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Yield and fracture in polycrystalline niobium
YIELD
AND M.
A.
FRACTURE ADAMS?,
IN POLYCRYSTALLINE
A.
NIOBIUM*
and R. E. SMALLMAN
C. ROBERTS1
Tensile tests on specimens prepared from an ingot of electron-bombardment melted niobium have shown that the material undergoes a ductile-brittle transition and can be made to twin. The variation of yield stress Upwith grain-size 2d has been used to determine the effect of temperature (293’K-20°K at a strain-rate of 2.02 x lo-* set-r) and strain-rate (2.02 x 1O-4 set-‘-6.18 x 10-e set-r at 77°K) on the values of oi and k, in a Petch type equation ov = oi + k,d-‘I”, the results indicating that the ductilebrittle transition characteristics are in accordance with Cottrell’s transition equation (uidllz + k,)k, = /lpy. Niobium shows a greater resistance to brittleness than carburized a-iron because it has a smaller k, value, and the reluctance of the material to twin except under extreme conditions of low temperature or high strain-rate is also attributed to a low value of k,. The mechanical behaviour of niobium relative to that of other body-centred cubic transition metals is discussed. DEFORMATION
ET
RUPTURE
DU
NIOBIUM
POLYCRISTALLIN
Les auteurs ont soumis a des essais de traction des Qchantillons de niobium prepares au four de fusion a bombardement d’electrons. 11 resulte de ces essais que ce metal possede une courbe de transition du type ductile-fragile et qu’il peut subir un maclage. La variation de la tension de deformation Us avec le grain-size 2d permet de determiner l’effet de la temperature (293”K-20°K pour une vitesse de deformation de 2.02 x lo-* set-r) et de la vitesse de deformation (2.02 x lo-* set-‘-6.18 x 1O-2 set-r a 77°K) sur lea valeurs de oi et k, dans l’equation de Petch o, = oi + k,d-1/2. Les resultats indiquent que les caracteristiques de la transition rupture fragile-rupture ductile sont en accord avec l’equation de Cottrell (o~&~ + k,)k, = @,uy. L e niobium montre une plus grande resistance a la fragilite que le fer c( carbure parce qu’il possede une valeur de k, plus faible. Exception faite de son comportement dans des conditions particulieres a basse temperature ou sous une vitesse de deformation &levee, la resistance de ce metal au maclage peut 6tre attribuee a la faible valeur de k,. Lea auteurs discutent enfin du comportement mecanique du niobium compare a celui des metaux de transition cristallisant Bgalement dans le systeme cubique cent&. FLIEBEN
UND
BRUCH
VON
VIELKRISTALLINEM
Niob
ZerreiDproben wurden aus Niob hergestellt, das duroh Elektronenbombardement erschmolzen worden war. Die Zugversuche zeigten, da13 bei diesem Material ein Ubergang duktil-sprode auftritt und da6 es sich verzwillingen 1iiDt. Die Abhangigkeit der Flieljgrenze IJ~ van der KorngrBDe 2d wurde beniitzt, urn den EinfluD der Temperatur (293°K - 20°K bei einer Dehnungsgeschwindigkeit van 2,02 x 1O-4 set-I) und der Dehnungsgeschwindigkeit (2,02 x 1O-4 sec- i - 6,18 x 1O-2 set-’ bei 77°K) auf die Parameter Us und k, in der Gleichung nach Petch a, = oi + k,d-‘ia zu bestimmen. Die Ergebnisse zeigen, da9 die GesetzmiiBigkeiten des Ubergangs duktil-sprode mit Cottrells Ubergangsgleichung ((aid1/e + k,)k, = b,u~iuy)iibereinstimmen. Niob zeigt einen grdljeren Widerstand gegen Sprodigkeit ala aufgekohltes a-Eisen wegen seines kleineren k,-Wertes. Die geringe Neigung des Materials zur Zwillingsbildung aul3er bei extremen Bedingungen tiefer Temperatur oder hoher Dehnungsgeschwindigkeit wird ebenfalls dem kleinen k,-Wert zugeschrieben. Das mechanische Verhalten van Niob wird mit dem anderer kubisch-raumzentrierter Ubergangsmetalle verglichen und diskutiert.
1. INTRODUCTION
Although and
brittle
received centred
years the plastic
fracture
behaviour
considerable
of
deformation
mild
cubic metals have been relatively
in behaviour
with
to the expected
a-iron,
and partly
of the high melting
point
vanadium,
tantalum,
niobium
industry.
However,
the
steel
other
attention(1-4)
This has been due partly usage
these
in recent
investigation
8, MAY
of niobium purified by electron-bombardment Tensile
to the small
refractory
tests
on
been described
metals
importance
1960
of their mechanical
similarity
commercially
and
properties.
pure
melting.
niobium
have
by Wessel and Lawthersc5).
For mild steel it has been shown, both theoretically
in
and
of
for yield propagation
experimentally,(3+-8)
according
VOL.
gas turbine
the need for a more
Work is described in this paper on the tensile behaviour
May 12, 1959. t Materials Research Corporation, Yonkers, New York, formerly Metallurgy Division, Atomic Energy U.S.A.; Research Establishment, Harwell. $ Metallurgy Division, Atomic Energy Research Establishment, Harwell. 5 Department of Physical Metallurgy, University of Birmingham; formerly Metallurgy Division, Atomic Energy Research Establishment, Harwell. METALLURGICA,
in the
detailed
* Received
ACTA
particularly
energy fields, indicates
neglected.
and molybdenum
increased
has
body-
metals,
nuclear
that
the
shear
stress
q,
varies with the grain diameter 2d
to the equation:
c21= oi + cc 11’2d-i’2 or
(1) a, = ai + k, d-ii2
where, following stress to unpin 328
(Ic, = aD ln2) i
Cottrell’s notation,(8) aI) is the shear a dislocation from its atmosphere,
ADAMS,
ROBERTS TAELE
Impurity elements per cent present ~________
/
SMALLMAN:
AND
Si
1 0.150
/
Fe
/
0,
j
H,
j
/
0.300
/
0.01
/
0.02
!
PROCEDURE
Specimens were made from an ingot of commerciahy pure niobium which had been melted by electron bombardment. This treatment reduces markedly the gaseous impurities oxygen and nitrogen without radically affecting the metallic impurities. A typical analysis after melting is shown in Table 1. Texture free wire of 1.25 mm diameter was prepared from the ingot by alternate cold swaging (50 per cent reduction in area) and annealing (1075’C for 1 hr in tantalum foil) treatments. After a final swage to 1 mm diameter, batches of 7.5-cm long wires were annealed (in tantalum foil) at temperatures from 1075°C to 1415°C to give the range of grain sizes shown in Table 2. 1075’C was established as the m~imum recrystallization temperature, giving grains of about 0.005 cm diameter, whilst the 1415°C anneal resulted in wires with some grains across the complete section. For these wires the grain diameter was taken as the major axis of a plane at 45” to the wire axis, this corresponding to the plane of maximum shear stress. All anneals were made in a dynamic vacuum of between IO-5 and lop6 mm Hg. Wires were mounted for straining by soldering their ends with Wood’s metal into close-fitting brass bosses fitted with loops to engage hooks in the tensile TABLE
2. Grain-sizes of the specimens
Heat treatment
-.-
d-‘/2 cm-112
Grain size Xd(cm) ---
--
1 1 1 3
hr Izt 1075°C hr at 119O’C hv at 1260°C hr at 1415°C
A1”V’D FRACTURE
1. Typioal anrtlysis for niobium melted by &&on
oi the shear stress resisting the movement of dislocations across the slip plane after they have been unpinned, and I the distance from piled-up dislocations at the head of the plastic front to the nearest FrankRead sources. In the present experiments the effect on 0; and & of varying temperature (293’K-20°K at a strain-rate of 2.02 x lOA se&) and strain-rate (2.02 x lo-4 sea-i-6.18 x 1OV see-r at 77°K) has been determined from measurements of yield stress on niobium specimens covering a range of grain sizes, and conditions for the occurrence of (a) twinning and (b) a ductile-brittle transition have been established. 2. EXPERIMENTAL
YIELD
0.00476 0.00951 0.0312 0.1414
’ 20.5
14.5 3.2 3.76
IN
bombardment
-&a 0.05
329
Nb
-_--
/
Ta
j
C
/
0.30
1
0.07
j others 1
0.03 .---.~_
machine. Each end of the wire was shotblasted and then electro-plated with a 0.025 mm copper layer to allow tinning. The Wood’s metal was held in a constant temperature water bath, so that the specimens never exceeded a temperature of 80°C. Tensile tests were made in the au~~aphi~ally tensile machine described by recording “hard” Adams(g). The gauge length of the specimens was 2.8 cm and for most of the tests the machine was driven at a constant cross-head speed of 0.00057 cm set-l (strain rate 2.02 X lo4 se&) ; in a series of fast strain-rate tests this speed was increased to 0.173 cm set-i (strain rate 6.18 x 10e2 set-I). 3. RESULTS
3.1 Slow strailt-rate tests at 293”K, 195*K, and 77°K Figure 1 shows ehara~~ristie stress-strain curves for specimens of the finest grain-size tested at 293*K, 195°K and 77’K, with a strain rate of 2.02 x 10” see-l. At the two highest temperatures the curves are typical of a strain-ageing material, and lowering the temperature from 293°K to 195°K changes the shape of the curve only slightly by increasing the size of the yield point and decreasing the amount of uniform elongation. A further lowering of the testing temperature to 77’K, however, causes a marked change in behaviour; the upper yield stress is not very sharp and after a very small uniform elongation, necking occurs, the load then dropping steadily until fracture. At this temperature the high stress required to move the first dislocations must be suflicient to overcome any internal stresses created in the lattice during deformation, All fractures were of the fibrous type and the ductility of the material, measured from the percentage reduction in area at the fracture, was decreased slightly with decreasing temperature from about 99 per cent at 293°K to about 80 per cent at 77°K. Typical curves for the coarest grained samples are shown in Fig. 2. The only marked difference from the fine-grained material is the reduced uniform elongation at 2Q3’K and 195°K. Necking in the coarse-grained specimens occurred across single grains at all three temperatures, resulting in knife-edge fractures. In Fig. 3 the lower yield tensile stress values of a series of niobium specimens are shown as a function of d-i/s at the three testing temperatures. For the
ACTA
METALLURGICA,
VOL.
