Effect of Grain Boundary Segregation of Interstitial Elementson Hall­Petch Coefficient in Steels

Setsuo Takaki1,2,+, Daichi Akama1,2, Nobuo Nakada1,2 and Toshihiro Tsuchiyama1,2

1Department of Materials Science and Engineering, Kyushu University, Fukuoka 819-0395, Japan2International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka 819-0395, Japan

The yielding behavior of interstitial-free steels and low-carbon steels with varying amounts of C and N were investigated in connectionwith the Hall­Petch relation. The Hall­Petch coefficient is as small as 150MPa·µm1/2 in interstitial-free steels but it increases to 600MPa·µm1/2

by adding solute carbon up to 60 ppm. Nitrogen does not have a significant effect on the Hall­Petch coefficient. The results of three-dimensional(3D) atom probe analysis indicated that carbon has 3­4 times greater segregation potential in comparison with nitrogen. The small effect ofnitrogen on the Hall­Petch coefficient in steel is probably due to the small segregation potential of nitrogen. It was also confirmed thatdiscontinuous yielding occurs when the difference between the yield stress and friction stress is increased by grain-refinement strengthening andthat yielding occurs by dislocation emission from grain boundaries where primary dislocations have piled up. Carbon atoms segregated at grainboundaries seem to play a role in stabilizing dislocation emission sites at the grain boundaries, which enhances the Hall­Petch coefficient of iron.These results support the dislocation pile-up model of explaining yielding in polycrystalline metals. [doi:10.2320/matertrans.MA201314]

(Received August 21, 2013; Accepted September 26, 2013; Published November 9, 2013)

Keywords: grain refinement strengthening, Hall­Petch coefficient, interstitial elements, grain boundary segregation, dislocation pile-up,interstitial free steel, discontinuous yielding

1. Introduction

It is well known that the yield strength of polycrystallinemetals, ·y, increases in inverse proportion to the square rootof the grain size, d, and this relation is called the Hall­Petchrelation (·y = ·0 + kyd¹1/2).1,2) In this equation, the constant,·0, and the slope, ky, are referred to as the friction stress andthe Hall­Petch coefficient (HP coefficient), respectively. Ingeneral, the HP coefficient increases with an increase in theshear modulus of metals but the other effects have not beenclarified yet. In the case of steel, elements such as C andN are contained interstitially and these elements have asignificant effect on yielding behavior. For example, a clearyield point appears in mild steel containing a small amount ofcarbon and the yield point is reduced by removing carbonand nitrogen using a wet hydrogen treatment.3) Therefore,for a long time, a Cottrell locking mechanism has beenaccepted to explain the appearance of yield points in steels.However, Tomimura et al. found that a yield point appearseven in an austenitic stainless steel with ultrafine grains lessthan 1 µm.4) Recently, discontinuous yielding has beenreported in aluminum with an ultrafine-grained structure.5)

This suggests that the appearance of a yield point is acommon phenomenon in polycrystalline metals strengthenedby grain refinement.

The reduction of the yield point by purification, asmentioned above, suggests that interstitial elements such asC and N have some influence on the yielding behaviorof steel. In this paper, the effect of carbon and nitrogenwas reviewed in terms of the yielding behavior of iron.The yielding mechanism of polycrystalline metals is alsodiscussed in connection with the dislocation pile-up modelproposed by Hall and Petch.1,2)

2. Friction Stress and the Hall­Petch Relation inInterstitial Free (IF) Steels

Before discussing the influence of interstitial elements onthe yielding behavior of iron, the yielding behavior of pureiron should be clarified. Figure 1 shows the change in yieldstrength of single-crystal pure iron as a function of testingtemperature. Since the iron used in this study was singlecrystal, the yield strength corresponds to the friction stressin this figure. The measurements were taken in the tensiledirection between [100] and [110] at each testing temper-ature.6) Therefore, in this figure, the crystal orientationdependence of the yield strength is displayed by error bars. Itwas found that the crystal orientation dependence of the yieldstrength was minimal above room temperature and the yieldstrength at 25°C was evaluated to be 50­60MPa. On theother hand, the effect of (C + N) on the friction stress of iron

