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Haibo Feng, Shaohua Li, Kexiao Wang, Junheng Gao, Shuize Wang, Haitao Zhao, Zhenyu Han, Yong Deng, Yuhe Huang, and Xinping Mao, Effect of deformation parameters on the austenite dynamic recrystallization behavior of a eutectoid pearlite rail steel, Int. J. Miner. Metall. Mater., 31(2024), No. 5, pp.833-841. https://dx.doi.org/10.1007/s12613-023-2805-4
Cite this article as: Haibo Feng, Shaohua Li, Kexiao Wang, Junheng Gao, Shuize Wang, Haitao Zhao, Zhenyu Han, Yong Deng, Yuhe Huang, and Xinping Mao, Effect of deformation parameters on the austenite dynamic recrystallization behavior of a eutectoid pearlite rail steel, Int. J. Miner. Metall. Mater., 31(2024), No. 5, pp.833-841. https://dx.doi.org/10.1007/s12613-023-2805-4
Research Article

Effect of deformation parameters on the austenite dynamic recrystallization behavior of a eutectoid pearlite rail steel

Author Affilications
  • Understandings of the effect of hot deformation parameters close to the practical production line on grain refinement are crucial for enhancing both the strength and toughness of future rail steels. In this work, the austenite dynamic recrystallization (DRX) behaviors of a eutectoid pearlite rail steel were studied using a thermo-mechanical simulator with hot deformation parameters frequently employed in rail production lines. The single-pass hot deformation results reveal that the prior austenite grain sizes (PAGSs) for samples with different deformation reductions decrease initially with an increase in deformation temperature. However, once the deformation temperature is beyond a certain threshold, the PAGSs start to increase. It can be attributed to the rise in DRX volume fraction and the increase of DRX grain with deformation temperature, respectively. Three-pass hot deformation results show that the accumulated strain generated in the first and second deformation passes can increase the extent of DRX. In the case of complete DRX, PAGS is predominantly determined by the deformation temperature of the final pass. It suggests a strategic approach during industrial production where part of the deformation reduction in low temperature range can be shifted to the medium temperature range to release rolling mill loads.
  • The heavy haul railway has become the preferred mode of freight transport in many countries due to its high capacity, high energy efficiency, high safety, low cost, and low emissions [1]. Owing to the increasing demand for railway loads, the railway is developing towards high speed and heavy loads, which requires higher strength and toughness for rail steels. However, in most cases, an increase in strength would inevitably lead to a decrease in toughness [23], which renders how to improve toughness without compromising strength an open issue for materials scientists [46].

    Pearlite steels are currently the most widely used rail steels, and a lot of research has been conducted for simultaneous strength and toughness enhancements [78]. Khiratkar et al. [9], Behera et al. [10], and Mishra and Singh [11] reported that pearlite nodule size, which is mainly dependent on prior austenite grain size, is one of the most important factors that affect the toughness of pearlite steels. However, it should be noted that the strength of pearlite steels is determined by pearlite interlamellar spacing, which can be effectively tuned by adjusting the phase transformation temperature [1214]. As pearlite nodule size and pearlite interlamellar spacing are determined by different factors for a specific alloy, it is possible to achieve high strength and high toughness simultaneously by optimizing the thermo-mechanical procedure to realize a fine the prior austenite grain size (PAGS) and small pearlite interlamellar spacing.

    The hot deformation process, as a necessary step in the production of pearlite rail steels, plays an extremely important role in refining the prior austenite grain because the dynamic recrystallization (DRX) that takes place during hot deformation is an effective route to refining PAGS [1518]. For example, Chamanfar et al. [19] reported that a coarse microstructure of a medium carbon low alloy steel with grain sizes of 280–595 µm was refined to 62–92 µm by a single-pass hot deformation at 1150–1200°C with a deformation reduction of 0.45 because the large deformation reduction can accelerate the DRX kinetics and results in the formation of fine equiaxed completely DRX microstructures. Ebrahimi et al. [20] studied the DRX behavior of a Nb-bearing high-Mn steel using a thermo-mechanical simulator with deformation temperatures and strain rates in the ranges of 850–1150°C and 0.001–1 s−1, respectively, and a deformation reduction of 0.45. Their results showed that a fine grain size of 13.1 µm was achieved by optimizing the deformation temperature and strain rate. Although fine austenite grain sizes can be achieved in different steels by tuning the hot deformation parameters, i.e., hot deformation temperature, deformation reduction, and strain rate, either these steels’ compositions or hot deformation parameters are significantly different from the compositions of pearlite rail steels and their practical hot deformation parameters [2123]. At present, studies on the DRX process in pearlite steels, particularly those near eutectoid compositions, mainly focus on kinetic calculations [24] or static recrystallization [25]. However, the employed experimental parameters, such as high deformation reductions (>0.4) or low strain rates (<1 s−1), differ significantly from those in practical industrial production.

