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Cold-work internal friction peak in iron
COLD-WORK
INTERNAL
D. P.
PETARRAt
FRICTION and
D. N.
PEAK
IN IRON*
BESHERSS
An investigation of the cold-work peak in iron containing N confirms in modified form, the saturation effect reported by Koster. This effect, coupled with strain-aging results, was used to estimate the number of N atoms per atomic length of dislocation that contribute to the damping peak, The complementary relationship between the Snoek and cold-work peak heights seen upon aging at temperatures greater than that of the cold-work peak is shown to be primarily the result of dislocation recovery upon which is superimposed a lesser thermal distribution effect. An experimental technique for evaluating the latter effect has been proposed, and the free energy expression governing the distribution of N atoms between lattice and dislocation sites has been found to be of the form: AG = -0.47 - 2.6 x lo-*!I’ eV. A residual cold-work peak has been found in specimens having no Snoek peak and is believed due to the migration of N atoms from low energy traps to freshlyintroduced dislocation sites. C is shown not to contribute to the cold-work peak and, in fact, to retard its formation. PIC
D’ECROUISSAGE
DANS
LE
FROTTEMENT
INTERIEUR
DU FER
Une reoherche du pio d’ecrouissage dans du fer contenant de l’azote oonfirme, sous une forme modifiee, l’effet de saturation rapporte par Koster. On utilise oet effet, en association avec les resultats de viei~is~ment apres hxouisstlgtt, pour astimer le nombre d’atomes d’azote par longueur atomique de disloaation contribuant au pit d’amortissement. Par vieillissement 8.des temperatures superieures a celle du pit d’ecrouissagc, on observe une relation complementaire entre la hauteur du pit de Snoek et celle du pit d’bcrouissage; on montre que oette relation resulte essentiellement de la restauration des dislocations, a laquelle se superpose nn effet plus petit de distribution thermique. On propose une technique experimentale pour &valuer oe dernier effet; l’expression de l’energie libre gouvernant la distribution des atomes d’azote entre le rtjseau et les sites de dislocations est de la forme: AG = -0,47-2,6 x 1O-4 T eV. Dans les Behantilions ne donnant pas de pit de Snook, on trouve un pie d’ecrouissage residue1 attribue a la migration d’atomes d’azote vers de nouveaux sites de dislocations a partir de pieges de basse Bnergie. C ne aontribue pas au pit d’ecrouissage et, en fait, retarde sa formation. DAS
KALTVERFOR~UNGSMA~I~L~
DER
INNEREN
REIBUNG
IN
EISEN
Eine Untemuohung des naoh Kaltverformung auftretenden Maximums der inneren R&bung in Eisen mit Stickstoffgehalt bestatigt, in modifizierter Form, den von Koster beobachteten Sattigungseffekt. Dieser Effekt sowie Ergebnisse der Reckalterung wurden zur Abschltzung der Zahl der Stiokstoffatome pro atomare Veraatzungsl&nge, die zu dem Diimpfungsmaximum beitragen, herangezogen. Die komplementare Beziehung der Hohen des Snoek-Maximums und des Kaltverfo~ungamaximums, die naeh Altern bei Temperaturen oberhalb des letzteren Maximums beobaobtet wird, hangt in erstor Linie mit der Versetzungserholung und schwiieher mit einem thermischen Verteilungseffekt zusammen. Es wird ein experimentelles Verfahren zur Auswertung des letzteren Effektes vorgeschlagen. Der Ausdruck fur die freie Energie, welcher die Verteilung von Stickstoffatomen zwischen Gitter- und Versetzungspositionen bestimmt, wurde zu AC = -0,47-2,6 X lo-* T eV bestimmt. In Proben ohne Snoekmaximum wurde ein restliohes Kaltverfo~ung~aximum gefunden. Es wird auf die Wanderung von Stickstoffatomen von niederenergetischen Haftstellen zu neugebildeten Versetzungspositionen zuriickgeftihrt. Kohlenstoff tragt nicht zum Kaltverformungsmaximum bei, sondern verlangsamt vielmehr seine Bildung.
1. INTRODUCTION
Since the discovery of the cold-work peak in iron(l) over two decades ago, many of its characteristics have been determined.{z-6) The peak is reported to occur in cold-worked iron containing N and/or C at approximately 220% at 1 c/s with an activation energy The height of the peak between 30 and 40 k&/mole. increases linearly with interstitial content to a maximum or saturation value; the saturation value, itself, increases roughly as the square root of the plastic T Received June 6, 1966; revised August 11, 1966. This work was supported by the U.S. Office of Naval Research. ow at: General Electric Co., Lamp Division, Nela Park, Cle!&nd Ohio 44112. $ Hen& Krumb School of Mines, Columbia University, New York, New York 10027. ACTA
METALLURGICA,
VOL.
15, MAY
1967
strain. The saturation effect has been interpreted by KGster et aZ.(*) to mean that a specific dislocationinterstitial configuration causes the cold-work peak and that any excess of either dislocations or interstitials is ineffective. A11(1+6) who have compared the effect of C and N have found differences, the tenor of which is that N is a more positive agent than C in causing the cold-work peak. Aging in the temperature range lOO’C--600°C reveals the complementary nature of the Snoek and cold-work peaks ;[email protected]. as the aging tern~~~ture is increased the height of the cold-work peak decreases while that of the Snoek peak increases. Kijster et al. have analyzed this behavior in terms of thermal unpinning of solute atoms from dislocation sites and 791
792
ACTA
METALLURGICA,
The tempera-
transfer of these atoms to solid solution. ture
dependence
of
unpinning
was
calculated
Beshers’7) based upon a Fermi distribution atoms
at the
dislocation.
Kamber
pointed out the importance reducing
their analysis of thermal
of solute
et aZ.c5) later
of dislocation
the peak height,
by
recovery in
but did not include unpinning.
it in
Van Bueren(s)
VOL.
~100
15, 1967
ppm).
A complete
zone refined
irons
analysis of the Swedish and
has been
reported(14)
The first step in the preparation bring all material
to a standard
fully recrystallized,
was to
state consisting
0.062 in. dia. rods.
then wet hydrogen
elsewhere.
of specimens
of
These were
annealed 70 hr at 720°C and cold-
drawn to a diameter of 0.026 in. The specimens were
has observed that the Koster et al. data show the cold-
then recrystallized
work peak undergoing a relatively larger decrease than
at 95O’C in a N, plus 1 y0 H, atmosphere
the
lized first to the desired grain size in an argon atmos-
corresponding
rise
in the
Snoek
indicates that solute atoms apparently Upon
recrystallization,
atoms
the
reappear :
entirely
however,
peak.
phere
become “lost”.
the
cold-work
This
“lost”
peak
solute
disappears
and the Snoek peak returns to its original
height. A number of mechanisms
to explain the cold-work
and nitrided either simultaneously
at a temperature
between
or recrystal-
580%
and 950°C
followed by nitriding at 580°C in a hydrogen-ammonia atmosphere.
Carburization
hydrogen-n-heptane
was accomplished
atmosphere
following
in a
recrystal-
lization in argon, both at 720°C.
The specimens were
then
quenched
solution
annealed,
water
im-
mediately
Suggestions may be classified according
to the nature
apparatus for the primary purpose of determining
of the moving
the anelastic
N or C content from the height of the Snoek peak (no
defect
which furnishes
inserted into the precooled
and
peak have been put forward, but none is established.
strain necessary for internal friction. Most investigators(4*9-11) have identified the source of strain as the
samples
dislocations,
quenched,
their motion
atmospheres(4J0) tions
either slowed
or affected
by Cottrell
by concomitant
in the size of carbide
which restrict their motion.
or nitride
oscilla-
particle@)
the reorientation
of non-spherical
or on
precipitates,03)
a
sort of grand Snoek effect. The work reported here is an experimental
investi-
cold-work
peak
et al.
investigating
in purer
iron
than
that
The work has the two-fold the peak
itself,
while
utilize it to gain further knowledge
used
by
attempting
apparatus.
in the
and reinserted Following
this
then reheated for a second measurement the effect
of aging.
aging results
cold-worked
to
In addition,
were obtained
specimens
3. EXPERIMENTAL
of the dislocation-
more
by heating
in the
temperature
PROCEDURE
The prom-
A, defined
by twice
Throughout
Internal friction was measured in a torsion pendulum
RESULTS
The internal friction data are given in terms of the decrement,
previously.
friction
annealed,
mostly
range 250°C-550°C prior to the initial measurement of the cold-work peak.
divided
which has been describedo4)
C and N).
purpose of
impurity interaction. 2. EXPERIMENTAL
of area (RA),
the
of the cold-work peak the apparatus was
force-cooled, to observe
both
cold-drawn,
reduction
measurement
freshly
to contain
were again solution
immediately
range 3-30%
quantitive
gation of the saturation effect and other aspects of the Koster
were treated
the specimens
into the internal
Others have focused on
a modified Snoek effect near the dislocationa
Next,
internal friction
as the energy
the stored
this investigation
energy
loss per cycle of oscillation.
the Snoek peak is taken
as a measure of the amount of C or N in solid solution through the relationship :05) wt. y. C or N = 0.4 Amax.
inent features include a rapid heating rate such that T-l,
reciprocal
in time.
of the absolute
temperature,
is linear
The time required to heat the specimen from
the Snoek peak to the cold-work was approximately
peak temperature
1 hr. A longitudinal d.c. magnetic
field of 200 Oe was applied to the specimen to eliminate magnetomechanical
contributions
to the damping.
