Modellingtheeffectsofalloyingelementsonprecipitationinferritic steels
You Fa Yin Roy G.Faulkner*
Btitste of Polmer Techology n Mterials Engeering (IPTME) Lohrogh Umierity Loghorogh Leicesterhre LE11 3TU UK
plant stees using a modified modelling technique. MTDATA is used to calceulate some of the thermodymamic parameters for the This paper reports a systemati study on the effets of different alloying lments on the precipitation of MCg particles in poweralloying system. The elements studied include tungsten aluminium silicon manganese cobalt copper nickel and molybdenumprecipitates at low concentrations. Coarsening rate decreases progressively with increasing concentration of Si Co Al and Cu. Ni with varying degrees of concentration. Results show that all the elements are beneficial in reducing the coarsening rate of MCcan be very harmful by increasing coarsening rate when its concentration is greater than about 0.4 at.%. Both Mn and W are quite effective in reducing coarsening rate when the concentrations are low. Extremely sharp increases in coarsening rate are found whenthe concentrations of these two elements exced about 0.5 at.%. Mo is significant in reducing the coarsening rate even at very low concentrations and the effect is more pronounced with increasing concentration. All these effects result from the change of solubilityof chromium in the matrix caused by the alloying elements.
2002 Elsevier Science B.V. All rights reserved.
Keywords: Precipitation; Modelling: Ferritic stees; Alloying elements; Grain boundary
1. Introduction
material. Therefore numerous experimental studieshave been carried out on the effects of different alloying elements on the microstructure and especially onproperties of steels [2.3]. The difficulty of this kind ofexperimental work on such a plex system is obvious. In recent years puter modelling and/or simulationof microstructure evolution and mechanical properties has bee more and more important. Compared withexperimental work puter modelling does not havemodelling can give insights of structure and property the difficulties of being lengthy or costly. Computerevolution and therefore is able to predict long timebehaviour of the material [4 5]. Examples of such modelling include the model developed by Bhadeshia’sgroup [6.7] and the model used in the DICTRA software [8.9]. Carolan and Faulkner [10] and more recently Jiang and Faulkner [11] proposed a model for inter-granular precipitation that is based on the concept of collector plate. It is unlike the above models that areconcentrated on intra-granular precipitation. This model has been reasonably successful when applied toaluminium alloys and austenitic steels [12 13]. However
In recent years there is increasing demand forincreasing power plant efficiency to reduce both theThis promotes the development of new steels used insupercritical power plant [1]. It is well known that microstructural evolution of the steels determines thelife and long time behaviour of the material. One of theprecipitate population. The coarsening rate of these main features of the microstructure of steels is its.mechanical properties of the steels. The stability of these second phase particles determines the degradation of theprecipitates depends on mainly the chemical posi-tion and heat treatment of the material.
It is of vital importance in the development of newalloys to understand the effects of different alloying elements on the microstructure and properties of the
there are no systematic studies of the effects of differentsystem and the lack of thermodynamic data available. alloying elements in steels due to the plexity of theMTDATA [14] developed by the National PhysicalLaboratory (NPL) provides a useful tool to calculate thermodynamic paramcters.
main alloying elements on the precipitation and coar- This paper reports a systematic study on the effect ofpower plant steels using puter modelling based on sening of inter- and intra-granular MzsC precipitates in[10 11] and MTDATA.
2. Modelling details
2.1. Inter-gramular precipitation model
Details of the model for inter-granular precipitationcan be found elsewhere [10 1l]. The model assumes that in Fig. 1. Basically the modelling includes four stages of the inter-granular precipitates are cap-shaped as shownacross the matrix is determined ie. segregation of solute calculation. (1) The solute concentration distributionatoms to grain boundaries during quenching (2) Calcu-lation of nucleation site density at the agcing tempera- ture at grain boundaries according to the soluteconcentration calculated during stage one. (3) The nuclei formed in stage two are allowed to grow at the ageingtemperature due to solute diffusion from grain centre tocentre to grain boundaries coarsening occurs where the boundary. (4) When all solute has diffused fromlarge precipitates grow while smaller ones dissolve although only the average size of particles is consideredin the actual modelling.
