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DETERMINISTIC EVALUATION OF DELAYED HYDRIDE CRACKING BEHAVIORS IN PHWR PRESSURE TUBES
DETERMINISTIC EVALUATION OF DELAYED HYDRIDE CRACKING BEHAVIORS IN PHWR PRESSURE TUBES
Nuclear Engineering and Technology. 2013. Apr, 45(2): 265-276
Copyright ©2013, Korean Nuclear Society
  • Received : April 04, 2012
  • Accepted : October 10, 2012
  • Published : April 25, 2013
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About the Authors
YOUNG-JIN OH
Power Engineering Research Institute, KEPCO Engineering and Construction 188 Gumi-dong, Bundang-gu, Seongnam-si, Gyeonggi-do 463-870, Republic of Korea
YOON-SUK CHANG
Department of Nuclear Engineering, Kyung Hee University 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 446-701, Republic of Korea
yschang@khu.ac.kr
Abstract
Pressure tubes made of Zr-2.5 wt% Nb alloy are important components consisting reactor coolant pressure boundary of a pressurized heavy water reactor, in which unanticipated through-wall cracks and rupture may occur due to a delayed hydride cracking (DHC). The Canadian Standards Association has provided deterministic and probabilistic structural integrity evaluation procedures to protect pressure tubes against DHC. However, intuitive understanding and subsequent assessment of flaw behaviors are still insufficient due to complex degradation mechanisms and diverse influential parameters of DHC compared with those of stress corrosion cracking and fatigue crack growth phenomena. In the present study, a deterministic flaw assessment program was developed and applied for systematic integrity assessment of the pressure tubes. Based on the examination results dealing with effects of flaw shapes, pressure tube dimensional changes, hydrogen concentrations of pressure tubes and plant operation scenarios, a simple and rough method for effective cooldown operation was proposed to minimize DHC risks. The developed deterministic assessment program for pressure tubes can be used to derive further technical bases for probabilistic damage frequency assessment.
Keywords
1. INTRODUCTION
A few hundred zirconium alloy pressure tubes in a pressurized heavy water reactor (PHWR) serve as the nuclear fuel channel as well as the reactor coolant pressure boundary. For safe operation of the PHWR, reliable performance of the tubes should be maintained throughout its harsh life environment. However, due to high temperature, pressure and neutron flux, Zirconium alloy pressure tubes may be subjected to aging mechanisms such as 'delayed hydride cracking (DHC)', 'irradiation enhanced deformation' and 'changes of material properties'. To date, some pressure tubes in early reactors have leaked and two pressure tubes have ruptured due to the DHC [1] .
In order to prevent incidents of tube failures, fitness for service assessment (FFSA) has to be carried out considering detected or postulated flaws [2] . The CANDU owners group (COG) developed the FFSA guidelines that were first published for trial use in 1991 [3] and updated in 1996 [4 , 5] . Subsequently, CSA N285.8 was published in 2005 as a code & standard for the FFSA of PHWR pressure tubes [6 , 7] . It provides extensive flaw assessment procedures and requires various input parameters such as flaw shapes (length, depth and root radius), tube geometries (diameter and thickness), hydrogen concentration of the tube and heatup / cooldown transients. Especially, the procedures for DHC initiation and growth assessment are very complicated compared with other procedures like ASME B&PV section XI or API (American Petroleum Institute) code. However, due to lack of details, it is difficult to understand how diverse input parameters affect the DHC and which of these parameters is more important than others.
The motivation for this research is to make technical bases of pressure tubes for the probabilistic assessment required by the code & standard as well as to recommend a simple method to reduce DHC risks. To get insight into the integrity of pressure tubes, we first developed a flaw assessment program according to CSA N285.8 procedures. Then, by using the program, effects of flaw shapes, pressure tube dimensional changes, hydrogen concentrations of pressure tubes and plant operation scenarios on DHC initiation and growth were examined. The present study on DHC behaviors of pressure tubes is restricted to the CSA N285.8 procedure, from a conservative point of view, which may lead to somewhat different results from real DHC behaviors of pressure tubes.
