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Burst investigation on zircaloy-4 claddings in inert environment
Annals of Nuclear Energy 69 (2014) 292–300
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Burst investigation on zircaloy-4 claddings in inert environment Mohd. Kaleem Khan a,⇑, Manabendra Pathak a, Siddharth Suman a, Anuj Deo b, Ritu Singh b a b
Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, India Atomic Energy Regulatory Board, Mumbai, India
a r t i c l e
i n f o
Article history: Received 2 May 2013 Received in revised form 4 January 2014 Accepted 21 February 2014 Available online 15 March 2014 Keywords: Claddings Ballooning Burst stress Burst temperature Semi-empirical correlation
a b s t r a c t An extensive burst investigation has been carried out on the zircaloy-4 claddings in an inert environment to simulate clad burst during a postulated loss-of-coolant-accident (LOCA) conditions. The parameters varied during the burst experiments were heating rate and internal overpressure. The temperature, internal overpressure and ballooning data were monitored online and recorded during the heating process of burst specimen. In addition, post-experiment measurements were also conducted on the burst specimen to determine various burst parameters–burst strains and burst stress. A semi-empirical correlation was developed to predict the burst stress for a given burst temperature. A reasonable agreement between the predicted and experimental data has been observed. The proposed correlation was also compared with available established correlation for steam environment. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The zircaloy-4 claddings are used as container of fuel pellets in nuclear reactors. These tubes also act as a barrier between the coolant and the fuel. The heat produced due to fission gets transferred to the coolant through these tubes. During loss of coolant accident (LOCA) scenario, the coolant supply is affected and as such the clad tube surface temperature rises. The continuous rise in temperature and consequent rise in fission gas pressure can cause extensive deformation of the clad tubes. As a result, the clad ballooning is accompanied with axial contraction. Another consequence of ballooning deformation is the thinning of the tube, which makes it difficult to withstand the excessive stresses causing the tube to burst. Further, heating of zircaloy clad tube causes a change in microstructure at 1085 K temperature from a-phase (hcp) to b-phase (bcc) at 1248 K. In fact, within temperature range 1085–1248 K both a and b phases co-exist. The change in phase causes a change in material properties of clad tube. An exhaustive review of literature by Alam et al. (2011) suggests that a lot of work has already been carried out to investigate the clad failure phenomena due to LOCA. In postulated LOCA experiments, the clad specimens are usually pressurized from inside by an inert gas either by helium or argon. The clad burst experiments are generally performed in various outside environments of air, inert gas, steam and vacuum. The operating variables are internal overpressure and heating rate or temperature. One of ⇑ Corresponding author. Tel.: +91 612 2552019; fax: +91 612 2277383. E-mail address: [email protected] (M.K. Khan). http://dx.doi.org/10.1016/j.anucene.2014.02.017 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
the ends of the clad specimen is kept unconstrained to allow the free contraction of the specimen during ballooning. Some of the important studies have been listed in Table 1. Such studies are helpful in formulating or improving the safety regulations of the nuclear reactor. The output of these studies also serves as valuable inputs for the designing of new reactors. From Table 1, it is clear that the burst studies are either conducted in constant temperature (isothermal) conditions or in constant heating rate conditions. Erbacher et al. (1982) performed an extensive experimental investigation on the bursting of zircaloy-4 cladding in steam environment. They also proposed a correlation for the burst stress as a function of burst temperature and oxygen content. Erbacher et al. (1982) and Neitzel and Rosinger (1980) developed the burst criterion of Zircaloy fuel claddings. The developed criterion was validated with the burst data of various researchers. Ferner and Rosinger (1985) found that azimuthal temperature difference played an important role in the ballooning deformation of the clad tube. Arai et al. (1987) developed the Larsen–Miller parameter (LMP) correlation for the combined data of isothermal and high thermal transient tests. They also demonstrated the suitability of LMP approach in predicting the cladding failure for wide range of time–temperature conditions. Zhou et al. (2004) performed short term rupture study on zircaloy clad tubes and they found that the burst test data followed the Larson–Miller parameter approach. Kim et al. (2004) conducted a study to see the changes in microstructure due to variation in thermal transients and temperature of the specimen. They found that the phase transformation from a-phase to b-phase played an important role in deformation of zircaloy-4. Seok et al. (2011) analyzed the creep data obtained
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Nomenclature C h p R t T TCE UCE
r e
circumference, m clad tube thickness, m internal overpressure, Pa clad tube radius, m time, s temperature, °C or K total circumferential elongation uniform circumferential elongation
stress, MPa strain
Subscripts B burst r radial direction o initial conditions h circumferential direction
Greek letters g heating rate, K/s
from the burst tests on ZIRLO claddings and ring-creep tests. The outcomes of the two tests were found to complement each other. Fewer studies are also available for zircaloy-4 clad tube bursting in outside inert atmosphere. The purpose of such studies is to set a reference for the zircaloy-4 cladding bursting in an outside oxidizing (steam) environment. One such study was conducted by Emmerich et al. (1969). They conducted experiments for very low range of internal overpressure as well as heating rate. Most recently, Khan et al. (2013) have developed a burst criterion for zircaloy-4 clad tubes in inert atmosphere. Keeping in view the importance of clad failure under LOCA conditions, there is a need to develop burst equation for zircaloy-4 clad tubes used in Indian pressurized heavy water reactors (PHWRs) for an outside inert environment. The objective of the present work is to study the effect of internal overpressure and heating rate on the ballooning and subsequent bursting of the clad tube and to evolve a semi-empirical burst stress correlation (burst equation). It has also been observed that the transient clad ballooning data is rarely available in open literature. In the present work, an attempt has been made to capture the ballooning data in terms of tube wall displacement. The tracking data may be of use for validation of various transient numerical clad deformation models.