2.1.1. Non-equiibriom and equilibrium segregotion
causes solute re-distribution in the material. It is thought Segregation of solute atoms to grain boundariesthat at ageing temperatures higher than 0.55 the meltingmust be considered while equilibrium segregation (ES) point of the alloy non-equilibrium segregation (NES)also is the main consideration at lower temperatures. The solute distribution across the matrix is a pli-
Fig. 1. The grain boundary precipitates formed by two sections of thesame sphere of radius r. GB stands for grain boundary and 9P is the contact angke.
cated function of the distance from the grain boundary.profile are as in Ref. [1l]. It is well known that the The expressions for calculating solute concentrationdriving force for nucleation is related to the super- saturation of solute atoms. Therefore this segregationprofile provides the basis for the subsequent nucleationdensity calculation.
2.1.2. Nucleation site density
grain boundary is given by The number of nuclei formed per unit area of the
phase G* is the Gibbs free energy of critical nucleus where x is the solute concentration in the precipitateformation N is the number of atom sites at the grainboundary k is the Boltzmann constant and 7u is the nucleation temperature. G* depends on the free energyinterfacial energy s at the interface between the change per unit volume of nucleus AGv and thenucleus and the matrix in accordance with the followingequation:
where y is the angle between the surface of nucleus andthe grain boundary (see Fig. I). This defines the shape of the nucleus. AGv is the driving force for the phasetransformation and can be estimated from
volume of nucleus C the solute concentration at grain where R is the universal gas constant V. the molarboundary and Ci is the equilibrium solute concen- tration at nucleation temperature. Nucleation is impor-tant in the following precipitation calculation. Thegrowth rate of precipitates depends on the average distance between the nuclei which is given by /I/N
2.1.3. Growth of precipitates
In the constant square collector plate model thesolute atom arrival rate at the collector plate determinesis the square with side length equal to the distance the growth rate of a precipitate. The collector plate areabetween adjacent precipitates.Therefore the initial collector plate area would be
N is defined in Eq. (1). Assuming that the ageing time is divided into a series of small time intervals &r the sizeof the precipitate at time rr is L1 and that at time
(1)
(2)
(c)
(4)
it is L then
2.2.1. Coarsering orset tine
determined using Eq. (6). This is based on the assump- In the previous model coarsening onset time istion that coarsening occurs when all solute atoms haveMC in ferritic steels this assumption is no longer been dragged from grain centre to the boundaries. Forvalid. Typical carbon content in 9 and 12 wt.% Cr ferritic steels is about 0.15 wt.%. Therefore only a smallfraction of chromium is precipitated in MsCg due to thefraction of M23Cs is determined by the carbon content very low carbon content. Thus the maximum volumefor the solute atoms supply from intra-granular pre- rather than chromium content. Also there is petitioncipitates.
(5)
4m1 is the collector plate area at 1&r D is thevolume diffusion coefficient at ageing temperature Cis the average solute concentration in the region from the grain boundary to a distance /2D&r into the grain C is the solute concentration in the precipitate phase temperature and p. and p. are molar density of thematrix and precipitate phase respectively. f() = 2π/sin²(2/3)cos (1/3)cos² ) defines the rela-tionship between the precipitate volume and the cube ofthe size parameter L. Thus given the initial collector plate area and precipitate size (the critical nucleus size atnucleation) precipitate size L at any time 1 afternucleation can be evaluated using Eq. (5). Nucleation times are very small of the order of milliseconds.
Generally when either all non-rate controlling atomsor all rate controlling atoms have been precipitated thevolume fraction of the precipitates would stop increas- ing with time. Thus the maximum possible volumefrom one of the following cquations: fraction of the precipitates Vmax can be estimated
(8)
(6)
2.1.4. Coarsening
would occur when all solute atoms have diffused from In the original model it was thought that coarseninggrain centre to the boundary. Therefore the coarseningonset time is determined by
In Eqs. (8) and (9) Ng and Nc are the number of ratethe formula MC of the precipitate C and C are controlling and non-rate controlling atoms as defined inthe contents of non-rate controlling and rate controllingfraetion of precipitates depends on which of the two elements respectively. The actual maximum volumevalues determined by Eqs. (8) and (9) is smaller. In the case of MCs in ferritic steels V is more than onesening onset time is determined by carbon contents.
