mst,87-eff comp y proc vars on nbcn prec in nb microal aust

8/12/2019 MST,87-Eff Comp y Proc Vars on NbCN Prec in Nb Microal Aust

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PublishedbyManeyPublish

ing(c)IOMCommunicationsLtd

Effect of

composition and

process

variables on

Nb(C, N)precipitation in

niobium

microalloyed

austenite

Nucleation theory and the solubility product of niobium, carbon, and nitrogen in

austenite have been used to derive equations for the start of Nb (C, N)

precipitation as a function of temperature and composition. The predicted curves

have been 'Compared with the experimental observations of several authors to

determine the effects of thermomechanical processing variables on the density of

preferred nucleation sites and to incorporate these in the equations. Good

agreement between the predicted and observed forms of precipitation curve is

obtained with consistent constants in the equations when account is taken of the

influence of different methods of detecting the onset of precipitation. Combining

the calculated precipitation start curves with the dependence of recrystallization

kinetics on composition and thermomechanical process variables when all niobium

is in solution leads to prediction of the lower temperature limit for complete

recrystallization and of the upper temperature limit for effective stoppage of

recrystallization by precipitation. The predictions are in good agreement with

observed results. MSTj495

B. Dutta

C. M. Sellars

1987 The Institute of Metals. Manuscript received 7 May 1986. When the workwas carried out the authors were in the Department of Metallurgy, University of

Sheffield; Dr Dutta is now with Tata Steel, Jamshedpur, India.

Predictions from nucleation theory

THERMODYNAMIC CONSIDERATIONS

The basic reaction for carbonitride formation may be

written as

where n has been taken as one or less and the influence of

nitrogen has been handled in different ways by different

authors.1-7 One commonly accepted approach is that

proposed by Irvine et al.1 in which n= 1 and the nitrogencontents at the typical levels in commercial steels are

considered to modify the effective carbon concentration to

be [C+ 12N/14]. This approach is followed here, but theeffect of alternative relationships is considered later.

The equilibrium constant K for precipitation from

equation (1) is given by

retarding recrystallization at temperatures of finish

controlled rolling operations. The kinetics of precipitation

have been studied in both undeformed and deformed

austenite by a number of workers. These studies have

shown that deformation greatly accelerates precipitation,

but the studies have used different conditions of

deformation, different steel compositions, and different

methods of detection of precipitates so that general

quantification of the influence of each of the variables is

not yet available.

In the present paper, an attempt is made to derive the

precipitation-time-temperature relationship on the basis of .

the thermodynamics of the system and diffusion controlled

nucleation theory, and then to correlate the predicted

relationship with the observations of various workers on

niobium carbonitride precipitation in HSLA steels in order

to obtain appropriate values of t he constants in the

relationship. The precipitation model is then used in

conjunction with relationships for recrystallization kinetics

to examine the influence of composition and process

variables on the temperature at which recrystallization is

retarded and effectively stopped by strain induced

precipitation.

(1)Nb+n(C, N)~Nb(C, N)n

a activity

aC[ lattice parameter of matrix phase

A constant in equation (16)

B constant in equation (12)

C constant in equation (12)

d grain sizedo original grain size

D eff effective diffusion coefficient

D o diffusion constantf modifying factorF effective fraction of precipitate

~ G v free enthalpy change per unit volume~ G o free enthalpy of formation

~G * free enthalpy of forming a critical nucleus

~ H O enthalpy

Js steady state nucleation rate

kB Boltzmann's constantks supersaturation ratio

K equilibrium constant

n number of atoms

N number of nucleation sites of a particular type per

unit volume

No Avagadro's numberN* number of nuclei per unit volume

Q d activation energy for diffusionR universal gas constant

~ S O entropy

t time

T absolute temperature

~ef absolute temperature of deformation

Vm molar volume of Nb(C, N)

x diffusion distance

X c[ solute concentrationZ Zener- Hollomon parameter

a constant in equation (10)

y interfacial energye strain

e strain rate

List of symbols

Introduction K = aNb(C. N)n

aNba(C,N)

(2)

It is well established that precIpItation of niobium

carbonitrides in austenite plays an important role in

where for a pure compound the activity aNb(C,N)n =1 and

for dilute solutions the activities aNb and a(C,N) are

Materials Science and Technology March 1987 Vol. 3 197


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198 Dutta and Sellars Effect of composition and process variables on Nb(C, N) precipitation

This supersaturation ratio determines the 'driving force',i.e. the free enthalpy change for precipitation to occur. Thecritical supersaturation level for nucleation in the case ofundeformed austenite is expected to be high. However, theintroduction of strain provides sites for nucleation andthen precipitation is observed at lower supersaturation.Cohen and Hansen8 observed precipitation in a single passrolling experiment with the ratio between 5 and 7'5 and

Chilton and Roberts9 obtained a value of 77 in their sixpass rolling schedule.

proportional to concentration: The equilibrium constant isrelated to the free enthalpy of formation AGo, the entropyASo, and the enthalpy AHOas

AGo= AHo-TASo = -RTlnK (3)

Thus, for solution of precipitates

In (aN b)(a(C ,N )n =L1.S0jR-AHOjRT (4)

Rewriting this equation in terms of wt-% niobium, carbon,and nitrogen in solution leads to the usual form ofsolubility product equation, which Irvine et al.1 give as

When the reheating temperature is above the absolutetemperature given by equation (5), the total niobium,carbon, and nitrogen contents of the steel should be insolution, but when the reheating temperature is lower theexpected amounts in solution are given by equation (5) ifequilibrium is attained. This may not necessarily be true inpractice.

