Research On Optimization Method of Fatigue Analysis for Nuclear Pipeline

The initial design life of nuclear power plant is 40 years. In 60 year life extending license application, the fatigue of component should be evaluated under the influence of the fatigue factors of the pressurized water reactor coolant environment. Because the original design used a more conservative analysis method, the result could not meet the requirement of Cumulative usage fatigue factor of RCC-M. An optimizing analysis method is studied, and as an example of application, optimizing fatigue analysis of Safety Injection Nozzle of Main Coolant Line is performed. The evaluation results show that the optimized fatigue analysis results meet the requirements of RCC-M.


Introduction
The repeated stress changes causing by changing pressures, thermal and mechanical loads acting on metal components can cause fatigue damage under sufficient stress cycles, and ultimately lead to component cracking. The latest research shows that in the reactor coolant environment, metal fatigue can be accelerated under specific temperature, strain rate, dissolved oxygen content and material conditions [1] .
There are researches on fatigue of nuclear grade stainless steel in high temperature water environment at home and abroad [2][3][4] .Restricted by calculation technology, in the early design of Pressurized Water Reactor (PWR) nuclear power plants, nuclear-grade pipelines mainly adopted simplified fatigue analysis methods, only calculating the stress value of a scalar (one-dimensional) over time, and for some factors affecting fatigue, envelope method were adopted to calculate stress and fatigue utilization factor. This method has been proven to be conservative in most cases and can be used by designers to get a good judgment, but it is often too conservative and leads to a small design margin. To obtain more accurate and realistic calculation results, it is necessary to study new calculation methods to replace the original simplified formula method. This paper proposed a fatigue optimization analysis method for the life extension of nuclear power plants, and used the safety injection nozzle as an example to calculate. According to the method specified in NUREG/CR-6909 [5] , the influence of the fatigue promotion of the coolant environment was considered, and the fatigue analysis results of the injector nozzle in service for 60 years were obtained.

Fatigue analysis optimization method
According to the actual situation of nuclear first-level pipelines of nuclear power plants, the fatigue optimization analysis method is mainly composed of four optimization methods, including three-dimensional analysis method, transient combination optimization, thermal expansion load combination optimization, and using transient times based on actual operation statistics.

Three-dimensional analysis method
The three-dimensional analysis method uses the threedimensional finite element method to calculate the pressure stress and thermal stress, which is more accurate than the one-dimensional calculation.

Transient combination optimization
In fatigue analysis, unless otherwise specified, the most demanding combination results of all transient pairwise combinations are selected. In the actual situation, it is impossible to directly combine some transients. For example, in the transient condition of cold shutdown, it needs to experience the transition transient from cold shutdown to hot shutdown before the transient operation of thermal shutdown and power operation can be achieved. Therefore, the number of transients from cold shutdown to hot shutdown limits the combination of cold shutdown transients, thermal shutdown and power operation transients.
To avoid the transient combination in the fatigue calculation process being too conservative, all transients can be divided into three groups:  The first group: cold state to cold shutdown  The second group: cold shutdown to hot shutdown  The third group: thermal shutdown to full power The transient times of the second group of working conditions limit the number of combinations of the first group and the third group of working conditions. After the number of combinations is exceeded, the first group and the third group will no longer be combined, only combined between internal transients.

Using thermal expansion load optimization
The thermal expansion load often uses the envelope value, and the calculated stress amplitude is relatively conservative. By adopting the thermal expansion load corresponding to each transient, the stress amplitude can be reduced, thereby obtaining a more accurate cumulative use factor.

Transient times based on actual running statistics
The operating practice of nuclear power plants shows that the number of design transients is often much larger than the number of transients in actual operation due to conservative assumptions. Through years of operating experience and statistical results of nuclear power plants, it is possible to effectively predict the expected number of transients in subsequent operations.
Using transient times based on actual operating statistics has a more obvious optimization effect on the fatigue analysis results.

