Recrystallization and Grain Growth of AISI 904L Super-Austenitic Stainless Steel: A Multivariate Regression Approach

: AISI 904L is a super-austenitic stainless steel that is remarkable for its mechanical properties and high corrosion resistance, which strictly depend on its chemical composition and microstructural features. The recrystallization process and grain growth phenomena play key roles in achieving high levels of material quality, as often requested by customers for speciﬁc applications. In this paper, the evolution of the microstructure and hardness values after cold rolling and subsequent annealing is reported, with the aim of optimizing the thermomechanical treatment conditions and improving the efﬁciency of the production process. The investigation was focused on three different cold reduction ratios (50%, 70% and 80%), while combining different annealing temperatures (950, 1050 and 1150 ◦ C) and soaking times (in the range of 20–180 s. The test results were organized using a data analysis and statistical tool, which was able to show the correlation between the different variables and the impacts of these on recrystallization and grain growth processes. For low treatment temperatures, the tested soaking times led to partial recrystallization, making this condition industrially unattractive. Instead, for the higher temperature, full recrystallization was achieved over a short time (20–40 s), depending on the reduction ratio. Regarding the grain growth behavior, it was found to be independent of the reduction ratio; for each treatment temperature, the grain growth showed a linear trend as a function of the soaking time only. Moreover, the static recrystallization kinetics were analyzed using a statistical analysis software program that was able to provide evidence indicating the most and least inﬂuential parameters in the process. In particular, taking into consideration the hardness values as output data, the temperature and soaking time were revealed to have major effects as compared with the reduction ratio, which was excluded from the statistical analysis. The prediction approach allowed us to formulate a regression equation in order to correlate the response and terms. Moreover, a response optimizer was used to predict the best solution to get as close as possible to the hardness target required by the market.


Introduction
Austenitic stainless steels are employed in a very wide variety of fields, thanks to the combination they show in terms of their hardness, strength and ductility [1,2], meaning they are extremely formable and weldable [3,4]. The high temperature and general corrosion resistance, furthermore, allow many grades, such as AISI 304 and AISI 316L, to be employed (AGG) or secondary recrystallization, characterized by the rapid growth of some grains at the expense of neighboring ones (e.g., [53,54]).
Many studies have aimed to investigate the effects of the cold rolling process on the recrystallization of austenitic stainless steels [55][56][57]. Belyakov et al. [51] investigated a static restoration mechanism operating during annealing on AISI 304 stainless steel. Their analysis showed that the annealing treatment is characterized by recovery, transient recrystallization and normal grain growth; in the first phase of annealing, recovery developed quickly at the grain boundaries, leading to a fast release of high internal stresses, after which a rapid grain growth phenomenon occurs. Finally, their analysis showed a large fraction of annealing twins in a fully recrystallized state. Di Schino et al. reported on the recrystallization behavior of AISI 316 [58], AISI 301 [59] and low-nickel austenitic stainless steels [60]. Other studies referring to super-austenitic stainless steel have not yet been fully consolidated.
Within this framework, in this paper the recrystallization and grain growth behavior of AISI 904L super-austenitic stainless steel is reported as a function of the thermomechanical parameters. The evolution of the microstructure and hardness of steel after cold rolling and subsequent annealing treatment was analyzed with the aim of optimizing the thermomechanical treatment conditions and improving the efficiency of the production process, also by means of a multivariate regression approach [61][62][63]. The investigation involved three different cold reduction ratios (50%, 70% and 80%), combining different annealing temperatures (950 • C, 1050 • C and 1150 • C) and soaking times in the range of 20-180 s. The execution of the experiments was managed through the use of a data analysis and statistical tool, which was able to show the correlation between the various process variables and the impacts of these on the recrystallization and grain growth processes. Considering the hardness target as required by the market, process parameters were established and optimized for industrial applications based on a multivariate approach.

