The shortest distance between the martensitic grains. YS: yield stress; UTS: ultimate tensile strength.

#### *3.2. Particle Precipitation*

The SEM analysis revealed 20–70 nm precipitates in the bainitic ferrite in all four studied conditions (Figure 5). However, the particle chemistry and number density varied with condition. In the MoNbV-steel, the particles were mainly of two types: NbV-containing with/without Mo and Mo-containing without Nb or V. In the CrNbV-steel, the particles were also of two types: NbV-containing and Nb-containing (Figure 6). Detailed characterisation of the particle compositions was outside of this paper scope; however, on the basis of previously published data we believe that NbV-containing particles were MX type NbV(CN) [44–46], MoNbV-containing ones were MoNbVC [13,47], and Mo-containing ones could be complex FeMoC [48]. The average particle number density and area fraction were lower in the MoNbV-steel, compared to the CrNbV-steel, for both processing conditions (Table 1). In the MoNbV-steel, with an increase in deformation strain the average >20 nm particle size decreased (from 42 ± 15 to 21 ± 4 nm), number density increased (from 0.27 to 0.91 μm−2), and the relative amount of Mo-containing particles to the total amount analysed also increased (from 25% to 64%). In the CrNbV-steel, the average >20 nm particle size and relative amount of Nb-containing particles did not show a significant variation with strain, although both the number density and area fraction increased (from 0.95 to 1.67 μm−<sup>2</sup> and from 0.0006 to 0.0011, respectively) with strain.

**Figure 5.** SEM images of precipitates in (**a**,**b**) MoNbV-steel and (**c**,**d**) CrNbV-steel after (**a**,**c**) low and (**b**,**d**) high strain processing.

**Figure 6.** Energy dispersive X-ray spectroscopy (EDS) spectra of (**a**) Mo and NbV containing particles in the MoNbV-steel and (**b**) Nb and NbV containing particles in the CrNbV-steel.

The TEM investigation showed presence of 2–8 nm precipitates in the bainitic ferrite in all four conditions (Figure 7). As the particles were too small for EDS, their nature was analysed using the selected area diffraction technique. Numerous calculations (omitted here) suggested absence of Mo-, Cr-, Nb- or V-rich carbides or nitrides in the TEM studied particle size range in both steels. Thus, the particles were identified as Fe3C exhibiting Bagaryatskii [49] orientation relationship to the bcc (bainitic ferrite) matrix: [011]matrix [001]Fe3C and [001]matrix [321]Fe3C (Figure 8). Measurements of d-spacing have shown *d*<sup>012</sup> = 0.306 nm, *d*<sup>111</sup> = 0.317 nm and *d*<sup>200</sup> = 0.358 nm, which was slightly larger than the theoretical values *d*<sup>012</sup> = 0.281 nm, *d*<sup>111</sup> = 0.302 nm and *d*<sup>200</sup> = 0.337 nm calculated using the Fe3C lattice parameters a = 0.674 nm, b = 0.509 nm and c = 0.453 nm [50]. The unit cell size of bcc (bainitic ferrite) matrix, measured using the TEM diffraction patterns, was also expanded to 0.306–0.312 nm (Table 1) from the theoretical value of 0.286 nm. The Fe3C expansion by 5–9% corresponds to this of matrix by 7–9%. It is important to note, that the matrix expansion was larger in the MoNbV-steel than that in the CrNbV-steel. The matrix expansion could result from an increased concentration of solid solute atoms [51]. The average Fe3C size did not vary significantly with steel composition and processing (was within the measurement error). However, the average Fe3C number density and area fraction were lower in the MoNbV-steel, compared to the CrNbV-steel, for both processing conditions (Table 1). With an increase in deformation strain the average 2–8 nm particle number density decreased from 15,667 to 9875 μm−<sup>3</sup> in the MoNbV-steel and from 25,595 to 16,744 μm−<sup>3</sup> in the CrNbV-steel. Within the 2–8 nm size range an opposite trend was observed for 2–3 nm and 3–8 nm particles: amount of 2–3 nm ones decreased with strain and this of 3–8 nm ones increased with strain (compared Figure 9a,b). An opposite trend with strain was also observed for the 2–8 nm particles (studied by TEM) compared to the >20 nm ones (studied by SEM): with an increase in strain the number density of >20 nm particles increased and this of 2–8 nm ones decreased.

