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The stability of grain boundary cavities in copper
THE
STABILITY
OF GRAIN
BOUNDARY A.
CAVITIES
IN
COPPER*
GITTINST
Direct evidence was obtained that gas diffuses into cavities formed in copper either by high temperature fatigue or creep. The gas pressure inside the cavity builds up and reduces the tendency for the cavity to collapse during isothermal annealing. Sintering was observed when the cavitated specimens were annealed in a hydrostatic pressure of 2000 lb/’m’ and this sintering was reversed by subsequent annealing in a vacuum.
LA STABILITE
DES CAVITES
AUX
JOINTS
DE GRAINS
DANS
LE CUIVRE
L’auteur a mis en bvidence le fait clue du paz diffuse dans les cavit& formbes dans le cuivre soit Dar fatigue soit par fluage Q haute temp&ture. B l’int&ieur de la cavitb la pression du gaz augmente et Eeci rend plus difficile la r&sorption de la cavitb au tours d’un recuit isotherme. Une certaine tendance 1 l’agglom&ation de celles-c‘i a BtB observbe quand les Bchantillons presentant des cavit& ont 6t& recuits sous une pression hydrostatique de 2000 lb/in %.Ce phbnombne s’est inverse par un recuit ult&ieur sous vide.
DIE
STABILITiiT
VON
KORNGRENZENHOHLRAUMEN
IN KUPFER
Es wurde direkt beobachtet, dass in Kupfer Gas in die durch Hochtemperaturermiidung oder Kriechen entstandenen Hohlriiume hineindiffundiert. Der Graadruck innerhalb des Hohlraumes nimmt zu und reduziert die Zerfallstendenz ‘bei isothermem Anlessen. Beim Anlassen der Hohlriiume enthaltenden Proben bei einem hydrostatischen Druck von 2000 lb/’m* wurde Sintern beobachtet. Bei anschliessendem Anlassen im Vakuum wurde das Sintern riickgiingig gemecht.
INTRODUCTION
During creep, cavities form on the grain boundaries of many
metals
and may
causing
intergranular
cavities
has been attributed
vacancies
eventually
failure.
link together
The growth
grain boundary. (l) Growth will only take place when
Other observations work
the
and the
would be expected
to
to the grain boundary. of grain boundaries to
was obtained
made on powder compacts’3) this
by Balluffi
and
on sintering have been of
grain
16, APRIL
1968
and the spectro-
are shown
a gauge
length from
in Table
25 mm
long
the extruded
having the same dimensions length
1. and
bars. as the
were also prepared ; speci-
being machined
After polishing
alternately
specimens
along
and controls
a grain size of 0.13 mm. Small into
grain
the copper
and 150 c/s.
boundary
cavities
were
introduced
by fatigue
at 4OO”C, 0 & 2.6 t.s.i.
Two specimens
from the first batch of
copper were given 5.4 x lo” cycles (specimen
from
1) and
2) which is approximately
the second
life respectively.
Two
cast were also fatigued
at 400°C under the same conditions
as specimen
2.
The control specimens were mounted alongside the fatigue specimen so that they experienced the same
pressure.
atmosphere
* Received August 16, 1967. -t Materials Division, Central Electricity Research Laboratories, Cleeve Road, Leatherhead, Surrey. VOL.
RESULTS
were annealed at 600°C for 20 hr in a vacuum to give
load.
ACTA METALLURGICA,
gauge
specimens
boundary
in vacua and under a hydrostatic
copper,
10% and 30% of the expected
and twisted wires.t4)
stability
purity
1.6 x lo6 cycles (specimen
cavities in copper, formed by either high temperature creep or high temperature fatigue, was investigated by annealing
with
a given bar.
stress is removed
collapse by losing vacancies Evidence of the importance
In
gas analyses
mens and controls
metal annealed then the cavity
Seigle.t2)
graphic
specimen
where y is the surface free energy and r the radius of
process
high
and
AND
has
were carried out on two batches of
vacuum-cast
Control specimens
27 O>r
If the applied
METHODS
6 mm dia. were machined
The condition
for cavity growth is
the sintering
elsewhere.c5)
Specimens
the applied stress o is greater than the surface tension
the cavity.
been published
The experiments
of
at the cavity surface from the neighbouring
forces which tend to collapse the cavity.
note on some of the observations
EXPERIMENTAL
of these
to the condensation
A preliminary
517
and temperature
but without
the fatigue
The specimen and control were water quenched
from 400°C to prevent during a slow cool.
sint’ering
that
may
occur
518
ACTA
METALLURGICA,
TAB-
VOL.