Materials and Methods
The nominal steel chemical composition of AISI 904L considered in this work, according to the normative UNI EN 10088, is shown in Table 1. The material was cold-worked according to three different cold rolling ratios (CR). After cold rolling, the material was heat-treated in an electric resistance oven (FM-77/H), at three different heating temperatures. The time evolution was considered at different temperatures while varying the soaking time (Table 2). After maintaining target treatment conditions, the samples were immediately cooled in water.
After heat treatment, the specimens were etched in a HNO 3 + H 2 O solution in an electrolytic cell using AISI 316L as the cathode. The microstructure was then analyzed using a light microscope (Eclipse LV150 NL, Nikon, Tokyo, Japan), and for the fully recrystallized samples, image analysis was performed using dedicated software (AlexaSoft, X-Plus, serial number: 6308919690486393, Florence, Italy). From the image analysis, it was possible to determine and compare the average grain size of AISI 904L steel as a function of the thermomechanical conditions. The hardness was measured using a Vickers durometer (HV-50, Remet, Bologna, Italy) with a 1 Kg load at 1 4 of the thickness. Three indentations were carried out for each specimen and the average value was considered. The recrystallized volume fraction (X v ) was evaluated starting from the hardness measurements according to Equation (1) based on [60]: where X v = recrystallized volume fraction; δ(t) = hardness value at specific soaking time; δ c = hardness value of deformed material at specific reduction ratio; δ R = hardness value of fully recrystallized material. The results were analyzed using a data analysis and statistical tool. Such analyses provide evidence of the effects of the different process parameters on the microstructural evolution (cold rolling ratio, annealing temperature, soaking time). The first variable was studied at 3 levels, while the annealing temperature was studied at 2 and the soaking time at 6 levels.

Deformed Material
The microstructure of the material, prior to cold rolling, is reported in Figure 1. Figure 1 shows a fully recrystallized material characterized by a homogeneous structure dominated by equiaxic grains. The cold-rolled material's microstructure evolution with increasing deformation rate is reported in Figure 2. This microstructure evolution leads to the work-hardening behavior reported in Figure 3 in terms of hardness.

Recrystallization Behavior
The effects of heat treatment parameters (temperature and soaking time) on the hardness values (HV 1 ) and recrystallization volume fraction (X v ) of AISI 904L steel after cold rolling down to 50% and annealing are reported in Figure 4a,b, respectively. It is worth noting that an annealing temperature of 950 • C is not sufficient to achieve full recrystallization after 180 s. The progressively decreasing trend of hardness values suggests that for longer soaking times, the materials would reach complete recrystallization. However, times longer than 180 s are industrially unattractive. Starting from hardness measurements and based on Equation (1), the recrystallized volume fraction was calculated for 50% cold-rolled steel as a function of the heat treatment conditions (Figure 4b). It is clearly visible that while for temperatures of 1050 • C and 1150 • C 100% recrystallization is achieved in 20-40 s, the maximum recrystallization fraction reached at 950 • C is about 90%. From the micrographic analysis, as indicated by red arrows in Figure 5, areas with partial recrystallization are clearly visible. On the other hand, a fully recrystallized microstructure is achieved at higher temperatures (both 1050 • C and 1150 • C) at times ranging 20-40 s ( Figure 6). The grain size distribution obtained from the image analysis relative to the samples in Figure 6 is shown in Figure 7.  Figure 1 shows a fully recrystallized material characterized by a homogeneous structure dominated by equiaxic grains. The cold-rolled material's microstructure evolution with increasing deformation rate is reported in Figure 2. This microstructure evolution leads to the work-hardening behavior reported in Figure 3 in terms of hardness.  Figure 1 shows a fully recrystallized material characterized by a homogeneous structure dominated by equiaxic grains. The cold-rolled material's microstructure evolution with increasing deformation rate is reported in Figure 2. This microstructure evolution leads to the work-hardening behavior reported in Figure 3 in terms of hardness.

Recrystallization Behavior
The effects of heat treatment parameters (temperature and soaking time) on the hardness values (HV1) and recrystallization volume fraction (Xv) of AISI 904L steel after cold rolling down to 50% and annealing are reported in Figure 4a,b, respectively. It is worth noting that an annealing temperature of 950 °C is not sufficient to achieve full recrystallization after 180 s. The progressively decreasing trend of hardness values suggests that for longer soaking times, the materials would reach complete recrystallization. However, times longer than 180 s are industrially unattractive. Starting from hardness measurements and based on Equation (1), the recrystallized volume fraction was calculated for 50% cold-rolled steel as a function of the heat treatment conditions (Figure 4b). It is clearly visible that while for temperatures of 1050 °C and 1150 °C 100% recrystallization is achieved in 20-40 s, the maximum recrystallization fraction reached at 950 °C is about 90%. From the micrographic analysis, as indicated by red arrows in Figure 5, areas with partial recrystallization are clearly visible. On the other hand, a fully recrystallized microstructure is achieved at higher temperatures (both 1050 °C and 1150 °C) at times ranging 20-40 s ( Figure 6). The grain size distribution obtained from the image analysis relative to the samples in Figure 6 is shown in Figure 7.

