Characterization and Modelling of Microstructure Evolution and Flow Stress of Single-Phase Austenite and Ferrite Phases in Duplex Stainless Steels

Abstract

This paper presents an experimental and modeling study to investigate and predict the microstructure evolution for single-phase austenite and ferrite steels with the chemistry of the corresponding phases in a duplex stainless steel SUS329J4L under hot forming conditions. For steels with the compositions corresponding to both austenite and ferrite phases, single-pass hot uniaxial compression tests, stress relaxation tests, and heat treatment tests have been conducted for a temperature range of 1000–1250 °C and strain rates ranging from 0.3 to 30 s⁻¹. The dynamic and static recrystallization mechanisms, as well as the grain growth behavior, were studied, and the material parameters of each mechanism were identified for a semi-empirical microstructure model called StrucSim. Double-compression tests in the same temperature and strain rate range were performed to validate the model, and a good correlation of the flow stress between the experiment and simulation was observed.

1. Introduction

Reaching carbon neutrality is currently the most urgent task faced by every sector in the world. New technologies to reduce carbon emissions are emerging, requiring materials with optimal properties for their products. One such example is duplex stainless steels (DSSs), which show excellent mechanical and corrosion properties under severe conditions and are expected to become an important material in carbon capture and storage (CCS) and geothermal power generation [1,2]. To be able to use DSSs in these new applications, existing products need to be adapted to meet the necessary requirements, e.g., changed properties or geometrical specifications. This requires an understanding of the deformation behavior and microstructure evolution under hot forming conditions as they are directly linked to the final properties. Particularly for dual-phase materials, such as DSSs, predicting load and microstructure remains difficult due to the interaction between the different phases. Many studies have been conducted to analyze the flow stress behavior and microstructure evolution of DSSs [3,4,5]. However, the authors in [6,7] concluded that the knowledge of the behavior of the individual ferrite and austenite phases under hot deformation is first required to fully analyze the behavior of DSSs.

For the individual ferrite and austenite phases with their phase chemistries in DSSs, Sasaki et al. [8] found that, in addition to austenite having a higher strength than the ferrite phase, the strength ratio is strongly influenced by the deformation temperature and strain rate. A higher austenite-to-ferrite strength ratio was observed at high temperatures and low strain rates. The strength ratio affects the distribution of strain between the two phases and has an important influence on the microstructure evolution. However, there is no study available that investigates and models the microstructure evolution for each phase in DSS under hot forming conditions, including the mechanisms of grain growth, dynamic recrystallization, and static recrystallization. For this reason, this study investigates the microstructure evolution and modeling of each phase in DSSs at various deformation temperatures for the three mechanisms. Further, a deformation sequence is studied to test the influence of different pause times on the softening behavior of both phases and the applicability of the microstructure model StrucSim.

2. Materials and Methods

2.1. Experimental Procedure

The single-phase materials have been prepared based on the chemical compositions and procedures described in [8]. For each test temperature, the specific chemical composition was calculated based on the temperature-dependent chemical composition of ferrite and austenite in the DSS SUS329J4L to ensure a single-phase material. The chemical composition for each test temperature remained the same at room temperature. All samples were produced by vacuum induction melting of steel ingots that were hot rolled to a thickness of 300 mm at 1200 °C. Further homogenization was done by heating and holding at the later test temperature of each sample for 30 min. However, for the low temperatures, remaining ferrite fractions were detected for the austenite single-phase material. An overview of the different chemical compositions, remaining second-phase fractions, and initial grain sizes is shown in

Table 1. Overview of chemical compositions, initial grain sizes, and remaining second-phase fractions for the single-phase materials. Data of chemical compositions reprinted from Ref. [8].

Ferrite	Chemical Composition								Initial Grain Size	Remaining Austenite
[°C]	Fe	Cr	Mo	Ni	Si	Mn	C	N	[µm]	[%]
1000	Balance	29.30	3.80	5.30	0.30	0.20	0.003	0.02	479	0.0
1100	Balance	27.50	3.50	5.90	0.30	0.30	0.004	0.02	741	0.0
1200	Balance	26.20	3.20	6.70	0.30	0.30	0.005	0.05	815	0.0
1250	Balance	26.00	3.10	7.20	0.30	0.30	0.009	0.06	1200	0.0
Austenite	Chemical Composition								Initial Grain Size	Remaining Ferrite
[°C]	Fe	Cr	Mo	Ni	Si	Mn	C	N	[µm]	[%]
1000	Balance	21.90	2.20	9.90	0.30	0.40	0.037	0.16	25	7.0
1100	Balance	21.60	2.00	10.10	0.30	0.40	0.044	0.19	29	3.9
1200	Balance	22.00	1.90	10.30	0.30	0.40	0.056	0.22	126	0.1
1250	Balance	22.00	1.90	10.50	0.30	0.40	0.070	0.24	133	0.2

.