16,
1. Chemical analysis of vacuum copper W.%)
Antimony hXliC
Bismuth Cobalt Iron Lead Phosphorus Silicon Manganeee Nickel Silver Tin Tellurium Zinc
n.d. n.d. n.d.
1968 cast
I :s~~~;) (‘$000;) 0:0003 0.0001 n.d. n.d. n.d. 0.0006 0.001 0.0005
n.d. n.d.
I;::Zt;
n.d. = not detected. Gee anelyeia of vacuum cast copper Total other than oxygen cm’!100 g
Specimen Number
% Oxygen (a)
I&G cm*/100 g
CO1 (type) cmS/lOO g(b)
H, cmS/lOO g
1
<0.02 <0.02
0.08 0.13
0.05 0.05
<0.02 <0.02
0.13 0.18
<0.02 0.02
0.09 0.08
0.05 0.06
<0.02 <0.02
0.14 0.16
3 4 All (a) (b) (c)
0.0006 0.0002
Xl (type) cma/lOO gtcl
figurea are average of 2 analyses. determined by HI reduction at 1150°C. includes SO* and NHs if present. includes inert gases if present.
Density measurements were used to estimate the total cavity volume introduced by fatigue. The fractional change in density, AD/D, between the specimen and control was determined psing the technique described by Day.@) Table 2 shows the values of AD/D for the four specimens after fatigue. When specimens 1 and 2 from the first batch of copper were annealed at 400°C in a vacuum it was found that AD/D decreased (i.e. the cavities shrank) for the first 30-60 min of annealing and then remained constant even after a prolonged anneal of 170 hr (Table 2). However when specimen 3 (from the second batch of copper) was annealed at 400°C for TABLE
Specimen Number
No. of cycles
1
5.4 x 10”
2
1.62 x 10‘
1.62 x 1Oa
1.62 x 10’
170 hr no change in AD/D was detected. The effect of annealing at 1000°C on the stability of the cavities in the two batches of copper was investigated. Table 2 shows that further sintering occurred in the first batch of copper while the cavities in the second batch of material expanded, the value of AD/D increasing from -2.85 x 10V3to -4.00 x 10Y3. Figure 1 shows the appearance of cavities in specimen 2 after fatigue, considerable cavity linkage having occurred. After a 170 hr anneal t.he cavities have become more spheroidal (Fig. 2), though still showing some elongation in the plane of the boundary. This lenticular shape of the cavities is dictated by the
2. Density changes after fatigue and annealing Treatment after fatigue at 4OO”C, 0 & 2.6 t.s.i. None Annealed Annealed None Annealed Annealed
170 hr 400°C 3 hr 400°C at 600 lb in ’ 170 hr 400°C 170 hr 400°C + 4 hr 1000°C
None Anneal 170 hr 400°C Anne81 170 hr 400°C + 3 hr 400°C at 2000 lb in-* Sone Annealed 4 hr 1000”c Annealed 4 hr 1000°C + 3 hr 400°C at 2000 lb in-*
an -
D
x 10’
- 1.80 -1.26 - 1.24 -3.46 -2.85 -2.32
f * f f, -f &
0.02 0.02 0.02 0.02 0.02 0.02
-2.83 -2.83 -2.37
f 0.02 f 0.02 + 0.02
-2.85 -4.00 -4.03
l 0.02
f 0.02 f 0.02
GITTINS:
FIG. 1. Typicel
Pm.
GRAIN
cavitation
2. Fatigue
BOUNDARY
CAVITIES
in copper after fatigue at 400°C.
cavities after 170 hr anneal at 4OO’C.
IN
Cu
x 2000
x 2000
519
620
ACTA
METALLURGICA,
balance of the grain boundary and surface freeenergies. All the cavities remained in the boundaries after the 400% anneal in~cating that little or no migration had taken place. ,Figure .3 shows the microstructure after a 4 hr anneal at 1000°C. Grain growth has left many cavities stranded in the grains and these have developed crystallographic facets to minimise their total surface energy. The effect of annealing cavitated specimens for 3 hr at 400°C under a hydrostatic pressure of argon at 2000 lb ine2 is shown in Table 2. Both specimen and control were placed in the pressure vessel and were cooled under pressure after the anneal. For specimen 3 which contained cavities on the grain boundaries, AD/D decreased slightly indicating that However the cavities had partially collapsed. specimen 4 where the cavities were situated mainly within the grains showed no tendency to sinter under the same hydrostatic annealing conditions. Also when
VOL.
