The impact of Nb on dynamic microstructure evolution of an Nb-Ti microalloyed steel

Materials Science & Engineering A 723 (2018) 194–203

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The impact of Nb on dynamic microstructure evolution of an Nb-Ti microalloyed steel

T

⁎

Mohammad Sadegh Mohebbia,b, , Mohammad Rezayatc, Mohammad Habibi Parsaa,d,e, Štefan Nagyf, Martin Noskof a

School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran Department of Mechanical Engineering, Qom University of Technology, P.O. Box 37195-1519, Qom, Iran c Department of Materials Engineering, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran d Center of Excellence for High Performance Materials, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran e Advanced Metal Forming and Thermomechanical Processing Laboratory, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran f Institute of Materials & Machine Mechanics, Slovak Academy of Sciences, Dúbravská cesta 9, 84104 Bratislava 4, Slovakia b

A R T I C LE I N FO

A B S T R A C T

Keywords: Nb-Ti microalloyed steel Dynamic recrystallization Grain size Precipitation

Dynamic recrystallization (DRX) grain size of a Nb-Ti microalloyed steel is investigated at various strain rates and temperatures. Electron microscopy reveals that Nb preferably precipitates on TiN particles at temperature range of T < 1100 °C. As a result, considerable data scatterings are observed for the power law relationship between the normalized DRXed grain size (DDRX/b) and the Zener-Hollomon parameter (Z), the peak strain (εp) and the normalized steady state stress (σss/E). Much better fittings are achieved, however, when distinct analyzes are carried out within the two temperature ranges of T < 1100 °C and T ≥ 1100 °C. It is found that the wellknown universal relationship suggested earlier for DDRX/b does not agree with the present results when they are analyzed separately at the two ranges of temperatures. Through this separation, an approach is developed for quantitative analysis of DRX retardation by Nb solute atoms. Moreover, the results show that separate analyses at the two temperature ranges result in almost similar dependencies of DDRX/b, εp and σss/E as a power function of Z with indexes in the range of 0.11–0.15.

1. Introduction High Strength Low Alloy (HSLA) steels have received increasing interest in numerous industrial applications owing to their high strength and toughness, good weldability and yet relatively low cost [1,2]. Superior performance of these steels are achieved by a proper design of chemical composition along with an optimized thermomechanical processing. The key factor is to develop a fine grained austenite during hot deformation which leads to form fine grained ferrite from the austenite phase transformation during cooling [3,4]. Therefore, it is of great importance to evaluate the austenite grain size during the thermomechanical processing. Generally, the austenite grain size can be affected by static and dynamic recrystallization (DRX) during and between hot deformation passes [5]. In addition to the hot deformation parameters, i.e. strain, strain rate and temperature, the microalloying elements, particularly Nb and Ti, play an important role in this way. They constitute various types of precipitates mainly in the forms of carbides, nitrides and carbonitrides [6,7]. These precipitates are very effective on the development of final strength and toughness of ⁎

the microalloyed steels through both grain refinement and precipitation hardening [8]. Ti-rich precipitates, in particular TiN, have been shown to be effective on preventing austenite grains growth at very high temperatures [9]. Nb, in both forms of solute atoms and precipitates, in particular NbC, plays an important role in microstructural evolutions of microalloyed steels during hot deformation. It can retard the occurrence of DRX by its pinning effect on the austenite grain boundaries during hot deformation [10]. Thus, the strain can be accumulated up to higher levels during hot deformation leading to enhanced grain refinement during phase transformation [11,12]. According to the mentioned role of microalloying elements, one can find that a proper design of thermomechanical processing requires a comprehensive knowledge of their mechanism of precipitation and interactions with the hot deformation parameters. Strain induced precipitation is considered as the most effective mechanism of NbC formation during hot deformation [13]. However, depending on the employed thermomechanical process, Nb precipitates can form in austenite during hot deformation, in ferrite after the phase transformation or during the austenite to ferrite phase transformation [14]. Increase in

Corresponding author at: Department of Mechanical Engineering, Qom University of Technology, P.O. Box 37195-1519, Qom, Iran. E-mail address: [email protected] (M.S. Mohebbi).

https://doi.org/10.1016/j.msea.2018.03.054 Received 10 February 2018; Received in revised form 12 March 2018; Accepted 13 March 2018 Available online 14 March 2018 0921-5093/ © 2018 Elsevier B.V. All rights reserved.