Temperature, T / °C

0 100 200−100

Low

er y

ield

str

ess,

L

/ MP

a

0

100

200

300

400

Strain rate: 4x10−3/s

25 °C

50~60MPa

σ

Fig. 1 Change in lower yield stress of single-crystal iron as a function oftesting temperature. Each plot shows the average of specimens tensiledeformed in the direction between [100] and [110].6)

+Corresponding author, E-mail: takaki@zaiko.kyushu-u.ac.jp

Materials Transactions, Vol. 55, No. 1 (2014) pp. 28 to 34Special Issue on Strength of Fine Grained Materials ® 60 Years of Hall­Petch®©2013 The Japan Institute of Metals and Materials OVERVIEW

at 18°C was investigated by Heslop7) and Cracknell8) andtheir results are shown in Fig. 2. Friction stress of metals iscomposed of two components; thermal component whichincreases with lowering temperature and non-thermal com-ponent which is changeable depending on the amount ofsolute alloying elements. In this figure, the value at 18°C isrepresented for the thermal component. The friction stress inthis figure was determined by the respective Hall­Petchrelation. The friction stress is 60MPa without C and N,which agrees well with the results shown in Fig. 1. Thefriction stress of iron is changeable depending on temperatureand strain rate, but it can be concluded that the friction stressof pure iron is 40­60MPa under conventional tensile testingconditions, i.e., a temperature of 10­30°C and a strain rate of10¹4­10¹3/s.

As for the Hall­Petch relation in interstitial-free (IF) steel,a few experimental results have been reported and aredisplayed in Fig. 3.9,10) A small difference is found in thefriction stress, but it is probably due to the solid-solutionstrengthening of excess Ti added to remove solute carbon andnitrogen as Ti(C,N), as well as the testing temperature and

strain rate. As a result, at room temperature, the followingHall­Petch equation was obtained for IF steel:

·y ½MPa� ¼ ð50� 10Þ þ 150 � d ½�m��1=2 ð1ÞThe stress­strain curve of a specimen with a grain size of30 µm is also displayed on the right side. The yielding ofIF steel is characterized by continuous yielding. In the caseof IF steel, the HP coefficient is as small as 150MPa·µm1/2,making it difficult to see the effect of grain-refinementstrengthening.

In terms of the effect of substitutional elements on the HPcoefficient, it is already known that chromium does not affectit,11) that phosphorus decreases it slightly,12) and that nickelincreases it.9) It has not been clarified yet why nickelincreases the HP coefficient, but the addition of Ni iseffective for enhancing grain-refinement strengthening iniron. For example, Fig. 4 shows the effect of 3%Ni additionon the HP relation and the yielding behavior in IF steel.Nickel increases the friction stress of iron through solid-solution strengthening and also enhances the HP coefficient.It should be noted in the stress­strain curve that discon-tinuous yielding appears and yield-point elongation occursafter yielding, even in IF steel. In comparison with Fig. 3,it was found that the difference between the yield stressand friction stress is increased by the addition of 3%Ni.This suggests that discontinuous yielding occurs when thedifference between the yield stress and friction stress hasbeen increased by grain-refinement strengthening. Thisconfirms the claim that the presence of solute C or N is notan essential condition for the occurrence of discontinuousyielding.

3. Hall­Petch Relation and Yielding Behavior in SteelsContaining Interstitial Elements

In low-carbon steels represented by mild steel, manystudies have been performed to discuss the HP relation.Figure 5 summarizes the data obtained in low-carbonsteels.13­15) In 1966, Morrison13) systematically examinedHP relations in steels with various carbon concentrations(0.005­0.2%) and reported the identical HP coefficient of600MPa·µm1/2 for every steel. This result indicates that there

0.030.020.010

(C+N), (mass%)

0

100

200

Thermal component at 18 °C (J.Heslop et al.)