10,
1968
specimen 1 was annealed at 400°C under a hydrostatic pressure of 500 lb in-% no sintefing occurred. Specimen 3 was then annealed at 400% & vacw, for periods of 16 hr. Figure 4 shows that the value of AD/D increased to the same value as before the hydrostatic anneal after 48 hr. Grain boundary cavities were also formed in a copper specimen creep tested at 4OO“Cunder a tensile stress of 2.6 t.s.i. The specimen was oooled under stress and AD/D determined at room temperature. The value of AD/D was unchanged after annealing for 170 hr at 400°C indicating that the cavit’ies were stable. DISCUSSION
Hull and Rimmer”) suggested that cavities grow during creep under the action of a normal stress CT by collecting vacancies by grain boundary diffusion. The rate of increase in oavity radius &-I& for cavities
FIG. 3. Fatigue cavities after 4 hr anneal at 1000°C.
x 1500
GITTINS:
2.9 -
GRAIN
BOUNDARY
IN
521
Cu
Therefore the time to collapse a cavity of radius R is given by
after 170 hrs. in vacuum
. --___ Q
2.8 -
t, = g;;;yn
[In W3
I
after
+
tl
(6)
For copper at 4OO”C,y - 1500 dynes cm-l, Q N 1.2 x 1O-23cm3, D, N lo-* cm2 see-l (estimated from the data by Hoffman and Turnbull@)) 82 N lo--’ cm and x is taken as 10V3cm. The annealing time required to collapse a cavity of radius R according to both equations (3) and (6) is compared in Table 3. Cavities
fatigue 2.7 Q 6 d 2.6 -
I
TABLE 3. Sintoring times for cavities predict.ed by equations (3) and (6)
2.5 -
2.4
P’
p.s.i.
i
L
1 0
I 20 Time,
I 60
I 40
4 80
x apart
is given
by
the
2lI520, ii.Z(u -
P,
-
approximate
equation dr
dt-
2y/r)
kTxr
(1)
where !A is the atomic volume, D, the grain boundary diffusion coefficient, 62 the grain boundary the superimposed hydrostatic its usual meaning.
width, PIi
pressure and kT has
Clearly in the absence of both an
pressure the cavity should collapse because of the surface tension forces of the cavity. The rate of shrinkage of a grain applied stress and a hydrostatic
boundary
cavity
is then given by: dr z=-
4IIRD,
_
6Zy
(2)
kTxr2
Integration of equation (2) between the limits R to 0 gives the time t,o collapse a cavity of radius R kTxR3 t, = 12Il D, SZysl
i.e.
(3)
Harris(7) suggested that cavities grow during creep when the rate of. grain boundary sliding exceeds a critical rate. Sintering was also thought to occur when the stress was removed, the rate being given by the equation dr z-
(cm)
Hull-Rimmer [equation(3)]
Harris [equation (S)]
IO-4 5 x 10-S 2 x 10-S
37 4.6 0.3
32 2.75 0.05
hr
Effect of normal and hydrostatic annealing on the fractional change in density AD/D of a fatigue specimen. 4.
a distance
Sintering time (hr)
Cavity _.,.,I:.... ItuuUcI
V
after 3 hrs, at2000
FIG.
