# Investigation on Analysis Method of Environmental Fatigue Correction Factor of Primary Coolant Metal Materials in LWR Water Environment

^{1}

^{2}

^{*}

## Abstract

**:**

_{en}) is mainly used to analyze the influence of the coolant environment on the fatigue life of primary metal materials. Because the calculation of the transformed strain rate is related to the stress history of the component structure, how to determine the strain rate is the most critical step in calculating the F

_{en}. The approaches of the detailed method were given by the Electric Power Research Institute (EPRI) guidelines and RCC-M-2017 Edition Section VI- RPP No. 3 separately, so a gap analysis was performed between the two methods. Furthermore, another average method was also proposed to determine the average strain rate and strain range. Based on the analysis benchmark provided in the EPRI guideline, a simple case study was performed to account for the effect on the fatigue life in applications with different strain rate approaches and different F

_{en}expressions. Finally, two industry case studies were also completed, including on materials of low alloy steel, austenitic stainless steel, and nickel-base alloy. We suggest adopting a more accurate detailed method, and its methodology is recommended to provide more reasonable solutions.

## 1. Introduction

_{en}); the second is to develop a new fatigue design curve suitable for a light water reactor (LWR).

_{en}expressions in reference to NUREG/CR-6909 [6]. Japan began to implement a large number of EAF-related research projects in the 1990s [7]. Japan’s Association of Mechanical Engineers (JSME) formulated the environmental fatigue assessment method (EFEM) and issued the environmental fatigue assessment specification (JSME NF1-2006), which was revised to JNES-SS-0701 (2007.4) in 2009 according to the EFT report. Because of the differences in specimens, test conditions, and test procedures, the F

_{en}formulas proposed by NUREG/CR-6909 in the United States and JNES in Japan are quite different. Therefore, the F

_{en}expressions and boundary conditions between the two editions of NUREG/CR-6909 [8] and the Japan Nuclear Safety Organization (JNES) [9] in Japan should be compared in detail.

_{en}expression was carried out by calculating the stress history of structures in the transient state. The calculation method from stress to strain rate and the selection of time history will directly affect the calculation results of the transformed strain rate. At present, there are two calculation methods—one is the modified rate approach, which considers the strain rate at each time point under the transient state; the other is the average rate approach, which considers the maximum and minimum strain values of each transient in the pair. The calculation method of the strain increment in the modified rate approach was given in the EPRI guideline [10] and AFCEN RCC-M 2017 Section VI-Probationary Phase Rules RPP3 [11], separately, but there is no process for the average rate approach. In this work, therefore, a kind of average rate approach was established by using the average strain rate and strain range based on stress calculation, and the influences of the modified rate approach and the average rate approach on the fatigue life were also compared.

_{en}was applied to the environmental fatigue assessment of the reactor pressure vessel’s inlet nozzle and the steam generator’s divider plate.

## 2. EAF Analysis Method and F_{en} Expression

_{en}expressions of austenitic stainless steel, nickel-based alloy, and low-alloy steel commonly used in nuclear power plants were presented in NUREG/CR6909. The effects of temperature, strain rate, dissolved oxygen in water, and sulfur content in steel materials on the expression are considered.

#### 2.1. EAF Analysis Method

_{en}methodology to evaluate the effects of the reactor water environment on fatigue proceeds as below.

- (1)
- Calculate the fatigue usage factor in the air for the key parts:
- The temperature and pressure transients of the model are calculated one by one, and the envelope curves of the design transient and the actual operation transient should be used for the temperature and pressure transient curves;
- The peak value of stress is selected as the event in fatigue analysis combined with the operation basis earthquake load;
- According to the fatigue calculation method of ASME or RCC-M and the fatigue curve in the air, the fatigue service factor is calculated. The number of each transient should consider the actual operation of the power plant. Assuming that the design life of the nuclear power plant is $T$ years and has been in operation for $H$ years, the nuclear power plant will apply for extending its life by $E$ years. The number of transients that have been in operation for $H$ years is the operated number ${N}_{\mathrm{H}}$, and the number of T − H + E year transients that have not been operated is $\left(T-H+E\right)/T$ of the original design transient numbers N
_{T}. Each transient number is the sum of these two parts, namely, ${N}_{\mathrm{H}}+{N}_{\mathrm{T}}\times \left(T-H+E\right)/T$.

