nuclear-fatigue

name	nuclear-fatigue
description	Nuclear fatigue — ASME Section III NB-3222.4 fatigue evaluation, design fatigue curves (air vs. water environment), environmentally-assisted fatigue (EAF) NUREG/CR-6909, cumulative usage factor (CUF), Fen correction, simplified elastic-plastic analysis (K_e), fatigue crack growth in LWR environment, Appendix L, and PWR/BWR cycling transient management.
metadata	{"priority":7,"promptSignals":{"phrases":["nuclear fatigue","ASME nuclear fatigue","CUF nuclear","environmentally assisted fatigue","EAF nuclear","NB-3222.4"],"minScore":3}}

Nuclear Fatigue — Complete Skill

Overview and Regulatory Background

Regulatory Framework

10 CFR 50 Appendix B: quality assurance for nuclear plants; includes fatigue as design consideration NRC Standard Review Plan (NUREG-0800) SRP 3.9.3: design of reactor coolant pressure boundary; requires ASME III NB-3200 compliance License Renewal (10 CFR 54.21): time-limited aging management for 60-year plant life; fatigue is TLA (Time-Limited Aging Analysis) GALL Report (NUREG-1801/2191): aging management programs for license renewal; AMP XI.M101 = fatigue monitoring

Key challenge: Original ASME III fatigue curves developed from air-environment tests; LWR water environment (PWR: high-temperature water at 288°C, boric acid; BWR: high-temperature water + dissolved O₂) accelerates fatigue crack initiation → EAF

ASME Section III Design Fatigue Curves

Basis and Assumptions

ASME III Appendix I design fatigue curves: Developed from smooth-bar specimen tests in air at RT and elevated temperatures Factors on air test data: factor of 2 on stress amplitude OR factor of 20 on cycles (whichever more conservative at each point) Purpose: account for scatter, surface condition, size effects, environment (conservatively assumed air)

Design life: unlimited cycles if below endurance limit (S_alt ≤ S_e_threshold) For austenitic stainless (no true endurance limit): use 10¹¹ cycles as virtual limit

Design Fatigue Curves (Key Data Points)

Carbon and Low-Alloy Steel (SA-508 Gr. 3, SA-533 Gr. B): S_alt [MPa] vs. N_f (allowable cycles) — Curve A of Appendix I:

S_alt (MPa)	N_f (cycles)
400	10³
200	4×10³
150	10⁴
100	5×10⁴
75	2×10⁵
55	10⁶
40	10⁷ (endurance limit)

Austenitic Stainless Steel (SA-182 F316, SA-312 TP304): Higher endurance — Curve B: S_alt = 415 MPa at N = 10³; 170 MPa at N = 10⁶; 125 MPa at N = 10⁸

Nickel-based alloys (Alloy 690, Alloy 600): Similar to austenitic; Appendix I Curve C Alloy 690 TT: improved resistance vs. Alloy 600 (especially PWSCC)

Interpolation between data points: Use log-log interpolation: log(S_alt) = A - B × log(N_f) ASME Code provides tabulated values + fit coefficients

Stress Amplitude Calculation

Alternating stress intensity (S_alt): S_alt = S_p / 2 [S_p = primary + secondary + peak stress intensity range in cycle; peak-to-peak] S_p = P_L + P_b + Q + F [summed stress intensity range over one transient cycle]

Stress concentration: Peak stress F includes elastic stress concentration factor K_t K_t for nozzle corners: 2–5 (stress concentration); Code provides design charts Fatigue penalty factor K_f = 1 + q × (K_t - 1) [q = notch sensitivity; ≈ 0.6–0.9 for steel]

Plasticity correction (K_e): Required when S_n = P_L + P_b + Q > 3S_m (outside shakedown range) K_e_low_alloy = 1 + (1-n)/(nm) × (S_n/(3S_m) - 1) [n = 0.2, m = 0.2 for carbon steel per Table NB-3228.5(b)-1] K_e_stainless = 1 + (1-n)/(nm) × (S_n/(3S_m) - 1) [n = 0.3, m = 0.2 for austenitic] K_e maximum: 3.33 (carbon steel); 2.0 (austenitic) Then: S_alt_effective = K_e × S_alt_elastic / 2