8,
1960
I
5
IO
% FIG.
20
15
25
30
35
ELONGATION
1. Effect of temperature on the stress-strain curve of specimens of the finest grain-size (2d = 0.00476 cm)
extended at a rate of 2.0% x lo-* see-‘.
195°K tests, specimens of four different grain-sizes were used whilst at the other two temperatures only the finest and coarsest grained samples were tested. Since in the tests at 77°K no clearly defined lower yield elongation was evident, it was necessary to estimate the position of the lower yield point. This was taken as the &rat inflexion in the stress-strain curve after the initial drop in load. Each point on the graph is the average for several tests at that temperature and grain size ; the maximum scatter on individu&l
tests amounted to about -&5 per cent of the mean value. From the curves of Fig. 3, a, and k;, for the three temperatures have been estimated (see Table 3). Here, shear stresses rather than tensile stresses (to a first approximation the shear stress is half the tensile stress) are used in accordance with equation (1). The oi values carry a possible error of about the same amount as the lower yield stresses, whilst the errors in &, may be larger, possibly &50 per cent.
ADAMS,
ROBERTS
AND
SMALLMAN:
YIELD
AND
Oo
FRACTURE
5I
IN
Nb
10 I
331
15 1
20 1
CM.-;
4 -f
FIG. 3. Variation of yield stress with grain-size for specimens extended at a rate of 2.02 x 1O-4 set-l at 293”K, 195’K and 77°K.
showed
completely
temperature behaviour centred could
293OK
7
at
to
(2.02 x lo4
a
This
metal of body-
see if
set-l)
brittleness a series of
tests was made
The results are summarized
by the represen-
curves of Fig. 4. Specimens
coarsest
failed
grain-size
macroscopic
plastic
intermediate
grain-sizes
by total
elongation.
cleavage Those
also cleaved,
plastically
of the
with no
of the
two
but only after
for a few per cent, and The finest grained
considerably.
material deformed plastically with rapid workhardening, necked and finally failed by a mixed shear less
slowly with decreasing temperature ; cri increases more rapidly with decreasing temperature, particularly between 195°K and 77”K, and is somewhat larger (about 25-50 per cent) than that for En2 steeloO) at all three temperatures.
and cleavage fracture at the neck. The stress-strain curves of all the specimens which extended
plastically
particularly
___.-
3.1 all specimens
showed
very
distinct
in the early stages of plastic flow.
jerks, Each
TABLE 3. Values of oi and k, at three temperatures. Strain rate = 2.02 X 10e4 see-’ _._ ~__
Temperature IJ~(lb/in*)
3.2 Xlow strain-rate tests at 20°K of Section
and
tative stress-strain
work-hardened
than that for En2 steel at 195”K,(10) and increases
In the experiments
even
at lower temperatures
they had elongated
ELONGATION
about an order of magnitude
in a transition
structure,
strain-rate
range.
FIG. 2. Effect of temperature on the stress-strain curve of specimens of the coarsest grain-size (2d = 0.1414 cm) extended at a rate of 2.02 x 1O-4 set-I. k, is very small,
fractures,
at 20°K on specimens covering the complete grain-size
O/o
is unusual cubic
be induced
slow
ductile
as low as that of liquid nitrogen.
k,
(c.g.s.)
1
195°K
293°K
I ~~48,000
;-~
18,000
10,000
) 5.18 x lo6
) 3.8 x IO0
1
77°K
A__
2.76 x lo6
332
ACTA
METALLURGICA,
VOL.
8,
1960
FIG. 4. Effect of grain-size on the stress-strain curves of specimens extended at a rate of 2.02 x 1OF set-l at 20°K; (a) grain-size 2d = 0.1414 cm, (b) grain-size 2d = 0.0312 cm, (c) grain-size 2d = 0.00951cm, (d) grain-size 2d = 0.00476 cm.
jerk was accompanied by an audible click, suggestive of deformation twinning. A metallographic examination confirmed that twins are formed. The specimen
have removed a low temperature martensite phase. The coarse-grained cleaved specimens also showed twin bands after polishing and etching (Fig. 6), but
surfaces showed slip lines and other markings resembling the Neumann bands observed in iron. These markings were removed by polishing but re-appeared
it is open to contention whether these twins were formed immediately prior to fracture (one of the stress-strain curves did show a twinning burst before the specimen broke) or were nucleated by shock
after etching (Fig. 5) and they persisted after an anneal of 1 hr at 85O”C, a heat treatment that would
waves
accompanying
the fracture.
Double
surface
.4DBMS,
ROBERTS
SMALLAMAN
AND
: YIELD
AND
FRACTURE
IN
Nb
333
from these tests, and the reliability ment is somewhat
uncertain.
of a oZ measure-
However,
the stress-
strain curves indicate some slip interspersed
with the
initial twins, which suggests that a value cz = 58,000 lb/in2 is reasonable.
Cleavage stress values, except for
the coarsest grained specimens,
all of which failed at
around
were very
116,000 lb/in2
tensile,
scattered.
They varied from 150,000 to 200,000 lb/in2 tensile in specimens
of 0.0095 cm grain size, and from 150,000
to 180,000 lb/in2 tensile for those of 0.031 cm grainsize.
Fracture stresses for the finest grained material,
subject to considerable of estimating
errors because of the difficulty
the area of the neck, ranged from about
250,000 to 280,000 lb/in2 tensile. A portion of a fractured specimen grain-size
FIG. 5. Deformation twins in a specimen of the second finest grain-size (2~2= 0.00951 cm) extended to fracture at 20°K. Polished and etched (95 per cent HNO,, 5 per cent HF) after tensile-testing. x 340 analysis
of several
sets of prominent
grains, using X-ray the
twinning
observations
as
(112)
with
deformed
examination
Analysis
at
was made
and etching.
of the three finer grain sizes the
curves indicate that the first macroscopic
deformation
occurred
116,000 lb/in2 in all cases. it is impossible
by twinning,
was within
to obtain
and the
a few per cent of
Because twinning interferes a direct
kY measurement
property
by increasing the strain-rate
the transition
plastic
the
back-reflection
cleavage
surface
of the two films gave the cleavage
mechanical
surface or after polishing
tensile stress at yield
to
changes
from lowering the testing temperature
of all the specimens tested at the higher temperatures. In no case was a twin band observed, either on the For the specimens
normal
3.3 Fast strain-rate tests at 77°K
Consequently,
stress-strain
the
of the coarsest
in a Laue
plane as (100).
Many
cubic metals.
twins in the specimens
a careful metallographic
beam.
Laue data, gave agreement
with
mounted
aligned at first parallel and then at 30” to the X-ray
bands on large
in
on other body-centred
After finding 20’K
back-reflection
plane
camera
was
which
arise
can be simulated
at constant temperature.
tests were made at 77’K
to see if an
increased strain-rate at this temperature to brittleness
would induce
observed
in the experi-
tests the strain-rate
was increased
ments of Section 3.2. In preliminary
by a factor of about 20. of all specimens
This raised the yield stress
by about
did not appreciably
10 per cent but otherwise
alter the form of the stress-strain
curve, or change the mode of deformation
or fracture.
Increasing the strain-rate 6.18 x 1O-2 set-l) resulted
a further 15 times (to in stress-strain curves of
the form shown in Fig. 7.