It should be noted that, in the case of the ferrite single-phase specimens, very large initial grain sizes are apparent. While these large grain sizes are not likely to occur in the actual DSS material, the general microstructure evolution of the ferrite phase during dynamic and static stages at elevated temperatures can still be studied.

Further heat treatment tests have been conducted using a conventional radiation furnace by Nabertherm GmbH (Lilienthal, Germany). Hot uniaxial compression tests were conducted on the servo-hydraulic press ServoTest by Servotest Testing Systems Ltd. (Egham, UK). Here, Rastegaev samples, i.e., cylindrical specimens (Ø10 × 15 mm) with a small cup hole on both end faces that act as “lubrication pockets”, were used with a glass powder lubricant to minimize friction and compression applied up to a strain of 0.8. The samples were heated using a radiation furnace that surrounded the test equipment. All samples were quenched in water following the compression with a quenching delay of approximately 2–5 s. All the tests were repeated twice. Stress relaxation tests were conducted using the dilatometer DIL805A/D by TA Instruments, Inc. (Hüllhorst, Germany). Based on the method introduced by Karjalainen in [9], compression is applied up to different pre-strains, and the deformation is upheld to measure the decrease in force during the holding time. Here, pre-strains of 0.15 and 0.2 were used for the austenite single-phase steel to prevent the onset of dynamic recrystallization (DRX) and be able to clearly distinguish between DRX and static recrystallization (SRX) effects. For the ferrite single-phase steel, higher pre-strains of 0.4 and 0.8 have been used as the compression tests from [8] indicated that no DRX was taking place. The samples were held for up to 10 min to record the full softening and then quenched immediately after reaching the final holding time using argon gas. Furthermore, the stress relaxation tests were interrupted at shorter holding times, and the microstructure was investigated to validate the softening curves.

Further experimental testing was performed to validate the microstructure model StrucSim. For this, double compression tests were conducted using the dilatometer DIL805A/D. After a first compression up to a strain of 0.3 or 0.4, the samples were held at the deformation temperature before a second compression was applied up to a final strain of 0.6. By using double compression tests, the influence of different pause times on the flow stress during the second compression was measured. The evolution of flow stress was compared to the microstructure model StrucSim, which will be explained in the following. The conditions for all experimental tests are listed in Figure 1. All samples were examined through metallographic preparation and light microscopy with aqua regia as the etchant. Additionally, EBSD measurements have been carried out on chosen samples to analyze the grain structure in more detail.

2.2. Parameter Identification for Microstructure Model StrucSim

The microstructure model StrucSim was developed at the Institute of Metal Forming (IBF). A detailed description of the model can be found in [10]. StrucSim uses an evolving substructure to model different metallurgical mechanisms. Here, during DRX or SRX a substructure with the size of the RX fraction is separated and treated independently. Averaging all substructures gives the overall average value for the RX fraction, grain size, and flow stress.

Five different data sets describing its own metallurgical mechanism are required to identify the material parameters for StrucSim, which are a description of the flow curves, static recrystallization kinetics, grain growth (${\mathrm{d}}_{\mathrm{GG}}$), grain size after DRX $\left({\mathrm{d}}_{\mathrm{DRX}}\right)$, and grain size after SRX $\left({\mathrm{d}}_{\mathrm{SRX}}\right)$. For the description of the flow curve, first, the peak strain ${\mathsf{\epsilon }}_{\mathrm{p}}$ is calculated as a function of temperature T and strain rate $\dot{\mathsf{\epsilon }}$ based on Equation (1).

$${\mathsf{\epsilon }}_{\mathrm{p}}={\mathrm{A}}_1·{\mathrm{d}}_0^{{\mathrm{A}}_2}·{\dot{\mathsf{\epsilon }}}^{{\mathrm{A}}_3}·\exp \left({\displaystyle \frac{{\mathrm{A}}_5}{\mathrm{R}·\mathrm{T}}}\right)$$

