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Measurements of crack sintering rates in UO2 pellets
JOURNAL
OF NUCLEAR
MATERIALS
47.(1973)
MEASUREMENTS
246-250.0
NORTH-HOLLAND
OF CRACK SINTERING
PUBLISHING
COMPANY
RATES IN UO, PELLETS
J.B. AINSCOUGH and F. RICBY UKAEA Reactor Group, Reactor Fuel Element Laboratories, Springfields, Preston PR4 ORR, U.K. Received
20 March
A feature of the metallography of irradiated UO, pellets is the predominantly radial crack pattern. Cracks form during the first rise to power if the thermal stress in the outer rim of the pellet exceeds the breaking tensile stress. In subsequent operation, provided the pellet is under compression, these cracks heal progressively outward from the centre until, when a sufficiently large power reduction occurs, new cracks open, this time from the centre. Healing takes place in two stages, crack closure followed by sintering. The rate of closure under irradiation is governed by the local creep and swelling characteristics of the fuel and is believed to be the faster of the two processes so that the rate-determining step in crack healing should be the rate at which the two faces of a crack, in contact with each other, sinter together.
1973
In order to measure crack-healing rates, specimens were prepared which incorporated a well-defined crack with matching faces of known geometric dimensions. This was achieved by cutting transverse slices, 3.43 mm thick, from annular sintered UO, pellets of nominal bore diameter 5.08 mm. A segment was then ground off the ring as shown schematically in fig. 1, leaving a minimum UO, thickness of 0.25 f 0.01 mm between the ground face and the bore. A crack was introduced, perpendicular to the ground flat surface in the plane of minimum wall thickness, by stacking a series of specimens vertically on a tungsten rod and generating a thermal stress by passing an electric current through the rod. The nominal surface area of each crack face was 0.87 mm2. Finally, a slit approximately 0.5 mm wide was cut into the ring opposite the flat
LOAD ALUMINA
ALUMINA
PUSH
ROD
GUIDE TUBE
HYDROGEN
Fig. 1. Schematic
diagram
showing
method
of load application.
J.B. Aimcough,
surface to leave a minimum wall thickness of 0.64 mm between the base of the slit and the bore surface. Afeature of the specimen design is that the matching faces of the crack are maintained in position relative to each other by the intact limb of the ring. The crack width is small (average 0.0 15 mm) and can only be seen after the specimen has been polished. A further advantage is that high pressure can be developed across the crack by relatively small applied loads positioned as shown in fig. 1. Loads, applied at the top end of the alumina push rod, are transferred to the top dead centre of the specimen, resulting in a mean normal interface pressure, assuming contact over the whole crack surface, of L/2A, where L is the applied load and A the nominal area of a crack face. Specimens were loaded while cold and then heated to the appropriate temperature in an atmosphere of flowing hydrogen with average water and oxygen con-
tents of 1 and 2 vpm respectively. In these gas conditions the O/U ratio of the specimens cannot be greater than 2.000, and on the basis of recent work [I] the oxide would be slightly hypostoichiometric. The technique used to measure the magnitude of crack sintering was essentially the reverse of that used to produce healing. A tensile stress, normal to the fully or partially healed crack, was applied to the specimen at room temperature and the load required to cause fracture was measured. Provided that some sintering has occured during the previous anneal, the applied load is again equally divided between the two limbs of the specimen but the tensile stress at the crack is now L/2A’ where A’ represents the actual sintered area. If no sintering occurred during the original test, the applied load simply imparts a bending moment to the untracked limb. An empirical relationship between the extent of crack sintering and the load necessary to
B - POINTS AND
lo-'
5
247
F. Rigby, Crack sintering rates in UO2 pellets
REPRESENTING
FULLY
NOT USED ,lN DERIVING
SINTERED
CRACKS
LINE
I
I
I
I
I
I
I
I
I
5.6
5.7
5.8
5.9
6.0
6,l
6.2
6.3
6,L
lo”/
Fig. 2. Arrhenius
T IK-‘1
plot for healing
of cracks.