Environmentally-Assisted Fatigue (EAF)

Physics of EAF in LWR Environment

Mechanisms: Hydrogen embrittlement: dissolved H₂ in PWR coolant → H absorption at crack tip → reduced fracture toughness Anodic dissolution: oxide film rupture at crack tip → bare metal dissolution → enhanced crack growth Sulfur species: MnS dissolution in steel → hydrogen sulfide → accelerated crack tip chemistry

Key environmental variables: Temperature T [°C]: fatigue life decreases with T in water (D₂O/H₂O) Strain rate ε̇ [%/s]: slower strain rate → longer exposure to aggressive environment per cycle → more damage Dissolved oxygen (DO) [ppm]: critical for carbon steel; high O₂ (BWR) → oxidizing environment → worse Sulfur content [wt%]: S > 0.015% in carbon steel → MnS dissolution → worse EAF

Effect on fatigue life: LWR water environment reduces fatigue life by factor of 10–30× vs. air at same S_alt and T

NUREG/CR-6909 Fen Model (ANL Model)

Environmental correction factor: N_water = N_air / F_en Actual cycles to failure in water: N_f_water = N_air_ASME × F_en_correction

F_en for Carbon Steel (LWR): ln(F_en) = (A_T) × (A_ε̇) × (A_O) × (A_S) [additive in ln space; multiplicative as factors] Simplified: ln(F_en) = 0.74 × T* × ε̇* × O* T* = 0 (T < 150°C); T* = (T - 150)/175 (150 ≤ T ≤ 325°C); T* = 1 (T > 325°C) ε̇* = 0 (ε̇ ≥ 1%/s); ε̇* = ln(ε̇/1.0) (0.001 ≤ ε̇ < 1%/s); ε̇* = ln(0.001) (ε̇ < 0.001%/s) O* = 0 (DO < 0.05 ppm); O* = 0.27 (DO ≥ 0.05 ppm)

F_en for Austenitic Stainless Steel: ln(F_en) = 0.935 × T* × ε̇* T* = 0 (T < 150°C); T* = (T - 150)/175 (150 ≤ T ≤ 325°C); T* = 1 (T > 325°C) ε̇* = 0 (ε̇ ≥ 0.4%/s); ε̇* = ln(ε̇/0.4) (0.0004 ≤ ε̇ < 0.4%/s); ε̇* = ln(0.0004) (ε̇ < 0.0004%/s) No DO dependence for austenitic (different mechanism)

Example calculation: SA-508 Gr. 3 (carbon steel); T = 288°C; ε̇ = 0.01%/s; DO = 0.005 ppm (PWR) T* = (288-150)/175 = 0.789; ε̇* = ln(0.01/1.0) = -4.605; O* = 0 (DO < 0.05) ln(F_en) = 0.74 × 0.789 × (-4.605) × 1 = -2.69 → F_en = e^(-2.69)... Wait: ln(F_en) = 0.74 × T* × |ε̇*| (positive for damage; ε̇* contribution is absolute value in some ANL formulations) Correct ANL: ln(F_en) = 0.74 × 0.789 × |-4.605| = 2.692 → F_en = e^2.692 = 14.8

Interpretation: fatigue life in PWR water is 14.8× shorter than ASME air curve → multiply N_air cycles by 14.8

Corrected CUF (CUF_en)

Standard CUF: U = Σ (n_i / N_i_air) [N_i from ASME Appendix I air curves]

Environmentally corrected CUF (CUF_en): CUF_en = Σ (n_i / N_i_water) = Σ (n_i × F_en_i / N_i_air) = Σ (n_i / N_i_air) × F_en_i

Acceptance criterion: CUF_en ≤ 1.0 [Code limit; some utilities use 0.8 margin] If CUF_en > 1.0: reduce transient cycles, change material, add weld overlay, or justify by test

Regulatory guidance: NRC RG 1.207: guidance on EAF evaluation; accepts NUREG/CR-6909 model Some utilities use alternative methods: EFS (Effective Flow Stress) model; ANL 2007 revised model