(1)

with A_i as material parameters, R as the universal gas constant and d₀ the initial grain size the influence of which is neglected in this study as only one initial grain size was produced for each single-phase material. For calculating the peak stress ${\mathsf{\sigma }}_{\mathrm{p}}$, the Zener–Hollomon-Parameter $\mathrm{Z}$ is taken from Equation (2), with Q_w as the activation energy, and used in Equation (3), where O_i describes the material parameters.

$$\mathrm{Z}=\dot{\mathsf{\epsilon }}·\exp \left({\displaystyle \frac{{\mathrm{Q}}_{\mathrm{w}}}{\mathrm{R}·\mathrm{T}}}\right)$$

(2)

$${\mathsf{\sigma }}_{\mathrm{p}}={\displaystyle \frac{1}{{\mathrm{O}}_3}}·\mathrm{arcsinh}\left({\mathrm{O}}_1·{\mathrm{Z}}^{{\mathrm{O}}_2}\right)$$

(3)

With ${\mathsf{\epsilon }}_{\mathrm{p}}$ and ${\mathsf{\sigma }}_{\mathrm{p}}$, the stress in the hardening regime of the flow curve ${\mathsf{\sigma }}_{\mathrm{DRV}}$ can be calculated based on Equation (4).

$${\mathsf{\sigma }}_{\mathrm{DRV}}={\mathsf{\sigma }}_{\mathrm{p}}·{\left({\displaystyle \frac{\mathsf{\epsilon }}{{\mathsf{\epsilon }}_{\mathrm{p}}}}·\exp \left(1-{\displaystyle \frac{\mathsf{\epsilon }}{{\mathsf{\epsilon }}_{\mathrm{p}}}}\right)\right)}^{\mathrm{C}}$$

(4)

Here, $\mathsf{\epsilon }$ describes the current strain value and C a material parameter. With the critical strain ${\mathsf{\epsilon }}_{\mathrm{c}}$ from Equation (5), the dynamically recrystallized fraction ${\mathrm{X}}_{\mathrm{DRX}}$ can be calculated from Equation (6) with D_i being material parameters.

$${\mathsf{\epsilon }}_{\mathrm{c}}={\mathrm{A}}_4·{\mathsf{\epsilon }}_{\mathrm{p}}$$

(5)

$${\mathrm{X}}_{\mathrm{DRX}}=1-\exp \left(-{\mathrm{D}}_1{\left({\displaystyle \frac{\mathsf{\epsilon }-{\mathsf{\epsilon }}_{\mathrm{c}}}{{\mathsf{\epsilon }}_{\mathrm{c}}}}\right)}^{{\mathrm{D}}_2}\right)$$

(6)

SRX is described by calculating the time for 50% of SRX (t50) to occur based on Equation (7) with F_i being material parameters. Using the t50-time, the SRX fraction X_SRX can be calculated based on Equation (8) with G describing the Avrami coefficient.

$${\mathrm{t}}_{50}={\mathrm{F}}_1 · {\mathsf{\epsilon }}^{{\mathrm{F}}_2} · {\mathrm{Z}}^{{\mathrm{F}}_3} · \exp \left({\displaystyle \frac{{\mathrm{F}}_4}{\mathrm{R} · \mathrm{T}}}\right)$$

(7)

$${\mathrm{X}}_{\mathrm{SRX}}=1-\exp \left(\ln (0.5) ·{\left({\displaystyle \frac{\mathrm{t}}{{\mathrm{t}}_{50}}}\right)}^{\mathrm{G}}\right)$$

(8)

Lastly, the grain size after DRX, SRX, and grain growth are calculated based on Equations (9)–(11). Here, B_i, CS_i, and HD_i describe the corresponding material parameters.

$${\mathrm{d}}_{\mathrm{DRX}}={\mathrm{B}}_1·{\mathrm{Z}}^{{\mathrm{B}}_2}$$

(9)

$${\mathrm{d}}_{\mathrm{SRX}}={\mathrm{CS}}_1·{{\mathrm{d}}_0}^{{\mathrm{CS}}_2}·{\mathrm{Z}}^{{\mathrm{CS}}_5}·\exp \left({\displaystyle \frac{{\mathrm{CS}}_4·{\mathrm{Q}}_{\mathrm{s}}}{\mathrm{R}·\mathrm{T}}}\right)$$