Three types of “pure” iron were used; in order of increasing purity they were : “Swedish iron” obtained from
A. D. Mackay
Co. (impurity
level ~2
x 10s
ppm), vacuum melted electrolytic iron from Westinghouse Electric Corp., and a similar iron which was zone refined
by the Battelle
American
Iron
Memorial
and Steel Institute
Institute
for the
(impurity
level
Carbon versu.s nitrogen All cold-worked specimens which contained C or N exhibited the cold-work peak. However, the characteristics of this peak were quite different for the two interstitial species. Carburized specimens exhibited a very small peak which was essentially of
C content
and
degree
of
independent
cold-work.
In
aged
specimens this peak became slightly larger, but still remained independent of C content and degree of cold-work. This behavior is illustrated in Figs. 1 and 2. The cold-work
peak obtained
with nitrided
speci-
mens was generally larger and, unlike the carburized specimens, sensitive to the solute level and degree of
PETARRA
BESHERS:
AND
200
150
100
COLD-WORK
INTERNAL
FRICTION
PEAK
793
250 ‘C
,
lL
SECOND
RUN
-J
I
3.0
1
I
I
2.6
2.6
(T’K
2.4 x
2.2
I
2.0
1.6
I
Moreover,
always
greater
illustrated
than
the
initial
in the
by the typical
peak
aged
height
condition,
work
was as
is
result shown in Fig. 3.
The cold-work
peak
increasing
height
was found
to depend
a-stage
manner.
a linear increase in peak height with
peak height;
Stage
positive
cold-work
height.
Specimens
II is a region of
and Stage
rapid rise in peak height.
Snoek
peak
Figs.
Group A consists
5-7.
different
nitrided
III
is a region of
A surprising
peak intercept annealed
feature
is the
at zero Snoek peak
of the
group
includes
at 950°C.
C zone
a summary
for several
purity
Both nitriding techniques
N concentration;
constant
and and
were of the same base metal
in a characteristic
Stage I represents
peak
cold-work specimens
Height of the cold-work peak upon N content
1000
FIG. 3. Effect of aging upon a vacuum melted iron specimen containing 16 x 1O-3 wt.% N and having 30% RA; frequency ~1 c/s.
Fro. 1. Effect of aging upon a vacuum melted specimen containing 15 x 1O-s wt.% C and having 15% RA; frequency ~1 o/s. cold-work.
x
toK
1000
irons
degrees
of
is shown
of vacuum
melted
in iron
The group B specimens and nitrided
at 580°C.
were used in the preparation refined
specimens.
of the significant
Table
features
curves shown in Figs. 5-7. Temperature of the cold-work peak The temperature found
of the cold-work
to be sensitive
to the
peak was also
N concentration
and
for a long time in wet
hydrogen and having no Snoek peak did, nevertheless, exhibit 4.
this residual cold-work
In the range 3-85%
peak
remained
decreased the
residual
impurity
unchanged
peak
level
peak as shown in Fig.
RA the height of the residual
with increasing
; the
peak
cold-work.
decreased
increased,
temperature The height
as the
and
of
substitutional
dropped
to
zero
in
Swedish iron. The relationship
d+ 010
l
0 SNOEK
between
20 PEAK
of the cold-
.
1
1
IO
the height
30 HT
40
(DEC. X 1000)
2. The relationship between the Snoek and coldwork peak heights before and after aging of 15% RA vaouum melted iron specimens containing C. FIG.
1
of the
g
0
I 3.5
3.0 +x
2.5
2.0
x 1000
FIG. 4. Internal friction results for vacuum melted iron specimens having 23 hr wet hydrogen anneal followed by 0, 3.1, and 85% RA; frequency ~1 c/s.
ACTA
794
METALLURGICA,
VOL.
15,
1967
0
I
MEAN GRAIN DIAMETER 0.013 mm 0050 mm 0.200 mm , 05oq rnnl
I
20
0 SNOEK
40 PEAK
60
80
HT.
(DEC.
X 1000)
FIG. 5. Cold-work peek height versus Snoek peak height, Group A; values in graph refer to RA.
degree of cold-work. The peak temperature increased with increasing N in a manner similar to Stage I and II. This result is shown in Pigs. 8 and 9 for zone refined and vacuum melted irons, respectively. A comparison of these two figures indicates that substitutional impurities cause a decrease in the peak temperature. The effect of cold-work is also seen to lower the peak temperature. 6 8 25 x
0
20
SNOEK
40
60
1 80
PEAK
HT.
(DEC.
100 X
120 1000)
FIG. 6. Cold-work peak height versus Snoek peak height, Group B; values in graph refer to RA.
”
0
20
SNOEK
40 PEAK
NITRIDED Nz +“z
x 0 NITRIDED A NH, :I I 00 60
HT.
(DEC.
100 x
120 1000)
FIG. 7. Cold-work peak height versus Snoek peak height, Group C; 14.8% RA.
Aging behavior
The aging characteristics of the cold-work peak were studied in detail. Nitrided specimens of vacuum melted iron were quenched from 58O”C, cold-worked and then aged for 1 hr in the temperature range 25O”G55O”C. They were then quenched from the annealing temperature for measurement of internal friction. The results shown in Table 2 indicate that an increasing aging temperature results in a decreasing cold-work peak height accompanied by an increasing Snoek peak height. To clarify the interpretation of the aging results a series of three further experiments was conducted. A brief outline of the experiments follows; the details are given in Table 3. Experiment 1. Two specimens were prepared with the same cold-work and N content. In one, the N was allowed to precipitate at a temperature higher than the cold-work peak temperature prior to measurement of the Snoek and cold-work peaks; in the other, the N was primarily in solid solution prior to the internal friction measurement. The cold-work peak heights were nearly equal whereas the Snoek peak heights were quite different. Experiment 2. Two identically prepared specimens
TABLE 1. Summary of cold-work peak height results
Specimen group
% RA
Height of residual peak (A x 1O8)
Slope of stege I
Dislocation satumtion concentration (wt.% N x 108)
Height of Stage II (A x 108)
3.1 14.8 28.4
3.7 4.3
0.47 0.47
1.0 __ __
4.6 7.6 -
B
14.8 30.1
4.9 5.7
0.67 0.50
4.6 11.2
11.6 19.8
C
14.8
7.5
0.64
5.1
15.0
x
PETARRA
BESHERS:
AND
COLD-WORK
INTERNAL
FRICTION
PEAK
795
TABLE 2. Effect
of aging temperature upon the cold-work and Snoek peak heights. The 14 and 26% RA specimens contained 18.4 x lO-s and 21.6 x 10V wt.% N, respectively
SNOEK
PEAK
HT.
(DEC.
X
1000)
Fla. 8. Cold-work peek temperature versus Snoek peak height in 15% RA zone refined iron.
gm
I
I
I
I
I
3,,
~_______________o______
k! 220- / ? : ,: 0 2 L 210 08’
p :: ti & $
x ._____X.___!?” c_“_~_________ ‘9 :, r______?_*_______.__________s___ &I _ *Jo :’ / . . : ’ _I I90 .’ : :a ;;” 180 :-’ 1
2 170z 0 SNOEK
20
I 40 PEAK
, 60 HT.
00 (DEC.
X 1000)
Pm. 9. Cold-work peak temperature versus Snoek peak height in vacuum melted iron; values in graph refer to RA.
Experiment number 1. &. b.
2. a.
b.
3. &.
b. c.
Snoek peak height (A x lo*)
% RA 14 14 14
250 450 550
12.0 7.4 3.7
23.0 42.0 45.5
26 26 26 26
250 300 500 550
23.5 18.7 8.0 7.5
17.0 25.6 47.2 52.7
were aged at the same temperature for different times and quenched for measurement of internal friction. The one aged for the longer time had the smaller coldwork and Snoek peaks. Experiment 3. A nitrided, cold-worked specimen was aged first at a high, then low temperature. It was quenched from the lower temperature for measurement of internal friction. The resulting cold-work peak was characteristic of the higher aging temperature. The specimen was then held at the lower temperature for a long time followed by remeasurement of internal friction. There was no appreciable change in the cold-work peak height.
Strain aging
1 100
TABLE
Cold-work peak height (A x 103)
Aging temp. (“C)
A specimen containing 12 x 10e3 wt.% N (Stage II) and one containing 41 x 10~~ wt.% N (Stage III) were each quenched from 55O”C, cold-worked 14.8% RA and aged at the temperature of the Snoek peak,
3. Details of aging experiments
Specimen treatment Nitride, quench, cold-work 50% RA, measure IF Nitride, quench, cold-work 50% RA, age 1 hr et 26O”C, quench, measure IF Nitride, quench, cold-work 50% RA, age 10 mm at 65O”C, quench, measure IF Nitride, quench, cold-work 50% RA, age 4 hr at 65O”C, quench, measure IF Nitride, quench, cold-work 14% RA, age 30 min at 460°C, quench, measure Snoek peak only age 75 min at 250°C, quench, measure IF age 14hrat250”C, quench, measure IF
Cold-work peak height (A x 10’)
Snoek peak height
14.2
40.0
13.4
18.0
14.0
30.5
4.0
19.5
-
48.0
7.0
43.0
6.6
5.9
(A x lo*)
ACTA
796
METALLURGICA,
VOL.
15,
1967
A is the constant describing the interaction between
a N impurity atom and a dislocation, D is the diffusion coefficient of the impurity, and kT is Boltzmann’s constant times the absolute temperature. A dislocation density of 1.7 x 10n cm/cm3 is obtained using Harper’s formula applied to the Stage II result. The formula was not applied to the Stage III specimen since the exponent, n, in this case equalled 1.35 during the early stages of precipitation and the data points fall along a curve rather than a straight line. p
n= 0.705
Activation energy -15’
’ 14
’
’ ’ 1.6 LOG,
f 2.2
’
’ 2.6
’
t
FIG. 10. Strain-aging results for zone refined iron containing N and having 14.8% RA.
