INFLUENCE OF MICROSTRUCTURE ON THE CARBON DAMPING PEAK IN

IRON-CARBON ALLOYS*?

PHILIP STARK,: B. L. AVERBACH and MORRIS COHEN5

The internal-friction peak due to the stress-induced migration of carbon in b.c.c. iron has been studied in a series of high-purity iron-carbon alloys with variations in grain size and intercarbide distance. It is found that when these microstructural parameters are small the height of the carbon damping peak does not correspond to the equilibrium solubility at the solutionizing temperature. An explanation is suggested in terms of the rapid precipitation of carbon during the quench from the solution temperature, the sites being provided by gram boundaries or ferrite-carbide interfaces. Only when the gram size and mean distance between carbides are sufficiently large can the equilibrated carbon content be retained in solution on quenching to room temperature. The same phenomena are involved when martensite is tempered to ferrite-carbide aggregates.

INFLUENCE DE LA MICROSTRUCTURE SUR LE PIC DE FRICTION INTERNE DU AU

CARBONE DANS LES ALLIAGES FER-CARBONE

L’autaur Btudie le pit de friction interne du L la diffusion du carbone dans le fer cubique cent& sous l’effet d’une tension, dans un ensemble d’alliages fer-carbone de haute purete distincts par la grosseur du grain et la distance entre les oarbures. 11 trouve que, lorsque ces parametres sont petits, la hauteur du pit du carbone ne correspond pas B, la solubilite a l’equilibre pour la temperature de mise en solution.

11 propose une explication ou il est tenu compte de la precipitation rapide du carbone au tours de la trempe a partir de la temperature de mise en solution, les sites de precipitation &ant con&it&s par les frontieres de grains ou par des interfaces ferrite-carbure.

Ce n’est que si la grosseur du grain et la distance moyenne entre carbures sont importantes que le pourcentage de carbone correspondant a l’equilibre peut 6tre meintenu en solution au tours de la trempe jusqu’a la temperature ambiante.

Les m6mes phenomenes interviennent au tours du revenu de la martensite pour dormer des agregats de ferrite et carbures.

EINFLUSS DER MIKROSTRUKTUR AUF DAS KOHLENSTOFF-DAMPFUNGS-MAXIMUM

IN EISEN-KOHLENSTOFF-LEGIERUNGEN.

Das von der spannungsinduzierten Wanderung von Kohlenstoff im kubisch raumzentrierten Eisen herriihrende Maximum der inneren Reibung wurde an einer Reihe von hochreinen Eisen-Kohlenstoff- Legierungen mit unterschiedlicher KorngrSsse und verschiedenem mittlerem Abstand zwischen den Karbidteilchen untersucht. Es wurde gefunden, dass dann, wenn diese mikrostrukturellen Parameter klein sind, die Hiihe des Kohlenstoff-Diimpfungsmaximums nicht der Gleichgewichtslijslichkeit bei der Normalisierungstemperatur entspricht. Zur Erkliirung dieses Befunds wird vorgeschlagen, dass w5hrend des Abschereckens von der Normalisierungstemperatur eine rasche Ausscheidung des Kohlen- staffs stattflndet, wobei die Korngrenzen oder die Ferrit-Karbid-Grenzen als Ausscheidungsstellen wirksam sein sollen. Nur wenn Korngrijsse und mittlerer Karbid-Abstand geniigend gross sind, ist es moglich, den ins Gleichgewicht gebrachten Kohlenstoffgehalt beim Abscbrecken auf Raumtemperatur in Liisung zu behalten. Dieselben Erscheinungen t&en auf, wenn Martensit zur Bildung von Ferrit- Karbid-Aggregaten getempert wird.

1. INTRODUCTION frequency is approximately 1 c/sec.o) The height of This investigation was prompted by recent internal- the peak, &,,-I, is proportional to the concentration of

friction studies which indicated that the carbon peak “mobile” carbon atoms in the lattice, and the tem- in a-iron depends on the microstructure. It is well perature at which the peak occurs is related to the established that there is an internal-friction peak in relaxation time for the stress-induced redistribution low-carbon b.c.c. iron at about 37°C (99°F) when the of the carbon atoms. This damping phenomenon is

* This paper is taken from a thesis presented in January considered to provide reliable measurements for both

1957 by Philip Stark in partial fultlllment of the requirements the diffusivity and the solubility of carbon in a-iron; for the Sc.D. degree in Metallurgy at the Massachusetts Institute of Technology.

