- Email: [email protected]
The effect of temperature and strain rate on the flow stress of iron
THE EFFECT
OF TEMPERATURE STRESS H. CONRAD?
AND STRAIN OF IRON*
and
RATE
ON THE
FLOW
S. FREDERICK?
Differential t,ype tests were employed to study the effect of temperature and strain rate on the flow stress of vacuum-melted electrolytic iron at low temperatures. The present results along with those of Basinski and Christian on Ferrovac iron indicate that a change in the flow parameters
with strain is due to an increase in the number of dislocations contributing to the deformation. Also, the variation of the activation energy and activation volume with stress is independent of strain and interstitial content and distribution. These results support overcoming the Peierls-Nabarro stress as the ratecontrolling mechanism in iron at temperatures below 300°K. L’INFLUENCE
DE
LA
TEMPERATURE LA
ET
TENSION
DE
LA
VITESSE
d’ECOULEMENT
DU
DE
DEFORMATIOS
SUR
FER
Des essais du type dif%rentiel ont &tB r8alisi?s pour Studier l’influence de la temperature et de la vit,essc de deformation sur la tension d’&coulement. de fer Blectrolytique fondu sous vide B basses temphratures. Les rbsultats prksents et ceux de Basinski et Christian sur du fer Ferrovac montrent qu’un changement dans les uaramktres d’kcoulement
en fonction de la deformation est dti Q un accroissement de nombre des dislocations d6formation. En plus, la variation de l’bnergie d’activation et du volume d’activation tension est indbpendante de la d&formation, ainsi que de la teneur en interstitiels et de Ces rbsultats suggbrent que le mbcanisme qui contr8le la vitesse de deformation du fer infkrieures B 300°K est le depassement des tensions de Peierls-Nabarro. EINFLUlj
VON
TEMPERATUR
UND
DEHUNGSGESCHWINDIGKEIT
FLIEDSPANNUNG
VON
contribuant it la en fonct,ion de la leur distribution. aux tempbratures
AUF
DIE
EISEN
Mit Hilfe van Differentialmessungen wurde der EinfluD van Temperatur und Dehungsgeschwindigkeit auf die Flieljspannung van Vakuum-geschmolzenem Elektrolyteisen bei niedrigen Temperaturen gemessen. Unsefe Ergebnisse ebenso wie die van Basinski und Christian an Ferrovac-Eisen w&en darauf hin, daB Anderung der FlieIjparameter
mit der Verformupg die zunehmende Anzahl der Versetzungen ist, die zu der Verformung beitragen. Ferner hiingt die Anderung van Aktivierungsenergie und Aktivierungs-volumen mit der Spannung mcht van der Verformung sowie der Anzahl und Verteilung der Zwischengitteratome ab. Diese Ergebnisse unterstiitzen iiberwiiltigend die Ansicht, daB bei Eisen unterhalb 300°K die Peierls-Nabarro-Spannung der geschwindigkeitsbestimmende Mechanismus ixt.
INTRODUCTION
Still unresolved is the question regarding the mecha-
In an earlier paper (l) it was shown that the temperature dependence was essentially
of the flow stress in elect’rolytic
controlling
iron
the same as that for the lower yield
stress, over the temperature suggested
nism which controls
range QO”-300°K.
that the same dislocation
during yielding and subsequent
therefore, that the strong temperature
temperature
Three mechanisms
was
1. Overcoming
flow and,
dependence
of
for the strong
of the yield and flow stress.
have been proposed : motion
force.(31435)
of jogs in screw dis-
locations.@) 3. Overcoming
rather than unlocking from a
of free dislocations
the Peierls-Nabarro
2. Non-conservative
the yield stress in b.c.c. metals was due to the movement of free dislocations,
dependence
This
mechanism
the velocity
in b.c.c. metals and is thus responsible
interstitial
atom precipitat,es.(‘)
Cottrell atmosphere. This conclusion was also reached from a detailed analysis of the data in the liter-
Some experimental support exists for each of these. The objective of the present investigation was, therefore, to provide additional information which might
ature on yielding and flow of iron and stee1.(233)
better
identify
approach * Received February 25, 1962. t Materials Sciences Laboratory, Segundo, California ACTA B
METALLURGICA,
VOL.
Aerospace
Corporation,
10, NOVEMBER
1962
El
the
employed
as the activation t’he frequency
1013
controlling
mechanism.
The
was to evaluate such parameters
energy, the activation
volume,
and
factor from the effect of temperature
ACTA
1014
VOL.
METALLURGICA,
straining
and strain rate on the flow stress of vacuum-melted electrolytic
iron and compare these with predictions
the proposed
dislocation
tive purposes,
mechanisms.
and to supplement
10,
1962
continued.
1 per cent strain;
For compara-
was employed
the present results,
data by Basinski and Christianc5) on Ferrovac iron are
temperatures
included in the present analysis.
location
The present
material
vacuum-melted
was from
electrolytic
used in the previous lowing composition
equipment
PROCEDURE
the same lot of
iron wire (1.6 mm dia.)
investigation(l) (wt. %)
and has the fol-
viouslv.(l)
N
0
0.014
0.003
0.005
Si
P
0.06
S
0.003
ml
0.011
0.002
the specimens
were heated for 20 min at 920°C in evacuated tubes and water quenched. about 10-l mm.