    In this study, we systematically investigated the DRX behavior of a eutectoid pearlite rail steel using deformation parameters similar to those employed in industrial production lines of pearlite rails. The experiments were conducted using a thermo-mechanical simulator for single-pass and three-pass hot deformation tests, with deformation temperatures in the range of 950–1200°C, deformation reductions of 0.1, 0.2, and 0.3, and a strain rate of 5 s−1. Studying the effect of these hot deformation parameters, closely resembling those applied in the practical production line on grain refinement, holds significance for industrial processes to simultaneously improve the strength and toughness of future rail steels.

    The material used in the present study was a eutectoid pearlite rail steel with the chemical composition (wt%) shown in Table 1. The experimental samples were cut into a cylindrical shape with a diameter of 10 mm and a height of 15 mm for hot deformation processes using a thermo-mechanical simulator, Gleeble 3800. Before hot deformation, the cylindrical sample was heated to 1250°C at a heating rate of 10°C/s and held at 1250°C for 300 s with the PAGS of 160 µm shown by Fig. S1. Then the samples were cooled to deformation temperatures of 950, 1000, 1050, 1100, 1150, 1200°C at 10°C/s, respectively, and held at each deformation temperature for 5 s before hot deformation. Deformation reductions were 0.1, 0.2, and 0.3 and the experimental strain rate ˙ε was set to 5 s−1, as shown in Fig. 1(a). For the three-pass hot deformation experiments, as shown in Fig. 1(b), the cylindrical sample was also held at 1250°C for 300 s and then cooled to the first hot deformation temperature at 10°C/s and held for 5 s. After the first deformation is finished, the sample is cool to the deformation temperature of second pass at 5°C/s and held for 2 s. The cooling rate and holding time between the second and third passes were also 5°C/s and 2 s. The specific deformation parameters are shown in Table 2.

    Table  1.  Chemical composition of experimental steel wt%
    Fe C Si Mn Cr V
    in balance 0.78 0.50–0.80 0.70–1.05 0.30–0.50 0.08
     | Show Table
    DownLoad: CSV
    Fig. 1.  Schematic diagrams of the (a) single-pass and (b) three-pass hot deformation schedules.
    Table  2.  Deformation parameters of three-pass hot deformation experiments
    Sample First pass Second pass Third pass
    Temperature / °C Deformation
    reduction
    Temperature / °C Deformation
    reduction
    Temperature / °C Deformation
    reduction
    R1 TR1-1 = 1200 0.3 TR1-2 = 1150 0.3 TR1-3 = 1100 0.2
    R2 TR2-1 = 1200 0.3 TR2-2 = 1150 0.2 TR2-3 = 1100 0.3
    R3 TR3-1 = 1200 0.3 TR3-2 = 1100 0.3 TR3-3 = 1050 0.2
    R4 TR4-1 = 1200 0.3 TR4-2 = 1100 0.2 TR4-3 = 1050 0.3
    R5 TR5-1 = 1150 0.3 TR5-2 = 1100 0.3 TR5-3 = 1050 0.2
    R6 TR6-1 = 1150 0.3 TR6-2 = 1100 0.2 TR6-3 = 1050 0.3
    R7 TR7-1 = 1100 0.3 TR7-2 = 1050 0.3 TR7-3 = 1000 0.2
    R8 TR8-1 = 1100 0.3 TR8-2 = 1050 0.2 TR8-3 = 1000 0.3
     | Show Table
    DownLoad: CSV