(10)

$${\mathrm{d}}_{\mathrm{GG}}={\left({\mathrm{d}}_0^{{\mathrm{HD}}_1}+\mathrm{t}·{\mathrm{HD}}_2·\exp \left(-{\displaystyle \frac{{\mathrm{Q}}_{\mathrm{GG}}}{\mathrm{R}·\mathrm{T}}}\right)\right)}^{{\displaystyle \frac{1}{{\mathrm{HD}}_1}}}$$

(11)

Each substructure follows the described set of equations, and the overall flow stress can be calculated by averaging the corresponding property over all the substructures weighted by their relative size [11]. It is important to note that, while metadynamic recrystallization (MDRX) is an important mechanism in the post-dynamic regime, the same equations and parameters as for SRX have been used in this study as it is expected to have the same influence on the flow stress response.

To determine the needed material parameters (A_i, B_i, C, D_i, F_i, G, O_i, Q_x, F_i, CS_i, HD_i), experimental tests are needed. Here, the previously described heat treatment tests are used for grain growth, compression tests for DRX, and stress relaxation tests for SRX. The parameters are then identified by minimizing the deviation between the experimental and simulative values for the single mechanisms. As no softening behavior in the flow curve, as well as no DRX or SRX grains, were observed in the case of ferrite (see Section 3), parameter identifications for Equations (2), (7), and (8) were left out. The validation of the model was performed using the previously described double compression tests.

3. Results and Discussion

3.1. Experimental Results

In the following, the results of all characterization experiments will be shown. It should be noted that, in all cases, the particular steel depends on temperature with each steel having a different chemical composition to stabilize either the ferrite or austenite phase at the testing temperature as indicated in Table 1.

3.1.1. Grain Growth Analysis

As a first step, the heat treatment tests were analyzed for the average grain size evolution (Figure 2a,d). For austenite, it can be seen that, at 1000 °C and 1100 °C, only small grain growth is taking place with final values of 26 ± 3 µm at 1000 °C and 72 ± 7 µm at 1100 °C after 120 min. This is due to remaining ferrite fractions in the microstructure, which act as an inhibitor to grain growth (see Figure 2b). At 1200 °C and 1250 °C, grain growth is taking place fast and reaching final values of 183 ± 14 µm at 1200 °C and 386 ± 92 µm at 1250 °C after 120 min. Here, no remaining ferrite fraction is visible as shown in Figure 2c. In the case of ferrite, no second phase fraction was visible in the microstructure (Figure 2e,f); thus, grain growth takes place without any obstacles. It can be seen that large average grain sizes of over 1000 µm are present at the highest temperatures. Overall, the results show that the single-phase materials allow fast grain growth, and this knowledge is necessary for the parameter identification of grain growth for the microstructure model StrucSim. However, it should be noted that, in the DSS structure, grain growth will be limited due to the interaction between the two phases, as already indicated by the austenite results at low temperatures, with the remaining second-phase fractions, and, therefore, the results of the very large ferrite grain sizes are not directly transferable.

3.1.2. DRX Analysis

The compression tests were analyzed in terms of flow curves and microstructure at the end of compression to use as an input for the microstructure model StrucSim. Compared to the analysis performed in the previous work [8], Rastegaev samples with glass powder lubricant were used to exclude friction, and the heating of the samples was based on radiation instead of induction heating, allowing for better temperature homogenization of the samples. Thus, friction and temperature gradients can be neglected during the microstructure analysis. Furthermore, calculation and temperature compensation of flow curves were performed with the IBF development flow stress utilities (FSUs), as described in [12]. Figure 3 and Figure 4 show the evaluated flow curves of all conditions for austenite and ferrite, respectively. It can be seen that the ferritic single-phase specimens show lower flow stress values compared to the austenitic single-phase specimens in all cases. In addition, the general dependency on temperature and strain rate is visible for both phases, i.e., lower stress values are reached with increasing temperature and decreasing strain rate, as previously shown in [8]. For austenite, at a strain rate of 0.3 s⁻¹, a peak in stress around a strain of 0.4 is visible for temperatures of 1100 °C and higher. The peak stress is followed by a slight stress decrease of around 5 MPa, indicating softening by recrystallization. In contrast, this stress decrease is not visible for the higher strain rates nor for the temperature at 1000 °C, which indicates a low amount of softening by DRX. In the case of the ferritic specimens, the flow curves do not show peaks in the stress or a subsequent softening behavior in any case. Instead, the stress reaches a saturation value at higher strains. This difference in stress values and flow curve shapes is due to different crystal structures and stacking fault energies. Austenite has an fcc structure with a low stacking fault energy. This means that the formation of stacking faults is easy, leading to the limited cross slip of dislocations during deformation and the occurrence of twinning. Therefore, the deformation can only take place under higher stresses, and the microstructure will undergo discontinuous DRX (DDRX), i.e., nucleation and growth of nuclei. On the other hand, ferrite has a bcc structure with a high stacking fault energy. Thus, the formation of stacking faults is difficult, and the cross slip of screw dislocations is possible. As a result, lower stresses are sufficient to deform the sample, and deformation up to high strain levels is possible. Here, the main metallurgical mechanism is dynamic recovery followed by continuous DRX (CDRX), i.e., subgrain rotation and transformation of low-angle to high-angle grain boundaries [13].