Werto) has thoroughly reviewed the methods and

t Received Se&ember 18. 1957. summarized the relevant data. i USAF, Wright-Petters& Air Force Base, Dayton, Ohio. 5 Department of Metallurgy, Massachusetts Institute of

Lagerberg and Josefsson(2) have reported, however,

Technology, Cambridge 39, Massachusetts. that the internal-friction peak varies with the grain

ACTA METALLURGICA, VOL. 6, MARCH 1968 149

1

150 ACTA METALLURGICA, VOL. 6, 1958

size of the a-iron. For a solution temperature of 630°C

(1165”F), they found the value of QmV1 to be 0.008*

when the grain size was 15-50 ,u, but &,,-I was 0.013

when the gram size was 0.5-2 mm. Only the higher

value is in line with the generally accepted equilibrium

solubility of carbon in b.c. iron at 630°C (1165°F).

Thus, the microstructural details may have appreciable

influence on these measurements, and the interpre-

tation becomes somewhat uncertain.

A similar conclusion is reached in the light of

internal-friction studies on tempered martensite in a

high-purity 0.78 per cent carbon allay.(3) No carbon

peak is observed in tetragonal martensite despite the

content of dissolved carbon, apparently because the

applied stress is insufficient to induce any significant

migration of the carbon atoms from their preferred

interstitial sites in the tetragonal lattice. Even after

the martensite is tempered at temperatures high

enough to produce b.c.c. ferrite, the carbon damping

peak barely begins to emerge at a tempering tempera-

ture of 485°C (900°F). Moreover, the full peak

expected from the equilibrium solubility of carbon in

ferrite is not achieved on tempering for 20 hr at 650%

(1200°F). Correcting for the amount of carbide present

does not remove the anomaly. Inasmuch as the

highly-tempered structure consists only of ferrite and

carbides, it appears that the internal-friction results

are influenced by the presence of carbides. Such

effects of microstructure have not been generally

recognized, and this investigation was undertaken in

order to help clarify the phenomena at play.

2. EXPERIMENTAL METHODS

An inverted torsional pendulum of the type sug-

gested by Chenc4) was constructed for this work. The

inverted arrangement allowed counterbalancing the

weight of the pendulum-bob and clamping assembly

so that the net longitudinal stress on the wire

specimen was very small. Test temperatures between

0 and 95°C (32 and 205’F) were uniformly maintained

by circulating water in a jacket surrounding the

specimen. Frequencies between 0.5 and 0.9 c/see were

employed, and

relationship : the damping was computed from the

(1)

where f is the frequency and t is the time for the

amplitude to decay to one-half of its initial value.

The specimens were in the form of 0.030 in. dia.

wires. During the torsional vibration, the maximum

shear strain on the surface was never more than

* Each 0.01 unit of &,-I is approximately equivalent to 0.01 wt. per cent of carbon in so1ution.u)

Weight per cent Normalizing SDecimen Treatment carbon treatment

0.025 720°C, 20 hr None Austenitized at 950°C, 15 min, brine-quenched Austenitized at 950°C, 5 hr, air-cooled Austenitized at 980°C, 5 hr, furnace-cooled Austenitized electrically in argon at temperature near melting point, 30 BBC, cooled in argon

0.29 87O"C, 1 hr Auatenitized at 770’%, 2 hr; transformed at 700°C, 24 hr Au&nit&d at 990°C, 5 hr; transformed at 710°C, 24 hr

-___ 0.62 815’C, 1 hr Austenitized at 790°C, 2 hr;

transformed at 720%. 4 hr Austenitized et 790°C, 2 hr; transformed at 720°C, 20 hr

0.78 815’C. 1 hr 10 Austenitized at 765”C, 2 hr; transformed at 720°C, 3 hc

11 Austenitized et 765”C, 2 hr; transformed at 720°C, 30 hr

12 Annealed et 650°C, 25 hr 13-37 Austenitized at 760°C, 30 min

oil-quenched; tempered from 110 to 650°C, 4 to 136 hr

TABLE 1. Heat treatments for varying the grain size and/or carbide dispersion of the internal-friction specimens

2 x 1O-5 A straight line was always obtained when

the logarithm of the amplitude was plotted against the

number of cycles, indicating that the internal friction

was independent of the amplitude and there was no

plastic deformation in the twisting.