J.B. Aimcough,
248
F. Rigby,
Crack sintering
cause rupture was derived by measuring the rupture load on the following types of specimen: (a) Untracked rings which had been annealed for 8 h at 1773 K in hydrogen under zero applied load. (b) Cracked rings annealed under the same conditions. (c) Untracked rings in which the thickness of the ring was reduced, in the region of the 0.25 mm wide web, from the standard 3.43 mm to 1.73,0.86,0.33 and 0 mm. These rings were annealed in the same way as (a). The measured rupture loads (L) are shown in table 1. These are, with the exception of the measurements made on completely cracked specimens, a linear function of the sintered area of the crack, with ,
L = 1.36 + 4.093 f(kg)
(1)
wherefis the fraction of crack area healed. The results obtained on the completely cracked specimens lie below the line defined by eq. (I), in agreement with theory which predicts a rapid decrease in L asf tends to zero. There is thus an area of uncertainty about 0% healing where the rupture load is difficult to define experimentally. The results of the crack-healing experiments are summarised in table 2. They comprise 11 sets of three measurements each. For each set a mean rupture load has been determined and converted to a percentage crack-healing, using eq. (1). Of these mean values, two are consistent with a negligible amount of healing, Table 1 Rupture load as a function of UO2 web thickness. Thickness of No. of specimens specimen at web (mm)
Mean load to rupture (kg)
3.43 1.73 0.86 0.33 0
5.221 3.244 2.051 1.603 0.658
19 4 4 4 20
f * f f *
1.604a) 0.826 0.873 0.559 0.185
a)One standard deviation.
while two others indicate complete sintering. The remaining seven have been used to derive an Arrhenius
type equation for the crack-sintering process. Assume the rate equation for crack-healing can be written $
= kp exp (-E/RT)
)
(2)
rates in lJO2 pellets
where p is the pressure acting at the portion of the crack surfaces in contact, E is the activation energy for the process(es) involved and R and T have their usual meanings. But if the whole crack surface comes into contact quickly so that sintering itself is the ratedetermining process, p = L/2A, so that .f=z
exp(-E/RT)
(0
(3)
Values of log (2AflLt) have been plotted against l/T in fig. 2 and from this graph (i.e. the best straight line) a rate equation f= 5.6 X IO5 pt exp (- 32000/T)
(4)
can be derived, where p is in MN/m2 and t is in hours. From eq. (4) the time for complete healing may be written as t = 1.8 X low6 exp (32OOO/T)/p
(h)
(5)
which is plotted in fig. 3 for an applied pressure of 1 MN/m2 across the crack. It has been assumed that the crack faces are in contact throughout the test and that the mean interface pressure is given by L/2A. At the instant of load application the contact pressure is less than this since some fraction of the load is required to produce the elastic displacement necessary to close the finite width of the crack. If, however, the time required for crack closure by plastic deformation is short relative to the time for healing, the calculated interface pressure will be attained shortly after load application. This means that the crack-healing rates given in table 2 are slightly lower than the true rates, but since the crack width is small, the error is believed to be negligible. Estimates of the time required for crack-healing in UC, have also been derived from post-irradiation metallography. Bridge and Banks [2] and Collins [3] have examined the crack-healing behaviour of UO, under low or medium [2] and high restraint conditions [3] respectively and derived expressions for the crackhealing rate as a function of temperature. Neither expression takes account of the pressure acting on the crack faces. Predicted healing rates are shown in fig. 3. It is now possible to get an idea of the magnitude of the pressures acting across crack faces in contact in a UC, pellet during irradiation. Thus, comparing the 1 MN/m2 line obtained from eq. (5) with that derived in ref. [2] for generally low-restraint conditions, the
J.B. Ainsco~tgh, I;: Rigby, Crack sitttcrittg rates in UOz pellets
Fig. 3. Crack-healing
time as a function
of temperature.