    For both single-pass and three-pass hot deformations, all samples were immediately water quenched after hot deformation to obtain the martensite microstructure for prior austenite grain size analysis. Water-quenched samples were cut in half in the hot deformation direction, followed by grounding and polishing, and then etching with saturated picric acid. The analysis positions were the geometrical center of all the samples. Optical microscope (OM) images of each sample’s center were taken with ZEISS Axio Vert.A1. Electron backscatter diffraction (EBSD) installed on a scanning electron microscope (SEM, TESCAN MIRA4) was used to further characterize the microstructures of the six critical samples: two samples hot deformed at 1050°C/1200°C with a deformation reduction of 0.1, two samples deformed at 1000°C/1200°C with a deformation reduction of 0.2, and two samples deformed at 950°C/1200°C with a deformation reduction of 0.3. The step size of EBSD mapping was 0.2 µm and EBSD data post-processing was conducted with Aztec Crystal software (Version 2.12). The PAGSs were measured from the OM images by Nano Measurer 1.2 software using the line intercept length method and more than 200 grains were measured for each sample.

    In the three-pass experiments, the critical strain εc and the peak strain εp were obtained by analyzing the true stress–true strain curve fitted by a 7th order polynomial [24].

    Fig. 2 shows the microstructures of samples hot deformed at temperatures of 950, 1000, 1050, 1100, 1150, and 1200°C with a deformation reduction of 0.1. Fig. 2(a) shows that, for the sample hot deformed at 950°C, deformed austenite grains were observed, as highlighted by the green arrows in Fig. 2(a), and the PAGS of the sample was 153.9 µm. For the sample hot deformed at 1000°C, serrated prior austenite grain boundaries were observed, as highlighted by the yellow arrows in Fig. 2(b), which would serve as effective nucleation sites for subsequent DRX [2627]. PAGS of sample hot deformed at 1000°C was 157.8 µm which was similar to that of the samples hot deformed at 950°C. When the deformation temperature was increased to 1050°C, several DRX grains with sizes of around 30 µm were observed at austenite grain boundaries as highlighted by the red arrows in Fig. 2(c), which resulted in a finer PAGS of 132.4 µm. With further increasing the hot deformation temperature to 1100 and 1150°C, more DRX grains were observed and the PAGSs were further refined to 102.5 and 96.7 µm respectively, which suggested that extensive DRX occurred during the hot deformation process, as shown in Fig. 2(d) and (e). When the deformation temperature was extended to 1200°C, as shown in Fig. 2(f), almost fully equiaxed microstructure was achieved, and the PAGS was 110.0 µm. In comparison with 1100 and 1150°C hot deformed samples, the relatively larger PAGS of the 1200°C hot deformed sample was attributed to the larger DRX grains which were generated during the hot deformation process at a relatively higher temperature.

    Fig. 2.  Microstructures of samples hot deformed at (a) 950°C, (b) 1000°C, (c) 1050°C, (d) 1100°C, (e) 1150°C, and (f) 1200°C with a deformation reduction of 0.1.

    Fig. 3 shows the samples hot deformed at temperatures of 950, 1000, 1050, 1100, 1150, and 1200°C with a deformation reduction of 0.2. Fig. 3(a) shows the microstructure of the sample hot deformed at 950°C. It can be seen that with an increase of deformation reduction to 0.2, serrated prior austenite grain boundaries were observed, as highlighted by the yellow arrows in Fig. 3(a). Deformed prior austenite grains were observed and the PAGS of deformed austenite grains was 145.7 µm. When the deformation temperature was increased to 1000°C, very fine DRX grains with sizes of 10–20 µm were observed at austenite grain boundaries, as highlighted by the red arrows in Fig. 3(b), and the PAGS was reduced to 82.7 µm. In comparison with the samples with a deformation reduction of 0.1 (Fig. 2), the temperatures at which serrated grain boundaries and DRX occurred in the samples with deformation reduction of 0.2 were reduced from 1000 and 1050°C to 950 and 1000°C, respectively, suggesting that an increase in deformation reduction accelerates the occurrence of DRX. When the deformation temperature was extended to 1050°C the amount of DRX grains increased greatly and the PAGS was further refined to 56.2 µm, as shown in Fig. 3(c). With further increasing the deformation temperature to 1100, 1150, and 1200°C, the microstructures were dominated by equiaxed DRX grains and for the sample hot deformed at 1200°C, almost fully equiaxed microstructure was achieved. It should be noted that, beyond 1050°C, the PAGSs increased gradually to 70.3, 73.8, and 80.0 µm for the samples hot deformed at 1100, 1150, and 1200°C, respectively, as shown in Fig. 3(d)–(f).

