for 483 h and 2996 h respectively. Cementite particles located at the ferrite grain boundaries were generally found to be coarser
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Modellingcarbide composition changes
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, M23C~, 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. M23C~, is found after 5 8 5 0 h at 640°C and M~,C after 9353 h, whereas after 9381 h at 565 °C only M23C ~ is found, and cementite remains the stable carbide after 12 887 h tempering at 525 °C. In addition to the chromium-rich M3C, M23C6and MvC 3 carbides, a fine dispersion of molybdenum- and vanadium-based carbides, M2C and MC respectively,
199
also precipitated during the stress-relief heat treatment and persisted throughout the tempering process. 3.2. Composition of the carbides The representative energy-dispersive X-ray spectra of the various carbides are presented in Fig. 2. M3C is characterized by low vanadium and molybdenum concentrations, whereas M23C~, has much higher chromium and molybdenum contents. M~,C contains a slightly smaller chromium content than M23C~,, but can be identified by its high molybdenum and silicon contents. Figure 2(d) illustrates the characteristic spectra from MC, a vanadium-based carbide which can dissolve some molybdenum, and Fig. 2(e) that from M2C, which is molybdenum rich, although it contains a signi-
Fig. 1. The development of the carbide distribution during long-term tempering at 640 °C: (a) after normalizing at 950 °C; (b) as (a), but additionally tempered at 690 °C for 1 h; (c) tempered at 640 °C for 483 h; (d) tempered at 640 °C for 1996 h.
200
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Modellingcarbide composition changes
Fear V Kcx
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Fig. 2. Characteristic energy-dispersive X-ray spvctra for the various alloy carbides found to precipitate during the tempering heat treatments: (a) M3C; (b) M23C6; (c) M6C; (d) MC; (e) M2C.
ficant 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 per cent, allowing for the stoichiometric carbon content in each alloy carbide (for example, 25 at.% C in cementite), are summarized in Table 2. The chromium content of the cementite was found to increase steadily with time at the tempering 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 M23C 6 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 M23C 6 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 M23C 6 occurred after the cementite had reached satu-
TABLE 2. Chemical composition ranges of the carbides M3C, M23C6 and M6C (at.%) Carbide
V
Cr
Mn
Mo
C
M3C Mz3C6 M6C
0.7-1.1 0.3-0.6 2.0-3.0
2.0-7.6 9.0-15.0 5.5-8.0
2.0-10.0 6.0-8.0 6.0-8.0
0.6-1.0 3.0-5.0 16.0-20.0
25.0 20.7 14.3
ration. The literature suggestst that the alloy carbide sequence usually involves first a transformation to M7C 3 prior to M2aC 6, but this sequence was not observed experimentally. A possible explanation for this is that the chromium content of the steel, and its ratio to the molybdenum content, was too low for MvC 3 to form. It is also probable that the small molybdenum-based carbides in the matrix limited the molybdenum content of the larger M23C 6 and M6C carbides, and stabilized the M23 C 6 to longer times.
4. Modelling of the diffusion process 4.1. Thermodynamic calculations Phase diagram calculations were performed using a computer package (called MTDATA) developed by the
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Modelling carbide composition changes
National Physical Laboratory, in which the equilibria in multicomponent multiphase systems are determined using critically assessed thermodynamic data [6]. The calculations are based on the minimization of the total Gibbs free energy for the system, and yield the chemistries and quantities of the phases in equilibrium at any temperature for the specified average composition (in this instance, steel M1). The calculations allowed for the elements iron, chromium, manganese, molybdenum, carbon, vanadium, silicon, nickel, tin, copper, phosphorus and sulphur and the phases M3C , M7C3, M 6C, M23 C6, Mo 2C, 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 (MozC is assumed to have all transformed to M6C under equilibrium conditions). Calculations were then performed by suppressing all carbides except cementite, thereby allowing the equilibria between the metastable cementite and the ferrite matrix to be studied. The calculated chromium levels in the ferrite and cementite are presented in Table 3. These data are also plotted in Fig. 3. It can be seen that the maximum permitted concentration of chromium in cementite increases with decreasing temperature, as observed experimentally. The equilibria between ferrite and M23C6 and between ferrite and M6C can also be calculated. The calculated equilibrium chromium concentration in M23C 6 varies between 7 and 9 at.% from 690 to 525 °C respectively, and that in M6C from 2 to 4 at.% over the same temperature range. These equilibrium calculations also predict that the level of molybdenum at equi-' librium is 10 at.% in M23C 6 and 45 at.% in M6C.