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the deformation temperature would restrict the Nb precipitation in austenite and enhance its precipitation in ferrite [15]. It has been shown that in a Nb-Ti microalloyed steel, this can result in higher strength due to finer Nb-rich precipitates, although the grain refinement contribution is decreased by increase of the deformation temperature [16]. Therefore, an optimized design of thermomechanical processing is required to get advantages of both precipitation hardening and grain refinement. As explained above, not only the hot deformation conditions, but also the state of the microalloying elements, Nb in particular, are effective on the austenite grain size before the phase transformation. Accordingly, it is of great importance to investigate and compare the austenite grain sizes in presence of Nb solute atoms versus Nb-rich precipitates during high temperature deformation. Therefore, the present study aims to investigate the austenite DRX grain size of a Nb-Ti microalloyed steel as a function of the deformation conditions in both states of Nb microalloying element: solute atoms and fine precipitates.

The flow curves show a plateau at large strains where a steady state deformation is expected. The classic features of dynamic recrystallization is seen in the curves, so that the flow stress increases by the strain up to the peak stress (σp) corresponding to the peak strain (εp) followed by a decrease until the steady state stress (σss). Under the conditions of high temperatures and low strain rates, i.e. low Zener-Hollomon parameter, multiple peaks are distinguished as the characteristic of DRX [19,20]. High temperature flow parameters of the present steel were analyzed and a phenomenological constitutive model of the classical hyperbolic sine equation was presented in the previously published paper [21]. The model was developed based on the theoretical activation energy of Q = 270 kJ/mol attributing to the austenite self-diffusion and the theoretical exponent of n = 5. The same value of Q is implemented here to calculate the Zener-Hollomon parameter (Z) at various deformation conditions:

2. Experimental procedure

in which ε ̇ is the strain rate, T′ is the absolute temperature and R is the ideal gas constant. Based on investigations of Cabrera et al. [22,23], in order to successfully apply the activation energy of self-diffusion and the theoretical exponent of n = 5, temperature dependence of the Young's modulus (E) should be taken into account. Therefore, σss is normalized by E in the present work. The Young's modulus temperature dependency within the applied range of temperatures is expressed as [24]:

Q ⎞ Z = ε ̇ exp ⎛ ⎝ RT ′ ⎠

A billet of Nb-Ti microalloyed steel with the chemical composition given in Table 1 was prepared by vacuum induction melting and homogenization at 1200 °C. The billet was hot rolled to a plate with thickness of 16 mm as the primary material. Hot compression specimens with length of 12 mm and diameter of 8 mm were prepared from center of the plate at rolling direction. Isothermal compression tests were implemented at temperatures of 850–1200 °C and strain rates of 0.01–1 s−1 up to high strain of 1.2 s−1 to ensure that DRX is occurred completely. In order to freeze the microstructure of hot compressed specimens, they were immediately water quenched after the hot compression test. The microstructures were investigated by light microscopy. Longitudinal sections of the specimens were polished and etched in a saturated aqueous picric acid solution to detect the primary austenite grain boundaries. Grain boundaries were highlighted for accurate detection by the image processing program, ImageJ [17]. Through this approach, the grain size was calculated as average of diameters of circles with equal area of the detected grain. Scanning Electron Microscopy (SEM) along with Energy Dispersive X-ray Spectroscopy (EDS) were implemented to analyze precipitates in specimens deformed at temperatures of 1000 and 1200 °C with strain rate of 0.1 s−1. A Schotky field emission SEM (JEOL JSM-7600F) equipped with an Energy-Dispersive Spectroscopy (EDS) X-ray analyzer (Oxford Instruments X-max 50 mm2) was employed at 15 kV for this purpose. Furthermore, nanometer-sized precipitates in specimen compressed at 1000 °C with strain rate of 0.1 s−1 were analyzed by Transmission Electron Microscopy (TEM). The 3-mm diameter TEM sample was punched out from a thin foil. Subsequently, it was subjected to Precision Ion Polishing System (PIPS) to prepare the thin electron transparent sample. TEM analyses were performed by a Jeol TEM 1200EX at 200 kV operating voltage.