CAVITIES
-+&$[exP(E)
-11
2
Since 2yQ2/kTr < 1 equation (4) becomes: dr
D, 6Z2yQ
z=
kT13 In x/2r
(4)
size formed by fatigue, R N 5 x 10” cm should have disappeared during the 170 hr anneal at 400°C. There are three factors which may inhibit the rate of sintering. 1. If grain boundary migration occurs leaving cavities within the grains the rate of sintering will be retarded since the kinetics of sintering will be controlled by the rate of removal of vacancies by lattice diffusion. This is not thought to be the reason for incomplete sintering in copper since no migration was observed at 4OO’C. Furthermore the observation that annealing at 1OOO’Ccaused cavities in the first batch of copper to shrink and those in the second batch to expand cannot be explained in this way. 2. The driving force for sintering 2y/r, decreases as y decreases. Inman et a.!.@) have suggested that impurities absorbed at the surface may lower the surface energy. However if this was the cause of incomplete sintering then y would have to decrease to a vanishingly small level according to the equations of Hull and RimmeG and Harris.(‘) 3. If, during fatigue, gas diffuses into the cavities it will tend to build up a pressure to balance the surface tension forces that are tending to close the cavity. At equilibrium P, = 2ylR,. If after fatigue the amount of gas that has diffused into the cavity is less than the equilibrium pressure then during annealing the cavity will shrink until the equilibrium pressure is attained. Equation (1) then becomes of the
t, =
kTxra dr TR” R 12IlD;6Z.y.s2
J
(7)
where R is the initial cavity radius and R, the radius
(5) at equilibrium. Typically the total cavity volume in
522
ACTA
METALLURGICA,
the first batch of copper decreased by 4 during annealing. If the average cavity radius before annealing is taken as 5 x 10e6 cm then at equilibrium the fmal radius will be 4.7 x 1O-5 cm. Integration of equation (7) between these limits gives t, N 3000 set in reasonable agreement with the results from the first batch of copper. The observation that cavities in the second batch of copper failed to collapse on aMding at 400% and expanded on annealing at 1000°C suggests that the gas content of this material was higher. The experiments of Harper et aZ.(lO) indicate that the most likely gas to collect inside cavities is steam. They found that copper con~i~ng between 0.02 and 0.06% oxygen embrittled when annealed in hydrogen. It was shown that hydrogen diffuses into the metal combining with cuprous oxide to form steam leading to intergranular cracking. Simple calculation shows that to till the observed number and sizes of cavities formed by fatigue requires only O.O~lO~ oxygen dissolved in the copper. Oxygen analysis by hydrogen reduction on the as-received material (Table 1) shows that the oxygen content isNO.OOOl%. Also a total gas content of 0.15 cm3/100 g (Table 1) is sufficient to fill the cavities to the equilibrium The sintering behaviour is probably pressure. sensitive to variations in oxygen concentration below that detectable by analysis. No change in density (<2 x 10W5)was observed when a sample of the as-received material was annealed in hydrogen at 6~‘C(11) in~oating that the oxygen content is too small to nucleate steam cavities directly. This shows that the nucleation and growth of grain boundary voids by fatigue at 400°C is not caused by condensation of steam into bubbles. However by diffusing into a void nucleus the steam can stabilize the void at an early stage of growth since the condition cr + P, - 2y/r > 0 where CTis
VOL.
16, 1968
the applied stress and P, the internal gas pressure is achieved at lower void radii. Annealing at 400% under a hyd~statio pressure of 2000 lb in-z after fatigue only caused sintering in specimens containing cavities on the grain boundaries. This suggests that sintering occurs by removal of vacancies along the gram boundary. The sintering induced by a hyd~stati~ anneal was reversed when the specimen was annealed in a vacuum at 400°C. Fig. 4 shows that gas had diffused into the cavities during fatigue. At equilibrium P, = 2y/R, so that for a cavity of 5 x 10” cm radius P,N 1000 lb in2. Sintering will only ooeur if the hydrostatic pressure exceeds this value explaining why no sintering was observed after a 500 lb in2 hydrostatic anneal, since this will only cause sintering if t,he cavities exceed 2 microns in diameter. ACKNOWLEDGMENTS
The author wishes to thank Dr. T. Broom for valuable discussions and Dr. J. S. Waddington for assistance with the hydrostatic annealing. This work is published by permission of the Central Elect’ricity Generating Board. REFERENCES 1. D. HULL and D. E. RIMMEB, Phil. .&fag. 4,673 (1959). 2. R. W. I%LLuFFIandL. L. ~EIOLE, Acta Met. 8,170 (1955). 3. F. TH~~MMLEBand W. THOMMA, Met. Rev. No. 115, 69 (1967). 4. B. H. ALEXANDER and R. W. BALLVFFI, Acta Met. 5, 666 (1967). 5. A. GITTII-TS,~~~t~~e,Land. 214, 586 (1967). 6. R. V. DAY, 3. Iwm Steel Imt. 203,279 (1965). 7. J. E. HARRIS, Trans. Am. Inst. Min. metall. h’ngrs 235, 1509 (1965). 8. R. E. HOFFMAN and D. TURNB~LL, J. uppl. Phys. 21, 437 (1961). 9. M. C. INMAN. D. MCLEAN and H. R. TIPLER. Proc. R. Sot. 273A, 538 (1963). IO. S. HARPER, V. A. CALLCUT, D. W. TOU.X?FJEND and R. EBOBALL, J. Inst. Metals 90, 423 (1962). 11. H. D. WILLIAMS, private communication.