Transient Cycle Counting

Nuclear Plant Transients

Class of transients: Normal (Level A): startup/shutdown, heat-up/cool-down (50°C/hr rate); normal power changes Upset (Level B): reactor trip (SCRAM), loss of feedwater, turbine trips Emergency (Level C): spurious safety injection, small LOCA Faulted (Level D): SSE seismic, large LOCA

Design transient count (typical PWR, 40-year life): Heat-up / Cool-down: 200 cycles (bounded) Reactor trips: 200 Loss of feedwater: 10 Steam line breaks: 1 (Level C) SSE seismic: 1 (Level D)

60-year life extension: Transient count scales proportionally; original 40-year design counts may be non-conservative Actual cycle tracking (fatigue monitoring) required for license renewal

Rainflow Cycle Counting

For complex variable-amplitude loading: ASTM E1049 Rainflow Counting Method Identifies closed hysteresis loops → each loop = one cycle at given amplitude Used when load history is time-series from plant data (SCADA, DTIS)

Steps:

1. Reduce load history to sequence of peaks and valleys
2. Apply rainflow algorithm (half-cycle matching rules)
3. Output: stress-range histogram (S_alt_i, n_i)
4. Apply Miner's rule: U = Σ n_i/N_i

Nuclear fatigue monitoring: Software systems (e.g., AREVA's Fatigue Monitoring System, Westinghouse FLORA) track actual transients Compare against design basis transient counts; alert if design limit approached Required for 60-year license renewal per NUREG-2191 XI.M101

Fatigue Crack Growth in LWR Environment

ASME Section XI Appendix L

Purpose: evaluate pre-existing flaws or fabrication indications for fatigue crack growth Reference fatigue crack growth law (ASME Sec. XI Appendix A): da/dN = C_env × (ΔK)^n [C_env = environmental factor × air rate; ΔK = stress intensity range]

Threshold ΔK_th: Air: ΔK_th ≈ 3 MPa√m (carbon steel); ΔK_th ≈ 4 MPa√m (austenitic) Water (PWR): ΔK_th effectively lower due to environment; use ASME XI Appendix A corrected values

LWR enhancement factor (C_env): Carbon steel in 288°C PWR: C_env × C_air; factor 2–10× depending on R-ratio and environment Austenitic stainless: less susceptible; factor 2–5×

ASME XI Appendix L: Alternative assessment method for flaw indications found in service (in-service inspection ISI) Evaluate remaining fatigue life using fracture mechanics with LWR crack growth rates Accept if a_final < a_allowable (remaining life > evaluation period with margin)

Standards and References

Standard	Scope
ASME BPVC Section III NB-3222.4	Fatigue evaluation of Class 1 components
ASME BPVC Appendix I	Design fatigue curves (air)
ASME BPVC Section XI App. L	Flaw evaluation (fracture mechanics)
NUREG/CR-6909 Rev. 1	EAF evaluation methodology (ANL)
NRC RG 1.207	Guidance for EAF using NUREG/CR-6909
NUREG-2191	GALL report (license renewal)
ASTM E1049	Rainflow cycle counting
MRP-195 (EPRI)	EAF methodology and margins

Output

Provide: component (material type; SA designation; operating environment PWR/BWR), transient list (each transient: name, Level A/B/C/D, n_applied cycles, ΔT [°C], ΔP [MPa]), stress analysis (S_alt [MPa] per transient pair from FEA or Code formula; K_e if S_n > 3S_m), N_air from ASME Appendix I for each S_alt [MPa], standard CUF_air = Σ n_i/N_i, Fen calculation per transient (T* and ε̇* and O*; F_en value), CUF_en = Σ (n_i × F_en_i)/N_i_air, acceptance vs. 1.0, if CUF_en > 1.0: recommended remediation (cycle reduction, ASME Code Case N-809 alternative fatigue method, weld overlay), fatigue monitoring program reference (NUREG-2191 XI.M101), and applicable standard (ASME III NB-3222.4, NUREG/CR-6909, NRC RG 1.207).