[MPa]=4500x(C+N)(A.Cracknell et al.)

150

50Friction stress

of pure iron at 18 °C

Δ σ

Fric

tion

stre

ss,

0/M

Pa

σ

Fig. 2 Effect of solute (C+N) on friction stress of iron at 18°C.7,8)

Elongation, (%)

1 2 3 40

Grain refinement strengthening (28MPa)

Friction stress

0

20

40

60

80

100

120

0 0.1 0.2 0.3d −1/2 /μm−1/2

: this study: R.Matoba et al.: W.B.Morrison et al.

Grain size, d /μm

25100 11

IF steel (Fe−0.02%Ti)

ky=150

Yie

ld s

tren

gth,

0.2

/ MP

aσ

Fig. 3 Hall­Petch plot and yielding behavior in IF iron without solute carbon or nitrogen.9,10)

Effect of Grain Boundary Segregation of Interstitial Elements on Hall­Petch Coefficient in Steels 29

is no carbon-concentration dependence regarding grain-refinement strengthening in steel, at least in the carbon-concentration range above 0.005%. After that, the currentauthors examined the HP relation in ultrafine-grained ironwith a grain size up to 0.2 µm and proposed the followingequation for polycrystalline iron:16­19)

·y ¼ 100þ 600 � d�1=2 ð2ÞIn the grain size region up to 1 µm, much data were addedas the result of national projects in Japan, and it was recon-firmed that the above equation holds in 0.15%C steel up toa grain size of 1 µm.14,15) As a result, it can be concludedthat the HP coefficient is approximately 600MPa·µm1/2

in steels with more than 0.005% carbon. In Fig. 5, the HPrelation in IF iron is shown by a broken line in order toclarify the difference with low-carbon steels. This resultsuggests some influence of a small amount of carbon on themechanism of grain-refinement strengthening.

On the other hand, Low et al. reported the effect ofpurification on yielding behavior in mild steel and the resultsare shown in Fig. 6.3) Purification was performed by a wethydrogen treatment at 725°C. As carbon and nitrogen areremoved from specimens as CO and NH3 by this treatment,specimens are purified more with increasing holding time.

The yielding of the original material is characterized bydiscontinuous yielding, and the yield point is reduced bythe purification and finally disappears. Because the Cottrelllocking model provides a convenient explanation for thisdiscontinuous yielding in steel, it has been accepted for along time. However, the current authors recently foundthat the HP coefficient is changeable in iron with less than0.005% carbon.20) Figure 7 shows the effect of solute carbonand nitrogen on the HP coefficient of iron. It was found thatthe HP coefficient is large enough in iron with 41 ppm solutecarbon, but the coefficient decreases with decreasing amountsof solute carbon. In contrast, nitrogen does not have asignificant influence on the HP coefficient. The differencebetween carbon and nitrogen will be discussed later inrelation to grain-boundary segregation behavior. For now, thebehavior shown in Fig. 6 can be explained as shown inFig. 8. Solute carbon enhances the friction stress slightlybut it has a greater effect on the HP coefficient. Thus, thedifference between yield stress and friction stress is increasedby increasing amounts of solute carbon. In other words, thedifference between yield stress and friction stress decreasesas a result of purification, which changes the yieldingbehavior from discontinuous yielding to continuous yielding.Here, it should be noted that very small amounts of carbon

0.8 1.00.60.40.200

100

200

300

400

500

600

700

800100 20 10 5 3 2 1

Grain size, d /μm

d −1/2 /μm−1/2

ky =600

Matsukura et al. (1999)

Morrison (1966)