(9)
where d is the grain size. During coarsening the size ofprecipitates as a function of time is given by [15]
(7)
When intra-granular precipitation occurs the intra-granular precipitates will also take solute atoms. There- fore Eq. (6) does not apply in such cases. However ifwe take the volume of both inter- and intra-granularvolume fraction either Eq. (8) or Eq. (9) still can be precipitates into account in calculating the precipitateapplied. The maximum volume fraction of MCg in the steels studied here calculated using Eq. (8) is in goodagreement with the equilibrium value calculated usingMTDATA. This to some extent justifies Eqs. (8) and (9). Therefore Eq. (8) or Eq. (9) is used instead of Eq. (6) tocalculate the coarsening onset time.
d is the grain boundary width D is the grain boundarydiffusion coefficient Lg is the precipitate size at the onset of coarsening Ic is the coarsening onset time asdefined in Eq. (6) 7 is the ageing temperature 4 is aconstant depending on the fraction of grain boundary constant determined by surface energies and B is also a
2.2. Modifications made to the model
In order to use Eq. (8) or Eq. (9) to determine thecoarsening onset time the total volume fraction of bothinter- and intra-granular precipitates is calculated after each time interval r from the precipitate size and thevolume fraction is pared with the maximum values number of the precipitates. Then the calculated totalas shown in Eqs. (8) and (9). When the calculated
The above model has been reasonably successful inpredicting grain boundary segregation and precipitation in aluminium alloys and austenitic steels [12 13]. How-ever when applied to ferritic steels there are some limitations in the model. Therefore modifications havebeen made to the model and are introduced below.
The nucleation of intra-granular precipitates is treatedhomogeneous nucleation the free energy can be written in a similar way to inter-granular precipitates. Assumeas
precipitate volume fraction reaches the maximum coarsening takes place.
2.2.2. Effects of tempering on ageing
In the previous model only one ageing temperaturecan be dealt with. Therefore tempering and subsequent ageing are treated separately. The modelling of temper-ing and ageing is exactly the same; i.e. precipitates nucleate and grow from the critical nucleus size at theageing. This means that tempering has no effect on the appropriate temperature both in the tempering andcerned. This is certainly not the case in reality. Thewould continue to grow. Therefore the model hasbeen modified to treat quench tempering and subse- quent ageing in a sequence that is during ageing thetempering. This treatment not only overes the precipitates will transform from the state at the end ofshortings in the previous model as mentioned above but also can be generalised to more plicated heat treatment conditions.
critical nucleus radius and corresponding free energy are where r is the radius of the spherical nucleus. Thethus as follows:
(11)
(z1)
Eq.(3） with solute concentration in the matrix C The free energy change Gv can be calculated fromWe believe that as this is a non-equilibrium situation; instead of solute concentration in grain boundary C.the chemical potentials within the grains leading up tothe grain boundary are never levelled out. Therefore the driving forces for inter- and intra-granular precipitationdiscussed above. The average intra-granular precipitate are different and can be estimated through Eq. (3) assize then is determined using Eq. (10) with initial nucleussize as r * rather than 0:
2.2.3. Interaction between intra- cnd inter-granular precipitation
In the previous model intra-granular precipitation isconsidered separately from inter-granular precipitation. The model used for calculating the growth of intra-granular precipitates is the simple Zener model in which the average particle size of intra-granular precipitates x is described by the following equation [13]:
(13)
The nucleation site density here is determined also usingEq. (l) with N being the number of atom sites per unitvolume of the matrix and using the intra-granular precipitate driving force. Thus it is also possible tocalculate the average particle spacing for intra-granular precipitates.
(10)
concentration in the matrix Ca the equibrium where D is the diffusion coefficient C is the solutethe precipitate phase and the time. A few problems are solute concentration C the solute concentration inassociated with such a model. Firstly no nucleation isconsidered. Therefore no information about the spacing and volume fraction of the precipitates is available.Secondly as intra-granular precipitation is considered separately the interaction between intra- and inter-granular precipitation is not considered. For very longageing time this might not be a big problem because a vast majority of the precipitates will be in the grainboundaries. However in the short term as intra- andthey would definitely affct each other’s growth rate. In inter-granular precipitates pete for solute atoms addition if intra-granular precipitates exist they will take up carbon and solute atoms and therefore shortenthe coarsening onset time. Therefore intra-granular precipitation has been included in the previous modelto give an integrated precipitation model.