STABILITY
OF GRAIN
BOUNDARY A.
CAVITIES
IN
COPPER*
GITTINST
Direct evidence was obtained that gas diffuses into cavities formed in copper either by high temperature fatigue or creep. The gas pressure inside the cavity builds up and reduces the tendency for the cavity to collapse during isothermal annealing. Sintering was observed when the cavitated specimens were annealed in a hydrostatic pressure of 2000 lb/’m’ and this sintering was reversed by subsequent annealing in a vacuum.
LA STABILITE
DES CAVITES
AUX
JOINTS
DE GRAINS
DANS
LE CUIVRE
L’auteur a mis en bvidence le fait clue du paz diffuse dans les cavit& formbes dans le cuivre soit Dar fatigue soit par fluage Q haute temp&ture. B l’int&ieur de la cavitb la pression du gaz augmente et Eeci rend plus difficile la r&sorption de la cavitb au tours d’un recuit isotherme. Une certaine tendance 1 l’agglom&ation de celles-c‘i a BtB observbe quand les Bchantillons presentant des cavit& ont 6t& recuits sous une pression hydrostatique de 2000 lb/in %.Ce phbnombne s’est inverse par un recuit ult&ieur sous vide.
DIE
STABILITiiT
VON
KORNGRENZENHOHLRAUMEN
IN KUPFER
Es wurde direkt beobachtet, dass in Kupfer Gas in die durch Hochtemperaturermiidung oder Kriechen entstandenen Hohlriiume hineindiffundiert. Der Graadruck innerhalb des Hohlraumes nimmt zu und reduziert die Zerfallstendenz ‘bei isothermem Anlessen. Beim Anlassen der Hohlriiume enthaltenden Proben bei einem hydrostatischen Druck von 2000 lb/’m* wurde Sintern beobachtet. Bei anschliessendem Anlassen im Vakuum wurde das Sintern riickgiingig gemecht.
INTRODUCTION
During creep, cavities form on the grain boundaries of many
metals
and may
causing
intergranular
cavities
has been attributed
vacancies
eventually
failure.
link together
The growth
grain boundary. (l) Growth will only take place when
Other observations work
the
and the
would be expected
to
to the grain boundary. of grain boundaries to
was obtained
made on powder compacts’3) this
by Balluffi
and
on sintering have been of
grain
16, APRIL
1968
and the spectro-
are shown
a gauge
length from
in Table
25 mm
long
the extruded
having the same dimensions length
1. and
bars. as the
were also prepared ; speci-
being machined
After polishing
alternately
specimens
along
and controls
a grain size of 0.13 mm. Small into
grain
the copper
and 150 c/s.
boundary
cavities
were
introduced
by fatigue
at 4OO”C, 0 & 2.6 t.s.i.
Two specimens
from the first batch of
copper were given 5.4 x lo” cycles (specimen
from
1) and
2) which is approximately
the second
life respectively.
Two
cast were also fatigued
at 400°C under the same conditions
as specimen
2.
The control specimens were mounted alongside the fatigue specimen so that they experienced the same
pressure.
atmosphere
* Received August 16, 1967. -t Materials Division, Central Electricity Research Laboratories, Cleeve Road, Leatherhead, Surrey. VOL.
RESULTS
were annealed at 600°C for 20 hr in a vacuum to give
load.
ACTA METALLURGICA,
gauge
specimens
boundary
in vacua and under a hydrostatic
copper,
10% and 30% of the expected
and twisted wires.t4)
stability
purity
1.6 x lo6 cycles (specimen
cavities in copper, formed by either high temperature creep or high temperature fatigue, was investigated by annealing
with
a given bar.
stress is removed
collapse by losing vacancies Evidence of the importance
In
gas analyses
mens and controls
metal annealed then the cavity
Seigle.t2)
graphic
specimen
where y is the surface free energy and r the radius of
process
high
and
AND
has
were carried out on two batches of
vacuum-cast
Control specimens
27 O>r
If the applied
METHODS
6 mm dia. were machined
The condition
for cavity growth is
the sintering
elsewhere.c5)
Specimens
the applied stress o is greater than the surface tension
the cavity.
been published
The experiments
of
at the cavity surface from the neighbouring
forces which tend to collapse the cavity.
note on some of the observations
EXPERIMENTAL
of these
to the condensation
A preliminary
517
and temperature
but without
the fatigue
The specimen and control were water quenched
from 400°C to prevent during a slow cool.
sint’ering
that
may
occur
518
ACTA
METALLURGICA,
TAB-
VOL.