- (2)
- Compute the ${\mathrm{F}}_{\mathrm{en},i}$ for each transient pair in the fatigue analysis.
- (3)
- Apply the ${\mathrm{F}}_{\mathrm{en},i}$ to the fatigue usage factor calculated for each transient pair $\left({\mathrm{U}}_{i}\right)$, to determine the cumulative fatigue usage factor considering the effect of the water environment (${\mathrm{CUF}}_{\mathrm{en}}$).$${\mathrm{CUF}}_{\mathrm{en}}{=\mathrm{U}}_{1}\times {\mathrm{F}}_{\mathrm{en},1}+\dots +{\mathrm{U}}_{n}\times {\mathrm{F}}_{\mathrm{en},n}$$

#### 2.2. F_{en} Expression

_{en}expression was proposed by NUREG/CR-6909, but the expressions and parameters of revision 1 (Rev.1) in 2014 cause a great change compared with those of revision 0 (Rev.0) in 2017, since the environmental effect should be neglected in some conditions. The F

_{en}value should be returned to 1, but the F

_{en}calculated by Rev.0 is still 2.083 in cases of a temperature less than 150 °C or a strain rate greater than 7%/s for austenitic stainless steel. In view of these problems, the expression of F

_{en}was updated in Rev.1 based on supplementing the latest environmental fatigue strength data. Because of the different experiment results, the F

_{en}formulas proposed by NUREG/CR-6909 and JNES are quite different. Taking austenitic stainless steel as an example, Equations (2)–(5) are F

_{en}expressions of JNES, Equations (6)–(9) are F

_{en}expressions of NUREG/CR-6909 Rev.1, and Equations (10)–(14) are obtained from the NUREG/CR-6909 Rev.0, where ${S}^{*}$, ${T}^{*}$, ${O}^{*}$, and ${\epsilon}^{*}$ are the transformed sulfur content, temperature, DO level, and strain rate, respectively.

_{en}expressions of JNES [9] are

_{en}expressions of NUREG/CR-6909 Rev.1 are

_{en}expressions of NUREG/CR-6909 Rev.0 are

## 3. Transformed Strain Rate of F_{en} Calculation

_{en}calculation. It is necessary to consider the structural stress state, the time history of stress, and the transient combination. Two kinds of analysis methods are established in the EPRI guidelines: a simplified method and a detailed method. The first method is an average strain approach considering the maximum and minimum strain values of each group of transient pairs, and the second involves calculating the strain rate at each transient time point shown in Figure 1.

#### 3.1. Detailed Method

_{en}were given by the EPRI guideline, as follows:

- (1)
- Calculate the stress range (${\sigma}_{\mathrm{x}}^{\prime}$, ${\sigma}_{\mathrm{y}}^{\prime}$, ${\sigma}_{\mathrm{z}}^{\prime}$, ${\sigma}_{\mathrm{xy}}^{\prime}$, ${\sigma}_{\mathrm{yz}}^{\prime}$, ${\sigma}_{\mathrm{zx}}^{\prime}$) between the (i−1)th and the ith time steps on a component basis;
- (2)
- From ${\sigma}_{\mathrm{x}}^{\prime}$, ${\sigma}_{\mathrm{y}}^{\prime}$, ${\sigma}_{\mathrm{z}}^{\prime}$, ${\sigma}_{\mathrm{xy}}^{\prime}$, ${\sigma}_{\mathrm{yz}}^{\prime}$ and ${\sigma}_{\mathrm{zx}}^{\prime}$, the principal stress ranges ${\sigma}_{1}^{\prime}$, ${\sigma}_{2}^{\prime}$, ${\sigma}_{3}^{\prime}$ and the stress intensity range (${\sigma}_{SI}^{\prime}$) can be computed;
- (3)
- A sign is then assigned to the stress intensity range based on the sign of the principal stress range with the largest magnitude, as shown in Equation (15).$$S\mathrm{g}n=\frac{{\sigma}_{M}^{\prime}}{\left|{\sigma}_{M}^{\prime}\right|}$$
- (4)
- The strain increment ($\Delta {\epsilon}_{i}$) is then computed so that only increments that are increasingly tensile will be included in the F
_{en}calculation, based on the following equation:$$\Delta {\epsilon}_{\mathrm{i}}=|\begin{array}{ll}\frac{{\sigma}_{SI}^{\prime}}{E}{K}_{\mathrm{e}}& ifSgn=1\\ 0& Otherwise\end{array}$$