Environmental fatigue correction factors
The influence of the reactor coolant environment on the fatigue life is expressed by the environmental influence factor F en , and the correction calculation is shown as follows: In the formula, n is the number of transient combinations, F en,i is the environmental impact factor corresponding to the i-th transient combination, and Ui is the cumulative use of fatigue before the i-th transient combination without considering the environmental impact factor.
According to NUREG/CR-6909, the environmental influence factor F en of austenitic stainless steel in the coolant environment is related to the coolant temperature, strain rate and the dissolved oxygen content of the coolant: The definition of O can be referred to NUREG/CR-6909.

Model and analysis path
Take the main pipeline safety injection nozzle as an example, using three-dimensional finite element to carry out fatigue analysis, as shown in Figure 1.

Loads and boundary conditions
(1) Thermal load and pressure load The transient frequency of the safety injection nozzle adopted the predicted number of 60 years of service, and the transient frequency took the envelope value of Unit 1 and Unit 2.
The inner surface is subjected to transient temperature load, and the heat transfer between the inner surface and the medium is determined by the medium temperature and heat transfer coefficient; and the outer surface is considered as adiabatic due to the covering of the insulation layer.
The pressure load is applied to the inner surface in the way of unit load, and the end effect caused by the pressure is considered. The stress cloud diagram is shown in Figure 3. (2) Other mechanical loads Other mechanical loads considered in the fatigue analysis mainly include thermal expansion load, pressure expansion load, dead weight load and OBE load.

Number of transients
The statistical value of the actual operating transients of the power plant is much smaller than the design transients. For example, the fatigue impact of the safety injection nozzle is the most obvious transient, the safety injection system abnormal startup transient, and the 40year design transient is 80 times, but according to statistics, it is estimated that the number of occurrences in 60 years is only 4, which is far lower than the design value.
Considering the 60-year transient times predicted based on the actual operating transient statistics of the power plant, the fatigue assessment results have a greater optimization effect.

Fatigue assessment
The fatigue assessment adopts the RCC-M standard Alevel criteria, and the stress combination method is based on RCC-M ZE200.
According to the requirements of the operation manual of a nuclear power plant: the dissolved oxygen content of the primary circuit coolant is controlled within 0.10ppm, so O'=0.281; according to the "Cold Pipe Section Safety Injection (6 in) Nozzle" 60 years of service transient prediction times fatigue analysis, the average value of the maximum temperature corresponding to the two transient combinations in the stress cycle of the contacting liquid surface should be less than 325℃, so the conservative value is T'=1; corresponding to the effect of strain rate on environmental fatigue, the conservative value should be -6.91 According to formula (2), the environmental fatigue correction factor F en of austenitic stainless steel is: Regardless of environmental fatigue, the evaluation results of the cumulative fatigue use factor of each sensitive position of the safety injection nozzle are shown in the third column of Table 2. The position with the largest cumulative use factor appears in the upstream section of the transition position between the connection pipe and the main pipeline, and the maximum cumulative use factor is 0.036, which meets the specification requirements.
Considering environmental fatigue, the cumulative fatigue use factor evaluation results of each sensitive position of the safety nozzle are shown in the 5th column of Table 2. The position with the largest cumulative use factor appears in the upstream section of the transition position between the connection pipe and the main pipeline, and the largest cumulative use factor is 0.523, which meets the specification requirements.
It can be seen from Table 1 that the position with the largest cumulative use factor appears in the upstream section of the transition position between the connection pipe and the main pipeline. Take this section as an example, the use factors generated by the first 5 transient combinations under the 60-year forecast times and the usage factors generated by 1.5 times the 40-year design transient times are compared in Table 1. It can be seen from Table 3 that because the 60-year forecast times are much less than 1.5 times the 40-year design transient times, resulting the calculation result of the fatigue cumulative use factor is significantly optimized compared with the 40-year design transient times.

Conclusion
The safety injection nozzle of the cold pipe section of the nuclear power plant bears the hot and cold transients in the main coolant loop system. The large temperature difference leads to large thermal stress, and the threeway structure causes stress concentration, which is a metal part with high fatigue accumulation factor and small evaluation margin in the fatigue analysis. In the life extension project of operating nuclear power plants, the cumulative use factor evaluation reported by the original designer for 60 years of service will be too conservative.