At any lower temperature the equilibrium amount of

[Nb][C+ 12Nj14]

in solution is again given by equation(5). The supersaturation ratio ks at this temperature isdefined as the ratio of the actual amount of [Nb][C+ 12Nj14] in solution to the equilibrium amount,Le.

(9)

(8)

expected to be incoherent, or at most semicoherent, withthe austenite matrix. For incoherent nucleation,lO

A * 16 ny 3jG = 3(AG

y)2

From the above considerations, equation (7) can berewritten for precipitation of Nb(C, N) as

[ b] (270000) (16ny3V~Nof)Js=etN exp -~ exp 3RT(-RTlnks

)2

. (10)

where f is a modifying factor that arises for nucleation atdislocations or at grain boundaries because of their strain

energy and surface energy, respectively, and which is lessthan unity for homogeneous nucleation.

The free enthalpy change arises from the chemicaldriving force and may include an additional term if excessvacancies are present.10 Considering only the chemicalterm, from equations (3) and (6) the value of AGy is relatedto k s as

Considering that a number N* of nuclei per unit volumemust be formed in time t for nucleation to be detected, then

t o c N*jJs (11 )

and equation (10) can be rewritten as

(270000) B

t=C[Nb] - 1exp ~ exp T3(ln ks

)2 . (12)

where C=N*j e t and for homogeneous nucleationB =16ny3V~Noj3R3. Substitution of the value of Vm of128 x 10-5 m3 mol-1 and the typical value19 of

y =O 5 J m - 2 for incoherent interfaces leads to a value of

. B = 36 X 1011K3In practice, nucleation of Nb(C, N) in austenite takes

place heterogeneously on preferential sites such as grainboundaries and dislocations, or more probably dislocationjunctions formed by interaction of individual dislocationsinside grains or in subgrain boundaries in the case ofdeformed austenite. For such sites the effective value ofB isreduced. The effect of reducing the value ofB in equation(12) by factor of 10 and 100 on the temperaturedependence of nucleation time is illustrated in Fig. 1. Thisshows the classical C curve for nucleation and illustratesthat the temperature of the nose and time to the nose aresensitive to the value ofB and therefore to the nature of theheterogeneous nucleation sites. To obtain the curves in

Fig. 1, ks was calculated for a steel of composition0lC-0007N-004Nb from equation (6) based on theequation of Irvine et al.1 for the solubility product. Figure2 shows the effect of using alternative equations forsolubility product for the same steel composition with aconstant value ofB = 36 X 1010K3 in equation (12). It canbe seen that, compared with the curve for the equation ofIrvine et al.,l the equation of Mori et al.2 for

NbCo'24No.63 leads to a curve with a nose at slightlyshorter times and ""'65C higher temperature, and theequations of Nordberg and Aronsson4 for NbCo'87 andNbC give curves with noses at times about a factor of twolonger and about 35C lower. However, the curves are allof the same form, and comparison with Fig. 1 shows thatrelatively small changes in the values of the constants B

and C in equation (12) would lead to essentially identicalresults. Thus, it is concluded that any of the equations forsolubility product can be used, but that values of Band Cdetermined by comparison with experimental observationsof precipitation kinetics will depend on the solubilityequation selected. In the remainder of this paper only theequation of Irvine et al. is considered.

(6)

(5)

ks = [Nb ][C + 12Nj14]solnjl02'26- 6770fT

log [Nb][C+ 12Nj14] =226-6770jT

KINETICS OF NUCLEATION

Diffusion controlled nucleation in solids has received muchtheoretical attention, which has recently been summarized

by Russell,1 who shows that the steady state nucleationrate Js can be expressed as

Js ~ (Nja ;') D ef fX (J . exp ( - AG*jkB T ) (7)

In dilute substitutional solid solutions Deff is the diffusioncoefficient of the solute.10 For precipitation of niobiumcarbonitride, diffusion of niobium, carbon, and nitrogen is

required. Measurements of diffusion coefficients inaustenite by several authorsl1-14 differ somewhat inabsolute value, but show that in the temperature range ofinterest diffusion of carbon and nitrogen is 5-7 orders ofmagnitude faster than diffusion of niobium. Thus, niobiumis expected to be the rate controlling element. Kurokawaet al.15 carried out a systematic study of the effects of otherelements on the diffusion coefficient of niobium in austeniteand found only marginal effects of elements such asmanganese and silicon. Thus for future calculation thediffusion coefficient is considered to be independent of steelcomposition and the values14 of D o = 14 X 10-4 m2 S-land Q d= 270 kJ mol-1 for diffusion of niobium inaustenite containing some silicon and manganese are usedto calculate Deff in equation (7). It is assumed that at the

relatively high temperatures of interest this volumediffusion coefficient is rate controlling even when

precipitation occurs on dislocations or grain boundaries.Lattice parameter measurements of austenite16 and

niobium carbonitride17 indicate that for the orientationrelation18 of precipitates there is about 23% mismatch inlattice spacings. Carbonitride precipitates are therefore

