# Environmental Fatigue Analysis of Nuclear Structural Components: Assessment Procedures, Loads, and a Case Study

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## Abstract

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## 1. Introduction

_{i}is the applied number of cycles of a given load pair, N

_{i}is the allowable number of cycles for this load pair (derived from design fatigue curves obtained for the particular environment and temperature being analysed), and m is the number of load pairs being considered.

_{en}, to adjust fatigue usage values (calculated with a design air curve) for environmental effects. The F

_{en}factor, which can be understood as an environmental correction factor in terms of cycles, has the following form [9]:

_{25}is the number of cycles required for the peak tensile stress to drop 25% from its initial value, N

_{25A}is the fatigue life (in cycles) in air at room temperature, N

_{25W}is the fatigue life (in cycles) in water at the temperature of interest, P is a constant for a given temperature and dissolved oxygen content, and ${\dot{\epsilon}}_{T}$ is the strain rate during the rising load phase (%·s

^{−1}).

_{en}factor is applied in the fatigue cumulative usage factor (CUF) derived from the Miner´s rule (or any other similar approach) as follows:

_{i}is the applied number of cycles of a given load pair, N

_{i}is the allowable number of cycles for this load pair (obtained from curves derived in air conditions), F

_{en,i}is the corresponding environmental factor, and m is the number of load pairs being considered. The F

_{en}factor depends, for a particular type of material, on the temperature, dissolved oxygen, sulphur content, and strain rate.

## 2. Incorporating Environmental Effects into Fatigue Assessments

#### 2.1. Former Fatigue Curves

_{a}-N data (corresponding to axial strain-controlled tests, conducted in air on small-scale polished specimens, with a strain ratio of −1). The strain amplitude ε

_{a}is converted into the stress amplitude S

_{a}using the Young’s modulus associated with the corresponding design curve. A mean stress correction is then applied to this equivalent S

_{a}-N mean curve, using the modified Goodman relationship. Finally, transference factors on life and stress amplitude are applied to the modified S

_{a}-N mean curves, in order to include the effects unaccounted for in laboratory testing.

_{a}is the strain amplitude. Here, Equation (4) will be referred to as the Langer curve [12]. Other fatigue models can be used, such as the Basquin model, which is as follows:

_{a}is the strain amplitude.

#### 2.2. NUREG/CR-6909

_{en}(environmental) factor in the former.

_{en}) expressions are simply established through a study of the data trends. The various effects are listed (surface finish, LWR environment, temperature, hold times, etc.) and conclusions are based on data showing an effect or non-effect of the parameter being studied experimentally ([3,13,14]).

#### 2.3. ASME Code Cases

#### 2.4. EN-13445

#### 2.5. RCC-M Approach

_{en}-integrated criterion. The F

_{en}-integrated quantity translates the part of environmental effects, which is considered to already be covered, or “integrated”, in the design fatigue curve. The general idea is to perform EAF assessment and evaluate the F

_{en}factor using the NUREG/CR-6909 approach, and then compare the F

_{en}value with the F

_{en}-integrated criterion. If the F

_{en}value is greater than the F

_{en}-integrated value, then the usage factor needs to include EAF; if the F

_{en}value is smaller than the F

_{en}-integrated value, the environmental effects are already covered by the design fatigue curve and no additional effort is required. This F

_{en}-integrated criterion was established thanks to French experimental campaigns [24] and a statistical calculation similar to NUREG/CR-6909. A summary of the methodology can be found in Table A1.

#### 2.6. DCFS Approach

_{alt}, by applying a fatigue strength reduction factor K

_{sf}[29]. This factor is determined through the analysis of experimental data, as a function of the maximum height of the profile R

_{z}, as defined in ISO 4287:1996 [30] (see [29] for more details). Finally, a coefficient employed to cover data scatter on life is applied. This coefficient is determined as the 95% percentile of the whole data set analysed and not obtained through the NUREG/CR-6909 methodology.

_{en}) expressions were simply established through a study of the data trends, which was an approach that was subsequently followed in NUREG/CR-6909. The overall approach is summarized in Table A1.

