3.3.2. Line Scan EDS Analysis for Alloying Concentration

To study the ferrite hardening mechanisms and related possibility of solid solution hardening effects of carbon and other alloying elements, the EDS line scan analyses were accomplished at various positions of ferrite grains as illustrated in Figure 6. The general microstructures of short (SQ5) and long time (SQ30) treated samples are depicted by electron micrographs presented in Figure 6a,b, respectively. The associated results of EDS analyses for C, Si, Cr, and Mn concentrations across the ferrite grains are illustrated in Figure 6a1–a4,b1–b4 taken from short (SQ5) and long time (SQ30) treated specimens, respectively. The carbon concentration from the central position of ferrite grains toward the ferrite area adjacent to the ferrite-prior austenite interfaces increased from 5.13 to 7.25 and 3.85 to 10.35 EDSNs, as respective SQ holding time increased from 5 to 30 min (Figure 6a1,b1). These results show that the prior austenite to ferrite phase transformation was related to a greater carbon concentration within ferrite areas formed at pre-existing defect regions of prior austenite grain boundaries and that the progress of ferrite formation was accompanied by further carbon rejection from ferrite to the remaining austenite regions, causing a considerable gradient in the carbon concentration across ferrite grains. The Si concentration from the ferrite region close to the ferrite-prior austenite interfaces, towards the central location of ferrite grains, increased from 1.12 to 1.44 and 1.07 to 1.54 EDSNs (Figure 6a2,b2), and also the Cr concentration increased from 0.78 to 1.00 and 0.75 to 1.11 EDSNs, with respective SQ holding time increasing from 5 to 30 min (Figure 6a2,a3,b2,b3). These results illustrate that Si and Cr atoms are distributed from the growing ferrite-prior austenite interfaces towards the ferrite grains. The Mn concentration, on the other hand, increased from 0.44 to 0.73 and 0.51 to 0.78 EDSNs for central locations of ferrite grains towards the ferrite regions adjacent to the ferrite-prior austenite interfaces of SQ5 and SQ30 samples, respectively (Figure 6a4,b4). The higher carbon and Mn concentrations of ferrite areas close to the ferrite-prior austenite areas can be associated to the considerable contribution of solid solution hardening for these ferrite regions.

## *3.4. Ferrite/Martensite Residual Stress Analysis*

Typical XRD analysis has been employed to detect and estimate the microstructural microconstituents and the associated results are shown in Figure 7 for various SQ heattreated specimens. All the patterns show almost the same BCC diffracted ferrite/martensite planes emphasizing that the peaks corresponding to ferrite or martensite microphases occurred in the same diffracted angles and it is typically difficult to distinguish between martensite and ferrite by XRD analysis because of low tetragonality of martensite developed in this low carbon low alloy steel. Approximately very small peaks of retained austenite (RA) can be also detected for ferrite-martensite DP specimens.

**Figure 6.** Electron micrographs along with carbon, Si, Cr and Mn EDS line-scan curves taken from short (SQ5) and long time (SQ30) treated samples presented in (**a**,**a1**–**a4**,) and (**b**,**b1**–**b4**); respectively. (**a**,**b**) represent electron micrographs in conjunction with hypothetical EDS scan lines expanded within ferrite grains followed in turn by (**a1**–**a4**); and (**b1**–**b4**) indicating the respective qualitative curves for carbon, Si, Cr and Mn concentrations within ferrite grains, respectively. Ferrite grains, pearlite and martensite are labeled as F, P and M symbols, respectively.

**Figure 7.** Comparison of XRD patterns of various SQ heat-treated specimens.

Residual stress "Sin2Ψ" analysis was carried out using the various (211) diffracted ferrite/martensite planes at Ψ angles including −30, −20, −10, 0, 15, 30 and 45 deg from the XRD results shown in Figure 7. A ferrite/martensite peak was chosen for the analysis because of the compositional effects, such as solute carbon variation in the prior austenite, which could also cause shifting of ferrite/martensite peak. Figure 8 shows the variation in residual stress values calculated from the Sin2Ψ analysis results obtained from various SQ heat-treated specimens. For these calculations, E ~ 177 GPa and *v* = 0.26 were used [28]. From the Sin2Ψ analyses, it has been determined that the d-spacing decreases with increasing Ψ, indicating that ferrite/martensite is under higher residual compressive stress condition in short-time treated SQ specimens. This phenomenon can be to correlated a higher mutual ferrite-martensite interaction, thereby generating a considerable density of geometrically necessary dislocations within lower ferrite containing SQ specimens. On the other hand, with increasing in SQ holding time at 720 ◦C, the progress of ferrite formation was enhanced, resulting in more recovered ferrite in the microstructures.