Materials Science and Technology March 1987 Vol. 3


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Dutta and Sellars Effect of composition and process variables on Nb(C, N) precipitation 199

1100

. (13)

o

o

o

" -

o

C h ardness Le Bon et a~

o extract ion Le Bon et al~' ~b ext ract i on Hoogendorn and

Spanraft29

Z =eexp400000jRTdef

~ 103

ZoI-l-

n.

U

w0 ::n.102

10' 10

EQUIVALENT STRAIN

3 Dependence of time for 500/0Nb(C, N) precipitation

on strain from observations of Le Bon et al.21 and

Hoogendorn and Spanraft29

after preliminary 'roughing' strains to recrystallize the

austenite.18,2S The kinetics have also been measured in as-

reheated austenite21,26-28 and in as-reheated and recrystal-

lized austenite.2s Different techniques of detection have

been used by different workers. The influence of detection

method is considered in some detail in the appendix, but at

this stage note that at the 5% precipitation level (and

above) the measured times are determined essentially by

precipitation in the matrix, rather than at grain

boundaries.

In deformed austenite, the density of preferential

nucleation sites is expected to be sensitive to the

dislocation density and dislocation arrangement, and

therefore to the conditions of the prior deformation,expressed in terms of the strain c, strain rate e and absolutetemperature Tdef of deformation. The effect of strain rate

has not been separately investigated and in the following

analysis it is combined with the effect of deformation

temperature in terms of the Zener-Hollomon parameter

EFFECT OF STRAIN

The influence of strain at a constant temperature of

deformation on subsequent precipitation kinetics of

Nb(C, N) has been studied by Le Bon et al.,21

Hoogendorn and Spanraft29 and Matzumata and

Roberts.3o All the results show that an increase in strain, at

temperatures below that at which recrystallizationintervenes before precipitation, reduces the time for

precipitation. However, Matzumata and Roberts30 used an

up-quenching technique which could have influenced the

precipitation times observed. In Fig. 3 the times to 50%

precipitation obtained by Le Bon et al.21 and Hoogendorn

and Spanraft29 are shown as a log-log relationship with

strain. There is clearly some discrepancy between the

104

TIME, S

o ~ :/ /O ~ A~ o V A ~

~ /' 0 NbCo.24 NO.63Mori et 01 .2

o OV6 0 Nb (C+12N/14) Irvine et 01 . '

\K . 6 Nb COoS?]NOrdberg and

.\\ "" v Nb C Aronsson4

0,,,,,

, " ' "06 0

800

1100

uo 1000

w0: ::JI--


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NN

+J~

CD

. 8 .~til LC 0

8 : 100+J 00"-'"

" - " 'Mw . . : -x x

10 10

o 06(,

~ ~10-'L- ----.L -l....- .L....-_----J

1017 10'8 10'9 1020

ZENER- HOLLOMON PARAMETER. s

4 Effect of Zener-Hollomon parameter on start of

strain induced Nb(C, N) precipitation from the data

of Le Bon et al.21

dependence shown by the two sets of results and in the

absolute times observed by Le Bon et al. using different

detection methods. The lines are drawn with a slope of -1,

which runs nearly midway between the data points. The

constant C in equation (12) is therefore considered todepend on strain as

C e x : 8-1 . (14)

.and in the subsequent anaJysis it is assumed that strain

only influences the density of sites and not their nature, i.e.

it has no effect on B. Equation (14) is only a simple

approximation, and even assuming the power relationship

is valid, the exponent has an uncertainty ranging from

-075 to -15.

EFFECT OF ZENER-HOLLOMON PARAMETER

Only Le Bon et al.21 have studied the effects both of

deformation at constant temperature (i.e. at constant Z) on

precipitation at different temperatures and of deformation

at the same temperature as that of the subsequent holding

point (i.e. at varying Z), but as pointed out in a previously

published paper,31 the forms of precipitation-time-

temperature curves observed by several authors fall into

two distinct groups depending on whether prior

deformation was given at constant or varying Z. A lower

temperature of deformation (i.e. higher Z) leads to shorter

times for precipitation. A plot of the data of Le Bon

et al.,21 shown as the ratio of the times for 5%

precipitation as a function of Z in Fig. 4, indicates that the'constant C in equation (12) depends on Z as

C e x : Z-0'5 . (15)

Again, this is an empirical approximation, but, as shown

below, it also seems satisfactory in describing the results ofother workers18,22,24 for precipitation after deformation at

different temperatures.