2. DETERMINISTIC FLAW ASSESSMENT PROGRAM
- 2.1 Assessment Program Summary
A deterministic flaw assessment program for pressure tubes was developed based on the procedure of CSA N285.8. It aims to predict crack initiation and growth by the DHC as well as final failure by fracture initiation and plastic collapse. Also, the program can provide the times for each event (crack initiation and final failure etc.) and consider the location of a flaw (channel location and axial position of the flaw in the pressure tube). The principal considerations for developing the assessment program are summarized in the following paragraph, which abide by the procedures prescribed in CSA N285.8.
Initial volumetric (blunt) flaws in the pressure tubes undergo normal operation and transient loads, which may lead to either fatigue crack and DHC initiation or plastic collapse during operation. Also, hydrogen concentration and neutron fluence increase continuously and nominal stresses increase due to dimensional change of the flawed tubes such as thickness reduction and diametral expansion. So, effects of the hydrogen concentration and neutron fluence increment as well as dimensional change in accordance with time elapse is taken into account for crack initiation evaluation. During these evaluations, the three aforementioned parameters are continuously revised and reevaluated at each time interval to justify the fracture initiation and plastic collapse. Fig. 1 shows a brief flow diagram for the assessment program developed in this study.
Lager Image
Flow Diagram of Deterministic Flaw Assessment for PHWR Pressure Tubes
CSA N285.8 specifies evaluation options on the DHC initiation in terms of hydrogen concentration. Because pressure tube material contain deuterium as well as hydro-gen in PHWR condition, the hydrogen equivalent concen-tration ( Heq ) is defined as follows
Lager Image
where, Hi is the initial hydrogen concentration and D is the deuterium uptake.
CSA N285.8 describes various options for DHC initiation assessment methods and their scope of application. In this study, the options are briefly depicted in Fig. 2 . The DHC initiation assessment methods are classified into two groups; (1) a process-zone evaluation procedure appropriate for pressure tubes with a constant temperature (normal operation) condition or a temperature decrease (cooldown operation) condition, and (2) a hydrided region overload evaluation procedure appropriate for pressure tubes with a temperature increase (upset or heatup transients) condition which has not been documented in CSA N285.8. While the former includes a few kinds of calculation options, such as a threshold peak stress evaluation method and several explicit process-zone methods, all the calculation options are based on the same theory and provide almost identical results for the DHC initiation. So, with regard to the DHC initiation, the threshold peak stress evaluation method with the shortest calculation time was adopted in the flaw assessment program through this research.
- 2.2 DHC Initiation Assessment
During the cooldown transient of a PHWR plant, internal pressure and temperature are slowly decreased. Hydrogen is dissolved at the matrix of pressure tube material under high temperature conditions and is precipitated under low temperature conditions. The aforementioned threshold peak stress evaluation method considers that DHC initiation
Lager Image
Flow Diagram of DHC Initiation Evaluation According to CSA N285.8
occurs when a maximum applied peak stress under hydride precipitation condition is higher than a threshold value. CSA N285.8 presents a hydride precipitation temperature as follows
Lager Image
where, Tp , VH , σhyd1 , σhyd2 , Qp , R , Cp and Hf are the hydride precipitation temperature, partial molar volume of hydrogen in zirconium, hydrostatic stress remote from the flaw tip, hydrostatic stress at the flaw tip, activation energy for hydrogen precipitation, gas constant, hydrogen precipitation constant and bulk hydrogen equivalent concentration in solution remote from the flaw, respectively.
The above equation represents that the higher hydrostatic stress gradient, the higher local concentration of hydrogen at the flaw tip which in turns lowers hydride precipitation temperature at the flaw tip. Here, the σhyd1 and σhyd2 are calculated by
Lager Image
where, σh is the nominal hoop stress, σa is the nominal axial stress, σ p is the peak principal flaw-tip stress and ν is the Poisson’s ratio. Because Tp is a function of σh , maximum peak stress under hydride precipitation condition has to be calculated iteratively for many small time steps of cooldown transient scenario.
