A. True stress-true strain curves

Figure 1 shows the true stress-true strain curves of the experimental steel deformed at different temperatures and strain rates. According to Ref. Reference Liu, Rong, Gao, Li, Liu and Wang12, a single peak flow curve is associated with the occurrence of dynamic recrystallization (DRX), while a constant flow stress is indicative of dynamic recovery (DRV). It can be easily observed that the investigated steel exhibited a representative DRX behavior, and the stress monotonous rose to a peak after the strain hardening, which was caused by the dislocation interaction and defects formed during the straining process. ^{Reference Zhong, Li, Song, Liang and Guo13} With the increase of the strain rate, the dislocation tangles or defects in the matrix reached saturation gradually. The matrix could provide maximum resistance to deformation, and the flow stress reached a peak value. The peak represented the beginning of dynamic recrystallization and then the flow curve followed by the steady state. The steady state occurred when a new balance between the work hardening and the dynamic softening was reached. ^{Reference Zhou, Liu, Zhou, Liu, Yu and Li14,Reference Liu, Guo, Li, Mei, Zhou, Huang and Li15}

FIG. 1.

True stress-true strain curves at different strain rates: (a) 0.01 s⁻¹; (b) 0.1 s⁻¹; (c) 1 s⁻¹; and (d) 10 s⁻¹.

The peak stress at different strain rates and deformation temperatures are shown in Table II. It can be seen that the peak stress increased with the decrease of the deformation temperature and the increase of the strain rate. It is due to that higher temperature or lower strain rate could provide a longer time for energy accumulation. This energy could provide the conditions for the nucleation and growth of dynamic recrystallized grains and dislocation annihilation, and therefore the flow stress decreased. ^{Reference Wu, Liu, Hu, Wang, Zhang, Tao and Liu16}

TABLE II.

The peak stress (MPa) of the samples under different conditions.

Under the higher strain rate of 10 s⁻¹, the flow stress curves had fluctuations, as illustrated in Fig. 1(d). This is due to the existence of an alternation between dynamic softening and work hardening, which was caused by the rapid growth of grains at high temperatures and DRX. ^{Reference Prasad, Sasidhara and Sikka17}

B. Constitutive equation

In the research of hot deformation behavior of experimental steel, the constitutive equation is an important method to establish the relationship among deformation temperature, flow stress, and strain rate. The Zener–Hollomon parameter is widely used to describe the hot deformation behaviors of steel and can be expressed as follows ^{Reference Mirzadeh, Cabrera, Prado and Najafizadeh18–Reference Kim, Lee, Lee and Yoo20} :

where A, α, n ₁ are the material constants, R is the gas constant (8.314 kJ/mol), T is the absolute temperature (K), Q is the activation energy of hot deformation (J/mol), $\dot \varepsilon$ is the strain rate (s⁻¹), and σ is the flow stress (MPa). The power function Eq. (2) can be used for lower stress (ασ < 0.8), the exponential function Eq. (3) is preferred for higher stress when ασ > 1.2, and the hyperbolic sine function Eq. (4) is suitable throughout the entire stress. ^{Reference Sellars and McTegart21} Peak stress, steady state stress, and stress under the specific strain can also be used to establish the constitutive equation. ^{Reference Li, Wang, Liang, Liu and Zhang22–Reference Zhang, Li and Wang24} Peak stress is usually chosen to estimate the Q value because the peak stress is more important for industrial production, and the steady state stress may not be obtained accurately. ^{Reference Huang, Zhang, Liu, Song, Geng and Wu25}

In this research, the peak stress σ_p is brought into the above equations. α is a stress multiplier, and the value of α can be defined as

where β and n ₁ are the average values of slopes obtained from the $\ln \dot \varepsilon$ − ln σ and $\ln \dot \varepsilon$ − σ as shown in Figs. 2(a) and 2(b), respectively. The β and n ₁ values were evaluated as 0.0627 and 8.3871, and therefore α = 0.0075.