VALUE OF CONSTANT B FOR STRAININDUCED PRECIPITATION

For the reasons discussed above, equation (12) has been

modified for strain induced precipitation in deformed

austenite by taking account of equations (14) and (15) to

give

-1 -1 -0.5 270000 Bto '05 =A[NbJ 8 Z exp~ exp T3(ln k

s)2

. (16)

In this equation, A is a constant, the absolute value ofwhich is discussed in relation to the detection method

employed by different authors in the appendix. For

comparison with experimental data in this section, the

value of A has been chosen to give agreement with

observed times for 5% precipitation at 9000e and the

optimum value of B has been determined by trial-and-error


computations using equation (16) to give the best fit of the

form of precipitation-time-temperature curve to the

observations. From all the available observations, the

mean value ofB obtained is 25 x 1010 K3, and so in Fig. 5the curves for this value of B are shown together with those

for the optimum value for each set of observations.

In Fig. 5a the two curves observed by Le Bon e t al. 21,26

for prior deformation at constant Z and 8 are compared

with the predictions of equation (16). It can be seen that

the optimum value of B =6xl010 K3 gives reasonably

good agreement with both experimental curves. Differences

at higher temperatures may arise from the occurrence of

partial recrystallization before precipitation. Use of the

mean value of B leads to some discrepancy in temperature

dependence and higher nose temperatures. Figure 5a also

compares the predicted and observed effects of strain at

9000e and, as expected from the earlier discussion, shows a

rather higher predicted influence of strain.

In Fig. 5b the results of Ouchi et al.,22 who used the

same deformation temperature as that of holding, are

compared with the predicted results. Again the optimum

value of B =1X 1010 K3 in this case gives good agreement

with observation and the mean value of B leads to adiscrepancy in the opposite sense to that in Fig. 5a.

Figure 5c shows the results for deformation at constant

Z for the two steels observed by Hansen et al.23 The

reheating temperature was not sufficiently high to take all

the niobium into solution in the higher niobium steel and

for the calculations the solubility product given by

equation (5) was taken. This leads to some uncertainty

because equilibrium may not have been attained during

reheating and, as discussed in a previously published

paper,32 more niobium may be in solution than calculated.

In Fig. 5 c a value of B =15 X 10 10 K3 gives the best

agreement with the temperature dependence of

precipitation times, but when the constant C is fixed by the

lower niobium steel, there is a discrepancy in precipitationtime for the higher niobium steel. This could arise from the

uncertainty in the amount of niobium in solution.

However, use of the mean value of B= 25 X 10 10 K3 givesgood agreement with the composition effect but a

discrepancy in temperature dependence. It could be argued

(see appendix) that this difference in temperature

dependence arises from the limited sensitivity of the

extraction replica technique employed for the

measurements.

In Fig. 5d, the results of Watanabe et al. 25 are shown.

Again deformation was at constant Z, but in this case after

preliminary roughing strains at higher temperatures to

obtain a recrystallized austenite before the. final

deformation. The optimum value of B is 4 X 10 10 K3, but

there is little difference between the predicted curves for

this value and for B =25 X 1010 K3 over the r ange of

experimental observation.

Figure 5e compares the results of Janampa18 withpredictions for B =1 and 25 x 1010 K3. Neithervalue gives

particularly good agreement with the observed curve,

although the former value is clearly better. Janampa also

gave a preliminary roughing deformation to recrystallize

the steel before the final deformation at varying Z was

applied, and it was found that in contrast to the

observations of Watanabe et al.,25 the roughing

deformation caused some grain boundary precipitation on

cooling for the finishing deformation. However, the total

niobium in solution after reheating was considered in the

calculation because, as discussed in the appendix, thecomposition in the bulk of the grains would be unaffected

by the local precipitation.

Figure 5f compares the results of Yamamoto et al.24 on

a steel of near stoichiometr ic composition with the

predicted results. Here, the value of B must be reduced to

025 x 1010 K3 to obtain an approximation to the


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1100 (a)-_-l)

1000

~we: :: : : >

~e: :w0-

~~ 900

800

./'"",,-

1'-/'"

t/,..,,/-,...,0

I ./

I ,0

I /

I ', /

7! : b S . calc. B,K'V 1x1010 2'5x1010r ~ , . ( ) 0

1 \, \~t\ ~o

E

08 T

10

I

1100 (c)

u1000

800

' ",0/'

(d)

/'

E033

calc. B,K3

0'25x1010

2'5x1010

() 0

E069

obs.

