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Spontaneous grain boundary swelling in irradiated copper-boron alloys
JOURNAL
OF NUCLEAR
SPONTANEOUS
MATERIALS
19
(1966)
GRAIN BOUNDARY
327-340.
SWELLING
P. VELA Department
of Mining
and Metallurgical
degeneration
annealing gated.
The
grain
temperatures they ments
boundary
particularly and
can
in its earliest
after
bubbles
at temperatures
by
absorbing
below
be
to
used
generation
at
is caused
this
growth
investigate
reached those
800’ C. The
at which
ultimate
conditions
in the absence
effort
Die
failure
de-
of grain
bulles aux
de gaz
contours
aux
temp&atures
temperatures en absorbant les contours
contribute
Korngrenzenblasen
de grains
unterhalb
wurden.
durant
le
sont
& 700” C
fiir
man
Temperatur
eine Unterbrechung
aux dans
vorkommt.
sont
sind
d&g&&escence
des
Aufliisung
stades. L’accroisse-
zwar
diese
bei
urn
das Wachstum
der
Blasen
une
produit
Wachstum
1.
des bulles
aux
une
contours
croissance de
grains
cataaux
begleiten,
Introduction
empfin
werden.
ermittelt,
der
bei
einnehmen,
die tritt
der Korngrenzen-
bei
Temperaturen,
Erscheinung von spont,ane
noch
etwa Die
bis zu einem eines
bei nicht
46 ppm
Korngrenzenendgiiltige
wird hervorgerufen
Die Bedingungen,
bei Abwesenheit wurden
von
erzeugt
des Prozesses
800” C zu verursachen.
dem sie sich beriihren.
d’dquilibre
das
der Korngrenzen
apr& que les bulles ont atteint
taille
schon
Gaskonzentrationen
hinreichend,
auflijsen
pour Studier
Absorption
herangezogen
des Wachstums
les lacunes
qui ont pris naissance
und
wurde bei Tem-
sind besonders
GleichgewichtsgrBsse
ment de la temperature strophique
d’un
der Korngrenzenauflijsung
Stadium
die
eine
de grains. Des mesures de r&istivitb
le processus dans ses tout premiers
ce qui
der Gliih-
Korngrenzen
die Untersuchung
friihesten
normalerweise
& la
l’absence
durch
den
zur Verfolgung
denen
Fjtre utilisees
en
wiihrend
Widerstandsmessungen
Blasen
stables
mais
in
plus &levees elles croissent spontanbment
sensibles
conditions
700” C. Bei hohen Temperaturen
ein
de grains et peuvent
Les
sind stabil
sie spontan
welche
kiinnen
Wenn
a BtB BtudiBe. Les
des grains
infhrieures
est
jusqu’8
Kupfer-Helium-Legierungen
wachsen
Leerstellen,
stress are
Korngrenzen
untersucht. dagegen
to
von
von
blasen
particuli&rement joints
des contours cuivre-hdlium
croissance
de grains
de grains
bulles
elles.
se
de gaz
sont examinkes.
Aufliisung
seinem des alliages
des
behandlung
ehlenswert
deg&&escence
entre
ceci
pour causer
des joints
croissance
$, cette
applique
und La
B laquelle
concentrations des contours
finale
se touchent
peraturen
until
examined.
recuit
la
contribuent
nor-
of bubbles
of an applied
Des
size
boundary
which
Amtralia
bubbles
it would
grain
B celles
spontanbe
rupture
par
qu’elles
as low as 46 ppm are
by the growth
and the
produite
the
an equilibrium
infbrieures normalement.
& 800” C. La
the tempera-
of grain boundary
Brisbane,
aussi basses que 46 ppm sont suffisantes
vacancies boundary
spontaneous
boundaries touch
produirait
une d&g&&escence
to grain
stages. Increasing
ALLOYS
1966
temperatures
at
sensitive
growth
to cause
they
stable
measure-
occur. Gas concentrations
sufficient
the
investi-
Resistivity
have
causes breakaway mally
are
CO., AMSTERDAM
COPPER-BORON
of Queensland,
University
14 March
during
has been
bubbles
in the grain boundaries.
degeneration ture
boundaries alloys
spontaneously
are
process
grain
PUBLISHING
IN IRRADIATED
Engineering,
below 700” C, but at higher temperatures
grow
generated
of
of copper-helium
NORTH-HOLLAND
and B. RUSSELL
Received
The
0
durch
Punkt,
an
welche dieses
iiusseren
Druckes
bestimmt.
at elevated temperatures in the absence of an applied stress can occur by the breakaway growth of grain boundary bubbles, while those bubbles which lie within the grains remain stable. The general principles of bubble behaviour have been investigated by Barnes 1) who
The behaviour of inert gas trapped in bubbles at grain boundaries has received some attention during the last few years l-4), because it can lead to early failure in the presence of an externally applied stress at high temperatures. Furthermore, swelling and cracking of materials 327
suggest’s that migrating bubblrh ilr(’ trapfwd at grain boundaries fwc-ausc of’s mutual int,erac+on which reduces the surface rllergy
of’ a fn~bble at,
these locations. (!oalescen(*e of bufjbles alrrad~. situated in a boundary dew tlot lead to an increase
of
t,hc
grain
boundar~~
area
the?
for
I)witka\v:tj.
t)uI)l~lf~ gro\s tlr. or
ii
clitiuhioli
of gas to t)lie I~ountiar~~ is also iitvolvt~ll. I1 \\,ould a,lso fw interext,ing to cwiifirni t tic’ itlt~il that grain bountlar~. fitilure is tlur t’c) the lateral wowtfi of buf)bles rnitil t’fie\, t0uc.h. The otlier ?alternative is that cwwks appear first ant1 itrc
occupy 5) and a, flow of gas. or f)erhaps va’(*anAes. is required for the t>,f)e of’ fmbble groR+h
tjhen filled nit h gas Ifi). The f)ossibilit~- tltst grain boundar), or f)uf)ble migrat~ion are nlfv~li-
which c-an lead to failure.
anisms bag \vhicsli bubbles
hare
grown
until
they
\\‘helr the bubbles towlr
cac*h
other.
cohesion a(aross tile grain bountfar~~ f&we lost and Che gas (‘an escafw.
is
Loomis and Pranht~ 3) altd ISarnrs 6) have observed tha,t the acwmulatioil of’ bubbles at, grain boundaries can be (*aused f,~, boundarymigrat’ion instead of bubble migration and. under conditions of grain growth. awelerat~ecl grain boundary swelling may O(Y’IW. An inrestjigatioii of t,llc> Iiigtr tjenif)eraturc~ t)ensile prop&ies of irradiated lwr~~lliuni led Hyam and Sumner 2) to the cwn(~lusion that bubbles will grow’ under the influenw of au applied st’ress 0. according to t,llc wlat,ionshif) : (7 -- I_)?’f( I /r)
(r,):‘;,“);
Wllere ;J is t’lie surface energ,r!~. 1.0 is the initial equilibrium bubble radius ill the absen(~e of stress and r is the final radius after t,fle stress is applied. There is carit’icnl radius of 1.53 1’0 above which t’fle hnf)blr will (Aontinue to grow under decreasing apfjlied st,rws. ()ne assumf)tion ma,de in this calculation is that the increase iI1 bubble volume is due 10 \3canc+s alone. Karnrs I) has extended thaw ideas to est,imate t’lie expected tluc+ifity at, frac+ure iti terms of grain size and initia.1 f~uf~ble radilis. (irain boundar). f’ailure in irradiat,ed xiuranium has been att)ributed to t,hermal cycling in the region of’ GO(F (’ and tjhe internal stress it, causes ;6). ‘I’he internal st)rrss is thought t,o create grain boundary fissures which are then tilled with gas. In order to obtain a clear experimental basis fbr the f)rocess of grain boundary swelling. a number of fwoposals relating t,o f’ailure need to be investigated. For instanc*f?. it is newssarJ. to know if vacancy flow. alone. c-all fw responsible ii
grain
fwiuidaries
should
are wcurniilated
at
also bf> iiivestigatJecI.