Recrystallization Behavior
The effects of heat treatment parameters (temperature and soaking time) on the hardness values (HV1) and recrystallization volume fraction (Xv) of AISI 904L steel after cold rolling down to 50% and annealing are reported in Figure 4a,b, respectively. It is worth noting that an annealing temperature of 950 °C is not sufficient to achieve full recrystallization after 180 s. The progressively decreasing trend of hardness values suggests that for longer soaking times, the materials would reach complete recrystallization. However, times longer than 180 s are industrially unattractive. Starting from hardness measurements and based on Equation (1), the recrystallized volume fraction was calculated for 50% cold-rolled steel as a function of the heat treatment conditions (Figure 4b). It is clearly visible that while for temperatures of 1050 °C and 1150 °C 100% recrystallization is achieved in 20-40 s, the maximum recrystallization fraction reached at 950 °C is about 90%. From the micrographic analysis, as indicated by red arrows in Figure 5, areas with partial recrystallization are clearly visible. On the other hand, a fully recrystallized microstructure is achieved at higher temperatures (both 1050 °C and 1150 °C) at times ranging 20-40 s ( Figure 6). The grain size distribution obtained from the image analysis relative to the samples in Figure 6 is shown in Figure 7.     Similar results can be seen for higher deformation ratios (70% and 80%) (Figures 8-11). Additionally, at high cold reduction ratios, a 950 °C annealing temperature is not sufficient to fully recrystallize the material up to 180 s holding time (Figures 8-10). The maximum recrystallization volume fractions (Figures 8b and 10b) relating to the heat treatment at 950 °C for 180 s are about 94% and 97%, respectively, for the CR ratios of 70% and 80%. Likewise, for the treatment temperatures of 1050 °C and 1150 °C, a full recrystallization is achieved for the higher CR ratios. In particular, for the CR at 70%, as for CR at 50%, the complete recrystallization (Figure 8a) occurs over a range of soaking times of 20-40 s as a function of annealing temperature. As expected, the recrystallization kinetics speed up as the heat treatment temperature increases. The microstructures as achieved after full recrystallization of steel cold-rolled at 70% and treated at 1050 °C for 40 s and at 1150 °C for 20 s are reported in Figure 9. For the higher CR ratio (80%), it is not possible to distinguish the effects of temperature on the recrystallization behavior due to the higher energy stored during the cold rolling.
After 20 s, the AISI 904L steel cold-rolled at 80% is fully crystalline at both 1050 °C and 1150 °C treatment temperatures. To confirm this statement, Figure 11 shows the microstructures, completely recrystallized, obtained after the annealing treatments for 20 s at 1050 °C and 1150 °C. The clear distinction between the two microstructures in Figure  11 is the grain size; for a very high CR ratio (80%) and with the same soaking time, a low treatment temperature (1050 °C) is sufficient to obtain a very fine microstructure. The results in terms of the average grain size obtained from the image analysis for the different Similar results can be seen for higher deformation ratios (70% and 80%) (Figures 8-11). Additionally, at high cold reduction ratios, a 950 • C annealing temperature is not sufficient to fully recrystallize the material up to 180 s holding time (Figures 8-10). The maximum recrystallization volume fractions (Figures 8b and 10b) relating to the heat treatment at 950 • C for 180 s are about 94% and 97%, respectively, for the CR ratios of 70% and 80%. Likewise, for the treatment temperatures of 1050 • C and 1150 • C, a full recrystallization is achieved for the higher CR ratios. In particular, for the CR at 70%, as for CR at 50%, the complete recrystallization (Figure 8a) occurs over a range of soaking times of 20-40 s as a function of annealing temperature. As expected, the recrystallization kinetics speed up as the heat treatment temperature increases. The microstructures as achieved after full recrystallization of steel cold-rolled at 70% and treated at 1050 • C for 40 s and at 1150 • C for 20 s are reported in Figure 9. For the higher CR ratio (80%), it is not possible to distinguish the effects of temperature on the recrystallization behavior due to the higher energy stored during the cold rolling.       After 20 s, the AISI 904L steel cold-rolled at 80% is fully crystalline at both 1050 • C and 1150 • C treatment temperatures. To confirm this statement, Figure 11 shows the microstructures, completely recrystallized, obtained after the annealing treatments for 20 s at 1050 • C and 1150 • C. The clear distinction between the two microstructures in Figure 11 is the grain size; for a very high CR ratio (80%) and with the same soaking time, a low treatment temperature (1050 • C) is sufficient to obtain a very fine microstructure. The results in terms of the average grain size obtained from the image analysis for the different considered cases are reported in Table 3 and clearly show that the finest microstructure is achieved after cold rolling at 80% and annealing at 1050 • C for 20 s.

