BS 7910:2019 Clause 8 — cycle-by-cycle integration of $da/dN=A(\Delta K)^m$ with periodic fracture checks
Answers "how many more cycles can a structure with a known initial flaw survive — and, for a given design life, how large an initial flaw is tolerable?". E2 integrates the crack growth law cycle-by-cycle (Section 8.4 general procedure):
\frac{da}{dN}=A(\Delta K)^m \quad (\Delta K\ge\Delta K_0;\ \text{else } 0), \qquad \Delta K=Y(\Delta\sigma)\sqrt{\pi a}
Two-point coupling integrates a and c from their own crack-front \Delta K (Section 8.4.3/8.4.4); flaws are re-characterised on ligament exhaustion (Section 8.4.7); the FAD fracture limit is checked periodically at peak stress (Section 8.4.6 via the E1 engine); ECA mode back-solves the tolerable initial flaw for a design life (Section 8.9).
Every \Delta K comes from the Annex M SIF building block; the fracture limit is the E1 engine; the critical-size guide is E3. E2 itself adds only the Clause 8 growth-law data layer (Tables 8.3/8.4/8.5, Eq. 8.7–8.9), the coupled integrator and the ECA bisection.
Follows the BS 7910:2019+A1:2020 Clause 8, Section 8.4 cycle-by-cycle procedure with the recommended growth laws of Table 8.3/8.4 (mean+2SD ≈ 97.7% survival, Section 8.3). This version does not include rainflow counting — variable-amplitude histories must be pre-counted into spectrum blocks — nor the \Delta K_{eff} near-threshold refinement (Eq. 8.4–8.6). Numerical integration (forward Euler, adjustable step count) is anchored against a closed-form analytic case to <2%. Results support, but do not replace, professional engineering judgement.
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