0.05C−1Si−1.5Mn−0.02Nb0.05C−1Si−1.5Mn

M. Etou et al. (2008)

0.09C0.20C

0.005C0.13C

0.05C0.15C

0.15C−0.74Mn

Low carbon steels (0.005 ~ 0.2%C)

IF steel

Yie

ld s

tren

gth,

y

/ MP

aσ

Fig. 5 Hall­Petch plots in low-carbon steels.13­15)

Elongation, (%)1

Grain refinement strengthening (75MPa)

Friction stress

0 2 3 4

100 50 20 15

Grain size, d / μm

0 0.1 0.2 0.3d- −1/2 / μm−1/2

0

50

100

150

200

Yie

ld s

tres

s,

0.2

/ MP

aky=290

Fe−3%Ni−0.008%Ti

IF steel

Solid solution strengthening

σ

Fig. 4 Hall­Petch plot and stress­strain curve in IF­3%Ni steel.

0.75h

1.5h

3h

0 10 20 30 40 50

300

0

100

200

Elongation, (%)

Fe−0.05%C

Holding time at 725 °C:5h Nom

inal

str

ess,

/ M

Pa

σ

Fig. 6 Effect of purification on yielding behavior of a low-carbon steel.Purification was performed by the wet hydrogen treatment at 725°C.3)

S. Takaki, D. Akama, N. Nakada and T. Tsuchiyama30

have a significant influence on yield strength by changing theHP coefficient. Thus, in a discussion of the HP relation, thetrue effect of substitutional elements cannot be evaluatedunder the coexistence with interstitial elements. In fact,completely different experimental results have been reportedfor HP coefficients in Fe­Cr­C alloys21) and Fe­P­Calloys,22) in contrast with our results in IF Fe­Cr alloys11)

and IF Fe­P alloys.12)

4. Mechanism of Yielding in Polycrystalline Metals

The dislocation pile-up model is a reasonable model forexplaining the yielding of polycrystalline metals, and somedirect evidences showing dislocation emission from grainboundaries has been reported.23­25) In 1965, dislocationemission from grain boundaries was found in opticalmicrographs of an Fe­3.65%Si alloy.23) In 304-type auste-nitic stainless steel, dislocation emission from grain bounda-ries was dynamically observed with transmission electronmicroscope (TEM).24) Recently, the current authors havesucceeded in observing dislocations emitted from a grainboundary to a neighboring grain in a high-nitrogen austeniticsteel.25) Figure 9 shows the TEM image of a specimenwith 0.2% tensile deformation. It was found that primary

dislocations pile up at grain boundaries and secondarydislocations are emitted from the area where primarydislocations have piled up. It was also confirmed that such

Grain size, d / μm

100

0

200

0 0.1 0.2d −1/2 / μm−1/2 d −1/2 / μm−1/2

100 2030

(a) Fe−C

Solute carbon: 41ppmC

IF steel

17ppmC

150

50

250

0.3

100

0

200

0 0.1 0.2

100 2030

(b) Fe−N

IF steel

Solute nitrogen: 48ppmN

20ppmN

0.3

250

150

50

Grain size, d / μm

Yie

ld s

tren

gth,

y

/ MP

aσ

Yie

ld s

tren

gth,

y

/ MP

aσ

Fig. 7 Effect of solute carbon (a) and nitrogen (b) on Hall­Petch coefficient. Specimens were water quenched from 700°C after holdingfor various lengths of time to control grain size.20)

Elongation, (%)2 3 410

100

0

200

0 0.1 0.2

100 2030

(a) Fe−C

Solute carbon: 41ppmC

IF steel

17ppmC

150

50

250

0.3

Grain size, d / μm

d −1/2 / μm−1/2

Yie

ld s

tren

gth,

y

/ MP

aσ

Fig. 8 Hall­Petch plots and stress­strain curves in IF iron and iron containing small amounts of solute carbon.

500nm

G.B.

Dislocations emitted from G.B.