pressurize test specimen (zircaloy-4 clad tube) at a given pressure, an argon gas cylinder with control valve is used. The internal overpressure has been monitored with the help of a pressure gauge and a pressure transducer. The test specimen is heated with the help of 64 kV A silicon controlled rectifier. The high magnitude direct current is transmitted to the specimen through copper bus bars and copper clamps. The magnitude of current passing through the specimen sets the desired rate of heating. Ungrounded K-type sheathed thermocouples (2 Nos.) have been spot welded on the outer surface of the clad specimen to measure the specimen temperature. To capture the ballooning of the heated specimen at three different axial positions, a frame holding three non-contact type displacement transducers (accuracy ±10 lm) has been fabricated. The wall displacement of the tube is transmitted to the displacement sensors with the help of extremely light ceramic rod-block assembly, shown in Fig. 2. One end of each ceramic rod has been fitted to a ceramic block placed on clad specimen while the other end has been glued to a small piece of galvanized iron sheet as the displacement transducers can only detect metals. The guide mechanism, consisting of short length copper tubes, allows the ceramic rods to move vertically upward towards the transducers, as shown in Fig. 2. An additional argon gas cylinder is used to conduct the burst experiments in inert atmosphere. The argon gas is purged through a perforated tube inside the enclosure right below the clad specimen, as shown in Fig. 1. This ensures the argon rich atmosphere near the clad specimen. Moreover, the purging is started a few
2. Experimental setup and procedure The schematic diagram of the experimental setup is shown in Fig. 1. It consists of a strong mild steel enclosure to carry out the clad burst safely at a required pressure and heating rate. To
Table 1 Some important experimental studies on clad failure. Author (s) (year)
Clad material
Inside clad fluid
Outside environment
Temperature conditions
Range of parameters
Emmerich et al. (1969)
Zircaloy-4
Helium
Argon
Constant heating rate
Erbacher et al. (1982)
Zircaloy-4
Helium
Steam
Constant heating rate
Ferner and Rosinger (1985)
Zircaloy-4
Inert gas
Steam
Constant heating rate
Arai et al. (1987)
Zircaloy-2
Argon
Atmosphere
Both constant heating rate and isothermal
Zhou et al. (2004)
Argon
–
Constant temperature (isothermal)
Kim et al. (2004)
Zircaloy-4 and Nb-modified Zircaloy-4 Zircaloy-4
Argon
Steam
Seok et al. (2011)
ZIRLO
Argon
Atmosphere
Both constant heating rate and isothermal Constant temperature (isothermal)
Khan et al. (2013)
Zircaloy-4
Argon
Argon
Constant heating rate
p = 2.5–11.9 bar g = 0.3–23.1 K/s p = 10–140 bar g = 1–30 K/s p = 3–29 bar g = 1–25 K/s p = 9.8–147.1 bar g = 5–200 K/s T = 923, 973 and 1073 K T = 723–773 K rB = 40–100 MPa p = 100–600 bar g = 1–100 K/s T = 365–570 °C rB = 40–520 MPa p = 20–80 bar g = 17.6–81.1 K/s
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Fig. 1. Schematic diagram of the experimental setup.
Fig. 2. Burst specimen and ballooning tracking mechanism.
minutes before switching ON the rectifier so that the entire enclosure is filled with argon. A vent is provided at the top of the enclosure to evacuate the air and excess argon. To allow free contraction of the specimen during ballooning, the free end of the clad specimen is attached to the bus bar by high capacity electric cable, also shown in Fig. 2. The cable also provides support to the free end and, thus, keeps the specimen straight
during heating. To capture the bursting phenomena, the video recording has been done using a high definition handycam as well as high speed camera. All the sensors have been calibrated prior to experimentation. The online temperature, pressure and ballooning data have been acquired and stored in the computer using high speed data acquisition system with LABVIEW 2009 software. Prior to experimentation, all the sensors have been calibrated. The rectifier has also been calibrated for different heating rates. The amount of current passing through the clad specimen corresponds to a particular heating rate. The heating rate is kept constant as far as possible by operating the rectifier knob. A 20-point calibration in the range 25–1000 °C has been performed on each thermocouple using a standard high temperature calibrator covering the entire range of temperature reached during burst experiments. The clad tube is initially pressurized to a required value with the help of pressure gauge. For continuous acquisition of pressure data, a pressure transducer has also been placed on the connecting line near the gauge. The pressure sensors (gauge and transducer) have been calibrated with the dead weight pressure tester. The displacement transducers’ outputs have been calibrated for different known positions of a metal target. The experimental procedure involves three major activities, viz. specimen preparation, leak testing and the burst experiment. The sample preparation required taking a fresh clad tube specimen of required length, spot welding of two K-type ungrounded sheathed thermocouple having 0.5 mm sheath diameter on the outer surface of clad specimen. The two thermocouples were used to capture the temperature data without fail, in case one of them comes out during ballooning. Since tube thickness is only 0.41 mm, cutting
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M.K. Khan et al. / Annals of Nuclear Energy 69 (2014) 292–300 Table 2 Operating parameters.
Table 3 Uncertainties in the measured/computed parameters.
Parameter
Range
Parameter
Accuracy/uncertainty
Clad tube outer diameter, mm Clad tube wall thickness, mm Clad tube total length, mm Clad tube effective heating length, mm Internal overpressure, bar Heating rates, K/s
13.08 0.41 245 200
Temperature Displacement Pressure Clad diameter Clad thickness Clad burst circumference Burst stress Burst strain
±1.5 °C ±10 lm 0.2% FS 0.01 mm 0.01 mm 1 mm 2.4944% 0.2518%
Wall displacement, mm
20, 40, 60 and 80 Low (17.6–26.6), medium (40.3–55.9) and (61.4–81.1) 0–10
threads was not feasible option. The ferrule joint was made on the open end of the clad specimen by using a brass ferrule (ring) and brass nut-connector assembly. The specimen was placed inside the enclosure and connected to the line to having argon cylinder. The nut on the clad specimen was tightened to the connector on connecting line such that the ferrule, between the connector and brass nut, gripped the clad specimen firmly. The joint was tested for leaks at pressures the burst experiment was supposed to be performed. The burst experiment began after making sure that all the sensors output were properly read in the data acquisition system. The required direct current was supplied (to achieve a particular heating rate) to the specimen by operating the rectifier knob. The temperature started rising with the switching on of rectifier. After reaching a certain value of temperature, the clad specimen ballooned and subsequently burst. The ballooning was tracked in most of the experiments. The data was stored in the computer for further analyses. The values of operating parameters have been mentioned in Table 2. Three different ranges of heating rates were applied, signified by low, medium and high categories and four different values of internal overpressure have been selected. The choice of loading conditions (internal overpressure and heating rate) is based on the literature reviewed and as per the requirements of the funding agency. The temperature, pressure and displacement data for given combination heating rate and internal overpressure were recorded. Three experiments were conducted for each combination of heating rate and overpressure. Thus, a total of 36 test experiments were conducted (a product of number of heating rates (3), number of internal overpressures (4) and repeatability (3)). Table 3 presents uncertainty in measured and computed parameters.
3. Experimental observations The experiments have been designed to monitor and store the online temperature, pressure and ballooning data as mentioned in the previous section. However, the quantities like burst strains (radial and circumferential both) and burst stress have been determined by conducting post-burst measurements. The uniform and total circumferential elongations are the measure of uniform and localized ballooning, respectively. The uniform circumferential
elongation measurement has been done on the specimen where the tube has undergone uniform ballooning. Likewise, the total circumferential elongation and burst strain measurements have been done at the ballooning site. The uniform and total circumferential elongations, in percent, are computed from the following relation:
UCE or TCE ½% ¼
C2 C1 100 C1
ð1Þ
where C1 is the initial circumference of clad specimen and C2 is the final circumference at uniform ballooning site for the uniform circumferential elongation (UCE) or localized ballooning site for the total circumferential elongation (TCE), as shown in Fig. 3. The consequence of ballooning deformation is increase in tube diameter along with the decrease in tube thickness. The engineering circumferential burst strain is given by
eh;B ¼
RB Ro ¼ TCE Ro
ð2Þ
where Ro and RB are the initial clad tube radius and clad tube radius at the burst location, respectively. The circumferential strain is, in fact, same as the total circumferential elongation. The burst circumference has been measured using a thread, shown in Fig. 4(a). The burst circumference is equal to the length of thread wrapped around the periphery of clad specimen at the burst location excluding burst opening. The clad tube radius at burst location has been determined by dividing the circumference by 2p. The engineering radial burst strain is given by
er;B ¼
hB ho ho
ð3Þ
where ho and hB are average clad tube thickness before and after the burst at the burst location, respectively. To measure the clad thickness at the bursting site, small piece/fragment from each burst sample is cut and its thickness is measured using screw gauge, Fig. 4(b). Another important parameter which is very useful in the burst study is the burst stress. It is defined as the hoop or circumferential stress at the time of burst and is given by
rB ¼ ro
pB ð1 þ eh;B Þ2 po
ð4Þ
where pB and po are burst and initial values of internal overpressures (Erbacher et al., 1982).
