*3.1. Fracture Results*

Figure 1 shows dimple and cleavage mix-mode fracture in all fractographies, but the average radius of dimples in S(540, 5) (Figure 1a) is smaller than the other samples including the reference weld without any heat treatment (Figure 1c), and S(640, 50) (Figure 1b).

**Figure 1.** Fracture surface after tensile test of following samples; (**a**) S(540, 5), shows ductile fracture of HAZ (**b**) S(640, 50), shows brittle fracture of HAZ and (**c**) reference weld.

## *3.2. Thermodynamic Modeling*

In order to understand the critical temperatures of phase transformation and formation of stable precipitates in an equilibrium condition of Domex 960, the amount of phases at different temperatures was calculated with Thermocalc [23]. Although the temperatures and amount of phases could be far from the real conditions during Q&P, this calculation could give a good overview of the most stable microconstituents. Figure 2 shows that Ti(C, N) has the highest tendency to form the first carbonitrides in this system. It will start when there is still some liquid in the system and the precipitation will continue until it reaches room temperature. After that, two other carbides (M7C3) and cementite will nucleate around 700 ◦C, but they are not stable and will disappear very soon around 600 ◦C, while their amount is also very small (e.g., 0.001 mol). The next important precipitate in this system in the critical temperature range of 440 ◦C to 640 ◦C, is MoC, as expected from its enthalpy for carbide formation in comparison with other alloying elements in this steel [26]. The kinetics of nucleation and growth of these elements modeled by the TC–Prisma [23] module are illustrated in Figure 3.

**Figure 2.** Amount of all phases calculated with Thermocalc: (**a**) full range of phases; (**b**) focus on carbides.

**Figure 3.** Time–temperature–precipitation (TTP) diagrams of (**a**) Ti(C, N); (**b**) MoC.

According to Figure 3a, Ti(C, N) nucleates at very high temperature, with a maximum rate at ca. 1150 ◦C, at which it takes only 0.2 s. At lower temperatures up to 800 ◦C, the nucleation takes under 10 s. The time for nucleation grows exponentially with decreasing temperature and nucleation takes a longer time than the longest partitioning time used in this work (maximum 50 s). On the other hand, Figure 3b shows that, although nucleation of this carbide (MoC) is very fast, 600 ◦C is a critical temperature for this Q&P, because below this temperature nucleation takes more than 100 s, which means that nucleation of MoC cannot occur during this heat treatment. In summary, Ti(C, N) precipitation could be an issue during welding and previous Ti(C, N) particles from casting could still remain in the structure, but MoC precipitation occurs during the partitioning stage at 640 ◦C.

#### *3.3. Carbon Partitioning*

Understanding the carbon movement during the partitioning stage at different temperatures with regard to the first quenched martensite and retained austenite grain boundaries has an important role in the prediction of the phase transformations. Comparison between the diffusion coefficient of carbon in austenite (*D*<sup>c</sup> <sup>γ</sup>) and ferrite (*D*<sup>c</sup> <sup>α</sup>) in Table 3 shows that for the temperature range of γ + α (440–640 ◦C in this case) the equilibrium '*D*' is more than 100 times higher in ferrite than austenite. This means that carbon can partition out of martensite rapidly but will then pile up behind the α /γ grain boundary.



In other words, this velocity is critical for the determination of the area of retained austenite around tempered martensite plates, especially for low-carbon steels, in order to design the structural and mechanical properties of the material, since three different phenomena could occur during the partitioning stage: (i) The amount of austenite's carbon enrichment to stabilize it after the final quench; (ii) Nucleation and growth of third phases (e.g., bainitic ferrite); and (iii) Carbide precipitation. Nishikawa et al. [27] modeled the influence of the bainite reaction on the kinetics of carbon redistribution during the Q&P process. Simulations indicate that the kinetics of carbon partitioning from martensite to austenite is controlled by carbon diffusion in austenite and is affected only to a small extent by the decomposition of austenite into bainitic ferrite.

Based on microscopy pictures of the samples, a model with 3 μm space for austenite until the next lath of martensite and a 2 μm space for ferrite, which represents martensite in this simulation, in a rectangular linear model with 50 nodes for calculations that are more frequent close to the interface, is assumed (see Figure 4).

Figure 5 shows the simulation results of carbon partitioning at 640 ◦C and 540 ◦C. Regarding the fact that Mn drops the chemical potential of carbon in austenite, it is expected that regions with high Mn concentration attract more carbon [13]. Therefore, adding 1.78 wt % Mn to the system makes carbon atoms pile up at the border of γ/α and causes a constant increase of the carbon content of austenite until 0.15 wt % after 50 s at 640 ◦C. If the partitioning process stops after 2 or 5 s, a small distance of approximately 0.5 μm could be enriched with up to 0.3 wt % C (Figure 5a). As can be seen in Figure 5b, diffusion at 540 ◦C is much slower and makes the boundary full of carbon up to 1.6 wt %.

**Figure 4.** (**a**) Optical microscopy (OM) and (**b**) SEM pictures of samples quenched to 350 ◦C; (**c**) rectangular model with linear mesh assumed for 3 μm austenite and 2 μm martensite.

**Figure 5.** Carbon content of (**a**) Fe–0.08 wt % C–1.78 wt % Mn system at 640 ◦C; (**b**) Fe–0.08 wt % C–1.78 wt % Mn system at 540 ◦C.

In order to find the reason for the very low impact toughness results of samples partitioned at 640 ◦C while they have very good tensile properties, simulations were focused on S(640, 50) and S(540, 5) for comparison. The effect of temperature is shown in Figure 6a. Figure 6b shows the carbon movement inside austenite close to the martensite interface for these two samples, and the existence of retained austenite after the final quench after partitioning can be predicted.

**Figure 6.** Comparison of samples partitioned at 540 ◦C, 5 s (blue) and 640 ◦C, 50 s (red), calculated using Dictra. (**a**) The composition of the interface as a function of the time; (**b**) carbon content vs. location γ/α interface is at 3 μm distance).

Minimum estimated amount of C to stabilize austenite, based on different equations [28–33] for this steel is 0.9 to 1.2 wt % C at ambient temperature. So, comparing with Figure 6b implies that there is no chance for stabilizing the retained austenite in S(640, 50), but there is some possibility in samples treated at 540 ◦C or less. This is also confirmed by XRD measurements of these two samples S(540, 5) and S(640, 50).

Wu et al. [34] investigated the effect of austenite on fracture resistance of Q&P and showed that the energy absorption by transformation from austenite to martensite postponed the crack propagation and enhanced the fracture resistance of Q&P steels. Even a small amount of retained austenite at room temperature could have a significant effect on energy absorption during crack propagation.