FIG. 2.

Linear relationships of (a) σ_p − $\ln \dot \varepsilon$ ; (b) ln σ_p − $\ln \dot \varepsilon$ ; (c) ln[sinh(ασ)] − $\ln \dot \varepsilon$ ; and (d) ln[sinh(ασ)] − 1000/T.

For a particular strain rate, the activation energy can be obtained from the following relationship:

where n ₂ is the average slope of $\ln \dot \varepsilon$ versus ln[sinh(ασ)] plots at various temperatures and b is the mean slope of ln[sinh(ασ)] − 1000/T plots at different strain stresses. Figures 2(c) and 2(d) show the linear fitting plots of $\ln \dot \varepsilon$ versus ln[sinh(ασ)] and ln[sinh(ασ)] − 1000/T, respectively. The average of n ₂ and b can be estimated to be 5.784 and 8.3424, and the value of Q is evaluated as 407.29 kJ/mol.

Combined Eqs. (1) and (4).

To determine the constitutive equation of investigated steel, the logarithm is taken on both sides of Eq. (7) to derive:

According to Eq. (8), the value of ln A and n can be determined by the intercept and the slope of ln Z versus ln[sinh(ασ)], as shown in Fig. 3. It can be observed that the correlation coefficient for the linear regression was 0.982, which indicates a good linear fitting for the experimental steel. The ln A and n were estimated as 35.21 and 5.773, and the value of A could be finally obtained to be 1.9566 × 10¹⁵. Therefore, the constitutive equation of the investigated Nb–V–Ti microalloyed ultra-high strength steel could be described as

FIG. 3.

Plots of ln Z versus ln[sinh(ασ)] for experimental steel.

The deformation activation energy in the constitutive equation indicates the difficulty of deformation and implies the deformation mechanism of the experimental steel. ^{Reference Zhao, Xu and Xu26} When the deformation activation energy is similar to the selfdiffusion activation energy, the diffusion or DRV softening mechanism is the main mechanism of hot deformation. When the deformation activation energy is much greater than the selfdiffusion activation energy, the dynamic recrystallization (DRX) plays a dominant role in hot deformation of the investigated steel. ^{Reference Han, Liu, Zou, Liu and Qiao23} The deformation activation energy in the constitutive equation was 407.29 kJ/mol, which is much greater than the selfdiffusion activation energy of 272 kJ/mol for the pure Fe. ^{Reference Mannan, Kostryzhev, Zurob and Pereloma27} It is believed that the dynamic recrystallization (DRX), originated dislocation slip or climb, is a main hot-deformation mechanism, ^{Reference Zhu, Feng, Sun, Han and Zhou28} which is consistent with stress–strain curves.

In addition, the flow stress which can be expressed by the hyperbolic sine equation as a function of the Z parameter is given by Eq. (10) ^{Reference Guo, Wang, Luo, Li, Chen and Su29} :

The expressions for the peak stresses of investigated steel are shown as follows:

Figure 4 shows the calculated peak stresses using Eq. (11) and experimental values of the peak stress. If all the points can be on a line with 45° to the X-axis, the equation is expected to be accurate. It is observed that most of the points are close to the prediction line, and the relative error of the calculated peak stress is less than 13%. The calculated values are in good agreement with the experimental results. It suggests that the constitutive equation can be used to accurately estimate the peak stress of the experimental steel.

FIG. 4.

Variation of the predicted flow stress with experimental flow stress for the investigated steel.