16,
1. Chemical analysis of vacuum copper W.%)
Antimony hXliC
Bismuth Cobalt Iron Lead Phosphorus Silicon Manganeee Nickel Silver Tin Tellurium Zinc
n.d. n.d. n.d.
1968 cast
I :s~~~;) (‘$000;) 0:0003 0.0001 n.d. n.d. n.d. 0.0006 0.001 0.0005
n.d. n.d.
I;::Zt;
n.d. = not detected. Gee anelyeia of vacuum cast copper Total other than oxygen cm’!100 g
Specimen Number
% Oxygen (a)
I&G cm*/100 g
CO1 (type) cmS/lOO g(b)
H, cmS/lOO g
1
<0.02 <0.02
0.08 0.13
0.05 0.05
<0.02 <0.02
0.13 0.18
<0.02 0.02
0.09 0.08
0.05 0.06
<0.02 <0.02
0.14 0.16
3 4 All (a) (b) (c)
0.0006 0.0002
Xl (type) cma/lOO gtcl
figurea are average of 2 analyses. determined by HI reduction at 1150°C. includes SO* and NHs if present. includes inert gases if present.
Density measurements were used to estimate the total cavity volume introduced by fatigue. The fractional change in density, AD/D, between the specimen and control was determined psing the technique described by Day.@) Table 2 shows the values of AD/D for the four specimens after fatigue. When specimens 1 and 2 from the first batch of copper were annealed at 400°C in a vacuum it was found that AD/D decreased (i.e. the cavities shrank) for the first 30-60 min of annealing and then remained constant even after a prolonged anneal of 170 hr (Table 2). However when specimen 3 (from the second batch of copper) was annealed at 400°C for TABLE
Specimen Number
No. of cycles
1
5.4 x 10”
2
1.62 x 10‘
1.62 x 1Oa
1.62 x 10’
170 hr no change in AD/D was detected. The effect of annealing at 1000°C on the stability of the cavities in the two batches of copper was investigated. Table 2 shows that further sintering occurred in the first batch of copper while the cavities in the second batch of material expanded, the value of AD/D increasing from -2.85 x 10V3to -4.00 x 10Y3. Figure 1 shows the appearance of cavities in specimen 2 after fatigue, considerable cavity linkage having occurred. After a 170 hr anneal t.he cavities have become more spheroidal (Fig. 2), though still showing some elongation in the plane of the boundary. This lenticular shape of the cavities is dictated by the
2. Density changes after fatigue and annealing Treatment after fatigue at 4OO”C, 0 & 2.6 t.s.i. None Annealed Annealed None Annealed Annealed
170 hr 400°C 3 hr 400°C at 600 lb in ’ 170 hr 400°C 170 hr 400°C + 4 hr 1000°C
None Anneal 170 hr 400°C Anne81 170 hr 400°C + 3 hr 400°C at 2000 lb in-* Sone Annealed 4 hr 1000”c Annealed 4 hr 1000°C + 3 hr 400°C at 2000 lb in-*
an -
D
x 10’
- 1.80 -1.26 - 1.24 -3.46 -2.85 -2.32
f * f f, -f &
0.02 0.02 0.02 0.02 0.02 0.02
-2.83 -2.83 -2.37
f 0.02 f 0.02 + 0.02
-2.85 -4.00 -4.03
l 0.02
f 0.02 f 0.02
GITTINS:
FIG. 1. Typicel
Pm.
GRAIN
cavitation
2. Fatigue
BOUNDARY
CAVITIES
in copper after fatigue at 400°C.
cavities after 170 hr anneal at 4OO’C.
IN
Cu
x 2000
x 2000
519
620
ACTA
METALLURGICA,
balance of the grain boundary and surface freeenergies. All the cavities remained in the boundaries after the 400% anneal in~cating that little or no migration had taken place. ,Figure .3 shows the microstructure after a 4 hr anneal at 1000°C. Grain growth has left many cavities stranded in the grains and these have developed crystallographic facets to minimise their total surface energy. The effect of annealing cavitated specimens for 3 hr at 400°C under a hydrostatic pressure of argon at 2000 lb ine2 is shown in Table 2. Both specimen and control were placed in the pressure vessel and were cooled under pressure after the anneal. For specimen 3 which contained cavities on the grain boundaries, AD/D decreased slightly indicating that However the cavities had partially collapsed. specimen 4 where the cavities were situated mainly within the grains showed no tendency to sinter under the same hydrostatic annealing conditions. Also when
VOL.