_{en}was also outlined in the RCC-M-2017 Edition Section VI- RPP No. 3, as follows:

- (1)
- From the stress tensor (${\sigma}_{x}$, ${\sigma}_{y}$, ${\sigma}_{z}$, ${\sigma}_{xy}$, ${\sigma}_{xz}$, ${\sigma}_{yz}$), the principal stresses are calculated (${\sigma}_{1}$, ${\sigma}_{2}$, ${\sigma}_{3}$);
- (2)
- The differences of principal stresses are then calculated,$$\begin{array}{l}{S}_{12}={\sigma}_{1}-{\sigma}_{2}\\ {S}_{23}={\sigma}_{2}-{\sigma}_{3}\\ {S}_{31}={\sigma}_{3}-{\sigma}_{1}\end{array}$$
- (3)
- The signed Tresca stress intensity is then defined as the largest absolute value of ${S}_{12}$, ${S}_{23}$ and ${S}_{31}$, with the maximum principal stress corresponding sign;
- (4)
- Lastly, the signed Tresca equivalent strain is obtained by dividing the previously obtained stress by the modulus of elasticity from the stress calculation.

#### 3.2. Simplified Method

- (1)
- Firstly, in the transient time history, the period when the stress increment is positive is selected to determine the maximum stress and minimum stress ${\sigma}_{\mathrm{max},x}$, ${\sigma}_{\mathrm{max},y}$, ${\sigma}_{\mathrm{max},z}$, ${\sigma}_{\mathrm{max},xy}$, ${\sigma}_{\mathrm{max},yz}$, ${\sigma}_{\mathrm{max},xz}$, ${\sigma}_{\mathrm{min},x}$, ${\sigma}_{\mathrm{min},y}$, ${\sigma}_{\mathrm{min},z}$, ${\sigma}_{\mathrm{min},xy}$, ${\sigma}_{\mathrm{min},yz}$, ${\sigma}_{\mathrm{min},xz}$;
- (2)
- The stress rates ${\dot{\sigma}}_{i}$ of the six components are determined by dividing the corresponding time increment;
- (3)
- According to the six components of the stress rate tensor, the rate of stress intensity ${\dot{\sigma}}_{\mathrm{SI}}$ is determined;
- (4)
- The strain rate and strain amplitude are then calculated as$$\dot{\epsilon}=\frac{{\dot{\sigma}}_{\mathrm{SI}}}{E}{K}_{e}$$$$\Delta \epsilon =\frac{{\sigma}_{\mathrm{SI}}}{E}{K}_{e}$$

## 4. The Simple Model Analysis and Comparison

#### 4.1. EPRI Guideline Case

_{en}. Compared with the results of the guidelines (GD), relatively good agreement is achieved, and the difference may be caused by the different stress time histories due to mesh sensitivity, transient stress histories, engineer tools, etc.

#### 4.2. The Influence of Different F_{en} Expressions

_{en}in different countries and reports. Table 4 tabulates the effect of F

_{en}expression on environmental fatigue life by using the F

_{en}expressions of JNES, CR6909 Rev.0, and CR6909 Rev.1, which are listed in Section 2.2. The reactor water’s dissolved oxygen content is 0.005 ppm. By comparison, the result for the environmental fatigue as calculated by NUREG/CR-6909 Rev.1 is the smallest, which may be caused by the improvement in F

_{en}expression based on more experimental data. The result of the JNES calculation is the largest, which shows that JNES in Japan achieves a more rigorous assessment of environmental fatigue.

#### 4.3. The Influence of Different Strain Rate Approaches

_{en}obtained by different strain rate approaches are given in Table 5. To compare with the results of GD, the model of example 1 and the transient calculation of F

_{en}are adopted, wherein “Detailed-GD” refers to the calculation results given by the detailed method in the EPRI guidelines, “Detailed-RPP3” refers to the calculation results given by the detailed method in RCC-M-2017 Edition Section VI-RPP3, and “Simplified method” represents the F

_{en}results calculated by using the simplified algorithm given in Section 3.1. It is found that the calculation results of the average algorithm are greater than those of the rate increment algorithm. Since the time history is not considered in the simplified method, the calculation result is more conservative. However, considering that the average method has to employ a complex procedure for the calculation of average strain rate and strain range through stress, the corresponding results are not as accurate as those of the detailed strain rate method. Therefore, it is recommended to adopt the detailed method for environmental fatigue assessment.