This gave a grain size of
The specimens were generally held at
room temperature To determine
quartz
a minimum
This type
of test
at different
could be made at a constant
dis-
of specimen
preparation
and the test described
pre-
For changes in st’rain rate, the cross-head
speed of the Instron tensile testing machine was cycled strain rates of 1
x
10e4 and 1
x
lop3
The temperature range covered was 90”-523°K.
The change in stress associated with a change in strain rate or temperature indicated
To eliminate the yield point elongation,
2.
between 0.02 and 0.2 in/min by means of a gear shift see-l.
C
Fig.
so that comparisons
were the same as those
lever, giving
:
strain rate changes
structure.
The method EXPERIMENTAL
again
of 10 : 1 were made at intervals of approximately
of
was determined
in Figs. 1 and 2.
in the manner
The stresses and strains
reported are t’rue stresses and true plastic strains and were obtained
by a computer
rections for the reduction
using appropriate
cor-
in cross section during ex-
tension and the elastic contribution
to the extension.
of 4 days before testing. EXPERIMENTAL
the effect of strain rate and tempera-
RESULTS
ture on the flow stress, two types of tests were con-
1. Effect of strain
ducted : Those in which the temperature
10 : 1 change in strain rate is given as a function of the
constant
throughout
Those
in which
the test and strain
the
rate
Fig. 1. specimens
strained at room temperature
J-Y&K
I
flow stress in Fig. 3. Values of are not included, resolve,
were
initially
to about 5 per cent
st)ra.in and then the temperature
0.04
changed
and
lo+-
I 0.08
Ao, for 373” and 523°K
for they were small and difficult to
especially
because
of irregularities
stress-st’rain curves due to strain aging; Where comparisons was found
were possible
10-3SEC-’
I
I
0.12
0.16
of strain rate changes on the flow stress of electrolytic iron.
I
0.20
in the
see Fig. 1.
(200’ and 90°K) it
ACT,was independent
that
TRUE PLASTIC STRAIN FIG. 1. Effect
AC, associated with the
The change in flow stress was maintained
changes of 10: 1 were made after approximately every 1 per cent strain;
rate
of the prior
CONRdD
AND
FREDERICK:
FLOW
STRESS
decreases
initially
OF
1015
and then remains essentially
stant. For comparison, no systematic
IRON
con-
Basinski and Christianc5) found
trend in A5, with stress (or strain) for
annealed vacuum-melted
iron (Ferrovac with 0.0031%
C + N) over the temperature
range
of
273”-78’K.
On the other hand, for t,he same material decarburized with web hydrogen, A5, decreased with stress at 273”K, was relatively
1
independent
of stress at, 180”K,
and
increased with stress at 78’K. The apparent linear decrease of A5, with 5 at 200”, 250’ and 300°K may actually
be due to the effect of
strain on ha, rather than the effect of stress per set, I
I
0.04
0
0.08 TRUE PLASTIC STRAIN
__I
0.12
0.16
FIG. 2. Effect of temperature and strain rate changes
on the flow stress of electrolytic iron.
straining history, i.e. Au, at a given stress (or strain} was the same for tests conducted
entirely at one tem-
perature as that for tests in which the specimen first strained
at 300°K
quent,ly changed.
and the temperature
was
subse-
Below 300°K Au, for an increase in
rate agreed with that. for a decrease.*
At 300°K A5,
for a decrease in rat,e was always less than that for an increase.
for as seen from Fig. 4, a linear relationship can also be inferred uhen A5, is plotted vs. strain. Thus the data allow for eit.her int,e~ret,ation of the change in Ao, with deformation. A plot of A5, vs. temperature T is given in Fig. 5(a). It, is here seen that Aa, increases with decrease in temperature from 300” to 150”K, is a maximum at approximately
but
is relatively
temperature.
for temperatures
of 15O’K and below, A5& is relatively
of stress
(or strain).
At, 200°K
and
250°K ha, decreases with stress, while at 300°K Ao, * At 90”K, An, for a decrease in rate was consistently less than for an increase in rata. However, t,he scatter in the dat,a at this temperature makes it. difficult t,o ascertain whether this effect is real.
both
independent
as found
Furthermorel
and
t,here is good
,;$Y);;
N
Y.s.
$_
+
250 *K a% V l-
0, 0
P = 10-4e10-3
SEC-'
OPEN SYMBOLS - STRAIN RATE INCREASED SOLID SYMBOLS-STRAIN RATE DECREASEQ_
40
60
cr, kg/mm’
lb. 3. The change in tensile stress Aoc associated with a 10: 1 change in strain rate as a function of the stress a at the strain r&e of lo-* see-‘.
specimens. the
a.nd t,hose of Basinski
8
z3 \ ,”
l/T
agreement, between
I
20:~mn
this
and Christian(5) for
decarburized
present, values of l/T and Christian.
150°K
below
linear decrease with tem-
by Basinski
t,heir annealed
above 150°K,
of strain
In Fig. 5(b) it. is seen that
an approximately
exhibits perature,
I
4-
Also, Ao, decreases
with &rain (or stress) for temperatures
One may interpret the data of Fig. 3 to indicate that, independent
150”K, and then decreases again with
further decrease in temperature.
80
ACTA
1016
METALLURGICA,
I
O&N CLOSED
iO-4~10-3
VOL.