24.5%. The internal friction values at this temperature were measured as a function of time and are plotted (Fig. 10) to determine the exponent, n, in the expression : A, = A,
+ (A,, -
A,)
exp
[
-
01 tn 7
(1) Null results
in which r is a time constant and Ac, A,, and At refer to the logarithmic decrement initially, finally, and at time t, respectively. Rearranging (1) and taking the natural logarithm of each aide gives:
(2) Taking the logarithm to the base 10 of each side of (2), it becomes apparent that if the data points in Fig. 10, fall on a straight line, the slope of the line is n. For Stage II, the data points do fall along a straight line of slope 0.705. This is close enough to the CottrellBilby(16) value of # to justify fitting the data to Harper’@‘) formula for strain-aging : f = 1-
exp [--ap(ADt/kT)2’3]
The temperature of the cold-work peak was measured as a function of frequency in the range 0.3-3.8 C/S. Three different specimens were studied: (1) zone refined iron, residual cold-work peak; (2) zone refined iron containing 2.0 x 10V3 wt.% N; and (3) Swedish iron containing 9.5 x 10m3 wt.% N. Preceding each measurement of peak temperature, each specimen was fully recrystallized, solution annealed, quenched, and cold-worked 15% RA. The activation energy results are given in Table 4.
(3)
where S = fraction of solute which has precipitated at time t, u = 3(.rr/2)n2, p is the dislocation density,
Several of the parameters investigated were found to have little or no effect upon the cold-work peak. Grain size, for example, affects neither the peak height nor temperature. This result is implicit in Figs. 7 and 8 which include specimens ranging in grain size from 1.2 x lop3 to 5.0 x 10-s mm average diameter. The magnetic field resulted in a reduction of the background damping level, but had little effect upon the height or temperature of the cold-work peak. Also, the peak was independent of strain amplitude over the range 1.5 x 1O-6 to 6.8 x 10-5. 4. DISCUSSION
The Koster saturation effect has been verified in a somewhat modified form with nitrided pure iron specimens. The novel features are the residual peak and Stage III. In addition the saturation effect was not observed with specimens containing C alone.
TABLE 4. Activation
Activation energy (kcal/mole) Freq. factor, ~~-1 (set-I) Peak-breath ratio av. experimental talc. for single 7 >
energy results
Zone refined iron (residual peak)
Zone refined iron (2.0 x 1O-3 wt.% N)
29 + -2
38 $ -2
Swedish iron (9.5 x 10mswt.“/o N) 38 + -3
10’4
10’S
10’8
1.8
2.4
1.8
AND
PETARRA
These resulted
BESHERS:
in an unexpectedly
peak, irrespective
COLD-WORK
small cold-work
IXTERNAL
FRICTIOS
with further cold-work
797
PEAK
(Fig. 4) and the height of the
peak is greater than that of cold-worked
of C content.
containing Stage III
C alone, regardless
specimens
of the concentration.
Aging of the C-bearing specimens causes the cold-work
We attribute tions beyond
Stage III, which occurs at concentra-
the range studied by Koster et al., to a
rise in dislocation
density
geneous precipitation Thus,
lattice. markedly
of nitride particles
the
between
resulting from the homo-
kinetics
of
within the
strain-aging
differ
Stage II and Stage III specimens.
peak to grow-but residual
only to a magnitude
peak.
The
data
equal to the
of KiY3) also show
this
residual cold-work peak although Ke, himself, attached little significance
to the observation.
Our interpretation
is that the purified
specimens
contain residual N atoms in low energy traps making
In the former case the observed t213time dependence is characteristic of diffusion to dislocations, while in
no contribution
the latter case strain aging occurs at a much acceler-
lower energy which attract the N atoms and give rise
ated initial rate indicating
to the residual cold-work
tation
is occurring
that substantial
in less time
diffusion to dislocations.
than
precipi-
required
The nuclei for precipitation
must be more finely spaced than the dislocations therefore,
were probably
generated
precipitate
Lattice
misfit at the interface
of the of fresh
which are then able to contribute
cold-work
damping
peak.
may be interpreted
to the
The data of KB et aZ.og)
as such an increase in dislocation
level due to Stage III precipitation. cold-work
by Keh
particles results in the generation
dislocations
and,
homogeneously
within the lattice as observed microscopically and Wriedt.o*)
for
peak was observed
In this case the
in unworked, quenched
introduced
to the Snoek peak.
during
contribute
cold-working peak.
to the cold-work
to the dislocations
C atoms likely do not
Thus, as shown in Fig. 2,
specimens
with a large C content
cold-work
peak.
upon aging is then explained
along the dislocations with N atoms. with the observation
that the C cold-work
in terms of quenching
feel that precipitation dislocation previously
and magnetic
dependent
dislocations. decrease
of Stage
was shown to be a “viscosity upon
Within
the
the
presence
of
mobile
Stage II the effect of N was to
dislocation
reduce
the background.
levels,
however,
resulted
effects reported(14)
support the above interpretation
The background
effect”
of C
of Kamber
et aZ.c5)
to grow during
aging at 24O’C long after the Snoek peak has completely
disappeared.
In addition
difference in activation peaks.
they observed
no
energy between the C and N
This further indicates
that the N
for the cold-work
peak and that the C atoms merely act to inhibit the peak in the manner described. At the present time we are unable to offer the reason
level.
The background III.
strains whereas we
is giving rise to the increase in
peak
This explanation
peak continues
cold-work
behavior
a minimal
by the replacement
species alone may be responsible
this
exhibit
The growth of the C cold-work
specimens of high N content and was not observed in Ke interpreted
still
ahead of the trapped N atoms, even
inhibit the peak formation.
is consistent
sites of
peak and, by diffusing
specimens
of lower N content.
The dislocations
offer
mobility At
increasing
and,
hence,
to
the higher
Stage
III
the
N
concentration
in an increase in background
accompanied
by a sharp drop in the magnetic damping.
Both
formation
of new dislocations
contribution
effects may be associated
to the
with the
resulting from nitride
precipitation.
for the marked
difference
atoms.
the different
Perhaps
the dislocation
in behavior electronic
of C and N states near
may bring about a chemical
reaction
for C and not N; one example would be the promotion of C to the tetrahedral
sites.
Saturation effect One of the most useful features peak is the saturation effect. work
the
linearly
height
of the
with increasing
limiting value.
of the cold-work
For a given level of cold
cold-work
peak
N content
(Stage
increases I) to a
At this point the available dislocations
are assumed to be saturated with N atoms and further increases in N content result in no further contribution
Residual peak and carbon behavior
to the damping (Stage II).
It has generally been assumed that cold-worked iron containing either C or N is a necessary and
It is interesting then to calculate the number of N atoms per unit length of dislocation which is required
sufficient
just to reach this saturation level.
condition
for
the
cold-work
peak.
Our
In this calculation
results indicate that even with no Snoek peak present in freshly quenched specimens prior to cold-working, a small residual cold-work peak appears following
the residual entrapped N should be taken into account. Extrapolation of Stage I to zero cold-work peak height gives a negative intercept which corresponds
cold-working.
to the magnitude
Once formed,
the peak does not grow
of Snoek peak for the entrapped
N.
798
ACTA
METALLURGICA,
For the zone refined iron this extrapolation gives a residual N concentration of 4.7 x 10-a wt.% while the saturation concentration at the 1.5% RA coldwork level equals 5.1 x low3 wt.%. The total of 9.8 x 10m3wt.% N corresponds to 3.3 x 1019 N atoms/cm3. If we take the strain-aging results at face value, the dislocation density of 1.7 x 10n cm/cm3 implies 1.94 x lo8 N atoms/cm of dislocation line. Along a screw dislocation, one atomic length is just the Burgers vector length; we will use this for all others as well. This gives a result of 4.75 N atoms per atomic length of dislocation. Alternatively, we may assume with Cochardt et aZ.(20) that there are three closest positions around a screw dislocation and assume further that only N atoms in those positions contribute to the cold-work peak. This condition will be met if in the calculation of dislocation density [equation (3)] the product aA213is set at 314.75 = 0.63 times the value given by Cottrell and Bilby. The Harper calculation has been called into question, most recently by Bullough and Newman(21) who conclude that Harper’s expression overestimates the dislocation density by a factor of about 3. If this result is valid we then conclude that the number of N atoms per atomic length of dislocation is (4.75 x 3) = 14.25. There is still uncertainty in the problem because we do not know the exact conditions at the dislocation. The solutions to the partial differential equation governing strain-aging are all obtained by supposing some configuration at the dislocation which enters the problem as a boundary condition on the solution and has a considerable effect on the final answer. The final interpretation of this part of our data must await further work. Aging behavior Specimens which are aged at temperatures above that of the cold-work peak then quenched show a reduction in the cold-work peak and an increase in the Snoek peak. This is shown in Table 2 and has been reported by other investigators’3-5) as well. This behavior has generally been attributed to thermal unpinning of solute atoms and binding energy calculations have been made(4,5p7)on that interpretation. However, the aging experiments (Table 3), which were designed to test this concept, clearly indicate that thermal unpinning is not the most significant factor in determining the aging behavior and that the binding energy calculation based only upon the variation of cold-work peak height with temperature is invalid. In the first experiment of Table 3 the dislocations
VOL.