**Figure 7.** TEM bright field images of precipitates in (**a**,**b**) MoNbV-steel and (**c**,**d**) CrNbV-steel after (**a**,**c**) low and (**b**,**d**) high strain processing.

**Figure 8.** Selected area diffraction patterns of Fe3C precipitates in (**a**) MoNbV-steel and (**b**) CrNbV-steel; (**c**) determination of the matrix-particle orientation relationship for image (**a**) and (**d**) this for image (**b**).

**Figure 9.** Number density distributions of precipitates studied by TEM for (**a**) >2 nm size range and (**b**) >3 nm size range.

#### *3.3. Dislocation Structure*

Typical dislocation structure in the middle of bainitic ferrite areas is shown in Figure 10 and some selected features are presented in Figure 11. In both steels, the average dislocation density in bainitic ferrite was at the level of (0.9 ± 0.15) × <sup>10</sup><sup>15</sup> <sup>m</sup>−<sup>2</sup> after low strain processing and (0.4 ± 0.10) × <sup>10</sup><sup>15</sup> <sup>m</sup>−<sup>2</sup> after high strain processing (Table 1). These values correspond to the reported in the literature for bainitic microstructures [52–54]. In the MoNbV-steel very high density dislocation walls surrounding a low density interior (arrangements resembling cells) where occasionally observed (Figure 11a), although they were not present in the CrNbV-steel. Bainitic ferrite areas closer to the martensite grains exhibited a higher local dislocation density than the overall average (Figure 11b). In both steels the dislocation arrays (Figure 11c,e), disintegrated walls (Figure 11d) and tangles (Figure 11f) were also observed, mainly after high strain processing.

**Figure 10.** Representative TEM images of dislocation structure in (**a**,**b**) MoNbV-steel and (**c**,**d**) CrNbV-steel after (**a**,**c**) low and (**b**,**d**) high strain processing.

**Figure 11.** Selected TEM images of dislocation structure in MoNbV-steel after (**a**,**b**) low and (**c**,**d**) high strain processing; and in CrNbV-steel after (**e**) low and (**f**) high strain processing.

#### *3.4. Mechanical Properties*

The MoNbV-steel showed higher strength, and slightly lower elongation, than the CrNbV-steel (Table 1, Figure 12). The variations in yield stress (YS) and ultimate tensile strength (UTS) with steel composition were higher for the low strain schedule: 85 MPa in YS and 200 MPa in UTS for the low strain and 75 MPa in YS and 115 MPa in UTS for the high strain schedule. It is worth to note an opposite trend in the elongation variation with strain: in the MoNbV-steel elongation slightly decreased with strain, and in the CrNbV-steel it increased with strain.

**Figure 12.** Engineering stress-strain curves for four studied conditions.

#### **4. Discussion**

According to various empirical equations [55–57]:

$$\mathbf{B\_{s}} = 830 - 270\mathbf{C} - 90\mathbf{M}\mathbf{n} - 37\mathbf{Ni} - 70\mathbf{Cr} - 83\mathbf{Mo},$$

$$\mathbf{B\_{s}} = 732 - 202\mathbf{C} + 216\mathbf{Si} - 85\mathbf{Mn} - 37\mathbf{Ni} - 47\mathbf{Cr} - 39\mathbf{Mo},$$

$$\mathbf{B\_{s}} = 745 - 110\mathbf{C} - 59\mathbf{Mn} - 39\mathbf{Ni} - 68\mathbf{Cr} - 106\mathbf{Mo} + 17\mathbf{Mn}\mathbf{Ni} + 6\mathbf{Cr}^{2} + 29\mathbf{Mo}^{2},$$