All internal friction results reported here are cor-

rected for background damping (0.001 units). A

correction has also been introduced for the volume

occupied by the carbides, since the carbon atoms in

this phase do not participate in the damping process.

The volume percentage of carbides was measured by

quantitative metallography as described later, and the

peak height was prorated to correspond to 100 per cent

ferrite. The maximum error in &,,-I was about fl0

per cent.

Four high-purity iron-carbon alloys were investi-

gated, as listed in Table 1. The original iron was

received from the Natimal Research Corporation in

the form of a Q in. dia. vacuum-cast hot-rolled rod,

containing 0.004 per cent carbon, 0.0005 per cent

nitrogen and 0.013 per cent oxygen. The rod was

reduced by cold swaging to 0.25 in. dia. and then

vacuum-annealed at 870°C (1600’F). This was followed

by carburizing at 700°C (1292’F) for 24 hr in hydrogen

saturated with normal heptane at room temperature.

STARK, AVERBACH AND COHEN: CARBON DAMPING PEAK IN IRON-CARBON ALLOYS 151

After furnace oooling, the alloy was machined to 0.190 in. dia., homogenized at 72O*C (1328’F) for 20 lsr, and then swaged and drawn to 0.030 in. dia. wire. The final carbon content was 0.025 per cent. The three higher-carbon alloys in Table 1 are identical with those used by Roberts et aZ.t5) These were swaged and drawn with intermediate anneals to 0.030 in. dia. wire.

Heat treatments to provide various ferrite grain sizes and/or different dispersions of the carbides were carried out, involving either long isothermal annealing or hardening and tempering as indicated in Table 1. In all cases, decarburization was carefully avoided, usually by sealing the specimens in evacuated Vycor tubes. Nearly all the annealing treatments of the three higher-carbon alloys in Table 1 consisted of austenitizing at the higher temperature shown in each instance, followed by hot quenching to the lower temperature for isothermal transformation to ferrite plus spheroi~ed carbides. The hardening and fem- pering treatments were applied only to the 0.78 per cent carbon alloy, with the tempering temperatures ranging from 110 to 650°C (230 to 1200°F).

Lineal analysis was used for the quantitative measurement of four microstructural parameters: (1) mean ferrite path between carbides, (2) mean ferrite path between grain boundaries, (3) mean free path between both carbides and grain boundaries, and (4) volume fractions of ferrite and carbide. The method and the equipment, consisting of a Hurlbut counter and a bench microscope, have been discussed in detail by Howard and Cohen.(G)

The mean ferrite path between carbides is given by: T

(2)

where L, is the total distance traversed in the ferrite phase and N, is the number of carbides intercepted during the traverse.

The mean ferrite path between ferrite grain boundaries is :

Lf cc2 = - Nf

where N, is the number of ferrite grains intercepted and L, is defined as in equation (2).

The mean free path in the ferrite, taking both carbide and grain boundary interruptions into account, is:

L,

where nf is the number of uninterrupted ferrite paths encountered during the transverse.

The volume fractions of ferrite, V,, and of carbide, V,, are given by:@)

(5)

and

v, = LL, (f-5) t

where L, (or &. + L,) is the total distance traversed, and 1;; is the distance traversed over the carbides. Four traverses, each of approximately 2 mm in length, were conducted on each sample.

For the specimens tempered between 425 and 540°C (800 and loafs, the carbide dispersions were too fine for quantitative metallography with the optical microscope, and hence electron microscopy was adopted. Fifteen electron micrographs at 14,000~ were taken of each sample, and the mean distance between carbide particles was measured on each plate with a millimeter scale. A linear traverse of 5 x 10” mm was made for such samples. Metallo- graphic measurements at lower tempering tempera- tures were unnecessary, because, as previously mentioned, a carbon peak was not observed for tempering treatments below 485°C (300°F).

The tempered specimens were all brine-quench~ in an effort to preserve the extent of carbon solution in the matrix prevailing at the end of the tempering treatment. Then the internal friction determinations were made.

In the case of the annealed specimens, ~ol~~~on treatments were carried out at temperatures between 425 and 705°C (800 and 1300°F) for 30 min, followed by brine-quenching. The internal friction was then measured. The maximum solutionizing temperature for a given specimen never exceeded the prior anneal- ing temperature that was used to 6x the grain size and/or carbide dispersion; hence, these metalio- graphic parameters were not materially altered by the final treatment which established the degree of carbon solution in the ferrite. The internal-friction results were not affected by increasing the solutionizing time from 30 min to 5 hr, in~eating that a state of equilibration was reached.