E = 233.7 − 100.36 T (GPa)

The microstructures along with maps of the grain boundaries after hot compression are illustrated in Figs. 2, 3 and 4 for strain rates of 0.01, 0.1 and 1 s−1, respectively. The grain size distributions are also presented in these figures by the relevant histograms. The micrographs are almost covered by equiaxed grains. The bimodal distributions of grain sizes in Fig. 2 (1100 °C and 1200 °C) can be attributed to the abnormal grain growth of some grains at low strain rate and high temperature. Effects of the strain rate and temperature on the average grain sizes of the present results are shown in Fig. 5(a). As can be found from these results, the DRX grain size is increased by the deformation temperature and decreased by the strain rate. In other words, the DRX grain size is decreased by the Z parameter. Similar dependency has been formulated in previous studies by a power law equation [25–27]. Here, the DRX grain size (DDRX) in the power law equation is normalized by the Burger's vector (b):

DDRX = C Z −m b

Flow curves obtained by hot compression tests at various strain rates and temperatures are depicted in Fig. 1. Effect of friction and strain rate variation was corrected by a mathematical approach [18]. Table 1 Chemical composition of the steel (wt%). Mn

Mo

Nb

Ti

N

Bal.

0.055

0.25

0.7

0.17

0.018

0.023

0.003

Fe

(3)

in which C and m are material constants. The Burger's vector is calculated at various temperatures form the lattice parameter of austenite [28]. ln(DDRX/b) of the present results is depicted versus ln(Z) in Fig. 5(b). As shown in this figure, a line can fit in accordance with Eq. (3). However, a large deviation from the fitted line is evident (Rsquared of 0.83). From Fig. 5(c), it is obvious that this deviation is much less when two different lines are fitted to data sets of T < 1100 °C and T ≥ 1100 °C. The relevant values of C and m are summarized in Table 2. The index m is almost the same for both fitted lines of Fig. 5(c), but different to that of Fig. 5(b). The natural logarithm of (DDRX/b) is also drawn against ln(εp) in Fig. 6(a). A large deviation from the fitted line is apparent (R-squared of 0.64). As can be seen in Fig. 6(b), much better fittings with Rsquared > 0.9 can be made when data points of T < 1100 °C and T ≥ 1100 °C are treated separately. In the earlier investigations, DDRX is treated as a function of the flow stress in the form of [29,30]:

3.1. Flow curves

Si

(2)

3.2. Grain size evolution

3. Results

C

(1)

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Fig. 1. Stress-strain curves of the steel during hot compression at various temperatures and strain rates of (a) 10−2 s−1, (b) 10−1 s−1 and (c) 10° s−1.

σss DDRX q ⎛ ⎞ = K1 E ⎝ b ⎠

similar to those shown in SEM micrographs, is seen in Fig. 8(a). Furthermore, a much finer cubic particle is shown by an arrow in Fig. 8(b). Particles like this are too small to be seen in SEM images. TEM observations along with SEM micrographs suggest that the sub-micron cubic/rectangular shape particles can be existed in a wide range of 20 to a few hundred nanometers. In addition to the mentioned particles, another kind of precipitates are revealed by TEM micrographs, as very fine particles with sizes of a few nanometers which can be seen in Fig. 8(b). The particles are confirmed as NbC by the diffraction pattern analyzing shown in Fig. 8(c). The TEM dark field image corresponding to the same area of Fig. 8(b) is presented in Fig. 8(d). The size and position of the used aperture for the dark field imaging is shown in Fig. 8(c). The corresponding dark field image of Fig. 8(d) illustrates the fine NbC precipitates distributed in the downward grain interior. An interesting feature of Fig. 8(d) is the bright area in the same position as the cubic particle was seen (shown by an arrow). In accordance with Fig. 7(a) and (b), this can be taken as another evidence for preferred distribution of the Nb-rich precipitates on the cubic/rectangular shaped particles in this specimen.