Fig. 3. Burst specimen.
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Fig. 4. (a) Burst circumference measurements and (b) thickness measurements.
The initial stress (ro) is computed using Eq. (5),
ro ¼
po Ro ho
ð5Þ
where po, Ro and ho are the initial values of internal overpressure, clad radius and clad thickness, respectively. The photographs of burst specimens for different internal overpressure and heating rates have been shown in Figs. 5 and 6. As a common observation all the burst specimens have been found to bend during the bursting of specimen (visible in Figs. 5(b) and 6(c)). This happens due to the reaction caused by rushing out of argon gas through burst opening. Apparently, the bending is more for higher internal overpressures. The reason may be attributed to the fact that the reaction of gases with higher pressure rushing out of the tube at the burst opening will be higher. Another common observation is localized ballooning at multiple sites. These two observations are irrespective of heating rate and internal overpressure. It has also been observed that the tube starts contracting axially with the onset of ballooning which makes the rupture opening to orient in the vertical direction. Fig. 5 shows the burst specimens for same heating rate of about 50 K/s and three different internal overpressures of 19.2 bar, 39.8 bar and 60 bar. It can be seen that the opening size is larger for higher internal over pressures. Also, the rupture opening becomes uneven for higher internal overpressures. In fact at low internal overpressure, the tearing of the tube is aligned axially. However, at higher internal overpressures, the rupture opening is more in circumferential direction.
Fig. 5. Burst specimen for constant heating rate and different internal overpressure.
Fig. 6. Burst specimen for constant internal overpressure and different heating rate.
4. Results and discussion As mentioned earlier, the heating rate is maintained constant as far as possible. The clad specimen is uniformly heated by the flow of direct current through it. Fig. 7 has been drawn for a particular data set (po = 80 bar and g = 66 K/s) to show the variation in temperature and pressure with time. The temperature varies almost linearly with time, which is an evidence of attainment of near constant heating rate. On the other hand, the fluctuations in pressure are observed during heating process. This may be attributed to the hyper-sensitivity of the pressure sensor or it may be due to noise. Despite of these pressure fluctuations, an increasing trend is visible with the rise in temperature till the clad specimen bursts. The burst time, burst temperature and burst pressure can easily be located on the diagram, as shown in Fig. 7. The ballooning data could not be tracked for all 36 experimental data sets with the arrangement shown in Fig. 2 in the previous section. The ballooning rate has been presented in terms of wall displacement of clad specimen at ballooning site. The effect of internal overpressure and heating rate has been presented separately in Figs. 8 and 9 respectively. Fig. 8 has been drawn to present the ballooning pattern for nearly 20 bar internal overpressure and for three different heating rates, 23.6 K/s, 51.5 K/s and 68.7 K/s. Other than the obvious observation that lower heating rates require more time for the clad specimen to burst, it has also been observed that in each case the tube first undergoes uniform ballooning followed by localized ballooning leading to bursting. Further, the tube exhibits a slight downward movement during the heating process followed by a sudden contraction (shown as a dip in each curve) immediately before the onset of localized
M.K. Khan et al. / Annals of Nuclear Energy 69 (2014) 292–300
297
Fig. 7. Variation of temperature and pressure during heating of clad specimen.
Fig. 8. Ballooning deformation for constant internal overpressure and different heating rate.
Fig. 9. Ballooning deformation for constant heating rate and different internal overpressure.
ballooning, which also signifies the beginning of plastic instability. The slight downward movement (sagging) may be the result of deformation caused during heating by the weight of copper clamps fixed at each end provided for continuous electric heating of
specimen. This slight downward movement of the tube during heating makes it impossible to track uniform ballooning online. Hence, from the present arrangement the uniform ballooning could not be tracked. However, for the determination of uniform ballooning, post experiment measurements were conducted on each burst specimen. A similar dip in the strain curve prior to the onset of plastic instability was observed in the Lin (1977) analytical model. During the localized ballooning, the tube wall moves upward and as such the curves become vertically straight. The effect of heating rate for a constant internal overpressure is that the burst time reduces with the increasing heating rate. In fact, the burst time reduces more as heating rate is increased from 23.6 to 51.5 K/s than that when it is increased from 51.5 to 68.7 K/s. The reduction in burst time is not proportional to the corresponding increase in heating rate. To see the effect of internal overpressure for constant heating rate, Fig. 9 has been drawn. The heating rate is fixed around 22– 23 K/s and the internal overpressure is varied from 20 to 60 bar. The burst time reduces with increasing internal overpressure. It can also be seen that when the internal overpressure is increased from 20 to 40 bar and from the 40 to 60 bar the reduction in burst time is almost same. The reduction in burst time is almost proportional to the increase in internal overpressure. The reason being is that the internal pressurization of the tube causes an increase in the magnitude of stresses developed. As a result, the deformation will begin earlier in the tubes with high internal overpressure. Also, the dip in the curve is more for higher internal overpressures. Fig. 10 shows a glimpse of experimental burst data of all the 36 test runs on a plot of burst temperature vs burst time for different heating rates and internal overpressures. The data in the graph for low, medium and high heating rates have been highlighted by dividing the graph in three zones using vertical dotted lines. For any heating rate, the burst temperature decreases with increase in internal overpressure. It is due to the larger magnitude of initial stresses developed due to higher internal overpressure. Also, the burst temperature decreases with decrease in heating rate for given internal overpressure, shown by the best fit lines. However, the effect of heating rate is not as significant as the effect of internal overpressure. This reduction may be attributed to the fact that slower heating rate will take longer time for the tube to reach burst temperature. Further higher heating rate would induce high rate of increase in thermal stresses in the material. Fig. 11 has been drawn to see the effect of initial stress on the burst temperature. The initial stress is developed due to the internal pressurization of clad tube specimen. For any heating rate, the
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Fig. 10. Burst temperature vs burst time.
