**4. Results and Discussion**

#### *4.1. Determination of Austenite–Ferrite Transformation Kinetic Mode*

Figure 5 shows the interruptedly quenched microstructure of type 430 stainless steel from the cyclic heat treatment with the RTC of 10 ◦C/min. The observed martensite, as indicated by the arrow, was transformed from the prior austenite by quenching. It is seen that, at each stage, i.e., -<sup>1</sup> , -<sup>2</sup> , -3 , and -<sup>4</sup> in Figure 2a, the prior austenite existed in the form of strips or islands in the ferritic matrix. The measured area fraction of austenite phase at -<sup>1</sup> , -<sup>2</sup> , -<sup>3</sup> , and -<sup>4</sup> is 13.6%, 27.3%, 12.8%, and 23.7%, respectively. When the RTC increased to either 100 ◦C/min or 200 ◦C/min, the area fraction of austenite at the end of cyclic heat treatment decreased largely to about 16.5%, as shown in Figure 6, which suggests the characteristic RTC dependence of phase transformation kinetics.

To interpret the observed results, DICTRA simulation [18–20] under the assumption of one-dimensional planar geometry was carried out, where Tcfe9 thermodynamic and Mob4 mobility databases were used. In order to reduce the amount of calculation while ensuring the quality of simulation, type 430 stainless steel was simplified to the Fe-C-N-Cr system. The simulation was initiated from the beginning of isothermal holding at 950 ◦C and a domain size of 50 μm was used. The equilibrium constituent phases at 1200 ◦C were set as the starting point, i.e., ferrite and austenite with a chemical composition of Fe-0.039C-0.038N-16.34Cr (wt %) and Fe-0.118C-0.198N-14.837Cr (wt %), respectively. The initial ferrite/austenite interface was located globally at 49.35 μm. The simulation was carried out under both LE and PE conditions.

Figure 7 presents the evolution of a Cr profile during the heating and cooling stage under the LE condition. By the end of isothermal holding at 950 ◦C, the Cr profile exhibited a zigzag shape at the interface position, suggesting partitioning behavior of Cr from austenite to ferrite. During heating to 1150 ◦C, the zigzag shape of the Cr profile shrank when the interface migrated towards the austenite region. Even though the rate of change in the Cr gradient at the interface decreases with the increasing of the heating rate, a negative Cr spike in front of the moving interface was formed by the end of the heating stage, i.e., at 1150 ◦C, indicating a shift in transformation kinetics from a slow PLE mode to a fast NPLE mode. A similar ferrite/austenite interface location was achieved irrespective of the heating rate. In contrast, the enrichment of Cr at the ferrite side and the depletion of Cr at the austenite side of the interface gradually built up when the interface was moving backward during the cooling stage, suggesting the transformation kinetics switched from fast NPLE mode to slow PLE mode. At this stage, the cooling rate exerts a noticeable effect on the interface migration since the diffusion of Cr is very time-consuming compared with that of C. Finally, the one-dimensional austenite fraction, which is defined as the length of the austenite region divided by total domain size, reached 29.1%, 24.3%, and 23.6% at the RTC of 10, 100, and 200 ◦C/min, respectively.

**Figure 5.** Optical micrograph showing the microstructure of an interruptedly quenched sample at (**a**) -1 ; (**b**) -2 ; (**c**) -3 ; (**d**) -4 during the cyclic heat treatment with the RTC of 10 ◦C/min.

**Figure 6.** Optical micrograph showing the final microstructure of cyclic heat treatment with the RTC of (**a**) 100 ◦C/min; (**b**) 200 ◦C/min.

**Figure 7.** The evolution of the Cr profile during cyclic heat treatment at the RTC of (**a**,**b**) 10 ◦C/min; (**c**,**d**) 100 ◦C/min, and (**e**,**f**) 200 ◦C/min, where (**a**,**c**,**e**) and (**b**,**d**,**f**) correspond to the heating and cooling stage, respectively.

Simulation results from the PE condition are presented in Table 2. Under the PE condition, carbon diffusion plays a determining role for interface migration while the substitutional element Cr does not redistribute among ferrite and austenite at the interface. Therefore, the RTCs employed in this study have negligible effect on the transformation kinetics. Results from experiments and DICTRA simulation are all summarized in Table 2. It is seen that, when the RTC increases from 10 to 200 ◦C/min, the one-dimensional austenite fraction at the end of the cyclic heat treatment from PE simulation decreases marginally by 0.4%, in contrast to the noticeable decrease of 7% from LE simulation. From the above experimental study and DICTRA simulation, one could summarize that the transformation kinetics in type 430 stainless steel can be better captured by the simulation under the LE condition even though the Fe-C-N-Cr system is only a simplified representative of type 430 stainless steel.


**Table 2.** Measured and simulated austenite fraction by the end of cyclic heat treatment in type 430 stainless steel.

<sup>1</sup> area fraction; <sup>2</sup> one-dimensional fraction. LE: local equilibrium; PE: para equilibrium.

