1. Introduction

Decarburizing of steel surface sometimes occurs duringhot rolling process or annealing process. Because the decar-burized steel causes several problems, for example, lower-ing of strength and fatigue life, when the decarburized steelis used to manufacture parts such as gears, springs or bear-ings therefore it is necessary to minimize the decarburizingdepth, especially for wire and rod steel. The microstruc-tures of decarburizing area after annealing have been re-ported.1)

It is widely known that ferrite decarburizing, which is de-fined as decarburizing whose areas consist of ferrite mi-crostructure, occurs on the surface of steel when the steel iskept at around the temperature at which the microstructureof the steel becomes ferrite and austenite duplex phase, i.e.from 1 000 K to 1 150 K.2) The effect of temperature on fer-rite decarburizing has been roughly measured,3) and the be-havior of C-curve has been found with maximum growthoccurring around 1 073 K.4–6) It has been reported that heat-ing and cooling rate affect the ferrite decarburizingdepth.2,6,7)

There are a lot of reports about the behavior of ferrite de-carburizing studied experimentally, as described above.However, an adequate model of decarburizing is not avail-able except for the model of decarburizing which occurredat a temperature at which the steel has an austenite mi-crostructure,8) because the mechanism of the ferrite decar-burizing is not clearly understood. Our study focused on theeffect of the chemical composition of steel and heating con-dition on the ferrite decarburizing depth, and attempted touse a model which has been solved to obtain a carbon diffu-

sion coefficient in ferrite for the calculation of the ferritedecarburizing depth. Furthermore, the propriety of the sim-ulation result was confirmed experimentally.

2. Model of Ferrite Decarburizing and Calculation

2.1. Effect of Chemical Composition of Steel

Ferrite decarburizing is a diffusion problem of carbonwith phase transformation, for example from austenite toferrite. When ferrite decarburizing occurs, a discontinuousconcentration profile of carbon is observed as shown in Fig.1. The discontinuous concentration profile is caused by thecontinuity of chemical composition of carbon in ferrite andaustenite.9) The diffusion equation has been solved byWagner in the case that phase transformation, which is con-

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Calculation of Ferrite Decarburizing Depth, Considering Chemical Composition of Steel and Heating Condition

Masahiro NOMURA, Hiroyuki MORIMOTO and Masao TOYAMA1)

Materials Research Laboratory, Kobe Steel, Ltd., 5-5, Takatsukadai 1-chome, Nishi-ku, Kobe 651-2271 Japan.1) Kobe Works, Kobe Steel, Ltd., 2 Nadahama Higashicho, Nada-ku, Kobe 657-0863 Japan.

(Received on December 9, 1999; accepted in final form on February 11, 2000 )

The calculation of ferrite decarburizing depth considering the effects of the chemical composition of steeland heating condition was attempted using a diffusion model and its propriety was confirmed by comparingwith the experimental results. The calculation values of ferrite decarburizing depth were almost the same asthe experimental values under most heating conditions, which indicates that the model is appropriate forsimulation of the ferrite decarburizing depth considering the steel composition and heating condition. Onlyin the case where steel with a high proportion of titanium, vanadium and chromium was heated to under973 K, did the ferrite decarburizing depth of the experiment show lower values than that of the calculation.It was speculated that small MC carbides as TiC or VC and chromium which stabilizes cementite affectedthe formation of ferrite decarburizing area.

KEY WORDS: ferrite decarburizing; diffusion of carbon; simulation; thermodynamics; wire and rod steel.