. - ~-""",_0

\

(0

---

I " - - - - - - - , . -< Ie,/I

I

I()

I,IL/

/~/

~

calc. B K3

1x1010 2'5x1010

() 0

TdefoC

T

"",,()

"""/,.()

I

/I

I /

{

1./,0

I '/ obs( ) P

V

n ~'\1 \

O( )

\ ", \\ \o ()

1100 (e)

800

~1000

we: :: : : >. -

~~ 900

10-1 10TIME, S

101

TIME, s

a 017C-0011 N-O'04Nb steel, dy = 250 J.lm, Le Bon e t a l . ;21.26 b 016C-00054N-0031 Nb steel, dy = 225 J.lm, Ouchi e t a l . ;22 c 01 OC-O'01 N-

O'095Nb steel, d),=140 J.lm, and 011 C-0'01 N-0'031 Nb steel, dy =405 J.lm, Hansen e t a l . , .23 d 0'063C-0'0058N-0'084Nb steel, dy =25 11m,Watanabe e t a l . ;25 e 0'080C-0'015N-0'060Nb steel, dy =70 11m,Janampa;18 f0'019C-0'0028N-0'095Nb steel, dy =140 11m,Yamamoto e t aU '

5 Comparison of observed precipitation start-time-temperature curves in deformed austenite (closed points) with

curves calculated from equation (16) with optimum value of 8 (half-open points) and mean value of

8=25X 1010 K 3 (open points)



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. (17)

experimental curve and a value of B =25 X 1010K3 isentirely unsatisfactory. This is considered to indicate thatthe solubility product equation of Irvine et al.1 is notapplicable to such steel compositions, in agreement withthe conclusion reached by Yamamoto et al.

With the exception of those reported in Fig. 5f, all theresults are for steels in the composition range

0'03-0'084%Nb, 0'06-0' 17%C, and 0'005-0'015%N, and inthis range satisfactory agreement between the prediction ofequation (16) and observed forms of precipitation-time-temperature curves is obtained with values of B in therange 1-6 x 1010K3. No systematic variation in theoptimum value of B could be detected with the steelcomposition or deformation conditions used by thedifferent authors, and all values fall within a factor of 25 ofthe mean value of B of 25 x 1010K3 For latercomputations of the interaction of precipitation andrecrystallization, the mean value has therefore beenadopted.

VALUE OF CONSTANT A FOR STRAININDUCED PRECIPITATION

The values of the constant A in equation (16) required forcoincidence of predicted and observed times at 900C, withB= 25 X 1010K3, are shown in Table 1. There is aconsiderable variation in these values, but as discussed inthe appendix, most of this variation is considered to arisefrom the different methods used for the detection of

precipitation by the different authors. When account istaken of this, the best values estimated for 5% matrix

precipitation in strained austenite generally fall close to amean of 15x 10- 5. The exception arises for the results ofJanampa,18 where A is about a factor of 5 smaller. This

smaller value of A i s in accord with more recentobservations33 when a roughing deformation leading torecrystallization and some grain boundary precipitation is

also employed. If a roughing deformation is not given, thehigher value of A for strain induced precipitation appearsto be appropriate. 33, 34 Although Watanabe et al. also used

roughing deformations to obtain recrystallized austenite,they also employed accelerated cooling and found no

precipitation after roughing. Their value of A agrees withother observations on reheated austenite rather than withthose of recrystallized austenite. The reason for thesedifferences is not understood, but it is possible thatroughing deformations, which lead to recrystallization ofthe austenite and some local grain boundary Nb(C, N)

precipitation, may in some way 'condition' the matrix sothat subsequent strain induced precipitation afterdeformation at lower temperature is accelerated. This

requires further investigation, but in later computations ofthe interaction of precipitation and recrystallization after

Table 1 Evaluation of constants in equations (16) and (12)

1100 ~ /0 ..0, .,/

/ ,/

/ /,

01

0

I I

I

I, I obs. caIe. B =25x 101OK3

~1000 0 .0 o Le Bon et al~l\\ o Watanabe et al~5w0 :: \:: >

l-t ? \ eo

\0 :: ' , .W0...

~2 :w 900- I-

\" ~~ .0 O.'.

,' "

" - .

" ' 0800~ 0I

10' 102 103 104

TIME,S

6 Comparison of observed precipitation start-time-

temperature curves in undeformed austenite with

curves calculated from equation (12) with

B=25 X 1010 K 3 for the data of Le Bon et al.21 andWatanabe et al.25 on the steels of composition and

grain size shown in Fig. 5a and d

roughing deformations have been carried out, the lowervalue of A is considered to be the appropriate value,leading to an equation for precipitation:

to .0 5 = 3 x 10- 6 [NbJ - 1e - 1Z - o 5

270000 25 x 1010x exp ~ exp T3 (In k

s)2

UNDEFORMED AUSTENITE

Precipitation of Nb(C, N) in undeformed austenite hasbeen studied by Le Bon et al.,21 Simoneau et al.,27 and

Jizaimaru e t a l.28 in austenite cooled directly to theprecipitation temperature after reheating to a hightemperature and by Watanabe et al.25 in austeniterecrystallized by high-temperature deformation beforecooling to the precipitation temperature. Figure 6compares the results of Le Bon et al.21 and Watanabee t a 1 .25 for 5% precipitation with the curves calculated

from equation (12) using the mean value of B =25 X 1010K3 found for strain induced precipitation.