10,
SYMBOLS-&RAIN
RATE
IN&EASED
SYMBOLS-STRAIN
RATE
DECREASED
SEC-’
ll
.
n
n
.
c
. u
.
.
’
.
a
l
n
-
D
I
I
0.04
0.08
150’ K . _
A
.
0
1962
0
I 200’
K
250” -
K
I .
TRUE
PLASTIC
n
I
012
0.16
0.20
STRPIN
FIG. 4. The change in tensile strength Ao, associated with a 10: 1 change in the strain rate as a function of strain. (The strains given are total strains, independent of history).
2. E#ect of temperature
exhibited
Figure 6 shows the effect of temperature tial yield stress, proportional
limit* (after E N 0.05),
and flow stress (e N 0.05) of the present material.
on the iniquenched
It is here seen that the temperature depend-
ence of the flow stress decreases with strain.
On the
other hand, the same material, but aged 24 hr at 15073, 5
I
I
dependence
independent
that the primary
of the tlow stress
of strain.(l)
difference
It is expected
between
the two treat-
ments is the amount of C and N in solution, pared to that precipitated.
For comparison,
and Christian(5) found that the temperature ence of their decarburized
as comBasinski depend-
iron decreased with strain,
while no effect of strain was reported for the annealed (not) decarburized)
I
‘a
a temperature
essentially
material,
Considering their results
along with the present data, it appears that decreasing the amount of precipitated
C and N gives a measurable
decrease in the temperature
dependence
of the flow
stress with strain. Since the proportional
‘W
4
condition
limit for the initial unstrained
of the present
material
is approximately
equal to the initial yield stress, it is seen from Fig. 6 24XlO-3
that the temperature
\
0’
b.
.-
\ 20 ---‘,
0 YIELD A c= 0.05 0 s=o. IO
\
dependence
of the proportional
limit decreases with strain even more than the tlow stress ; i.e. the temperature
dependence
portional limit is significantly
less than that of the flow
of the pro-
stress. This difference is larger than is expected purely on the basis of the difference
in plastic
strain rate
existing at these stresses. DISCUSSION
AND
CONCLUSIONS
Previous workc3) indicated that yielding and flow in iron can be described by TEMPERATURE,
T electrolytic
9 = pbsv* exp -
“K
with temperature
Hs
for
iron.
* The proportional limit represents the first measurable departure from the elastic line. The plastic strain rate at the proportional limit is ~10-~ set-I.
where + is the strain rate, p the density of dislocations participating
in the deformation,
b the Burgers vector,
s the average distance a dislocation successful
thermal
fluctuation,
moves after every
v* the frequency
of
CONRAD
AND
FREDERICK:
FLOW
STRESS
OF IRON
1017
60
0 INITIAL
YIELD
X PROPORTIONAL %
40
A
FLOW STRESS,
LIMIT. f = 0.03 E= 0.05
E . r s g 20 I c
100
200
300 TEMPERATURE
400
3oO
,“K
FIG. 6. Effect of temperature on the initial yield stress, proportional limit and flow stress of electrolytic iron.
vibration of the dislocation segment8involved in the thermal activation process, and N the activation energy, which is a decreasing function of the effective shear stress T*, given by the difference between the applied shear stress T and the long range internal stress T!~(i.e. T* = r - T,).? N may be written as H =: N* -
v*7*
(2)
where H* and zi* are functions of 7*. v* is termed the activation volume. Differentiating, one obtains -
7~In (pbsv*lli) =;
zzx
?I*
*
(3)
p = 0.7i. for 2
A rearrangement of equation (I) gives H = kT In (v&f
dislocations in iron is overcoming the Peier~-~aba~o stress, one does not expect a direct effect of strain on r*, rather any effect of strain will be on v, or more specifically on the dislocation density p. On the other hand, for the nonconservative motion of jogs in screw dislocations, or the overcoming of interstitial atom precipitates, it is expected that the effect of strain will be for the most, part on o* rather than on Y. In the following, these points were checked using the present data and those of Basinski and Christian(5). For the present analysis, it was assumed that r = to and
(4)
where v = pbsv* and it follows that
Finally, one can show that’s)
A consideration of equations (l-5) indicates that a
Al.so,
was approximated by
is small compared to
Eq~~ations(4) and (5) indicate that the value of y can be obtained from the slope of the slope of a plot of H vs. temperature. Such plots are given in Figs. 7 and 8 for the present data and in Figs. 9 and 10 for the data by Basinski and Christian. The values of v obtained from the slopes of these plots and the values of p derived from Y by taking sv* = lo6 cm/see [which value was obtained in ref. (3) from the dislocation mobility studies in silicon-iron of Stein and LOW(~)]are given in Table 1. It is seen from this
change in the parameters represents a change in either v or v* (or perhaps both). If the rate-controlling mechanism for the motion of t 7,‘ is proportional to the shear modulus ~1 and depends onty on the structure, which includes dislocations on parallel planes, C + N in solution, precipitates, etc,
i3a
(!
occurs with strain, there occurs an increase aT * in Y with strain, and consequently in p. Fu~he~ore, the values of p and their change with strain are in reasonable agreement with measurements of p in
and
ACTA
1018
zz_.-
_y-
TABLE
1.
