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1. Where fatigue crack growth sits in an LBB analysis

At the core of a Leak-Before-Break (LBB) argument: you must show that, over the service life, the time for an initial non-penetrating surface flaw to grow by subcritical crack growth through the wall and cause a leak — and the time from leak to growth to the critical fracture size — is long enough for the monitoring system to detect it and act.

Unlike early simplified assessments, modern mainstream LBB and fitness-for-service standards (KTA 3206, SRP 3.6.3, R6, API 579, FITNET) all require a crack growth estimate without exception.

1.1 The basic principle of fatigue crack growth in KTA 3206

The relation between the fatigue crack growth rate $\frac{da}{dN}$ and the stress intensity factor range $\Delta K$ usually splits, on log-log axes, into three regions:

  1. Region I (threshold region): there is a threshold $\Delta K_{th}$ below which the crack cannot grow.
  2. Region II (steady-state region): a linear relation, the main range for engineering calculation.
  3. Region III (unstable, accelerating region): approaching the material’s critical fracture toughness $\Delta K_c \approx K_{Ic}$, where unstable fracture occurs.

Applicability limit: for practical KTA 3206 use, crack growth is computed with the steady-state Region II only. The stress intensity factor results must also lie within the valid boundaries (e.g. the geometric applicability ranges of $s/R_m$, $a/s$, $a/c$).

2. The core equation and derivation (Paris-Erdogan equation)

KTA 3206 uses the classic Paris-Erdogan equation to approximate the Region II crack growth behaviour:

$$ \frac{da}{dN} = C \cdot (\Delta K)^m $$
  • $\frac{da}{dN}$: the crack extension per load cycle.
  • $\Delta K$: the stress intensity factor range ($\Delta K = K_{max} - K_{min}$).
  • $C, m$: material-dependent constants.

2.1 Ferritic steels and austenitic steels in air

For ferritic materials, and for austenitic materials without a medium (i.e. in air), the constants $C$ and $m$ depend on the stress ratio $R = K_{min}/K_{max}$ and the temperature, and can be estimated with the two-slope envelope data given in ASME BPVC Section XI.

2.2 Austenitic steels in water (high-temperature-water corrosion fatigue)

A high-temperature-water environment (such as the primary or secondary side of a light-water reactor) markedly accelerates crack growth in austenitic steel. KTA 3206 requires a medium contribution to be added for austenitic materials in water:

$$ \left(\frac{da}{dN}\right)_{total} = \left(\frac{da}{dN}\right)_{Luft} + \left(\frac{da}{dN}\right)_{Medium} $$

(the subscript “Luft” is German for “air”). The medium-driven part is computed per NUREG/CR-6176:

$$ \left(\frac{da}{dN}\right)_{Medium} = C_{Medium} \cdot S(R)^{0.5} \cdot T_R^{0.5} \cdot (\Delta K)^{1.65} $$

where the stress-ratio correction factor $S(R)$ is:

$$ S(R) = 1 + 1.8 \cdot R \quad \text{(for } R \leq 0.8 \text{)} $$

$$ S(R) = -43.35 + 57.97 \cdot R \quad \text{(for } R > 0.8 \text{)} $$
  1. $C_{Medium}$ (environment constant): depends on the dissolved-oxygen content of the water.
  2. $T_R$ (load rise time): the time (in seconds) of the load-rise stage in each stress cycle. The slower the loading (larger $T_R$), the longer the corrosive medium acts on the crack tip and the faster the growth.

3. A worked example and system check

Example: growth check for austenitic steel in 0.2 ppm dissolved oxygen

Per the above, with the following case:

  • $\Delta K = 25$ MPa√m,
  • $R = 0.5$
  • $T_R = 10.0$ s
  • dissolved-oxygen level $DO_{level} = 0.2$ ppm

the system derives and outputs the following whitebox steps:

  1. $S(R) = 1 + 1.8 \times 0.5 = 1.900$
  2. $(\frac{da}{dN})_{Luft} = 3.43 \times 10^{-12} \times 1.900 \times (25)^{3.3} \approx 2.508 \times 10^{-7} \text{ m/cycle}$
  3. $(\frac{da}{dN})_{Medium}$, through the acceleration effect, adds a large growth term $\approx 5.5 \times 10^{-7} \text{ m/cycle}$
  4. the pure-SCC-driven part is also activated.

Using the Fracture Mechanics → Fatigue Crack Growth module in the site’s left sidebar, click “Load Example 1 (Austenitic – water environment)” to generate the detailed derivation charts and final data in one click.

📖 References:

  1. KTA 3206 (2014-11) — Bruchausschluss für drucktragende Komponenten in Kernkraftwerken
  2. NUREG/CR-6176 — Review of Environmental Effects on Fatigue Crack Growth of Austenitic Stainless Steels
  3. ASME Section XI, Appendix A / Appendix O