Annex M: SIF Alpha · 2026-06-24

BS 7910:2019 Annex M — Analytical SIF solutions for 34 crack geometries

BS 7910 Annex M — Analytical Stress Intensity Factor (K_I)

Based on BS 7910:2019+A1:2020 Annex M, this calculator computes the Mode I stress intensity factor K_I for 34 crack geometries — flat plates, curved shells, cylinders, spheres, nozzle corners, round bars and bolts, plus weld-toe and weld-root flaws. Results are reported at the crack-front positions that apply to the chosen geometry:

• a semi-elliptical surface or corner crack — at its deepest point and its surface point;
• an embedded crack — at the two ellipse tips nearest each surface;
• a through-wall crack — which spans the full thickness and so has no deepest point — at a single front.

K_I is assembled from the membrane and bending stress factors M_m/M_b, the ellipse shape parameter \Phi, and a finite-width correction f_w (Eq. M.3–M.5). Secondary (residual or thermal) stresses Q_m/Q_b reuse the same primary geometry factors. Where a solution is table-based (Tables M.1–M.14), values are interpolated strictly within the printed grids, with no extrapolation. An optional weld-toe magnification M_k raises K_I for cracks at a weld toe.

Validity follows Annex M.2:

• surface flaws are limited near a/B = 1;
• an aspect ratio above a/c = 2.0 is conservatively clamped to 2.0;
• edge through-thickness cracks are rejected beyond a/W = 0.6;
• a finite-width warning is raised for 2c/W > 0.5 (surface) or 2a/W > 0.7 (centre through cracks).

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