The flxf)eriments refwrt’ed below art’ designed to investigate these factors iri tlie caopfwrlieliurn 2.
system.
Experimental
techniques
An alloy of copper csontaining 0.0-Z wt y/OlnK was irradiated t,o a t’hermal neutron dose of 2;. f(P nr-t to In-oducr O.OS at o. of aHe. fjetaifs of tht, metjhods used to prepare’ tht, alloJ,s and det,ermine t)he concentration of’ -‘He prodwed have been described previously ii. *). Ir sf)e&nens were made from o.-‘() (m dia. \vire a,~rtl die resistance rati(J, R,, R, (resistancae of t,lie sl)~~(~imeii)~(r~~sistali(~~~ of’ ii standard). was measured as a functjioll ot annealing time and ttmf)f3-aturf~ iti tlicb rntlgt of 600 (’ to !)OO (‘. \vitli all il(’ tCSiStil,ll(Y~ c*omparator !I) at 10 ’ ( ‘. l’etisilc~ tj&s were wrriecl out on IO (*in long. 0.3) cm dia. wire spcc%nens with a hard fwam tensile tt%ttal’ iLt 0’ (’ alld itt il st’raiii I’atC 01’ 1.ci IO yw. Thin foils of 12.’ /Amthickness ~\ercbirradiat,etl. annealed i II va(wo at) t hc rcquirtd trmf)erature and tflinne(l cle~trolytic~ally iu a solutJioll of 3)’ (‘. 30 ‘;I~, HN03 and 70 “o rnet~hanol at in order to f)ref)are transmission sfwimetls f’ol elec+ron mi(*roscof)y. The sf)ecsimens used fi)r tfic fractograf)hs were made from O.r’O cm dia. wire Ivhic~li had been a~nnealcd for various times at) tjc~mperaturcx f,et,w.ren 600c C! iLIlt !bOO“ ( I. After amleafing, encall specimen was f)rokcn by impac+ and a replic:a of t,he fract~ure surf’aw bras prepared frorn an impression in Bex film. moist’ened wit,fi acetone. The impressions were sliatlowrd \+3tlr Pt-I’d and a (barbon film \vas layed down. The Bcx tifm was dissolved in
GRAIN
1 IO’
BOUNDARY
I -1
SWELLING
I
IN
IRRADIATED
1.
The
rvsist,anc*e rat,io, Rx/R,,
is shown
2 TIME,Mlnutes)
acetone. All of the electron micrographs were taken upon a Siemens Elmiskop 1. Metallographic specimens were prepared from 0.20 cm dia. wire after annealing to produce the desired bubble distribution. 3.
Experimental
3.1.
RESISTIVITY
results AND
LATTICE
PARAMETER
MEASGREMENTS
329
I
I
A
4
5
as a function of annealing
500” C and 900” C as a function
ALLOYS
3
-1
0 LOG10 (ANNEALING
Fig.
COPPER-BORON
tilne, at temperatures
bPt,ween
of tixnr.
subject to interference from the presence of bubbles. A sample containing 0.02 at yi He u-as annealed at 550’ for increasing times and fig. 2, which represents the change in lattice parameter. (dcrla), shows that all the detectable gas had been precipitated after half an hour. A detailed description of the relationship between dissolved gas and the lattice parameter is given elsewhere 7, 17) but, the stage at’ which
The resistance ratio R,/Rs which was measured as a function of time and temperature of annealing is shown in fig. 1. At temperatures of 700’ C and below, the ratio decreased to a constant level as annealing time increased and no further change was observed at longer times. This behaviour is consistent with the change in resistance expected as gas is removed from solution. At 700’ C all of the gas had been precipitated after one minute whereas it took approximately 104 min for the resistance to become constant at 600” C. Lattice parameter measurements are slightly less sensitive to the presence of gas than the resistivity measurements but’ they are not
Fig.
2.
an alloy
The change containing
in lattice 0.02 at
parameter,
(AU/B), for
“/& He during
annealing
at 550’ C.
330
1’.
the lattice
parameter
is taken
t)o represent
the
has
gas
constant
the condition
when all
precipitated
to
time and growth which occurs not due to gas precipitation. decreased
initially
AND
finally becomes form
Clearly all the gas is precipitated
At temperatures
VELA
above
bubbles.
after a short
subsequently
is
I3.
RC'SSELL
sample
One
The resistance temperature
continued was raised
and then increased
rapidly.
This anomaly is due to grain boundary failure, which progressively reduces the effective crosssectional area of the specimen during annealing. The resistance measurements are most sensitive to this type of failure and the effect is registered much earlier than on other properties such as strength and ductility. Two samples which had been annealed at 600” C and 700” C until all the gas had left solution were heated a further 100” C to temperatures of 700” C and 800” C respectively. In both cases the resistance increased progressively at the higher temperatures and grain boundary failure took place. Furtherwhich contained only more, one specimen 46 ppm of 4He. was heated to X00” C for three hours and showed a similar though less rapid increase in resistance. It is clear that very low gas concentrations can initiate grain boundary failure provided the temperature is sufficiently high. I
to decrease when the t’o 600” (I and
700’ C the resistance
grain
boundary
damage
as shown
3.
33
B
-A
A
-0
0
The ult,imate at
to
by an in-
began to decrease indicating
that some of t’he
grain boundary damage was repaired bJ’ annealing at the lower temperature. All of these results are shown in fig. 1. 3.2.
TENSILE
PROPERTIES
The tensile properties are much less sensitive to grain boundary degeneration as shown in fig. 3 where the ultimate tensile strength, 0.2 y0 proof st’ress and elongation to fracture are given as a function of annealing time and temperature. Although the first evidence of grain boundary failure at 800” C appears after only one minute (fig. I), there is no evidence of failure in t’erms of strength and ductility until 100 min have passed. Even after 10 h there is no sudden change in the 0.1 y/, proot
1
I
V,O,ZO/o PROOF STRESS i 35
A -A
-A-A-
I 1 LOGIO(AhNEAL'NG
I 0 Fig.
began
creasing resistance. When annealing was continued at 600” C the resistance of both specimens
45
annealed
VOW
increase. Finally. two samples were aunealed at 800” C for different times to produce some
I
0,EL.
to an advanc~t~d
tinued to decrease at an annealing temperature of 660” C. At
700” C the resistance
0,O.A. UT5
\vas annealed
stage at 500” C aud the resistance was measured.
tensile
temperat,ures
strength, of
600” C,
elongat’ion 700” C
I 2 TIME-Minutes1
at fracture
.Ijc
and 0.2 ‘:A. Proof
and 800” C, are
shown
as
a
3" stress, for
function
of
irradiated
alloys
annealing
times.
GRAIN
Fig. 4.
BOUNDARY
SWELLING
IN
IRRADIATED
The unetched microstructure of an irradiated copper-boron x 400
stress. At temperatures of 700’ C and below no evidence of grain boundary failure can be found after annealing for times of up to 10 h. All of these tests were carried out at constant testing temperature of 0“ C and it is possible that changes in t,he properties might appear at higher testing temperatures, particularly when the temperature is high enough to give a copious supply of thermal vacancies. 4.