Fig. 1. Schematic carbon concentration profile under the condi-tion in which ferrite decarburizing occurs. The mi-crostructure as a function of distance from the surface ispresented using symbols of a , g and q which representferrite, austenite and cementite, respectively.

trolled by concentration of the diffusing element, occurs ata constant temperature,9) and it has been clarified that thesolution could be approximated, as in the following equa-tion, when the solution is applied to the diffusion problemof carbon in ferrite.10)

.............................(1)

where, X is the ferrite decarburizing depth shown in Fig. 1,and Cb, C1 are the solubility of carbon in ferrite shown as abold line in Fig. 2, and the initial concentration of carbon insteel, respectively. D and t are diffusion coefficient of car-bon in ferrite and time, respectively. Here, Eq. (1) is applic-able in the temperature ranges of A and B shown in Fig. 2.In these ranges, ferrite decarburizing depth is controlled bythe diffusion of carbon in ferrite. In the temperature rangeof C, the ferrite decarburizing depth is controlled by thecarbon diffusion in both ferrite and austenite, thus Eq. (1) isnot applicable in a strict sense. However, it was assumed inthis paper that Eq. (1) could be used approximately in thetemperature range of C. In the temperature range of D, fer-rite decarburizing does not occur because ferrite does notappear even if the carbon concentration is zero, and thesimulation model of carbon concentration profile has beenreported,8) therefore the authors did not pay attention to thediffusion problem in the range of D.

Equation (1) has been solved in order to obtain D underthe condition that X, Cb, C1 and t were known,10) however,under conditions of D, Cb, C1 and t known, the ferrite de-carburizing depth, X, could be calculated. D050.394[mm2/s], Q580.22 [kJ/mol] were used as the preexponen-tial factor and activated energy of D, respectively. Theyhave been obtained as a impurity diffusion data under esti-mation using pure iron.11) In this paper, the effects of alloy-ing elements for diffusion of carbon was ignored. Cb wascalculated using the thermodynamics database system,Thermo-Calc12) and C1 was known from the analysis ofchemical composition of steel. For each kind of steel, it isconsidered that the ferrite decarburizing depth is calculatedby substituting C1 and Cb, if the effect of scale, which is theiron oxide formed on the surface of the steel, on the ferritedecarburizing is small.

The ferrite decarburizing depth of the steels shown in

Table 1 was calculated under the condition whereby thetemperatures were kept constant for 100 min. There wasless distinction between ferrite and ferrite with very smallMC carbides as TiC or VC under the microstructure esti-mation, thus, the boundary concentrations of carbon be-tween (ferrite1MC carbide)/(ferrite1MC carbide1cemen-tite), (ferrite1MC carbide)/(ferrite1MC carbide1austen-ite) or ferrite/(ferrite1austenite), for example shown in Fig.3 as a bold line on the calculated phase diagram of SUP7,were used as the data of Cb, which is the critical concentra-tion of ferrite decarburizing depth. As shown in Fig. 4, thecalculated results indicate that almost all the ferrite decar-burizing occurred around the temperature where the steelshave a ferrite and austenite duplex microstructure and thatthe growth rate of the ferrite decarburizing had C-curve be-havior with a maximum around the 1 073 K. That was thesame behavior as experimental results have reported.2,4–6)

XC D t

C C5

2

6

3 21

b

b

⋅ ⋅

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Fig. 2. Schematic phase diagram in Fe–C binary system. Cb ateach temperature is defined as concentration value on thebold line, and C1 means initial carbon concentration.

Fig. 3. Calculated phase diagram of SUP7. The bold line showsCb value.

Fig. 4. Ferrite decarburizing depth of SUP7, SUP6 and SRS60after heating for 100 min keeping temperature constant.

Table 1. Chemical compositions of steels. (mass%)

2.2. Effect of Heating Condition

When the temperature at which the ferrite decarburizingoccurs is not constant, the ferrite decarburizing depth is cal-culated as follows by integrating Eq. (1).