C. Processing map

Generally, the low strain and high temperature are beneficial to the microstructure reconstruction, and the low flow stress in the DRX may result in a low production efficiency and grain coarsening. While the high strain rate may generate an adiabatic temperature rise or strain hardening, resulting in the deformation failure or instable flow. ^{Reference Kai, Chen, Sun, Wang and Zhao30} Based on the dynamic materials model, the hot processing map originally proposed by Raj ^{Reference Fréour, Gloaguen, Francois and Guillén31} and developed by Prasad and Seshacharyulu ^{Reference Prasad and Seshacharyulu32} is an effective method to evaluate the hot deformation process of metal materials. The hot deformation of experimental steels is a process of power dissipation, and the whole power dissipation can be divided into two parts ^{Reference Prasad and Seshacharyulu33} :

where G is the power content, which is the power dissipated by the plastic work; J is the power co-content, which related to the microstructural evolution during deformation; σ is the flow stress (MPa); and $\dot \varepsilon$ is the strain rate (s⁻¹). The strain rate sensitivity coefficient m can be calculated as follows:

The dissipator co-content J can be defined as follows ^{Reference Venugopal, Mannan and Prasad34} :

For a linear dissipation process, m = 1 and J = P/2. The efficiency of power dissipation η can be expressed as follows:

The criterion of continuous instability is established to determine the flow instability region in the form of ^{Reference Prasad and Seshacharyulu33} :

The variation of η and ξ with the strain rate and deformation temperature constitute the power dissipation map and the flow instability map, respectively. The processing map can be constructed by superimposing the flow instability map on the power dissipation map. ξ is the instable factor, and the experimental steel may exhibit a deformation instability phenomenon when the value of ξ is negative. The processing map can be used to optimize the processing parameters during the hot deformation process.

With calculation and analysis, the processing maps of the investigated steel deformed at strains of 0.2, 0.4, 0.6, and 0.8 were established as shown in Figs. 5(a)–5(d), respectively. The different color contours indicate the efficiency of power dissipation, and the shaded domains represent the flow instability zones. The values of η slightly increased as the strain increased, and the instability region decreased with the increase of the strain. It can also be observed that these maps demonstrated a similar characteristic, where flow instability occurred at lower temperatures and higher strain rates.

FIG. 5.

Processing maps for the experimental steel at a true strain of: (a) 0.2; (b) 0.4; (c) 0.6; (d) 0.8; and (e) the processing map indicating different deformation regions with a true strain of 0.6.

At the strain of 0.6 in Fig. 5(e), six domains (A–F) were observed at the deformation temperature range from 900 to 1200 °C with strain rates from 0.01 to 10 s⁻¹. Figure 6 shows the typical microstructure of experimental steel deformed at different deformation conditions. According to Figs. 6 and 7, these six domains can be divided into three major classifications.

1. (i) Flow instability zone. At the strain of 0.6, the flow instability zones appeared in two regions. One was at the deformation temperature around 900 °C and the strain rate was about 0.1 s⁻¹ (A zone); the other one was at the deformation temperature at about 1100 °C and the strain rate was around 10 s⁻¹ (B zone) as covered by gray color in Fig. 5(e). Figures 6(a) and 6(b) represent the microstructures of the instability zone A and B in the processing maps, respectively. In Fig. 6(a), it can be seen that the grains of the A zone in the processing maps were elongated, and only a few recrystallized grains were observed as indicated by the black arrows. This means that the softening mechanism of the A region was mainly a dynamic recovery. As illustrated in Fig. 6(b), there are some recrystallized grains observed, especially in the shear zone as marked by the black arrows. This means that the DRX was incomplete in domain B. Therefore, these instability regions should be avoided during hot deformation.

2. (ii) Unsafe zone. In region D (900 °C, 10 s⁻¹) with a relatively high strain rate, the deformation time is too short to dissipate heat. The temperature increased with a localized plastic flow resulting in the formation of shear bands and cracks in the shear planes. ^{Reference Ning, Guo, Cao, Wang, Li and Sun35} Some recrystallized grains around original grain boundaries and shear bands as pointed out by the black arrows are shown in Fig. 6(c). This means that the DRX is incomplete in domain D and a mixed grain microstructure was obtained. In the F zone, larger dynamic recrystallization grains formed due to the high temperature and low strain rate. The microstructure of the domain F deformed at 1200 °C and 0.1 s⁻¹ is shown in Fig. 6(d). In this region, the size of the dynamic recrystallization grain coarsened significantly. This can be attributed to the reason that recrystallized grains at high temperatures had a large driving force for nucleation and growth. ^{Reference Kong, Chang, Li, Xie and Zhu36} Thus, D and F domains are also considered to be unsafe. Based on the above analysis, these hot deformation conditions should be avoided for the investigated steel.