Grain Growth Behavior
Grain growth phenomena after full recrystallization in AISI 904L were evaluated by quantifying the average grain size dependence on the process parameters (CR, temperature and soaking time). The results in terms of the grain size evolution as a function of the soaking time at annealing temperatures of 1050 and 1150 • C are reported in Figure 12. Moreover, the relevant microstructures are shown in Figures 13 and 14. The results show that the average grain size increases with increasing heat treatment temperature and soaking time and is independent of the cold rolling ratio. Furthermore, for each temperature, the grain size grows linearly as a function of the soaking time.
Grain growth phenomena after full recrystallization in AISI 904L were evaluated by quantifying the average grain size dependence on the process parameters (CR, temperature and soaking time). The results in terms of the grain size evolution as a function of the soaking time at annealing temperatures of 1050 and 1150 °C are reported in Figure 12. Moreover, the relevant microstructures are shown in Figures 13 and 14. The results show that the average grain size increases with increasing heat treatment temperature and soaking time and is independent of the cold rolling ratio. Furthermore, for each temperature, the grain size grows linearly as a function of the soaking time. As shown in Figure 12 and in the microstructural evolution in Figure 13, no significative grain growth can be observed at 1050 °C for any of the treatment times tested. At 1150 °C (Figure 14), the grain growth at high temperature is evident for short treatment times; already after 40 s of heat treatment at 1150 °C, the average grain size is almost double the maximum value at 1050 °C after 120 s. Therefore, the grain growth kinetics of AISI 904L super-austenitic stainless steel are strongly intensified by the temperature and less so by the soaking time. Indeed, it is well known that the grain growth kinetics depend on the grain boundary migration, and hence the atomic diffusion [53]. Furthermore, at high temperatures (about 1100 °C for austenitic stainless steels [64]), the Zener pinning of the grain boundaries is mitigated by the dissolution or coarsening of the precipitates [65]. As shown in Figure 12 and in the microstructural evolution in Figure 13, no significative grain growth can be observed at 1050 • C for any of the treatment times tested. At 1150 • C (Figure 14), the grain growth at high temperature is evident for short treatment times; already after 40 s of heat treatment at 1150 • C, the average grain size is almost double the maximum value at 1050 • C after 120 s. Therefore, the grain growth kinetics of AISI 904L super-austenitic stainless steel are strongly intensified by the temperature and less so by the soaking time. Indeed, it is well known that the grain growth kinetics depend on the grain boundary migration, and hence the atomic diffusion [53]. Furthermore, at high temperatures (about 1100 • C for austenitic stainless steels [64]), the Zener pinning of the grain boundaries is mitigated by the dissolution or coarsening of the precipitates [65].