10,
1968
specimen 1 was annealed at 400°C under a hydrostatic pressure of 500 lb in-% no sintefing occurred. Specimen 3 was then annealed at 400% & vacw, for periods of 16 hr. Figure 4 shows that the value of AD/D increased to the same value as before the hydrostatic anneal after 48 hr. Grain boundary cavities were also formed in a copper specimen creep tested at 4OO“Cunder a tensile stress of 2.6 t.s.i. The specimen was oooled under stress and AD/D determined at room temperature. The value of AD/D was unchanged after annealing for 170 hr at 400°C indicating that the cavit’ies were stable. DISCUSSION
Hull and Rimmer”) suggested that cavities grow during creep under the action of a normal stress CT by collecting vacancies by grain boundary diffusion. The rate of increase in oavity radius &-I& for cavities
FIG. 3. Fatigue cavities after 4 hr anneal at 1000°C.
x 1500
GITTINS:
2.9 -
GRAIN
BOUNDARY
IN
521
Cu
Therefore the time to collapse a cavity of radius R is given by
after 170 hrs. in vacuum
. --___ Q
2.8 -
t, = g;;;yn
[In W3
I
after
+
tl
(6)
For copper at 4OO”C,y - 1500 dynes cm-l, Q N 1.2 x 1O-23cm3, D, N lo-* cm2 see-l (estimated from the data by Hoffman and Turnbull@)) 82 N lo--’ cm and x is taken as 10V3cm. The annealing time required to collapse a cavity of radius R according to both equations (3) and (6) is compared in Table 3. Cavities
fatigue 2.7 Q 6 d 2.6 -
I
TABLE 3. Sintoring times for cavities predict.ed by equations (3) and (6)
2.5 -
2.4
P’
p.s.i.
i
L
1 0
I 20 Time,
I 60
I 40
4 80
x apart
is given
by
the
2lI520, ii.Z(u -
P,
-
approximate
equation dr
dt-
2y/r)
kTxr
(1)
where !A is the atomic volume, D, the grain boundary diffusion coefficient, 62 the grain boundary the superimposed hydrostatic its usual meaning.
width, PIi
pressure and kT has
Clearly in the absence of both an
pressure the cavity should collapse because of the surface tension forces of the cavity. The rate of shrinkage of a grain applied stress and a hydrostatic
boundary
cavity
is then given by: dr z=-
4IIRD,
_
6Zy
(2)
kTxr2
Integration of equation (2) between the limits R to 0 gives the time t,o collapse a cavity of radius R kTxR3 t, = 12Il D, SZysl
i.e.
(3)
Harris(7) suggested that cavities grow during creep when the rate of. grain boundary sliding exceeds a critical rate. Sintering was also thought to occur when the stress was removed, the rate being given by the equation dr z-
(cm)
Hull-Rimmer [equation(3)]
Harris [equation (S)]
IO-4 5 x 10-S 2 x 10-S
37 4.6 0.3
32 2.75 0.05
hr
Effect of normal and hydrostatic annealing on the fractional change in density AD/D of a fatigue specimen. 4.
a distance
Sintering time (hr)
Cavity _.,.,I:.... ItuuUcI
V
after 3 hrs, at2000
FIG.