the bainite transformation start temperature, Bs, was similar in both steels: 605–628 ◦C in the MoNbV-steel and 612–631 ◦C in the CrNbV-steel. These values can decrease by 40–70 ◦C, if 0.06 wt. % of Nb additions and 30 ◦C·s−<sup>1</sup> cooling rate are taken into account [58,59], reaching ~560 ◦C in the MoNbV-steel and ~565 ◦C in the CrNbV-steel. A possible effect of deformation on Bs is difficult to assess quantitatively. Although it is known that pre-strain may increase Bs [60], due to an increase in the number of bainite nucleation sites, and retard the bainite transformation rate following mechanical stabilisation of austenite [61,62]. Thus, it is obvious that for 500 ◦C finish cooling/holding temperature we observed the bainitic microstructure in both steels. However, the Mo and Cr additions, and strain variation did show some effects on: (i) dislocation structure in the bainitic ferrite and morphology of martensite; and (ii) particle precipitation. Consequently, the mechanical properties varied.

#### *4.1. Strain Effect on Phase Transformation and Precipitation*

In both steels, higher strains should have enhanced DRX (dynamic recrystallization) and strain induced precipitation. Although, the absolute values of grain size, particle number density and solid solute concentrations could have been expected to differ with Mo and Cr contents. Thus, with strain increase: (i) the average dislocation density in bainitic ferrite decreased in both steels; (ii) dislocation cell arrangements did not form in the MoNbV-steel and disintegrated walls were present instead; (iii) the fraction of martensite decreased in both steels, although by a different value: by 1.8 times in the MoNbV-steel and by 15% in the CrNbV-steel; and (iv) the average and maximum sizes of blocky and elongated crystals of martensite either remained constant or decreased in the MoNbV-steel, although they have increased in the CrNbV-steel. All these could be explained if after higher strain processing and more intense dynamic recrystallization of austenite (DRX) the prior austenite grain size (PAGS) was smaller in the MoNbV-steel, due to more effective grain boundary pinning by Mo solute atoms, and coarser in the CrNbV-steel, due to grain growth. Smaller PAGS would increase Bs temperature and help nucleation of the bainitic ferrite. With sufficient holding time, this would result in a low retained austenite fraction available for the martensitic transformation. A slightly lower dislocation density in bainitic ferrite after high strain schedule compared to the low strain one (Table 1), could be explained by the increased Bs temperature and longer time at high temperature available for re-arrangement of dislocations after bainitic ferrite formation.

With strain increase the >20 nm particles area fraction and number density increased and the <20 nm volume fraction and number density decreased in both steels. This indicates faster nucleation and growth of precipitates for the higher strain schedule. In addition, the amount of Mo-containing particles in the MoNbV-steel increased with strain. All these support the expected intensification of strain induced precipitation of NbV-containing particles in both steels and Mo-containing ones in the MoNbV-steel with strain increase.

Enhancement of strain induced precipitation should have resulted in decreased element concentrations in solid solution and possible prior austenite strength decrease. If this occurred, low strength austenite would be faster transforming to bainite (faster growth of the bainitic ferrite would take place) [54], resulting in a lower fraction of retained austenite available for the transformation to martensite during cooling to room temperature after holding. This could be another reason, in addition to PAGS size variation, leading to a decreased fraction of martensite after the higher strain processing.

#### *4.2. Mo and Cr Effects on Phase Transformation*

For the low strain schedule, we observed insignificant effect of 0.2 wt. % Mo or Cr additions on phase characteristics, in particular, the average size of bainitic ferrite areas, dislocation density in bainitic ferrite, size of blocky and elongated grains of martensite, and martensite fraction. Although, the maximum sizes of blocky and elongated martensite slightly increased with Mo content. This could result from the variation in recrystallization stop temperature, Tnr, and prior austenite grain size (PAGS) in the studied steels. Our measurements have shown Tnr to be higher in the MoNbV-steel, ~1000 ◦C, compared to the CrNbV-steel, ~975 ◦C, which is in-line with Mo being a stronger recrystallization retarding element than Cr [36,37]. Therefore, after 0.3 strain at 1175 ◦C and 0.35 strain at 1100 ◦C (modest strain levels with respect to the rate of DRX) the PAGS could be slightly larger in the MoNbV-steel as a result of partial DRX. A larger PAGS would result in a larger size of austenite retained after holding at 500 ◦C and, subsequently, a coarser martensite formed during the final cooling to the room temperature. Presence of diverse dislocation structure (cell walls) in the MoNbV-steel after low strain processing could also result from a larger PAGS. Larger PAGS was observed accelerating the bainite growth rate in low carbon steels [63].