At this very fast rate of
testing without the
specimens
of the coarsest
macroscopic
three
finer
plastic
grain-sizes
grain-size
deformation deformed
cleaved
; those of
plastically
constant stress for a few per cent elongation finally failed by a shear fracture after necking. No curves,
jerks
were seen in any
of the
stress-strain
but all test pieces were polished
and carefully gauge-length.
examined
at and
and etched,
for twins over the complete
Some of the specimens
of each grain-
size showed small twins on two or three of their grains. whilst in other samples no twinning was observed at all. By comparison all specimens deformed at 20°K showed FIG. 6. Deformation twins in a specimen of the coarsest grain-size (2d = 0.1414 cm) extended to fracture at 20°K. Polished and etched (95 per cent HNO,. 5 per cent HF) after tensile te&ing. x 140 4k-(4ppJ
well marked
twins on at least half of their
grains. Cleavage and yield stress figures obtained from the fast strain-rate tests are plotted as a function of d-1/2
ACTA
METALLURGICA,
VOL.
8, 1960
FIG. 8. Variation of yield (or cleavage) stress with grain-size for specimens extended at 77°K at rates of 2.02 x 1O-4 see-l and 6.18 x 1O-2 set-I.
account
for the detailed differences
between niobium
and other metals of like structure properties
have been investigated.
Deformation A notable above,
whose mechanical
by slip feature of the experiments
in which plastic
or predominantly
deformation
at 77°K and
occurred
solely
by slip, is that the yield propagation
stress increases
only slightly
size ; rE, for niobium
with decreasing
grain-
is almost an order of magnitude
smaller than that for En2 steel(rO) at 77”K, and over 20 times 293°K.
smaller
than
that
for molybdenum(ll)
On the basis of equation
in niobium purified by electron-bombardment the atmosphere
at
(1) this means that
locking of dislocations
melting
is rather slight.
This result may seem surprising since the stress-strain curves at 293’K FIG. 7. Effect of grain-size on the stress-strain curve of specimens extended at a rate of 6.18 x IO-* set-1 at 77°K; (a) grain-size 2d = 0.1414 cm, (b) grain-size
2~1= 0.06476 cm. Specimens of the two intermediate grain-sizes give curves of the same form as (b).
in Fig. 8 which also shows, for comparison, strain-rate specimens lying
results.
values
are used, the scatter
within
graph
Average
gives
the limits a
quoted
value
of
the slow
from
several
on individual in Section
tests
3.1.
The
oi = 56,500 lb/ins
and
,$, = 7.25 x lo6 c.g.s. at the fast strain-rate. 4. DISCUSSION The present experiments
have shown that niobium
follows the same general pattern of mechanical behaviour as other body-centred cubic transition metals.
Thus, one can obtain by a suitable choice of
temperature or strain-rate a change from complete ductility to complete brittleness, and from slip to twinning as a possible mode of deformation. It remains now to examine those factors which may
and
lower
and 195°K show a well-marked
yield
point.
It
must
be
upper
remembered,
however, that the size of the yield drop is an unreliable quantitative locking
measure
of the amount
because the experimental
yield stress depends sensitively
of dislocation
value of the upper
on specimen preparat-
ion and on tensile machine characteristics.(is-i4)
One
way in which the form of the curves does indicate small k, value is from the amount elongation. portion
If for the tests at 293°K
of the curve immediately
elongation
is extrapolated
value obtained equation
and 195°K the
following
the yield
to zero strain, the stress
is a rough measure of ci.
(l), the difference
a
of the lower yield
Then, from
in stress AC between the
lower yield stress and the extrapolated value is equal to Ie,d-1/2. With small lower yield elongations and low rates of work hardening immediately
afterwards,
as observed in the present tests, the values of Aa and consequently of lcQ,are small. The yield strength of niobium deformed by slip can be attributed
chiefly
to the friction
stress
e’i
ADAMS,
ROBERTS
resisting the movement
of dislocations
unpinned from their atmospheres, of the yield strength arises
primarily
resistance
from
by (a) randomly
that have been
and the dependence
on temperature variations
to dislocation
of
oi.
impurity
atoms
(b) precipitated
locations
in the lattice, (d) the Peierls-Nabarro
It is not immediately
impurities,
in solid
solution,
obvious
force.
of ai to tempera-
but the work
Petch(15) on steel suggests
dis-
which of these is most
likely to give the required sensitivity ture and strain-rate,
(c) other
of Heslop
Twinning only
under
and
that the Peierls-Nabarro
or high strain-rate.
niobium
can be found
Biggs and PrattV)
have recently
Entwisle’ls)
and
to explain
of iron crystals.
developed
Bilby(17)
and
from the Bilby
and
their results on the twinning
The theory shows that twin nucleation
Pratt suggest that nucleation stress concentration array of dislocations
and Biggs and
at the head of a rapidly piled-up by a burst of slip as a
as
carburized
dislocations niobium slight context small
(large
a-iron
strongly
than
in one
Ic, value)
in which the dislocation
(small to
value
of le,).
in a material
with
such
as
locking is relatively
It is of interest
note
that tantalum Ic, value(*) and exhibits,
reluctance to twin.(lg) All the specimens which
locked
apparently has like niobium, plastically
20°K showed the same pattern of behaviour;
the
a a
at
(a) small
amounts of slip interspersed between extensive bursts of twinning in the early stages of deformation,
in
twins the
is as
rapid
ductile
samples
En2
carburized
a-iron.
became
and only
completely
tested
at
the
the
finest
brittle
why,
grained at
were
the coarsest
brittle at 20°K ; same
strain-rate, greater than
niobium
77”K.(1°)
are
To
of the two materials,
show the greater resistance
to
In the
tests all the specimens
at 77”K,
steel
transition
of a grain size only slightly
of
reasons
ductile-brittle
it is again instructive
with
present slow strain-rate
find
almost possible
niobium
to brittleness brittle
should
in tensile
fracture
theory
of Cottrell@).* Developing fracture
the idea that the difficult
process
is crack
crack nucleation, slip planes. gliding
propagation
Cottrell proposes
stage in the rather
than
a mechanism
for
on intersecting
It is shown that two (111) dislocations
in { 1 lo} pl anes can react with a lowering
energy to form a pure edge dislocation
of
in the (100)
cleavage plane. *a[1111 + +a[1111 -+ a[OOl]. The new dislocation, “cleavage
wedge”
equivalent
geometrically
of material between adjacent
faces, is thought to be the crack nucleus.
to a (100)
The nucleus
dislocations
run into it
until it reaches a size of the same order of length as the slip bands becomes the
deformed
results
will grow easily as successive
in this
of
at 20°K.
of niobium
comparisons
With other things equal it should be easier to produce such
will then no
action
dislocations observed
considering
source is released from its atmosphere.
a slip burst suitable for twin nucleation
the
forming crack nuclei from dislocations
is brought about by the
produced
335
of slip dislocations
tests we turn to the recent
in the ideas that
is more difficult than twin propagation,
Frank-Read
for
A general explanation
for this behaviour Cottrell
When
completely
can be
compared
slip
characteristics
that
low temperature
Thus, although
Nb
Cleavage
grained
in the present experiments
of extreme
example with carburized u-iron.
of
to
specimens
made to twin it does so with reluctance,
theories
barriers
completely
by twinning conditions
IN
Presumably
work-hardening
with
was observed
FRACTURE
and the generation
make
force probably makes the most significant contribution. Deformation
AND
suppressed.
Frictional be caused
could
YIELD
longer occur in sharp bursts so that twin nucleation
and strain-rate
movement
dispersed
SMALLMAN:
AND
directly
crack
forming
it.
The applied
responsible
size is greater
fracture
will result;
ductile.
A calculation
for crack growth than
otherwise
that the ductile-brittle
stress then
the
Griffith
the material
and if value will be
of the critical crack size shows transition
will occur
when
modulus,
y the
the relationship
(b) a preponderence of slip with only occasional twinning as deformation was continued, (c) an ability (in contrast at 77°K)
to t,he behaviour
to work-harden
of specimens
whilst
deforming
tested by slip.
These observations are again in accord with the model of twinning discussed above. Twins, once formed, may themselves act as dislocation pile-up and
barriers, further
allowing further twin nucleation.
After
most
the
a time,
however,
of
Frank-Read
sources will have been released from their atmospheres,
is satisfied,
where
,U is the
shear
effective surface energy for the propagation of cracks and ,!I a constant equal to 1 for uniaxial tension (ordinary tensile test) and + for triaxial tension (tests * See also Petch’s’20) recent theory of the ductile-brittle transition in impact tests on notched specimens. This theory can be extended to tensile tests, and gives R transition equation of the same form as that developed by Cot,trcll witah t,hr constants slightly altered
336
ACTA
VOL.
8,
1960
TABLE 4. Critical velues of (ui c/i/z + &)ky on either side of the ductile-brittle transition point -__~..-_____.~~-.. __.