#### 2.7. KTA Approach

_{S}), thickness (f

_{e}), and mean stress (f

_{m}) and a coefficient on data scatter of 1.27.

_{en}factor values for the Reactor Cooling System (RCS) and dividing the fatigue criteria of 1 by the F

_{en}factor. The actions encompass online monitoring, experimental testing, and analytical calculations. In the case of analytical calculations, the NUREG/CR-6909 method can be used in conjunction with realistic boundary conditions [33]: these include approaches such as the one presented in RCC-M or the introduction of a transferability factor determined by experimental work [8], which includes beneficial and aggravating effects (hold times, transients, etc.). The overall approach is summarized in Table A1.

#### 2.8. General Remarks

_{en}factor vs. specific curves, to cover environmental conditions.

## 3. Design Loads vs. Real Loads

- -
- Safety of the NPP. Assessments are performed using real conditions, so the resulting evaluations are more accurate and representative of the actual conditions of the structural components;
- -
- Economic benefits, given that unnecessary repairs, replacements, and/or inspections are avoided;
- -
- Operational advantages. Fatigue has been identified as a Time-Limited Ageing Analysis (TLAA) and its assessment is mandatory for long-term operation (LTO) in NPPs;
- -
- Organizational aspects, such as (a) an automated register of the transients, avoiding a manual register and the associated inaccuracies and the necessary conservative treatment of data; (b) automated real-time assessments, avoiding human errors; and (c) detection of those areas in the NPP with a higher CUF, prioritizing inspections and optimizing operational decisions.

## 4. The Case Study

_{en}. In this case, the NUREG/CR-6909 Rev.0 [14] formulation provided for stainless steels was used, together with the NUREG/CR-6909 new design fatigue curve for stainless steels in air (Table 9 in [14]):

_{en}= exp(0.734-T*·O*·(dε/dt)*),

_{en}expressions provided by alternative procedures may be consulted in [39]. Such differences are generally very moderate, although significant variations (up to 80%) have been detected for some particular cases. In the case of austenitic stainless steel 304L, a difference of 30% was observed in the worst case [39].

_{en}factor), the stress values derived in the analyses exhibit peak values (then, stress ranges) which are significantly different when considering design and real (in-plant) transients.

_{en}refers to the cumulative usage factor considering the environmental effects (CUF

_{en}= CUF·F

_{en}). Cycle counting was performed by employing the Rainflow approach, following the guidelines presented in [40].

_{en}factor, the CUF

_{en}factor is reduced by a factor of 1785 (first sequence) or 816 (second sequence). Therefore, for the cases analysed here, the consideration of real data (vs. design data) not only reduces the loads (and stress ranges) used in fatigue analysis, but also reduces the environmental effects through a lower F

_{en}factor. All this has evident consequences for the structural integrity assessment of the components and demonstrates the overconservatism associated with the use of design transients.

## 5. Conclusions

_{en}) is drastically reduced when using real loads provided by monitoring systems. In this case, when no environmental effects are considered, the CUF obtained using real data is approximately two orders of magnitude times lower than that obtained from design transients, for the two sequences of transients considered here. When environmental effects are considered through the F

_{en}factor methodology, the CUF

_{en}obtained using real transients is around three orders of magnitude lower that that derived from design transients.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Approach | Former Fatigue Curves | NUREG/CR-6909 | CC N-761 | EN-13445 (Non- Weld.) | EN-13445 (Weld) | RCC-M | DCFS | KTA | |
---|---|---|---|---|---|---|---|---|---|

Cases used or future use | Over past 50 years to design PWR NPP | For license extension in USA | N/A | Non-nuclear industries & some conventional island components | For EDF NPP life extension | N/A | Fatigue monitoring in Germany | ||

Data fitting equation | Langer equation | Specific fitting eq. including UTS | Basquin eq. | Langer equation | |||||

Fatigue curve | Mean air curve with total least squares fit | Mean air curve with total least square fit and endurance determined separately | Mean air curve with total least squares fit | Mean air curve with total least squares fit and endurance determined separately | Mean air curve with total least squares fit | ||||

