BS 7910:2019 Annex N — low-constraint toughness elevation $K_{mat}^c$ and constraint-modified FAD
Standard fracture toughness tests use deeply-cracked bend specimens, which have high crack-tip constraint and give a conservative lower-bound K_{mat}. Many real flaws — shallow flaws, or flaws under tension loading — have lower constraint, where the material behaves tougher, so its effective toughness is higher. BS 7910 Annex N estimates that toughness gain, the constraint-corrected toughness K_{mat}^c, and the constraint-modified FAD, raising the reserve factors for such cases.
Constraint is measured by a normalized parameter \beta (negative = low constraint, higher toughness): the T-stress form \beta_T is recommended for L_r \le 1 and the Q-parameter form \beta_Q for L_r > 1 (N.2.4.2). You can enter \beta directly, or have it computed for one of 12 standard geometries (centre-cracked, edge-notched, compact tension, surface-cracked plate, internally-cracked cylinder, etc.) from the tabulated \beta_T polynomial coefficients in N.3.2 (Tables N.1–N.12). The toughness gain K_{mat}^c comes either from a direct \alpha / k relation or from a Master Curve temperature shift.
Two procedures are available:
The result reports K_{mat}^c, the constraint factor and the constraint-modified assessment quantities. Constraint relaxation is an optional refinement to the standard assessment and should be used with care, since it claims extra margin from the lower constraint of the real geometry.
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