Authors
Effect of
~ET~LL~RGIC~,
strain
---
on
the
dislocation
VOL. density
10, 1962
participsting
Strain
Xaterial
in
the
Vat. Melt. Electrolytic Iron-W.&.
Hasinski and
from 920°C
Ferrovar-Decarb.
Christian (5)
~.--
.“._---
I
I
I
I
4
8
12
16
kg/mm2
FIG.
7. Plot of ($s.
+(&jr
1.2 x 19’
3 x 19’
8.4 x 108
7.5 x 10’
9 x 10’
3.3 x 108
1.9 x 10s
6.9 s IO@
I.5 x 10s
10 x IO -2
9.9 x 10”
2.4 x 108
6.6 x 108
>5
x 10-z
‘K
for electrolytic
iron water-quenched from 920°C (present tests).
deformed iron by Keh and ~e~ssrnann(lO~using electron transmission microscopy. Of significance is a comparison of t’he variation of H and v* with stress, as derived from the present data and those of Basinski and Christian, with that obtained previously from data in the literature on yielding and flow in iron. Such a comparison is shown in Figs. 11 and 12.t We see from these figures Ohatthe present results and those derived from the data of Basinski and Christian are in good agreement, with those obt’ained previously. The decrease in Ao, with strain at temperatures above 150°K and its relative independence of strain at lower temperatures can be understood from the curves in Figs. 11 and 12. It is here seen that for values of (r -
Average
1 x 10--a
0 0
p(cm-“) Figs. 8 & 10
5 x IO--2 2 x IO-2 20 x 10.-a
Ferro~rae-annealer -~ -...__-
of iron
flow
v(Sec-‘) Figs. 7 & 9
Present
phst,ic
4.5 x 109
6.9 x lo9
2.1 x 19”’
4.5 x 109
6.0 x lo9
2.1 x 111’1
__.~__ -.--______ ._
--.-_ ~I-_x_~ ““__
__. .I_L:
function of the stress, while for (7 - 7’) greater than 12 kg/mm2, v* changes only slightly with stress. Referring to Fig. 6, one notes that for yielding 7 - TO= 12 kg/mm2 occurs at approximately 150°K. Now, sinee the flow of iron is given by equations (1) and (2), any increase in dislocation density with strain will result in a decrease in the effective stress required to maintain a constant strain rate. At temperatures above 150°K, t,his decrease in stress will result in a 8 In+ signi~cant increase in r* = kT and hence a i ar 1I’ measurable decrease in Aa, with strain. On the other hand, at temperatures below 150°K. the decrease in stress does not materially affect, t,he value of V* and heuce no measurable change in Aa, occurs. Thus the effect of strain on V* is through its effect on p rather than directly on v*. Two conclusions can t,husbe drawn from the present results along with those of Basinski and Christian: 1.
chke in ~~~~
The
~~~~*~ith
strain is due
to an increase in v, or more specifically in the number of dislocations contributing bo the deformation. 0.60
I
1
I :
=
I
IXIO+SEC”’
T”) less than 12 kg/mm2, v* = $TF is a sensitive
t 7’ given in these figures is dellned as previously,‘3’ i.e. the value of stress at 2WK and a strain rate of 10-l ax-‘. The value of r” for the present tests, which are at a strain rate of 10-e se&, was obtained by adding 1.5 kg/mm* to the value of the present shear stress a% 300°K [the value of 1.5 kg/mm” was obtained from Fig. 2 in ref. (3)].
ov 0
t
I
I
I
100 TEMPERATURE,
200
I
J
300
OK
Fro. 8. Variation of activation energy with temperature for electrolytic iron water-quenched from 920°C (present test).
ACTA
1020
METALLURGICA,
VOL.
10, 1962
weaker than that of the flow stress, even when the
authors wish to express their appreciation
difference in plastic st’rain rate is taken into considera-
house for permission to publish the data.
tion.
A plausible explanation
limit represents the motion
is that the proportional of dislocations
located in
regions of the crystal where the internal stress field is most favorable,
and hence they can move at somewhat
lower stresses than the majority must move through
of dislocations,
a larger average
field, and thus are only activated
which
internal
stress
at the flow stress.
ACKNOWLEDGMENTS
The experimental conducted
during
Westinghouse
part
of this investigation
H. Conrad’s
Research
t’o Westing-
association
Laboratories.
The
was
with the present
REFERENCES 1. 2. 3. 4. 5.
H. CONRAD and G. SCHOECK,Acta Met. 8, 591 (1960). H. CONRAD, Phil. Msg. 5, 745 (1960). H. CONRan, J. Iron 8. Inst. 198, 364 (1961). J. HESLOP and X. J. PETCH, Phil. Mng. 1, 866 (1956). 2. S. BASINSKI and J. W. CHRISTIAN, Au&. J. Phys. 13, 299 (1960). 6. G. SCHOECK, A& Met. 9, 382 (1961). 7. B. L. MORDIKE and P. HAASEN, Phil. Mrcg. 7, 459 (1962) 8. H. CONR~II and H. WIEDERSICH, Actn Met. 8, 128 (1960). 9. D. F. STEIN and J. R. Low, J. AppZ. Phys. 31,362(1960). 10. A. KEH and S. WEISSMAXN, Conference on The Impact of Transmission Electron hlicroscopy on Theories of theStrength of Crystdv. Berkeley (1961). To be published. 11. IV. C. T~RSI,IE, Actcr aWet. 9, 1001 (1961).