**Figure 8.** Compressive residual stress values (σφ) obtained from Sin2Ψ analyses versus SQ holding time.

## *3.5. Ferrite Hardening Mechanism*

The experimental results indicate that not only the ferrite hardening is quite variable as a function of volume fraction of ferrite, but also it has changed across a specific ferrite grain (from central location towards the ferrite-martensite interfaces) for a particular SQ heat-treated sample (Figures 3 and 4). For ferrite-martensite DP samples containing large fractions of martensite, a significant contribution to ferrite hardening can be associated to the high level of carbon concentration and of course, residual compressive stresses extended within finer ferrite grains (Table 3, Figures 5a and 8). Fine ferrite grains with high carbon concentrations indicate that in addition to the other ferrite hardening mechanisms such as refinement of ferrite crystallite size as well as ferrite-martensite interaction, the solid solution hardening effect of C should be considered to account for the variations in ferrite hardness of short-time treated SQ specimens. Ferrite grains with higher carbon concentrated will have inevitable occurrence of lattice distortion and creation of stress field around solute iron atoms that can be contributed in part to the higher mechanical behavior of ferrite in the ferrite-martensite DP samples containing higher martensite volume fraction. On the other hand, it is obvious that the comprehensive partitioning of carbon will be faster at ferrite-prior austenite interfacial regions with significant density of defects. This is accompanied by the progress of prior austenite to ferrite phase transformation that can be associated to the possibility of greater segregation of carbon atoms to the induced dislocations as well as increased interaction of iron atoms with its stress fields leading to a greater capability to constrain the mobility of geometrically necessary dislocations, which raises the ferrite resistance to deformation through solid solution hardening mechanism [29,30].

The higher ferrite hardening in SQ heat-treated samples containing lower volume fraction of ferrite can be made according to the enhanced interaction of martensite with fine ferrite grains generating higher residual compressive stresses within ferrite (Figure 8). The formation of greater martensite volume fraction in the short-time treated SQ samples means that a smaller ferrite crystallite size is often surrounded by greater numbers of martensitic packets. As a result, the lower fraction of an individual ferrite grain in the short-time treated ferrite-martensite SQ samples experiences a higher localized compressive residual stresses in comparison with the long-time treated ferrite-martensite SQ samples, and hence, the ferrite hardness increases because of the lower mean spacing between dislocations [15,31,32]. This ferrite hardening mechanism seems to be more and more effective in the ferrite-martensite DP specimens containing a higher volume fraction of martensite, beside the occurrence of finer grain boundary ferrite crystals in comparison to the those of DP specimens containing lower volume fractions of martensite. Therefore, it is reasonable to conclude that the short-time treated SQ specimens are characterized by a higher density of dislocations caused by shear and extensive strain generated by the associated martensitic phase transformation, since this path is expected to minimize the accommodation strain energy for the formation of ferrite-martensite interfaces [33,34].

An abnormal trend in ferrite microhardness data occurred in respect of ferrite formation in the case of prolonged-time treated ferrite-pearlite SQ30 samples in comparison to the ferrite-martensite DP microstructures of shorter-time treated SQ samples (Figure 3c). This is interesting to emphasize that an abnormal high ferrite hardness occurred in the SQ30 heat-treated samples containing the maximum level of 15% ferrite with lower carbon concentration in association with the remaining 85% soft pearlite regions. These results indicate that the abnormal ferrite hardening cannot be related to the solid solution hardening effect of carbon and ferrite-martensite interaction, and that this ferrite hardening phenomenon can be associated to a higher redistribution of Si and Cr atoms within ferrite as shown in Figure 9. The Si and Cr concentrations within the central regions of ferrite grains increased by gentle slopes comprising 1.39 to 1.51 and 1.01 to 1.09 EDSNs, respectively, as the SQ holding time increased from 15 to 30 min, while the Si and Cr concentrations were almost constant for the central martensite areas. Therefore, intense solid solution hardening effects of Si and Cr atoms would give rise to the greater hardening of resultant ferrite crystals in the prolonged-time treated SQ30 samples (Figures 3c and 9).

**Figure 9.** Changes in ferrite microhardness, ferrite carbon content and ferrite Si content as a function of progress of ferrite formation for the various SQ heat treated samples.

In addition to a greater solid solution hardening effect caused by relatively higher carbon concentration in ferrite areas adjacent to the ferrite-prior austenite interfaces, the corresponding higher ferrite hardness can also be in part related to the prior austenite to martensite phase transformation causing localized higher residual compressive stresses within adjacent ferrite regions. This is due to the generation of a high dislocation density within ferrite, following water quenching from 720 ◦C to room temperature. The accommodation of compressive residual stresses generated during prior austenite to martensite phase transformation can also be related to the generation of a greater level of mobile dislocation in the vicinity of ferrite areas leading to a greater magnitude of ferrite microhardness that increases from the central position toward the interfacial ferrite regions [35–37]. Therefore, besides uneven partitioning of a greater concentration of carbon within ferrite region adjacent to martensite, the mutual ferrite-martensite interaction generating a considerable density of geometrically necessary dislocations within ferrite can be also considered to be responsible in part for the higher hardening of ferrite area close to the ferrite-martensite interfaces.