.......................(2)

here, Cb and D become functions of t1/2 by converting fromthe functions of temperature using the heating condition ofannealing, i.e. temperature–time function. Through the inte-gration of Eq. (2) from 0 to t1

1/2, ferrite decarburizing depthafter annealing which takes from 0 to t1 is calculated if theinitial depth of ferrite decarburizing at t50 is zero. Thevalue of {6CbD/(3C122Cb)}

1/2 was plotted as a function oft1/2, and measured the surrounding area of the plotted dia-gram in order to obtain the solution of Eq. (2) as the ferritedecarburizing depth. In fact, the ferrite decarburizing depthof the steels shown in Table 1 was calculated under the con-dition of temperature changing. Calculated results will bepresented later.

3. Experimental

In order to confirm the propriety of the calculation re-sults, experiments were done using the steels shown inTable 1. To avoid the effect of surface decarburizing asrolled condition, the wires were cut longitudinally into theshape shown in Fig. 5, and the specimens were placed in afurnace kept at a constant temperature of 973 K, 1 123 K,1 173 K and 1 223 K for 100 min under the air atmosphere.After the heating, the specimens were cooled in air. As theother annealing condition, the specimen was heated fromroom temperature to 973 K and then cooled to room tem-perature in the furnace as shown in Fig. 6. After the anneal-ing, sectional microstructures, where the longitudinal cutsection became the surface, were observed to estimate theferrite decarburizing depth, which was measured as the

thickness of ferrite band on the surface of the steel. Fromthe definition of the ferrite decarburizing depth in industry,the ferrite band which include the small MC carbides, forexample TiC or VC, was estimated as the area of ferrite de-carburizing.

4. Results and Discussion

4.1. Effect of Chemical Composition of Steel onFerrite Decarburizing Depth

The microstructures of the SUP7 after annealing for100 min with temperature kept constant at several tempera-tures are presented in Fig. 7. It was found that the ferritedecarburizing depth had the C-curve behavior as seen in thecalculated result shown in Fig. 4. The other steels, SUP6and SRS60, also had the same behavior. In Fig. 4, the fer-rite decarburizing depth of the steels estimated from the mi-crostructure is shown. Comparing the values of the resultsbetween experiments and calculations, it was found thatboth results mostly coincided, especially over 1 100 K,therefore it is considered that the model of ferrite decarbur-izing, which includes the factor of the chemical composi-tion of steel as shown in Eq. (1) is basically applicable.

The details of the results can be described as follows. At973 K, as for SUP7, the results of calculation and experi-ment were 60 mm and 50 mm, respectively, and they coin-cided well. On the other hand, as for SUP6 and SRS60, theresults of experiments had the values less than that of cal-culations at 973 K. As shown in Table 1, the steels of SUP6and SRS60 included vanadium of 0.01 and 0.17 mass%, re-spectively, therefore it is expected that they had smaller MCcarbides as VC or TiC. Furthermore for SRS60, morechromium, which makes cementite stable, was alloyed. At973 K, the ferrite band caused by decarburizing observedon the surface of the steels was formed by the dissolution ofcementite in pearlite microstructure. It is speculated that the

XC D

C Cdt5

2

6

3 21

1 2b

b

⋅∫ /

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Fig. 5. Schematic of specimen. Longitudinal cut section be-comes the surface of the steel under the microstructureestimation for ferrite decarburizing depth.

Fig. 6. One of the annealing conditions.

Fig. 7. The microstructures of SUP7 after heating for 100 min at973 K; (a), 1 123 K; (b), 1 173 K; (c) and 1 223 K; (d).

small MC carbides and more chromium affected the disso-lution of cementite at this temperature, then the experimen-tal ferrite decarburizing depth of SUP6 and SRS60 had lowvalues compared with the calculated values.

At 1 123 K, the calculated result and experimental resultof each steel were almost the same as shown in Fig. 4. Atthis temperature, the ferrite band was not formed by disso-lution of cementite but formed by phase transformationfrom austenite to ferrite, and it is considered that the effectof the MC carbide on the formation mechanism of the fer-rite band was different. Furthermore, the solution limit ofthe MC carbide becomes large around 1 123 K as seen inFig. 3, the MC carbides were expected to dissolve more asthe temperature increased. Thus, the effect of one of thedisorder factors for the model, i.e. the effect of the MC car-bides, became slight, then it is considered that the ferritedecarburizing in fact occurred as calculated. Above1 173 K, both values of calculation and experiment also co-incided well for each steel as shown in Fig. 4.