3. EXPERIMENTAL RESULTS

Table 2 presents the Q,l data as a function of tempering temperature and time for a 0.78 per cent carbon martensite. As previously reported,t3) no internal-friction peak is found until the tempering temperature reached about 485°C (900°F). Between 485 and 650°C (900 and 1200°F), &,-I attains a plateau value characteristic of each tempering

162 ACTA METALLURGICA, VOL. 6, 1958

TABLE 2. Q,-1 * for tempered marten&e (0.78 per cent C) _ TABLE 3. Qtn-l * as a function of solutionizing temperature and grain size (0.025 per cent C)

__.:

a,* Solutio~z~ temperature (“C) Tempering

time Wsf

1

: 10 15 48 52 78

136

Tempering temperature (“C)

595 s,

M 425 I 485 540 595 650

--

0.002 - -

0.004 0.003

0.003 9 -

9-14 - 100 130 0.003 0.006 150 - 0.005

-

ferZi%- 1 corrected for background damping and 100 per cent

t as is the mean ferrite path between grain boundaries. The avera.ge grain d&meter is 1.65 GC~(?)

0.006 - -

0.009 0.008

-

I:_

0.009 0.009 0.012 0.012 0.012

485 540 650

0.004 0.006 0.007 0.009 0.009

0.009 0.009

425

0.000

0.000

L. -

__

-

0.003

0.004 0.005 0.005 0.005

0.001 i 0.0014

0.001 0.003 0.003

0.002 1 0.003 0.009 0.005 size is sufficiently large, i.e. the average grain- boundary intercept (a& must, be at least l&l00 ,u. This is in line with the findings of Lagerberg and Josefsson(2) and demonstrates that the anomalously low values are not attributable t,o the damping apparatus used here.

In the oase of the three higher-carbon alloys, the carbide dispersion becomes an important metallo- graphic variable along with the grain size. An example of the role of intercarbide distance (al) is shown in Fig. 1 for a sol&ionizing temperature of 650°C (I2~*F). When a1 is less than about 10 ,u, the internal friction increases rapidly with ul, but then levels off at a value which is below the carbon solu- bility limit at 650°C. This situation is essentially independent of the carbon content, and prevails for all the solutionizing tern~ratures (Rg. 2), the plateau value (apparent solubilityf increasing with

o 0-62XC, IsothermalIy Annealed

CI O~P§%C,lsothermatty Annealed

* &,,,-I corrected for background damping and 100 per cent ferrite.

temperature within a few hours of tempering. Although the plateaus increase with the tempering tem~rature, they fall appreciably below the carbon levels oor- responding to the equilibrium solubilities in ferrite at these temperatures. Even after tempering for 136 hr at 650°C ( 1200°F), Q,l is only 0.009, whereas ferrite saturated with carbon at this temperature should have a &,-I value of 0.012.

It is important to note that the internal-friction level reached at each tempering temperature can be approached from higher temperatures as well as from below, the latter being the usual case. As shown in Table 2, after tempering for 30 hr at 650% (12OO~F), retempering for $ hr at temperatures between 425 and 595°C (795 and 925*F) causes Q+,,-l to drop back to the aforementioned plateau values for these tempera- tures.

Smaller carbon-damping peaks than those ordinarily reported for low-carbon ferrite are also observed in annealed 0.29, 0.62, and 0.78 per cent carbon alloys. When these materials are heat treated to produce coarsely spheroidized structures (Table l), and then solutionized at a series of temperatures, the resulting &,I values (after brine-quenching) are almost identi- cal with the plateau values of the tempered marten- site. Here again, the same dependence of &,I on solutionizing temperature is found whether the temperature is approached from above or below.

In the light of this anomalous behavior, it seemed desirable to determine if the generally accepted damping values for low-carbon ferrite (~thout excess carbides) could be reproduced. The relevant data are given in Table 3; Q,,-l increases with the grain size, and does not attain the equilibrium solubility vs. solutionizing temperature unless the ferrite grain

True Carbon Solubility _-_-__---__--- ----_

6

4

:o~ 5 IO 15 20 25 30 35 40 45 0

0, (Microns)

FIG. 1. Qm-l as a function of the mean ferrite path between carbides (ccl) for iron-carbon alloys solution treated at 650°C.