    Fig. 3.  Microstructures of samples hot deformed at (a) 950°C, (b) 1000°C, (c) 1050°C, (d) 1100°C, (e) 1150°C, and (f) 1200°C with a deformation reduction of 0.2.

    Fig. 4 shows the samples hot deformed at temperatures of 950, 1000, 1050, 1100, 1150, and 1200°C with a deformation reduction of 0.3. Fig. 4(a) shows that, when the deformation reduction was increased to 0.3, serrated prior austenite grain boundaries, deformed austenite grains, and very fine DRX grains with a size of about 10 µm can all be observed in the sample hot deformed at 950°C with the PAGS of 72.9 µm. When the deformation temperature was extended to 1000 and 1050°C, the amount of DRX grains was increased greatly and the PAGSs were significantly refined to 58.4 and 39.0 µm respectively, as shown in Fig. 4(b) and (c). As the temperature was further increased to 1100, 1150, and 1200°C, almost fully equiaxed microstructures were obtained and the PAGSs increased gradually to 49.9, 58.9, and 72.9 µm with increasing temperature, as shown in Fig. 4(d)–(f).

    Fig. 4.  Microstructures of samples hot deformed at (a) 950°C, (b) 1000°C, (c) 1050°C, (d) 1100°C, (e) 1150°C, and (f) 1200°C with a deformation reduction of 0.3.

    Fig. 5(a) and (b) shows the inverse pole figure (IPF) map of martensitic and IPF + grain boundary (GB) map of prior austenite for the sample hot deformed at 1050°C with a deformation reduction of 0.1. Both DRX grains with an average grain size of 33.1 µm distributed at grain-boundary triple junctions (highlighted by white arrows) and slightly deformed austenite grains were observed in Fig. 5(b), which correspond well with the results observed in Fig. 2(c). Fig. 5(c) and (d) shows the IPF map of martensitic and IPF + GB map of prior austenite for the sample hot deformed at 1000°C with a deformation reduction of 0.2. It can be seen when the deformation reduction was increased to 0.2, a greater number of DRX grains were observed at conventional grain boundaries of the deformed austenite grains and the average size decreased to 20.7 µm, which are consistent well with the results observed in Fig. 3(b). When the deformation reduction was further increased to 0.3 while the deformation temperature was decreased to 950°C, as shown in Fig. 5(e) and (f), finer DRX grains with an average grain size of 17.5 µm were observed at conventional deformed austenitic grain boundaries. Fig. 5(a)–(f) shows that the size and number of DRX grains changed with different deformation conditions. It is worth noting that the DRX grains size shown by Fig. 5(a)–(f) decreased from 33.1 to 17.5 µm because of the decreased deformation temperature from 1050 to 950°C. While the increase in the number of DRX grains from Fig. 5(a)–(f) can be attributed to the enhancement of deformation reduction because the decrease in deformation temperature does not favor the DRX, which correspond well with the OM images in Figs. 24. Fig. 5(g)–(l) shows the IPF maps of martensitic and IPF + GB maps of prior austenite for samples that deformed at 1200°C with deformation reductions of 0.1, 0.2, and 0.3, respectively. It shows that equiaxed grains dominate the microstructure of all three samples, and the grain sizes were 96.6, 77.8, and 63.3 µm, respectively, which are consistent with the OM images in Figs. 2(f), 3(f), and 4(f). It further supports that the extent of DRX increases with the deformation reduction increasing from 0.1 to 0.3.

    Fig. 5.  (a, c, e, g, i, k) IPF maps for martensitic and (b, d, f, h, j, l) IPF+GB maps for prior austenite of samples hot deformed at (a, b) 1050°C with a deformation reduction of 0.1, (c, d) 1000°C with a deformation reduction of 0.2, (e, f) 950°C with a deformation reduction of 0.3, (g, h) 1200°C with a deformation reduction of 0.1, (i, j) 1200°C with a deformation reduction of 0.2, and (k, l) 1200°C with a deformation reduction of 0.3.