Fig. 12. Burst strain vs burst temperature.
reduction in burst temperature is observed with the increase in initial stress. At low pressure, the initial stress is low and accordingly the tube will sustain higher temperature before it collapses. Further at lower pressures (20 bar and 40 bar with low and medium heating rates), the tube undergoes a phase change from a-phase (hcp) to the mixed (a + b)-phase (bcc + hcp). The phase change may have some effect on the deformation leading to bursting. At higher pressures (40 bar with high heating rate, 60 bar and 80 bar), on the other hand, the value of initial stress is high; the tube collapses earlier at a lower value of temperature within a-phase. The similar variation in burst temperature with initial stress was also reported by Neitzel and Rosinger (1980). In Fig. 12, the burst strains in circumferential and radial directions have been plotted against the burst temperature. The burst strain is positive in circumferential direction due to ballooning of the tube whereas it is negative in radial direction due to thinning of the tube, prior to bursting. The low pressure data (20 bar and 40 bar with low and medium heating rates) lies in the mixed (a + b) phase while for other internal overpressures (i.e., 40 bar with high heating rate, 60 bar and 80 bar), the burst data lies in a-phase. In a-region, with burst temperature, the circumferential burst strain increases whereas radial burst strain decreases. In fact, higher the pressure, smaller is the circumferential burst strain and greater is the radial burst strain (shown by best fit lines). The reason may be that at higher pressure the clad tube material more stressed causing the tube to burst earlier. The ballooning deformation of the tube would, thus, be restricted. Further, the stresses induced are large and, thus, less time is required for the clad to burst.
However, in the mixed (two) phase (a + b) region, the burst strain in each direction decreases with burst temperature as the material properties change with the change in phase. The variation of circumferential burst strain with burst temperature is in-line with the Erbacher et al. (1982) findings. However, they did not discuss the radial burst strain variation with burst temperature.
Fig. 11. Burst temperature vs initial stress.
5. Burst correlation One of the important aspects of the present study is to develop a correlation to predict the burst stress for a given burst temperature. The burst stress is calculated for all the 36 data sets using Eq. (4). The burst stress is then plotted against the burst temperature, as shown in Fig. 13. It can be seen that there is a decrease in burst stress with burst temperature. Neitzel and Rosinger (1980) proposed that for the clad burst in an inert environment, the burst stress and the burst temperature can be related by an exponential decay function given by
rB ¼ a expðbT B Þ
ð6Þ
where constants a and b have been determined by conducting the regression analysis on the burst data. For different phases, the values of constants are found to be different and they have been mentioned below in Table 4. The constants of Erbacher et al. (1982) correlation have also been mentioned in the table. Also, in the mixed (two) phase region burst stress shows strong temperature dependence as compared to single phase region.
Fig. 13. Burst stress vs burst temperature.
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M.K. Khan et al. / Annals of Nuclear Energy 69 (2014) 292–300 Table 4 Values of constants.
Table 5 Comparison of operating parameters.
Correlation
Phases
Present correlation (inert environment) Erbacher et al. (1982) correlation (steam environment)
a (TB < 1085 K) a + b (1085 K < TB < 1248 K) a (TB < 1085 K) a + b (1085 K < TB < 1248 K)
Constants a
b
989.2 161572965.4 830 3000
0.0017 0.0127 0.001 0.003
Operating parameters
Present study
Erbacher et al. (1982) study
Clad material Clad tube dimensions
Zircaloy-4 OD = 13.08 mm ho = 0.41 mm Argon gas (inert) 17.6–81.1 K/s 20–80 bar
Zircaloy-4 OD = 10.75 mm ho = 0.725 mm Steam environment 1–30 K/s 10–140 bar
Outside environment Range of heating rate Range of internal over pressure
The mean percentage deviation has been computed for both the correlations using the following equation:
Mean percentage deviation ¼
N 1X rB;predicted;i rB;actuali 100 N i¼1 rB;actual;i ð8Þ
Fig. 14. Predicted burst stress vs actual burst stress.
In order to compare the burst stress predicted by the proposed correlation with the experimental burst stress, Fig. 14 has been drawn. The burst stress predicted by the proposed correlation is in good agreement with the experimental burst stress as 61% predicted burst stress data lies in the error band of ±10%. However, 83% of the predicted burst stress data lies in the error band of ±20%. In Fig. 15, the proposed correlation has been compared with already established correlation of Erbacher et al. (1982). The constants for the Erbacher et al. (1982) correlation have already been mentioned in Table 4. The percentage deviation appearing in Fig. 15 is evaluated using the following equation:
rB;predicted rB;actual Percentage deviation ¼ 100 rB;actual
ð7Þ
It is evident from Fig. 15 that Erbacher et al. (1982) correlation overpredicts the burst stress. The percentage deviation for the proposed correlation mostly lies in the range of ±50% compared to the percentage deviation for the Erbacher et al. (1982) correlation which lies approximately in the range 50% to 150%.
The mean percentage deviation for the proposed correlation is 14.2 whereas for Erbacher et al. (1982) correlation is 65. The reason for the large deviation in the prediction of two correlations may be attributed to the difference in operating conditions in which the two studies were conducted, as mentioned in Table 5. The major reason for high prediction of burst stress by Erbacher et al. (1982) correlation is that the study was conducted on thicker clad tube which can resist more stress prior to burst. Another important reason is that Erbacher et al. (1982) study was conducted in steam environment. Clad tube heating in steam environment accompanied by the oxidation of the outside surface. The oxidation does have an effect on clad tube ballooning and bursting. In fact, the Erbacher et al. (1982) burst stress correlation has a factor for oxidation content in its expression, which has been ignored in this comparison.
6. Conclusions Following conclusions can be drawn from the present study: The online ballooning is successfully captured for most of the clad burst experiments. The tube undergoes an axial contraction during ballooning and bursting. Also the rushing of gases from the burst opening causes the tube to bend. The transient ballooning data obtained in the present work can be used by the researchers for validation of analytical or numerical models. For the burst in a-phase, the circumferential burst strain increases and the radial burst strain decreases with the increase in burst temperature whereas for the burst in (a + b)-phase, both circumferential as well as radial burst strains decrease with the increase in burst temperature. A semi empirical correlation has been proposed for the prediction of burst stress as function of burst temperature. The predicted 83 percent burst stress data lie in the error band of ±20 percent from the proposed correlation. The proposed correlation is also compared with Erbacher et al. (1982) correlation. The mean percentage deviation for proposed correlation is 14.2 whereas for Erbacher et al. (1982) correlation it is 65.
Acknowledgments
Fig. 15. Comparison between the predictions from the proposed correlation and the Erbacher et al. (1982) correlation.
We sincerely acknowledge Atomic Energy Regulatory Board (AERB) and Nuclear Fuel Complex (NFC) India, for providing the support needed to carry out the present work.
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Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.anucene.2014. 02.017.