(4)

where q and K1 are material constants. Note that in the relation presented by Twiss [29] and Derby [30], the stress is normalized by the shear modulus. However, for consistency in the present study, it is normalized by the Young modulus. Plots of ln(DDRX/b) versus ln(σss/E) for all data points and also for separated data points (below and above 1100 °C) are presented in Fig. 6(c) and (d), respectively. Again much less deviations from the fitted lines are seen in Fig. 6(d) as compared to that of Fig. 6(c). Values of the constants q and K1 are presented in Table 2. In a similar manner to the index m, the index q is almost the same for both lines of Fig. 6(d), but different to that of Fig. 6(c). 3.3. Electron microscopy Back scatter SEM micrographs of specimens deformed at 1000 and 1200 °C are displayed in Fig. 7. Cubic or rectangular shaped precipitates can be found with sizes either over a few micrometers or sub-micrometer. EDS analyzes reveal that these particles are rich of Ti and N. The most remarkable difference between the two specimens is that precipitates in the specimen deformed at 1000 °C are also Nb-rich, while those in the other specimen are not. TEM micrographs of specimen deformed at 1000 °C are shown in Fig. 8. A rectangular particle with size of a few hundred nanometers,

Fig. 2. Optical microstructures and highlighted maps of grain boundaries after compression at various temperatures and strain rate of 10−2 s−1.

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Fig. 3. Optical microstructures and highlighted maps of grain boundaries after compression at various temperatures and strain rate of 10−1 s−1.

4. Discussion

Different kinds of precipitates in SEM and TEM micrographs of the present study were addressed in Section 3.3. It is well established that particles with regular morphologies (cubic/rectangular) in Ti and Nb-Ti microalloyed steels, such as those seen in Fig. 7 and 8, are TiN [9]. Moreover, nanometer sized precipitates with globular morphology (Fig. 8(b) and (d)) are known to be NbC [14]. Yuan and Liang [35] studied an as forged Nb-Ti microalloyed steel and found coarse Ti-rich particles formed during solidification and fine strain induced Nb-rich precipitates formed during hot deformation. Moreover, Vervynckt et al. [14] addressed very fine Nb-rich particles formed during either the austenite to ferrite phase transformation or cooling of ferrite. One important aspect of precipitates in Nb-Ti microalloyed steels is the interaction between Ti-rich and Nb-rich precipitates. NbC precipitates are

4.1. Precipitates Results of the present study (Fig. 5) reveal a transition between the two temperature ranges of T < 1100 °C and T ≥ 1100 °C. This transition is congruous with the stability temperature of Nb precipitates in literature. Several researchers pointed out that NbC dissolution temperature in various microalloyed steels is in the range of 1050–1100 °C [31–34]. In other words, Nb-rich precipitates are thermodynamically stable at T < 1100 °C and soluble at T ≥ 1100 °C. Nb-Ti microalloyed steels should be discussed in terms of precipitates with respect to the both microalloying elements (Nb and Ti).

Fig. 4. Optical microstructures and highlighted maps of grain boundaries after compression at various temperatures and strain rate of 10° s−1.

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Fig. 5. (a) Variation of DDRX with temperature at various strain rates; and ln(DDRX/b) versus ln(Z) with (b) a single line fitted to all data and (c) two different lines fitted to data of various temperature ranges.

(TixNb1-x)(CyN1-y). Thermodynamic models in compliance with experimental results show increase of x along with decrease of y by temperature, so that above 1100 °C the x value is higher than 0.95. In other words, only TiN particles are stable at very high temperatures [37]. In accordance with this fact, the EDS analyses of Fig. 7(c) and (d) show no Nb concentration at precipitates in sample deformed at 1200 °C.

Table 2 Values of constants of Eqs. (3)–(5). Parameter

for all data

for data of < 1100 °C

for data of ≥ 1100 °C

C m K1 q a σss /E

8933618 0.179 5.61 0.76 2.87 × 10−5 0.135

1535802 0.114 688.8 1.195 2.63 × 10−5 0.138

2713942 0.112 2376.2 1.227 1.91 × 10−5 0.147

0.0298

0.0126

0.0233

0.098

0.13

0.113

b σss /E a εp b εp

4.2. DRX grain size The steady state grain size of DRX is believed to be independent of the initial grain size [5]. The hot deformation conditions, however, are thought to have great effects on its evolution [25,27]. The dependency of DDRX to the Z parameter (Fig. 5) can be explained through these effects. In general, the steady state grain size decreases with increasing the Z parameter [38]. As addressed in Section 4.1, depending upon stability or instability of the NbC precipitates, a discrete variation of DDRX versus Z is seen in Fig. 5(c). Interestingly, similar value of index m is determined for both sets of data (Table 2). This implies that the NbC precipitates have no considerable influence on the decreasing rate of ln(DDRX/b) by ln(Z). In