15, 1967
of specimen a may be assumed to be relatively free of N atoms before the internal friction measurements were made, while those of specimen b are saturated as a result of the 25O’C aging treatment; yet the coldwork peaks were approximately equal. We conclude that the degree of dislocation saturation prior to measurement of the cold-work peak is of little consequence. The N atoms are able to diffuse to the dislocations within the time required to make the measurement. Thus, under the condition of surplus N, the cold-work peak height will be determined solely by the dislocation density. Experiment 2 illustrates the effect of aging time at 550°C. If the thermal distribution of N atoms were the primary factor then one might expect to see little difference between the 10 min and 4 hr treatments, because the equilibrium distribution of N atoms between the dislocation and interstitial sites should have been attained within the shorter time and not changed appreciably as a result of prolonging the time at temperature. However, the longer anneal did result in a markedly reduced cold-work peak which can best be explained in terms of dislocation rearrangement and annihilation. This is further substantiated by the results of Experiment 3. In this case the specimen was first aged at 450°C and then at 250°C. The resulting cold-work peak was characteristic of the higher temperature treatment despite the fact that the quench took place from the lower temperature. This clearly indicates that the effect of aging is nonreversible. Prolonged aging at the lower temperature does not much affect the cold-work peak height, indicating that the changes which occur at the higher temperature cause a stabilization of the structure with respect to the lower temperature. On the basis of the aging experiments, we conclude that two primary effects are occurring in the coldworked specimens while at elevated temperatures : first, and most importantly, the number of active dislocation sites is reduced through the process of recovery causing N atoms to be rejected into interstitial sites and second, a partitioning of N atoms occurs between the remaining dislocation sites and the lattice sites. Moreover, this distribution may be “frozen in” by means of rapid quenching, but cannot be evaluated by a measurement of the cold-work peak height alone, inasmuch as it has been shown that a new distribution will have occurred (one characteristic of the temperature of the cold-work peak) well within the time required to make the measurement. Even so, a binding energy expression in terms of measurable quantities can be set up and the calculations
PETARRA
carried out.
describes
AND
_~
nd
Nd
-
of solute
and lattice interstitial
of occupied dislocation ni, respectively; interstitial
AG = (H, -
-AG ni =--Ni - ni exp kT
nd
(4)
atoms
sites.
between
The numbers
and interstitial sites are nd and
the total numbers of dislocation
sites are Nd and Ni, respectively;
as follows:
and
aging experiment
some temperature, freezing
to obtain
in the N distribution
characteristic
of the
(5)
difference,
the
equal to the binding energy. and the results
free energy and deviation from AG = -0.466 - 2.58 X 10m4 T
Acf (talc.)
Aging temp.
A measure of the Snoek peak at
ni = clPsn where c1 is the well known
and entropy
TAS
in Table 5. It is to be noted that the
least squares fit:
and aged at
this point sufbces to give both ni and nd in the following manner:
799
SJ = AH -
T(S, -
the enthalpy
TABLE5. Calculated
T. The specimen is then quenched,
aging temperature.
PEAK
A least squares analysis was performed
should proceed
cold-worked,
Hi) -
are summarized
A specimen is nitrided to a known Stage
II level, C,, then quenched,
FRICTION
former being essentially
and AG
is the difference in free energy between the two types of occupied sites. The appropriate
INTERNAL
applied to the further relationship :
The expression:
the distribution
dislocation
COLD-WORK
BESHERS:
(“K)
(eV)
523 723 823
-0.609 -0.678 -0 660
523 573 773* 823
-0.576 -0.626 -0.767 -0.679
the
from A@least squares)
Deviation
(% difference) - 1.3 -3.9 2.8 4.3 -1.9 -15.3 0
* This datum point was treated as an outlier included in the least squares analysis.
and
not
constant relating the Snoek peak height, P,,, and the
binding energy result, 0.47 eV, justifies our assumption
interstitial
of dislocation
content;
of the N not at interstitial locations
ni assuming that all
nd = Co -
sites is bound to the dis-
(a point to be discussed
further).
Ni, the
total number of interstitial sites may be taken as 3 per
cold-work
saturation
peak.
at the temperature
Wriedt and Darken,(22) using a chemical technique, have recently determined the thermodynamic
sites at the instant of quench as the remaining unknown
describing
quantity.
between
approximation,
assume
that
peak and, as a first the
peak
obtained
the equilibrium interstitial
lower energy
distribution
sites in iron
sites.
They found
for screw dislocation
of saturation
of the dislocations
type of site, with a binding
of course, depends
sisted
on the value of the binding energy). of dislocation
The total number
sites, Nd, will thus just equal the number
of N atoms which are contributing ured cold-work determined
peak height.
to P,,,
This number
from the known relationship
where cz is the reciprocal Nd could
P,,
be determined
specimen from the temperature
elczPcw. by
of the cold-work peak,
then (P,,
be -
given
P,,‘).
lost from
by
the
expression:
Nd will
Nd = nd + c1
This again assumes that the N atoms
interstitial
sites diffused sites.
friction
Thomas
technique
investigation.
microcrack
54%
However,
exclusively
working
of
to the present
the binding
in iron to be approximately
and a single quench
of
an internal
of N to dislocations
energy 0.8 eV.
with the Snoek peak
technique,
they were forced to
estimate the total number of dislocation sites, whereas the present procedure
for
necessarily equilibrated
Either
Leak’23) used
similar in principle
technique
Nd may serve as a check on the other;
or
the concentration
They determined
this
dislocation
energy of 0.89 eV, con-
dislocations
and
the
unoccupied
energy
sites equals approximately
to saturate
determining
distinct
the two types of sites would just equal the present
the total.
the
edge
binding energy result, providing
= c2PGw Alterna-
and two the binding
It may be noted that a weighted average of
screw dislocation
quenching
and measuring the resulting Snoek peak P,,‘;
surfaces.
either
may be
of the slope of Stage I.
Thus, Nd is equal to the quantity tively,
the meas-
of
relations
of N atoms
sites to be 0.11 eV ; the second
(the actual degree of occupation,
reflects a condition
need
not be corrected.
lattice site leaving Nd, the total number of dislocation
We next measure the cold-work
of the
Thus, the first approximation
quantity.
In
employs
addition,
a direct measure their
specimens
of
were
in the rather low temperature
range of 100°C to 270°C because
of the assumption
in this investigation the remeasurement of the Snoek peak was overlooked and, hence, only the former
that the number of dislocation sites did not vary with temperature. Thus, the deviation from saturation of
determination was possible. The data of Table 2 were applied
the dislocations must have difficult to detect accurately.
to the above
analysis ; ci was taken as 0.4 x 56/14 at.% N per unit Snoek peak height and cz was taken as 110.47 (Group A, Table 1). The calculated values of AG were then
As previously
mentioned,
been
quite
inherent
small
and
in the present
calculation of binding energy is the requirement that the N atoms be distributed only between dislocation
ACTA
800
and interstitial
sites.
The aging results
indicate that this condition cold-work
is upheld.
peaks are of the form:
constant,
the constant
the total N content.
being roughly
compared observed
0.42
proportional
I (0.47
to
is of further
for vacuum
technique.
elimination
We
importance
when
et al. They
to the opposite result of K6ster complete
P,,r
check upon the value
for the slope of Stage this result
2
the above relation-
melted iron) by the direct quenching feel that
of Table
The Snoek and
PC,+
In addition,
ship serves as an independent obtained
METALLURGICA,
of the cold-work
value. peak
peak
had returned
Increasing to return
remaining
to only 3 its original
the temperature
caused the Snoek
to its full size, the
absent.
cold-work
peak
It would appear that at one point
are contributing to some 6 of the interstitials neither peak. Also, it should be noted that present results
show
temperatures
a
sizable
which
cold-work
caused
peak
KGster’s
at
peaks
aging to dis-
These differences may stem from the fact appear. that KGster’s specimens contained both C and N and probably
a greater
impurity
level than
those employed in the present investigation.
One may
speculate within
substitutional
on some unique
the
specimen
dislocation
partitioning
such
that
the
of C and N C occupies
sites while the N is present
As discussed
previously,
the cold-work
the C will not contribute
in dislocation
C atoms will add to the magnitude Alternatively, interaction
the
differences
precipitates
to
which
redissolve
at
from
the
the
aging it is with
specimens
that
cause,
higher
clear that the aging studies should be conducted purity
the
stem
with N or C to form however,
high
Whatever
sites the rejected of the Snoek peak.
may
of the substitutionals
temperatures.
the
interstitially.
peak whereas with higher temperature
aging and reduction
contain
only
interstitial species. The important remaining
question
cold-work
The interaction
peak mechanism.
is that
15,
1967
dislocations
and N atoms
factor
the
but
determined. level
increasing
is, of course,
configuration
It is interesting
ture is highest purity
exact
increases,
then
the latter
by Boone
and WertF
system.
and other
observations
energy must ultimately
in terms of an accepted
been
damping
substitutional
levels
behavior
been observed the activation
not
that the peak tempera-
in the iron of highest and
N content, This
the primary
has
off,
with
having also
for the Cb-N pertaining
to
be interpreted
model.
peak
upon heating just above 3OO”C, while at the same time the Snoek
VOL.
a single
of the between
REFERENCES 1. J. L. SNOEK, Physica 8, 711 (1941). 2. W. A. WEST, Trans. Am. Inst. Min. metall. Engrs 167, 192 (1946). 3. T. S. Kfi, Trans. Am. Inst. Min. metall. Enars 176. 488 119481. 4. ‘W. ~&TER, L. BAN~ERT and R. HAHN, Arch. Eisenhiitt Wes. 25, 569 (1954). 5. K. KAMBER, 0. KEEFER and C. WERT, Acta Met. 9, 569 (1961). 6. L. J. DIJKSTRA, Discussion to Ref. 3. 7. D. N. BESHERS,Acta Met. 6, 521 (1958). 8. H. G. VANBUEREN, Imperfections in Crystals, p. 390. North-Holland. Amsterdem f1961). 9. G. SCHOECK and M. MOND&O, J: phys. Sot. Japan 18, Supplement I, 149 (1963). 10. G. SCHOECK,Acta Met. 11, 617 (1963). 11. T. MURA, J. TAMURA and J. 0. BRITTAIN, J. appl. Phys. 32, 92 (1961). 12. N. OKAZAKI, Mem. Inst. scient. ind. Res. Osaka Univ. 15, 67 (1958). 13. D. H. BOONE and C. A. WERT, J. phys. Sot. Japan 18, Suaalement I. 141 11963). 14. D.‘@. PETAR&A anA D. ‘N. BESHERS, J. appl. Phys. 34, 2739 (1963). 15. C. WERT and D. KEEFER, Am. Inst. Min. metall. Engra IMD SDecial Reoort Series 6. 41 (1957). 16. A. H. kOTTRELLI&ndB. A. B~LBY; Pro;. phys. Sot., Lond. A62, 49 (1949). 17. S. HARPER, Phys. Rev. 83, 709 (1951). 18. A. S. KEH and H. A. WRIEDT. Trans. Am. Inst. Min. metall. Engrs 224, 560 (1962). 19. T. S. K&, P. T. Yuxa and Y. N. YANQ, ScientiaSinica.4, 263 (1955). 20. A. COCRARDT, G. SCHOECK and W. WIEDERSICH, Acta Met. 3, 533 (1955). 21. R. BULLOUGH and R. C. NEWMAN, Proc. R. Sot. A249, 427 (1959); A266, 198, 209 (1962). 22. H. A. WRIEDT and L. S. DARKEN, Trans. Am. Inst. Min. metall. Engrs 233, 111, 122 (1965). 23. W. R. THOMAS and G. M. LEAK, Proc. phys.Soc., Lond. B68, 1001 (1955).