Gap between laboratory and component | Life | Translation coefficients with multiplication | Aggravating effects ranges with statistical combination | Factor on life and cycles (safety factor or 3 standard deviation of data scatter) + explicit factor for aggravating parameters | Aggravating effects ranges with statistical combination | Factor for data scatter (β on cycles) + factor surface roughness | Aggravating effects ranges with statistical combination | ||

Strain amplitude | Highest coefficient identified through literature review | Highest coefficient identified as being data scatter – Evaluation of its value through statistical approaches | Factor for data scatter (α on stress) + factor surface roughness | Multiplication of factors taken from EN-13445 and coefficient on data scatter | |||||

Mean stress | Goodman correction | Factor f_{m} to account for mean stress | N/A | Goodman correction | Smith-Watson-Topper corrections | Factor from EN-13445 | |||

Environmental effects | N/A | F_{en} factor determined through study of data trends | Integrated as part of the fatigue curve through a factor on life | N/A | F_{en} NUREG/CR-6909 + F_{en-integrated} criteria determined through French testing campaigns | F_{en} factor determined through study of data trends (JNES) | EAF thresholds on the usage factor + use of F_{en} factor with a transferability factor to include realistic conditions |

## Appendix B

**Table A2.**Calculations performed to derive the cumulative usage factor (CUF) and the cumulative usage factor considering the environmental effects (CUF

_{en}) in the first sequence of design transients. ΔS

_{p}: total stress range in the pair; ΔS

_{n}: primary + secondary stress range in the pair; K

_{e}: elastic-plastic penalty factor; S

_{alt}: alternative stress; N: number of cycles; N

_{a}: maximum number of allowable cycles.

Cycle Start | Cycle End | ΔS_{p} | ΔS_{n} | K_{e} | S_{alt} | N | N_{a} | CUF | F_{en} | CUF_{en} |
---|---|---|---|---|---|---|---|---|---|---|

07/05/1999 00:00:00 | 10/05/1999 21:56:59 | 146.2 | 54.30 | 1 | 76.87 | 0.5 | 2877 | 1.737·10^{−4} | 1 | 1.737·10^{−4} |

10/05/1999 21:56:59 | 25/05/1999 09:41:54 | 275.8 | 94.75 | 2.54 | 368.6 | 0.5 | 59 | 8.465·10^{−3} | 9.20 | 7.792·10^{−2} |

25/05/1999 00:00:00 | 25/05/1999 09:06:09 | 29.79 | 25.65 | 1 | 16.48 | 1 | 1,933,875 | 5.170·10^{−7} | 1 | 5.170·10^{−7} |

25/05/1999 09:41:54 | 26/05/1999 00:00:00 | 129.5 | 41.42 | 1 | 64.99 | 0.5 | 5082 | 9.838·10^{−5} | 1 | 9.838·10^{−5} |

- | - | - | - | - | - | - | Total | 8.74·10^{−3} | - | 7.82·10^{−2} |

**Table A3.**Calculations performed to derive CUF and CUF

_{en}in the first sequence of real transients. ΔS

_{p}: total stress range in the pair; ΔS

_{n}: primary + secondary stress range in the pair; K

_{e}: elastic-plastic penalty factor; S

_{alt}: alternative stress; N: number of cycles; N

_{a}: maximum number of allowable cycles.

Cycle Start | Cycle End | ΔS_{p} | ΔS_{n} | K_{e} | S_{alt} | N | N_{a} | CUF | F_{en} | CUF_{en} |
---|---|---|---|---|---|---|---|---|---|---|

07/05/1999 00:00:00 | 25/05/1999 01:36:00 | 58.54 | 52.34 | 1 | 30.78 | 0.5 | 73,633 | 6.790·10^{−6} | 5.37 | 3.646·10^{−5} |

25/05/1999 01:36:00 | 30/05/1999 15:24:09 | 59.64 | 52.77 | 1 | 31.37 | 0.5 | 68,572 | 7.291·10^{−6} | 1 | 7.291·10^{−6} |

- | - | - | - | - | - | - | Total | 1.41·10^{−5} | - | 4.38·10^{−5} |

**Table A4.**Calculations performed to derive CUF and CUF

_{en}in the second sequence of design transients. ΔS

_{p}: total stress range in the pair; ΔS

_{n}: primary + secondary stress range in the pair; K

_{e}: elastic-plastic penalty factor; S

_{alt}: alternative stress; N: number of cycles; N

_{a}: maximum number of allowable cycles.