For the high strain schedule, the effect of steel composition on microstructure was more pronounced. Mo addition led to a decreased size (average and maximum) and lower fraction of martensite. This could be explained if after a higher strain PAGS was smaller in the MoNbV-steel (opposite trend to the low strain schedule). High strain levels would increase the rate of DRX in both steels. However, in the MoNbV-steel the recrystallized fine grain size would be preserved by Mo solute atoms pinning the grain boundaries and preventing the grain growth. In contrast, the solute drag effect of Cr atoms was weaker and the grain growth took place in the CrNbV-steel. Smaller PAGS (larger grain boundary area) can facilitate nucleation of bainitic ferrite and increase the Bs temperature [64]. Therefore, in the MoNbV-steel smaller PAGS resulted in smaller size and lower fraction of the martensite.

#### *4.3. Mo and Cr Effects on Precipitation*

The effect of 0.2 wt. % Mo addition on precipitation was more pronounced than that of 0.2 wt. % Cr. In the MoNbV-steel, Mo was present in >20 nm particles, although in the CrNbV-steel Cr did not precipitate. The number density and area fraction of >20 nm Mo/MoNbV-containing particles were 3.5 and 2 times lower, for the low strain schedule, and 1.8 and 3.7 times lower, for the high strain schedule, in the MoNbV-steel compared to the corresponding parameters of Nb/NbV-containing particles in the CrNbV-steel. This indicates a stronger potential of Mo to increase solubility of C and possibly of Nb and V in austenite than that of Cr, thus delaying the precipitation. The effect of Mo addition on the C solubility was reported previously [65].

The number density and volume fraction of <20 nm Fe3C particles were 1.6 and 3 times lower, for the low strain schedule, and 1.7 and 1.5 times lower, for the high strain schedule, in the MoNbV-steel. This suggests a stronger ability of Mo to retard Fe3C precipitation than this of Cr. A combination of several factors might be responsible for this. The tendency for C atoms to form Mo-C dipoles in preference to Fe-C ones was reported previously [66]. This is linked to a higher binding energy between Mo-C atoms (0.45–0.5 eV [67]) compared to the binding energy between the Fe and C in cementite (0.40–0.42 eV [68,69]). A higher binding energy means that a higher activation energy is required for C atom to jump into another position. The carbon diffusivity in Fe also changes in the presence of different solutes and it was reported for both Cr and Mo that the activation enthalpy for carbon diffusion in iron increases [70–72]. However, the carbon diffusivity in ferrite was decreased more in the presence of Mo than of Cr [73]. Absence of Mo-, Cr-, Nb- or V-rich particle precipitation in the <20 nm size range in both steels increased concentrations of these elements, carbon and, maybe, nitrogen in solid solution. In addition, the solid solute concentrations could be higher in the MoNbV-steel, due to less developed precipitation. This would correspond to a larger unit cell expansion of the bainitic ferrite in the MoNbV-steel (0.310–0.312 nm) than that in the CrNbV-steel (0.306–0.308 nm). A larger

effect of Mo than Cr on Fe lattice expansion is related to larger atom radius mismatch between Fe (126 pm) and Mo (139 pm) than between Fe and Cr (128 pm) [74].

#### *4.4. Microstructure-Mechanical Properties Relationship: Role of Solute Atoms*

In spite of similar phase balance, grain size and dislocation density, and less pronounced precipitation, the MoNbV-steel exhibited higher strength than the CrNbV-steel for both processing conditions (Table 1). This could result from higher solid solution strengthening from Mo, Cr, Nb, V, C and N atoms in the MoNbV-steel. To clarify this the contributions to yield stress from various microstructural parameters have been calculated as follows:

• from grain boundaries using the Hall–Petch equation:

$$
\sigma\_{\mathfrak{g}s} = \sigma\_0 + \mathbf{k} \cdot \mathbf{d}^{-1/2} \rho
$$

where <sup>σ</sup><sup>0</sup> = 15 MPa and k = 21.4 MPa·mm1/2 are accepted for pure iron [75], and d is the size of bainitic ferrite areas (the shortest distance between the martensitic grains);