OF TEMPERATURE STRESS H. CONRAD?
AND STRAIN OF IRON*
and
RATE
ON THE
FLOW
S. FREDERICK?
Differential t,ype tests were employed to study the effect of temperature and strain rate on the flow stress of vacuum-melted electrolytic iron at low temperatures. The present results along with those of Basinski and Christian on Ferrovac iron indicate that a change in the flow parameters
with strain is due to an increase in the number of dislocations contributing to the deformation. Also, the variation of the activation energy and activation volume with stress is independent of strain and interstitial content and distribution. These results support overcoming the Peierls-Nabarro stress as the ratecontrolling mechanism in iron at temperatures below 300°K. L’INFLUENCE
DE
LA
TEMPERATURE LA
ET
TENSION
DE
LA
VITESSE
d’ECOULEMENT
DU
DE
DEFORMATIOS
SUR
FER
Des essais du type dif%rentiel ont &tB r8alisi?s pour Studier l’influence de la temperature et de la vit,essc de deformation sur la tension d’&coulement. de fer Blectrolytique fondu sous vide B basses temphratures. Les rbsultats prksents et ceux de Basinski et Christian sur du fer Ferrovac montrent qu’un changement dans les uaramktres d’kcoulement
en fonction de la deformation est dti Q un accroissement de nombre des dislocations d6formation. En plus, la variation de l’bnergie d’activation et du volume d’activation tension est indbpendante de la d&formation, ainsi que de la teneur en interstitiels et de Ces rbsultats suggbrent que le mbcanisme qui contr8le la vitesse de deformation du fer infkrieures B 300°K est le depassement des tensions de Peierls-Nabarro. EINFLUlj
VON
TEMPERATUR
UND
DEHUNGSGESCHWINDIGKEIT
FLIEDSPANNUNG
VON
contribuant it la en fonct,ion de la leur distribution. aux tempbratures
AUF
DIE
EISEN
Mit Hilfe van Differentialmessungen wurde der EinfluD van Temperatur und Dehungsgeschwindigkeit auf die Flieljspannung van Vakuum-geschmolzenem Elektrolyteisen bei niedrigen Temperaturen gemessen. Unsefe Ergebnisse ebenso wie die van Basinski und Christian an Ferrovac-Eisen w&en darauf hin, daB Anderung der FlieIjparameter
mit der Verformupg die zunehmende Anzahl der Versetzungen ist, die zu der Verformung beitragen. Ferner hiingt die Anderung van Aktivierungsenergie und Aktivierungs-volumen mit der Spannung mcht van der Verformung sowie der Anzahl und Verteilung der Zwischengitteratome ab. Diese Ergebnisse unterstiitzen iiberwiiltigend die Ansicht, daB bei Eisen unterhalb 300°K die Peierls-Nabarro-Spannung der geschwindigkeitsbestimmende Mechanismus ixt.
INTRODUCTION
Still unresolved is the question regarding the mecha-
In an earlier paper (l) it was shown that the temperature dependence was essentially
of the flow stress in elect’rolytic
controlling
iron
the same as that for the lower yield
stress, over the temperature suggested
nism which controls
range QO”-300°K.
that the same dislocation
during yielding and subsequent
therefore, that the strong temperature
temperature
Three mechanisms
was
1. Overcoming
flow and,
dependence
of
for the strong
of the yield and flow stress.
have been proposed : motion
force.(31435)
of jogs in screw dis-
locations.@) 3. Overcoming
rather than unlocking from a
of free dislocations
the Peierls-Nabarro
2. Non-conservative
the yield stress in b.c.c. metals was due to the movement of free dislocations,
dependence
This
mechanism
the velocity
in b.c.c. metals and is thus responsible
interstitial
atom precipitat,es.(‘)
Cottrell atmosphere. This conclusion was also reached from a detailed analysis of the data in the liter-
Some experimental support exists for each of these. The objective of the present investigation was, therefore, to provide additional information which might
ature on yielding and flow of iron and stee1.(233)
better
identify
approach * Received February 25, 1962. t Materials Sciences Laboratory, Segundo, California ACTA B
METALLURGICA,
VOL.
Aerospace
Corporation,
10, NOVEMBER
1962
El
the
employed
as the activation t’he frequency
1013
controlling
mechanism.
The
was to evaluate such parameters
energy, the activation
volume,
and
factor from the effect of temperature
ACTA
1014
VOL.
METALLURGICA,
straining
and strain rate on the flow stress of vacuum-melted electrolytic
iron and compare these with predictions
the proposed
dislocation
tive purposes,
mechanisms.
and to supplement
10,
1962
continued.
1 per cent strain;
For compara-
was employed
the present results,
data by Basinski and Christianc5) on Ferrovac iron are
temperatures
included in the present analysis.
location
The present
material
vacuum-melted
was from
electrolytic
used in the previous lowing composition
equipment
PROCEDURE
the same lot of
iron wire (1.6 mm dia.)
investigation(l) (wt. %)
and has the fol-
viouslv.(l)
N
0
0.014
0.003
0.005
Si
P
0.06
S
0.003
ml
0.011
0.002
the specimens
were heated for 20 min at 920°C in evacuated tubes and water quenched. about 10-l mm.