4.2. Finite difference modelling Of all the substitutional solute elements, chromium is ideal as an indicator of composition change; the iror~ content mostly mirrors the changes in chromium content. It can be seen in Fig. 3 that the absolute levels of chromium and manganese in cementite are similar at the temperatures of interest; however, chromium is of greater importance when transformation to chromiumbased alloy carbides occurs. Molybdenum has a much larger atomic mass compared with iron, chromium or manganese. Since the microanalytical 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). A computer model has been developed [7] to study the kinetics of changes in cementite composition during tempering. This uses a finite difference method
201
TABLE 3. Equilibriumconcentration(at.%) of chromiumin ferrite and cementite calculated using MTDATAas a function of temperature in steel M1 Temperature (°C)
Chromium content
690 640 630 620 610 590 575 565 525
N \
Ferrite
Cementite
0.25 0.23 0.22 0.22 0.21 0.20 0.19 0.18 0.16
5.53 6.35 6.53 6.72 6.91 7.31 7.63 7.85 8.77
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Temperature /'C Fig. 3. Equilibrium substitutional alloying content of cementite as a function of temperature, calcuated using MTDATA: manganese; ..... , chromium;- - -, molybdenum.
to provide numerical solutions to the equations governing the diffusion processes. Soft impingement, i.e. the overlap of the diffusion fields between adjacent particles, is also taken into account. The input parameters required by the model are the starting concentrations in the cementite and the ferrite, the concentrations at the interface, the temperature, the diffusion coefficients of chromium in cementite and ferrite (which are assumed to be the same due to there being no reliable data on the diffusion of chromium in cementite itself) and the size of the particle. The initial compositions in the cementite and ferrite are obtained by assuming that there is no partitioning of the substitutional solute elements during transformation. Interface concentrations are determined by the requirement that there should be no build-up of solute at the interface, and they therefore gradually approach the equilibrium values. The diffusion coefficients used in the model are chemical interdiffusion coefficients
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202
Modelling carbide composition changes
[8]. The value for the interdiffusion coefficient D of chromium in iron is given by D = D 0 exp ( - ~ - T ) where D Ois 1.5 × 10-4 m 2 s- l, Q is 240 000 J mol- 1, R is the gas constant and T is the temperature in Kelvins. The particle size used in the model was 175 nm; 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 Fig. 4 for particles of 150, 175 and 200 nm 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 1 h 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 Figs. 5(a)-5(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 Mo2 C in the steel, precipitated during the stress-relief heat treat-
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ment, 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 M23C 6 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 M23C 6 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 molybdenum is tied up in fine Mo2C precipitates, reducing the amount of molybdenum available for inclusion in M23C 6 and M 6C. The effect of the Mo2C 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 cementite in pearlitic steels is found to be somewhere between equilibrium and paraequilibrium 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 partitioning of substitutional solute elements during transformation. It can be seen in Fig. 5 that there is an error in the predicted starting composition of the pearlitic cementite after the stress-relief heat treatment because any partitioning occurring on transformation is not taken into account. To allow for this problem with the initial 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 tempering at 690 °C for 18 h rather than the 1 h 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 predicted and measured values is shown by the dotted curves superimposed on the graphs in Fig. 5. This problem will be overcome when a theoretical basis for the precipitation of pearlitic cementite during transformation can be established. 4.3. Particle size
It has been demonstrated [7] that for the early stages of carbide enrichment (in the absence of soft impingement in the matrix) the kinetics of composition
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Fig. 5. A comparison of experimental measurements of chromium concentration in cementite with computer modelling, at (a) 640 °C, (b) 630 °C, (c) 620 °C, (d) 610 °C, (e) 590 °C, (f) 575 °C, (g) 565 °C and (h) 525 °C: e, M3C; + , M23C6; z~, M6C; , model; ..... , fixed (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.
