BS 7910:2019 §8.9 / Clause 7 — reverse-solve the critical flaw size $a_{crit}$
Answers "under the current loading, how large a flaw can this structure tolerate before it fails" — the basis for setting flaw-acceptance criteria. E3 runs a one-dimensional bisection reverse-solve on the E1 fracture assessment calculator: holding loads, material and geometry fixed, it searches along flaw size a for the critical a_{crit} where the assessment point just touches the failure assessment line (FAL) or the plastic-collapse cut-off. It adds no new fracture mechanics — E1 is called at every iteration.
You fix the flaw shape during the search either by a fixed a/c ratio (so a and c grow together) or by a fixed half-length c (so only depth a grows). The method assumes monotonic behaviour — acceptability gets worse as a grows, which holds for primary-stress-dominated cases — and the search interval end-points are checked explicitly so boundary states are reported (for example, safe across the whole range). The physical scope matches E1: the same crack types, FAD Option 1 / 2, K_{mat} entered directly or from Annex J, and additive \rho or multiplicative V plasticity.
v1 is a one-dimensional solve only: a two-dimensional (a, c independent) search is not included. Polynomial through-wall stress, residual-stress profiles and stress magnifiers (k_{tm} / M_{km} / k_m) are not reverse-solved in v1 (their defaults apply). The default search upper bound 0.95B suits surface flaws; through-thickness types need a manual bound (about 0.95\,W/2).
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