INTERNAL
D. P.
PETARRAt
FRICTION and
D. N.
PEAK
IN IRON*
BESHERSS
An investigation of the cold-work peak in iron containing N confirms in modified form, the saturation effect reported by Koster. This effect, coupled with strain-aging results, was used to estimate the number of N atoms per atomic length of dislocation that contribute to the damping peak, The complementary relationship between the Snoek and cold-work peak heights seen upon aging at temperatures greater than that of the cold-work peak is shown to be primarily the result of dislocation recovery upon which is superimposed a lesser thermal distribution effect. An experimental technique for evaluating the latter effect has been proposed, and the free energy expression governing the distribution of N atoms between lattice and dislocation sites has been found to be of the form: AG = -0.47 - 2.6 x lo-*!I’ eV. A residual cold-work peak has been found in specimens having no Snoek peak and is believed due to the migration of N atoms from low energy traps to freshlyintroduced dislocation sites. C is shown not to contribute to the cold-work peak and, in fact, to retard its formation. PIC
D’ECROUISSAGE
DANS
LE
FROTTEMENT
INTERIEUR
DU FER
Une reoherche du pio d’ecrouissage dans du fer contenant de l’azote oonfirme, sous une forme modifiee, l’effet de saturation rapporte par Koster. On utilise oet effet, en association avec les resultats de viei~is~ment apres hxouisstlgtt, pour astimer le nombre d’atomes d’azote par longueur atomique de disloaation contribuant au pit d’amortissement. Par vieillissement 8.des temperatures superieures a celle du pit d’ecrouissagc, on observe une relation complementaire entre la hauteur du pit de Snoek et celle du pit d’bcrouissage; on montre que oette relation resulte essentiellement de la restauration des dislocations, a laquelle se superpose nn effet plus petit de distribution thermique. On propose une technique experimentale pour &valuer oe dernier effet; l’expression de l’energie libre gouvernant la distribution des atomes d’azote entre le rtjseau et les sites de dislocations est de la forme: AG = -0,47-2,6 x 1O-4 T eV. Dans les Behantilions ne donnant pas de pit de Snook, on trouve un pie d’ecrouissage residue1 attribue a la migration d’atomes d’azote vers de nouveaux sites de dislocations a partir de pieges de basse Bnergie. C ne aontribue pas au pit d’ecrouissage et, en fait, retarde sa formation. DAS
KALTVERFOR~UNGSMA~I~L~
DER
INNEREN
REIBUNG
IN
EISEN
Eine Untemuohung des naoh Kaltverformung auftretenden Maximums der inneren R&bung in Eisen mit Stickstoffgehalt bestatigt, in modifizierter Form, den von Koster beobachteten Sattigungseffekt. Dieser Effekt sowie Ergebnisse der Reckalterung wurden zur Abschltzung der Zahl der Stiokstoffatome pro atomare Veraatzungsl&nge, die zu dem Diimpfungsmaximum beitragen, herangezogen. Die komplementare Beziehung der Hohen des Snoek-Maximums und des Kaltverfo~ungamaximums, die naeh Altern bei Temperaturen oberhalb des letzteren Maximums beobaobtet wird, hangt in erstor Linie mit der Versetzungserholung und schwiieher mit einem thermischen Verteilungseffekt zusammen. Es wird ein experimentelles Verfahren zur Auswertung des letzteren Effektes vorgeschlagen. Der Ausdruck fur die freie Energie, welcher die Verteilung von Stickstoffatomen zwischen Gitter- und Versetzungspositionen bestimmt, wurde zu AC = -0,47-2,6 X lo-* T eV bestimmt. In Proben ohne Snoekmaximum wurde ein restliohes Kaltverfo~ung~aximum gefunden. Es wird auf die Wanderung von Stickstoffatomen von niederenergetischen Haftstellen zu neugebildeten Versetzungspositionen zuriickgeftihrt. Kohlenstoff tragt nicht zum Kaltverformungsmaximum bei, sondern verlangsamt vielmehr seine Bildung.
1. INTRODUCTION
Since the discovery of the cold-work peak in iron(l) over two decades ago, many of its characteristics have been determined.{z-6) The peak is reported to occur in cold-worked iron containing N and/or C at approximately 220% at 1 c/s with an activation energy The height of the peak between 30 and 40 k&/mole. increases linearly with interstitial content to a maximum or saturation value; the saturation value, itself, increases roughly as the square root of the plastic T Received June 6, 1966; revised August 11, 1966. This work was supported by the U.S. Office of Naval Research. ow at: General Electric Co., Lamp Division, Nela Park, Cle!&nd Ohio 44112. $ Hen& Krumb School of Mines, Columbia University, New York, New York 10027. ACTA
METALLURGICA,
VOL.
15, MAY
1967
strain. The saturation effect has been interpreted by KGster et aZ.(*) to mean that a specific dislocationinterstitial configuration causes the cold-work peak and that any excess of either dislocations or interstitials is ineffective. A11(1+6) who have compared the effect of C and N have found differences, the tenor of which is that N is a more positive agent than C in causing the cold-work peak. Aging in the temperature range lOO’C--600°C reveals the complementary nature of the Snoek and cold-work peaks ;[email protected]. as the aging tern~~~ture is increased the height of the cold-work peak decreases while that of the Snoek peak increases. Kijster et al. have analyzed this behavior in terms of thermal unpinning of solute atoms from dislocation sites and 791
792
ACTA
METALLURGICA,
The tempera-
transfer of these atoms to solid solution. ture
dependence
of
unpinning
was
calculated
Beshers’7) based upon a Fermi distribution atoms
at the
dislocation.
Kamber
pointed out the importance reducing
their analysis of thermal
of solute
et aZ.c5) later
of dislocation
the peak height,
by
recovery in
but did not include unpinning.
it in
Van Bueren(s)
VOL.
~100
15, 1967
ppm).
A complete
zone refined
irons
analysis of the Swedish and
has been
reported(14)
The first step in the preparation bring all material
to a standard
fully recrystallized,
was to
state consisting
0.062 in. dia. rods.
then wet hydrogen
elsewhere.
of specimens
of
These were
annealed 70 hr at 720°C and cold-
drawn to a diameter of 0.026 in. The specimens were
has observed that the Koster et al. data show the cold-
then recrystallized
work peak undergoing a relatively larger decrease than
at 95O’C in a N, plus 1 y0 H, atmosphere
the
lized first to the desired grain size in an argon atmos-
corresponding
rise
in the
Snoek
indicates that solute atoms apparently Upon
recrystallization,
atoms
the
reappear :
entirely
however,
peak.
phere
become “lost”.
the
cold-work
This
“lost”
peak
solute
disappears
and the Snoek peak returns to its original
height. A number of mechanisms
to explain the cold-work
and nitrided either simultaneously
at a temperature
between
or recrystal-
580%
and 950°C
followed by nitriding at 580°C in a hydrogen-ammonia atmosphere.
Carburization
hydrogen-n-heptane
was accomplished
atmosphere
following
in a
recrystal-
lization in argon, both at 720°C.
The specimens were
then
quenched
solution
annealed,
water
im-
mediately
Suggestions may be classified according
to the nature
apparatus for the primary purpose of determining
of the moving
the anelastic
N or C content from the height of the Snoek peak (no
defect
which furnishes
inserted into the precooled
and
peak have been put forward, but none is established.
strain necessary for internal friction. Most investigators(4*9-11) have identified the source of strain as the
samples
dislocations,
quenched,
their motion
atmospheres(4J0) tions
either slowed
or affected
by Cottrell
by concomitant
in the size of carbide
which restrict their motion.
or nitride
oscilla-
particle@)
the reorientation
of non-spherical
or on
precipitates,03)
a
sort of grand Snoek effect. The work reported here is an experimental
investi-
cold-work
peak
et al.
investigating
in purer
iron
than
that
The work has the two-fold the peak
itself,
while
utilize it to gain further knowledge
used
by
attempting
apparatus.
in the
and reinserted Following
this
then reheated for a second measurement the effect
of aging.
aging results
cold-worked
to
In addition,
were obtained
specimens
3. EXPERIMENTAL
of the dislocation-
more
by heating
in the
temperature
PROCEDURE
The prom-
A, defined
by twice
Throughout
Internal friction was measured in a torsion pendulum
RESULTS
The internal friction data are given in terms of the decrement,
previously.
friction
annealed,
mostly
range 250°C-550°C prior to the initial measurement of the cold-work peak.
divided
which has been describedo4)
C and N).
purpose of
impurity interaction. 2. EXPERIMENTAL
of area (RA),
the
of the cold-work peak the apparatus was
force-cooled, to observe
both
cold-drawn,
reduction
measurement
freshly
to contain
were again solution
immediately
range 3-30%
quantitive
gation of the saturation effect and other aspects of the Koster
were treated
the specimens
into the internal
Others have focused on
a modified Snoek effect near the dislocationa
Next,
internal friction
as the energy
the stored
this investigation
energy
loss per cycle of oscillation.
the Snoek peak is taken
as a measure of the amount of C or N in solid solution through the relationship :05) wt. y. C or N = 0.4 Amax.
inent features include a rapid heating rate such that T-l,
reciprocal
in time.
of the absolute
temperature,
is linear
The time required to heat the specimen from
the Snoek peak to the cold-work was approximately
peak temperature
1 hr. A longitudinal d.c. magnetic
field of 200 Oe was applied to the specimen to eliminate magnetomechanical
contributions
to the damping.