CAVITIES
-+&$[exP(E)
-11
2
Since 2yQ2/kTr < 1 equation (4) becomes: dr
D, 6Z2yQ
z=
kT13 In x/2r
(4)
size formed by fatigue, R N 5 x 10” cm should have disappeared during the 170 hr anneal at 400°C. There are three factors which may inhibit the rate of sintering. 1. If grain boundary migration occurs leaving cavities within the grains the rate of sintering will be retarded since the kinetics of sintering will be controlled by the rate of removal of vacancies by lattice diffusion. This is not thought to be the reason for incomplete sintering in copper since no migration was observed at 4OO’C. Furthermore the observation that annealing at 1OOO’Ccaused cavities in the first batch of copper to shrink and those in the second batch to expand cannot be explained in this way. 2. The driving force for sintering 2y/r, decreases as y decreases. Inman et a.!.@) have suggested that impurities absorbed at the surface may lower the surface energy. However if this was the cause of incomplete sintering then y would have to decrease to a vanishingly small level according to the equations of Hull and RimmeG and Harris.(‘) 3. If, during fatigue, gas diffuses into the cavities it will tend to build up a pressure to balance the surface tension forces that are tending to close the cavity. At equilibrium P, = 2ylR,. If after fatigue the amount of gas that has diffused into the cavity is less than the equilibrium pressure then during annealing the cavity will shrink until the equilibrium pressure is attained. Equation (1) then becomes of the
t, =
kTxra dr TR” R 12IlD;6Z.y.s2
J
(7)
where R is the initial cavity radius and R, the radius
(5) at equilibrium. Typically the total cavity volume in
522
ACTA
METALLURGICA,
the first batch of copper decreased by 4 during annealing. If the average cavity radius before annealing is taken as 5 x 10e6 cm then at equilibrium the fmal radius will be 4.7 x 1O-5 cm. Integration of equation (7) between these limits gives t, N 3000 set in reasonable agreement with the results from the first batch of copper. The observation that cavities in the second batch of copper failed to collapse on aMding at 400% and expanded on annealing at 1000°C suggests that the gas content of this material was higher. The experiments of Harper et aZ.(lO) indicate that the most likely gas to collect inside cavities is steam. They found that copper con~i~ng between 0.02 and 0.06% oxygen embrittled when annealed in hydrogen. It was shown that hydrogen diffuses into the metal combining with cuprous oxide to form steam leading to intergranular cracking. Simple calculation shows that to till the observed number and sizes of cavities formed by fatigue requires only O.O~lO~ oxygen dissolved in the copper. Oxygen analysis by hydrogen reduction on the as-received material (Table 1) shows that the oxygen content isNO.OOOl%. Also a total gas content of 0.15 cm3/100 g (Table 1) is sufficient to fill the cavities to the equilibrium The sintering behaviour is probably pressure. sensitive to variations in oxygen concentration below that detectable by analysis. No change in density (<2 x 10W5)was observed when a sample of the as-received material was annealed in hydrogen at 6~‘C(11) in~oating that the oxygen content is too small to nucleate steam cavities directly. This shows that the nucleation and growth of grain boundary voids by fatigue at 400°C is not caused by condensation of steam into bubbles. However by diffusing into a void nucleus the steam can stabilize the void at an early stage of growth since the condition cr + P, - 2y/r > 0 where CTis
VOL.
16, 1968
the applied stress and P, the internal gas pressure is achieved at lower void radii. Annealing at 400% under a hyd~statio pressure of 2000 lb in-z after fatigue only caused sintering in specimens containing cavities on the grain boundaries. This suggests that sintering occurs by removal of vacancies along the gram boundary. The sintering induced by a hyd~stati~ anneal was reversed when the specimen was annealed in a vacuum at 400°C. Fig. 4 shows that gas had diffused into the cavities during fatigue. At equilibrium P, = 2y/R, so that for a cavity of 5 x 10” cm radius P,N 1000 lb in2. Sintering will only ooeur if the hydrostatic pressure exceeds this value explaining why no sintering was observed after a 500 lb in2 hydrostatic anneal, since this will only cause sintering if t,he cavities exceed 2 microns in diameter. ACKNOWLEDGMENTS
The author wishes to thank Dr. T. Broom for valuable discussions and Dr. J. S. Waddington for assistance with the hydrostatic annealing. This work is published by permission of the Central Elect’ricity Generating Board. REFERENCES 1. D. HULL and D. E. RIMMEB, Phil. .&fag. 4,673 (1959). 2. R. W. I%LLuFFIandL. L. ~EIOLE, Acta Met. 8,170 (1955). 3. F. TH~~MMLEBand W. THOMMA, Met. Rev. No. 115, 69 (1967). 4. B. H. ALEXANDER and R. W. BALLVFFI, Acta Met. 5, 666 (1967). 5. A. GITTII-TS,~~~t~~e,Land. 214, 586 (1967). 6. R. V. DAY, 3. Iwm Steel Imt. 203,279 (1965). 7. J. E. HARRIS, Trans. Am. Inst. Min. metall. h’ngrs 235, 1509 (1965). 8. R. E. HOFFMAN and D. TURNB~LL, J. uppl. Phys. 21, 437 (1961). 9. M. C. INMAN. D. MCLEAN and H. R. TIPLER. Proc. R. Sot. 273A, 538 (1963). IO. S. HARPER, V. A. CALLCUT, D. W. TOU.X?FJEND and R. EBOBALL, J. Inst. Metals 90, 423 (1962). 11. H. D. WILLIAMS, private communication.