3.1 Numerical simulation
3.1.1 Microstructure characteristics of hollow axle at different location
The rolling conditions are set with a temperature T = 1100℃ and an axial traction speed Vz = 20mm/s, to study the characteristics of microstructure distribution in the 30CrMoA hollow axle. As shown in Fig. 8(a), the grain refinement in the axle is quite significant compared to the initial grain size in the first deformed section due to the large radial compression and large contact area of the billet. As shown in Fig. 8(b), the contact area between roll and workpiece is smaller in the second deformed section, and the grain size in the deformation zone is significantly smaller, whereas the grain size in the non-deformation zone is larger. The grain size in the third deformed section is larger than the grain size in the first and second deformed sections in Fig. 8(c), indicating that greater radial compression results in smaller grain size. The diameter of the fourth deformed section is relatively larger in Fig. 8(d), but the surface grain size is still significantly refined and uniformly distributed, indicating that the TRSR process can effectively improve surface microstructure quality. The fifth deformed zone is depicted in Fig. 8(e) with similar grain size and distribution results as in the third deformed section due to the identical radial compression. Figure 8(f) shows the sixth deformed section, the grain size is unevenly distributed along the rolling direction due to the influence of diameter reduction, and the grain size near the next deformation zone is smaller. Figure 8(g) shows the seventh deformed section of the skew rolling, and it should be noted that the surface grain size is gradually decreasing along the rolling direction because the greater relative plastic deformation leads to more significant refinement. Overall, with the progress of rolling, the grain size of the already formed area will slightly increase. The average surface grain size is refined from 62.6 µm to 15–25 µm, demonstrating that the TRSR technique can refine the grain size and improve the microstructure properties of the hollow axle .
Figure 9 shows the distribution of grain size in the selected cross-sections at T = 1100°C and Vz = 20mm/s. The outer core and inner layer are defined in Fig. 9. It can be seen that the average grain size of the core and inner layer gradually increases along the rolling direction, while the change in the outer layer is negligible. The average grain size in the core is the largest and the average grain size in the direct contact area between roll and billet is the smallest. It can be observed that the grain is refined in the non-deformation zone but near the deformation area, and the grain size is reduced by half compared with the initial size. The average grain size in the deformed section is refined to 14.5µm ~ 20µm. The grain size in the core layer gradually increases along the rolling direction. Meanwhile, this pattern gradually diffuses to the inner layer, leading to similar grain size in core the and inner layer at the end of the workpiece.
The average grain size of the outer core and inner layer at different cross-sections is shown in Fig. 10 with T = 1100°C and Vz = 20mm/s. From Fig. 10, the grain refinement in the outer layer is the most noticeable, especially at cross-sections F, G, while the core and inner have a similar trend of grain refinement. The grain size gradually increases along the rolling direction for both the core and inner layer, while the opposite pattern was found for the outer layer. Under the same amount of radial compression, the average grain size in core and inner layer is smaller at the early stages rolling process, while the outer layer has the smaller grain size at the late stage of the rolling process. The results in Fig. 10 indicate that the rolling process has more influence on the grain refinement at the outer layer than at other layers, and the rolling sequence also plays an important factor in further refinement.
In summary, the three-roll skew-rolling process will promote the microstructure distribution and grain refinement, in particular at the outer surface layer, thus, the microstructure properties of the hollow axle can be improved via this process.
3.1.2 Effect of processing parameters on average grain size
The rolling temperature has a significant effect on the grain size. Figure 11 compares the grain size of the inner and outer layer at 1000°C and 1100°C, to further understand the temperature effect. In Fig. 11, the initial grain size at 1100°C is approximately three times greater than the grain size at 1000°C, and the overall average grain size at 1100°C is 5 µm greater than at 1000°C. The curve pattern in the figure shows a similar trend of outer and inner layer between two temperatures, indicating the temperature mainly affect the grain size rather than changing other microstructure characteristics between outer and inner layers. Overall, the higher the rolling temperature, the larger the initial grain size, the larger the final grain size, but the relative changes in refinement are more significant at the higher temperature.