Three types of “pure” iron were used; in order of increasing purity they were : “Swedish iron” obtained from
A. D. Mackay
Co. (impurity
level ~2
x 10s
ppm), vacuum melted electrolytic iron from Westinghouse Electric Corp., and a similar iron which was zone refined
by the Battelle
American
Iron
Memorial
and Steel Institute
Institute
for the
(impurity
level
Carbon versu.s nitrogen All cold-worked specimens which contained C or N exhibited the cold-work peak. However, the characteristics of this peak were quite different for the two interstitial species. Carburized specimens exhibited a very small peak which was essentially of
C content
and
degree
of
independent
cold-work.
In
aged
specimens this peak became slightly larger, but still remained independent of C content and degree of cold-work. This behavior is illustrated in Figs. 1 and 2. The cold-work
peak obtained
with nitrided
speci-
mens was generally larger and, unlike the carburized specimens, sensitive to the solute level and degree of
PETARRA
BESHERS:
AND
200
150
100
COLD-WORK
INTERNAL
FRICTION
PEAK
793
250 ‘C
,
lL
SECOND
RUN
-J
I
3.0
1
I
I
2.6
2.6
(T’K
2.4 x
2.2
I
2.0
1.6
I
Moreover,
always
greater
illustrated
than
the
initial
in the
by the typical
peak
aged
height
condition,
work
was as
is
result shown in Fig. 3.
The cold-work
peak
increasing
height
was found
to depend
a-stage
manner.
a linear increase in peak height with
peak height;
Stage
positive
cold-work
height.
Specimens
II is a region of
and Stage
rapid rise in peak height.
Snoek
peak
Figs.
Group A consists
5-7.
different
nitrided
III
is a region of
A surprising
peak intercept annealed
feature
is the
at zero Snoek peak
of the
group
includes
at 950°C.
C zone
a summary
for several
purity
Both nitriding techniques
N concentration;
constant
and and
were of the same base metal
in a characteristic
Stage I represents
peak
cold-work specimens
Height of the cold-work peak upon N content
1000
FIG. 3. Effect of aging upon a vacuum melted iron specimen containing 16 x 1O-3 wt.% N and having 30% RA; frequency ~1 c/s.
Fro. 1. Effect of aging upon a vacuum melted specimen containing 15 x 1O-s wt.% C and having 15% RA; frequency ~1 o/s. cold-work.
x
toK
1000
irons
degrees
of
is shown
of vacuum
melted
in iron
The group B specimens and nitrided
at 580°C.
were used in the preparation refined
specimens.
of the significant
Table
features
curves shown in Figs. 5-7. Temperature of the cold-work peak The temperature found
of the cold-work
to be sensitive
to the
peak was also
N concentration
and
for a long time in wet
hydrogen and having no Snoek peak did, nevertheless, exhibit 4.
this residual cold-work
In the range 3-85%
peak
remained
decreased the
residual
impurity
unchanged
peak
level
peak as shown in Fig.
RA the height of the residual
with increasing
; the
peak
cold-work.
decreased
increased,
temperature The height
as the
and
of
substitutional
dropped
to
zero
in
Swedish iron. The relationship
d+ 010
l
0 SNOEK
between
20 PEAK
of the cold-
.
1
1
IO
the height
30 HT
40
(DEC. X 1000)
2. The relationship between the Snoek and coldwork peak heights before and after aging of 15% RA vaouum melted iron specimens containing C. FIG.
1
of the
g
0
I 3.5
3.0 +x
2.5
2.0
x 1000
FIG. 4. Internal friction results for vacuum melted iron specimens having 23 hr wet hydrogen anneal followed by 0, 3.1, and 85% RA; frequency ~1 c/s.
ACTA
794
METALLURGICA,
VOL.
15,
1967
0
I
MEAN GRAIN DIAMETER 0.013 mm 0050 mm 0.200 mm , 05oq rnnl
I
20
0 SNOEK
40 PEAK
60
80
HT.
(DEC.
X 1000)
FIG. 5. Cold-work peek height versus Snoek peak height, Group A; values in graph refer to RA.
degree of cold-work. The peak temperature increased with increasing N in a manner similar to Stage I and II. This result is shown in Pigs. 8 and 9 for zone refined and vacuum melted irons, respectively. A comparison of these two figures indicates that substitutional impurities cause a decrease in the peak temperature. The effect of cold-work is also seen to lower the peak temperature. 6 8 25 x
0
20
SNOEK
40
60
1 80
PEAK
HT.
(DEC.
100 X
120 1000)
FIG. 6. Cold-work peak height versus Snoek peak height, Group B; values in graph refer to RA.
”
0
20
SNOEK
40 PEAK
NITRIDED Nz +“z
x 0 NITRIDED A NH, :I I 00 60
HT.
(DEC.
100 x
120 1000)
FIG. 7. Cold-work peak height versus Snoek peak height, Group C; 14.8% RA.
Aging behavior
The aging characteristics of the cold-work peak were studied in detail. Nitrided specimens of vacuum melted iron were quenched from 58O”C, cold-worked and then aged for 1 hr in the temperature range 25O”G55O”C. They were then quenched from the annealing temperature for measurement of internal friction. The results shown in Table 2 indicate that an increasing aging temperature results in a decreasing cold-work peak height accompanied by an increasing Snoek peak height. To clarify the interpretation of the aging results a series of three further experiments was conducted. A brief outline of the experiments follows; the details are given in Table 3. Experiment 1. Two specimens were prepared with the same cold-work and N content. In one, the N was allowed to precipitate at a temperature higher than the cold-work peak temperature prior to measurement of the Snoek and cold-work peaks; in the other, the N was primarily in solid solution prior to the internal friction measurement. The cold-work peak heights were nearly equal whereas the Snoek peak heights were quite different. Experiment 2. Two identically prepared specimens
TABLE 1. Summary of cold-work peak height results
Specimen group
% RA
Height of residual peak (A x 1O8)
Slope of stege I
Dislocation satumtion concentration (wt.% N x 108)
Height of Stage II (A x 108)
3.1 14.8 28.4
3.7 4.3
0.47 0.47
1.0 __ __
4.6 7.6 -
B
14.8 30.1
4.9 5.7
0.67 0.50
4.6 11.2
11.6 19.8
C
14.8
7.5
0.64
5.1
15.0
x
PETARRA
BESHERS:
AND
COLD-WORK
INTERNAL
FRICTION
PEAK
795
TABLE 2. Effect
of aging temperature upon the cold-work and Snoek peak heights. The 14 and 26% RA specimens contained 18.4 x lO-s and 21.6 x 10V wt.% N, respectively
SNOEK
PEAK
HT.
(DEC.
X
1000)
Fla. 8. Cold-work peek temperature versus Snoek peak height in 15% RA zone refined iron.
gm
I
I
I
I
I
3,,
~_______________o______
k! 220- / ? : ,: 0 2 L 210 08’
p :: ti & $
x ._____X.___!?” c_“_~_________ ‘9 :, r______?_*_______.__________s___ &I _ *Jo :’ / . . : ’ _I I90 .’ : :a ;;” 180 :-’ 1
2 170z 0 SNOEK
20
I 40 PEAK
, 60 HT.
00 (DEC.
X 1000)
Pm. 9. Cold-work peak temperature versus Snoek peak height in vacuum melted iron; values in graph refer to RA.
Experiment number 1. &. b.
2. a.
b.
3. &.
b. c.
Snoek peak height (A x lo*)
% RA 14 14 14
250 450 550
12.0 7.4 3.7
23.0 42.0 45.5
26 26 26 26
250 300 500 550
23.5 18.7 8.0 7.5
17.0 25.6 47.2 52.7
were aged at the same temperature for different times and quenched for measurement of internal friction. The one aged for the longer time had the smaller coldwork and Snoek peaks. Experiment 3. A nitrided, cold-worked specimen was aged first at a high, then low temperature. It was quenched from the lower temperature for measurement of internal friction. The resulting cold-work peak was characteristic of the higher aging temperature. The specimen was then held at the lower temperature for a long time followed by remeasurement of internal friction. There was no appreciable change in the cold-work peak height.
Strain aging
1 100
TABLE
Cold-work peak height (A x 103)
Aging temp. (“C)
A specimen containing 12 x 10e3 wt.% N (Stage II) and one containing 41 x 10~~ wt.% N (Stage III) were each quenched from 55O”C, cold-worked 14.8% RA and aged at the temperature of the Snoek peak,
3. Details of aging experiments
Specimen treatment Nitride, quench, cold-work 50% RA, measure IF Nitride, quench, cold-work 50% RA, age 1 hr et 26O”C, quench, measure IF Nitride, quench, cold-work 50% RA, age 10 mm at 65O”C, quench, measure IF Nitride, quench, cold-work 50% RA, age 4 hr at 65O”C, quench, measure IF Nitride, quench, cold-work 14% RA, age 30 min at 460°C, quench, measure Snoek peak only age 75 min at 250°C, quench, measure IF age 14hrat250”C, quench, measure IF
Cold-work peak height (A x 10’)
Snoek peak height
14.2
40.0
13.4
18.0
14.0
30.5
4.0
19.5
-
48.0
7.0
43.0
6.6
5.9
(A x lo*)
ACTA
796
METALLURGICA,
VOL.