- 2.3 DHC Growth Assessment
CSA N285.8 considers that DHC growth occurs when the applied stress intensity factor is greater than a threshold value ( KIH ) and temperature is lower than a specific value ( TcDHC ). The KIH and TcDHC are presented in CSA N285.8 as follows
Lager Image
where, KIH , TcDHC , ΔTcDHC , QD and CD are the threshold stress intensity factors for the onset of DHC from a crack, maximum temperature for DHC growth during continuous cooling, undercooling for TcDHC during continuous cooling, activation energy for hydrogen dissolution and hydrogen dissolution constant, respectively. Under the DHC growth condition, flaw growth rate varies according to temperature conditions and is not influenced by applied stress intensity factors. A strong correlation was observed between increased temperatures and the flaw growth rate.
- 2.4 Reliability of Flaw Assessment Program
The reliability of the flaw assessment program should be verified through a feasibility demonstration for key parameters such as the peak stress and stress intensity factor described above. However, since there are no comparable papers or open literature addressing DHC behavior in relation to CSA N285.8, validities of the key parameter calculation algorithms employed in the program were approved according to in-house qualification procedures. For example, a previous study by Lee et al. [8] showed that the stress intensity factor calculation formula contained in CSA N285.8 provides reliable calculation results compared with corresponding detailed finite element analysis results. Prior to this, also, another study by Kim et al. [9] examined various kinds of engineering formulae for the peak stress calculation of pressure tubes with a volumetric flaw. It showed that the peak stress value obtained from CSA N285.8 is a little bit conservative in general but sufficiently reliable when compared with three-dimensional finite element analysis result. Therefore, we consider that the program developed in this study can be used for deterministic evaluation of the DHC behaviors based on the peak stress and stress intensity factor in PHWR pressure tubes.
3. EFFECTS OF FLAW SIZE AND HYDROGEN CONCENTRATION
The DHC behaviors of volumetric flaws were estimated by using the program to investigate the effects of varying input parameters. Even though fatigue remains a more plausible crack initiation mechanism than delayed hydride cracking, in general, evaluation of the fatigue crack initiation was excluded by considering inherent over-conservatism of the relevant procedure in CSA N285.8-05 [6] and prime object dealing with the DHC assessment of the present study.
A postulated volumetric flaw at the center of a high power fuel channel, which is 3,000mm away from the inlet burnish mark of a pressure tube, was chosen for the evaluation under a representative cooldown transient. Fig. 3 shows the resulting flaw behaviors, in which the crack initiation and growth from the volumetric flaw are dependent on the initial flaw size, Heq and pressure tube dimensional change. Here, constant flaw depths mean that the DHC initiation does not occur from the volumetric flaw. However, as the elapse of operation time, the flaw depth increases due to crack initiation and growth to culminate in failure conditions of the pressure tubes by the fracture initiation or plastic collapse.
Fig. 3 (a) illustrates that the crack initiation time is slightly retarded with a decrease of the flaw depth from 1.0mm to 0.7mm and crack initiation does not occur when
Lager Image
Flaw Behaviors at Operating PHWR Pressure Tubes
the initial flaw depth is sufficiently shallow like 0.6mm. Fig. 3 (b) shows that the onset of crack initiation with an increase of Heq rate from 0.50ppm/EFPY to 1.50ppm/ EFPY. In Fig. 3 (c), the effect of pressure tube deformation on the crack initiation time and growth rate is negligible. However, on the whole, the final failure time decreases rapidly as the increase of the pressure tube deformation because the corresponding failure crack length becomes shorter due to the increase of the nominal stress. Effects of the initial flaw depth and pressure tube deformation were not significant comparing with those of the Heq rate.
