Master Curve Reference Temperature T₀

ASTM E1921 — Reference Temperature of Ferritic Steels in the Transition Range

1. The Master Curve concept

For ferritic steels in the ductile-to-brittle transition range, cleavage fracture toughness scatters widely but follows a common curve shape. ASTM E1921 characterizes this with a single index temperature T_0, defined as the temperature at which the median K_{Jc} of 1T (25.4 mm thick) specimens equals 100\,\mathrm{MPa}\sqrt{m}.

K_{Jc(med)} = 30 + 70\,\exp[0.019(T - T_0)] \quad \mathrm{MPa}\sqrt{m}

2. Three-parameter Weibull + weakest-link size effect

Toughness data follow a three-parameter Weibull distribution with fixed slope b = 4 and threshold K_{min} = 20\,\mathrm{MPa}\sqrt{m}. All data are first size-adjusted to the 1T reference thickness:

K_{Jc(1T)} = 20 + (K_{Jc} - 20)\left(\frac{B_0}{25.4}\right)^{1/4}

3. Determining T₀

Multi-temperature data are fit by the maximum-likelihood equation (Eq 24), solved iteratively for T_{0Q} using only data within -50 \le T_i - T_{0Q} \le 50\,°C. Single-temperature data sets use the closed form K_0 → K_{Jc(med)} = 20 + 0.91(K_0-20) → T_{0Q} (Eq 26–28).

4. Censoring, tolerance bounds and margin

Data exceeding the specimen capacity K_{Jc,limit} (Eq 3) or with excessive ductile tearing are censored. Tolerance bounds (Eq 32) bracket the scatter; a margin-adjusted T_{0,mar} = T_0 + \sigma Z_y (Eq 33–35) covers the small-sample uncertainty.

Enter each specimen's test temperature, measured K_{Jc}, thickness, and (optionally) its K_{Jc,limit}. A minimum of 6 uncensored results is required for a valid T₀.

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