15,
1967
A is the constant describing the interaction between
a N impurity atom and a dislocation, D is the diffusion coefficient of the impurity, and kT is Boltzmann’s constant times the absolute temperature. A dislocation density of 1.7 x 10n cm/cm3 is obtained using Harper’s formula applied to the Stage II result. The formula was not applied to the Stage III specimen since the exponent, n, in this case equalled 1.35 during the early stages of precipitation and the data points fall along a curve rather than a straight line. p
n= 0.705
Activation energy -15’
’ 14
’
’ ’ 1.6 LOG,
f 2.2
’
’ 2.6
’
t
FIG. 10. Strain-aging results for zone refined iron containing N and having 14.8% RA.
24.5%. The internal friction values at this temperature were measured as a function of time and are plotted (Fig. 10) to determine the exponent, n, in the expression : A, = A,
+ (A,, -
A,)
exp
[
-
01 tn 7
(1) Null results
in which r is a time constant and Ac, A,, and At refer to the logarithmic decrement initially, finally, and at time t, respectively. Rearranging (1) and taking the natural logarithm of each aide gives:
(2) Taking the logarithm to the base 10 of each side of (2), it becomes apparent that if the data points in Fig. 10, fall on a straight line, the slope of the line is n. For Stage II, the data points do fall along a straight line of slope 0.705. This is close enough to the CottrellBilby(16) value of # to justify fitting the data to Harper’@‘) formula for strain-aging : f = 1-
exp [--ap(ADt/kT)2’3]
The temperature of the cold-work peak was measured as a function of frequency in the range 0.3-3.8 C/S. Three different specimens were studied: (1) zone refined iron, residual cold-work peak; (2) zone refined iron containing 2.0 x 10V3 wt.% N; and (3) Swedish iron containing 9.5 x 10m3 wt.% N. Preceding each measurement of peak temperature, each specimen was fully recrystallized, solution annealed, quenched, and cold-worked 15% RA. The activation energy results are given in Table 4.
(3)
where S = fraction of solute which has precipitated at time t, u = 3(.rr/2)n2, p is the dislocation density,
Several of the parameters investigated were found to have little or no effect upon the cold-work peak. Grain size, for example, affects neither the peak height nor temperature. This result is implicit in Figs. 7 and 8 which include specimens ranging in grain size from 1.2 x lop3 to 5.0 x 10-s mm average diameter. The magnetic field resulted in a reduction of the background damping level, but had little effect upon the height or temperature of the cold-work peak. Also, the peak was independent of strain amplitude over the range 1.5 x 1O-6 to 6.8 x 10-5. 4. DISCUSSION
The Koster saturation effect has been verified in a somewhat modified form with nitrided pure iron specimens. The novel features are the residual peak and Stage III. In addition the saturation effect was not observed with specimens containing C alone.
TABLE 4. Activation
Activation energy (kcal/mole) Freq. factor, ~~-1 (set-I) Peak-breath ratio av. experimental talc. for single 7 >
energy results
Zone refined iron (residual peak)
Zone refined iron (2.0 x 1O-3 wt.% N)
29 + -2
38 $ -2
Swedish iron (9.5 x 10mswt.“/o N) 38 + -3
10’4
10’S
10’8
1.8
2.4
1.8
AND
PETARRA
These resulted
BESHERS:
in an unexpectedly
peak, irrespective
COLD-WORK
small cold-work
IXTERNAL
FRICTIOS
with further cold-work
797
PEAK
(Fig. 4) and the height of the
peak is greater than that of cold-worked
of C content.
containing Stage III
C alone, regardless
specimens
of the concentration.
Aging of the C-bearing specimens causes the cold-work
We attribute tions beyond
Stage III, which occurs at concentra-
the range studied by Koster et al., to a
rise in dislocation
density
geneous precipitation Thus,
lattice. markedly
of nitride particles
the
between
resulting from the homo-
kinetics
of
within the
strain-aging
differ
Stage II and Stage III specimens.
peak to grow-but residual
only to a magnitude
peak.
The
data
equal to the
of KiY3) also show
this
residual cold-work peak although Ke, himself, attached little significance
to the observation.
Our interpretation
is that the purified
specimens
contain residual N atoms in low energy traps making
In the former case the observed t213time dependence is characteristic of diffusion to dislocations, while in
no contribution
the latter case strain aging occurs at a much acceler-
lower energy which attract the N atoms and give rise
ated initial rate indicating
to the residual cold-work
tation
is occurring
that substantial
in less time
diffusion to dislocations.
than
precipi-
required
The nuclei for precipitation
must be more finely spaced than the dislocations therefore,
were probably
generated
precipitate
Lattice
misfit at the interface
of the of fresh
which are then able to contribute
cold-work
damping
peak.
may be interpreted
to the
The data of KB et aZ.og)
as such an increase in dislocation
level due to Stage III precipitation. cold-work
by Keh
particles results in the generation
dislocations
and,
homogeneously
within the lattice as observed microscopically and Wriedt.o*)
for
peak was observed
In this case the
in unworked, quenched
introduced
to the Snoek peak.
during
contribute
cold-working peak.
to the cold-work
to the dislocations
C atoms likely do not
Thus, as shown in Fig. 2,
specimens
with a large C content
cold-work
peak.
upon aging is then explained
along the dislocations with N atoms. with the observation
that the C cold-work
in terms of quenching
feel that precipitation dislocation previously
and magnetic
dependent
dislocations. decrease
of Stage
was shown to be a “viscosity upon
Within
the
the
presence
of
mobile
Stage II the effect of N was to
dislocation
reduce
the background.
levels,
however,
resulted
effects reported(14)
support the above interpretation
The background
effect”
of C
of Kamber
et aZ.c5)
to grow during
aging at 24O’C long after the Snoek peak has completely
disappeared.
In addition
difference in activation peaks.
they observed
no
energy between the C and N
This further indicates
that the N
for the cold-work
peak and that the C atoms merely act to inhibit the peak in the manner described. At the present time we are unable to offer the reason
level.
The background III.
strains whereas we
is giving rise to the increase in
peak
This explanation
peak continues
cold-work
behavior
a minimal
by the replacement
species alone may be responsible
this
exhibit
The growth of the C cold-work
specimens of high N content and was not observed in Ke interpreted
still
ahead of the trapped N atoms, even
inhibit the peak formation.
is consistent
sites of
peak and, by diffusing
specimens
of lower N content.
The dislocations
offer
mobility At
increasing
and,
hence,
to
the higher
Stage
III
the
N
concentration
in an increase in background
accompanied
by a sharp drop in the magnetic damping.
Both
formation
of new dislocations
contribution
effects may be associated
to the
with the
resulting from nitride
precipitation.
for the marked
difference
atoms.
the different
Perhaps
the dislocation
in behavior electronic
of C and N states near
may bring about a chemical
reaction
for C and not N; one example would be the promotion of C to the tetrahedral
sites.
Saturation effect One of the most useful features peak is the saturation effect. work
the
linearly
height
of the
with increasing
limiting value.
of the cold-work
For a given level of cold
cold-work
peak
N content
(Stage
increases I) to a
At this point the available dislocations
are assumed to be saturated with N atoms and further increases in N content result in no further contribution
Residual peak and carbon behavior
to the damping (Stage II).
It has generally been assumed that cold-worked iron containing either C or N is a necessary and
It is interesting then to calculate the number of N atoms per unit length of dislocation which is required
sufficient
just to reach this saturation level.
condition
for
the
cold-work
peak.
Our
In this calculation
results indicate that even with no Snoek peak present in freshly quenched specimens prior to cold-working, a small residual cold-work peak appears following
the residual entrapped N should be taken into account. Extrapolation of Stage I to zero cold-work peak height gives a negative intercept which corresponds
cold-working.
to the magnitude
Once formed,
the peak does not grow
of Snoek peak for the entrapped
N.
798
ACTA
METALLURGICA,
For the zone refined iron this extrapolation gives a residual N concentration of 4.7 x 10-a wt.% while the saturation concentration at the 1.5% RA coldwork level equals 5.1 x low3 wt.%. The total of 9.8 x 10m3wt.% N corresponds to 3.3 x 1019 N atoms/cm3. If we take the strain-aging results at face value, the dislocation density of 1.7 x 10n cm/cm3 implies 1.94 x lo8 N atoms/cm of dislocation line. Along a screw dislocation, one atomic length is just the Burgers vector length; we will use this for all others as well. This gives a result of 4.75 N atoms per atomic length of dislocation. Alternatively, we may assume with Cochardt et aZ.(20) that there are three closest positions around a screw dislocation and assume further that only N atoms in those positions contribute to the cold-work peak. This condition will be met if in the calculation of dislocation density [equation (3)] the product aA213is set at 314.75 = 0.63 times the value given by Cottrell and Bilby. The Harper calculation has been called into question, most recently by Bullough and Newman(21) who conclude that Harper’s expression overestimates the dislocation density by a factor of about 3. If this result is valid we then conclude that the number of N atoms per atomic length of dislocation is (4.75 x 3) = 14.25. There is still uncertainty in the problem because we do not know the exact conditions at the dislocation. The solutions to the partial differential equation governing strain-aging are all obtained by supposing some configuration at the dislocation which enters the problem as a boundary condition on the solution and has a considerable effect on the final answer. The final interpretation of this part of our data must await further work. Aging behavior Specimens which are aged at temperatures above that of the cold-work peak then quenched show a reduction in the cold-work peak and an increase in the Snoek peak. This is shown in Table 2 and has been reported by other investigators’3-5) as well. This behavior has generally been attributed to thermal unpinning of solute atoms and binding energy calculations have been made(4,5p7)on that interpretation. However, the aging experiments (Table 3), which were designed to test this concept, clearly indicate that thermal unpinning is not the most significant factor in determining the aging behavior and that the binding energy calculation based only upon the variation of cold-work peak height with temperature is invalid. In the first experiment of Table 3 the dislocations
VOL.