STARK, AVERBACH AND COHEN: CARBON DAMPING PEAK IN IRON-CARBON ALLOYS 153

0 o 13 IO 20 30 40 50 60

a, (Microns)

FIG. 2. Superimposed curves of Q,-’ vs. mean ferrite path between carbides (al) for all solution temperatures.

the solutionizing temperature. Below some inter-

carbide spacing which depends on the solutionizing

temperature, &,,-I is a strong function of ar; but

when the plateau is reached for each temperature,

Qm-r becomes quite insensitive to the carbide dis-

persion.

The carbon contents corresponding to the apparent

solubility in Fig. 2 are plotted in Fig. 3, along with

the normal carbon solubility in ferrite.(*pg) It is

evident that the difference between the apparent and

equilibrium solubility curves tends to disappear with

decreasing temperature. On the other hand, when

the logarithm of the carbon content is plotted against

the reciprocal of the absolute temperature, the two

curves become straight and parallel, with a slope of

900, , , , I I I I I

t

Apparent Carbon Solubility 800 a This Investigation

600

E

” 500

2 ; 400

(58qlubility

A Lindstrand (9) a+ Fe3C l This Investigation

300 1 i

:I$ , , , , ] , , , , 0 *OlO a020 -030 so40

-I Q, = wt. i/0 c

FIG. 3. True and apparent solubilities of carbon in a-iron.

0 0.78%C, Tempered Mortensite

0 0.29%C, Isothermally Annealed

0 0.025% C, Al lay

0 40 80 120 160 Qz (M icrons)

FIG. 4. &,-I aa a function of the mean ferrite path between grain boundaries (an) for iron-carbon alloys solution treated

at 650°C.

about 12,500 Cal/mole. This agrees with Lindstrand’s(g)

value of 12,100 Cal/mole for the heat of solution.*

The discrepancy between the two curves is related

to the ferrite grain size. The specimens on the curve

labeled “apparent solubility” in Fig. 2 were extremely

fine-grained. Even when ur was as large as 45 ,u,

us was only about 10 ,u because of grain-growth

inhibition due to carbides at the boundary junctures.

The role of grain size is indicated in Fig. 4 for a

solutionizing temperature of 650°C (1200°F). Unfortu-

nately, the intercarbide distance is not fixed in this

plot, and hence us is not the only variable at play.

However, it may be noted that, unless a2 is well

above 10 p, &,,-I does not approach the true carbon

solubility. The only points that actually lie at the

equilibrium solubility level are those for the coarse-

grained 0.025 per cent carbon alloy. Nevertheless, it

is now clear that even the higher-carbon alloys can

display the true carbon solubility provided that the

grain size and carbide dispersion are sufficiently

coarse. The point at us = 10 ,u for the 0.29 per cent

carbon alloy in Fig. 4 was obtained with the first

isothermal annealing treatment listed in Table 1

(specimen 6). tci was then 45 p, giving a Q,,-l value

of 0.009 on the plateau of Fig. 1. With the second

isothermal annealing treatment (specimen 7) the

intercarbide spacing increased somewhat to 62 ,u, but

the principal change was an increase in us to 25 p.

Correspondingly, Q,r increased to 0.011, as shown in

Fig. 4.

The internal friction is plotted in Fig. 5 against the mean ferrite path (a,), taking both grain-boundary

and carbide interruptions into account. The initial

steep slope is mainly due to variations in the carbide

* Wert”’ gives 9700 cal/mole for the heat of solution, placing more weight on lower solutionizing temperatures than were used here.

154 ACTA METALLURGICA, VOL. 6, 1958

-- True Carbon Solubility -1

0.78% C, Tempered Mortensite ?

0.62% C, Isothermally Annealed

0.29%C, Isothermoily Annealed

O.O25%C Alloy

0: 0 40 80 120 I60 200

a3 (Microns)

FIG. 5. &,,-I as & function of the mean free path (cq,) for iron-carbon alloys solution treated cat 650°C.

dispersion in this range, while the subsequent bending of the curve at ~xa > 20 p and the gradual approach to the equilibrium solubility level are controlled by the grain size.