generally formed by the strain induced precipitation during hot deformation. However, TiN in Nb-Ti microalloyed steels can act as substrate for growth of NbC during cooling from hot temperatures [31,36]. Concentration of Nb on precipitates in Fig. 7(a) and (b) along with the white area shown by an arrow in the dark field TEM micrograph of Fig. 8(d) (on the nanometer TiN particle) can be explained though this phenomenon. Accordingly, some researchers have generally addressed nitrides, carbides and carbonitrides in Nb-Ti microalloyed steels as

Fig. 6. Experimental data of ln(DDRX /b) versus ln(εp) ((a) and (b)), and versus ln(σSS/E) ((c) and (d)) along with the fitted equation; (a) and (c) a single line fitted to all data and (b) and (d) two different lines fitted to data of various temperatures.

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Fig. 7. SEM micrographs and EDS analyses of coarse (> 1 µm) ((a) and (c)) and sub-micrometer sized ((b) and (d)) precipitates in specimens deformed with strain rate of 0.1 s−1 at 1000 °C ((a) and (b)) and 1200 °C ((b) and (d)).

parameters such as the peak strain and the steady state stress can be described as a power function of Z [39,40]. Therefore, εp and σss/E are defined as:

other words, existence of these carbides causes to reduce DDRX in almost the same extent at various deformation conditions. However, more investigations on similar steels are required to extend such a finding as a general DRX feature. As mentioned in Section 3.2, Eq. (4) is a popular relation to achieve a general formulation for various materials and conditions. This equation can also be directly acquired from combination of Eq. (3) and the Z dependency of σss/E. It is well established that many hot deformation

⎛

εp

⎜ σss

⎝

E

= a Zb (5)

Values of a and b obtained by curve fitting to the experimental data are presented in Table 2. It can be simply shown from Eqs. 3–5 that: 199

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Fig. 8. (a) and (b) TEM bright field images of specimen deformed at 1000 °C with strain rate of 0.1 s−1, (c) corresponding diffraction pattern of (b), and (d) TEM dark field image taken from the same area of (b) with size and position of objective aperture shown in (c).

bσss m

(6)

K1 = aσss C q

(7)

q=

data are treated) with the suggested relations by Twiss [29] and Derby [30], conveys no physical meaning. In fact, regarding the evolution of DDRX, specimens having Nb precipitates cannot be categorized in a group with those having no Nb precipitates. Therefore, a relation with similar constants cannot be used to analyze their results together. It is necessary to note that Eq. (8) is not a cause and effect relationship between the flow stress and the grain size (such as the wellknown Hall-Petch relationship [41]). In fact, both σss and DDRX are shown to change with the Z parameter as an independent variable (Eqs. (3) and (5)), and as shown above, Eqs. (4) and (8) address interconnections between the two parameters by which some researchers tried to establish a universal relation. The effect of grain size on the flow stress should be analyzed at least at a constant Z and precipitation conditions, instead. In Section 3.2, ln(DDRX/b) was depicted versus ln(Z), ln(εp) and ln (σss/E). The three plots are analyzed and discussed in this section. It follows from the results and the above discussion that DDRX is a function of the deformation conditions (Z) and the NbC precipitates, so that at a constant precipitation condition, i.e. either temperature ranges of T < 1100 °C or T ≥ 1100 °C, a linear relation can well describe ln (DDRX/b) against ln(Z). This is observable in Fig. 5. Retardation effects of microalloying elements on both static and dynamic recrystallization phenomena are well known. Nb, in particular, is known as the strongest element in this regard [23,34,42]. Some researchers believe that the solute Nb is more effective to retard DRX. The static recrystallization (SRX) between hot deformation passes, on the other hand, is thought to be mainly inhibited by the strain induced Nb precipitation [12,42,43]. Retardation of DRX can be quantitatively examined by the critical/peak strain. In other words, the higher the