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Erbacher, F.J., Neitzel, H.J., Rosinger, H.E., Schmidt, H., Weihr, K., 1982. Burst criterion of zircaloy fuel claddings in a loss-of-coolant accident. ASTM-STP 754, 271–283. Ferner, J., Rosinger, H.E., 1985. The effect of circumferential temperature variation on fuel cladding failure. J. Nucl. Mater. 132, 167–172. Khan, M.K., Pathak, M., Deo, A., Singh, R., 2013. Burst criterion for zircaloy-4 cladding in an inert environment. Nucl. Eng. Des. 265, 886–894. Kim, J.H., Lee, M.H., Choi, B.K., Jeong, Y.H., 2004. Deformation of zircaloy-4 cladding during a LOCA Transient up to 1200 °C. Nucl. Eng. Des. 234, 157–164. Lin, E.I.H., 1977. Analysis of the ballooning deformation of an internally pressurized thin-wall tube during fast thermal transients. In: 4th SMIRT Conference, San Francisco, USA. Neitzel, H.J., Rosinger H.E., 1980. The development of a burst criterion for zircaloy fuel cladding under LOCA conditions, KfK2893 AECL-6420. Seok, C.S., Marple, B., Song, Y.J., Gollapudi, S., Charit, I., Murty, K.L., 2011. High temperature deformation characteristics of ZIRLO™ tubing via ring-creep and burst tests. Nucl. Eng. Des. 241, 599–602. Zhou, Y., Devarajan, B., Murty, K.L., 2004. Short term rupture studies of zircaloy-4 tubing using closed-end internal pressurization. Nucl. Eng. Des. 228, 3–13.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Burst investigation on zircaloy-4 claddings in inert environment Mohd. Kaleem Khan a,⇑, Manabendra Pathak a, Siddharth Suman a, Anuj Deo b, Ritu Singh b a b
Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, India Atomic Energy Regulatory Board, Mumbai, India
a r t i c l e
i n f o
Article history: Received 2 May 2013 Received in revised form 4 January 2014 Accepted 21 February 2014 Available online 15 March 2014 Keywords: Claddings Ballooning Burst stress Burst temperature Semi-empirical correlation
a b s t r a c t An extensive burst investigation has been carried out on the zircaloy-4 claddings in an inert environment to simulate clad burst during a postulated loss-of-coolant-accident (LOCA) conditions. The parameters varied during the burst experiments were heating rate and internal overpressure. The temperature, internal overpressure and ballooning data were monitored online and recorded during the heating process of burst specimen. In addition, post-experiment measurements were also conducted on the burst specimen to determine various burst parameters–burst strains and burst stress. A semi-empirical correlation was developed to predict the burst stress for a given burst temperature. A reasonable agreement between the predicted and experimental data has been observed. The proposed correlation was also compared with available established correlation for steam environment. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The zircaloy-4 claddings are used as container of fuel pellets in nuclear reactors. These tubes also act as a barrier between the coolant and the fuel. The heat produced due to fission gets transferred to the coolant through these tubes. During loss of coolant accident (LOCA) scenario, the coolant supply is affected and as such the clad tube surface temperature rises. The continuous rise in temperature and consequent rise in fission gas pressure can cause extensive deformation of the clad tubes. As a result, the clad ballooning is accompanied with axial contraction. Another consequence of ballooning deformation is the thinning of the tube, which makes it difficult to withstand the excessive stresses causing the tube to burst. Further, heating of zircaloy clad tube causes a change in microstructure at 1085 K temperature from a-phase (hcp) to b-phase (bcc) at 1248 K. In fact, within temperature range 1085–1248 K both a and b phases co-exist. The change in phase causes a change in material properties of clad tube. An exhaustive review of literature by Alam et al. (2011) suggests that a lot of work has already been carried out to investigate the clad failure phenomena due to LOCA. In postulated LOCA experiments, the clad specimens are usually pressurized from inside by an inert gas either by helium or argon. The clad burst experiments are generally performed in various outside environments of air, inert gas, steam and vacuum. The operating variables are internal overpressure and heating rate or temperature. One of ⇑ Corresponding author. Tel.: +91 612 2552019; fax: +91 612 2277383. E-mail address: [email protected] (M.K. Khan). http://dx.doi.org/10.1016/j.anucene.2014.02.017 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
the ends of the clad specimen is kept unconstrained to allow the free contraction of the specimen during ballooning. Some of the important studies have been listed in Table 1. Such studies are helpful in formulating or improving the safety regulations of the nuclear reactor. The output of these studies also serves as valuable inputs for the designing of new reactors. From Table 1, it is clear that the burst studies are either conducted in constant temperature (isothermal) conditions or in constant heating rate conditions. Erbacher et al. (1982) performed an extensive experimental investigation on the bursting of zircaloy-4 cladding in steam environment. They also proposed a correlation for the burst stress as a function of burst temperature and oxygen content. Erbacher et al. (1982) and Neitzel and Rosinger (1980) developed the burst criterion of Zircaloy fuel claddings. The developed criterion was validated with the burst data of various researchers. Ferner and Rosinger (1985) found that azimuthal temperature difference played an important role in the ballooning deformation of the clad tube. Arai et al. (1987) developed the Larsen–Miller parameter (LMP) correlation for the combined data of isothermal and high thermal transient tests. They also demonstrated the suitability of LMP approach in predicting the cladding failure for wide range of time–temperature conditions. Zhou et al. (2004) performed short term rupture study on zircaloy clad tubes and they found that the burst test data followed the Larson–Miller parameter approach. Kim et al. (2004) conducted a study to see the changes in microstructure due to variation in thermal transients and temperature of the specimen. They found that the phase transformation from a-phase to b-phase played an important role in deformation of zircaloy-4. Seok et al. (2011) analyzed the creep data obtained
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Nomenclature C h p R t T TCE UCE
r e
circumference, m clad tube thickness, m internal overpressure, Pa clad tube radius, m time, s temperature, °C or K total circumferential elongation uniform circumferential elongation
stress, MPa strain
Subscripts B burst r radial direction o initial conditions h circumferential direction
Greek letters g heating rate, K/s
from the burst tests on ZIRLO claddings and ring-creep tests. The outcomes of the two tests were found to complement each other. Fewer studies are also available for zircaloy-4 clad tube bursting in outside inert atmosphere. The purpose of such studies is to set a reference for the zircaloy-4 cladding bursting in an outside oxidizing (steam) environment. One such study was conducted by Emmerich et al. (1969). They conducted experiments for very low range of internal overpressure as well as heating rate. Most recently, Khan et al. (2013) have developed a burst criterion for zircaloy-4 clad tubes in inert atmosphere. Keeping in view the importance of clad failure under LOCA conditions, there is a need to develop burst equation for zircaloy-4 clad tubes used in Indian pressurized heavy water reactors (PHWRs) for an outside inert environment. The objective of the present work is to study the effect of internal overpressure and heating rate on the ballooning and subsequent bursting of the clad tube and to evolve a semi-empirical burst stress correlation (burst equation). It has also been observed that the transient clad ballooning data is rarely available in open literature. In the present work, an attempt has been made to capture the ballooning data in terms of tube wall displacement. The tracking data may be of use for validation of various transient numerical clad deformation models.