4. DISCUSSION OF RESULTS

Inasmuch as the elastic modulus and intensity of the carbon peak depend upon the crystallographic direction in the b.c.c. lattice, consideration was given to the possibility that the observed variations in damping capacity might be caused by changes in texture occurring in the annealing treatments employed to alter the grain size and carbide d.is- persion . However, back-reflection Laue patterns disclosed no pronounced texture in any of the speci- mens. Furthermore, in systematic series of heat t~atments to vary u1 or as, and hence Q,-“, the natural frequency remained constant, indicating that there was no pronounced change in the elastic modulus or average grain orientation of the polycrystalline specimens.

Tests were also conducted to determine whether carbide precipitation might occur at room temperature during the 10 min elapsed between the brine-quench from the solutionizing temperature and the subsequent damping tests. Resistivity measurements during this period at room temperature gave no evidence of carbon loss from the ferrite lattice. In addition, aging experiments by KumP*) suggest that, in the first 10 min at room temperature following the quench, the amount of carbon migrating to disloca- tions is much too small to account for the present discrepancies.

The most probable explanation of the findings reported here is that the grain boundaries and excess carbides provide effective sites for the precipitation of carbon, even during the brine-quenching of0.030 in. dia. specimens. Hence, if the grain size and/or inter-

carbide distance is very small, significant depletion of the ferrite solution may take place on quenching from the solutio~zing temperature. In other words, metallographic conditions may exist such that the equilibrium concentration at the solutionizing tem- perature cannot be preserved in the ferrite lattice at the lower temperatures where the carbon damping peak is found.

The reasonableness of this h~othes~ may be checked by considering the distance that carbon atoms can diffuse during the time of quench. The effective time of quenching, t, is about 1 set, and the weighted average diffusion coefficient, D, is of the order of lo-* cm2/sec. The approximate diffusion distance, (Dt)1~2t is then 1OW cm. Thus, a region of 1 p on either side of a grain boundary or surrounding an existing carbide particle can be substantially depleted of carbon during the quench. This is con- sistent with the experimenta findings, in that &,,-I is relatively small when a1 or cc2 is of the order of 1 ,Q; under such conditions the ferrite lattice seems to lose an appreciable part of the carbon that had been dissolved at the quenching temperature.

Seeman and Diekenscheid(ll) have arrived at a similar interpretation on the basis of electrical resistivity me~urements of aging in iron-carbon alloys. These investigators found that the extent of aging decreased markedly with increasing carbon content. They also noted that a 0.16 per cent carbon ahoy, aged at 350°C (66O’YE’) following a quench from just beIow the eutectoid temperature, contained precipitation-free zones around the pearlite patches. It was concluded that the cementite in the pearlite acts as precipitation sites for carbon during the quench and thus reduces the capacity for subsequent aging. In addition, Seeman and Dickenscheidoik reported that fine-grained ferrite retains less carbon in solution on quenching than does coarse-grained ferrite.

Lagerberg and Josefsson(2) have accounted for their grain-size effects in a-iron by assuming that carbon atoms are both absorbed at, and immobilized by, grain boundaries. Their results indicate that carbon is more soluble in fine-grained than in coarse- grained ferrite because of the presence of a thin austenite film (due to impurities) along the grain boundaries at the high solutionizing temperatures used.* However, in the high-purity alloys studied here, the eompli~ation of au&mite existing below the eutectoid temperature oan be ruled out, as shown by Lagerberg and Lement.02)

* The carbon dissolved in the f.c.c. austenite does not contribute to the damping peak.

STARK, AVERBACH AND COHEN: CARBON DAMPING PEAK IN IRON-CARBON ALLOYS 155

If, on the other hand, carbon atoms are assumed

not to be concentrated in grain boundaries, but

immobilized in the ferrite lattice on either side of the

boundaries, the influence of the boundaries would

have to be felt at a distance of at least 1 ,u to explain

the abnormally low &,,-I values. This concept is in

disagreement with recent models of the strain field

in the neighborhood of a grain boundary.

The conclusion that carbon atoms migrate to

nearby grain boundaries (as well as to existing

carbides) during the quench from the solutionizing

temperature raises the obvious question as to what,

then, happens to these carbon atoms at the grain

boundaries. Assuming that the width of a grain

boundary is one unit cell on either side and that the

carbon atoms lost during a quench from 650°C (1200’F)

go to grain boundaries when uz is smaller than 10 p,

the localized carbon concentration would be over 2

ca.rbon atoms per grain-boundary iron atom, This

high concentration suggests that the carbon actually

precipitates, rather than being merely entrapped

along the grain boundaries.