Piled up dislocations

Fig. 9 Transmission electron micrograph showing dislocations emittedfrom grain boundary (G.B.) in Fe­25%Cr­1%N austenitic alloy tensiledeformed by 0.2%.

Effect of Grain Boundary Segregation of Interstitial Elements on Hall­Petch Coefficient in Steels 31

microyielding takes place in each crystal grain and that thenumber of microyielded grains increases during macroscopicyielding.23) The authors pointed out that macroscopicyielding starts when the total amount of microyielded crystalgrains has reached 70­80% in volume fraction.10)

According to dislocation pile-up models,1,2) the followingequation has already been proposed for explaining grain-refinement strengthening in shear stress "¸y:

�¸y ¼ ðGb¸�=k³Þ1=2d�1=2 ð3Þwhere G, b, k, d and ¸* denote, respectively, shear modulus,the Burgers vector, a constant depending on the character ofthe dislocation, the grain size, and the critical grain boundarystrength, which corresponds to the shear stress required forgenerating dislocations at grain boundaries. Grain boundariesform barriers against dislocations generated from a Frank­Read source, whereas they work as dislocation sourceswhen the pile-up stress has exceeded ¸*. In bcc metals, thefollowing equation is constructed for the theoretical HPrelation by including a Taylor factor of 2:

·y ¼ ·0 þ 2ðGb¸�=k³Þ1=2d�1=2 ð4Þwhere ·0 is the friction stress. The HP coefficient, ky, is givenby ky = 2(Gb¸*/k³)1/2 and, in steel, it has experimentallybeen obtained as a function of solute carbon content, asshown in Fig. 7. Figure 10 shows changes of ky and ¸* thatwere calculated from ky and eq. (4) as a function of solutecarbon content. In specimens water quenched from 700°C, kyincreased with increasing carbon content, and it becameconstant at approximately 600MPa·µm1/2 above 60 ppmcarbon. The value of ¸* also increased with increasing carboncontent, corresponding to the change of ky. It should be notedthat ¸* is as small as 0.4GPa in IF steel, but it is significantlyenhanced by adding small amounts of carbon. For instance,

¸* becomes about 6GPa by adding 60 ppm carbon. Thecarbon concentration at grain boundaries increases withincreasing carbon content of steel. The above results suggestthat dislocation emissions from grain boundaries becomemore prevalent when carbon has segregated at the grainboundaries. Thus, Wilson examined the effect of 90°C agingon the value of ky in an Fe­0.003%C alloy water quenchedfrom 700°C26) and Fig. 11 shows the results. In the as-quenched specimen, ky is 310MPa·µm1/2, and this is areasonable value in comparison with our results shown inFig. 10. At 90°C, C atoms can move within a bcc Fe latticebut it is difficult to form carbide precipitates. Here, it isinteresting that ky gradually increases with increased holdingtime at 90°C, and it finally levels off at approximately700MPa·µm1/2. This result enables us to imagine that Catoms segregated at grain boundaries during 90°C aging,which enhanced the stability of the dislocation emission siteat the grain boundaries. The value of ¸* should be enhancedby this stabilizing dislocation emission site at the grainboundaries and lead to an increase of ky. In polycrystallineiron, it is probable that yielding starts by dislocation emissionat grain boundaries and that carbon has a significant influenceon the mechanism of grain-refinement strengthening.

5. Grain-Boundary Segregation of Carbon and Nitrogen

As mentioned above, carbon has the ability to increase theHP coefficient but nitrogen does not. If the dislocation pile-up model is acceptable as the mechanism of grain-refinementstrengthening, such a difference between carbon and nitrogenmay occur depending on the grain-boundary segregationbehavior of each element. Figure 12 displays the results ofthree-dimensional (3D) atom probe analysis showing theamount of C and N segregated at the grain boundaries inFe­C and Fe­N alloys.27) Each specimen was prepared tohave the same atomic fraction of C or N, 0.02 at%, and it wasconfirmed that the amount of solute C and N was 0.0019 at%in both specimens. However, apparent differences can beseen between carbon and nitrogen in terms of grain-boundarysegregation behavior, in that carbon has an approximately3­4 times greater segregation potential. In the Fe­N alloys,it should be noted that almost the same amount of C and Nwas detected at the grain boundaries, even though the bulkcarbon content was only one-tenth that of the nitrogencontent. This demonstrates that carbon has a greater potential