pressurize test specimen (zircaloy-4 clad tube) at a given pressure, an argon gas cylinder with control valve is used. The internal overpressure has been monitored with the help of a pressure gauge and a pressure transducer. The test specimen is heated with the help of 64 kV A silicon controlled rectifier. The high magnitude direct current is transmitted to the specimen through copper bus bars and copper clamps. The magnitude of current passing through the specimen sets the desired rate of heating. Ungrounded K-type sheathed thermocouples (2 Nos.) have been spot welded on the outer surface of the clad specimen to measure the specimen temperature. To capture the ballooning of the heated specimen at three different axial positions, a frame holding three non-contact type displacement transducers (accuracy ±10 lm) has been fabricated. The wall displacement of the tube is transmitted to the displacement sensors with the help of extremely light ceramic rod-block assembly, shown in Fig. 2. One end of each ceramic rod has been fitted to a ceramic block placed on clad specimen while the other end has been glued to a small piece of galvanized iron sheet as the displacement transducers can only detect metals. The guide mechanism, consisting of short length copper tubes, allows the ceramic rods to move vertically upward towards the transducers, as shown in Fig. 2. An additional argon gas cylinder is used to conduct the burst experiments in inert atmosphere. The argon gas is purged through a perforated tube inside the enclosure right below the clad specimen, as shown in Fig. 1. This ensures the argon rich atmosphere near the clad specimen. Moreover, the purging is started a few
2. Experimental setup and procedure The schematic diagram of the experimental setup is shown in Fig. 1. It consists of a strong mild steel enclosure to carry out the clad burst safely at a required pressure and heating rate. To
Table 1 Some important experimental studies on clad failure. Author (s) (year)
Clad material
Inside clad fluid
Outside environment
Temperature conditions
Range of parameters
Emmerich et al. (1969)
Zircaloy-4
Helium
Argon
Constant heating rate
Erbacher et al. (1982)
Zircaloy-4
Helium
Steam
Constant heating rate
Ferner and Rosinger (1985)
Zircaloy-4
Inert gas
Steam
Constant heating rate
Arai et al. (1987)
Zircaloy-2
Argon
Atmosphere
Both constant heating rate and isothermal
Zhou et al. (2004)
Argon
–
Constant temperature (isothermal)
Kim et al. (2004)
Zircaloy-4 and Nb-modified Zircaloy-4 Zircaloy-4
Argon
Steam
Seok et al. (2011)
ZIRLO
Argon
Atmosphere
Both constant heating rate and isothermal Constant temperature (isothermal)
Khan et al. (2013)
Zircaloy-4
Argon
Argon
Constant heating rate
p = 2.5–11.9 bar g = 0.3–23.1 K/s p = 10–140 bar g = 1–30 K/s p = 3–29 bar g = 1–25 K/s p = 9.8–147.1 bar g = 5–200 K/s T = 923, 973 and 1073 K T = 723–773 K rB = 40–100 MPa p = 100–600 bar g = 1–100 K/s T = 365–570 °C rB = 40–520 MPa p = 20–80 bar g = 17.6–81.1 K/s
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Fig. 1. Schematic diagram of the experimental setup.
Fig. 2. Burst specimen and ballooning tracking mechanism.
minutes before switching ON the rectifier so that the entire enclosure is filled with argon. A vent is provided at the top of the enclosure to evacuate the air and excess argon. To allow free contraction of the specimen during ballooning, the free end of the clad specimen is attached to the bus bar by high capacity electric cable, also shown in Fig. 2. The cable also provides support to the free end and, thus, keeps the specimen straight
during heating. To capture the bursting phenomena, the video recording has been done using a high definition handycam as well as high speed camera. All the sensors have been calibrated prior to experimentation. The online temperature, pressure and ballooning data have been acquired and stored in the computer using high speed data acquisition system with LABVIEW 2009 software. Prior to experimentation, all the sensors have been calibrated. The rectifier has also been calibrated for different heating rates. The amount of current passing through the clad specimen corresponds to a particular heating rate. The heating rate is kept constant as far as possible by operating the rectifier knob. A 20-point calibration in the range 25–1000 °C has been performed on each thermocouple using a standard high temperature calibrator covering the entire range of temperature reached during burst experiments. The clad tube is initially pressurized to a required value with the help of pressure gauge. For continuous acquisition of pressure data, a pressure transducer has also been placed on the connecting line near the gauge. The pressure sensors (gauge and transducer) have been calibrated with the dead weight pressure tester. The displacement transducers’ outputs have been calibrated for different known positions of a metal target. The experimental procedure involves three major activities, viz. specimen preparation, leak testing and the burst experiment. The sample preparation required taking a fresh clad tube specimen of required length, spot welding of two K-type ungrounded sheathed thermocouple having 0.5 mm sheath diameter on the outer surface of clad specimen. The two thermocouples were used to capture the temperature data without fail, in case one of them comes out during ballooning. Since tube thickness is only 0.41 mm, cutting
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M.K. Khan et al. / Annals of Nuclear Energy 69 (2014) 292–300 Table 2 Operating parameters.
Table 3 Uncertainties in the measured/computed parameters.
Parameter
Range
Parameter
Accuracy/uncertainty
Clad tube outer diameter, mm Clad tube wall thickness, mm Clad tube total length, mm Clad tube effective heating length, mm Internal overpressure, bar Heating rates, K/s
13.08 0.41 245 200
Temperature Displacement Pressure Clad diameter Clad thickness Clad burst circumference Burst stress Burst strain
±1.5 °C ±10 lm 0.2% FS 0.01 mm 0.01 mm 1 mm 2.4944% 0.2518%
Wall displacement, mm
20, 40, 60 and 80 Low (17.6–26.6), medium (40.3–55.9) and (61.4–81.1) 0–10
threads was not feasible option. The ferrule joint was made on the open end of the clad specimen by using a brass ferrule (ring) and brass nut-connector assembly. The specimen was placed inside the enclosure and connected to the line to having argon cylinder. The nut on the clad specimen was tightened to the connector on connecting line such that the ferrule, between the connector and brass nut, gripped the clad specimen firmly. The joint was tested for leaks at pressures the burst experiment was supposed to be performed. The burst experiment began after making sure that all the sensors output were properly read in the data acquisition system. The required direct current was supplied (to achieve a particular heating rate) to the specimen by operating the rectifier knob. The temperature started rising with the switching on of rectifier. After reaching a certain value of temperature, the clad specimen ballooned and subsequently burst. The ballooning was tracked in most of the experiments. The data was stored in the computer for further analyses. The values of operating parameters have been mentioned in Table 2. Three different ranges of heating rates were applied, signified by low, medium and high categories and four different values of internal overpressure have been selected. The choice of loading conditions (internal overpressure and heating rate) is based on the literature reviewed and as per the requirements of the funding agency. The temperature, pressure and displacement data for given combination heating rate and internal overpressure were recorded. Three experiments were conducted for each combination of heating rate and overpressure. Thus, a total of 36 test experiments were conducted (a product of number of heating rates (3), number of internal overpressures (4) and repeatability (3)). Table 3 presents uncertainty in measured and computed parameters.