Microstructural
features
A typical cross-sectional area of a wire sample heated to 900” C for one hour is shown in fig. 4. On a macro-scale, the wire surface was split and some cracks extended from one end of the 10 cm length to the other. This behaviour was associated with overall swelling of the sample to the extent of 10 to 15 O/*.Most of the larger bubbles formed were confined to grain boundaries. The full length of some boundaries had lost cohesion and wide cracks or voids were formed, while other boundaries were characterised either by no bubbles at all, or strings of separated bubbles. Clearly the loss of grain boundary cohesion is caused by the progressive growth of bubbles. A similar though less marked tendency towards grain boundary failure is
COPPER-BORON
alloy,
ALLOYS
annertled for
1 h at
331
900”
c.
shown in fig. 5 which represents a typical section of a specimen annealed at 800” C for one hour. Samples annealed at 700’ C for 10 h showed no evidence of large grain boundary bubbles. At the higher magnifications
which
can be
obtained by thin film microscopy there is some evidence that the bubbles associated with grain boundaries are larger than those which lie within the grains. This is shown in fig. 6 which is a normal transmission micrograph and in fig. 7 which is a shadow-graph made from a thick foil. One important feature of fig. 7 is the typical, irregularly faceted shape of equilibrium grain boundary bubbles. The bubbles do not approximate to the spherical shape which is assumed in all theories of bubble growth. A large number of observations has led to the conclusion that the dimension of the equilibrium bubbles in the plane of the boundary is approximately twice that normal to the i.e. c/a=4 in fig. 9, which is a boundary, schematic representation of a grain boundary bubble. The idea that most of the vacancies which contribute to bubble growth originate at grain boundaries 10) is supported by the fact that grain boundary bubbles often have the
Fig.
6.
A The
thitl
foil
grain
of
irradiated
boundary
Cki-loU
bubbles
are
alloy larger
containing
0.04 at
‘$,
than
of those
which
most
He
annealed
for
lie within
the grains.
2 h at
700” C.
GRAIN
BOUNDARY
SWELLING
IN
IRRADIATED
5.
COPPER-BORON
ALLOYS
333
Discussion
5.1.
THE
CONDITIONS
The anomaly
REQUIRED
which occurs in the resistivity
results at temperatures above 700” C has been attributed to the degeneration of grain boundaries caused by growth and coalescence of bubbles situated within them. This idea has been checked exhaustively by means of electron microscopy. Furthermore, since growth can occur
Fig.
7.
A shadow
graph of a thin foil of irradiated
Cu-1OB alloy containing 0.04 wt y0 He after annealing for five hour at 700” C.
x 8000
equilibrium faceted shape, while those which lie within the grains remain spherical. The fractographs in fig. 8 (a, b, c, d, e and f) show various stages of grain boundary degeneration in a sample annealed at 900” C for one hour. Clearly the process is a progressive one in which small grain boundary bubbles grow until they touch each other. There appear to be two processes involved: 1. the growth of individual bubbles (fig. 8 a, b and c) and 2. the coalescence of bubbles (fig. 8 d, e and f). Furthermore, at an early stage of the process the bubbles appear to be flattened in the plane of the boundary (fig. 8 b, c and d) and at a late stage they develop facets which are typical of bubbles which have approached an equilibrium condition (fig. 8 e and f).
in a sample
after
all of
the
gas has
been precipitated (fig. l), bubble growth can arise from the condensation of vacancies alone. Although significant degeneration did not occur during uniform annealing at 700” C for 10 h the grain boundary bubbles appear to have an equilibrium size which is larger than that of bubbles which lie within the grains (figs. 6 and 7). This feature could represent an early stage of grain boundary degeneration which may lead to complete failure at very long annealing times. However, there does appear to be a threshhold temperature for spontaneous growth at 700” C under the conditions imposed. It may be significant that this is alittle below the minimum temperature at which rapid grain growth is observed in copper 1s). The experiments in which two samples were brought to equilibrium at 600’ C and 700” C respectively and then heated a further 100’ C (fig. 1) show that, although a high vacancy concentration is necessary to cause rapid bubble growth, it is not the only condition required. Growth which does not normally occur at 700” C can be forced to occur by a prior annealing treatment at 600” C. Growth can also be forced to occur at 700” C by annealing first at 500” C. However, prior heat treatment will not promote growth at temperatures below 700” C. Clearly, the equilibrium concentration of vacancies at 700” C is adequate for rapid bubble growth and the increase in temperature has been sufficient to upset the equilibrium condition to such an extent that the bubbles became unstable. This confirms the idea that the pressure inside a bubble is related to its equilibrium radius and
(8)
(b)
-GRAIN
BOUNDARY
SWELLING
IN
IRRADIATED
Cd)
COPPER-BOROB
ALLOYS
335
(f) Fig.
8.
A
sequence
of’ fractographs
showing
the degeneration
of’ grain boundaries
at 900” 0.
GRAIN
BOUNDARY
SWELLING
IN IRRADIATED
COPPER-BORON
nor thermal
cycling
for grain boundary tures above factors can
are necessary degeneration
700’ C, although
accelerate
337
ALLOYS
bubble
conditions at tempera-
both of growth.
these It is
surprising that a concentration of gas as low as 46 ppm is sufficient to start spontaneous grain boundary degeneration at a temperature of 800"C, but it is clear that relatively minor gas evolution
during
irradiation
can have
a
significant effect upon the properties. Since bubbles situated within the grains do not become Fig. 9. A schematic representation of grain boundary bubble growth. The black areas represent the changes which take place in the size of a growing-bubble.
that increasing the pressure, in this case by heating, causes the bubbles to grow. Another factor isolated by these experiments is that grain boundary migration is not one of the necessary conditions for swelling because significant grain growth occurs only at temperatures above 700” C during the times involved. Furthermore, the average bubble spacing within the grains is of the same order as the initial spacing of bubbles within the grain boundaries, and not lower, as would be expected if bubbles were swept up by moving boundaries or if bubbles migrated to the boundaries. The swelling process does not depend upon any special distribution, accumulation or regrouping of bubbles in the grain boundary, because the bubble distributions obtained at all temperatures between 450” C and 700” C are identical, to within a factor of 10, in copperhelium alloys heated uniformly in the absence of a steep temperature gradient 11). A close investigation of foils containing 0.01 at o/o He showed little change in the distribution of bubbles which lie within the grains after annealing for times of up to 5 h in the range of temperatures between 700” C and 900'C. Low helium foils were used to determine this because foils with a higher helium content could not be satisfactorily thinned. Neither the application of an external stress,
unstable
under the imposed
con-
ditions, it is clear that the unique conditions imposed by grain boundaries are necessary for breakaway bubble growth. 5.2.
THE
MECHANISM
OF GRAIN
BOUNDARY
SWELLING The results shown in fig. 1 suggest that bubbles formed in grain boundaries at temperatures above 700” C are unstable and continue to grow
spontaneously
by absorbing
vacancies.
At lower temperatures the bubbles reach an equilibrium size and shape, and no breakaway growth occurs unless the equilibrium is upset by, either the application of an external stress z), or a change in the thermal condition. Bubbles annealed to an equilibrium condition at 500” C, 600” C or 700” C become unstable if the temperature is raised. The most likely explanation for this behaviour lies in the relationship between the internal pressure of a spherical bubble, P, its radius, r and its surface energy y, which is given by the equation P=2ylr. When the temperature of an equilibrium bubble is raised by 100” C in the region of 700” C, its internal pressure is increased by approximately 10 y. and the bubble will tend to grow to a new equilibrium radius by absorbing vacancies. Unfortunately the bubbles do not stop growing and other factors, such as kinetic or geometric conditions, can influence the stability of grain boundary bubbles once their equilibrium has been upset. Barnes 10) has shown that the major thermal vacancy sources during bubble growth are the grain boundaries and Hull et ~~1.15)have stated
t Id
during the gro\4+h of grain boundary
voids
in creep experiments. 94 o/o of all t’hcbvacancies absorbed arrive at, the periphery of t*he void in the plane of t,he grain boundary. mechanism being grain boundary
the transport, diffusion. The
other 6 y,, enter through the bubble surface by volume diffusion from within the grains. Eelson
et crZ.1’) have calculat’ed
equilibrium
shapes for bubbles situat’ed at grain boundaries in t’erms of t,he anisotropic dist’ribution of
The fact that tllc grO\\.tll sllal)C~ is Ilot equilibrium one is demonstrat,ed calearl>-by tllca ill1
experiment in which t’he resistivity of a specimen annealed at’ 600” C aft,er a prior heat treat’ment at X00” C to produce some grain boundary failure. decreased with annealing time. These experiments
are explained
as follows.