-__~ Temp. of testing
/ /
("W
I
-~--
METALLURGICA,
77 20 77 77 20
Strain r&e
(see-l)
i
1
(lb$ie)
___6.18 x 1O-2 2.02 x 10-4 2.02 x IO-4
~
56,500 58,000
’
48,000
1 1
--1
k
(0.g.s. “x 10’) 7.25 5.87* 5.18
Grain size 2d (cm)
- -___--__
0.1414 0.1414 0.1414 0.0312 0.0312
. .__.~__ * Estimated by extrapolating the k, values measured at the higher temperatures. on notched specimens). oi, Xc, and d retain the same significance as in equation (1). Cottrell also points out that equation (2), although obtained originally from a detailed analysis of the above process, should be valid quite generally for the growth of cracks created by the conversion of glide dislocations into cavity dislocations. Under conditions where the value of the left hand side of equation (2) is less than the value of the right hand side, ductile behaviour should be observed; when the left hand side exceeds the right hand side the behaviour should be brittle. In a given material brittleness should be favoured by low temperature and high strain-rate (large values of criand kJ and by large grain size, which is in qualitative agreement with the present results. To test the theory quantitatively we note that in our experiments the transition from ductile to completely brittle behaviour has been approached in four different ways: (i) by changing the strain-rate from 2.02 x low4 see-r to 6.18 x 1O-2 se& in tests at 77’K on specimens with a grain diameter 2d = 0.1414 cm; (ii) by changing the grain diameter from 2d = 0.0312 cm to 2d = 0.1414 cm in the fast strain-rate tests at 77’K; (iii) by changing the testing temperature from 77’K to 20°K in the slow strain-rate tests on specimens with a grain diameter of 2d = 0.1414 cm ; (iv) by changing the grain diameter from 2d = 0.0312 cm to 2d = 0.1414 cm in the tests at 20°K. p * ,u * y may be reasonably assumed to remain insensitive to the various experimental changes so that if the theory is correct the value of (ci S’s + kv)ks in every case where the behaviour is brittle should exceed any value of (oi d1J2 + k,)k, for an experiment in which ductility is observed. The values listed in Table 4 show that the results are in fact in accord with the theory. The closest limits we have from the experiments show that a transition from ductile to completely brittle behaviour occurs when (oi dxj2 + kJk, changes from 4.59 x lo16 c.g.s. to 6.28 x 1015c.g.s. Thus with @ = 1 and ,LL= 4 x loll dyne cm-s we find that the effective surface energy y is given by 1.57 x lo4 ergs cin2 > y > 1.15 x 104 ergs cm-.2; or y = 1.36 x IO4
! Behaviour
(qW
___ + k,)k
(0.g.s. x 1015;
/---
___
brittle brittle ductile ductile ductile
l--l__---7.57 6.28 4.59 3.47 2.88
ergs cm-2 5 15 per cent. This value is close to the experimentally determined value of y for En2 steel,‘lc) and about 5 times larger than the true surface energy of niobium, 2.7 x lo3 ergs cm-2, estimated from the data of Taylor(21’. An effective surface energy greater than the true one appears to be a general feature of brittle fracture results, and is thought to be mainly due to the irreversible work of tearing at river lines and grain boundaries.(s2) Whilst showing some ductility, the specimens of the three finer grain sizes tested at 20’K did finally fail by cleavage (or by a mixed shear and cleavage fracture in the finest grain-size case). For such specimens, in which oi is raised by work-hardening during the test, the theory predicts a linear increase in fracture stress or with d-1’2 along a line which extrapolates to of = 0 at d-rJ2 = 0. From the few rather scattered results obtained in the present experiments it appears that specimens of the second coarsest grain-size give approximately the correct fracture stress values, whilst those of the two finer grain sizes have fracture stresses that are too low: further results covering the grain-size range more fully would, however, be required to test this part of the theory properly. The increased tendency towards brittleness in En2 steel compared with niobium is to be expected from equation (2). At comparable temperatures and strain-rates oi and y are similar for the two materials ; but kg for En2 steel is about 10 times as large as that of niobium and y is about twice as large. Therefore, at a given temperature the transition value of d-1/2 for En2 steel should be about 5 times larger than that for niobium. The measured transition &‘I2 for En2 steel at 77°K is about 17 cm-1’2, and the estimated transition d-i12 from the niobium experiments at the same temperature and strain-rate is 3.2 cm-*‘2; the ratio of the two values is in fair agreement with the theoretical predictions. Cottrell’s transition formula gives a good explanation of the present results, which suggests that the growth of the crack is the critical stage in the fracture process. The mechanism whereby glide dislocations
ADAMS,
ROBERTS
AND
SMALLMAN:
change to cavity dislocations to nucleate a crack is still in some doubt.(23) Other processes in which cracks grow out of slip or deformation twin bands cannot be ruled out, since a similar formula is to be expected for these also. The possible importance of twins in the nucleation of cracks has been stressed by Bell and CahncZ4),and by Biggs and Pratt (l@. The present experiments demonstrate, however, that twinning is not always essential to brittle fracture, since examples were obtained in the fast strain-rate tests at 77°K of cleaved specimens which contained no twins. The fact that so often in body-centred cubic transition metals the onset of twinning and cleavage occurs under similar conditions is probably explained by the close dependence of both phenomena on the strength of the dislocation locking. 5. CONCLUSIONS
(1) The general mechanical behaviour of niobium is similar to that of the other body-centred cubic transition metals in that the material undergoes a ductile-brittle transition and can be made to twin. (2) The ductile-brittle transition characteristics of niobium are adequately described by Cottrell’s transition equation. The purified niobium used in the present tests shows a greater resistance to brittleness than carburized u-iron because of the smaller value of its dislocation locking term k,. (3) The small value of the dislocation locking strength is the reason why purified niobium is reluctant to twin. (4) Twinning is not essential to cleavage in niobium. Twinning and cleavage are generally found under similar conditions of temperature and strain-rate in the body-centred cubic transition metals because both phenomena depend on the dislocation locking strength.
YIELD
AND
FRACTURE
IN
Nb
337
ACKNOWLEDGMENTS
The authors are indebted to Professor A. H. Cottrell P.R.S. for many useful discussions, and to Dr. D. Hull for assistance &h the experiments at 20’K. REFERENCES 1. W. P. REES, B. E. HOPKINS and H. R. TIPLER, J. Iron St. I?&& 69, 157 (1951). American 2. Behaviour of Metals at Low Te?qeTatures. Society for Metals, Cleveland (1953). 3. N. J. PETCH, J. Iron&% In&. 118,25 (1953). Union of Theoretical and 4. J. R. Low, in International
Applied Mechanics. Madrid Colloquium on Deformation and Flow of Solids, p. 60. Springer, Berlin (1956). 5. E. T. WESSEL and D. D. LAWTHERS, Westinghouse Res. Lab. Sci. Paper 6-94701-5-Pl, (1957). 6. E. 0. HALL, Proc. Phys. Sot., Land. 64B, 747 (1951). 7. 5. R. Low, Sywqosium on Relation of Properties to Microstructure, p. 163. American Society for Metals, Cleveland
8. 9.
10. :;: 13. 14. ::: 17. 18. 19.
Z: 22.
23.
24.
(1953). A. H. COTTFLELL,Trans. Amer. Inst. Min. (Metall.) Engrs. 212, 192 (1958). M. A. ADAMS. Rev. U.K. Atom. Energy __ Res. Estab. No. M/R2604 (1958). D. HULL and I. MOCFORD, Phil. Mag. 3, 1213 (1958). A. A. JOHNSON, Phil. Mag. 4, 194 (1959). J. G. DOCRERTY and F. W. TRORNE, Engng. Land. 152, 295 (1931). W. SYLVESTROWICZ and E. 0. HALL, Proc. Phys. Sot. Lond. 648, 495 (1951). H. W. PAXTON, J. Appl. Phys. 24, 104 (1953). J. HESLOP and N. J. PETCH, Phil. Msg. 1, 866 (1956). W. D. BIGGS and P.L. PRATT, Acta Met. 6, 694 (1958). A. H. COTTRELL and B. A. BILBY, Phil. Mag. 42, 573 (1951). B. A. BILBY and A. R. ENTWISLE, Acta Met. 2, 15 (1954). C. S. BARRETT and R. BAKISH, Trans. Amer. Inst. Min. (Metall.) Engrs. 212, 122 (1958). N. J. PETCH, Phil. Mag. 3, 1089 (1958). J. W. TAYLOR, J. Inst. Met. 86, 456, (1958). J. J. GILMAN and W. G. JOHNSTON, Dislocations and Mechanical Properties of Crystal8 (Ed. by J. C. FISHER, W. A. JOHNSTON, R. THOMSON and T. VREELAND, JR.) p. 116. Wiley, New York (1957). A. N. STROH, Crack Nucleation in Body-centred Cubic Metals, Paper given at Fracture Conference, April 12-14 (1959), Swampscott, Mass., U.S.A. R. L. BELL and R. W. CAHN, Proc. Roy. Sot. A239, 494 (1957).