To further analyze the different flow curve behavior, EBSD, as well as light microscopy analysis of the microstructure, has been carried out. Figure 5 and Figure 6 show the results for the cases at 1000 °C and 0.3 s⁻¹, 1250 °C and 0.3 s⁻¹, and 1250 °C and 30 s⁻¹ for austenite and ferrite, respectively. In the case of austenite, a fine recrystallized microstructure is visible at 1000 °C in the inverse pole figure (IPF) of the EBSD measurement. This indicates that, even though the flow curve did not show a softening behavior, nucleation was taking place, and the recrystallized grains replaced the deformed grains. Furthermore, the phase map, as well as the light microscopy images, clearly show the remaining second-phase fractions that did not change during the deformation compared to the grain growth examples in Figure 2b. Thus, no dynamic transformation has been taking place. In both cases, at 1250 °C, no deformed grains are visible, which indicates that recrystallization has taken place. Thus, for austenite, the statement can be made that DDRX is occurring but seems to have only a small influence on the flow stress behavior.

In the case of ferrite, large deformed grains are visible at 1000 °C and 1250 °C at 0.3 s⁻¹. However, the image quality map shows clear sub-grain formation. This is due to CDRX taking place. However, the time was not sufficient for completion. At 1250 °C and 30 s⁻¹, undeformed grains are visible in the ferrite microstructure caused by a quenching delay after the end of deformation. Therefore, it is considered to be an SRX effect rather than an effect of the deformation. Furthermore, slip bands can be seen within the grains.

Overall, the DRX results demonstrate that different DRX mechanisms and flow stress values might occur in the actual DSS depending on the thermomechanical history and the phase fractions present.

3.1.3. SRX Analysis

Softening of the single-phase steels is recorded during the stress relaxation tests from the decrease in the compression force during the holding time. For austenite, Figure 7a shows the results for a strain rate of 0.3 s⁻¹ and a pre-strain of 0.15. It can be seen that the end of the first linear region with a low slope, which indicates the beginning of SRX, as suggested by Karjalainen [9], for all temperature cases, is shortly before the 1 s holding time. This observation agrees with the measurements performed on a plastodilatometer by Vervynckt et al. in [14]. On the other hand, the beginning of the second linear region with a low slope indicating the end of SRX shows a temperature dependency. Here, higher temperatures show an earlier start of that second linear region. The linear stages represent softening by recovery and creep for the first region and grain growth and creep for the second region. Thus, the curves were evaluated based on the Karjalainen method, as described in Section 2, with two linear slopes that are fitted to the relaxation curve. The recrystallization kinetics can then be calculated based on Equation (12), where $\mathsf{\sigma }$ marks the true stress value while ${\mathsf{\sigma }}_{\mathrm{i}}$ and ${\mathsf{\alpha }}_{\mathrm{i}}$ mark the constants and slopes of the two linear regions, respectively.

$$\mathrm{X}={\displaystyle \frac{{\mathsf{\sigma }}_1-{\mathsf{\alpha }}_1·\log \left(\mathrm{t}\right)-\mathsf{\sigma }}{\left({\mathsf{\sigma }}_1 -{\mathsf{\sigma }}_2\right)-({\mathsf{\alpha }}_1-{\mathsf{\alpha }}_2)·\log \left(\mathrm{t}\right)}}$$

(12)

Based on this evaluation, the t50-time is taken and the Avrami coefficient G evaluated using Equation (13).