The decrease in resist,ance which occurs during annealing at, 600” (3; is caused 1))~a progressive decrease in the grain boundary
area occupied
surface energy in fee met’als and a typical shape is shown schematically in fig. !la. Man;7
by lenticular bubbles formed at 800” C. It is thought. that the rate at which the bubble
bubbles wit,11 similar shapes were observed in t’he copper-helium s?.xtem and one of these is shown in fig. 5. The following factors should be considered in a satisfact,or? model for grain boundary swelling. If most, of t’he vacancies arrive at a bubble in the plane of the grain boundary its shape will tend to become distorted from that in fig. !)a t)o that, in fig. !tb. Unless the surface and volume diffusion are sufficient,ly rapid t’o correct. t’he shape and maintain a constant (:/cl ratio. hhe angle 0 along the boundary x--5’ will become very acute as shown in fig. 9~. Furthermore if t*his mode of growth is con t’inued. t,he rate ab which the grain boundary is consumed by bubbles is much higher than would be expect’ed for a unit increase in the volume of spherical bubbles. Another import(ant consideration is that the energy of a grain boundary is higher t,han that of t,he surrounding ma’trix and. energetically: it, is easier to form a new surface in the grain boundary than it is elsewhere. As a bubble grows larger, its peripheral surface, which lies in the boundary, increases rapidly a,nd more vacancies per unit) time can enter the bubble. The surface area of the bubble increases simultaneously and the number of atoms which must be moved to restore the equilibrium shape becomes larger, consequently it, becomes more dificult for an equilibrium shape to be realised and an extreme condition of bubble shape develops as shown in fig. 8b and schematicallS in fig. DC.
shape is readjusted by surface and volume diffusion at the lower temperature, exceeds the rat’e at which the new vacancies enter t,he bubble. Although the volume of grain boundary bubbles is not necessarily decreased, the bubbles readjust their shape from a t’hin lens to that of an equilibrium bubble. As a result’ they occupy less area in the grain boundar),. It is possible that this process is aided by t,he rcabsorption of some vacancies from the sharp angles situated around the periphery of the bubbles. This mechanism is analogous to the behaviour of voids during sinking. It follows, t#hat, although the energy of t’hc system must decrease during grain boundary bubble growt,h it> does not decrease as rapidly as it would if t’he bubbles maintained a spherical growth shape. Therefore. any model developed to explain these effec& must be based upon dynamic. rat)her than equilibrium. considorations. A bubble which lies within a grain does not, become unstable. because vacancies arrive at, random points around its surfaces and the equilibrium shape is not seriously disturbed during growt’h. One further point is that during growth. tile bubbles maintain the shape of a thin lens in the plane of the grain boundary as shown in fig. x b. c. As the bubbles approach each other, the area of grain boundary within which vacancies can be generated is reduced and the vacancy flux is reduced by competJition between bubbles. This slowing down of vacancy formation enables the bubbles to move towards an
GRAIN
equilibrium and they
BOUNDARY
SWELLING
IN IRRADIATED
shape at a late stage of the process begin
to develop
crystal
facets
COPPER-BORON
339
ALLOYS
to generate a large number of mobile vacancies,
as
the effect upon strength would be marked after
shown in fig. 8 cl, e, f. When the bubbles finally touch, the grain boundary represents a crack from which the gas can escape if there is
a much shorter annealing time, because bubble growth under the influence of stress would contribute the failure. A loss of high temperature ductility is expected even with very low
access to the surface of the specimen. Unstable growth can be started factor which upsets the equilibrium
by any of grain
boundary bubbles in the temperature range where thermal vacancies are plentiful. Hull et aZ.15) and Hyam et aZ.2) have considered conditions for void and bubble growth
the re-
spectively, in the presence of an applied tensile stress. Provided the stress lies above a critical level the bubbles will grow until they touch. In this case the driving force is supplied in part, by the applied stress. Thermal cycling can also cause grain boundary swelling because the pressure inside the bubbles is periodically increased. It is probably the first high temperature cycle which changes the bubble shape away from equilibrium and starts a process which could continue spontaneously at the high temperature.
5.3.
THE
EFFECT
TENSILE
OF SWELLING
UPON
THE
STRENGTH
It is interesting to note that although the grain boundaries begin to deteriorate after annealing for only a few minutes at 800” C, no significant change in the tensile strength, measured at 0’ C, occurs until the annealing has proceeded for more than 2 h. The 0.2 y. proof stress remains unaffected for longer times but both the UTS and ductility start to decrease. The loss of ductility corresponds with the formation of numerous very large grain boundary bubbles and the complete degeneration of some grain boundaries. It is difficult to understand why the strength does not decrease at a much earlier stage when grain boundary degeneration first begins, but it is assumed that the Griffith conditions for crack propagation are not met at the sharp edges of grain boundary bubbles. It is likely that, if the tests were carried out at a temperature sufficient
gas contents. 6. I.
Conclusions At temperatures
above 700’ C grain bounda-
ry bubbles in a copper alloy containing at o/0 of 4He grow spontaneously
0.05
until they
touch. 2. Spontaneous bubble growth can take place in the absence of grain boundary or bubble migration, bubble re-distribution, applied stress and thermal cycling. However, these factors may accelerate the process under certain conditions. 3. Resistivity mesaurement is a very sensitive technique for following grain boundary degeneration. 4. Grain boundary degeneration must reach an advanced stage before it affects the strength and ductility at 0’ C, although reduced ductility at high testing temperatures is to be expected at a much earlier stage. _ 0. Breakaway growth can occur solely by the migration of vacancies along grain boundaries after all the helium has been precipitated. after bubbles 6. Increasing the temperature have reached equilibrium can provide a sufficient driving force to initiate breakaway growth at temperatures as low as 700” C. of helium in the region of 7. Concentrations 46 ppm are sufficient to cause spontaneous grain boundary degeneration at elevated temperatures. 8. During swelling the grain boundary bubbles adopt a lenticular shape and if the temperature is lowered some of the damage can be repaired by a mechanism in which the bubbles resume an equilibrium shape.
340
F . VELA
AND
Acknowledgements The authors Atomic
to the Australian
Commission
who financed
work and gave permission They
RUSSELL
“)
are grateful
Energy
B.
are also grateful
this
for its publication.
to Professor
held with Mr. B. S. Hickman,
Dr. D. G. Walker
and Mr. I. J. Hastings during t,he course of t’his work were also invaluable.
S.
“Enrico (1965)
9
R.
E. D. Hyam (Venice, 1962)
S. Barnes,
3)
B.
A.
(U.S.A.) 4)
R.
S.
134655
Loomis Report Barnes, (1964)
J. Nucl. and 323 and
Mat.
G. D.
ANL Harwell
11 (1964)
Sumner, W.
6532
IAEA
Pracht,
135
(1962)
(UK)
AERE
Report,
Proc.