3. Experimental observations The experiments have been designed to monitor and store the online temperature, pressure and ballooning data as mentioned in the previous section. However, the quantities like burst strains (radial and circumferential both) and burst stress have been determined by conducting post-burst measurements. The uniform and total circumferential elongations are the measure of uniform and localized ballooning, respectively. The uniform circumferential
elongation measurement has been done on the specimen where the tube has undergone uniform ballooning. Likewise, the total circumferential elongation and burst strain measurements have been done at the ballooning site. The uniform and total circumferential elongations, in percent, are computed from the following relation:
UCE or TCE ½% ¼
C2 C1 100 C1
ð1Þ
where C1 is the initial circumference of clad specimen and C2 is the final circumference at uniform ballooning site for the uniform circumferential elongation (UCE) or localized ballooning site for the total circumferential elongation (TCE), as shown in Fig. 3. The consequence of ballooning deformation is increase in tube diameter along with the decrease in tube thickness. The engineering circumferential burst strain is given by
eh;B ¼
RB Ro ¼ TCE Ro
ð2Þ
where Ro and RB are the initial clad tube radius and clad tube radius at the burst location, respectively. The circumferential strain is, in fact, same as the total circumferential elongation. The burst circumference has been measured using a thread, shown in Fig. 4(a). The burst circumference is equal to the length of thread wrapped around the periphery of clad specimen at the burst location excluding burst opening. The clad tube radius at burst location has been determined by dividing the circumference by 2p. The engineering radial burst strain is given by
er;B ¼
hB ho ho
ð3Þ
where ho and hB are average clad tube thickness before and after the burst at the burst location, respectively. To measure the clad thickness at the bursting site, small piece/fragment from each burst sample is cut and its thickness is measured using screw gauge, Fig. 4(b). Another important parameter which is very useful in the burst study is the burst stress. It is defined as the hoop or circumferential stress at the time of burst and is given by
rB ¼ ro
pB ð1 þ eh;B Þ2 po
ð4Þ
where pB and po are burst and initial values of internal overpressures (Erbacher et al., 1982).
Fig. 3. Burst specimen.
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Fig. 4. (a) Burst circumference measurements and (b) thickness measurements.
The initial stress (ro) is computed using Eq. (5),
ro ¼
po Ro ho
ð5Þ
where po, Ro and ho are the initial values of internal overpressure, clad radius and clad thickness, respectively. The photographs of burst specimens for different internal overpressure and heating rates have been shown in Figs. 5 and 6. As a common observation all the burst specimens have been found to bend during the bursting of specimen (visible in Figs. 5(b) and 6(c)). This happens due to the reaction caused by rushing out of argon gas through burst opening. Apparently, the bending is more for higher internal overpressures. The reason may be attributed to the fact that the reaction of gases with higher pressure rushing out of the tube at the burst opening will be higher. Another common observation is localized ballooning at multiple sites. These two observations are irrespective of heating rate and internal overpressure. It has also been observed that the tube starts contracting axially with the onset of ballooning which makes the rupture opening to orient in the vertical direction. Fig. 5 shows the burst specimens for same heating rate of about 50 K/s and three different internal overpressures of 19.2 bar, 39.8 bar and 60 bar. It can be seen that the opening size is larger for higher internal over pressures. Also, the rupture opening becomes uneven for higher internal overpressures. In fact at low internal overpressure, the tearing of the tube is aligned axially. However, at higher internal overpressures, the rupture opening is more in circumferential direction.
Fig. 5. Burst specimen for constant heating rate and different internal overpressure.
Fig. 6. Burst specimen for constant internal overpressure and different heating rate.
4. Results and discussion As mentioned earlier, the heating rate is maintained constant as far as possible. The clad specimen is uniformly heated by the flow of direct current through it. Fig. 7 has been drawn for a particular data set (po = 80 bar and g = 66 K/s) to show the variation in temperature and pressure with time. The temperature varies almost linearly with time, which is an evidence of attainment of near constant heating rate. On the other hand, the fluctuations in pressure are observed during heating process. This may be attributed to the hyper-sensitivity of the pressure sensor or it may be due to noise. Despite of these pressure fluctuations, an increasing trend is visible with the rise in temperature till the clad specimen bursts. The burst time, burst temperature and burst pressure can easily be located on the diagram, as shown in Fig. 7. The ballooning data could not be tracked for all 36 experimental data sets with the arrangement shown in Fig. 2 in the previous section. The ballooning rate has been presented in terms of wall displacement of clad specimen at ballooning site. The effect of internal overpressure and heating rate has been presented separately in Figs. 8 and 9 respectively. Fig. 8 has been drawn to present the ballooning pattern for nearly 20 bar internal overpressure and for three different heating rates, 23.6 K/s, 51.5 K/s and 68.7 K/s. Other than the obvious observation that lower heating rates require more time for the clad specimen to burst, it has also been observed that in each case the tube first undergoes uniform ballooning followed by localized ballooning leading to bursting. Further, the tube exhibits a slight downward movement during the heating process followed by a sudden contraction (shown as a dip in each curve) immediately before the onset of localized
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297
Fig. 7. Variation of temperature and pressure during heating of clad specimen.
Fig. 8. Ballooning deformation for constant internal overpressure and different heating rate.
Fig. 9. Ballooning deformation for constant heating rate and different internal overpressure.
ballooning, which also signifies the beginning of plastic instability. The slight downward movement (sagging) may be the result of deformation caused during heating by the weight of copper clamps fixed at each end provided for continuous electric heating of
specimen. This slight downward movement of the tube during heating makes it impossible to track uniform ballooning online. Hence, from the present arrangement the uniform ballooning could not be tracked. However, for the determination of uniform ballooning, post experiment measurements were conducted on each burst specimen. A similar dip in the strain curve prior to the onset of plastic instability was observed in the Lin (1977) analytical model. During the localized ballooning, the tube wall moves upward and as such the curves become vertically straight. The effect of heating rate for a constant internal overpressure is that the burst time reduces with the increasing heating rate. In fact, the burst time reduces more as heating rate is increased from 23.6 to 51.5 K/s than that when it is increased from 51.5 to 68.7 K/s. The reduction in burst time is not proportional to the corresponding increase in heating rate. To see the effect of internal overpressure for constant heating rate, Fig. 9 has been drawn. The heating rate is fixed around 22– 23 K/s and the internal overpressure is varied from 20 to 60 bar. The burst time reduces with increasing internal overpressure. It can also be seen that when the internal overpressure is increased from 20 to 40 bar and from the 40 to 60 bar the reduction in burst time is almost same. The reduction in burst time is almost proportional to the increase in internal overpressure. The reason being is that the internal pressurization of the tube causes an increase in the magnitude of stresses developed. As a result, the deformation will begin earlier in the tubes with high internal overpressure. Also, the dip in the curve is more for higher internal overpressures. Fig. 10 shows a glimpse of experimental burst data of all the 36 test runs on a plot of burst temperature vs burst time for different heating rates and internal overpressures. The data in the graph for low, medium and high heating rates have been highlighted by dividing the graph in three zones using vertical dotted lines. For any heating rate, the burst temperature decreases with increase in internal overpressure. It is due to the larger magnitude of initial stresses developed due to higher internal overpressure. Also, the burst temperature decreases with decrease in heating rate for given internal overpressure, shown by the best fit lines. However, the effect of heating rate is not as significant as the effect of internal overpressure. This reduction may be attributed to the fact that slower heating rate will take longer time for the tube to reach burst temperature. Further higher heating rate would induce high rate of increase in thermal stresses in the material. Fig. 11 has been drawn to see the effect of initial stress on the burst temperature. The initial stress is developed due to the internal pressurization of clad tube specimen. For any heating rate, the
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Fig. 10. Burst temperature vs burst time.