AND M.
A.
FRACTURE ADAMS?,
IN POLYCRYSTALLINE
A.
NIOBIUM*
and R. E. SMALLMAN
C. ROBERTS1
Tensile tests on specimens prepared from an ingot of electron-bombardment melted niobium have shown that the material undergoes a ductile-brittle transition and can be made to twin. The variation of yield stress Upwith grain-size 2d has been used to determine the effect of temperature (293’K-20°K at a strain-rate of 2.02 x lo-* set-r) and strain-rate (2.02 x 1O-4 set-‘-6.18 x 10-e set-r at 77°K) on the values of oi and k, in a Petch type equation ov = oi + k,d-‘I”, the results indicating that the ductilebrittle transition characteristics are in accordance with Cottrell’s transition equation (uidllz + k,)k, = /lpy. Niobium shows a greater resistance to brittleness than carburized a-iron because it has a smaller k, value, and the reluctance of the material to twin except under extreme conditions of low temperature or high strain-rate is also attributed to a low value of k,. The mechanical behaviour of niobium relative to that of other body-centred cubic transition metals is discussed. DEFORMATION
ET
RUPTURE
DU
NIOBIUM
POLYCRISTALLIN
Les auteurs ont soumis a des essais de traction des Qchantillons de niobium prepares au four de fusion a bombardement d’electrons. 11 resulte de ces essais que ce metal possede une courbe de transition du type ductile-fragile et qu’il peut subir un maclage. La variation de la tension de deformation Us avec le grain-size 2d permet de determiner l’effet de la temperature (293”K-20°K pour une vitesse de deformation de 2.02 x lo-* set-r) et de la vitesse de deformation (2.02 x lo-* set-‘-6.18 x 1O-2 set-r a 77°K) sur lea valeurs de oi et k, dans l’equation de Petch o, = oi + k,d-1/2. Les resultats indiquent que les caracteristiques de la transition rupture fragile-rupture ductile sont en accord avec l’equation de Cottrell (o~&~ + k,)k, = @,uy. L e niobium montre une plus grande resistance a la fragilite que le fer c( carbure parce qu’il possede une valeur de k, plus faible. Exception faite de son comportement dans des conditions particulieres a basse temperature ou sous une vitesse de deformation &levee, la resistance de ce metal au maclage peut 6tre attribuee a la faible valeur de k,. Lea auteurs discutent enfin du comportement mecanique du niobium compare a celui des metaux de transition cristallisant Bgalement dans le systeme cubique cent&. FLIEBEN
UND
BRUCH
VON
VIELKRISTALLINEM
Niob
ZerreiDproben wurden aus Niob hergestellt, das duroh Elektronenbombardement erschmolzen worden war. Die Zugversuche zeigten, da13 bei diesem Material ein Ubergang duktil-sprode auftritt und da6 es sich verzwillingen 1iiDt. Die Abhangigkeit der Flieljgrenze IJ~ van der KorngrBDe 2d wurde beniitzt, urn den EinfluD der Temperatur (293°K - 20°K bei einer Dehnungsgeschwindigkeit van 2,02 x 1O-4 set-I) und der Dehnungsgeschwindigkeit (2,02 x 1O-4 sec- i - 6,18 x 1O-2 set-’ bei 77°K) auf die Parameter Us und k, in der Gleichung nach Petch a, = oi + k,d-‘ia zu bestimmen. Die Ergebnisse zeigen, da9 die GesetzmiiBigkeiten des Ubergangs duktil-sprode mit Cottrells Ubergangsgleichung ((aid1/e + k,)k, = b,u~iuy)iibereinstimmen. Niob zeigt einen grdljeren Widerstand gegen Sprodigkeit ala aufgekohltes a-Eisen wegen seines kleineren k,-Wertes. Die geringe Neigung des Materials zur Zwillingsbildung aul3er bei extremen Bedingungen tiefer Temperatur oder hoher Dehnungsgeschwindigkeit wird ebenfalls dem kleinen k,-Wert zugeschrieben. Das mechanische Verhalten van Niob wird mit dem anderer kubisch-raumzentrierter Ubergangsmetalle verglichen und diskutiert.
1. INTRODUCTION
Although and
brittle
received centred
years the plastic
fracture
behaviour
considerable
of
deformation
mild
cubic metals have been relatively
in behaviour
with
to the expected
a-iron,
and partly
of the high melting
point
vanadium,
tantalum,
niobium
industry.
However,
the
steel
other
attention(1-4)
This has been due partly usage
these
in recent
investigation
8, MAY
of niobium purified by electron-bombardment Tensile
to the small
refractory
tests
on
been described
metals
importance
1960
of their mechanical
similarity
commercially
and
properties.
pure
melting.
niobium
have
by Wessel and Lawthersc5).
For mild steel it has been shown, both theoretically
in
and
of
for yield propagation
experimentally,(3+-8)
according
VOL.
gas turbine
the need for a more
Work is described in this paper on the tensile behaviour
May 12, 1959. t Materials Research Corporation, Yonkers, New York, formerly Metallurgy Division, Atomic Energy U.S.A.; Research Establishment, Harwell. $ Metallurgy Division, Atomic Energy Research Establishment, Harwell. 5 Department of Physical Metallurgy, University of Birmingham; formerly Metallurgy Division, Atomic Energy Research Establishment, Harwell. METALLURGICA,
in the
detailed
* Received
ACTA
particularly
energy fields, indicates
neglected.
and molybdenum
increased
has
body-
metals,
nuclear
that
the
shear
stress
q,
varies with the grain diameter 2d
to the equation:
c21= oi + cc 11’2d-i’2 or
(1) a, = ai + k, d-ii2
where, following stress to unpin 328
(Ic, = aD ln2) i
Cottrell’s notation,(8) aI) is the shear a dislocation from its atmosphere,
ADAMS,
ROBERTS TAELE
Impurity elements per cent present ~________
/
SMALLMAN:
AND
Si
1 0.150
/
Fe
/
0,
j
H,
j
/
0.300
/
0.01
/
0.02
!
PROCEDURE
Specimens were made from an ingot of commerciahy pure niobium which had been melted by electron bombardment. This treatment reduces markedly the gaseous impurities oxygen and nitrogen without radically affecting the metallic impurities. A typical analysis after melting is shown in Table 1. Texture free wire of 1.25 mm diameter was prepared from the ingot by alternate cold swaging (50 per cent reduction in area) and annealing (1075’C for 1 hr in tantalum foil) treatments. After a final swage to 1 mm diameter, batches of 7.5-cm long wires were annealed (in tantalum foil) at temperatures from 1075°C to 1415°C to give the range of grain sizes shown in Table 2. 1075’C was established as the m~imum recrystallization temperature, giving grains of about 0.005 cm diameter, whilst the 1415°C anneal resulted in wires with some grains across the complete section. For these wires the grain diameter was taken as the major axis of a plane at 45” to the wire axis, this corresponding to the plane of maximum shear stress. All anneals were made in a dynamic vacuum of between IO-5 and lop6 mm Hg. Wires were mounted for straining by soldering their ends with Wood’s metal into close-fitting brass bosses fitted with loops to engage hooks in the tensile TABLE
2. Grain-sizes of the specimens
Heat treatment
-.-
d-‘/2 cm-112
Grain size Xd(cm) ---
--
1 1 1 3
hr Izt 1075°C hr at 119O’C hv at 1260°C hr at 1415°C
A1”V’D FRACTURE
1. Typioal anrtlysis for niobium melted by &&on
oi the shear stress resisting the movement of dislocations across the slip plane after they have been unpinned, and I the distance from piled-up dislocations at the head of the plastic front to the nearest FrankRead sources. In the present experiments the effect on 0; and & of varying temperature (293’K-20°K at a strain-rate of 2.02 x lOA se&) and strain-rate (2.02 x lo-4 sea-i-6.18 x 1OV see-r at 77°K) has been determined from measurements of yield stress on niobium specimens covering a range of grain sizes, and conditions for the occurrence of (a) twinning and (b) a ductile-brittle transition have been established. 2. EXPERIMENTAL
YIELD
0.00476 0.00951 0.0312 0.1414
’ 20.5
14.5 3.2 3.76
IN
bombardment
-&a 0.05
329
Nb
-_--
/
Ta
j
C
/
0.30
1
0.07
j others 1
0.03 .---.~_
machine. Each end of the wire was shotblasted and then electro-plated with a 0.025 mm copper layer to allow tinning. The Wood’s metal was held in a constant temperature water bath, so that the specimens never exceeded a temperature of 80°C. Tensile tests were made in the au~~aphi~ally tensile machine described by recording “hard” Adams(g). The gauge length of the specimens was 2.8 cm and for most of the tests the machine was driven at a constant cross-head speed of 0.00057 cm set-l (strain rate 2.02 X lo4 se&) ; in a series of fast strain-rate tests this speed was increased to 0.173 cm set-i (strain rate 6.18 x 10e2 set-I). 3. RESULTS
3.1 Slow strailt-rate tests at 293”K, 195*K, and 77°K Figure 1 shows ehara~~ristie stress-strain curves for specimens of the finest grain-size tested at 293*K, 195°K and 77’K, with a strain rate of 2.02 x 10” see-l. At the two highest temperatures the curves are typical of a strain-ageing material, and lowering the temperature from 293°K to 195°K changes the shape of the curve only slightly by increasing the size of the yield point and decreasing the amount of uniform elongation. A further lowering of the testing temperature to 77’K, however, causes a marked change in behaviour; the upper yield stress is not very sharp and after a very small uniform elongation, necking occurs, the load then dropping steadily until fracture. At this temperature the high stress required to move the first dislocations must be suflicient to overcome any internal stresses created in the lattice during deformation, All fractures were of the fibrous type and the ductility of the material, measured from the percentage reduction in area at the fracture, was decreased slightly with decreasing temperature from about 99 per cent at 293°K to about 80 per cent at 77°K. Typical curves for the coarest grained samples are shown in Fig. 2. The only marked difference from the fine-grained material is the reduced uniform elongation at 2Q3’K and 195°K. Necking in the coarse-grained specimens occurred across single grains at all three temperatures, resulting in knife-edge fractures. In Fig. 3 the lower yield tensile stress values of a series of niobium specimens are shown as a function of d-i/s at the three testing temperatures. For the
ACTA
METALLURGICA,
VOL.
