Fig. 1 Schematic description of heating curve and its staircase curve approximation

Fig. 2 Computation of the new precipitate formed a and dissolved b

Fig. 3 Simplified flow chart for the computer program (V0: the amount of sigma phase before heating)

Fig. 4 Micrograph of DSS in as-received conditions (dark phase ferrite; white phase austenite)

Fig. 5 Temperature during the non-isothermal σ phase dissolution tests and chalk mould (with samples) used for the experiments

Fig. 6 σ phase evolution during ageing heat treatment at 1123 K: comparison between experimental (points) and analytical results (n = 1.6, c = 0, Teq = 1176.5 K, T* = 1123 K, dgrain = 10 μm, M = 42 × 106 J m mol-1 s-1)

Fig. 7 Temporal isothermal evolution of σ phase volume fraction (x) at 1273 K; the discrete symbols are from experiments, and the curve is from Eq. (13) (Vσi = 24.0 vol.%, nd = 1.6, cd = 0, ω0 = 1.9 × 105 s-1, Qd = 202 kJ mol-1)

Fig. 8 Micrographs showing the initial percentage of σ phase (dark phase Vσi; white phase austenite; grey phase ferrite), before the non-isothermal dissolution heat treatments: aσ = 10.8 vol. %, bσ = 24.0 vol.%

Fig. 9 Temporal non-isothermal evolution of σ phase amount (V) for different initial σ phase contents: aV0 = 10.8 vol.%, bV0 = 24.0 vol.%. The discrete symbols are from experiments, and the curve is from the model (nd = 1.6, cd = 0, Qd = 202 kJ mol-1)