Condition of Precipitation detection

Author Reference austenite method

Le Bon et al. 21,26 Reheated and Microhardnessdeformed

Ouchi et al. 22 Reheated and Microhardness

deformed

Hansen et al. 23 Reheated and Extraction replica

deformed

Watanabe et al. 25 Recrystallized and Electrolytic extraction

deformed and filtrationJanampa 18 Recrystallized and Electrolytic extraction

deformed and centrifuging

Le Bon et al. 21 Reheated (undeformed) Microhardness

Watanabe et al. 25 Reheated and Electrolytic extraction

recrysta II ized and filtration


Value of constant

to match data Best value of

at 900C constant

Constant A Constant A92x10-5 15x10-5

59 X 10-5 10 x 10-5

53 X 10-5 10 x 10-5

45x10-5 25x10-5

2'5x10-6 30 x 10-6

Constant C Constant C31 x 10-12 30 X 10-11

15 X 10-12 80 x 10-13


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* NB Cuddy calls this the "recrystallization stop temperature".

0'01%Nb

o R L To R ST

0'095%Nb

to '05 0'0650/0 Nb

800

1100

uo ~1000w0 ::

:JI-


8/10




50

o RST

E O' O'410260-12

~start

ROLLING REDUCTION,o/o

20 30 4010950

EFFECT OF GRAIN SIZE

In deformed austenite an effect of grain size is expected onthe recrystallization time, as indicated in equation (18), butnot on strain induced matrix precipitation (equation (16)).In reheated austenite, the grain size is expected to be""225 Jlm and for a steel of composition 01C-0'007N-0'04Nb the interaction of precipitation and recrystal-lization is shown by the solid lines in Fig. 11 and leads to avalue of RST of 960C. If a grain size of 40 Jlm could beobtained in reheated austenite, the broken line forrecrystallization indicates that RST would be reduced by

about 80C. However, in practice a grain size of 40Jlmco~ld only be obtained by recrystallization after roughingreductions and, as discussed above, this is expected toadvance the precipitation kinetics, as shown by the brokencurve, leading to an increase in RST for this grain size of -about 40C. If some grain boundary precipitation takes

place during roughing, this could have a retarding effect onrecrystallization, which would further increase RST. Theeffect of changing grain size by modifying the roughingrolling sequence could therefore be rather more complexthan implied by equations (16) and (18) and further studyis required.

rolling ("" 2 s between first and second finishing passes),Fig. 9 shows that recrystallization may effectively stop at

considerably higher temperatures,' even without theoccurrence of strain induced precipitation.

101 102

TIME;s

9 Influence of strain on interaction of recrystallization

and start of strain induced precipitation, showing

effect on RST for O'07C-O'004N-O'035Nb steel

u1000

recrystallizatio

o start

0'1

.008

.002o

observed by Cuddy

o predicted for matrix precipitat ion

1100 0predicted for grain boundary ..0"

precipitation ~,,"

Y

"""0. ., 0

//. .

// ...0

e /O // 0

e l lI 0

. 0 /o

z900o~

: : J. . . . J

~ 800uW0 ::

W0 ::

:J~

~1000

2wI-

~

2: : J

u

0-04 006

Nb,wt.O/o

8 Comparison of RLT predicted for strain induced

matrix and grain boundary precipitation with values

observed by Cuddy39,40 on O'07C-O'004N steels

boundary precipitation could be represented simply byshifting the curves in Fig. 7 by an order of magnitude toshorter times, and that RLT is determined by grain

boundary precipitation, then the effect of niobiumconcentration would be given by the broken line in Fig. 8.This line is about 25C above the one for matrix

precipitation and is in equally good agreement withCuddy's observations. It is unlikely that grain boundary

precipitation would have the sa~e value of B in equation(16) as matrix precipitation and so the form of t~e

precipitation start curve might change. However, graInboundary precipitation could weIr determine RLT, whereasit is generally thought that strain induced matrix

precipitation is required to ensure the complete st?ppag~ ofrecrystallization. This would have the effect of IncreasIngthe temperature intervals between RLT and RST by about25C more than indicated in Fig. 7. Some support for this

is given by the observations of Dutta and Sellars41 inexperimental rolling which leads to a temperature intervalof ""60 between RLT and RST and a higher value of RLTthan predicted for strain induced matrix precipitation.

RST

0-802800

o 004 06 STRAIN

10 Dependence of RST on strain for O'07C-O'004N-

O'035Nb steel

u ~900w0: ::JI-

< t:0::W0 . . . .