This gave a grain size of
The specimens were generally held at
room temperature To determine
quartz
a minimum
This type
of test
at different
could be made at a constant
dis-
of specimen
preparation
and the test described
pre-
For changes in st’rain rate, the cross-head
speed of the Instron tensile testing machine was cycled strain rates of 1
x
10e4 and 1
x
lop3
The temperature range covered was 90”-523°K.
The change in stress associated with a change in strain rate or temperature indicated
To eliminate the yield point elongation,
2.
between 0.02 and 0.2 in/min by means of a gear shift see-l.
C
Fig.
so that comparisons
were the same as those
lever, giving
:
strain rate changes
structure.
The method EXPERIMENTAL
again
of 10 : 1 were made at intervals of approximately
of
was determined
in Figs. 1 and 2.
in the manner
The stresses and strains
reported are t’rue stresses and true plastic strains and were obtained
by a computer
rections for the reduction
using appropriate
cor-
in cross section during ex-
tension and the elastic contribution
to the extension.
of 4 days before testing. EXPERIMENTAL
the effect of strain rate and tempera-
RESULTS
ture on the flow stress, two types of tests were con-
1. Effect of strain
ducted : Those in which the temperature
10 : 1 change in strain rate is given as a function of the
constant
throughout
Those
in which
the test and strain
the
rate
Fig. 1. specimens
strained at room temperature
J-Y&K
I
flow stress in Fig. 3. Values of are not included, resolve,
were
initially
to about 5 per cent
st)ra.in and then the temperature
0.04
changed
and
lo+-
I 0.08
Ao, for 373” and 523°K
for they were small and difficult to
especially
because
of irregularities
stress-st’rain curves due to strain aging; Where comparisons was found
were possible
10-3SEC-’
I
I
0.12
0.16
of strain rate changes on the flow stress of electrolytic iron.
I
0.20
in the
see Fig. 1.
(200’ and 90°K) it
ACT,was independent
that
TRUE PLASTIC STRAIN FIG. 1. Effect
AC, associated with the
The change in flow stress was maintained
changes of 10: 1 were made after approximately every 1 per cent strain;
rate
of the prior
CONRdD
AND
FREDERICK:
FLOW
STRESS
decreases
initially
OF
1015
and then remains essentially
stant. For comparison, no systematic
IRON
con-
Basinski and Christianc5) found
trend in A5, with stress (or strain) for
annealed vacuum-melted
iron (Ferrovac with 0.0031%
C + N) over the temperature
range
of
273”-78’K.
On the other hand, for t,he same material decarburized with web hydrogen, A5, decreased with stress at 273”K, was relatively
1
independent
of stress at, 180”K,
and
increased with stress at 78’K. The apparent linear decrease of A5, with 5 at 200”, 250’ and 300°K may actually
be due to the effect of
strain on ha, rather than the effect of stress per set, I
I
0.04
0
0.08 TRUE PLASTIC STRAIN
__I
0.12
0.16
FIG. 2. Effect of temperature and strain rate changes
on the flow stress of electrolytic iron.
straining history, i.e. Au, at a given stress (or strain} was the same for tests conducted
entirely at one tem-
perature as that for tests in which the specimen first strained
at 300°K
quent,ly changed.
and the temperature
was
subse-
Below 300°K Au, for an increase in
rate agreed with that. for a decrease.*
At 300°K A5,
for a decrease in rat,e was always less than that for an increase.
for as seen from Fig. 4, a linear relationship can also be inferred uhen A5, is plotted vs. strain. Thus the data allow for eit.her int,e~ret,ation of the change in Ao, with deformation. A plot of A5, vs. temperature T is given in Fig. 5(a). It, is here seen that Aa, increases with decrease in temperature from 300” to 150”K, is a maximum at approximately
but
is relatively
temperature.
for temperatures
of 15O’K and below, A5& is relatively
of stress
(or strain).
At, 200°K
and
250°K ha, decreases with stress, while at 300°K Ao, * At 90”K, An, for a decrease in rate was consistently less than for an increase in rata. However, t,he scatter in the dat,a at this temperature makes it. difficult t,o ascertain whether this effect is real.
both
independent
as found
Furthermorel
and
t,here is good
,;$Y);;
N
Y.s.
$_
+
250 *K a% V l-
0, 0
P = 10-4e10-3
SEC-'
OPEN SYMBOLS - STRAIN RATE INCREASED SOLID SYMBOLS-STRAIN RATE DECREASEQ_
40
60
cr, kg/mm’
lb. 3. The change in tensile stress Aoc associated with a 10: 1 change in strain rate as a function of the stress a at the strain r&e of lo-* see-‘.
specimens. the
a.nd t,hose of Basinski
8
z3 \ ,”
l/T
agreement, between
I
20:~mn
this
and Christian(5) for
decarburized
present, values of l/T and Christian.
150°K
below
linear decrease with tem-
by Basinski
t,heir annealed
above 150°K,
of strain
In Fig. 5(b) it. is seen that
an approximately
exhibits perature,
I
4-
Also, Ao, decreases
with &rain (or stress) for temperatures
One may interpret the data of Fig. 3 to indicate that, independent
150”K, and then decreases again with
further decrease in temperature.
80
ACTA
1016
METALLURGICA,
I
O&N CLOSED
iO-4~10-3
VOL.