8,
1960
I
5
IO
% FIG.
20
15
25
30
35
ELONGATION
1. Effect of temperature on the stress-strain curve of specimens of the finest grain-size (2d = 0.00476 cm)
extended at a rate of 2.0% x lo-* see-‘.
195°K tests, specimens of four different grain-sizes were used whilst at the other two temperatures only the finest and coarsest grained samples were tested. Since in the tests at 77°K no clearly defined lower yield elongation was evident, it was necessary to estimate the position of the lower yield point. This was taken as the &rat inflexion in the stress-strain curve after the initial drop in load. Each point on the graph is the average for several tests at that temperature and grain size ; the maximum scatter on individu&l
tests amounted to about -&5 per cent of the mean value. From the curves of Fig. 3, a, and k;, for the three temperatures have been estimated (see Table 3). Here, shear stresses rather than tensile stresses (to a first approximation the shear stress is half the tensile stress) are used in accordance with equation (1). The oi values carry a possible error of about the same amount as the lower yield stresses, whilst the errors in &, may be larger, possibly &50 per cent.
ADAMS,
ROBERTS
AND
SMALLMAN:
YIELD
AND
Oo
FRACTURE
5I
IN
Nb
10 I
331
15 1
20 1
CM.-;
4 -f
FIG. 3. Variation of yield stress with grain-size for specimens extended at a rate of 2.02 x 1O-4 set-l at 293”K, 195’K and 77°K.
showed
completely
temperature behaviour centred could
293OK
7
at
to
(2.02 x lo4
a
This
metal of body-
see if
set-l)
brittleness a series of
tests was made
The results are summarized
by the represen-
curves of Fig. 4. Specimens
coarsest
failed
grain-size
macroscopic
plastic
intermediate
grain-sizes
by total
elongation.
cleavage Those
also cleaved,
plastically
of the
with no
of the
two
but only after
for a few per cent, and The finest grained
considerably.
material deformed plastically with rapid workhardening, necked and finally failed by a mixed shear less
slowly with decreasing temperature ; cri increases more rapidly with decreasing temperature, particularly between 195°K and 77”K, and is somewhat larger (about 25-50 per cent) than that for En2 steeloO) at all three temperatures.
and cleavage fracture at the neck. The stress-strain curves of all the specimens which extended
plastically
particularly
___.-
3.1 all specimens
showed
very
distinct
in the early stages of plastic flow.
jerks, Each
TABLE 3. Values of oi and k, at three temperatures. Strain rate = 2.02 X 10e4 see-’ _._ ~__
Temperature IJ~(lb/in*)
3.2 Xlow strain-rate tests at 20°K of Section
and
tative stress-strain
work-hardened
than that for En2 steel at 195”K,(10) and increases
In the experiments
even
at lower temperatures
they had elongated
ELONGATION
about an order of magnitude
in a transition
structure,
strain-rate
range.
FIG. 2. Effect of temperature on the stress-strain curve of specimens of the coarsest grain-size (2d = 0.1414 cm) extended at a rate of 2.02 x 1O-4 set-I. k, is very small,
fractures,
at 20°K on specimens covering the complete grain-size
O/o
is unusual cubic
be induced
slow
ductile
as low as that of liquid nitrogen.
k,
(c.g.s.)
1
195°K
293°K
I ~~48,000
;-~
18,000
10,000
) 5.18 x lo6
) 3.8 x IO0
1
77°K
A__
2.76 x lo6
332
ACTA
METALLURGICA,
VOL.
8,
1960
FIG. 4. Effect of grain-size on the stress-strain curves of specimens extended at a rate of 2.02 x 1OF set-l at 20°K; (a) grain-size 2d = 0.1414 cm, (b) grain-size 2d = 0.0312 cm, (c) grain-size 2d = 0.00951cm, (d) grain-size 2d = 0.00476 cm.
jerk was accompanied by an audible click, suggestive of deformation twinning. A metallographic examination confirmed that twins are formed. The specimen
have removed a low temperature martensite phase. The coarse-grained cleaved specimens also showed twin bands after polishing and etching (Fig. 6), but
surfaces showed slip lines and other markings resembling the Neumann bands observed in iron. These markings were removed by polishing but re-appeared
it is open to contention whether these twins were formed immediately prior to fracture (one of the stress-strain curves did show a twinning burst before the specimen broke) or were nucleated by shock
after etching (Fig. 5) and they persisted after an anneal of 1 hr at 85O”C, a heat treatment that would
waves
accompanying
the fracture.
Double
surface
.4DBMS,
ROBERTS
SMALLAMAN
AND
: YIELD
AND
FRACTURE
IN
Nb
333
from these tests, and the reliability ment is somewhat
uncertain.
of a oZ measure-
However,
the stress-
strain curves indicate some slip interspersed
with the
initial twins, which suggests that a value cz = 58,000 lb/in2 is reasonable.
Cleavage stress values, except for
the coarsest grained specimens,
all of which failed at
around
were very
116,000 lb/in2
tensile,
scattered.
They varied from 150,000 to 200,000 lb/in2 tensile in specimens
of 0.0095 cm grain size, and from 150,000
to 180,000 lb/in2 tensile for those of 0.031 cm grainsize.
Fracture stresses for the finest grained material,
subject to considerable of estimating
errors because of the difficulty
the area of the neck, ranged from about
250,000 to 280,000 lb/in2 tensile. A portion of a fractured specimen grain-size
FIG. 5. Deformation twins in a specimen of the second finest grain-size (2~2= 0.00951 cm) extended to fracture at 20°K. Polished and etched (95 per cent HNO,, 5 per cent HF) after tensile-testing. x 340 analysis
of several
sets of prominent
grains, using X-ray the
twinning
observations
as
(112)
with
deformed
examination
Analysis
at
was made
and etching.
of the three finer grain sizes the
curves indicate that the first macroscopic
deformation
occurred
116,000 lb/in2 in all cases. it is impossible
by twinning,
was within
to obtain
and the
a few per cent of
Because twinning interferes a direct
kY measurement
property
by increasing the strain-rate
the transition
plastic
the
back-reflection
cleavage
surface
of the two films gave the cleavage
mechanical
surface or after polishing
tensile stress at yield
to
changes
from lowering the testing temperature
of all the specimens tested at the higher temperatures. In no case was a twin band observed, either on the For the specimens
normal
3.3 Fast strain-rate tests at 77°K
Consequently,
stress-strain
the
of the coarsest
in a Laue
plane as (100).
Many
cubic metals.
twins in the specimens
a careful metallographic
beam.
Laue data, gave agreement
with
mounted
aligned at first parallel and then at 30” to the X-ray
bands on large
in
on other body-centred
After finding 20’K
back-reflection
plane
camera
was
which
arise
can be simulated
at constant temperature.
tests were made at 77’K
to see if an
increased strain-rate at this temperature to brittleness
would induce
observed
in the experi-
tests the strain-rate
was increased
ments of Section 3.2. In preliminary
by a factor of about 20. of all specimens
This raised the yield stress
by about
did not appreciably
10 per cent but otherwise
alter the form of the stress-strain
curve, or change the mode of deformation
or fracture.
Increasing the strain-rate 6.18 x 1O-2 set-l) resulted
a further 15 times (to in stress-strain curves of
the form shown in Fig. 7.