$$\mathrm{X} =1-\exp \left[-0.693{\left({\displaystyle \frac{\mathrm{t}}{{\mathrm{t}}_{50}}}\right)}^{\mathrm{G}}\right]$$

(13)

Figure 7b shows as an example the comparison of the evaluated SRX curve from Equation (12) and the fit from Equation (13) for the relaxation curve at 1000 °C and 0.3 s⁻¹ with a pre-strain of 0.15. It is visible that the recrystallization start for the evaluated SRX curve is marked at the end of the first linear region and finished at the beginning of the second linear region of the corresponding stress relaxation curve from Figure 7a. While the t50-time is correctly depicted with the fit from Equation (13), it still leads to an earlier SRX start and end compared to the experimental measurements. This might be a result of the idealized curve shape resulting from Equation (13) and using an averaged Avrami coefficient for the whole curve even though the beginning and end of the evaluated SRX curve show different slopes.

An overview of the fitted SRX curves for all temperatures is given in Figure 7c, and the general temperature dependency of the SRX end from the stress relaxation test is depicted. Figure 7d shows further the evolution of the t50-times for all temperatures and pre-strains at a strain rate of 0.3 s⁻¹. It can be seen that shorter t50-times are needed at higher temperatures, meaning faster SRX with increasing temperature. Regarding the dependency on pre-strain, no clear trend is observed as the values at 1100 °C and 1200 °C match almost identically with around 2.5 s and 2 s, respectively.

Figure 8a shows the results of the stress relaxation tests for ferrite for a strain rate of 0.3 s⁻¹ and a pre-strain of 0.4. Here, due to the lower flow stress levels of ferrite, the force starts at lower values but a first linear regime is again noticeable and the end is marked between 0.1 s and 1 s of holding time. The further softening, however, takes place much faster compared to austenite. Looking at the corresponding softening kinetics in Figure 8b, it is noticeable that full softening is reached in less than 10 s and that the dependence on temperature is not as clearly distinguishable as in the austenite case. Thus, the evaluated t50-times (Figure 8c) show similar values of from around 1.5 to 2 s for all temperatures. Also, the different pre-strains have no clear influence on the kinetics of softening.

To better understand the softening behavior in ferrite during the holding time, three different points of the relaxation curve were quenched at 1100 °C, and the microstructure was analyzed after a holding time of 1 s, 10 s, and 600 s by light microscopy and EBSD (see Figure 9). It can be seen that, although the relaxation curve and corresponding softening kinetics curve show almost 50% softening after 1 s and full softening after 10 s, the microstructure itself continues to show deformed grains and no sign of recrystallization. Thus, the softening is not caused by SRX but rather by recovery, as is typical for ferritic steels [15]. However, subgrains are visible in the EBSD imaging, and, after 600 s, the microstructure appears to have rearranged itself without a significant grain refinement present.

While the limitation of the stress relaxation approach for ferrite is clearly shown and no apparent recrystallization detected, the measured softening mechanism still has an important influence on the flow stress calculation for the microstructure model StrucSim. Thus, the t50-times will still be used for the calculation of softening in the static regime of the validation tests.

If the results are transferred to the DSS structure, it is likely that rapid softening will occur in the DSS material within a few seconds to minutes, depending on the phase fractions present. However, the reason for the softening might not necessarily be due to SRX if the influence of the ferrite phase is high.

