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Thermal cycling of a high-silicon spheroidal graphite cast iron within the ferritic domain has recently been shown to lead to marked coalescence of graphite particles with the development of dendritic protuberances on the largest ones.[1] The alloy which was investigated consisted of 3.10 wt pct carbon, 4.45 wt pct silicon, 0.25 wt pct manganese and 0.0037 wt pct antimony (Fe balance) and had an as-cast fully ferritic matrix stable up to 850 °C as verified with differential thermal analysis. Samples 2 9 10 9 10 mm3 were subjected to thermal cycles which were each 480 seconds long and included a hold at 800 °C ± 10 °C for 60 seconds. The evolution of the microstructure was

TITO ANDRIOLLO and NIELS TIEDJE are with the Department of Mechanical Engineering, Technical University of Denmark, Anker Engelunds Vej 101A, 2800, Kgs. Lyngby, Denmark. JACQUES LACAZE is with the CIRIMAT, Universite´ de Toulouse, 4 alle´e Monso, BP 44362, 31030, Toulouse Cedex 4, France. Contact e-mail: [email protected] Manuscript submitted December 7, 2019.

METALLURGICAL AND MATERIALS TRANSACTIONS A

investigated after 1000, 2000 and 3000 cycles, this later value corresponding to a cumulative length of time at 800 °C of 50 hours. Comparing the microstructure of the as-cast material in Figure 1(a) and after 2000 cycles in Figure 1(b) illustrates the marked coalescence undergone by the graphite precipitates. Figure 1(c) shows at higher magnification that growth of the large precipitates proceeds by the development of dendrite-like protuberances instead of a homogeneous increase of the diameter of the spheroids. Coalescence of the graphite particles is expected to occur provided the maximum temperature reached during the thermal cycles is high enough for some dissolution of graphite to occur. Upon cooling, carbon is seen to re-deposit in selected locations as protuberances rather than homogeneously around the largest particles. This schematic would imply the formation of a gap between the graphite particles and the surrounding matrix upon heating as carbon dissolves within ferrite. Upon cooling, it would be expected that this gap remains in locations where carbon does not re-precipitate. With cycling, dendritic protuberances grow and the gap would thus have enlarged which is not observed. As a matter of fact, the ferritic matrix appears in close contact of graphite all around the precipitates. This suggests that creep of the matrix occurred at a rate that was sufficient for the gap to be closed even where carbon does not redeposit. The aim of this work was thus to model the creep of ferrite occurring while a graphite protrusion develops due to the inhomogeneous precipitation of carbon during successive thermal cycles. Inspired by previous micro-mechanical studies of spheroidal graphite cast iron,[2,3] a unit cell containing a single graphite spheroid was considered, see Figure 2(a). The spheroid is initially spherical with radius R0 and it is embedded in a cylinder of ferrite with initial height 2  L0 and initial radius L0 . The value of L0