At this very fast rate of
testing without the
specimens
of the coarsest
macroscopic
three
finer
plastic
grain-sizes
grain-size
deformation deformed
cleaved
; those of
plastically
constant stress for a few per cent elongation finally failed by a shear fracture after necking. No curves,
jerks
were seen in any
of the
stress-strain
but all test pieces were polished
and carefully gauge-length.
examined
at and
and etched,
for twins over the complete
Some of the specimens
of each grain-
size showed small twins on two or three of their grains. whilst in other samples no twinning was observed at all. By comparison all specimens deformed at 20°K showed FIG. 6. Deformation twins in a specimen of the coarsest grain-size (2d = 0.1414 cm) extended to fracture at 20°K. Polished and etched (95 per cent HNO,. 5 per cent HF) after tensile te&ing. x 140 4k-(4ppJ
well marked
twins on at least half of their
grains. Cleavage and yield stress figures obtained from the fast strain-rate tests are plotted as a function of d-1/2
ACTA
METALLURGICA,
VOL.
8, 1960
FIG. 8. Variation of yield (or cleavage) stress with grain-size for specimens extended at 77°K at rates of 2.02 x 1O-4 see-l and 6.18 x 1O-2 set-I.
account
for the detailed differences
between niobium
and other metals of like structure properties
have been investigated.
Deformation A notable above,
whose mechanical
by slip feature of the experiments
in which plastic
or predominantly
deformation
at 77°K and
occurred
solely
by slip, is that the yield propagation
stress increases
only slightly
size ; rE, for niobium
with decreasing
grain-
is almost an order of magnitude
smaller than that for En2 steel(rO) at 77”K, and over 20 times 293°K.
smaller
than
that
for molybdenum(ll)
On the basis of equation
in niobium purified by electron-bombardment the atmosphere
at
(1) this means that
locking of dislocations
melting
is rather slight.
This result may seem surprising since the stress-strain curves at 293’K FIG. 7. Effect of grain-size on the stress-strain curve of specimens extended at a rate of 6.18 x IO-* set-1 at 77°K; (a) grain-size 2d = 0.1414 cm, (b) grain-size
2~1= 0.06476 cm. Specimens of the two intermediate grain-sizes give curves of the same form as (b).
in Fig. 8 which also shows, for comparison, strain-rate specimens lying
results.
values
are used, the scatter
within
graph
Average
gives
the limits a
quoted
value
of
the slow
from
several
on individual in Section
tests
3.1.
The
oi = 56,500 lb/ins
and
,$, = 7.25 x lo6 c.g.s. at the fast strain-rate. 4. DISCUSSION The present experiments
have shown that niobium
follows the same general pattern of mechanical behaviour as other body-centred cubic transition metals.
Thus, one can obtain by a suitable choice of
temperature or strain-rate a change from complete ductility to complete brittleness, and from slip to twinning as a possible mode of deformation. It remains now to examine those factors which may
and
lower
and 195°K show a well-marked
yield
point.
It
must
be
upper
remembered,
however, that the size of the yield drop is an unreliable quantitative locking
measure
of the amount
because the experimental
yield stress depends sensitively
of dislocation
value of the upper
on specimen preparat-
ion and on tensile machine characteristics.(is-i4)
One
way in which the form of the curves does indicate small k, value is from the amount elongation. portion
If for the tests at 293°K
of the curve immediately
elongation
is extrapolated
value obtained equation
and 195°K the
following
the yield
to zero strain, the stress
is a rough measure of ci.
(l), the difference
a
of the lower yield
Then, from
in stress AC between the
lower yield stress and the extrapolated value is equal to Ie,d-1/2. With small lower yield elongations and low rates of work hardening immediately
afterwards,
as observed in the present tests, the values of Aa and consequently of lcQ,are small. The yield strength of niobium deformed by slip can be attributed
chiefly
to the friction
stress
e’i
ADAMS,
ROBERTS
resisting the movement
of dislocations
unpinned from their atmospheres, of the yield strength arises
primarily
resistance
from
by (a) randomly
that have been
and the dependence
on temperature variations
to dislocation
of
oi.
impurity
atoms
(b) precipitated
locations
in the lattice, (d) the Peierls-Nabarro
It is not immediately
impurities,
in solid
solution,
obvious
force.
of ai to tempera-
but the work
Petch(15) on steel suggests
dis-
which of these is most
likely to give the required sensitivity ture and strain-rate,
(c) other
of Heslop
Twinning only
under
and
that the Peierls-Nabarro
or high strain-rate.
niobium
can be found
Biggs and PrattV)
have recently
Entwisle’ls)
and
to explain
of iron crystals.
developed
Bilby(17)
and
from the Bilby
and
their results on the twinning
The theory shows that twin nucleation
Pratt suggest that nucleation stress concentration array of dislocations
and Biggs and
at the head of a rapidly piled-up by a burst of slip as a
as
carburized
dislocations niobium slight context small
(large
a-iron
strongly
than
in one
Ic, value)
in which the dislocation
(small to
value
of le,).
in a material
with
such
as
locking is relatively
It is of interest
note
that tantalum Ic, value(*) and exhibits,
reluctance to twin.(lg) All the specimens which
locked
apparently has like niobium, plastically
20°K showed the same pattern of behaviour;
the
a a
at
(a) small
amounts of slip interspersed between extensive bursts of twinning in the early stages of deformation,
in
twins the
is as
rapid
ductile
samples
En2
carburized
a-iron.
became
and only
completely
tested
at
the
the
finest
brittle
why,
grained at
were
the coarsest
brittle at 20°K ; same
strain-rate, greater than
niobium
77”K.(1°)
are
To
of the two materials,
show the greater resistance
to
In the
tests all the specimens
at 77”K,
steel
transition
of a grain size only slightly
of
reasons
ductile-brittle
it is again instructive
with
present slow strain-rate
find
almost possible
niobium
to brittleness brittle
should
in tensile
fracture
theory
of Cottrell@).* Developing fracture
the idea that the difficult
process
is crack
crack nucleation, slip planes. gliding
propagation
Cottrell proposes
stage in the rather
than
a mechanism
for
on intersecting
It is shown that two (111) dislocations
in { 1 lo} pl anes can react with a lowering
energy to form a pure edge dislocation
of
in the (100)
cleavage plane. *a[1111 + +a[1111 -+ a[OOl]. The new dislocation, “cleavage
wedge”
equivalent
geometrically
of material between adjacent
faces, is thought to be the crack nucleus.
to a (100)
The nucleus
dislocations
run into it
until it reaches a size of the same order of length as the slip bands becomes the
deformed
results
will grow easily as successive
in this
of
at 20°K.
of niobium
comparisons
With other things equal it should be easier to produce such
will then no
action
dislocations observed
considering
source is released from its atmosphere.
a slip burst suitable for twin nucleation
the
forming crack nuclei from dislocations
is brought about by the
produced
335
of slip dislocations
tests we turn to the recent
in the ideas that
is more difficult than twin propagation,
Frank-Read
for
A general explanation
for this behaviour Cottrell
When
completely
can be
compared
slip
characteristics
that
low temperature
Thus, although
Nb
Cleavage
grained
in the present experiments
of extreme
example with carburized u-iron.
of
to
specimens
made to twin it does so with reluctance,
theories
barriers
completely
by twinning conditions
IN
Presumably
work-hardening
with
was observed
FRACTURE
and the generation
make
force probably makes the most significant contribution. Deformation
AND
suppressed.
Frictional be caused
could
YIELD
longer occur in sharp bursts so that twin nucleation
and strain-rate
movement
dispersed
SMALLMAN:
AND
directly
crack
forming
it.
The applied
responsible
size is greater
fracture
will result;
ductile.
A calculation
for crack growth than
otherwise
that the ductile-brittle
stress then
the
Griffith
the material
and if value will be
of the critical crack size shows transition
will occur
when
modulus,
y the
the relationship
(b) a preponderence of slip with only occasional twinning as deformation was continued, (c) an ability (in contrast at 77°K)
to t,he behaviour
to work-harden
of specimens
whilst
deforming
tested by slip.
These observations are again in accord with the model of twinning discussed above. Twins, once formed, may themselves act as dislocation pile-up and
barriers, further
allowing further twin nucleation.
After
most
the
a time,
however,
of
Frank-Read
sources will have been released from their atmospheres,
is satisfied,
where
,U is the
shear
effective surface energy for the propagation of cracks and ,!I a constant equal to 1 for uniaxial tension (ordinary tensile test) and + for triaxial tension (tests * See also Petch’s’20) recent theory of the ductile-brittle transition in impact tests on notched specimens. This theory can be extended to tensile tests, and gives R transition equation of the same form as that developed by Cot,trcll witah t,hr constants slightly altered
336
ACTA
VOL.
8,
1960
TABLE 4. Critical velues of (ui c/i/z + &)ky on either side of the ductile-brittle transition point -__~..-_____.~~-.. __.