3.1.4. DRX and SRX Grain Size Analysis

Besides the flow curves and stress relaxation curves, StrucSim needs DRX and SRX grain sizes for full parameter identification. For this, the recrystallized grain size after the end of the compression tests has been studied for austenite, as nucleation was observed in these microstructures. Figure 10a shows the corresponding final grain sizes as a function of the test temperature at the three different strain rates. It can be seen that the average grain size increases with increasing temperatures while no influence of the strain rate is observed between 1000 and 1200 °C. One exception is at 1250 °C, where the average grain size at 0.3 s⁻¹ is 30 µm higher than the other strain rates. However, it is expected that this deviation is caused by a quenching delay at the end of the compression tests, as the samples need to be manually quenched in water. During this procedure, quenching delays of 2–5 s can appear and cause grain growth at high temperatures. It should be noted that these quenching delays might influence all results at high temperatures of 1200 °C and 1250 °C in a similar manner. However, still significant grain refinement is apparent with a reduction in the initial average grain size from 126 µm and 133 µm (see Table 1) to 40–55 µm at 1200 °C and 1250 °C, respectively. Furthermore, to study the SRX grain size, the average grain size evolution at different holding times of the stress relaxation tests is depicted in Figure 10b. Here, it can also be seen that the average grain size is higher at higher temperatures. Furthermore, a decrease in the average grain size for all temperatures is visible in the first 10 s. This is caused by ongoing SRX, which leads to nucleation and smaller grains in the microstructure. With longer holding times, the average grain size is increasing due to complete SRX and grain growth taking over. These results are confirmed by the IPF pictures of the EBSD images in Figure 10c–g. Here, the microstructures at 1100 °C after a compression until a pre-strain of 0.2 and a strain of 0.3 s⁻¹ are shown for the different holding times between 1 and 600 s. It can be seen that the microstructure after 1 s shows very small grains around the deformed grain boundaries. This indicates that nucleation has started. After 10 s, the grain structure is more homogeneous with an overall lower grain size distribution compared to 1 s. Thus, a recrystallized microstructure is present. With higher holding times, much bigger grains start to appear, which means that grain growth has started. Therefore, the average grain sizes after 10 s are chosen for the parameter identification in StrucSim. Comparing the results at the pre-strains of 0.15 and 0.2, no influence of the pre-strain on the average grain size evolution is visible.

3.2. Parameter Identification

As described in Section 2.2, parameter identification for StrucSim was performed by minimizing the deviation between the experimental and simulative values. Figure 11 shows the results of the fitting procedure for austenite and ferrite. Here, Figure 11a,b shows the fitting results for the grain growth tests for austenite and ferrite, respectively. Good agreement between the experimental and fitted results are achieved in all the cases and the much bigger average grain sizes in ferrite can be depicted by StrucSim. In Figure 11c,d, a comparison of the flow curves is shown with the examples at 1000 °C and 1200 °C. Here, very good accuracy is achieved in the flow stress calculation by StrucSim. The dependencies on temperature, strain rate, and strain are clearly visible. Furthermore, SRX parameter identification has been done using the evaluated t50-times for the stress relaxation tests. Figure 11e,f shows the results. It can be seen that StrucSim is able to depict the dependencies of temperature and pre-strain for all cases. An overview of the final StrucSim parameters is given in

Table 2. Overview of StrucSim parameters for austenite and ferrite.

Austenite				Ferrite
QGG	8.88 × 105	E1	3.08	QGG	4.63 × 105	E1	1
HD1	4.97	B1	12,500	HD1	8.68	B1	-
HD2	8.89 × 1038	B2	−0.19	HD2	2.72 × 109	B2	-
Qw	338,650	D1	−1.855	Qw	338,650	D1	-
A1	0.2729	D2	2.347	A1	0.763	D2	-
A2	0	O1	9.31 × 10−3	A2	0	O1	9.16 × 10−7
A3	0.263	O2	0.164	A3	0.0035	O2	0.52
A4	0.649	O3	6.32 × 10−3	A4	10	O3	0.033
A5	3683	C	0.205	A5	1	C	0.205
F1	2.40 × 10−3	CS1	3.65 × 104	F1	2.76 × 10−2	CS1	-
F2	0	CS2	0	F2	0	CS2	-
F3	0.46	CS3	0	F3	0.1	CS3	-
F4	−0.35	CS4	−0.71	F4	0.01	CS4	-
Qs	2.18 × 105	CS5	0.23	Qs	4.00 × 104	CS5	-
g1		0.83		g1		0.86

.