## 5. Reactor Pressure Vessel and Steam Generator EAF Evaluation

#### 5.1. Environmental Fatigue Calculation of RPV

_{en}expression, which are 2007 or 2018, respectively. For example, the F

_{en}value was calculated by GD using F

_{en}expression of the NUREG/CR-6909 Rev.0, is expressed as F

_{en-GD-V0}, and the cumulate usage factor is marked as CUF

_{GD-V0}. The CUF

_{CONSER}is calculated by assuming conservative parameters. This method directly conserves the values of parameters in F

_{en}’s expression. For austenitic stainless steel, the maximum value of transient temperature is 294 °C, and the strain rate is less than 0.0004%/s, so the maximum value of F

_{en}is 10.3. For low-alloy steel, the maximum temperature is 294 °C, the sulfur content is 0.025 wt. %, the oxygen content is 0.1 ppm, and the strain rate is less than 0.0004%/s conservatively, and thus the responding maximum value of F

_{en}is 12.18.

_{en}to obtain the fatigue usage factor, considering the environmental effect.

#### 5.2. Environmental Fatigue Calculation of Steam Generator

_{en}values of the steam generator channel head divider plate. Compared with the GD method, some results calculated by the RPP3 method are increased, while others are decreased. The maximum difference is 2.11 to 1.88, which is reduced by 16.7%. The influence of expression is that all results of the V1 version are reduced. The biggest difference is from 2.26 to 1.83, which causes a decrease of 19.1%. Table 9 shows the fatigue results considering the environmental impact. Since the fatigue usage factor in the air is small, the environmental fatigue analysis result considering coolant is still less than 1, so there is no risk of environmental fatigue in this component. For PWR, assuming the temperature is 325 °C, the maximum value of F

_{en}for austenitic stainless steel is 12.8, and that of nickel-based alloy is 15.4. Therefore, if the fatigue usage factor of the austenitic stainless steel parts in the air is less than 0.065, the influence of environmental fatigue can be ignored; if the fatigue usage factor of nickel-based alloy parts in the air is less than 0.078, the influence of environmental fatigue can be ignored.

## 6. Summary

- (1)
- By comparing the detailed method with the average strain and conservative method, the detailed strain rate method can more accurately evaluate the environmental fatigue life of the structure and can be applied to the analysis of the metal fatigue time-limit aging of key components in the nuclear power plant;
- (2)
- Compared with F
_{en}expressions of JNES, CR6909 Rev.0 and CR6909 Rev.1, NUREG/CR-6909 Rev.1 has the smallest result and JNES has the largest result, which indicates that JNES in Japan allows a more rigorous assessment of environmental fatigue; - (3)
- The influence of the F
_{en}expression for low-alloy steel is opposite to that for austenitic stainless steel and nickel-based alloy. The calculation results of version 1 are greater than those of version 0, and the maximum difference increases by 62.6%; - (4)
- Compared with the GD method, the RPP3 method has a lesser effect on the maximum differences between the austenitic stainless steel and low-alloy steel at the inlet nozzle of the pressure vessel, which are 1.9% and 5.1%, respectively. For the nickel-based alloy of the steam generator’s divider plate, the maximum difference is 16%;
- (5)
- If the fatigue usage factor of austenitic stainless steel in the air is less than 0.065 and that of nickel-based alloy is less than 0.078, the influence of environmental fatigue can be ignored.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Transient | Time T/s | Temperature/°C | Heat Transfer/(W·m^{−2}·K^{−1}) | Pressure/MPa | Moment/(kN·m) |
---|---|---|---|---|---|

