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 Paris-law crack growth rate da/dN=A(\Delta K)^m cycle-by-cycle following the BS 7910:2019 Clause 8, Section 8.4 general procedure, with periodic fracture checks (via the E1 / Annex M building blocks) and a tolerable initial-flaw back-solve (ECA, Section 8.9).
Each spectrum block applies its rows in the given list order; when the real load sequence is unknown, put the most damaging row first (Section 8.4.2). For welded joints the law always uses the R \ge 0.5 branch and the full stress range, regardless of the applied R (Section 8.2.1.4). Residual stress is treated as static — it enters the periodic fracture check only and never the cyclic \Delta K (Section 8.2.1.1). Integration is a fixed-step forward Euler scheme (default 2000 increments, with a growth guard that sub-steps), anchored against a closed-form analytic case to within 2%.
v1 has no rainflow counting — variable-amplitude histories must be pre-counted into spectrum blocks (Section 8.2.1.5). The near-threshold \Delta K_{eff} refinement (Eq. 8.4–8.6) is not included; below the threshold \Delta K_0, da/dN = 0 (Section 8.2.3.1). The crack-type list is a 22-type whitelist: polynomial-stress, hole-corner and thick-wall types are excluded in v1. Growth-law validity is advisory (a warning, not a hard stop):
The fracture check supports the additive \rho route only.
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