Inlern.
18 (1961)
and
of
beryllium
p. 372 School
of Physics,
861
I. J. Hastings,
J. Nucl.
Mat.
17
17 (1965)
86
30
B. Russell
R3162
and B. J. Heffernan,
Ibid,
P. Vela and B. Russell,
13
R.
)
R.
14)
Report,,
(1959)
1’)
Symp. Argonne
1963)
“1 B. Russell, J. Sci. Instr., in press R. S. Barnes, Harwell (UK) AERE 9
S. Nelson, Mag. (1963)
Cottrell,
D. and
J. Nucl. Mat. 19 (1966) 312
J. Mazey
11 (1965)
S. Barnes
A275
2)
metallurgy
Hall,
Fermi”,
‘1 B. Russell
13)
1)
The
and
6) R. S. Barnes,
Phil.
References
Barnes,
(Chapman
F. T. 81.
White for his encouragement and for provision of facilities in his laboratories. The discussions
R.
R.
S. Barnes,
D. J. Mazey,
Proc.
Phil.
Sot.
47
Structural
report
no. 70 (Iron
1961)
1
processes
D. Hull and D. E. Rimmer,
16)
S. F.
17)
1. J. Hastings
1s)
Metals
J. Nucl. and
Handbook
in
creep,
and Steel Institute,
15)
Pugh,
and
91
Phil. Meg. 4 (1959) 673
Mat.
4 (1961)
B. Russell, (1948)
special London)
260
177
to be published
OF NUCLEAR
SPONTANEOUS
MATERIALS
19
(1966)
GRAIN BOUNDARY
327-340.
SWELLING
P. VELA Department
of Mining
and Metallurgical
degeneration
annealing gated.
The
grain
temperatures they ments
boundary
particularly and
can
in its earliest
after
bubbles
at temperatures
by
absorbing
below
be
to
used
generation
at
is caused
this
growth
investigate
reached those
800’ C. The
at which
ultimate
conditions
in the absence
effort
Die
failure
de-
of grain
bulles aux
de gaz
contours
aux
temp&atures
temperatures en absorbant les contours
contribute
Korngrenzenblasen
de grains
unterhalb
wurden.
durant
le
sont
& 700” C
fiir
man
Temperatur
eine Unterbrechung
aux dans
vorkommt.
sont
sind
d&g&&escence
des
Aufliisung
stades. L’accroisse-
zwar
diese
bei
urn
das Wachstum
der
Blasen
une
produit
Wachstum
1.
des bulles
aux
une
contours
croissance de
grains
cataaux
begleiten,
Introduction
empfin
werden.
ermittelt,
der
bei
einnehmen,
die tritt
der Korngrenzen-
bei
Temperaturen,
Erscheinung von spont,ane
noch
etwa Die
bis zu einem eines
bei nicht
46 ppm
Korngrenzenendgiiltige
wird hervorgerufen
Die Bedingungen,
bei Abwesenheit wurden
von
erzeugt
des Prozesses
800” C zu verursachen.
dem sie sich beriihren.
d’dquilibre
das
der Korngrenzen
apr& que les bulles ont atteint
taille
schon
Gaskonzentrationen
hinreichend,
auflijsen
pour Studier
Absorption
herangezogen
des Wachstums
les lacunes
qui ont pris naissance
und
wurde bei Tem-
sind besonders
GleichgewichtsgrBsse
ment de la temperature strophique
d’un
der Korngrenzenauflijsung
Stadium
die
eine
de grains. Des mesures de r&istivitb
le processus dans ses tout premiers
ce qui
der Gliih-
Korngrenzen
die Untersuchung
friihesten
normalerweise
& la
l’absence
durch
den
zur Verfolgung
denen
Fjtre utilisees
en
wiihrend
Widerstandsmessungen
Blasen
stables
mais
in
plus &levees elles croissent spontanbment
sensibles
conditions
700” C. Bei hohen Temperaturen
ein
de grains et peuvent
Les
sind stabil
sie spontan
welche
kiinnen
Wenn
a BtB BtudiBe. Les
des grains
infhrieures
est
jusqu’8
Kupfer-Helium-Legierungen
wachsen
Leerstellen,
stress are
Korngrenzen
untersucht. dagegen
to
von
von
blasen
particuli&rement joints
des contours cuivre-hdlium
croissance
de grains
de grains
bulles
elles.
se
de gaz
sont examinkes.
Aufliisung
seinem des alliages
des
behandlung
ehlenswert
deg&&escence
entre
ceci
pour causer
des joints
croissance
$, cette
applique
und La
B laquelle
concentrations des contours
finale
se touchent
peraturen
until
examined.
recuit
la
contribuent
nor-
of bubbles
of an applied
Des
size
boundary
which
Amtralia
bubbles
it would
grain
B celles
spontanbe
rupture
par
qu’elles
as low as 46 ppm are
by the growth
and the
produite
the
an equilibrium
infbrieures normalement.
& 800” C. La
the tempera-
of grain boundary
Brisbane,
aussi basses que 46 ppm sont suffisantes
vacancies boundary
spontaneous
boundaries touch
produirait
une d&g&&escence
to grain
stages. Increasing
ALLOYS
1966
temperatures
at
sensitive
growth
to cause
they
stable
measure-
occur. Gas concentrations
sufficient
the
investi-
Resistivity
have
causes breakaway mally
are
CO., AMSTERDAM
COPPER-BORON
of Queensland,
University
14 March
during
has been
bubbles
in the grain boundaries.
degeneration ture
boundaries alloys
spontaneously
are
process
grain
PUBLISHING
IN IRRADIATED
Engineering,
below 700” C, but at higher temperatures
grow
generated
of
of copper-helium
NORTH-HOLLAND
and B. RUSSELL
Received
The
0
durch
Punkt,
an
welche dieses
iiusseren
Druckes
bestimmt.
at elevated temperatures in the absence of an applied stress can occur by the breakaway growth of grain boundary bubbles, while those bubbles which lie within the grains remain stable. The general principles of bubble behaviour have been investigated by Barnes 1) who
The behaviour of inert gas trapped in bubbles at grain boundaries has received some attention during the last few years l-4), because it can lead to early failure in the presence of an externally applied stress at high temperatures. Furthermore, swelling and cracking of materials 327
suggest’s that migrating bubblrh ilr(’ trapfwd at grain boundaries fwc-ausc of’s mutual int,erac+on which reduces the surface rllergy
of’ a fn~bble at,
these locations. (!oalescen(*e of bufjbles alrrad~. situated in a boundary dew tlot lead to an increase
of
t,hc
grain
boundar~~
area
the?
for
I)witka\v:tj.
t)uI)l~lf~ gro\s tlr. or
ii
clitiuhioli
of gas to t)lie I~ountiar~~ is also iitvolvt~ll. I1 \\,ould a,lso fw interext,ing to cwiifirni t tic’ itlt~il that grain bountlar~. fitilure is tlur t’c) the lateral wowtfi of buf)bles rnitil t’fie\, t0uc.h. The otlier ?alternative is that cwwks appear first ant1 itrc
occupy 5) and a, flow of gas. or f)erhaps va’(*anAes. is required for the t>,f)e of’ fmbble groR+h
tjhen filled nit h gas Ifi). The f)ossibilit~- tltst grain boundar), or f)uf)ble migrat~ion are nlfv~li-
which c-an lead to failure.
anisms bag \vhicsli bubbles
hare
grown
until
they
\\‘helr the bubbles towlr
cac*h
other.
cohesion a(aross tile grain bountfar~~ f&we lost and Che gas (‘an escafw.