249
J.B. Ainscough,
250
Table 2 Crack healing T
as a function
of time, temperature
F. Rigby,
Crack sintering
rates in UOz pellets
and pressure.
_._~
W
:h)
L/2A (MN/m*)
Rupture load (kg)
1573 1573 1573
32 32 32
24.0 24.0 24.0
2.135 4.285 6.065
1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673
8 8 8 8 8 8 32 32 32 32 32 32
6.0 6.0 6.0 24.0 24.0 24.0 1.5 1.5 1.5 6.0 6.0 6.0
0.595 1.065 2.545 4.025 5.125 5.825 0.485 0.695 0.845 3.725 4.395 5.065
1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773
2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 32 32 32
6.0 6.0 6.0 24.0 24.0 24.0 1.5 1.5 1.5 6.0 6.0 6.0 24.0 24.0 24.0 1.5 1.5 1.5
0.535 1.100 1.380 2.475 2.905 6.645 1.505 1.750 1.995 2.195 6.180 8.645 6.255 6.325 6.465 1.145 1.335 3.435
average interface pressure during crack-healing at 1273 K appears to be about 1 MN/m2 but only 0.3 MN/m2 at 1473 K and 0.1 MN/m2 at 1673 K. On the other hand, the line derived for fairly high-restraint conditions suggests that the faster crack-healing rates are consistent with an interface pressure of 1 MN/m2 at about 1750 K and 3.6 MN/m2 at 1473 K. The actual interface pressure acting across a crack is a complex function of the external restraint on the fuel and of its densification and swelling rates, but values derived
% crack
Mean rupture load (kg)
4.162
74
1.402
7
4.992
94
0.675
0
4.395
80
1.005
0
4.008
70
1.750
15
5.673
100
6.348
100
1.972
20
area healed
from fig. 3 may provide an approximate likely magnitude.
guide to their
References [l]
V.J. Wheeler and I.G. Jones, J. Nucl. Mater. 42 (1972) 117. [2] D.A. Banks and D.G. Bridge, UKAEA internal document. [ 3] D.A. Collins, private communication.
OF NUCLEAR
MATERIALS
47.(1973)
MEASUREMENTS
246-250.0
NORTH-HOLLAND
OF CRACK SINTERING
PUBLISHING
COMPANY
RATES IN UO, PELLETS
J.B. AINSCOUGH and F. RICBY UKAEA Reactor Group, Reactor Fuel Element Laboratories, Springfields, Preston PR4 ORR, U.K. Received
20 March
A feature of the metallography of irradiated UO, pellets is the predominantly radial crack pattern. Cracks form during the first rise to power if the thermal stress in the outer rim of the pellet exceeds the breaking tensile stress. In subsequent operation, provided the pellet is under compression, these cracks heal progressively outward from the centre until, when a sufficiently large power reduction occurs, new cracks open, this time from the centre. Healing takes place in two stages, crack closure followed by sintering. The rate of closure under irradiation is governed by the local creep and swelling characteristics of the fuel and is believed to be the faster of the two processes so that the rate-determining step in crack healing should be the rate at which the two faces of a crack, in contact with each other, sinter together.
1973
In order to measure crack-healing rates, specimens were prepared which incorporated a well-defined crack with matching faces of known geometric dimensions. This was achieved by cutting transverse slices, 3.43 mm thick, from annular sintered UO, pellets of nominal bore diameter 5.08 mm. A segment was then ground off the ring as shown schematically in fig. 1, leaving a minimum UO, thickness of 0.25 f 0.01 mm between the ground face and the bore. A crack was introduced, perpendicular to the ground flat surface in the plane of minimum wall thickness, by stacking a series of specimens vertically on a tungsten rod and generating a thermal stress by passing an electric current through the rod. The nominal surface area of each crack face was 0.87 mm2. Finally, a slit approximately 0.5 mm wide was cut into the ring opposite the flat
LOAD ALUMINA
ALUMINA
PUSH
ROD
GUIDE TUBE
HYDROGEN
Fig. 1. Schematic
diagram
showing
method
of load application.