As depicted in Fig. 3 , higher Heq rate and tube deformation rate with deeper initial flaw depth make the DHC initiation faster under a representative cooldown transient. These behaviors are simple and easy to understand, however, the characteristics of cooldown transient can affect the DHC behavior in more complicated ways as explained in Section 2 of this paper. Therefore, the effects of the cooldown transient on DHC evaluation according to CSA N285.8 are discussed in the following two sections.
4. EFFECTS OF COOLDOWN TRANSIENTS
- 4.1 Simplified Cooldown Transients
In order to exclude effects of complexity of the plant cooldown transient in a PHWR reactor and to facilitate the understanding of cooldown transient effects, the DHC behaviors were evaluated under simplified hypothetical cooldown transients. The simplified cooldown transient #1 in Fig. 4 (a) represents the case that operating pressure is sustained until temperature becomes sufficiently low. The simplified cooldown transient #2 in Fig. 4 (b) defines that two step depressurization operation is conducted at temperature of 260℃ and 150℃, respectively. In the simplified cooldown transient #3 shown in Fig. 4 (c), additional depressurization is assumed when the temperature reaches to 100℃. Fig. 4 (d) represents the plot of three simple cooldown transients in a pressure-temperature plane.
- 4.2 DHC Initiation under Simplified Cooldown Transients
Characteristics of threshold bulk Heq to cause the DHC initiation were examined for various flaw shapes. The volumetric flaw was postulated at the center of a pressure tube at a high power channel and simple cooldown transients were applied. In order to exclude unanticipated complications from diverse input parameters, changes of Heq rate and pressure tube deformation rate were not considered.
Fig. 5 represents variation of the threshold bulk Heq for the DHC initiation against flaw depths ( a ) and radii at the tip of a blunt volumetric flaw (ρ) under the simplified cooldown transients. As shown in the figure, at a given flaw depth, the threshold bulk Heq increases as the increase of ρ. It can be explained that higher bulk Heq is needed for the DHC initiation because stress gradients and local Heq at the flaw-tip decrease as the increase of ρ. However, the DHC can be initiated as a result of an increase in the flaw depth because a deeper flaw contributes to a larger stress gradient and higher local Heq at the flaw tip. Meanwhile, we can find out the effects of the change of simplified cooldown transients; for instance, in the case of cooldown transient #3 with three steps of depressurization, further higher threshold bulk Heq is anticipated for the DHC initiation although the flaw depth is deep and ρ is small.
Fig. 6 (a) and 6 (b) are to compare effects of three
Lager Image
Simplified Hypothetical Cooldown Transients
Lager Image
Threshold Bulk Heq for DHC Initiation under Simplified Cooldown Transients
kinds of simplified cooldown transients on the DHC initiation when ρ=0.01mm and 0.10mm cases, respectively, in which differences among these transients are illustrated by shaded regions. It has to be recalled from Fig. 4 (d) that three kinds of simplified cooldown transient are plotted on the internal pressure against temperature. By transforming the temperature of Fig. 4 (d) to terminal solid solubility of hydride precipitation (TSSP) and exchanging x- and yaxes of the graph, we can make Fig. 6 (c) that is similar to Fig. 6 (a) and 6 (b). Here, the TSSP is a kind of threshold Heq for hydride precipitation at the material bulk region under a continuous cooling condition. In addition, Fig. 7
Lager Image
Understanding the Effect of Cooldown Transient on DHC Initiation
shows the relationship between TSSP and temperature presented in CSA N285.8, which is used in the evaluation.
The evaluation results can be interpreted that, at a certain bulk Heq , possibility of the DHC initiation reduces under the cooldown transient condition with early depressurization because of the increase of threshold flaw size for the DHC initiation. Using the similarities of Fig. 6 (a) ~ Fig. 6 (c), we can estimate the most effective depressurization procedure under a cooldown operation to minimize the DHC initiation possibility considering average Heq level of a given reactor.