is
Loomis and Pranht~ 3) altd ISarnrs 6) have observed tha,t the acwmulatioil of’ bubbles at, grain boundaries can be (*aused f,~, boundarymigrat’ion instead of bubble migration and. under conditions of grain growth. awelerat~ecl grain boundary swelling may O(Y’IW. An inrestjigatioii of t,llc> Iiigtr tjenif)eraturc~ t)ensile prop&ies of irradiated lwr~~lliuni led Hyam and Sumner 2) to the cwn(~lusion that bubbles will grow’ under the influenw of au applied st’ress 0. according to t,llc wlat,ionshif) : (7 -- I_)?’f( I /r)
(r,):‘;,“);
Wllere ;J is t’lie surface energ,r!~. 1.0 is the initial equilibrium bubble radius ill the absen(~e of stress and r is the final radius after t,fle stress is applied. There is carit’icnl radius of 1.53 1’0 above which t’fle hnf)blr will (Aontinue to grow under decreasing apfjlied st,rws. ()ne assumf)tion ma,de in this calculation is that the increase iI1 bubble volume is due 10 \3canc+s alone. Karnrs I) has extended thaw ideas to est,imate t’lie expected tluc+ifity at, frac+ure iti terms of grain size and initia.1 f~uf~ble radilis. (irain boundar). f’ailure in irradiat,ed xiuranium has been att)ributed to t,hermal cycling in the region of’ GO(F (’ and tjhe internal stress it, causes ;6). ‘I’he internal st)rrss is thought t,o create grain boundary fissures which are then tilled with gas. In order to obtain a clear experimental basis fbr the f)rocess of grain boundary swelling. a number of fwoposals relating t,o f’ailure need to be investigated. For instanc*f?. it is newssarJ. to know if vacancy flow. alone. c-all fw responsible ii
grain
fwiuidaries
should
are wcurniilated
at
also bf> iiivestigatJecI.
The flxf)eriments refwrt’ed below art’ designed to investigate these factors iri tlie caopfwrlieliurn 2.
system.
Experimental
techniques
An alloy of copper csontaining 0.0-Z wt y/OlnK was irradiated t,o a t’hermal neutron dose of 2;. f(P nr-t to In-oducr O.OS at o. of aHe. fjetaifs of tht, metjhods used to prepare’ tht, alloJ,s and det,ermine t)he concentration of’ -‘He prodwed have been described previously ii. *). I
GRAIN
1 IO’
BOUNDARY
I -1
SWELLING
I
IN
IRRADIATED
1.
The
rvsist,anc*e rat,io, Rx/R,,
is shown
2 TIME,Mlnutes)
acetone. All of the electron micrographs were taken upon a Siemens Elmiskop 1. Metallographic specimens were prepared from 0.20 cm dia. wire after annealing to produce the desired bubble distribution. 3.
Experimental
3.1.
RESISTIVITY
results AND
LATTICE
PARAMETER
MEASGREMENTS
329
I
I
A
4
5
as a function of annealing
500” C and 900” C as a function
ALLOYS
3
-1
0 LOG10 (ANNEALING
Fig.
COPPER-BORON
tilne, at temperatures
bPt,ween
of tixnr.
subject to interference from the presence of bubbles. A sample containing 0.02 at yi He u-as annealed at 550’ for increasing times and fig. 2, which represents the change in lattice parameter. (dcrla), shows that all the detectable gas had been precipitated after half an hour. A detailed description of the relationship between dissolved gas and the lattice parameter is given elsewhere 7, 17) but, the stage at’ which
The resistance ratio R,/Rs which was measured as a function of time and temperature of annealing is shown in fig. 1. At temperatures of 700’ C and below, the ratio decreased to a constant level as annealing time increased and no further change was observed at longer times. This behaviour is consistent with the change in resistance expected as gas is removed from solution. At 700’ C all of the gas had been precipitated after one minute whereas it took approximately 104 min for the resistance to become constant at 600” C. Lattice parameter measurements are slightly less sensitive to the presence of gas than the resistivity measurements but’ they are not
Fig.
2.
an alloy
The change containing
in lattice 0.02 at
parameter,
(AU/B), for
“/& He during
annealing
at 550’ C.
330
1’.
the lattice
parameter
is taken
t)o represent
the
has
gas
constant
the condition
when all
precipitated
to
time and growth which occurs not due to gas precipitation. decreased
initially
AND
finally becomes form
Clearly all the gas is precipitated
At temperatures
VELA
above
bubbles.
after a short
subsequently
is
I3.
RC'SSELL
sample
One
The resistance temperature
continued was raised
and then increased
rapidly.
This anomaly is due to grain boundary failure, which progressively reduces the effective crosssectional area of the specimen during annealing. The resistance measurements are most sensitive to this type of failure and the effect is registered much earlier than on other properties such as strength and ductility. Two samples which had been annealed at 600” C and 700” C until all the gas had left solution were heated a further 100” C to temperatures of 700” C and 800” C respectively. In both cases the resistance increased progressively at the higher temperatures and grain boundary failure took place. Furtherwhich contained only more, one specimen 46 ppm of 4He. was heated to X00” C for three hours and showed a similar though less rapid increase in resistance. It is clear that very low gas concentrations can initiate grain boundary failure provided the temperature is sufficiently high. I
to decrease when the t’o 600” (I and
700’ C the resistance
grain
boundary
damage
as shown
3.
33
B
-A
A
-0
0
The ult,imate at
to
by an in-
began to decrease indicating
that some of t’he
grain boundary damage was repaired bJ’ annealing at the lower temperature. All of these results are shown in fig. 1. 3.2.
TENSILE
PROPERTIES
The tensile properties are much less sensitive to grain boundary degeneration as shown in fig. 3 where the ultimate tensile strength, 0.2 y0 proof st’ress and elongation to fracture are given as a function of annealing time and temperature. Although the first evidence of grain boundary failure at 800” C appears after only one minute (fig. I), there is no evidence of failure in t’erms of strength and ductility until 100 min have passed. Even after 10 h there is no sudden change in the 0.1 y/, proot
1
I
V,O,ZO/o PROOF STRESS i 35
A -A
-A-A-
I 1 LOGIO(AhNEAL'NG
I 0 Fig.
began
creasing resistance. When annealing was continued at 600” C the resistance of both specimens
45
annealed
VOW
increase. Finally. two samples were aunealed at 800” C for different times to produce some
I
0,EL.
to an advanc~t~d
tinued to decrease at an annealing temperature of 660” C. At
700” C the resistance
0,O.A. UT5
\vas annealed
stage at 500” C aud the resistance was measured.
tensile
temperat,ures
strength, of
600” C,
elongat’ion 700” C
I 2 TIME-Minutes1
at fracture
.Ijc
and 0.2 ‘:A. Proof
and 800” C, are
shown
as
a
3" stress, for
function
of
irradiated
alloys
annealing
times.
GRAIN
Fig. 4.
BOUNDARY
SWELLING
IN
IRRADIATED
The unetched microstructure of an irradiated copper-boron x 400
stress. At temperatures of 700’ C and below no evidence of grain boundary failure can be found after annealing for times of up to 10 h. All of these tests were carried out at constant testing temperature of 0“ C and it is possible that changes in t,he properties might appear at higher testing temperatures, particularly when the temperature is high enough to give a copious supply of thermal vacancies. 4.