By presenting the following equation:

σss DDRX q ⎛ ⎞ = K2 G⎝ b ⎠

(8)

(where σ is normalized to the shear modulus, G, instead of the Young modulus, E), Twiss [29] claimed that a universal relationship can be expressed for several materials with constants K2 = 15 and q = 0.8. As can be seen in Table 2, from fitting to data of all temperatures, K1 and q are obtained as 5.61 and 0.76, respectively. Having the Poisson's ratio of ν = 0.33 to substitute E by G [18]:

G=

E 2(1 + ν )

(9)

K2 is obtained as 14.92. At first glance, one may conclude that the claim of Twiss [29] is confirmed by results of the present study. However, it is entirely invalidated when values from separate fittings at the two different temperature ranges are taken, so that q is about 1.2 and K2 is too much different from 15. The observation that two different lines are distinguished in Fig. 6(d), can disprove the universal constants, as well. The constants as suggested by Twiss [29] were also criticized by Derby [30]. Through examination of a number of metals and minerals, he claimed that q = 2/3 and 1 < K2 < 10 are more reliable. Nonetheless, this is also not acceptable for the present results when two sets of data are individually treated below and above Nb carbide dissolution temperature. Therefore, the coincidence of the present result (when all 200

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Fig. 9. Analyses of ln(DDRX /b) versus (a) ln(εp) and (b) ln(σSS/E) at the two temperature ranges.

σ′ ln ⎛ ss ⎞ = ln (aσss ) + bσss ln(ZII ) ⎝E⎠

critical/peak strain, the more retardation of DRX [44,45]. Results of the present study show a difference between DDRX at T < 1100 °C and T ≥ 1100 °C which is attributed to the solution temperature of NbC. Accordingly, it would be meaningful to plot ln(DDRX /b) versus ln(εp). Such a plot was presented in Fig. 6(c). The difference between the two lines at a specific ln(εp) is attributed to the grain refinement effect of fine NbC precipitates. Likewise, comparison of the two lines at a specific ln(DDRX /b) can be helpful to examine the retardation effect of Nb solute atoms on DRX. When ln(DDRX/b) is depicted versus ln(εp) and ln(σss/E), attention must be paid on the fact that the deformation conditions, i.e. the Z parameter, may also change as an internal variable. The two plots are represented in Fig. 9(a) and (b). In these figures, the relevant values of ln(Z) are displayed next to each point. Moreover, the fitted lines of T ≥ 1100 °C are extrapolated to higher values of ln(εp) and ln(σss/E) to highlight the difference between the two lines. It can be found from the values of ln(Z) in these figures that at a constant ln(DDRX/b), ln(Z) corresponding to the data set of T ≥ 1100 °C is much higher than that of T < 1100 °C. In fact, since larger grain sizes are to develop at T ≥ 1100 °C, where no NbC precipitation is expected, higher Z parameter is required to achieve DDRX similar to that developed at the temperature range of NbC precipitation (T < 1100 °C). As a result of higher Z parameter, higher εp and σss/E are expected at a constant DDRX/ b. Therefore, it is possible to examine data from the two ranges of temperature according to the Z effect. The effect of Z difference between the two lines at a specific ln (DDRX/b) can be compensated. Therefore, the two lines are treated at a specific ln(DDRX/b):

D D ln ⎛ DRX ⎞ = ln ⎛ DRX ⎞ ⎝ b ⎠ II ⎝ b ⎠I

⎜

1 C m ln ⎛ I ⎞ + I ln(ZI ) (at a constant ln(DDRX / b)) mII ⎝ CII ⎠ mII ⎜

(10)

DDRX

⎛ b ⎜ εp ∝ Z ±(0.11 − 0.15) ⎜ σss ⎝ G

1 C ln ⎛ I ⎞ + ln(ZI ) (at a constant ln(DDRX / b)) m ⎝ CII ⎠ ⎜

(15)

⎟

(11)

It suggests that when other effective factors (precipitates in case of the present work) are fixed, various hot deformation parameters, even the microstructure, have similar dependency to the deformation conditions, i.e. Z. This finding can provide a basis for subsequent works aiming at development of less constants models and formulations describing the hot deformation aspects of steels and may be other alloys.