2 :~850

EFFECT OF STRAIN

The effect of strain, or rolling reduction, in the firstfinishing pass on the RST does not appear to have beenstudied experimentally, but equations (17) and (18) suggestthat it should have a significant effect. Figure 9 shows theinteraction of precipitation and recrystallization expectedfor a steel of composition 0'07C-0'004N-0'035Nb fordifferent levels of strain. This shows that RST should

decrease with increase in strain, as illustrated in Fig. 10.For this steel composition, Fig. 10 also indicates that for15% reduction (8 =0'19), typical of plate rolling, RST isexpected to be about 915C, and finish rolling should notcommence above this temperature, in agreement withnormal controlled rolling practice. For 50% reduction(e=0'8), typical of strip rolling, RST is only .8200~.However, because times between passes are short In stnp



9/10




1100

C=3x10-6

- l5x10-5

precipitation

start

10' 102

TIME,s

11 Effect of grain size on interaction of recrystal-

lization and start of strain induced precipitation in

as-reheated austenite (solid line) and in previously

recrystallized austenite (broken line) for 01C-0'007N-O'04N b steel

Conclusions

The forms of precipitation start curves for Nb(C, N)precipitation derived from equations based on nucleationtheory and the solubility product for niobium, carbon, andnitrogen in austenite match well with observed curveswhen the equations include the influence of thermo-mechanical processing conditions on the density of

preferred nucleation sites. The constants required in the

equations are affected by the different detection methodsused by different authors, but when account is taken of thedetection method, the available data show consistenteffects arising from composition, strain, and temperature ofdeformation.' The results also indicate that the nature ofthe preferred nucleation sites is unchanged by thermo-mechanical processing, but their density is stronglyinfluenced.

Combining the calculated precipitation start curves withequations for recrystallization when all the niobium is insolution allows predictions of the lower limit oftemperature for complete recrystallization (recrystallizationlimit temperature, RLT) and the upper limit of temperaturefor effective stoppage of recrystallization (recrystallizationstop temperature, RST), both in good agreement with the

observed effects of composition. It also suggests that RLTmay be determined by strain induced grain boundary

precipitation, whereas RST requires matrix precipitation.Furthermore, the calculations show that RST depends onstrain in the first finishing pass in rolling, and on theaustenite grain size and thermo mechanical history duringthe roughing stage of rolling.

Acknowledgments

The authors are grateful to Tata Steel, India, for leave ofabsence given to Dutta, and to Davy McKee (Sheffield)Ltd. for their support of the research project. .

References

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1711-1721.10. K. C. RUSSELL: Adv. Colloid Interface Sci., 1980, 13, 205-318.11. J. ASHELL: 'Alloys and simple oxides'; 1970, New York,

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13. B. SPARKE, D. W. JAMES, and G. M. LEAK: J. Iron Steel Inst.,1965, 203, 152-153.

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Annual Congr., ABM, Recife, Brazil, July 1981, Vol. 1,47-63.

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36-40.

22. C. OUCHI, T . SAMPE I, T . OKITA, and I. KOZASU: in 'Hotdeformation of austenite', (ed. J. B. Ballance), 316-340; 1977,New York, The Metallurgical Society of AIME.

23. s. S. HANSEN, J. B. VANDERSANDE, and M. COHEN: Metall. Trans.,1980, IIA, 387-402.

24. S. YAMAMOTO, C. OUCHI, and T. OSUKA: 'Thermo mechanicalprocessing of microalloyed austenite', (eds. P. J. Wray, A. J.DeArdo, G. A. Ratz), 613-638; 1982, Warrandale, Pa., TheMetallurgical Society of AIME.

25. A. WAT ANABE, Y. E . SMITH, and R. D. PEHLKA: in 'Hotdeformation of austenite', (ed. J. B. Ballance), 140-168, 1977,New York, The Metallurgical Society of AIME.

26. A. Le BON, 1. ROFES-VERNIS, and c. ROSSARD: Mem. Sci. Rev.Metall., 1973, 70, 577-588.

27. R. SIMONEAU, G. BEGIN, and A. H. MARQUIS: Met. Sci., 1978, 12,381-387.

28. J. JIZAIMARU, H. KOBAYASHI, and T. KOSAKA: Tetsu-to-Hagane(J. Iron Steel Inst. Jpn), 1974, 60, 177.29. T. M. HOOGENDORN and M. J. SPANRAFT: 'Microalloying '75',

75-87; 1977,New York, Union Carbide Corporation.30. Y. MATZUMATA and w. ROBERTS: Personal communication,

Swedish Institute of Metals Research.31. c. M. SELLARS: 'Deformation, processing and structure', (ed.

G. Krauss), 245-277; 1982, Metals Park, Ohio, AmericanSociety for Metals.

32. c. M. SELLARS: in Proc. Conf. 'HSLA Steels '85', Beijing,People's Republic of China, Nov. 1985, Chinese Society ofMetals.

33. B. DUTTA: PhD thesis, 1986, University of Sheffield.34. E. VALDES: PhD research, 1986, University of Sheffield.35. J. 1. JONAS and I. WEISS: Met. Sci., 1979, 13, 238-245.36. T. TANAKA: 'Hot deformation of steels', 55-72; 1980, Tokyo,

Iron and Steel Institute of Japan.37. c. M. SELLARS: 'Hot working and forming processes', (eds.

C. M. Sellars and G. J. Davies), 3-15; 1980, London, TheMetals Society.

38. L. J. CUDDY: Metall. Trans., 1981, I2A, 1313-1320.39. L. J. CUDDY: 'Thermo-mechanical processing of microalloyed

austenite', (eds. P. J. Wray, A. J. DeArdo, and G. A. Ratz),129-140; 1982, Warrendale, Pa, The Metallurgical Society ofAIME.