change are given by
t~ -
16Da(c~O
c0)] 2 - ?)2
where tc is the time required for the carbide to reach a concentration c ° x ° is the thickness of the carbide
plate, D a is the diffusion coefficient for the substitutional alloying element in ferrite (assumed to also represent diffusion in the carbide), ca 0 is the concentration of the substitutional solute element of interest and ~ is the corresponding bulk concentration in the alloy. This equation shows clearly that the degree of enrichment to be found after any specified heat treatment will depend
X. Duet al. /
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Particle size / n m (f) Particle size / n m (el Fig. 6. Chromium concentration in cementite plotted against particle size for specimens tempered for various times: (a) normalized at 950 °C and tempered at 690 *C for 1 h; (b)-(f) tempered at 640 °C for (b) 51 h, (c) 483 h, (d) 1482 h, (e) 1842 h and (f) 2996 h.
on the particle size. Consequently, measurements of carbide compositions should be presented alongside the corresponding particle sizes, the latter measured in a way related to the problem. 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 Figs. 6(a)-6(f). The situation is compli-
cated by the fact that the initial cementite lamellae appe/tr to spheroidize 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
x. Duet al.
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Modelling carbide composition changes
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 c o varies inversely with particle size x °. Thus c o will only be sensitive to x ° when the latter is small. This is illustrated in Fig. 4, where variations in x ° within the expected range for the present study do not cause very large changes in c o when compared with experimental error. Nevertheless it is evident from the data presented in Fig. 6 that the dependence of c o on x 0 begins to emerge with statistical significance only at the longest tempering time studied. It should be noted that even longer times could not be studied because of the onset of alloy carbide formation.
5. Conclusions 1 1 l In a :Cr~MoaV steel after normalization at 950 °C followed by a stress-relief heat treatment at 690 °C for I h, the cementite composition varies on further tempering at temperatures in the range 640-525 °C. The chromium and manganese contents of the cementite increase with tempering time at the expense of the ferrite content. After the equilibrium composition ot the cementite has been reached, transformation to the alloy carbides M23C ~ 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. Comparison of the experimentally determined chromium concentration in cementite, after a particular operating time, with the
205
predictions of the numerical model of the diffusion process can therefore be used to estimate the service temperature of power plant components.
Acknowledgments Financial support is acknowledged from the Chinese Government by X. Du, and from the Science and Engineering Research Council and National Power by R. C. Thomson. H. K. D. H. Bhadeshia's contribution was made under the auspices of the Atomic Arrangement, Design and Control project, which is a collaborative venture between the University of Cambridge and the Japan Research and Development Corporation. Special thanks are due to Dr. M. J. Collins of the Scientific Services Department of the former Central Electricity Generating Board, North Eastern Region (X. Du). R. C. Thomson is grateful to Professor C. Humphreys for the provision of laboratory facilities at the University of Cambridge.
References 1 R.B. Carruthers and M. J. Collins, Quantitative Microanalysis with High Spatial Resolution, Metals Society, London, 1981, pp. 108-111. 2 S.A. Al-Salman, G. W. Lorimer and N. Ridley, Metall. Trans. A, 10(1979)1703-1709. 3 J. Chance and N. Ridley, Metall. Trans. A, 12 (1981) 1205-1213. 4 M. Hillert, The Formation of Pearlite, in V. F. Zackay and H. Aaronson (eds.), The Decomposition of Austenite by Diffusional Processes, Interscience, New York, NY, 1962, pp. 197-247. 5 R. B. Carruthers and M. J. Collins, CEGB Rep. NER/SSD/M/ 80/327, 1980. 6 MTDA TA -- Metallurgical and Thermochemical Databank,
National Physical Laboratory, Teddington, 1989. 7 H. K. D. H. Bhadeshia, Mater. Sci. TeehnoL, 5 (1989) 131-137. 8 J. Fridberg, L.-E. T6rndahl and M. Hillert, Jernkontorets Ann., 153 (1969) 263-276.