10,
SYMBOLS-&RAIN
RATE
IN&EASED
SYMBOLS-STRAIN
RATE
DECREASED
SEC-’
ll
.
n
n
.
c
. u
.
.
’
.
a
l
n
-
D
I
I
0.04
0.08
150’ K . _
A
.
0
1962
0
I 200’
K
250” -
K
I .
TRUE
PLASTIC
n
I
012
0.16
0.20
STRPIN
FIG. 4. The change in tensile strength Ao, associated with a 10: 1 change in the strain rate as a function of strain. (The strains given are total strains, independent of history).
2. E#ect of temperature
exhibited
Figure 6 shows the effect of temperature tial yield stress, proportional
limit* (after E N 0.05),
and flow stress (e N 0.05) of the present material.
on the iniquenched
It is here seen that the temperature depend-
ence of the flow stress decreases with strain.
On the
other hand, the same material, but aged 24 hr at 15073, 5
I
I
dependence
independent
that the primary
of the tlow stress
of strain.(l)
difference
It is expected
between
the two treat-
ments is the amount of C and N in solution, pared to that precipitated.
For comparison,
and Christian(5) found that the temperature ence of their decarburized
as comBasinski depend-
iron decreased with strain,
while no effect of strain was reported for the annealed (not) decarburized)
I
‘a
a temperature
essentially
material,
Considering their results
along with the present data, it appears that decreasing the amount of precipitated
C and N gives a measurable
decrease in the temperature
dependence
of the flow
stress with strain. Since the proportional
‘W
4
condition
limit for the initial unstrained
of the present
material
is approximately
equal to the initial yield stress, it is seen from Fig. 6 24XlO-3
that the temperature
\
0’
b.
.-
\ 20 ---‘,
0 YIELD A c= 0.05 0 s=o. IO
\
dependence
of the proportional
limit decreases with strain even more than the tlow stress ; i.e. the temperature
dependence
portional limit is significantly
less than that of the flow
of the pro-
stress. This difference is larger than is expected purely on the basis of the difference
in plastic
strain rate
existing at these stresses. DISCUSSION
AND
CONCLUSIONS
Previous workc3) indicated that yielding and flow in iron can be described by TEMPERATURE,
T electrolytic
9 = pbsv* exp -
“K
with temperature
Hs
for
iron.
* The proportional limit represents the first measurable departure from the elastic line. The plastic strain rate at the proportional limit is ~10-~ set-I.
where + is the strain rate, p the density of dislocations participating
in the deformation,
b the Burgers vector,
s the average distance a dislocation successful
thermal
fluctuation,
moves after every
v* the frequency
of
CONRAD
AND
FREDERICK:
FLOW
STRESS
OF IRON
1017
60
0 INITIAL
YIELD
X PROPORTIONAL %
40
A
FLOW STRESS,
LIMIT. f = 0.03 E= 0.05
E . r s g 20 I c
100
200
300 TEMPERATURE
400
3oO
,“K
FIG. 6. Effect of temperature on the initial yield stress, proportional limit and flow stress of electrolytic iron.
vibration of the dislocation segment8involved in the thermal activation process, and N the activation energy, which is a decreasing function of the effective shear stress T*, given by the difference between the applied shear stress T and the long range internal stress T!~(i.e. T* = r - T,).? N may be written as H =: N* -
v*7*
(2)
where H* and zi* are functions of 7*. v* is termed the activation volume. Differentiating, one obtains -
7~In (pbsv*lli) =;
zzx
?I*
*
(3)
p = 0.7i. for 2
A rearrangement of equation (I) gives H = kT In (v&f
dislocations in iron is overcoming the Peier~-~aba~o stress, one does not expect a direct effect of strain on r*, rather any effect of strain will be on v, or more specifically on the dislocation density p. On the other hand, for the nonconservative motion of jogs in screw dislocations, or the overcoming of interstitial atom precipitates, it is expected that the effect of strain will be for the most, part on o* rather than on Y. In the following, these points were checked using the present data and those of Basinski and Christian(5). For the present analysis, it was assumed that r = to and
(4)
where v = pbsv* and it follows that
Finally, one can show that’s)
A consideration of equations (l-5) indicates that a
Al.so,
was approximated by
is small compared to
Eq~~ations(4) and (5) indicate that the value of y can be obtained from the slope of the slope of a plot of H vs. temperature. Such plots are given in Figs. 7 and 8 for the present data and in Figs. 9 and 10 for the data by Basinski and Christian. The values of v obtained from the slopes of these plots and the values of p derived from Y by taking sv* = lo6 cm/see [which value was obtained in ref. (3) from the dislocation mobility studies in silicon-iron of Stein and LOW(~)]are given in Table 1. It is seen from this
change in the parameters represents a change in either v or v* (or perhaps both). If the rate-controlling mechanism for the motion of t 7,‘ is proportional to the shear modulus ~1 and depends onty on the structure, which includes dislocations on parallel planes, C + N in solution, precipitates, etc,
i3a
(!
occurs with strain, there occurs an increase aT * in Y with strain, and consequently in p. Fu~he~ore, the values of p and their change with strain are in reasonable agreement with measurements of p in
and
ACTA
1018
zz_.-
_y-
TABLE
1.
Authors
Effect of
~ET~LL~RGIC~,
strain
---
on
the
dislocation
VOL. density
10, 1962
participsting
Strain
Xaterial
in
the
Vat. Melt. Electrolytic Iron-W.&.