3.3. Validation Experiments

Double-compression tests were carried out to validate the StrucSim parameters as described in Section 2.1 using the deformation dilatometer based on the flow stress evolution. Figure 12a,b shows the comparison between the experimental and StrucSim results for austenite at 1000 °C and 3 s⁻¹ and for ferrite at 1100 °C and 3 s⁻¹. In the case of austenite (Figure 12a), a first compression until a strain of 0.4 is applied. After a holding time of 10 s, the material is partially softened as the flow stress during the second compression with a final strain of 0.2 does not continue from the last value before the pause time. However, a longer holding time of 100 s leads to more recrystallization, and, thus, softening with lower flow stress responses. The simulations in StrucSim are able to depict the flow stresses correctly with only differences of around 10 MPa for 10 s and a complete flow stress representation for 100 s, respectively. It should be noted that, while the second compression matches the flow stress values accurately, the first compression already shows a scatter in the experimental data and higher values than the flow curves recorded in Figure 3b for the same conditions. The difference lies in the experimental setup used as the validation tests have been conducted on the deformation dilatometer where friction, as well as a temperature gradient along the sample, cannot be avoided. This leads to higher stress values and, overall, more scatter. For ferrite, the same strains of 0.4 for the first compression and 0.2 for the second compression were used, and the holding times varied with values of 2 s and 20 s (Figure 12b). It can be seen that the overall stress level differences are much lower than for austenite. Hence, a lower effect of the softening during the pause time on the flow stress is also observed. However, in the experiments, the flow stress after a pause time of 2 s is around 10 MPa higher than the flow stress at 20 s. StrucSim is able to display this difference as well. Despite different pause times, a comparison for different temperatures at a strain rate of 0.3 s⁻¹ and strains of 0.3 for both compression steps has also been analyzed. Figure 12c shows the results for austenite with a pause time of 100 s between the two compression steps. It can be seen that, while the flow stress response for the second compression at 1000 °C and 1100 °C is in good agreement between the experiments and the Strucsim calculations, StrucSim overestimates the flow stress values at higher temperatures of above 1200°C. The reason for this might be that the discussed experimental setup differed from the regular compression tests, leading to more scatter overall. However, the qualitative stress differences between the curves at 1200 °C and 1250 °C are still in good agreement between StrucSim and the experiments with values around 10 MPa. This indicates that the temperature influence itself can be represented. For ferrite, the same comparison at a strain rate of 0.3 s⁻¹ and a strain of 0.3 for both compression steps is shown in Figure 12d. Here, the flow stress calculation by StrucSim represents the experimental curves accurately overall, with the biggest deviations occurring at the beginning of the second compression at 1000 °C with values of 20 MPa. The reason here might be the mentioned influence of friction and temperature inhomogeneity in the experimental setup of the deformation dilatometer. Figure 12e shows a qualitative example of the evolution of the microstructure properties DRX and SRX fraction as well as the average grain size during a simulation with StrucSim at 1200 °C, 0.3 s⁻¹, and 100 s pause time, and strains of 0.3 in both compression steps. It should be noted again that no distinction between SRX and MDRX was made in the StrucSim calculations, and the term SRX here represents both mechanisms. During the first compression, DRX starts and reaches a final value of around 10%. With the end of the first compression, SRX takes over, and the material fully recrystallizes in the pause time. During the second compression, the material hardens again and starts a second recrystallization cycle with a final fraction of around 10% DRX. The average grain size decreases accordingly during the first recrystallization cycle. After approx. 20 s, a slight increase is visible where grain growth takes over. With the second compression, a second drop in the grain size is visible due to the newly started recrystallization cycle.

4. Conclusions

In the present work, single-phase austenite and ferrite steel based on their chemical composition in DSS are investigated with regard to the material behavior under hot forming conditions. Further, the parameters for the microstructure model StrucSim are identified and validated by means of double-compression tests to be able to investigate the microstructure evolution and flow stress response of each phase under different hot forming conditions and, thus, gain an important understanding of the mechanisms in duplex stainless steels. The following conclusions can be drawn:

• Austenite and ferrite single-phase steels show different grain growth kinetics and recrystallization mechanisms during dynamic and static characterization experiments. While grain refinement was observed with EBSD measurements during compression and stress relaxation tests in austenite, the ferrite samples show the development of a substructure leading to new globular grains without a significant refinement in grain size.
• The parameters for StrucSim were successfully identified, and a good agreement was found between the experimental and fitted flow stress values. However, large initial grain sizes in the ferrite single-phase steels were present that could influence the results and need to be considered for future studies.
• The flow stress evolution during double compression tests calculated with StrucSim shows a good agreement with the experiments. StrucSim is able to depict the softening behavior during different pause times appropriately and a qualitative analysis of the microstructure properties DRX, SRX, and average grain size shows a realistic microstructure evolution. It should be noted, however, that, due to the experimental setup using a deformation dilatometer, friction could not be excluded from the measurements, leading to a scatter in the experimental results that it was not possible to model.

The next steps include the investigation of the microstructure evolution of single-phase austenite and ferrite during industrial process conditions. In addition, the DSS material will be tested using compression tests, and the microstructure will be analyzed. Using the results of the single-phase specimen, a comparison will be made between the flow curves and microstructure evolution with the DSS material. This will help to obtain a better understanding of the material behavior of DSS under hot forming conditions.