Fe−30ppmC

k y/ M

Pa·

μm1/

2

600

700

500

400

300

200

100

0101 102 103 104 105

Aging time at 90 °C, t / min

IF steel

Slowly cooled from 700 °C

Water−quenched from 700 °C

Fig. 11 Effect of aging at 90°C on Hall­Petch coefficient, ky, of Fe­0.003%C alloy that was water quenched from 700°C.26)

0 20 40 60 80 100

Edge (k=0.72)

Screw (k=1)

Solute carbon, (ppm)

IF iron (0.4GPa)0

2

4

6

8

k=0.86

(b)

100

200

300

400

500

600

700k y

/ MP

a·μm

1/2

0

(a)

(700 °C WQ)AuthorW.B.Morrison

/G

Pa

τ∗

Fig. 10 Changes in (a) Hall­Petch coefficient, ky, and (b) critical grainboundary strength, ¸*, as a function of solute carbon in Fe­C alloy.13,20)

S. Takaki, D. Akama, N. Nakada and T. Tsuchiyama32

than nitrogen in terms of grain-boundary segregation. So far,it is unknown whether nitrogen itself has a significant effecton grain-refinement strengthening similar to carbon or not,but it is clear that the effect of nitrogen on the HP coefficientof iron is difficult to determine owing to its small segregationpotential.

If the HP relation is affected by the segregation of alloyingelements, the grain-size dependence of the concentration atthe grain boundary, Xb, should be taken into consideration.Xb will decrease with decreasing grain size, d, because thegrain boundary area per unit volume, Sb, increases withdecreasing grain size (Sb ; 3=d). The results shown inFig. 12 do not give the value of Xb directly, but it can beroughly evaluated as follows: The molar volume of bcc ironis about 7.1 cm3/mol at room temperature, and therefore, thenumber of Fe atoms per unit volume, NFe, is evaluated to be85 atoms/nm3. The number of carbon atoms in the matrix iscalculated to be 0.016 atoms/nm3, which corresponds to asolute carbon content of 41 ppm. The atomic density aroundgrain boundaries must be smaller than that in the matrix butits actual value is unknown. Therefore, the current authorsevaluated it by grain-boundary simulation using steel ballsand obtained a value of approximately 90% as the relativeatomic density at a grain boundary layer 1 nm thick. Thus, thenumber of Fe atoms around the grain boundary is estimatedto be 76 atoms/nm3. Since the number of excess C atoms atthe grain boundary was 7.6 atoms/nm2 in the Fe­C specimen,Xb can be evaluated as 0.10 [= (7.6 + 0.016)/76] bypresuming that C atoms are replaced with Fe atoms at thegrain boundary and that C atoms are distributed uniformlywithin the 1-nm-thick grain boundary layer. On the otherhand, the volume fraction of the grain boundary, Vb, is givenby Vb = t·(3/d) under the condition d º t, where t denotesthe thickness of the grain boundary layer. From a viewpointof mass balance, the following equation should be realizedbetween Xb, the concentration in the matrix, Xm, and the meanconcentration, X0:

X0 ¼ Vb �Xb þ ð1� VbÞ �Xm ð5ÞHere, the segregation coefficient, K (= Xb/Xm), is unknownbut the enrichment factor, ¡ (= Xb/X0), is given as 522(= 0.10/0.00019) for the Fe­C specimen. The value ofK must be slightly larger than that of ¡, so K = 530 wasapplied for calculating the relation between d and Xb. Theresults obtained from eq. (5) are shown in Fig. 13. The grainsize dependence of Xb becomes significant below 20µmbut it is small above 20 µm. This means that the carbonconcentration at the grain boundaries is almost the same asfar as grain size of specimens has been controlled to be largerthan 20 µm. In our study, the HP relation was examinedin the grain size region above 10 µm, as shown in Fig. 7.It is concluded that the HP coefficient was reasonablyevaluated under the same conditions as the carbon concen-tration at the grain boundaries. It is understood that the resultsdisplayed in Fig. 13 are changeable depending on the carboncontent of steels, but it is true that the carbon concentrationat grain boundaries is markedly reduced by grain refinementto a sub-micron level. Regarding the discussion of the HPrelation in metals, especially in ultrafine-grained metals, weshould pay attention to the segregation behavior of alloyingelements and impurities, which is changeable depending ongrain size.

6. Conclusions

In this review, the yielding behavior of interstitial-free (IF)steel and low-carbon steels containing different C and Namounts were discussed in connection with the Hall­Petchrelation and the following conclusions were obtained:

(1) The friction stress of pure iron is 50 « 10MPa at roomtemperature at a strain rate of 10¹4­10¹3/s, which is usuallyapplied to tensile testing.

(2) The Hall­Petch coefficient in IF steel is as small as150MPa·µm1/2, but the value increases with increasingamounts of solute carbon. It reaches 600MPa·µm1/2 byadding 60 ppm carbon but tends to level off at this value inthe carbon concentration range above 60 ppm. The change ofyield strength by purification in low-carbon steel wasreasonably explained by the carbon-concentration depend-ence of the Hall­Petch coefficient.

Solute N: 0.0191 at%Solute C: 0.0191 at%

0

2

4

6

8

10

(a) Fe−56ppmC−11ppmN(Grain size: 20μm)

Δ N

, (at

oms/

nm )2

(b) Fe−5ppmC−54ppmN(Grain size: 20μm)

: C

: N

7.6

2.1

1.5

Fig. 12 Results of 3D atom probe analysis showing the difference betweencarbon and nitrogen on grain boundary segregation.27) ¦N denotes thenumber of excess atoms per unit grain boundary area. Specimens wereheld at 700°C for 90 s and then quenched in water.

Atomic fraction of C at grain boundary; Xb

Grain size, d /μm

Xb

Segregation coefficient; K =530 (=Xb / Xm )

20μm

0

0.02

0.04

0.06

0.08

0.10

0.12

0 10 20 30 40 50 60 70 80 90 100

Fig. 13 Effect of grain size on carbon concentration at grain boundary.Mean solute carbon concentration is 0.000191 in atomic fraction (41 ppmin mass fraction). Xm denotes atomic fraction of C in matrix.

Effect of Grain Boundary Segregation of Interstitial Elements on Hall­Petch Coefficient in Steels 33

(3) Discontinuous yielding is a common phenomenonthat appears in polycrystalline metals when the differencebetween yield stress and friction stress has been increasedby grain-refinement strengthening. It is probable that theyielding of polycrystalline iron is caused by dislocationemissions from grain boundaries where primary dislocationshave piled up and segregated carbon atoms have stabilizedthe dislocation source at the grain boundaries. These resultssupport a dislocation pile-up model to explain yielding inpolycrystalline metals.

(4) In polycrystalline iron, carbon enhances the Hall­Petchcoefficient significantly but nitrogen does not. Three-dimen-sional atom probe analysis showed significant grain boundarysegregation of carbon but little segregation of nitrogen inspecimen that were water quenched from 700°C. It seemsthat carbon has 3­4 times larger segregation potential incomparison with nitrogen. The small effect of nitrogen on theHall­Petch coefficient in iron is probably due to the smallsegregation potential of nitrogen.

Acknowledgment

This work was supported by Grant-in-Aid for ScientificResearch B Number 23360310.

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