Statistical Analysis
The statistical analysis of annealing process data, obtained by setting the different reduction ratios, temperatures and soaking time conditions, was performed using the design of experiments (DOE) approach. This is the most popular statistical technique for the design of tests and is useful for reducing the process organization time while providing greater reliability in the results. To reduce the complexity of the study, due to the differences in soaking times for the temperature of 950 • C compared to 1050 • C and 1150 • C, the analysis was performed by considering only the last two annealing temperatures, along with their respective reduction ratios and soaking times. The objective was to evaluate the influence of the variables involved during the annealing process through the microstructure and laboratory testing and then to compare them with the solutions made available using the statistical analysis software Minitab. The first step was to associate each treatment condition with the respective hardness value (as discussed in Section 2) in such a way as to create a database with the input-output data. Then, the general linear model (GLM), a useful framework for comparing how several variables affect the process, was chosen due to the presence of a large number of levels associated with the three different considered parameters. The GLM is the foundation for several statistical tests, including the analysis of variance (ANOVA) approach, the technique used in this case. The first step of a variance analysis is the setting of a proper null hypothesis (H 0 ), a statement assumed true until there is clear evidence to the contrary. In this study, H 0 refers to the parameters involved regarding their great influence (or lack thereof) on the annealing process and related recrystallization phenomena. Below, the variables involved are listed, as mentioned in Section 2:   The GLM allows one to evaluate the influence of individual parameters, as well as the influence of their interactions (double interaction in this case study). The results of the analysis are shown in Figure 15. By looking at the Pareto chart, it is easy to understand which parameters have a greater effect according to the software. The interpretation of p-value coefficients, therefore, confirms the assessments referred to in the graph, with the p-value being defined as the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis. In particular, for p > 0.05 (called the level of significance), the probability of error in not considering a variable is considered low. Otherwise, if the p-value is lower than 0.05, the parameter must be considered in the analysis and is relevant for the process. The p-values associated with the parameters and their interactions are shown in Table 4. Referring to the condition expressed above, the reduction ratio (B), the temperature-reduction ratio (AB) and the soaking time-reduction ratio (BC) show values higher than 0.05, meaning they can be removed from the analysis.    As expected, the temperature and soaking time are the terms with a meaningful effect on the process, which is in accordance with the results obtained through laboratory analysis. During an annealing process, a higher treatment temperature and a longer soaking time will affect the hardness of the material, as shown in Figure 16.   The above analysis allowed us to formulate the following regression Equation (2): The level of reliability associated with this regression equation can be measured through an indicator defined as the coefficient of determination (R-sq), which in this case is equal to 94%.
Considering the hardness target value imposed by the market (around 160 Vickers), the response optimizer tool allows us to set the values of the different parameters involved in such a way as to obtain the required result. In this way, Minitab calculates an optimal solution by identifying the combination of input variable settings (Table 5). The "hardness fit" represents the hardness value to be reached by setting the temperature and soaking time to 1050 • C and 120 s. This value is very close to the target; the slight difference is justified by the term "composite desirability", which can be considered as a parameter of the response optimizer accuracy. The prediction approach in this way allows us to exclude from the analysis the parameters and the combination of terms not relevant in the process, providing a solution that is as close as possible to the required hardness target.

Conclusions
The recrystallization and grain growth behavior of AISI 904 L steel have been reported here as functions of the thermomechanical parameters (cold reduction ratio and heat treatment conditions).
The results are summarized below: 1.
Soaking at 950 • C did not appear to be effective in achieving a fully recrystallized fraction; 2.
Steel fully recrystallized after soaking at 1050 • C and 1150 • C; 3. Soaking at 1050 • C was shown to be the best condition in terms of grain size refinement; 4.
For the cold rolling ratios of 50% and 70%, a strong temperature effect was detected. In particular, the recrystallization process appeared to be fastest at 1150 • C with respect to the lower annealing temperature; 5.
For the cold rolling ratio of 80%, the difference in terms of the recrystallization rates exerted by both 1050 • C and 1150 • C was negligible, following the high energy storage related to the heavy reduction ratio; 6.
Grain growth phenomena after full recrystallization for treatment temperatures of 1050 • C and 1150 • C showed a linear trend as a function of the treatment time, independently of the cold reduction ratio. A slight increase in grain size was observed at 1050 • C for each treatment time tested. Otherwise, at 1150 • C, significant grain growth occurred within short soaking times; 7.
As expected, the results from a statistical analysis based on GLM confirmed that the temperature and soaking time are the factors that have meaningful effects on the process.
For the first time, the thermal-mechanical treatment of AISI 904L steel was comprehensively studied. Evidence from a laboratory analysis in terms of the most relevant thermomechanical parameters in the process was confirmed using a predictive approach. This was established in the form of an equation with a coefficient of determination of 94% and a response optimizer with a given accuracy of 97%, which allowed us to specify a solution for hardness target demands. The further development of this theme is justified by the increasingly specific customer requirements, and it might be possible to apply this approach to other steels and specific market demands.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.