• from precipitation of >20 nm particles using the Ashby-Orowan equation [76], which assumes the dislocation looping around relatively large particles:

$$
\Delta \sigma\_{\rm ps1} = \frac{10.8 \sqrt{\text{f}}}{\text{D}} \ln \left( \frac{\text{D}}{6.125 \times 10^{-4}} \right) / 2
$$

where f is the particle volume fraction and D is the particle diameter in μm;

• from precipitation of <20 nm particles using the order strengthening relationship [77], which assumes the dislocation cutting of relatively small, coherent particles:

$$
\Delta \sigma\_{\text{p<2}} = 0.81 \cdot \text{M} \cdot \frac{\text{\textdegree } \text{\textdegree}}{2 \text{b}} \cdot \left(\frac{3 \pi \text{f}}{8}\right)^{0.5} \text{\textdegree}
$$

where M = 3 is the matrix orientation factor, b = 0.312–0.306 nm is Burgers vector accepted according to the measured unite cell size of bainitic ferrite (Table 1), γ is the matrix-particle interface energy assumed for the Fe-Fe3C interface to be <sup>γ</sup> = 0.5 J·m−<sup>2</sup> [78], and f is the particle volume fraction;

• from dislocations using the long range work hardening theory [79]:

$$
\Delta \sigma\_{\rm wh} = \frac{\alpha}{2\pi} \text{Gb} \sqrt{\rho}\_{\prime}
$$

where α = 0.5 is a constant, G = 85,000 MPa is the shear modulus, b = 0.312–0.306 nm is the Burgers vector and ρ is the measured dislocation density;

• the solid solution strengthening contribution from Mn and Si was estimated using the matrix concentrations of these elements and the following relationship [76]:

$$
\Delta \sigma\_{\text{ss(Si,Mn)}} = 83 \text{C}\_{\text{Si}} + 32 \text{C}\_{\text{Mn}}.
$$

where CSi = 0.3 wt. % and CMn = 1.5 wt. % are Si and Mn concentrations in the bainitic ferrite matrix, respectively.

A possible effect of martensite on the yield stress of studied steels was neglected in the calculation, due to the martensite requiring higher stresses and strains, than bainitic ferrite, to start yielding.

As can be seen from Table 2, for both steels the major contribution to the YS was coming from grain boundary strengthening, which is quite reasonable for the size of bainitic ferrite areas being below 1 μm. Contributions from dislocations were in the same range of values, which is in-line with similar dislocation densities measured in the studied steels. The solid solution strengthening from Si and Mn was the same for all four conditions, because the contents of these elements were similar in both steels and their precipitation was not observed. For three cases, namely the CrNbV-steel in both processing conditions and the MoNbV-steel after high strain processing, calculations overestimated the yield stress (a negative value for the difference between the measured and total calculated yield stress, Δ, was observed, Table 2). This can be related to two major reasons: (i) incomplete number of dislocation-obstacle interactions really occurring, compared to the theoretical maximum assumed in the applied equations; and (ii) the material inhomogeneity. Some volumes of the bainitic ferrite matrix could be softer, due to lower solute atom concentrations or/and lower number density of precipitates or/and lower dislocation density. These softer volumes would start yielding first. However, for the MoNbV-steel processed according to the lower strain schedule the measured yield stress was 89 MPa (~12%) higher than the calculated value. This is in contrast to the lowest precipitation strengthening contribution calculated for the MoNbV-steel subjected to the lower strain processing. The additional strengthening in this condition could originate from two sources: (i) solid solute atoms of Mo, C and, possibly, N; and (ii) atom clusters of Mo, Nb and V. Substantial strengthening from atom clusters was recently reported for microalloyed steels [80–83]. In spite of qualitatively similar effects of Mo and Cr on solubility of other elements, in the CrNbV-steel a possible strengthening from solute atoms and atom clusters did not exhibit itself. Obviously, a quantitatively weaker effect of Cr on solubility resulted in more pronounced precipitation and lower concentrations of microalloying elements available for solid solution and cluster strengthening.