    Fig. 6 shows the effect of deformation temperature on PAGSs for samples with deformation reductions of 0.1, 0.2, and 0.3, respectively. It can be seen that for a specific temperature, the PAGSs decrease with increasing deformation reduction because greater extents of DRX occurred in samples with larger deformation reductions. The relationship between the volume fraction of DRX (XDRX) and deformation reduction can be expressed by Eq. (1) [22], which indicates that XDRX increases with true strain (deformation reduction).

    Fig. 6.  Evolution of PAGSs with deformation temperature for samples hot deformed with reductions of 0.1, 0.2, and 0.3.
    XDRX=1exp[kD(εεcεp)n1] (εεc) (1)

    where kD and n1 are constants. ε is true strain and positively related to deformation reduction. εc and εp can be expressed with the Zener-Hollomon parameter Z which describes the effect of strain rate and deformation temperature on DRX as Eq. (2) [28] and Eq. (3) [29].

    εc=aεp=CZq1 (2)
    Z=˙εexp(QRT) (3)

    where a, C, and q1 are constants, Q is the hot deformation activation energy, R is the universal gas constant, T is the deformation temperature, and ˙ε is strain rate of 5 s−1.

    The dynamic recrystallisation grain size dDRX can be expressed as Eq. (4) [22,25].

    dDRX=BZp1 (4)

    where B and p1 are constants.

    It should be noted that when ε is smaller than the critical strain εc, DRX would not occur and the PAGSs vary slightly, as highlighted by the yellow ellipse in Fig. 6. When ε is larger than εc, DRX occurs and DRX volume fraction increases with ε and T which results in a decrease in the PAGS [2930].

    Furthermore, as highlighted by the red ellipses in Fig. 6, the PAGSs decrease initially with an increase of deformation temperature from 950 to 1150°C for the samples hot deformed with a reduction of 0.1 and from 950 to 1050°C for the samples hot deformed with reductions of 0.2 and 0.3. When the deformation temperature is beyond 1150 or 1050°C, the PAGSs of samples with a deformation reduction of 0.1 or with a deformation reduction of 0.2 and 0.3 start to increase with increasing temperature, as shown by the green ellipses in Fig. 6. As the XDRX is positively correlated with temperature while dDRX is negatively correlated, it is worthy to note that the PAGS is mainly determined by the balance of the XDRX and dDRX. At lower temperatures, as the temperature increases, the XDRX increases rapidly, and thus the PAGS decrease rapidly. While at higher temperatures, numerous DRX grains have been generated and thus dDRX dominates at this stage which increases with increasing temperature as shown by Eqs. (3) and (4). It should be noted that with an increase of deformation reduction from 0.1 to 0.2 and 0.3, the temperature at which the PAGS start to increase decreased from 1150 to 1050°C, which is attributed to a substantial increase in XDRX due to the increase of deformation reduction.

    Fig. 7 shows the microstructures and PAGS of the samples after three-pass hot deformation with different parameters. Fig. 7(a) and (b) shows the microstructures of R1 and R2, respectively. When shifting the 0.1 deformation reduction in the second pass of R1 to the third pass (see Table 2), the PAGS was reduced from 55.7 (R1) to 49.6 µm (R2), which could be contributed to the fact that complete DRX was not achieved in R1. This result also suggests that for the case of partial DRX, shifting part of the deformation reduction of the first or second pass to the third pass is helpful to realize complete DRX and a finer grain size. The same phenomenon was also observed in R3 and R4. As shown in Fig. 7(c) and (d), when shifting the 0.1 deformation reduction in the second pass of R3 to the third pass, the PAGS was reduced from 42.6 (R3) to 35.8 µm (R4). It should be noted that as the deformation temperatures of the second and third pass of R3 and R4 were 50°C lower than that of R1 and R2, the PAGSs were reduced by about 13 µm, respectively. Fig. 7(e) and (f) shows the microstructures of R5 and R6, respectively. Instead of a decrease in PAGS, when shifting the 0.1 deformation reduction in the second pass of R5 to the third pass, the PAGSs of R5 and R6 were very similar (R5 is 36.9 µm and R6 is 38.2 µm), which indicated that complete DRX occurred in both R5 and R6. This result suggests that in the case of complete DRX, shifting part deformation reduction in the third pass to the second pass with a relatively higher deformation temperature does not affect the grain size. It should be noted that the PAGS of R5 decreased by 5.7 µm compared to R3 because the first pass deformation temperature of R5 was reduced by 50°C. Fig. 7(g) and (h) shows the microstructures of R7 and R8, respectively. Akin to R5 and R6, when the 0.1 deformation reduction in the second pass of R7 was shifted to the third pass, they shared identical PAGS of 34.6 µm. It also corroborated that in the case of complete DRX, shifting part deformation reduction of deformation pass with lower deformation temperature to prior deformation pass would not affect the grain refining effect.