Note that according to similar values of mI and mII (Table 2), Eq. (11) may be reduced as:

ln(ZII ) =

(14)

The lines compensated for the effect of Z difference are drawn in Fig. 9(a) and (b). As can be seen in Fig. 9(a), the line I is shifted to higher values of ln(εp) by implementing the effect of Z difference. This is attributed to the expected DRX retardation by increase of Z. Yet, such a compensated line does not match with data set of T ≥ 1100 °C (line II). This implies that at a specific DDRX/b, in addition to the effect of Z difference, another factor must have been incorporated in DRX retardation at T ≥ 1100 °C as compared with T < 1100 °C. As discussed before, the Nb solute atoms can result in DRX retardation at temperatures above the Nb precipitation range. The horizontal distance between the compensated line and line II in Fig. 9(a) is, therefore, correlated to the further DRX retardation by the Nb solute atoms. Thus, the procedure presented in this study can be taken as an approach to quantitatively analyze the retardation effect of Nb solute atoms on DRX at hot deformation of steels. In case of ln(σ ′ss / E ) in Fig. 9(b), it appears that the compensated line for the effect of Z difference at a constant ln(DDRX/b) matches well with data set of T ≥ 1100 °C (line II). This signifies that at a specific DDRX/b, σss/E can be treated as a function of only Z parameter. One important conclusion which can be drawn from this study is that application of the temperature compensated strain rate, Z parameter, in Nb-Ti microalloyed steels is confined to the temperature stability range of either Nb solute atoms or Nb precipitates. This parameter cannot be implemented for the whole common temperature range of steels hot working. An interesting consequence of the separation of the two temperature ranges can be found in Table 2. One can see that when Z affected parameters are treated separately at the two temperature ranges as a power function of Z, the index values are almost similar, in the range of 0.11–0.15:

in which the subscripts I and II refer to T < 1100 °C and T ≥ 1100 °C, respectively. According to Eq. (3), ln(ZII) correlated with ln(ZI) at a specific ln(DDRX/b) can be defined as:

ln(ZII ) =

⎟

⎟

(12)

5. Conclusions

Having ln(ZII), ln(εp′ ) as the compensated ln(εp) can be obtained from Eq. (5) as:

ln(εp′ ) = ln (a εp) + bεp ln(ZII )

Dynamic recrystallization grain size of a Nb-Ti microalloyed steel during hot compression was analyzed with regard to the role of microalloying elements. The major conclusions can be listed as below:

(13)

Similarly, ln(σss/E) compensated for the effect of Z difference (ln(σss′ / E ) ) can be defined by Eq. (5):

1. Nanometer sized Nb precipitates form at T < 1100 °C. TiN particles 201

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2.

3.

4.

5.

act as preferred substrates for Nb precipitation at this range of temperature. This phenomenon is responsible for distinct evolutions of DDRX along with other hot deformation parameters at the two temperature ranges of T < 1100 °C and T ≥ 1100 °C. ln(DDRX/b) is depicted versus ln(Z), ln(εp) and ln(σss/E). The results show that within either range of temperature, a line can fit well to the plots. Comparison of the two lines at a specific ln(Z) signifies the retardation effect of Nb precipitation on DRX and consequently on the grain size. Although the well-known universal relationships between DDRX/b and σss/E suggested by Twiss [29] and Derby [30] match with results of the present work at the whole temperature range, a large deviation attributed to the effect of Nb precipitation is observed. However, when the relationships are treated within the separate temperature ranges, the obtained constants do not agree with those suggested in the universal relationships. An approach is developed by which the effect of Nb solute atoms on retardation of DRX can be quantitatively analyzed. Based on this approach, effect of Z difference between the two lines of T < 1100 °C and T ≥ 1100 °C is compensated. The remaining difference is attributed to the DRX retardation by Nb solute atoms. When the two temperature ranges are analyzed separately, almost similar values of indexes in the range of 0.11–0.15 are obtained to describe Z affected parameters, such as DDRX/b, εp and σss/E, as a power function of Z (which is calculated based on the theoretical Q = 270 kJ/mol attributing to the austenite self-diffusion). This can be helpful to develop phenomenological models for various aspects of hot deformation with less constants.

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