Tran1 N = 20 | 0 | 315.6 | 8831 | 15.513 | −338.97 |

5 | 315.6 | 8831 | 15.513 | −338.97 | |

205 | 37.8 | 8831 | 6.895 | 112.99 | |

100 | 37.8 | 8831 | 6.895 | 112.99 | |

1200 | 315.6 | 8831 | 15.513 | −338.97 | |

3000 | 315.6 | 8831 | 15.513 | −338.97 | |

Tran 2 N = 50 | 0 | 260.0 | 8831 | 10.342 | −282.48 |

5 | 260.0 | 8831 | 10.342 | −282.48 | |

405 | 315.6 | 8831 | 15.513 | 112.99 | |

1500 | 315.6 | 8831 | 15.513 | 112.99 | |

1900 | 260.0 | 8831 | 13.790 | −282.48 | |

2500 | 260.0 | 8831 | 13.790 | −282.48 | |

Tran 3 N = 20 | 0 | 232.2 | 8831 | 3.103 | −225.98 |

5 | 232.2 | 8831 | 3.103 | −225.98 | |

14,000 | 21.1 | 8831 | 3.034 | 169.49 | |

16,000 | 21.1 | 8831 | 2.758 | 169.49 | |

20,000 | 176.7 | 8831 | 2.758 | −225.98 | |

24,000 | 176.7 | 8831 | 2.758 | −225.98 |

Section | Pair | TranA | TranB | U_{i} | F_{en} | F_{en-GD} | U_{i}·F_{en} | CUF_{-water} |
---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 0.72676 | 5.0271 | 5.1166 | 3.6535 | 4.3092 |

2 | 2 | 2 | 0.16684 | 3.9304 | 3.9854 | 0.65575 | ||

3 | 3 | 3 | 0 | 2.7225 | 2.7153 | 0 |

Section | Pair | U_{i} | CUF_{-air} | F_{en} | U_{i}·F_{en} | CUF_{-water} | CUF_{-water-GD} |
---|---|---|---|---|---|---|---|

1 | 1 | 0.6706 | 1.3498 | 4.79 | 3.2115 | 5.7088 | 5.4521 |

2 | 0.5580 | 3.87 | 2.1618 | ||||

3 | 0.0756 | 2.66 | 0.2010 | ||||

4 | 0.0256 | 2.49 | 0.0637 | ||||

5 | 0.0154 | 2.71 | 0.0418 | ||||

6 | 0.0027 | 6.37 | 0.0173 | ||||

7 | 0.0012 | 8.09 | 0.0094 | ||||

8 | 0.0002 | 1.00 | 0.0002 | ||||

9 | 0.0005 | 4.09 | 0.0022 | ||||

2 | 1 | 0.0914 | 0.131 | 11.60 | 1.0594 | 1.2381 | 1.5979 |

2 | 0.0349 | 4.51 | 0.1574 | ||||

3 | 0.0015 | 6.74 | 0.0102 | ||||

4 | 0.0015 | 2.76 | 0.0041 | ||||

5 | 0.0011 | 3.53 | 0.0040 | ||||

6 | 0.0002 | 4.09 | 0.0008 | ||||

7 | 0.0002 | 5.04 | 0.0008 | ||||

8 | 0.0001 | 8.61 | 0.0009 | ||||

9 | 0.0001 | 8.60 | 0.0005 |

Transient | NUREG/CR-6909Rev.0 | NUREG/CR-6909Rev.1 | JNES |
---|---|---|---|

1 | 5.0271 | 4.2856 | 7.0267 |

2 | 3.9304 | 3.0306 | 5.7055 |

3 | 2.7470 | 1.9071 | 4.1400 |

Transients | Detailed-GD | Detailed-RPP3 | Simplified Method |
---|---|---|---|

1 | 5.0271 | 4.991 | 6.5470 |

2 | 3.9304 | 3.874 | 4.9870 |

3 | 2.7470 | 2.718 | 3.5420 |

Node | Pair | TranA | TranB | U_{i} | F_{en-GD-V0} | F_{en-GD-V1} | F_{en-RPP-V0} | F_{en-RPP-V1} |
---|---|---|---|---|---|---|---|---|