40. B. MIGAUD: 'Hot working and forming processes', (eds. C. M.

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Sellars and G. J. Davies), 67-76; 1980, London, The MetalsSociety.

41. B. DUTTA and c. M. SELLARS: Mater. Sci. Technol., 1986, 2,146-153.

Appendix

Influence of detection method

The detection methods employed by different authorsdiffer in their ability to reveal the true onset of

precipitation. For example, Dutta and Sellars41 found thatextraction replicas only reveal particles >2-3 nm in size.Thus, after rolling at 950C and holding at 900C, straininduced precipitates were first observed on extractionreplicas after 80 s holding, whereas precipitationstrengthening of austenite was a maximum after 50 sholding.41 After rolling at 900C, profuse fine precipitateswere observed33 in thin foils (Fig. 12) on cooling to 800C.

This coincided with the maximum austenite strengthening,whereas precipitates were only observed on replicas after100 s holding at 850C, when softening had alreadycommenced. Electrolytic extraction showed about 22%

precipitation to have taken place when fine matrixprecipitates are first observed on extraction replicas.Extraction replicas are therefore considered to lead .to

precipitation start times about a factor of 5 longer than thetrue values, and in Table 1 this factor has been applied toobtain the best estimate of the true value of A in equation(16) from the data of Hansen et al.23 Since particle size isexpected to be smaller for increased supersaturation, thisfactor could well vary with composition and withtemperature. In the latter case, slower particle coarsening

could also contribute to an increase in the factor withdecrease in temperature so that the constant B in equation(16) is also affected.

Measurements of precipitation hardening obtained byaging ferrite after different prior thermomechanicaltreatments of the austenite provides an indirect method ofassessing the amount of Nb(C, N) previously precipitatedin the austenite, but it is not clear what volume fractioncan first be detected. Le Bon et al.21,26 found that indeformed austenite the hardness method gave times for thestart of precipitation considerably longer than thoseobtained using a chemical extraction technique and theconverse was true in reheated and undeformed austenite.These observations imply that the hardness technique isinfluenced by the distribution of precipitates in austeniteand possibly by other factors as well as the volume fractionof precipitation. In Table 1 the best estimates of A inequation (16) and C in equation (12) for the microhardnesstechnique have therefore been adjusted on the basis of thecomparative times obtained by chemical extraction.

The methods of chemical or electrolytic dissolution andthen filtration or centrifuging are considered to be the most 'reliable. In the extraction process care has to be taken toavoid raising the temperature because this could lead todissolution of very fine Nb(C, N) precipitates, especiallywhen using hydrochloric acid. For filtration, the choice offilter size is important, and for centrifuging the time mustbe sufficiently long to avoid loss of the very fine particles.However, agglomeration of the fine particles in suspension

probably makes these risks less than might be anticipated.Clearly, these methods reveal particles precipitated at grain

12 Transmission electron micrograph of strain

induced matrix precipitates of Nb(C, N) in 01C-

0'012N-0'031 Nb steel recrystallized to 45 Jimaustenite grain size and then rolled to strain of 019

at 900C, air cooled to 800C, and quenched

boundaries as well as in the matrix. Hansen e t a1.23 haveshown that grain boundary precipitation is expected tooccur earlier than matrix precipitation, but simplecalculation shows that grain boundary precipitates havelittle influence on measured times to 5% precipitation bythe extraction methods.

Considering that diffusion of niobium controlsprecipitation, and that the diffusion distance x in time t isgiven by x2 = Dt, then, if all the niobium within thedistance x from a grain boundary was precipitated at the

boundary, the effective fraction F of niobium precipitatedwould be given by

F=1-(d-2x)3/d3 . (19)

where d is the austenite grain diameter. Taking thediffusion coefficient of niobium as16

D = 14 x 10-4exp -270000/RTm2 S-1 . (20)

gives x =01 Jlm after 10 s at 1000C and from equation'(19) f= 02% and 1% for grain sizes of 250 and 50 Jlm,respectively. The effect is thus negligible for coarse grainsizes, but in Table 1 the best estimate ofA in equation (16)has been rounded up for Janampa's data.1s The results forWatanabe et al.25 have been reduced by a factor of 18because their steel contained some molybdenum, which isknown to retard Nb(C, N) precipitation.42

From these considerations it can be seen that the bestvalues of A in Table 1 show differences arising from thethermomechanical treatment of the austenite rather thanfrom the detection method. A similar analysis cannot becarried out for the constant B in equation (16), but it isconsidered that the scatter in optimum values by a factorof 25 about the mean arises mainly from the differentdetection methods used by different workers.

References

42. M. G. AKBEN, B. BACROIX, and J. J. JONAS: Acta Metall., 1983,31,161-174.
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mst,87-eff comp y proc vars on nbcn prec in nb microal aust

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