#### *4.2. Mechanism for the Formation of Cr-Rich Precipitates at the Interphase Boundary in Type 430 Stainless Steel*

Figure 8 shows the interruptedly quenched microstructure of the sample from the continuous cooling experiment, as shown in Figure 2b. Type 410S stainless steel is included here for comparison. The cooling rate employed, i.e., 30 ◦C/min was the same as the on-site measured value during the hot-rolling process. As the same as Figure 5, the observed martensite was transformed from the prior austenite by quenching. It is seen that, when samples were quenched at 850 ◦C, as shown in Figure 8a,c, ferrite and martensite were the only two constituent phases. After further slow cooling to 200 ◦C, the interphase precipitates as indicated by the arrow in Figure 8b were formed in type 430 stainless steel in contrast to its absence in type 410 stainless steel, as shown in Figure 8d, under the same heat treatment condition. Based on the calculated phase diagram in Figure 1, it is proposed that the Cr-rich precipitates at the interphase boundary were formed during the slow cooling process from 850 to 200 ◦C.

**Figure 8.** Optical micrographs showing the microstructure quenched from (**a**,**c**) 850 ◦C and (**b**,**d**) 200 ◦C, where (**a**,**b**) and (**c**,**d**) are from type 430 and 410S stainless steel, respectively.

The samples quenched at 850 ◦C from the continuous cooling experiment were subsequently re-examined by SEM with EDS to reveal the Cr profile across interphase boundaries. Figures 9 and 10 present the line scanning results at interphase boundaries in type 430 and 410S stainless

steel, respectively. The line scanning was conducted at a sampling rate of 6 nm/point and under a magnification of ×20,000. The black rectangular data points in Figures 9 and 10 were the raw data from line scanning. Using the "adjacent-averaging method", where 50 neighboring data points included in the adjacent 0.3 μm length line were averaged to substitute the original data point, the Cr profiles were smoothed and more clearly presented in red lines. In type 430 stainless steel, as shown in Figure 9a,b, a substantial enrichment of Cr existed in the ferrite adjacent to the interphase boundary, i.e., 17.59% relative to 15.78% at the far-end of the ferrite matrix. While, in type 410S stainless steel, as shown in Figure 10a,b, the maximum Cr% in ferrite adjacent to the interphase boundary and at the far-end of the ferrite matrix was 12.77% and 12.52%, respectively. When ferrite is enclosed by austenite, soft impingement occurs. As illustrated in Figure 9c,d and Figure 10c,d, the average Cr% in ferrite enriched to 17.2% and 12.85% in type 430 and 410S stainless steel, respectively. Thus, the formation of Cr-rich precipitates at the interphase boundaries were facilitated by the segregated Cr in type 430 stainless steel. In type 410S stainless steel, the enrichment level, if represented by the difference of Cr% in the neighboring area of interphase boundaries from the far end of the ferrite region, was much lower, i.e., 0.25% in contrast to 1.8% in type 430 stainless steel.

**Figure 9.** The Cr concentration profile across (**a**,**b**) single and (**c**,**d**) dual interphase boundaries in type 430 stainless steel interruptedly quenched at 850 ◦C.

**Figure 10.** The Cr concentration profile across (**a**,**b**) single and (**c**,**d**) dual interphase boundaries in type 410S stainless steel interruptedly quenched at 850 ◦C.

In order to further interpret the formation of Cr enrichment, DICTRA simulation under the pre-determined LE condition in Section 4.1 is carried out where the Fe-C-N-Cr system was used as a representative of type 430 or 410S stainless steel as well. As shown in Figure 11, when the temperature decreases from 1200 to 900 ◦C, the interface is migrating toward the ferrite region and partitioning of Cr from austenite to ferrite can be seen. Further temperature decreases led to the backward migration of the interface and a switch of transformation kinetics to NPLE mode where a Cr spike exists in front of the interface. There are two interesting characteristics in this simulation. Firstly, the interface velocity during earlier austenite formation or the later austenite-to-ferrite transformation is much faster in type 410S stainless steel, possibly due to a large driving force as suggested by the phase diagram in Figure 1. Secondly, by the end of the simulation, a substantial Cr enrichment remains at the ferrite side of the interphase boundary in type 430 stainless steel. Compared with the line scanning results in Figures 9 and 10, an astonishing agreement has been achieved in terms of not only the shape of the Cr profile but also the Cr% in the adjacent region of the interphase boundary. Therefore, the experiment and simulation results have strongly supported the correlation between the formation of Cr-rich precipitates at the prior austenite/ferrite interphase boundary and the austenite–ferrite transformation kinetics.

**Figure 11.** The evolution of the Cr profile during continuous cooling for type (**a**,**b**) 430; (**c**,**d**) 410S stainless steel.

#### **5. Conclusions**

The formation of Cr-rich precipitates at the interphase boundary in type 430 stainless steel, which not only induces intergranular corrosion and intergranular stress corrosion cracking but also significantly deteriorates the ductility and toughness, was investigated from the perspective of austenite–ferrite transformation kinetics. The following conclusions were drawn from this work.


**Author Contributions:** Conceptualization, T.J. and J.S.; methodology, R.N. and T.J.; data curation, investigation and formal analysis, R.N. and T.J.; validation, H.W.; supervision, T.J.; writing—original draft preparation, review and editing, T.J.; resources, J.S. and Z.W.

**Funding:** This research was funded by the National Key R&D Program of China (2017YFB0304201) and the Fundamental Research Funds for the Central Universities (N180702012).

**Conflicts of Interest:** The authors declare no conflict of interest.