Lager Image
TSSD and TSSP of Pressure Tube Material
- 4.3 DHC Growth under Simplified Cooldown Transients
For investigating characteristics of flaw growth, the amount of DHC growth rates during single cooldown operation was calculated using the developed assessment program. Similar to the previous section, an initial crack was postulated at the center of a pressure tube at a high power channel under simplified hypothetical cooldown transient conditions. Also, in order to exclude unnecessary complications from diverse input parameters, changes of Heq rate and pressure tube deformation rate were not considered.
Fig. 8 represents variation of the DHC growth rates against the initial crack depth with different Heq . As shown in the figure, although the initial crack depth does not significantly affect the crack growth rate, early depressurizations under cooldown transients #2 and #3 lead to deeper threshold crack depths for the DHC growth. The increase of the bulk Heq decreases TcDHC that widens temperature ranges and results in the increase of flaw growth under a cooldown operation. In contrast, for the deeper initial crack depth over 0.8mm approximately, DHC growth rates are not affected by the initial crack depth and cooldown transient. While the deeper crack causes larger applied stress intensity factor than KIH but the DHC growth rate does not depend on the applied stress intensity factor as described in Section 2.3. Due to little difference in time-temperature curves among cooldown transients as shown in Fig 4 (a) ~ Fig. 4 (c), there is no difference in the amount of DHC growth for the deeper crack.
Fig. 9 represents variation of the DHC growth during single cooldown operation against bulk Heq when the initial crack is sufficiently deep as aini .=1.0mm. As shown in the figure, there was no effect of cooldown transient on DHC growth if the initial crack is sufficiently deep. The Region-1 in Fig. 4 (a) representing later half of the cooldown operation can also be used to explain characteristics of the Region-1 in Fig. 9 (a) and 9 (b), in which the
Lager Image
Effect of Crack Size and Heq on DHC Growth under Simplified Cooldown Transients
amount of DHC growth increases gradually according to the increasing bulk Heq at low level of Heq . This means that increasing bulk Heq increases the DHC growth period during later half of the cooldown operation as shown in Fig. 9 (c).
Especially, the amount of crack growth abruptly increases when the bulk Heq is about 35ppm and the region with constant crack growth rate is followed by the Region- 2 in Fig. 9 (a) and 9 (b). When the Heq increases from 33ppm to 35ppm, the terminal solid solubility for dissolution (TSSD) temperature increases from 258℃ to 260℃ (refer to Fig. 7 ). The small increment of TSSD temperature
Lager Image
Understanding the Effect of Heq on DHC Growth under Normal Operation and Cooldown Transients
induces large increment of the DHC growth period, about 15 minutes in Region-2, which phenomenon is graphically illustrated in Fig. 9 (c).
A similar trend is observed in the region with the Heq of 50ppm, which corresponds to the Region-3 in Fig. 4 (a). Subsequently, significant crack growth occurs in the Region- 4 since this region is pertinent to sustained normal operation conditions at high temperatures. Fig. 9 (d) represents that the DHC growth rate of pressure tube material is rapidly increased at higher temperature as described in CSA N285.8. Therefore, during early part of cooldown operation (high temperature part), relatively small increment of DHC growth period may lead to large amount of increment of DHC growth by single cooldown operation.
- 4.4 DHC Behaviors under Plant Cooldown Transients
In the previous sections, effects of the initial flaw size and Heq on the DHC initiation and growth were investigated under simplified hypothetical cooldown transients. In this section, the simple cooldown transients were expanded to the cases by employing plant cooldown transients. Fig. 10 (a) and 10 (b) represent two kinds of measured cooldown transients at Korean PHWR plants [10] ; the former shows a typical past cooldown transient without depressurization before cooling to 50℃. The latter shows a cooldown transient with two step depressurization at high temperature (about 250℃) and intermediate temperature (about 150℃). Additionally, Fig. 10 (c) represents the cooldown transient contained in a design stress report of a Korean PHWR plant [11] . Fig. 11 compares pressure-temperature curves of all the cooldown transients. The one in the design stress report shows the highest temperature at a given pressure, which can provide conservative design. However, since the DHC initiation occurs from the precipitation of the flaw-tip hydrides at lower temperature as explained in Section 4.2, the design cooldown transient will be a nonconservative one from the DHC initiation evaluation point of view.