Cycle Start | Cycle End | ΔS_{p} | ΔS_{n} | K_{e} | S_{alt} | N | N_{a} | CUF | F_{en} | CUF_{en} |
---|---|---|---|---|---|---|---|---|---|---|

07/05/1999 00:00:00 | 10/05/1999 21:56:59 | 141.3 | 79.82 | 1.77 | 131.7 | 0.5 | 596 | 8.389·10^{−4} | 1 | 8.389·10^{−4} |

10/05/1999 21:56:59 | 06/07/1999 00:05:10 | 288.9 | 151.7 | 3.33 | 506.2 | 0.5 | 31 | 1.628·10^{−2} | 8.46 | 1.378·10^{−1} |

21/06/1999 03:35:39 | 21/06/1999 03:35:56 | 15.33 | 18.19 | 1 | 8.499 | 1 | - | 0 | 1 | 0 |

06/07/1999 00:05:10 | 06/07/1999 07:17:00 | 142.3 | 97.46 | 2.69 | 202.2 | 0,5 | 216 | 2.315·10^{−3} | 1 | 2.315·10^{−3} |

06/07/1999 03:05:00 | 06/07/1999 03:55:00 | 15.92 | 8.199 | 1 | 8.069 | 1 | - | 0 | 1 | 0 |

06/07/1999 04:05:00 | 06/07/1999 04:55:00 | 32.63 | 19.66 | 1 | 16.87 | 1 | 1,669,719 | 5.989·10^{−7} | 1 | 5.989·10^{−7} |

06/07/1999 05:05:00 | 06/07/1999 05:55:00 | 34.82 | 23.25 | 1 | 18.38 | 1 | 972,874 | 1.027·10^{−6} | 1 | 1.027·10^{−6} |

06/07/1999 06:05:00 | 06/07/1999 06:55:00 | 36.75 | 26.49 | 1 | 19.83 | 1 | 624,502 | 1.601·10^{−6} | 1 | 1.601·10^{−6} |

06/07/1999 07:17:00 | 09/07/1999 05:01:54 | 121.0 | 89.77 | 2.30 | 146.6 | 0.5 | 456 | 1.095·10^{−3} | 9,09 | 9.963·10^{−3} |

09/07/1999 00:07:38 | 09/07/1999 04:40:19 | 35.13 | 39.80 | 1 | 19.38 | 1 | 714,816 | 1.398·10^{−6} | 1 | 1.398·10^{−6} |

09/07/1999 05:01:54 | 10/07/1999 00:00:00 | 124.4 | 57.14 | 1 | 62.39 | 0.5 | 5850 | 8.547·10^{−5} | 1 | 8.547·10^{−5} |

- | - | - | - | - | - | - | Total | 2.06·10^{−2} | - | 1.51·10^{−1} |

**Table A5.**Calculations performed to derive CUF and CUF

_{en}in the second sequence of real transients. ΔS

_{p}: total stress range in the pair; ΔS

_{n}: primary + secondary stress range in the pair; K

_{e}: elastic-plastic penalty factor; S

_{alt}: alternative stress; N: number of cycles; N

_{a}: maximum number of allowable cycles.