Microstructural
features
A typical cross-sectional area of a wire sample heated to 900” C for one hour is shown in fig. 4. On a macro-scale, the wire surface was split and some cracks extended from one end of the 10 cm length to the other. This behaviour was associated with overall swelling of the sample to the extent of 10 to 15 O/*.Most of the larger bubbles formed were confined to grain boundaries. The full length of some boundaries had lost cohesion and wide cracks or voids were formed, while other boundaries were characterised either by no bubbles at all, or strings of separated bubbles. Clearly the loss of grain boundary cohesion is caused by the progressive growth of bubbles. A similar though less marked tendency towards grain boundary failure is
COPPER-BORON
alloy,
ALLOYS
annertled for
1 h at
331
900”
c.
shown in fig. 5 which represents a typical section of a specimen annealed at 800” C for one hour. Samples annealed at 700’ C for 10 h showed no evidence of large grain boundary bubbles. At the higher magnifications
which
can be
obtained by thin film microscopy there is some evidence that the bubbles associated with grain boundaries are larger than those which lie within the grains. This is shown in fig. 6 which is a normal transmission micrograph and in fig. 7 which is a shadow-graph made from a thick foil. One important feature of fig. 7 is the typical, irregularly faceted shape of equilibrium grain boundary bubbles. The bubbles do not approximate to the spherical shape which is assumed in all theories of bubble growth. A large number of observations has led to the conclusion that the dimension of the equilibrium bubbles in the plane of the boundary is approximately twice that normal to the i.e. c/a=4 in fig. 9, which is a boundary, schematic representation of a grain boundary bubble. The idea that most of the vacancies which contribute to bubble growth originate at grain boundaries 10) is supported by the fact that grain boundary bubbles often have the
Fig.
6.
A The
thitl
foil
grain
of
irradiated
boundary
Cki-loU
bubbles
are
alloy larger
containing
0.04 at
‘$,
than
of those
which
most
He
annealed
for
lie within
the grains.
2 h at
700” C.
GRAIN
BOUNDARY
SWELLING
IN
IRRADIATED
5.
COPPER-BORON
ALLOYS
333
Discussion
5.1.
THE
CONDITIONS
The anomaly
REQUIRED
which occurs in the resistivity
results at temperatures above 700” C has been attributed to the degeneration of grain boundaries caused by growth and coalescence of bubbles situated within them. This idea has been checked exhaustively by means of electron microscopy. Furthermore, since growth can occur
Fig.
7.
A shadow
graph of a thin foil of irradiated
Cu-1OB alloy containing 0.04 wt y0 He after annealing for five hour at 700” C.
x 8000
equilibrium faceted shape, while those which lie within the grains remain spherical. The fractographs in fig. 8 (a, b, c, d, e and f) show various stages of grain boundary degeneration in a sample annealed at 900” C for one hour. Clearly the process is a progressive one in which small grain boundary bubbles grow until they touch each other. There appear to be two processes involved: 1. the growth of individual bubbles (fig. 8 a, b and c) and 2. the coalescence of bubbles (fig. 8 d, e and f). Furthermore, at an early stage of the process the bubbles appear to be flattened in the plane of the boundary (fig. 8 b, c and d) and at a late stage they develop facets which are typical of bubbles which have approached an equilibrium condition (fig. 8 e and f).
in a sample
after
all of
the
gas has
been precipitated (fig. l), bubble growth can arise from the condensation of vacancies alone. Although significant degeneration did not occur during uniform annealing at 700” C for 10 h the grain boundary bubbles appear to have an equilibrium size which is larger than that of bubbles which lie within the grains (figs. 6 and 7). This feature could represent an early stage of grain boundary degeneration which may lead to complete failure at very long annealing times. However, there does appear to be a threshhold temperature for spontaneous growth at 700” C under the conditions imposed. It may be significant that this is alittle below the minimum temperature at which rapid grain growth is observed in copper 1s). The experiments in which two samples were brought to equilibrium at 600’ C and 700” C respectively and then heated a further 100’ C (fig. 1) show that, although a high vacancy concentration is necessary to cause rapid bubble growth, it is not the only condition required. Growth which does not normally occur at 700” C can be forced to occur by a prior annealing treatment at 600” C. Growth can also be forced to occur at 700” C by annealing first at 500” C. However, prior heat treatment will not promote growth at temperatures below 700” C. Clearly, the equilibrium concentration of vacancies at 700” C is adequate for rapid bubble growth and the increase in temperature has been sufficient to upset the equilibrium condition to such an extent that the bubbles became unstable. This confirms the idea that the pressure inside a bubble is related to its equilibrium radius and
(8)
(b)
-GRAIN
BOUNDARY
SWELLING
IN
IRRADIATED
Cd)
COPPER-BOROB
ALLOYS
335
(f) Fig.
8.
A
sequence
of’ fractographs
showing
the degeneration
of’ grain boundaries
at 900” 0.
GRAIN
BOUNDARY
SWELLING
IN IRRADIATED
COPPER-BORON
nor thermal
cycling
for grain boundary tures above factors can
are necessary degeneration
700’ C, although
accelerate
337
ALLOYS
bubble
conditions at tempera-
both of growth.
these It is
surprising that a concentration of gas as low as 46 ppm is sufficient to start spontaneous grain boundary degeneration at a temperature of 800"C, but it is clear that relatively minor gas evolution
during
irradiation
can have
a
significant effect upon the properties. Since bubbles situated within the grains do not become Fig. 9. A schematic representation of grain boundary bubble growth. The black areas represent the changes which take place in the size of a growing-bubble.
that increasing the pressure, in this case by heating, causes the bubbles to grow. Another factor isolated by these experiments is that grain boundary migration is not one of the necessary conditions for swelling because significant grain growth occurs only at temperatures above 700” C during the times involved. Furthermore, the average bubble spacing within the grains is of the same order as the initial spacing of bubbles within the grain boundaries, and not lower, as would be expected if bubbles were swept up by moving boundaries or if bubbles migrated to the boundaries. The swelling process does not depend upon any special distribution, accumulation or regrouping of bubbles in the grain boundary, because the bubble distributions obtained at all temperatures between 450” C and 700” C are identical, to within a factor of 10, in copperhelium alloys heated uniformly in the absence of a steep temperature gradient 11). A close investigation of foils containing 0.01 at o/o He showed little change in the distribution of bubbles which lie within the grains after annealing for times of up to 5 h in the range of temperatures between 700” C and 900'C. Low helium foils were used to determine this because foils with a higher helium content could not be satisfactorily thinned. Neither the application of an external stress,
unstable
under the imposed
con-
ditions, it is clear that the unique conditions imposed by grain boundaries are necessary for breakaway bubble growth. 5.2.
THE
MECHANISM
OF GRAIN
BOUNDARY
SWELLING The results shown in fig. 1 suggest that bubbles formed in grain boundaries at temperatures above 700” C are unstable and continue to grow
spontaneously
by absorbing
vacancies.
At lower temperatures the bubbles reach an equilibrium size and shape, and no breakaway growth occurs unless the equilibrium is upset by, either the application of an external stress z), or a change in the thermal condition. Bubbles annealed to an equilibrium condition at 500” C, 600” C or 700” C become unstable if the temperature is raised. The most likely explanation for this behaviour lies in the relationship between the internal pressure of a spherical bubble, P, its radius, r and its surface energy y, which is given by the equation P=2ylr. When the temperature of an equilibrium bubble is raised by 100” C in the region of 700” C, its internal pressure is increased by approximately 10 y. and the bubble will tend to grow to a new equilibrium radius by absorbing vacancies. Unfortunately the bubbles do not stop growing and other factors, such as kinetic or geometric conditions, can influence the stability of grain boundary bubbles once their equilibrium has been upset. Barnes 10) has shown that the major thermal vacancy sources during bubble growth are the grain boundaries and Hull et ~~1.15)have stated
t Id
during the gro\4+h of grain boundary
voids
in creep experiments. 94 o/o of all t’hcbvacancies absorbed arrive at, the periphery of t*he void in the plane of t,he grain boundary. mechanism being grain boundary
the transport, diffusion. The
other 6 y,, enter through the bubble surface by volume diffusion from within the grains. Eelson
et crZ.1’) have calculat’ed
equilibrium
shapes for bubbles situat’ed at grain boundaries in t’erms of t,he anisotropic dist’ribution of
The fact that tllc grO\\.tll sllal)C~ is Ilot equilibrium one is demonstrat,ed calearl>-by tllca ill1
experiment in which t’he resistivity of a specimen annealed at’ 600” C aft,er a prior heat treat’ment at X00” C to produce some grain boundary failure. decreased with annealing time. These experiments
are explained
as follows.