The axial traction speed directly affects the deformation rate, forming time, and potentially affects the temperature field during the process, resulting in the corresponding change in microstructure. Figure 12 shows the grain size distribution with different axial traction speeds at 1100°C, 10 mm/s, 20 mm/s, and 30 mm/s, respectively. Figure 12(a), (b), (c) shows the individual grain size distribution at each axial traction speed and Fig. 12(d) shows the overall distribution with all three speeds included. Figure 12(a) indicates that radial compression has more influence on the grain size in outer layer than other layers. It can be seen from Fig. 12(b) and (c), the grain size distribution with 20 mm/s and 30 mm/s are similar, only 30 mm/s has a slightly larger grain size than 20 mm/s. From Fig. 12(d), the curve pattern for each speed is relatively unanimous, which indicates different axial traction speed has a similar effect on grain distribution in different layers. With increasing traction speed, the average grain size becomes larger in these layers. It should be noted that the increasing rate of grain size slows down when traction speed is adjusted from 20 mm/s to 30mm/s. This is because, during the rolling process, the deformation zone will have more plastic deformation cycles, eventually resulting in more refined grains. When the axial traction speed is 20 mm/s, the curves have the smallest fluctuation rate, suggesting a more uniformly distributed microstructure along the axle.
It can be concluded that the rolling temperature has an imperative influence on the initial grain size. With the higher temperature, the grain size will be larger. However, the relative grain refinement is more significant. Furthermore, the greater the axial traction speed, the larger the grain size is. With the smaller traction speed, the relative grain refinement is more noticeable. It was found that 20 mm/s had a more evenly distributed microstructure.
3.2 Experimental analysis
Figure 13 shows the microstructure at the second cross-section, where there is the largest radial compression zone, in the rolled piece # 1 (1000℃, Vz = 20mm/s). Figure 13 (a), (b) and (c) represent the outer, core and inner layer, respectively. It can be seen that the grain size is significantly increased from the outer layer to the inner layer. In the meantime, outer layer has better grain refinement and even distribution, indicating the larger plastic deformation contributes to the grain refinement and distribution. Figure 14 shows the microstructure in the outer layer at cross-sections No. 2, No. 3, and No. 4 in rolled piece #1, where the radial compression is correspondingly decreased from No. 2 to No. 4. It can be found with the finest grain at the second cross-section zone and the coarsest grain at the fourth cross-section. This indicates radial compression has a significant influence on the grain size, the larger the radial compression, the better grain refinement is.
The average grain size at all cross-sections of the #1 rolled piece is shown in Fig. 15. According to the figure, the TRSR process can significantly refine the grains, especially in the outer layer of the hollow axle. The radial compression has the most noticeable grain refinement to the outer layer. The greater the radial compression, the better the refinement is. However, radial compression has a limited effect on refinement at the core layer and inner layer. Compared to the same radial compression, the average grain size is much smaller in the early rolling than in the late rolling part, this phenomenon is more obvious in the core and inner layer.
Figure 16 shows the average grain size at different cross-sections of the #2 rolled piece (T = 1100°C, Vz = 20mm/s). It can be found that the grain refinement at cross-sections 2, 3, and 4 gradually improved with decreasing the radial compression. Interestingly, the same pattern was found at cross-sections 8, 9, and 10 with increasing the radial compression. The outer layer is the most consistent one in grain refinement, while the inner and core layers present stochastic patterns. Considering the nature of the rolling process, the outer layer is the direct contact deformation zone. It is inevitable to have more influence on grain refinement on the outer surface than others. Furthermore, grain distribution and grain size in the core and inner layers can be further refined by heat treatment .
The #1 (1000°C) and #2 (1100°C) rolled pieces are used to compare the temperature effect on the grain size and microstructure distribution. The initial grain size is affected significantly by the temperature results, going from 22.45 µm to 62.6 µm as the temperature increases. However, when compared to the relative refinement level, the higher temperature experiences a huge change in regards to the grain size, and the experimental results also agree with this with the simulation results. Furthermore, when rolling the long shaft parts, the dynamic recrystallization becomes weaker as the length of the shaft increases. This phenomenon is particularly obvious at higher temperatures.