Cycle Start | Cycle End | ΔS_{p} | ΔS_{n} | K_{e} | S_{alt} | N | N_{a} | CUF | F_{en} | CUF_{en} |
---|---|---|---|---|---|---|---|---|---|---|

07/05/1999 00:00:00 | 12/06/1999 06:59:00 | 59.86 | 73.22 | 1.42 | 44.34 | 0.5 | 18,737 | 2.668·10^{−5} | 5.12 | 1.366·10^{−4} |

12/06/1999 06:59:00 | 12/07/1999 22:20:00 | 64.48 | 76.22 | 1.56 | 53.02 | 0.5 | 10,244 | 4.880·10^{−5} | 1 | 4.880·10^{−5} |

- | - | - | - | - | - | - | Total | 7.55·10^{−5} | - | 1.85·10^{−4} |

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**Figure 1.**Fatigue curves for non-welded components in EN-13445 (reproduced from [19], European Committee for Standardization, 2014). The different fatigue curves each correspond to a different ultimate tensile strength (UTS) level. The dashed lines correspond to fatigue endurance limits in the case of variable amplitude loads [19]. Δσ

_{R}represents the stress range.

**Figure 2.**(

**a**) Evolution of a particular stress component provided by a monitoring system in a Safe End; (

**b**) evolution of the temperature at the same timing and location. The sequence includes six consecutive design transients (corresponding to the different colored lines) [36].

**Figure 3.**Scheme of the different components involved and location of the charging nozzle within the whole system. Yellow arrows indicate the direction of flow.

**Figure 4.**(

**a**) Scheme of the charging nozzle and the cold leg, with the inner radius location. (

**b**) FE model used in stress analysis. Yellow arrows indicate the direction of flow.

**Figure 5.**Temperature evolution in both the cold leg and the charging line during design and in-plant transients. (

**a**) Design heat-up; (

**b**) design cool-down; (

**c**) in-plant heat-up; (

**d**) in-plant cool-down.

**Figure 6.**Temperature and stress evolution in both the cold leg and the charging line during the first sequence of transients. (

**a**) Design temperature; (

**b**) design stresses; (

**c**) in-plant temperature; (

**d**) in-plant stresses. Dates on the horizontal axes do not necessarily correspond to actual dates.

**Figure 7.**Temperature and stress evolution in both the cold leg and the charging line during the second sequence of transients. (

**a**) Design temperature; (

**b**) design stresses; (

**c**) in-plant temperature; (

**d**) in-plant stresses. Dates on the horizontal axes do not necessarily correspond to actual dates.

Transient | Description | Design Occurrences |
---|---|---|

A | Heat-up at 100 °F/h | 200 |

B | Cool-down at 100 °F/h | 200 |

C | Unit loading at 5% of full power/min | 18,300 |

D | Unit unloading at 5% of full power/min | 18,300 |

E | Loss of load from full power | 80 |

F | Reactor trip from full power | 400 |

G | Charging rate increased by 50% | 24,000 |

H | Letdown rate decreased by 50% | 2000 |

I | Charging rate decreased by 50% | 24,000 |

J | High head safety injection | 50 |

**Table 2.**Transients of the second sequence. Dates do not necessarily correspond to actual dates, but the sequence itself, the distribution over time, and the duration of transients correspond to real data.

Transient | Start | End | Name |
---|---|---|---|

A | 10/05/1999 17:10:00 | 02/06/1999 02:46:00 | Heat-up at 100 F/h |

C | 25/05/1999 20:18:00 | 29/05/1999 13:12:00 | Unit loading at 5% of full power/min |

D | 03/06/1999 00:57:00 | 03/06/1999 20:11:00 | Unit unloading at 5% of full power/min |

C | 04/06/1999 00:16:00 | 04/06/1999 16:15:00 | Unit loading at 5% of full power/min |

D | 05/06/1999 00:30:00 | 05/06/1999 09:36:00 | Unit unloading at 5% of full power/min |

C | 05/06/1999 19:23:00 | 06/06/1999 05:31:00 | Unit loading at 5% of full power/min |

D | 07/06/1999 08:36:00 | 07/06/1999 10:46:00 | Unit unloading at 5% of full power/min |

D | 08/06/1999 09:21:00 | 08/06/1999 12:52:00 | Unit unloading at 5% of full power/min |

D | 09/06/1999 09:09:00 | 09/06/1999 13:36:00 | Unit unloading at 5% of full power/min |