3. (iii) Safety zone. Domains C and E are the stable zones with a peak efficiency of power dissipation at about 16%. Karami et al. ^{Reference Karami and Mahmudi37} clearly showed that a higher η value means that the material dissipates more energy through the microstructure evolution, such as DRX. The DRX process is regarded as the best deformation mechanism and provides a stable flow stress and produces fewer defects. Figures 6(e) and 6(f) show the typical microstructures of safety zones C and E. Both small equiaxed grains along the grain boundaries and uniform grain are observed under these two deformation conditions. These features imply that the DRX occurs completely. Therefore, domains C and E are considered as the safe region for hot deformation.

FIG. 6.

Optical micrographs of the investigated steel deformed at (a) 900 °C/0.1 s⁻¹; (b) 1100 °C/10 s⁻¹; (c) 900 °C/10 s⁻¹; (d) 1200 °C/0.1 s⁻¹; (e) 1000 °C/0.01 s⁻¹; and (f) 1200 °C/10 s⁻¹.

FIG. 7.

Optical micrographs and the TEM micrographs of specimens deformed at 1200 °C with the strain rate of (a), (e) 0.01 s⁻¹; (b), (f) 0.1 s⁻¹; (c), (g) 1 s⁻¹; and (d), (h) 10 s⁻¹.

D. Microstructure evolution

The effect of the strain rate on the microstructure evolution at the deformation temperature of 1200 °C is shown in Fig. 7. It can be seen from Figs. 7(a) to 7(d) that the average grain size decreased with increasing the strain rate. The average grain size of the investigated steel under different strain rates were about 91.17, 58.70, 30.67, and 22.73 μm, respectively. DRX started at the grain boundaries with a high dislocation density, where it had high stored energy. Enhancing the strain rate can increase the work hardening rate, which is beneficial for the recrystallization. In addition, more dislocations were produced. ^{Reference Xiao, Huang and Liu38} With the increase of strain rate, the dislocation and energy caused by work hardening increased, while the time for the growth of grains decreased simultaneously. Therefore, the grains became finer when the strain rate increased from 0.01 to 10 s⁻¹.

To further analyze the microstructure evolution during the DRX process, the TEM micrographs of samples deformed under different strain rates at 1200 °C are shown in Figs. 7(e)–7(h). All microstructures exhibited a typical martensite structure. With the increase of the strain rate, the width of the martensite lath decreased, and the dislocation (as pointed by black arrows) density increased gradually. The average width of the martensite lath under different strain rates were about 178.45, 134.48, 109.52, and 87.60 nm, respectively.

E. Precipitation behavior

Figure 8 illustrates the TEM micrographs of precipitates in the specimens deformed at different deformation conditions. Considerable amount of needle-like precipitates, the square or rectangular precipitates, and nanosized spherical shape particles can be observed from the samples. In the previous works, ^{Reference Yang, Peng, Ren, Wen, Su and Xie4,Reference Shahrani, Yazdipour, Dehghan-Manshadi, Gazder, Cayron and Pereloma5} it has identified the crystal structure of these three types of particles. The needle-like precipitates (orthorhombic) could be identified as M₃C carbides and rich in Fe with a small amount of Mn and Cr. The PDF number is 35–6772, α = β = γ = 90°, and a = 5.091 nm, b = 6.743 nm, and c = 4.526 nm. The other two types of precipitates are both f.c.c cubic structures with α = β = γ = 90°. The square or rectangular larger precipitates (PDF: 65-7931) were rich-Ti MC carbides, mainly containing Ti with minor Nb and V, and a = b = c = 4.225 nm. The smaller spherical precipitates were rich-Nb MC carbides, mainly containing Nb with minor Ti and V. The PDF number is 47–1418 and a = b = c = 4.427 nm. The differences in morphology and composition can be attributed to different nucleation temperatures of the precipitates. M₃C carbide is one type of precursor carbide precipitated during the early period of self-tempering. ^{Reference Zhou, Liu, Yu, Liu and Li39} Some investigations ^{Reference Lee, Hong, Park and Park40} reported that the larger rich-Ti MC formed in the austenite region had a K–S relationship with austenite and the small rich-Nb MC carbides were formed in the ferrite region and satisfied the B–N relationship with ferrite.