J.B. Aimcough,
surface to leave a minimum wall thickness of 0.64 mm between the base of the slit and the bore surface. Afeature of the specimen design is that the matching faces of the crack are maintained in position relative to each other by the intact limb of the ring. The crack width is small (average 0.0 15 mm) and can only be seen after the specimen has been polished. A further advantage is that high pressure can be developed across the crack by relatively small applied loads positioned as shown in fig. 1. Loads, applied at the top end of the alumina push rod, are transferred to the top dead centre of the specimen, resulting in a mean normal interface pressure, assuming contact over the whole crack surface, of L/2A, where L is the applied load and A the nominal area of a crack face. Specimens were loaded while cold and then heated to the appropriate temperature in an atmosphere of flowing hydrogen with average water and oxygen con-
tents of 1 and 2 vpm respectively. In these gas conditions the O/U ratio of the specimens cannot be greater than 2.000, and on the basis of recent work [I] the oxide would be slightly hypostoichiometric. The technique used to measure the magnitude of crack sintering was essentially the reverse of that used to produce healing. A tensile stress, normal to the fully or partially healed crack, was applied to the specimen at room temperature and the load required to cause fracture was measured. Provided that some sintering has occured during the previous anneal, the applied load is again equally divided between the two limbs of the specimen but the tensile stress at the crack is now L/2A’ where A’ represents the actual sintered area. If no sintering occurred during the original test, the applied load simply imparts a bending moment to the untracked limb. An empirical relationship between the extent of crack sintering and the load necessary to
B - POINTS AND
lo-'
5
247
F. Rigby, Crack sintering rates in UO2 pellets
REPRESENTING
FULLY
NOT USED ,lN DERIVING
SINTERED
CRACKS
LINE
I
I
I
I
I
I
I
I
I
5.6
5.7
5.8
5.9
6.0
6,l
6.2
6.3
6,L
lo”/
Fig. 2. Arrhenius
T IK-‘1
plot for healing
of cracks.
J.B. Aimcough,
248
F. Rigby,
Crack sintering
cause rupture was derived by measuring the rupture load on the following types of specimen: (a) Untracked rings which had been annealed for 8 h at 1773 K in hydrogen under zero applied load. (b) Cracked rings annealed under the same conditions. (c) Untracked rings in which the thickness of the ring was reduced, in the region of the 0.25 mm wide web, from the standard 3.43 mm to 1.73,0.86,0.33 and 0 mm. These rings were annealed in the same way as (a). The measured rupture loads (L) are shown in table 1. These are, with the exception of the measurements made on completely cracked specimens, a linear function of the sintered area of the crack, with ,
L = 1.36 + 4.093 f(kg)
(1)
wherefis the fraction of crack area healed. The results obtained on the completely cracked specimens lie below the line defined by eq. (I), in agreement with theory which predicts a rapid decrease in L asf tends to zero. There is thus an area of uncertainty about 0% healing where the rupture load is difficult to define experimentally. The results of the crack-healing experiments are summarised in table 2. They comprise 11 sets of three measurements each. For each set a mean rupture load has been determined and converted to a percentage crack-healing, using eq. (1). Of these mean values, two are consistent with a negligible amount of healing, Table 1 Rupture load as a function of UO2 web thickness. Thickness of No. of specimens specimen at web (mm)
Mean load to rupture (kg)
3.43 1.73 0.86 0.33 0
5.221 3.244 2.051 1.603 0.658
19 4 4 4 20
f * f f *
1.604a) 0.826 0.873 0.559 0.185
a)One standard deviation.