15, 1967
of specimen a may be assumed to be relatively free of N atoms before the internal friction measurements were made, while those of specimen b are saturated as a result of the 25O’C aging treatment; yet the coldwork peaks were approximately equal. We conclude that the degree of dislocation saturation prior to measurement of the cold-work peak is of little consequence. The N atoms are able to diffuse to the dislocations within the time required to make the measurement. Thus, under the condition of surplus N, the cold-work peak height will be determined solely by the dislocation density. Experiment 2 illustrates the effect of aging time at 550°C. If the thermal distribution of N atoms were the primary factor then one might expect to see little difference between the 10 min and 4 hr treatments, because the equilibrium distribution of N atoms between the dislocation and interstitial sites should have been attained within the shorter time and not changed appreciably as a result of prolonging the time at temperature. However, the longer anneal did result in a markedly reduced cold-work peak which can best be explained in terms of dislocation rearrangement and annihilation. This is further substantiated by the results of Experiment 3. In this case the specimen was first aged at 450°C and then at 250°C. The resulting cold-work peak was characteristic of the higher temperature treatment despite the fact that the quench took place from the lower temperature. This clearly indicates that the effect of aging is nonreversible. Prolonged aging at the lower temperature does not much affect the cold-work peak height, indicating that the changes which occur at the higher temperature cause a stabilization of the structure with respect to the lower temperature. On the basis of the aging experiments, we conclude that two primary effects are occurring in the coldworked specimens while at elevated temperatures : first, and most importantly, the number of active dislocation sites is reduced through the process of recovery causing N atoms to be rejected into interstitial sites and second, a partitioning of N atoms occurs between the remaining dislocation sites and the lattice sites. Moreover, this distribution may be “frozen in” by means of rapid quenching, but cannot be evaluated by a measurement of the cold-work peak height alone, inasmuch as it has been shown that a new distribution will have occurred (one characteristic of the temperature of the cold-work peak) well within the time required to make the measurement. Even so, a binding energy expression in terms of measurable quantities can be set up and the calculations
PETARRA
carried out.
describes
AND
_~
nd
Nd
-
of solute
and lattice interstitial
of occupied dislocation ni, respectively; interstitial
AG = (H, -
-AG ni =--Ni - ni exp kT
nd
(4)
atoms
sites.
between
The numbers
and interstitial sites are nd and
the total numbers of dislocation
sites are Nd and Ni, respectively;
as follows:
and
aging experiment
some temperature, freezing
to obtain
in the N distribution
characteristic
of the
(5)
difference,
the
equal to the binding energy. and the results
free energy and deviation from AG = -0.466 - 2.58 X 10m4 T
Acf (talc.)
Aging temp.
A measure of the Snoek peak at
ni = clPsn where c1 is the well known
and entropy
TAS
in Table 5. It is to be noted that the
least squares fit:
and aged at
this point sufbces to give both ni and nd in the following manner:
799
SJ = AH -
T(S, -
the enthalpy
TABLE5. Calculated
T. The specimen is then quenched,
aging temperature.
PEAK
A least squares analysis was performed
should proceed
cold-worked,
Hi) -
are summarized
A specimen is nitrided to a known Stage
II level, C,, then quenched,
FRICTION
former being essentially
and AG
is the difference in free energy between the two types of occupied sites. The appropriate
INTERNAL
applied to the further relationship :
The expression:
the distribution
dislocation
COLD-WORK
BESHERS:
(“K)
(eV)
523 723 823
-0.609 -0.678 -0 660
523 573 773* 823
-0.576 -0.626 -0.767 -0.679
the
from A@least squares)
Deviation
(% difference) - 1.3 -3.9 2.8 4.3 -1.9 -15.3 0
* This datum point was treated as an outlier included in the least squares analysis.
and
not
constant relating the Snoek peak height, P,,, and the
binding energy result, 0.47 eV, justifies our assumption
interstitial
of dislocation
content;
of the N not at interstitial locations
ni assuming that all
nd = Co -
sites is bound to the dis-
(a point to be discussed
further).
Ni, the
total number of interstitial sites may be taken as 3 per
cold-work
saturation
peak.
at the temperature
Wriedt and Darken,(22) using a chemical technique, have recently determined the thermodynamic
sites at the instant of quench as the remaining unknown
describing
quantity.
between
approximation,
assume
that
peak and, as a first the
peak
obtained
the equilibrium interstitial
lower energy
distribution
sites in iron
sites.
They found
for screw dislocation
of saturation
of the dislocations
type of site, with a binding
of course, depends
sisted
on the value of the binding energy). of dislocation
The total number
sites, Nd, will thus just equal the number
of N atoms which are contributing ured cold-work determined
peak height.
to P,,,
This number
from the known relationship
where cz is the reciprocal Nd could
P,,
be determined
specimen from the temperature
elczPcw. by
of the cold-work peak,
then (P,,
be -
given
P,,‘).
lost from
by
the
expression:
Nd will
Nd = nd + c1
This again assumes that the N atoms
interstitial
sites diffused sites.
friction
Thomas
technique
investigation.
microcrack
54%
However,
exclusively
working
of
to the present
the binding
in iron to be approximately
and a single quench
of
an internal
of N to dislocations
energy 0.8 eV.
with the Snoek peak
technique,
they were forced to
estimate the total number of dislocation sites, whereas the present procedure
for
necessarily equilibrated
Either
Leak’23) used
similar in principle
technique
Nd may serve as a check on the other;
or
the concentration
They determined
this
dislocation
energy of 0.89 eV, con-
dislocations
and
the
unoccupied
energy
sites equals approximately
to saturate
determining
distinct
the two types of sites would just equal the present
the total.
the
edge
binding energy result, providing
= c2PGw Alterna-
and two the binding
It may be noted that a weighted average of
screw dislocation
quenching
and measuring the resulting Snoek peak P,,‘;
surfaces.
either
may be
of the slope of Stage I.
Thus, Nd is equal to the quantity tively,
the meas-
of
relations
of N atoms
sites to be 0.11 eV ; the second
(the actual degree of occupation,
reflects a condition
need
not be corrected.
lattice site leaving Nd, the total number of dislocation
We next measure the cold-work
of the
Thus, the first approximation
quantity.
In
employs
addition,
a direct measure their
specimens
of
were
in the rather low temperature
range of 100°C to 270°C because
of the assumption
in this investigation the remeasurement of the Snoek peak was overlooked and, hence, only the former
that the number of dislocation sites did not vary with temperature. Thus, the deviation from saturation of
determination was possible. The data of Table 2 were applied
the dislocations must have difficult to detect accurately.
to the above
analysis ; ci was taken as 0.4 x 56/14 at.% N per unit Snoek peak height and cz was taken as 110.47 (Group A, Table 1). The calculated values of AG were then
As previously
mentioned,
been
quite
inherent
small
and
in the present
calculation of binding energy is the requirement that the N atoms be distributed only between dislocation
ACTA
800
and interstitial
sites.
The aging results
indicate that this condition cold-work
is upheld.
peaks are of the form:
constant,
the constant
the total N content.
being roughly
compared observed
0.42
proportional
I (0.47
to
is of further
for vacuum
technique.
elimination
We
importance
when
et al. They
to the opposite result of K6ster complete
P,,r
check upon the value
for the slope of Stage this result
2
the above relation-
melted iron) by the direct quenching feel that
of Table
The Snoek and
PC,+
In addition,
ship serves as an independent obtained
METALLURGICA,
of the cold-work
value. peak
peak
had returned
Increasing to return
remaining
to only 3 its original
the temperature
caused the Snoek
to its full size, the
absent.
cold-work
peak
It would appear that at one point
are contributing to some 6 of the interstitials neither peak. Also, it should be noted that present results
show
temperatures
a
sizable
which
cold-work
caused
peak
KGster’s
at
peaks
aging to dis-
These differences may stem from the fact appear. that KGster’s specimens contained both C and N and probably
a greater
impurity
level than
those employed in the present investigation.
One may
speculate within
substitutional
on some unique
the
specimen
dislocation
partitioning
such
that
the
of C and N C occupies
sites while the N is present
As discussed
previously,
the cold-work
the C will not contribute
in dislocation
C atoms will add to the magnitude Alternatively, interaction
the
differences
precipitates
to
which
redissolve
at
from
the
the
aging it is with
specimens
that
cause,
higher
clear that the aging studies should be conducted purity
the
stem
with N or C to form however,
high
Whatever
sites the rejected of the Snoek peak.
may
of the substitutionals
temperatures.
the
interstitially.
peak whereas with higher temperature
aging and reduction
contain
only
interstitial species. The important remaining
question
cold-work
The interaction
peak mechanism.
is that
15,
1967
dislocations
and N atoms
factor
the
but
determined. level
increasing
is, of course,
configuration
It is interesting
ture is highest purity
exact
increases,
then
the latter
by Boone
and WertF
system.
and other
observations
energy must ultimately
in terms of an accepted
been
damping
substitutional
levels
behavior
been observed the activation
not
that the peak tempera-
in the iron of highest and
N content, This
the primary
has
off,
with
having also
for the Cb-N pertaining
to
be interpreted
model.
peak
upon heating just above 3OO”C, while at the same time the Snoek
VOL.
a single
of the between
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