Figure 17 shows the comparison between #1 and #2 rolled pieces in different layers. The grain size in the outer layer Fig. 17(a) is refined to 10 µm at 1000°C and around 15 µm at 1100°C. It can be found that the cross-section 2–4 present different curve trends at 1000°C and 1100°C, with the average grain size in the #2 decreasing instead of increasing at the higher temperature, indicating that the temperature has a significant effect on the outer layer, as the grain refinement by dynamic recrystallization and static grain growth dominate in these sections. Figure 17(b) presents the grain size distribution in the core layer. The figure shows that in the #1 rolled piece, the grain refinement caused by dynamic recrystallization gradually becomes weaker from cross-section 2 to cross-section 8, on the other hand, the grain growth effect is enhanced. In the #2 rolled piece, the grain refinement is enhanced from cross-section 2 to cross-section 6, and the refinement becomes much weaker from cross-section 6 to cross-section 8. Both rolled pieces have a very similar variation trend from cross-section 8 to cross-section 11, and the average grain size of #2 is about twice that of #1. Results show that the grain refinement in cross-sections 8–11 is dominated by recrystallization, and the temperature has a significant influence on the average grain size. Figure 17(c) shows the grain size at different locations in the inner layer. It can be seen that in the beginning stage of rolling, dynamic recrystallization plays a dominant role in grain refinement. At the lower temperature, the growth of recrystallized grains plays a key role in refinement, in particular at the middle and late stages of rolling. At the higher temperature, the growth of recrystallized grains dominates in the middle stage when the radial compression is small. Dynamic recrystallization dominates in the late stage of rolling as the radial compression gradually increases.
In summary, by analyzing the microstructure of the hollow axle in the TRSR process, it can be found that the outer layer has the most refined grain size. Grain size in the first half of the axle along the rolling direction is outer < core < inner, and outer < inner < core in the second half. The average grain size in the outer layer is enlarged in the diameter increasing section, vice versa. At lower rolling temperatures, the growth of recrystallized grain dominates in the core layer and inner layer. At higher rolling temperatures, dynamic recrystallization dominates the grain refinement at the core layer in the first half of the axle, and growth of recrystallization dominates the core layer in the second half. Furthermore, as the temperature increased, the final grain size also increased.
3.3 Model validation
As shown in Fig. 18a, the simulation and experimental results are more consistent in the early stage from cross-section A to cross-section D, and there are more fluctuations at cross-sections E and F. It should be noted that when performing the experiment, the rolled piece is taken from the furnace to the TRSR machine by manual operation. The rolled piece will experience some temperature loss, and the temperature gradient will have a direct impact on the dynamic recrystallization and eventually affect the grain size. Due to the temperature loss during the experiment, the actual grain size is influenced and eventually leads to the difference with the simulation. Figure 18b shows the overall comparison between simulation results and experimental results, which shows the mean and standard deviation of simulation (13.9 ± 0.85; 19.6 ± 1.1) and experiment (13.1 ± 2.9; 19.3 ± 7.1) at 1000°C and 1100°C. The relative error between simulation and experiment is 16.3% (mean absolute error: 2.3 µm) at 1000°C and 30.7% (mean absolute error: 5.8 µm) at 1100°C, according to relative error analysis. As discussed in the above section, the microstructure of 30CrMoA is susceptible to higher temperature, in particular at 1100°C, and the grain size will experience significant changes correspondingly. Due to this reason, the temperature loss at higher temperatures plays a huge impact on the final grain size and the larger differences occurred between simulation and experiments. In Fig. 18c, the trends of microstructure evolution in simulation and experiment are consistent with the polynomial fit, and the fitting formula can be further used to precisely predict the experiment with the appropriate offset. In summary, the established constitutive model provides valuable information and can be used to predict the microstructure evolution of TRSR.