As shown in Fig. 7, the specimens heated to over 1 123 Khave the gradation of ferrite plus pearlite microstructureunder the ferrite band. The fraction of ferrite decreased to-ward the center of the steel. Since 1 123 K is the tempera-ture range of C shown in Fig. 2, diffusion of carbon also oc-curs in austenite and it is expected that the carbon concen-tration profile under the conditions of constant temperaturehad the concentration gradation in austenite as shown inFig. 8. Thus, it is considered that the concentration grada-tion in austenite causes the gradation of ferrite plus pearlitemicrostructure through the cooling process. The graduationlength of ferrite plus pearlite became larger as temperatureincreased. That is considered to be a reflection of the largegradation length of carbon concentration in austenite.

As described above, the ferrite decarburizing depth bycalculations basically coincided with that by experiments,and it is considered that the ferrite decarburizing depth canbe calculated considering the chemical composition ofsteel, using a model as in Eq. (1). The coincidence betweencalculations and experiments indicates that the effect of thescale at the surface of the steel was small in our experimen-tal conditions, though it has been reported that there aresome effects of the scale on decarburizing.13) In fact, someamount of the scale was observed as shown in Fig. 7.Outside of the specimen after annealing showed smoothsurface, and crack under the scale shown in Fig. 7 was

formed during cutting or polishing process after the anneal-ing. It is considered that consideration of scale effect on theferrite decarburizing model will be required for more com-mon use. This point will be future work.

4.2. Effect of the Heating Condition on the FerriteDecarburizing Depth

Effect of the heating condition was estimated usingSUP7. From the microstructure of SUP7 shown Fig. 9,which was heated in the condition of Fig. 6, the ferrite de-carburizing depth was measured to be about 20 mm. On theother hand, the ferrite decarburizing depth calculated by themethod of Eq. (2) became about the same value under thesame conditions as the experiment. From this fact, it is con-sidered that the ferrite decarburizing depth can be calculateconsidering heating condition using a model as in Eq. (2).Equation (2) was obtained by integrating Eq. (1) which is amodel considering the chemical composition of steel. Thisindicates that it is possible to calculate ferrite decarburizingdepth considering the both effects of chemical compositionof steel and heating condition simultaneously by using Eq.(2).

5. Conclusions

A calculation model of ferrite decarburizing depth con-sidering the effects of chemical composition of steel andheating condition was attempted and its propriety was con-firmed by comparing with the experimental results. The fol-lowing conclusions were obtained.

(1) The ferrite decarburizing depth by calculations con-sidering the chemical composition of steel was almost thesame as that by experiments under constant temperatureconditions, though both values were somewhat different forSUP6 and SRS60 at 973 K. It is considered that the modelis applicable to calculation of the ferrite decarburizingdepth considering the steel composition.

(2) Calculated ferrite decarburizing depth consideringthe heating condition was the same as experimental one. Itis considered that it is possible to calculate ferrite decarbur-izing depth considering both effects of chemical composi-tion of steel and heating condition.

(3) The accuracy of calculation was not good for thesteel which included a large proportion of titanium, vanadi-um and chromium in the condition heated to 973 K. It isspeculated that small MC carbides as TiC or VC andchromium which stabilizes cementite affect the formationof the ferrite decarburizing area.

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Fig. 8. Carbon concentration profile when the ferrite decarburiz-ing occurs at C range temperature. The gradation of car-bon concentration appears in the austenite area.

Fig. 9. The microstructures of SUP7 after annealing in the con-dition shown in Fig. 6.

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