Hasinski and
from 920°C
Ferrovar-Decarb.
Christian (5)
~.--
.“._---
I
I
I
I
4
8
12
16
kg/mm2
FIG.
7. Plot of ($s.
+(&jr
1.2 x 19’
3 x 19’
8.4 x 108
7.5 x 10’
9 x 10’
3.3 x 108
1.9 x 10s
6.9 s IO@
I.5 x 10s
10 x IO -2
9.9 x 10”
2.4 x 108
6.6 x 108
>5
x 10-z
‘K
for electrolytic
iron water-quenched from 920°C (present tests).
deformed iron by Keh and ~e~ssrnann(lO~using electron transmission microscopy. Of significance is a comparison of t’he variation of H and v* with stress, as derived from the present data and those of Basinski and Christian, with that obtained previously from data in the literature on yielding and flow in iron. Such a comparison is shown in Figs. 11 and 12.t We see from these figures Ohatthe present results and those derived from the data of Basinski and Christian are in good agreement, with those obt’ained previously. The decrease in Ao, with strain at temperatures above 150°K and its relative independence of strain at lower temperatures can be understood from the curves in Figs. 11 and 12. It is here seen that for values of (r -
Average
1 x 10--a
0 0
p(cm-“) Figs. 8 & 10
5 x IO--2 2 x IO-2 20 x 10.-a
Ferro~rae-annealer -~ -...__-
of iron
flow
v(Sec-‘) Figs. 7 & 9
Present
phst,ic
4.5 x 109
6.9 x lo9
2.1 x 19”’
4.5 x 109
6.0 x lo9
2.1 x 111’1
__.~__ -.--______ ._
--.-_ ~I-_x_~ ““__
__. .I_L:
function of the stress, while for (7 - 7’) greater than 12 kg/mm2, v* changes only slightly with stress. Referring to Fig. 6, one notes that for yielding 7 - TO= 12 kg/mm2 occurs at approximately 150°K. Now, sinee the flow of iron is given by equations (1) and (2), any increase in dislocation density with strain will result in a decrease in the effective stress required to maintain a constant strain rate. At temperatures above 150°K, t,his decrease in stress will result in a 8 In+ signi~cant increase in r* = kT and hence a i ar 1I’ measurable decrease in Aa, with strain. On the other hand, at temperatures below 150°K. the decrease in stress does not materially affect, t,he value of V* and heuce no measurable change in Aa, occurs. Thus the effect of strain on V* is through its effect on p rather than directly on v*. Two conclusions can t,husbe drawn from the present results along with those of Basinski and Christian: 1.
chke in ~~~~
The
~~~~*~ith
strain is due
to an increase in v, or more specifically in the number of dislocations contributing bo the deformation. 0.60
I
1
I :
=
I
IXIO+SEC”’
T”) less than 12 kg/mm2, v* = $TF is a sensitive
t 7’ given in these figures is dellned as previously,‘3’ i.e. the value of stress at 2WK and a strain rate of 10-l ax-‘. The value of r” for the present tests, which are at a strain rate of 10-e se&, was obtained by adding 1.5 kg/mm* to the value of the present shear stress a% 300°K [the value of 1.5 kg/mm” was obtained from Fig. 2 in ref. (3)].
ov 0
t
I
I
I
100 TEMPERATURE,
200
I
J
300
OK
Fro. 8. Variation of activation energy with temperature for electrolytic iron water-quenched from 920°C (present test).
ACTA
1020
METALLURGICA,
VOL.
10, 1962
weaker than that of the flow stress, even when the
authors wish to express their appreciation
difference in plastic st’rain rate is taken into considera-
house for permission to publish the data.
tion.
A plausible explanation
limit represents the motion
is that the proportional of dislocations
located in
regions of the crystal where the internal stress field is most favorable,
and hence they can move at somewhat
lower stresses than the majority must move through
of dislocations,
a larger average
field, and thus are only activated
which
internal
stress
at the flow stress.
ACKNOWLEDGMENTS
The experimental conducted
during
Westinghouse
part
of this investigation
H. Conrad’s
Research
t’o Westing-
association
Laboratories.
The
was
with the present
REFERENCES 1. 2. 3. 4. 5.
H. CONRAD and G. SCHOECK,Acta Met. 8, 591 (1960). H. CONRAD, Phil. Msg. 5, 745 (1960). H. CONRan, J. Iron 8. Inst. 198, 364 (1961). J. HESLOP and X. J. PETCH, Phil. Mng. 1, 866 (1956). 2. S. BASINSKI and J. W. CHRISTIAN, Au&. J. Phys. 13, 299 (1960). 6. G. SCHOECK, A& Met. 9, 382 (1961). 7. B. L. MORDIKE and P. HAASEN, Phil. Mrcg. 7, 459 (1962) 8. H. CONR~II and H. WIEDERSICH, Actn Met. 8, 128 (1960). 9. D. F. STEIN and J. R. Low, J. AppZ. Phys. 31,362(1960). 10. A. KEH and S. WEISSMAXN, Conference on The Impact of Transmission Electron hlicroscopy on Theories of theStrength of Crystdv. Berkeley (1961). To be published. 11. IV. C. T~RSI,IE, Actcr aWet. 9, 1001 (1961).