FIG. 8.

The TEM micrographs of M₃C carbides, rich-Ti MC, and rich-Nb MC precipitates deformed at 1200 °C with a strain rate of (a), (c), and (e) 0.01 s⁻¹; (b), (d), and (f) 10 s⁻¹.

As demonstrated in Fig. 8, the amount of precipitates decreased with the decrease of strain rates. Furuhara et al. ^{Reference Furuhara and Maki41} reported that dislocations, grain, and subgrain boundaries can act as the nucleation sites for carbides. With the increase of the strain rate, the stress value in unit time increased gradually. The stress applied during the deformation steps gives rise to an increase in the dislocation density. ^{Reference Gomes, Menina and Valles42} As shown in Fig. 7 above, the average grain size decreased with increasing the strain rate; furthermore, the number of grain boundaries in the unit volume subsequently increases. The rise in the strain rate leads to an increase in the number of available sites for the nucleation of carbides. Thus, the amount of carbides increased with the increasing strain rate. Meanwhile, the size of carbides also decreased gradually with the increase of the strain rate. With the increase of the strain rate, the standing time of samples at relatively high temperatures decreased gradually. Carbides could not grow adequately, and therefore, the size of carbides decreased with the increase of the strain rate. The average length of M₃C at different strain rates were 97.77 and 65.33 nm, the rich-Ti MC had an average dimension around 70.52 and 58.74 nm, and the rich-Nb MC had an average diameter about 8.67 and 5.34 nm when the strain rates are 0.01 s⁻¹ and 10 s⁻¹, respectively, as shown in Fig. 8.

Prikyl et al. ^{Reference Prikryl, Kroupa, Weatherly and Subramanian43} suggested that the stable TiN particles were the most effective microalloyed precipitation particles to retard the grain growth. On the other hand, other investigations indicated that Nb (C,N) had a dominant role in inhibiting the growth of austenite grains, compared to TiN. ^{Reference Alogab, Matlock, Speer and Kleebe44} Fu et al. ^{Reference Fu, Wang, Wang and Shan45} reported that niobium is the most effective microalloyed element to refine the final grain structure. In the previous work, ^{Reference Alogab, Matlock, Speer and Kleebe46} the pinning effect of Nb-rich MC was much larger than that of Ti-rich MC, and therefore, it can be concluded that fine Nb-rich MC plays a leading role in controlling the grain growth behavior. Fernández et al.’s ^{Reference Fernández, Uranga, López and Rodriguez-Ibabe47} research also indicates that Nb had an effect stronger than that of Ti in retarding DRX in the Nb–Ti steel.

As observed above, the amounts of Nb-rich MC increased and the average sizes of the Nb-rich MC decreased gradually with the increasing strain rate. It can be observed from Fig. 1 that the peak stress increased with the increasing strain rate under the same temperature condition. The increase in the amount of finer Nb-rich MC plays a more retarding effect on the dynamic recrystallization. Therefore, the peak stress increased with the increasing strain. The increase in the amount of Nb-rich MC could also play a stronger pinning effect on the recrystallized grains; thus, the size of the dynamically recrystallized grain decreased gradually with an increase in strain rates. It can be concluded that the decrease of carbides size after hot deformation at a higher strain rate could lead to a refinement of the recrystallization grain.