Fig. 12 shows characteristics of the bulk Heq for the DHC initiation under each transient. As depicted in the figure, the DHC initiates in the lower Heq under the measured cooldown transient #1 with low temperature and high pressure. The DHC initiation estimation under the design cooldown transient is non-conservative compared with the estimation under the measured cooldown transients. CSA N285.8-10 introduces a factor to mitigate the overconservatism for flaw-tip hydride non-ratcheting conditions with low Heq . Fig. 13 represents effects of the non-ratchet factor, in which the over-conservatism of the CSA N285.8- 05 reduces a little through the shift of threshold Heq - threshold flaw depth curves to the right hand side.
Fig. 14 shows characteristics of the DHC growth by single cooldown operation. In this figure, depressurized transients increase the threshold crack depth for DHC growth. However, when the initial crack is deeper than 0.9mm, early depressurization effects are disappeared. In
Lager Image
Cooldown Transients for Korean PHWR Plants
Lager Image
Pressure-Temperature Curve for Plant Cooldown Transients
Lager Image
Threshold Bulk Heq for DHC Initiation under Plant Cooldown Transients
Lager Image
Effect of Factor of Non-ratchet on DHC Initiation under the Measured Cooldown Transient #1
Lager Image
Effect of Crack Size and Heq on DHC Growth under Plant Cooldown Transients
case of the measured cooldown transient #2 with two-step depressurization, the crack growth rate is greater than that of the measured cooldown transient #1 as shown in Fig. 15 . This DHC growth behavior can be interpreted as the increased crack growth period effect according to the decrease of average cooldown rate, i.e. the increased period at high temperature during a cooldown, instead of the depressurization effect. It is also supported by the evaluation results depicted in Fig. 9 , in which the pressure reduction effect is not observed under the simplified hypothetical cooldown transients having the same cooldown rate. Therefore, it can be summarized that the early depressurization can contribute to the increase of the threshold initial crack size for the DHC growth under the cooldown transient
Lager Image
Effect of Heq on DHC Growth under Plant Cooldown Transients
and rapid cooling from high temperature is effective to reduce the amount of DHC growth during a cooldown operation.
5. EFFECTS OF HEATUP OPERATION SCENARIO
While the DHC growth has been evaluated under the normal and cooldown operating conditions, in case of the DHC initiation, heatup operation should also be considered. As illustrated in Fig. 2 , the DHC initiation under the heatup operation can be evaluated by using the process-zone evaluation procedure or the hydrided region overload evaluation procedure. However, since details of the latter procedure are not established yet but the former procedure is available from CSA N285.8, characteristics related to the DHC initiation were examined in this section based on the process-zone evaluation procedure. Fig. 16 represents two kinds of heatup transients; the one in Fig. 16 (a) is measured from a Korean PHWR plant [10] and the other in Fig. 16 (b) is extracted from a design stress report of the same plant [11] . These plant heatup transients were translated into the corresponding pressure-temperature curves as shown in Fig. 17 . Here, the pressure in the design stress report is lower than the measured one for a given temperature.
CSA N285.8 recommends that evaluation of hydride existing conditions during heatup transients have to be based on the TSSD instead of the TSSP. This is because pressure tube materials have undergone a dissolution process due to the increase in temperature, when the hydrides precipitate, during the heatup operation. Therefore, the pressure-TSSP curve in Fig. 7 to represent the DHC initiation characteristics during the cooldown operation should be converted to the pressure-TSSD curve during the heatup operation. Fig. 18 compares the pressure-TSSP curves during the cooldown operation and pressure- TSSD curves during heatup operation. From the figure, it is anticipated that the measured heatup curve evaluates the
Lager Image
Plant Heatup Transients
Lager Image
Pressure-Temperature Characteristics of Plant Heatup Transients
DHC initiation at lower hydrogen equivalent concentration than the measured cooldown transient #2 curve.