14054 (F316) | 1 | 1 | 6 | 0.00056 | 8.13 | 7.13 | 8.05 | 7.05 |

2 | 6 | 15 | 0.00025 | 6.81 | 5.97 | 6.68 | 5.86 | |

3 | 6 | 6 | 0.00044 | 6.81 | 5.97 | 6.68 | 5.86 | |

8089 (SA-508) | 1 | 1 | 3 | 0.15256 | 6.18 | 9.95 | 5.98 | 9.57 |

2 | 1 | 5 | 0.02080 | 6.42 | 10.41 | 6.23 | 10.05 | |

3 | 5 | 6 | 0.00008 | 5.01 | 7.35 | 5.05 | 7.23 | |

4 | 6 | 6 | 0.01322 | 5.69 | 8.14 | 5.81 | 7.99 | |

5 | 5 | 6 | 0.00002 | 5.01 | 7.35 | 5.05 | 7.02 | |

6 | 13 | 14 | 0.00016 | 2.02 | 2.19 | 2.02 | 2.10 | |

7 | 5 | 11 | 0.00024 | 3.81 | 5.59 | 3.73 | 5.44 | |

8 | 10 | 11 | 0.00066 | 2.68 | 3.63 | 2.59 | 3.47 | |

9 | 10 | 12 | 0.00029 | 5.77 | 8.98 | 5.65 | 8.64 | |

10 | 13 | 13 | 0.00150 | 2.02 | 2.22 | 2.02 | 2.14 | |

11 | 13 | 14 | 0.00006 | 2.02 | 2.19 | 2.02 | 2.10 | |

12 | 10 | 11 | 0.00002 | 2.98 | 4.17 | 2.86 | 3.96 | |

13 | 10 | 15 | 0.00001 | 7.04 | 11.46 | 7.05 | 11.47 |

**Table 7.**The cumulate fatigue usage factor in air and water environments using different strain rate approaches and F

_{en}expressions of RPV inlet nozzle.

Node | CUF_{-air} | CUF_{-water-GD-V0} | CUF_{-water-GD-V1} | CUF_{-water-RPP-V0} | CUF_{-water-RPP-V1} | CUF_{-water-}_{CONSER} |
---|---|---|---|---|---|---|

14,054 | 0.00125 | 0.00931 | 0.00816 | 0.00917 | 0.00804 | 0.01288 |

8089 | 0.18962 | 1.15985 | 1.85393 | 1.12715 | 1.78466 | 2.30957 |

Node | TranA | TranB | U_{i} | F_{en-GD-V0} | F_{en-GD-V1} | F_{en-RPP-V0} | F_{en-RPP-V1} |
---|---|---|---|---|---|---|---|

69587 | 2 | 31 | 0.00146 | 3.16 | 2.60 | 3.39 | 2.80 |

2 | 37 | 0.00154 | 3.15 | 2.58 | 3.37 | 2.78 | |

2 | 34 | 0.00012 | 3.30 | 2.70 | 3.56 | 2.92 | |

2 | 26 | 0.00066 | 3.27 | 2.68 | 3.55 | 2.92 | |

2 | 36 | 0.00003 | 3.18 | 2.61 | 3.52 | 2.89 | |

21 | 36 | 0.00003 | 2.66 | 2.17 | 2.37 | 1.92 | |

21 | 22 | 0.00002 | 2.65 | 2.16 | 2.35 | 1.91 | |

14 | 21 | 0.00030 | 2.77 | 2.26 | 2.32 | 1.88 | |

3 | 21 | 0.00027 | 2.62 | 2.13 | 2.26 | 1.83 | |

1 | 3 | 0.00009 | 3.27 | 2.68 | 3.56 | 2.94 |

Node | CUF_{-air} | CUF_{-water-GD-V0} | CUF_{-water-GD-V1} | CUF_{-water-GD-RPP-V0} | CUF_{-water-GD-RPP-V1} |
---|---|---|---|---|---|

69,587 | 0.00452 | 0.01407 | 0.01154 | 0.01474 | 0.01214 |

58,140 | 0.00146 | 0.00423 | 0.00346 | 0.00350 | 0.00287 |

69,489 | 0.00341 | 0.01054 | 0.00864 | 0.01093 | 0.00901 |

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**MDPI and ACS Style**

Shao, X.; Xie, H.; Zhang, Y.; Xiong, F.; Bai, X.; Jiang, L.; Kan, Q.
Investigation on Analysis Method of Environmental Fatigue Correction Factor of Primary Coolant Metal Materials in LWR Water Environment. *Metals* **2021**, *11*, 233.
https://doi.org/10.3390/met11020233

**AMA Style**

Shao X, Xie H, Zhang Y, Xiong F, Bai X, Jiang L, Kan Q.
Investigation on Analysis Method of Environmental Fatigue Correction Factor of Primary Coolant Metal Materials in LWR Water Environment. *Metals*. 2021; 11(2):233.
https://doi.org/10.3390/met11020233

**Chicago/Turabian Style**

Shao, Xuejiao, Hai Xie, Yixiong Zhang, Furui Xiong, Xiaoming Bai, Lu Jiang, and Qianhua Kan.
2021. "Investigation on Analysis Method of Environmental Fatigue Correction Factor of Primary Coolant Metal Materials in LWR Water Environment" *Metals* 11, no. 2: 233.
https://doi.org/10.3390/met11020233