Fig. 12. Burst strain vs burst temperature.
reduction in burst temperature is observed with the increase in initial stress. At low pressure, the initial stress is low and accordingly the tube will sustain higher temperature before it collapses. Further at lower pressures (20 bar and 40 bar with low and medium heating rates), the tube undergoes a phase change from a-phase (hcp) to the mixed (a + b)-phase (bcc + hcp). The phase change may have some effect on the deformation leading to bursting. At higher pressures (40 bar with high heating rate, 60 bar and 80 bar), on the other hand, the value of initial stress is high; the tube collapses earlier at a lower value of temperature within a-phase. The similar variation in burst temperature with initial stress was also reported by Neitzel and Rosinger (1980). In Fig. 12, the burst strains in circumferential and radial directions have been plotted against the burst temperature. The burst strain is positive in circumferential direction due to ballooning of the tube whereas it is negative in radial direction due to thinning of the tube, prior to bursting. The low pressure data (20 bar and 40 bar with low and medium heating rates) lies in the mixed (a + b) phase while for other internal overpressures (i.e., 40 bar with high heating rate, 60 bar and 80 bar), the burst data lies in a-phase. In a-region, with burst temperature, the circumferential burst strain increases whereas radial burst strain decreases. In fact, higher the pressure, smaller is the circumferential burst strain and greater is the radial burst strain (shown by best fit lines). The reason may be that at higher pressure the clad tube material more stressed causing the tube to burst earlier. The ballooning deformation of the tube would, thus, be restricted. Further, the stresses induced are large and, thus, less time is required for the clad to burst.
However, in the mixed (two) phase (a + b) region, the burst strain in each direction decreases with burst temperature as the material properties change with the change in phase. The variation of circumferential burst strain with burst temperature is in-line with the Erbacher et al. (1982) findings. However, they did not discuss the radial burst strain variation with burst temperature.
Fig. 11. Burst temperature vs initial stress.
5. Burst correlation One of the important aspects of the present study is to develop a correlation to predict the burst stress for a given burst temperature. The burst stress is calculated for all the 36 data sets using Eq. (4). The burst stress is then plotted against the burst temperature, as shown in Fig. 13. It can be seen that there is a decrease in burst stress with burst temperature. Neitzel and Rosinger (1980) proposed that for the clad burst in an inert environment, the burst stress and the burst temperature can be related by an exponential decay function given by
rB ¼ a expðbT B Þ
ð6Þ
where constants a and b have been determined by conducting the regression analysis on the burst data. For different phases, the values of constants are found to be different and they have been mentioned below in Table 4. The constants of Erbacher et al. (1982) correlation have also been mentioned in the table. Also, in the mixed (two) phase region burst stress shows strong temperature dependence as compared to single phase region.
Fig. 13. Burst stress vs burst temperature.
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M.K. Khan et al. / Annals of Nuclear Energy 69 (2014) 292–300 Table 4 Values of constants.
Table 5 Comparison of operating parameters.
Correlation
Phases
Present correlation (inert environment) Erbacher et al. (1982) correlation (steam environment)
a (TB < 1085 K) a + b (1085 K < TB < 1248 K) a (TB < 1085 K) a + b (1085 K < TB < 1248 K)
Constants a
b
989.2 161572965.4 830 3000
0.0017 0.0127 0.001 0.003
Operating parameters
Present study
Erbacher et al. (1982) study
Clad material Clad tube dimensions
Zircaloy-4 OD = 13.08 mm ho = 0.41 mm Argon gas (inert) 17.6–81.1 K/s 20–80 bar
Zircaloy-4 OD = 10.75 mm ho = 0.725 mm Steam environment 1–30 K/s 10–140 bar
Outside environment Range of heating rate Range of internal over pressure
The mean percentage deviation has been computed for both the correlations using the following equation:
Mean percentage deviation ¼
N 1X rB;predicted;i rB;actuali 100 N i¼1 rB;actual;i ð8Þ
Fig. 14. Predicted burst stress vs actual burst stress.
In order to compare the burst stress predicted by the proposed correlation with the experimental burst stress, Fig. 14 has been drawn. The burst stress predicted by the proposed correlation is in good agreement with the experimental burst stress as 61% predicted burst stress data lies in the error band of ±10%. However, 83% of the predicted burst stress data lies in the error band of ±20%. In Fig. 15, the proposed correlation has been compared with already established correlation of Erbacher et al. (1982). The constants for the Erbacher et al. (1982) correlation have already been mentioned in Table 4. The percentage deviation appearing in Fig. 15 is evaluated using the following equation:
rB;predicted rB;actual Percentage deviation ¼ 100 rB;actual
ð7Þ
It is evident from Fig. 15 that Erbacher et al. (1982) correlation overpredicts the burst stress. The percentage deviation for the proposed correlation mostly lies in the range of ±50% compared to the percentage deviation for the Erbacher et al. (1982) correlation which lies approximately in the range 50% to 150%.
The mean percentage deviation for the proposed correlation is 14.2 whereas for Erbacher et al. (1982) correlation is 65. The reason for the large deviation in the prediction of two correlations may be attributed to the difference in operating conditions in which the two studies were conducted, as mentioned in Table 5. The major reason for high prediction of burst stress by Erbacher et al. (1982) correlation is that the study was conducted on thicker clad tube which can resist more stress prior to burst. Another important reason is that Erbacher et al. (1982) study was conducted in steam environment. Clad tube heating in steam environment accompanied by the oxidation of the outside surface. The oxidation does have an effect on clad tube ballooning and bursting. In fact, the Erbacher et al. (1982) burst stress correlation has a factor for oxidation content in its expression, which has been ignored in this comparison.
6. Conclusions Following conclusions can be drawn from the present study: The online ballooning is successfully captured for most of the clad burst experiments. The tube undergoes an axial contraction during ballooning and bursting. Also the rushing of gases from the burst opening causes the tube to bend. The transient ballooning data obtained in the present work can be used by the researchers for validation of analytical or numerical models. For the burst in a-phase, the circumferential burst strain increases and the radial burst strain decreases with the increase in burst temperature whereas for the burst in (a + b)-phase, both circumferential as well as radial burst strains decrease with the increase in burst temperature. A semi empirical correlation has been proposed for the prediction of burst stress as function of burst temperature. The predicted 83 percent burst stress data lie in the error band of ±20 percent from the proposed correlation. The proposed correlation is also compared with Erbacher et al. (1982) correlation. The mean percentage deviation for proposed correlation is 14.2 whereas for Erbacher et al. (1982) correlation it is 65.
Acknowledgments
Fig. 15. Comparison between the predictions from the proposed correlation and the Erbacher et al. (1982) correlation.
We sincerely acknowledge Atomic Energy Regulatory Board (AERB) and Nuclear Fuel Complex (NFC) India, for providing the support needed to carry out the present work.
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Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.anucene.2014. 02.017.
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