The decrease in resist,ance which occurs during annealing at, 600” (3; is caused 1))~a progressive decrease in the grain boundary
area occupied
surface energy in fee met’als and a typical shape is shown schematically in fig. !la. Man;7
by lenticular bubbles formed at 800” C. It is thought. that the rate at which the bubble
bubbles wit,11 similar shapes were observed in t’he copper-helium s?.xtem and one of these is shown in fig. 5. The following factors should be considered in a satisfact,or? model for grain boundary swelling. If most, of t’he vacancies arrive at a bubble in the plane of the grain boundary its shape will tend to become distorted from that in fig. !)a t)o that, in fig. !tb. Unless the surface and volume diffusion are sufficient,ly rapid t’o correct. t’he shape and maintain a constant (:/cl ratio. hhe angle 0 along the boundary x--5’ will become very acute as shown in fig. 9~. Furthermore if t*his mode of growth is con t’inued. t,he rate ab which the grain boundary is consumed by bubbles is much higher than would be expect’ed for a unit increase in the volume of spherical bubbles. Another import(ant consideration is that the energy of a grain boundary is higher t,han that of t,he surrounding ma’trix and. energetically: it, is easier to form a new surface in the grain boundary than it is elsewhere. As a bubble grows larger, its peripheral surface, which lies in the boundary, increases rapidly a,nd more vacancies per unit) time can enter the bubble. The surface area of the bubble increases simultaneously and the number of atoms which must be moved to restore the equilibrium shape becomes larger, consequently it, becomes more dificult for an equilibrium shape to be realised and an extreme condition of bubble shape develops as shown in fig. 8b and schematicallS in fig. DC.
shape is readjusted by surface and volume diffusion at the lower temperature, exceeds the rat’e at which the new vacancies enter t,he bubble. Although the volume of grain boundary bubbles is not necessarily decreased, the bubbles readjust their shape from a t’hin lens to that of an equilibrium bubble. As a result’ they occupy less area in the grain boundar),. It is possible that this process is aided by t,he rcabsorption of some vacancies from the sharp angles situated around the periphery of the bubbles. This mechanism is analogous to the behaviour of voids during sinking. It follows, t#hat, although the energy of t’hc system must decrease during grain boundary bubble growt,h it> does not decrease as rapidly as it would if t’he bubbles maintained a spherical growth shape. Therefore. any model developed to explain these effec& must be based upon dynamic. rat)her than equilibrium. considorations. A bubble which lies within a grain does not, become unstable. because vacancies arrive at, random points around its surfaces and the equilibrium shape is not seriously disturbed during growt’h. One further point is that during growth. tile bubbles maintain the shape of a thin lens in the plane of the grain boundary as shown in fig. x b. c. As the bubbles approach each other, the area of grain boundary within which vacancies can be generated is reduced and the vacancy flux is reduced by competJition between bubbles. This slowing down of vacancy formation enables the bubbles to move towards an
GRAIN
equilibrium and they
BOUNDARY
SWELLING
IN IRRADIATED
shape at a late stage of the process begin
to develop
crystal
facets
COPPER-BORON
339
ALLOYS
to generate a large number of mobile vacancies,
as
the effect upon strength would be marked after
shown in fig. 8 cl, e, f. When the bubbles finally touch, the grain boundary represents a crack from which the gas can escape if there is
a much shorter annealing time, because bubble growth under the influence of stress would contribute the failure. A loss of high temperature ductility is expected even with very low
access to the surface of the specimen. Unstable growth can be started factor which upsets the equilibrium
by any of grain
boundary bubbles in the temperature range where thermal vacancies are plentiful. Hull et aZ.15) and Hyam et aZ.2) have considered conditions for void and bubble growth
the re-
spectively, in the presence of an applied tensile stress. Provided the stress lies above a critical level the bubbles will grow until they touch. In this case the driving force is supplied in part, by the applied stress. Thermal cycling can also cause grain boundary swelling because the pressure inside the bubbles is periodically increased. It is probably the first high temperature cycle which changes the bubble shape away from equilibrium and starts a process which could continue spontaneously at the high temperature.
5.3.
THE
EFFECT
TENSILE
OF SWELLING
UPON
THE
STRENGTH
It is interesting to note that although the grain boundaries begin to deteriorate after annealing for only a few minutes at 800” C, no significant change in the tensile strength, measured at 0’ C, occurs until the annealing has proceeded for more than 2 h. The 0.2 y. proof stress remains unaffected for longer times but both the UTS and ductility start to decrease. The loss of ductility corresponds with the formation of numerous very large grain boundary bubbles and the complete degeneration of some grain boundaries. It is difficult to understand why the strength does not decrease at a much earlier stage when grain boundary degeneration first begins, but it is assumed that the Griffith conditions for crack propagation are not met at the sharp edges of grain boundary bubbles. It is likely that, if the tests were carried out at a temperature sufficient
gas contents. 6. I.
Conclusions At temperatures
above 700’ C grain bounda-
ry bubbles in a copper alloy containing at o/0 of 4He grow spontaneously
0.05
until they
touch. 2. Spontaneous bubble growth can take place in the absence of grain boundary or bubble migration, bubble re-distribution, applied stress and thermal cycling. However, these factors may accelerate the process under certain conditions. 3. Resistivity mesaurement is a very sensitive technique for following grain boundary degeneration. 4. Grain boundary degeneration must reach an advanced stage before it affects the strength and ductility at 0’ C, although reduced ductility at high testing temperatures is to be expected at a much earlier stage. _ 0. Breakaway growth can occur solely by the migration of vacancies along grain boundaries after all the helium has been precipitated. after bubbles 6. Increasing the temperature have reached equilibrium can provide a sufficient driving force to initiate breakaway growth at temperatures as low as 700” C. of helium in the region of 7. Concentrations 46 ppm are sufficient to cause spontaneous grain boundary degeneration at elevated temperatures. 8. During swelling the grain boundary bubbles adopt a lenticular shape and if the temperature is lowered some of the damage can be repaired by a mechanism in which the bubbles resume an equilibrium shape.
340
F . VELA
AND
Acknowledgements The authors Atomic
to the Australian
Commission
who financed
work and gave permission They
RUSSELL
“)
are grateful
Energy
B.
are also grateful
this
for its publication.
to Professor
held with Mr. B. S. Hickman,
Dr. D. G. Walker
and Mr. I. J. Hastings during t,he course of t’his work were also invaluable.
S.
“Enrico (1965)
9
R.
E. D. Hyam (Venice, 1962)
S. Barnes,
3)
B.
A.
(U.S.A.) 4)
R.
S.
134655
Loomis Report Barnes, (1964)
J. Nucl. and 323 and
Mat.
G. D.
ANL Harwell
11 (1964)
Sumner, W.
6532
IAEA
Pracht,
135
(1962)
(UK)
AERE
Report,
Proc.
Inlern.
18 (1961)
and
of
beryllium
p. 372 School
of Physics,
861
I. J. Hastings,
J. Nucl.
Mat.
17
17 (1965)
86
30
B. Russell
R3162
and B. J. Heffernan,
Ibid,
P. Vela and B. Russell,
13
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)
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Symp. Argonne
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