    Fig. 7.  Microstructural analysis of (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7, and (h) R8.

    From Eq. (1) to Eq. (4), we can see that in the case of complete DRX, PAGS is equal to dDRX and only dependent on ˙ε and T. In this work, ˙ε is a constant of 5 s−1, so the DRX grain size is only dependent on T which corroborates that R5 and R6, R7 and R8 have similar grain sizes. Furthermore, as the deformation temperatures of the final pass for R1–R2, R3–R6, and R7–R8 were 1100, 1050, and 1000°C, the PAGSs of R1 and R2 were larger than that of R3–R6 and R7–R8, which is consistent with Fig. 7.

    As DRX is a dynamic equilibrium microstructure, a certain amount of strain is retained even in a completely DRX microstructure [31]. This strain is usually removed in the inter-pass by static recovery and static recrystallization. However, when the insulation temperature is low or the inter-pass time is short, some of this stain will be retained until the next deformation pass [32] which is known as accumulated strain. Accumulated strain can contribute to an increase in flow stresses during hot deformation and raise the DRX driving force [33], contributing to the DRX process.

    Fig. 8(a) and (b) shows the plots of critical strain εc–peak strain εp for different deformation passes of R1–R4 and R5–R8, respectively, which are frequently used to analyze the DRX behaviors of metallic materials [28,34]. For hot deformation, εc/εp is constant [28], which is not significantly related to temperature and grain size [24]. However, in this work, εc/εp of R5–R8 decreased with an increasing number of deformation passes and for the third pass of R5–R8, the εc/εp decreased from 0.70 to 0.53 compared with that of R1–R4, which could be attributed to the fact that strain is accumulated during the first and second deformation passes of R5–R8. At higher deformation temperatures, accumulated strain can be easily released, thus contributing less to the DRX processes [35]. Therefore, accumulated strain did not play an important role in promoting DRX for R1 and R3, so relatively coarse grains were observed in R1 and R3. However, for R5–R8, relatively lower deformation temperatures were employed in all the three passes, and the accumulated strain could be effectively retained during the hot deformation process, which promoted the realization of complete DRX in R5–R8. Therefore, shifting part deformation reduction of the third pass with a lower deformation temperature to the second pass did not affect the grain refining effect.

    Fig. 8.  Plots of critical strain εc–peak strain εp for different hot deformation passes of (a) R1–R4 and (b) R5–R8.

    The DRX behaviors of a eutectoid pearlite rail steel were investigated by single- and three-pass hot deformation experiments, employing parameters close to those used in practical industrial rail production. The key conclusions are drawn as follow.

    (1) Single-pass hot deformation results show that the PAGSs for samples with different deformation reductions initially decrease with an increase in deformation temperature. When the deformation temperatures reach 1150, 1100, and 1050°C with deformation reductions of 0.1, 0.2, and 0.3 respectively, the PAGSs start to increase, which is attributed to the different roles of XDRX and dDRX at different temperatures.

    (2) Three-pass hot deformation results demonstrate that in the case of complete DRX, shifting 0.1 deformation reduction from deformation pass with deformation temperature between 1000 and 1050°C to prior deformation pass with deformation temperature in the range of 1050–1100°C would not affect the grain refining effect. In such scenarios, the accumulated strain plays a crucial role in enhancing the extent of DRX and the PAGS is primarily determined by the deformation temperature of final pass.

    (3) With optimized hot deformation parameters, the PAGS was effectively refined from 160 to 34.6 µm by a three-pass hot deformation process.

    This work was financially supported by the National Natural Science Foundation of China (Nos. 52293395 and 52293393) and the Xiongan Science and Technology Innovation Talent Project of MOST, China (No. 2022XACX0500).

    Xinping Mao is an advisory board member for this journal and was not involved in the editorial review or the decision to publish this article. The authors have no conflict of interest to declare.

    The online version contains supplementary material available at https://doi.org/10.1007/s12613-023-2805-4

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