-__~ Temp. of testing
/ /
("W
I
-~--
METALLURGICA,
77 20 77 77 20
Strain r&e
(see-l)
i
1
(lb$ie)
___6.18 x 1O-2 2.02 x 10-4 2.02 x IO-4
~
56,500 58,000
’
48,000
1 1
--1
k
(0.g.s. “x 10’) 7.25 5.87* 5.18
Grain size 2d (cm)
- -___--__
0.1414 0.1414 0.1414 0.0312 0.0312
. .__.~__ * Estimated by extrapolating the k, values measured at the higher temperatures. on notched specimens). oi, Xc, and d retain the same significance as in equation (1). Cottrell also points out that equation (2), although obtained originally from a detailed analysis of the above process, should be valid quite generally for the growth of cracks created by the conversion of glide dislocations into cavity dislocations. Under conditions where the value of the left hand side of equation (2) is less than the value of the right hand side, ductile behaviour should be observed; when the left hand side exceeds the right hand side the behaviour should be brittle. In a given material brittleness should be favoured by low temperature and high strain-rate (large values of criand kJ and by large grain size, which is in qualitative agreement with the present results. To test the theory quantitatively we note that in our experiments the transition from ductile to completely brittle behaviour has been approached in four different ways: (i) by changing the strain-rate from 2.02 x low4 see-r to 6.18 x 1O-2 se& in tests at 77’K on specimens with a grain diameter 2d = 0.1414 cm; (ii) by changing the grain diameter from 2d = 0.0312 cm to 2d = 0.1414 cm in the fast strain-rate tests at 77’K; (iii) by changing the testing temperature from 77’K to 20°K in the slow strain-rate tests on specimens with a grain diameter of 2d = 0.1414 cm ; (iv) by changing the grain diameter from 2d = 0.0312 cm to 2d = 0.1414 cm in the tests at 20°K. p * ,u * y may be reasonably assumed to remain insensitive to the various experimental changes so that if the theory is correct the value of (ci S’s + kv)ks in every case where the behaviour is brittle should exceed any value of (oi d1J2 + k,)k, for an experiment in which ductility is observed. The values listed in Table 4 show that the results are in fact in accord with the theory. The closest limits we have from the experiments show that a transition from ductile to completely brittle behaviour occurs when (oi dxj2 + kJk, changes from 4.59 x lo16 c.g.s. to 6.28 x 1015c.g.s. Thus with @ = 1 and ,LL= 4 x loll dyne cm-s we find that the effective surface energy y is given by 1.57 x lo4 ergs cin2 > y > 1.15 x 104 ergs cm-.2; or y = 1.36 x IO4
! Behaviour
(qW
___ + k,)k
(0.g.s. x 1015;
/---
___
brittle brittle ductile ductile ductile
l--l__---7.57 6.28 4.59 3.47 2.88
ergs cm-2 5 15 per cent. This value is close to the experimentally determined value of y for En2 steel,‘lc) and about 5 times larger than the true surface energy of niobium, 2.7 x lo3 ergs cm-2, estimated from the data of Taylor(21’. An effective surface energy greater than the true one appears to be a general feature of brittle fracture results, and is thought to be mainly due to the irreversible work of tearing at river lines and grain boundaries.(s2) Whilst showing some ductility, the specimens of the three finer grain sizes tested at 20’K did finally fail by cleavage (or by a mixed shear and cleavage fracture in the finest grain-size case). For such specimens, in which oi is raised by work-hardening during the test, the theory predicts a linear increase in fracture stress or with d-1’2 along a line which extrapolates to of = 0 at d-rJ2 = 0. From the few rather scattered results obtained in the present experiments it appears that specimens of the second coarsest grain-size give approximately the correct fracture stress values, whilst those of the two finer grain sizes have fracture stresses that are too low: further results covering the grain-size range more fully would, however, be required to test this part of the theory properly. The increased tendency towards brittleness in En2 steel compared with niobium is to be expected from equation (2). At comparable temperatures and strain-rates oi and y are similar for the two materials ; but kg for En2 steel is about 10 times as large as that of niobium and y is about twice as large. Therefore, at a given temperature the transition value of d-1/2 for En2 steel should be about 5 times larger than that for niobium. The measured transition &‘I2 for En2 steel at 77°K is about 17 cm-1’2, and the estimated transition d-i12 from the niobium experiments at the same temperature and strain-rate is 3.2 cm-*‘2; the ratio of the two values is in fair agreement with the theoretical predictions. Cottrell’s transition formula gives a good explanation of the present results, which suggests that the growth of the crack is the critical stage in the fracture process. The mechanism whereby glide dislocations
ADAMS,
ROBERTS
AND
SMALLMAN:
change to cavity dislocations to nucleate a crack is still in some doubt.(23) Other processes in which cracks grow out of slip or deformation twin bands cannot be ruled out, since a similar formula is to be expected for these also. The possible importance of twins in the nucleation of cracks has been stressed by Bell and CahncZ4),and by Biggs and Pratt (l@. The present experiments demonstrate, however, that twinning is not always essential to brittle fracture, since examples were obtained in the fast strain-rate tests at 77°K of cleaved specimens which contained no twins. The fact that so often in body-centred cubic transition metals the onset of twinning and cleavage occurs under similar conditions is probably explained by the close dependence of both phenomena on the strength of the dislocation locking. 5. CONCLUSIONS
(1) The general mechanical behaviour of niobium is similar to that of the other body-centred cubic transition metals in that the material undergoes a ductile-brittle transition and can be made to twin. (2) The ductile-brittle transition characteristics of niobium are adequately described by Cottrell’s transition equation. The purified niobium used in the present tests shows a greater resistance to brittleness than carburized u-iron because of the smaller value of its dislocation locking term k,. (3) The small value of the dislocation locking strength is the reason why purified niobium is reluctant to twin. (4) Twinning is not essential to cleavage in niobium. Twinning and cleavage are generally found under similar conditions of temperature and strain-rate in the body-centred cubic transition metals because both phenomena depend on the dislocation locking strength.
YIELD
AND
FRACTURE
IN
Nb
337
ACKNOWLEDGMENTS
The authors are indebted to Professor A. H. Cottrell P.R.S. for many useful discussions, and to Dr. D. Hull for assistance &h the experiments at 20’K. REFERENCES 1. W. P. REES, B. E. HOPKINS and H. R. TIPLER, J. Iron St. I?&& 69, 157 (1951). American 2. Behaviour of Metals at Low Te?qeTatures. Society for Metals, Cleveland (1953). 3. N. J. PETCH, J. Iron&% In&. 118,25 (1953). Union of Theoretical and 4. J. R. Low, in International
Applied Mechanics. Madrid Colloquium on Deformation and Flow of Solids, p. 60. Springer, Berlin (1956). 5. E. T. WESSEL and D. D. LAWTHERS, Westinghouse Res. Lab. Sci. Paper 6-94701-5-Pl, (1957). 6. E. 0. HALL, Proc. Phys. Sot., Land. 64B, 747 (1951). 7. 5. R. Low, Sywqosium on Relation of Properties to Microstructure, p. 163. American Society for Metals, Cleveland
8. 9.
10. :;: 13. 14. ::: 17. 18. 19.
Z: 22.
23.
24.
(1953). A. H. COTTFLELL,Trans. Amer. Inst. Min. (Metall.) Engrs. 212, 192 (1958). M. A. ADAMS. Rev. U.K. Atom. Energy __ Res. Estab. No. M/R2604 (1958). D. HULL and I. MOCFORD, Phil. Mag. 3, 1213 (1958). A. A. JOHNSON, Phil. Mag. 4, 194 (1959). J. G. DOCRERTY and F. W. TRORNE, Engng. Land. 152, 295 (1931). W. SYLVESTROWICZ and E. 0. HALL, Proc. Phys. Sot. Lond. 648, 495 (1951). H. W. PAXTON, J. Appl. Phys. 24, 104 (1953). J. HESLOP and N. J. PETCH, Phil. Msg. 1, 866 (1956). W. D. BIGGS and P.L. PRATT, Acta Met. 6, 694 (1958). A. H. COTTRELL and B. A. BILBY, Phil. Mag. 42, 573 (1951). B. A. BILBY and A. R. ENTWISLE, Acta Met. 2, 15 (1954). C. S. BARRETT and R. BAKISH, Trans. Amer. Inst. Min. (Metall.) Engrs. 212, 122 (1958). N. J. PETCH, Phil. Mag. 3, 1089 (1958). J. W. TAYLOR, J. Inst. Met. 86, 456, (1958). J. J. GILMAN and W. G. JOHNSTON, Dislocations and Mechanical Properties of Crystal8 (Ed. by J. C. FISHER, W. A. JOHNSTON, R. THOMSON and T. VREELAND, JR.) p. 116. Wiley, New York (1957). A. N. STROH, Crack Nucleation in Body-centred Cubic Metals, Paper given at Fracture Conference, April 12-14 (1959), Swampscott, Mass., U.S.A. R. L. BELL and R. W. CAHN, Proc. Roy. Sot. A239, 494 (1957).