Fig. 19 represents the threshold bulk Heq for the DHC initiation under the plant heatup transients, in which the DHC initiates at lower level of the bulk Heq than that under the cooldown transients. These evaluation results are not consistent with previous experimental studies [12 , 13] that reported the DHC growth is not easily observed in test
Lager Image
Comparison of Pressure vs. Hydride Existence between Cooldown and Heatup Transients
Lager Image
Threshold Bulk Heq for DHC Initiation under Plant Heatup Transients
specimens during specimen heating as compared with specimen cooling. So, the DHC initiation evaluation by using the process-zone evaluation procedure is thought to be overly conservative. In this context, the hydrided region overload evaluation procedure [14 - 17] being developed may be more appropriate to derive meaningful results on the DHC initiation under the heatup transient and upset condition in the future.
6. DISCUSSION ON COOLDOWN OPERATION PROCEDURE
Except for early PHWR reactors, the initial hydrogen concentration of the pressure tubes is about 2~6ppm, and the increasing rate of Heq is less than 1ppm/EFPY in the body region of most pressure tubes in Korea. Considering general Heq trend and the DHC characteristics shown in Figs. 5 (a) and 7 , we can make brief recommendations for a cooldown operation guideline to minimize DHC risks of PHWRs as follows:
  • (1) Depressurization during cooldown operation can contribute to reducing DHC risks but it must not cause diminishment of the reactor stability. For example, the depressurization under lower temperature than 100℃ is not effective to reduce the DHC risk. Depressurization with a temperature higher than 150℃ is more effective to reduce the DHC risk, especially for the pressure tubes which have higherHeq.Figs. 5(a) and7can be used for determining most effective depressurization temperature taking into account plant specificHeq.
  • (2) Rapid cooling from high temperature is effective to reduce the amount of DHC growth during a cooldown operation. The cooling rate must not be higher than the limit value from original design specification or operating procedure of the plant.
In addition, a probabilistic assessment program for pressure tube flaw integrity is being developed based on the present study. It is expected that, in the near future, effective cooldown procedures can be deduced from probabilistic assessment techniques and plant specific quantitative analyses for reduced DHC risks depending on cooldown operating scenarios.
7. CONCLUSIONS
In this research, a deterministic DHC evaluation program was developed based on CSA N285.8 procedure prior to expanded probabilistic damage frequency assessment. It was used for systematic structural integrity assessment of the pressure tubes with a volumetric flaw, from which the following conclusions were made.
  • (1) The DHC initiation time of volumetric flaws is mainly dependent on the flaw size, radius at the flaw-tip, initial hydrogen equivalent concentration, deuterium uptake rate (Heqrate), cooldown and heatup operation scenarios. The effect of the pressure tube deformation was relatively insignificant.
  • (2) The DHC can be initiated earlier for sharper flaw, deeper flaw and higherHeq.
  • (3) The DHC initiation can be roughly estimated by using the pressure-TSSP curve translated from the cooldown operation curve.
  • (4) The DHC initiation and subsequent growth can be mitigated through a cooldown operation with depressurization at higher temperature. However, this beneficial effect disappeared when the initial crack was large enough to cause the crack growth.
  • (5) Application of the process-zone evaluation procedure led to overly conservative results during the heatup process.
  • (6) Brief recommendations to reduced DHC risks were derived from deterministic evaluation results. Further specific recommendations can be deduced based on probabilistic assessment techniques, which will be reported for the next step of this study.
Acknowledgements
The authors wish to thank Dr. Han-Sub Chung and Dr. Seong-Nam Choi of KHNP central research institute and Dr. Young-Suk Kim of Korea atomic energy research institute for their valuable discussions.
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