When coarsening occurs the size of intra-granularprecipitates changes with time according to the follow- ing equation [16 17]:
(14)
where r is the radius of the precipitate at the beginning of coarsening.
2.3. Applications of the model
on the alloy 5 supplied by CORUS. The chemical Modelling has been carried out on a model steel basedposition of the steel sample is shown in Table 1.The alloy is initially treated as a FeCrC ternary system as the basis for parison. Then the alloy isfollowing main alloying elements: Al Si W Mn Mo treated as FeCrCX system with X being one of theCo Cu and Ni. MTDATA is used to calculate the
Table 1Chemical positions of Corus alloy 5 (Fe balance)
Cr 0.15 C 0.55 W Mo Mn !S P S Co 9N V 0.061 N Cu B A1wt.% at.% 11.4 12.2 0.69 0.17 1.52 0.88 z0 0.40 0.81 0.82 0.27 0.53 0.014 0.025 0.009 0.016 2.24 2.11 0.07 00 0.24 0.26 0 0.48 0.42 0.005 0.026 0.01 0.021
equilibrium solute concentration as a function of temperature and of concentration of different alloyingelements. In the calculation using MTDATA all fourelements in the FeCrCX systems were considered and all possible phases identified by MTDATA wereincluded in the calculation (refer to Figs. 57 for the phases included). The result then is used as an input tocach system at different concentrations of alloying the modelling and model calculations are carried out onelements and at two ageing temperatures 600 and650C for up to 100 000 h. The solution heat treatment q . sdto ambient temperature. The alloy is then tempered at 760 °C for 1 h. These heat treatment conditions are inaccordance with the heat treatment of the CORUS alloy5. The main parameters used in the modelling are shown in Table 2.
steels do not have significant effects on either the [23]. The results show that these major phases in ferriticvolume fraction or the coarsening rate of M3Cs particles. We believe that this is because of the highchromium content of the steels studied in our modellingand simulation. The amount of NbC present in the steel is small due to the low content of Nb. Therefore theand coarsening rate of MCg particles very much. This presence of NbC would not affect the volume fractionto some extent justifies the application of the approachdiscussed above to the steels studied. However attempts are being made to revisit this problem using our morerecently developed Monte Carlo approach where weinto consideration. can take multi-ponent and several second phases
In such a treatment the interactions between differentalloying elements are neglected. The reason is that the plexity of the phase diagrams and thus the difficultyin getting reliable results on the equilibrium concentra- tion increases sharply with increasing the number ofalloying elements. However even with this limitation this study can give insights and guidelines of the effectsof different alloying clements on the precipitation andcoarsening of MsCg in ferritic steels.
3. Results and discussion
3.1. Precipitation cuerres
base alloy (i.e. FeCrC system) aged at 600 °C for up Fig. 2 shows the modelled precipitation curve of theto 100o00 h. The data points are experimental measure-MC precipitates in Corus alloy 5 creep tested (stress: ments of the average size of inter- and intra-granular154 MN m 2) at the same temperature for 6378 h. Forcquivalent circle radius (ECR) i.e. the radius of a circle inter-granular precipitates the size is described by thewith the same area. Although the sample is creep tested and strain will accelerate coarsening we do not expectthere is much difference between the sizes of the particlesin the aged and creep tested samples as the time is not very long. Therefore the prediction in Fig. 2 is in
We also acknowledge that in the stels studied here there are many second phases in addition to M2sC6such as laves phase and vanadiumnitride particles. In our more recent simulations of precipitation in a similarwe considered simultaneous precipitation of MsC6 ferritic steel P92 using a new Monte Carlo approach laves phase and vanadiumnitride particles and theMTDATA by taking all the clements into consideration thermodynamic parameters are calculated using
Table 2Main parameters used in the modelling of precipitation kinetis
Parameter Unit Value ReferenoesPo molar density precipitate Px. molar density matrix molm mol m" 5496 110497 [18] [19]D grain boundary diffusion pre-exponential term Q grain boundary diffusion activation enengy m²s- kJ mol-1 502 283.1 [20]° [20]Dv volume diffusion pre-exponential term Qv volume difusion activation energy kJ mol1 m² s1 8.5 × 104 240 [21] [21] contact angle interfacial energy degree 0.668 57 [10] [22]
* Calculated from triple produet taking = 5 × 1o * m and = 1.