When a, and uz have the same value, it turns out

that there is one-half as much grain-boundary area as

ferrite-carbide interface per unit volume. However,

since carbon atoms can approach a grain boundary

from both sides, a unit grain-boundary area should

be about twice as effective as a unit ferrite-carbide

interface from the standpoint of carbon drainage.

Thus, if ai and ua are small and of the same order of

magnitude, both the carbide dispersion and ferrite

grain size should influence the amount of carbon lost

during the quench. When one of these parameters is

much smaller than the other, the smaller one controls

extent of depletion; for example, in Fig. 2, Q,,-l

depends strongly on u1 when the latter is small, but

becomes insensitive to cc1 when the latter is large. At

the plateaus, ui > a2 and the small grain size then

prevents the observed Q,,-l from reaching the equili-

brium solubility value.

However, the emergence of grain size as the

primary factor does not occur when a1 is exactly

equal to tcs. a1 can be somewhat larger than uz and

still exert an effect. Possibly, even when the carbides

are rather far apart, they can still provide potent

sinks for the carbon atoms if the grain boundaries

act as collectors along which the carbon can find

short-circuiting paths to the carbides.

In the light of these explanations, the carbon loss

on quenching should increase with the solutionizing

temperature because of the higher rate of diffusion

involved, and not because of any difficulty in attaining

equilibrium at the solutionizing temperature. This

accounts for the increasing disparity (Fig. 3) between

the equilibrium and apparent solubilities as the

solutionizing temperature is raised, whether the latter

is approached from above or below. At the same

time, the amount of carbon remaining in solution

likewise increases with the solutionizing temperature.

However, when cc1 and a2 (and hence a.J are sufficiently

large, &,,-I then approaches the equilibrium value

corresponding to the solutionizing temperature.

5. CONCLUSIONS

The height of the internal-friction peak associated

with the stress-induced migration of carbon in b.c.c.

iron does not correspond to the true solubility at the

solutionizing temperature when the grain size or

intercarbide distance is small. Under such conditions,

part of the dissolved carbon precipitates, despite

rapid quenching, at grain boundaries or existing

carbides. Thus, the ferrite at room temperature does

not retain the carbon content that prevails in solution

at the equilibrating temperature. These effects are

essentially independent of the overall carbon content

for a given grain size and intercarbide distance.

Similar findings are observed on the tempering of

martensite to ferrite plus carbides, the tempering

then playing the part of a solutionizing treatment.

ACKNOWLEDGMENTS The authors wish to acknowledge the support of the M.I.T. Instrumentation Laboratory and the U.S. Air Force for this research.

1.

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REFERENCES C. WERT Modern Research Techniqueces in Physical Metallurgy. p. 225 (1953). G. LAGERBERU and A. JOSEFSSON Influence of grain boundaries on the behaviour of carbon and nitrogen in a-iron. Acta Met. 3, 236 (1955). P. STARK, B. L. AVERBACH and M. COHEN Internal friction measurements on tempered martensite. Acta Met. 4, 91 (1956). N. K. &EN. Private communication. C. S. ROBERTS, B. L. AVERBACH and M. COHEN The mechanism and kinetics of the first stage of tempering. Trans. Amer. Sot. Metals 45, 576 (1953). R. T. HOWARD and M. COHEN Quantitative metallography by point counting and lineal analysis Tram. Amer. Iwt. Min. (Met&., Erqw. 172, 413(1947). B. S. LEMENT, B. L. AVERBACH and M. COHEN Micro- structural changes on tempering iron-carbon alloys. Trans. Amer. Sot. Metals 46, 581 (1954). C. J. DIJKSTRA Precipitation phenomena in solid solutions of C and N in u-iron below the eutectoid temperature. Trane. Amer. Inst. Min. (Met&.) Engra. 185, 253 (1949). E. LINDSTRAND A method for the measurement of elastic relaxation, and its use for the determination of the solubility of carbon in a-iron. Acta Met. 3,431 (1955). W. KUNZ The segregation of carbon in iron single crystals aa studied by torsion pendulum damping. Acta Met. 3, 126 (1955). H. J. SEEMAN and W. DICKENSCEEID Contribution a l’etude du vieillissement des alliagea fer-carbone par la mesure de la conductibilite-electrique. Rev. Met. 49, 379 (1952). G. LAOERBERO and B. S. LEMENT Precipitation of carbon and nitrogen from supersaturated solution in ferrite. Amer. Sot. Metals Preprint (1957).