Annex L: Weld Master Curve MML

BS 7910:2019 Annex L — characteristic toughness $K_{mat}$ of welds / HAZ / inhomogeneous material via three-stage MML

1. Welds & inhomogeneous material (Annex L)

For homogeneous ferritic steel, the Master Curve reference temperature T_0 follows ASTM E1921. Welds, HAZ and inhomogeneous parent material show extra scatter and low-tail outliers, so BS 7910 Annex L applies the Master Curve Maximum Likelihood (MML) three-stage method to estimate a conservative reference index and the characteristic toughness K_{mat}.

K_{mat(0.025)} = 20 + \{11 + 77\,e^{0.019(T - T_0)}\}\,[-\ln(1-P_f)]^{0.25} \quad \mathrm{MPa}\sqrt{m}

2. Three-stage MML

Stage 1 — maximum-likelihood T_0 (multi-temperature, Eq.L.3) or median K_0 (single-temperature, Eq.L.8). Stage 2 — lower-tail censoring iterated to convergence (Eq.L.4/L.9). Stage 3 (3 \le z < 10) — extreme-value minimum estimate with a small-set safety correction (Eq.L.5/L.6 or L.10/L.11). A homogeneity check (§L.9.4.3 / §L.9.5.4) selects the representative index.

3. Size correction to K_{mat}

The reference toughness K_{mat(0.025)} at the 0.025 m basis is corrected to the structural crack-front length l (Eq.L.14): K_{mat} = 20 + [K_{mat(0.025)} - 20]\,(0.025/l)^{0.25}, with l from the flaw type (l=2c surface, 4c embedded, 2B through) or entered directly.

Enter each specimen's test temperature, measured K_B, thickness B and (optionally) its K_{B,limit}. A minimum of 3 specimens is required for the three-stage analysis. The loading-rate correction (Eq.L.15/L.16) is deferred to v2.

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