while two others indicate complete sintering. The remaining seven have been used to derive an Arrhenius
type equation for the crack-sintering process. Assume the rate equation for crack-healing can be written $
= kp exp (-E/RT)
)
(2)
rates in lJO2 pellets
where p is the pressure acting at the portion of the crack surfaces in contact, E is the activation energy for the process(es) involved and R and T have their usual meanings. But if the whole crack surface comes into contact quickly so that sintering itself is the ratedetermining process, p = L/2A, so that .f=z
exp(-E/RT)
(0
(3)
Values of log (2AflLt) have been plotted against l/T in fig. 2 and from this graph (i.e. the best straight line) a rate equation f= 5.6 X IO5 pt exp (- 32000/T)
(4)
can be derived, where p is in MN/m2 and t is in hours. From eq. (4) the time for complete healing may be written as t = 1.8 X low6 exp (32OOO/T)/p
(h)
(5)
which is plotted in fig. 3 for an applied pressure of 1 MN/m2 across the crack. It has been assumed that the crack faces are in contact throughout the test and that the mean interface pressure is given by L/2A. At the instant of load application the contact pressure is less than this since some fraction of the load is required to produce the elastic displacement necessary to close the finite width of the crack. If, however, the time required for crack closure by plastic deformation is short relative to the time for healing, the calculated interface pressure will be attained shortly after load application. This means that the crack-healing rates given in table 2 are slightly lower than the true rates, but since the crack width is small, the error is believed to be negligible. Estimates of the time required for crack-healing in UC, have also been derived from post-irradiation metallography. Bridge and Banks [2] and Collins [3] have examined the crack-healing behaviour of UO, under low or medium [2] and high restraint conditions [3] respectively and derived expressions for the crackhealing rate as a function of temperature. Neither expression takes account of the pressure acting on the crack faces. Predicted healing rates are shown in fig. 3. It is now possible to get an idea of the magnitude of the pressures acting across crack faces in contact in a UC, pellet during irradiation. Thus, comparing the 1 MN/m2 line obtained from eq. (5) with that derived in ref. [2] for generally low-restraint conditions, the
J.B. Ainsco~tgh, I;: Rigby, Crack sitttcrittg rates in UOz pellets
Fig. 3. Crack-healing
time as a function
of temperature.
249
J.B. Ainscough,
250
Table 2 Crack healing T
as a function
of time, temperature
F. Rigby,
Crack sintering
rates in UOz pellets
and pressure.
_._~
W
:h)
L/2A (MN/m*)
Rupture load (kg)
1573 1573 1573
32 32 32
24.0 24.0 24.0
2.135 4.285 6.065
1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673
8 8 8 8 8 8 32 32 32 32 32 32
6.0 6.0 6.0 24.0 24.0 24.0 1.5 1.5 1.5 6.0 6.0 6.0
0.595 1.065 2.545 4.025 5.125 5.825 0.485 0.695 0.845 3.725 4.395 5.065
1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773 1773
2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 32 32 32
6.0 6.0 6.0 24.0 24.0 24.0 1.5 1.5 1.5 6.0 6.0 6.0 24.0 24.0 24.0 1.5 1.5 1.5
0.535 1.100 1.380 2.475 2.905 6.645 1.505 1.750 1.995 2.195 6.180 8.645 6.255 6.325 6.465 1.145 1.335 3.435
average interface pressure during crack-healing at 1273 K appears to be about 1 MN/m2 but only 0.3 MN/m2 at 1473 K and 0.1 MN/m2 at 1673 K. On the other hand, the line derived for fairly high-restraint conditions suggests that the faster crack-healing rates are consistent with an interface pressure of 1 MN/m2 at about 1750 K and 3.6 MN/m2 at 1473 K. The actual interface pressure acting across a crack is a complex function of the external restraint on the fuel and of its densification and swelling rates, but values derived
% crack
Mean rupture load (kg)
4.162
74
1.402
7
4.992
94
0.675
0
4.395
80
1.005
0
4.008
70
1.750
15
5.673
100
6.348
100
1.972
20
area healed
from fig. 3 may provide an approximate likely magnitude.
guide to their
References [l]
V.J. Wheeler and I.G. Jones, J. Nucl. Mater. 42 (1972) 117. [2] D.A. Banks and D.G. Bridge, UKAEA internal document. [ 3] D.A. Collins, private communication.