C | 09/06/1999 22:04:00 | 10/06/1999 17:13:00 | Unit loading at 5% of full power/min |

G | 11/06/1999 05:02:00 | 11/06/1999 05:16:20 | Charging rate increased by 50% |

H | 11/06/1999 05:16:20 | 11/06/1999 05:45:20 | Letdown rate decreased by 50% |

C | 11/06/1999 21:51:00 | 14/06/1999 17:50:00 | Unit loading at 5% of full power/min |

D | 15/06/1999 21:45:00 | 16/06/1999 08:38:00 | Unit unloading at 5% of full power/min |

C | 16/06/1999 11:50:00 | 17/06/1999 02:44:00 | Unit loading at 5% of full power/min |

D | 18/06/1999 14:31:00 | 19/06/1999 01:33:00 | Unit unloading at 5% of full power/min |

D | 19/06/1999 09:53:00 | 19/06/1999 17:16:00 | Unit unloading at 5% of full power/min |

C | 19/06/1999 21:39:00 | 20/06/1999 02:31:00 | Unit loading at 5% of full power/min |

E | 21/06/1999 03:34:00 | 21/06/1999 11:16:00 | Loss of load from full power |

C | 22/06/1999 21:48:00 | 23/06/1999 16:09:00 | Unit loading at 5% of full power/min |

D | 24/06/1999 04:29:00 | 24/06/1999 22:25:00 | Unit unloading at 5% of full power/min |

C | 25/06/1999 08:58:00 | 29/06/1999 12:09:00 | Unit loading at 5% of full power/min |

D | 30/06/1999 07:30:00 | 30/06/1999 18:34:00 | Unit unloading at 5% of full power/min |

I | 01/07/1999 09:11:00 | 01/07/1999 09:34:00 | Charging rate decreased by 50% |

C | 02/07/1999 18:42:00 | 05/07/1999 04:36:00 | Unit loading at 5% of full power/min |

F | 06/07/1999 00:00:00 | 08/07/1999 00:00:00 | Reactor trip from full power |

J | 06/07/1999 00:05:00 | 06/07/1999 12:40:00 | High head safety injection |

B | 09/07/1999 00:00:00 | 12/07/1999 08:57:00 | Cool-down at 100 F/h |

**Table 3.**Environmental fatigue assessment (EFA) of the inner radius location for the two sequences of transients being considered.

Sequence | Design Transients | Real Transients | CUF_{desig}/CUF_{real} | CUF_{en,desig}/CUF_{en,real} | |
---|---|---|---|---|---|

1 | CUF | 8.74·10^{−3} | 1.41·10^{−5} | 620 | 1785 |

CUF_{en} | 7.82·10^{−2} | 4.38·10^{−5} | |||

F_{en} | 8.95 | 3.11 | |||

2 | CUF | 2.06·10^{−2} | 7.55·10^{−5} | 272 | 816 |

CUF_{en} | 1.51·10^{−1} | 1.85·10^{−4} | |||

F_{en} | 7.33 | 2.45 |

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**MDPI and ACS Style**

Cicero, S.; Metais, T.; Voloshyna, Y.; Cuvillez, S.; Arrieta, S.; Cicero, R.
Environmental Fatigue Analysis of Nuclear Structural Components: Assessment Procedures, Loads, and a Case Study. *Metals* **2020**, *10*, 609.
https://doi.org/10.3390/met10050609

**AMA Style**

Cicero S, Metais T, Voloshyna Y, Cuvillez S, Arrieta S, Cicero R.
Environmental Fatigue Analysis of Nuclear Structural Components: Assessment Procedures, Loads, and a Case Study. *Metals*. 2020; 10(5):609.
https://doi.org/10.3390/met10050609

**Chicago/Turabian Style**

Cicero, Sergio, Thomas Metais, Yuliya Voloshyna, Sam Cuvillez, Sergio Arrieta, and Román Cicero.
2020. "Environmental Fatigue Analysis of Nuclear Structural Components: Assessment Procedures, Loads, and a Case Study" *Metals* 10, no. 5: 609.
https://doi.org/10.3390/met10050609