Artificial Intelligence Inspired Design of Non-Isothermal Heat Treatments for γ - γ' Two-phase Ni-based Alloys

doi:10.21203/rs.3.rs-2593940/v1

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Artificial Intelligence Inspired Design of Non-Isothermal Heat Treatments for γ - γ' Two-phase Ni-based Alloys

https://doi.org/10.21203/rs.3.rs-2593940/v1

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In this paper, a state-of-the-art Artificial Intelligence (AI) technique is used for a precipitation hardenable Ni-based alloy to predict more flexible non-isothermal heat treatment and to examine the possible heat treatment routes for the enhancement in strength that may be practically achieved. Additionally, AI is used to integrate with Materials Integration by Network Technology, which is a computational workflow utilized to model the microstructure evolution and evaluate the 0.2% proof stress for isothermal heat treatment (IHT) and non-isothermal heat treatment (non-IHT). As a result, it is possible to find enhanced 0.2% proof stress for non-IHTs for a fixed time of 10 minutes compared to the IHT benchmark. The entire search space for heat treatment scheduling was ~ 3 billion. Out of 1620 non-IHTs, we succeeded in designing the 110 non-IHTs schedules that outperformed the IHT benchmark. Interestingly, it is found that early-stage high-temperature for a shorter time increases the γ' precipitate size up to the critical size and later heat treatment at lower temperature increases the γ' fraction with no anomalous change in γ' size. Therefore, employing this essence from AI, we designed a heat treatment route in which we attained an outperformed 0.2% proof stress to AI-designed non-IHT routes.

Physical sciences/Materials science/Theory and computation/Computational methods

Physical sciences/Materials science/Structural materials/Metals and alloys

Heat treatment (HT) scheduling is an important process to refine the mechanical properties of industrial metallurgical materials by several processes such as annealing, case hardening, precipitation strengthening, tempering, carburizing, normalizing and quenching. Naturally, even with the same chemical composition and pre-processing history, such properties could differ drastically after different HT schedulings. Optimum HT is a part of the manufacturing formula for successful commercial products such as, for example, the heat-resisted Ni-based superalloys with excellent tensile strength and creep properties for land-based and aircraft turbine parts ^1,2. Though the first “superalloys” started to appear in the late 20th of the last century ^3,4, the quests for new chemicals ⁵, metalworking, and HT formulations ^6–10 are still hot topics in the research community. With the development of new alloys, the manufacturer should also need to find the optimal HT scheduling for better properties. There is a high demand for methodologies that can effectively optimize the HT schedule for these alloys.

The mechanical properties of Ni-based superalloys are intrinsically governed by the interplay between ordered γ'-L1₂ Ni₃(Al, Ti, Ta) intermetallic compound precipitates with the morphologies (i.e., cubes, rounded cubes, spheres, or platelets) and disordered γ-fcc Ni solid solution matrix with Co, Mo, Cr, Ta, Hf, Nb, and W elements. Therefore, the precipitation hardening by the γ' precipitates and solid solution hardening significantly improves the mechanical properties ^2,11–13. The morphology and volume fraction of γ'-precipitate expose the HT history and critically affects the alloy’s mechanical properties by acting as barriers to dislocation motions ^14–20.

The industrial HT could be further improved, which is reflected by rich literature and industrial interest on this subject ^2,21. In the literature, the HT scheduling (i.e., non-IHT) approach has been proposed to improve the mechanical properties of alloys ²². For instance, there are a couple of examples of other systems, such as Fe-Cu ²³, Al-Zn-Mg ²⁴ and Al-Zn-Mg-Cu ^25–27 which showed the advantage of non-IHT in achieving enhanced mechanical strength. The influence of non-IHT investigations on precipitation hardening and microstructure evolution has been studied ^23,24,27 and has achieved excellent results, as summarized in Table 1. For instance, Hutchinson et al. ²³ observed an enhancement in the strength of non-IHT conditions by 8% compared to the IHT case in Fe-Cu binary alloy. Nicolas et al. ²⁴ proposed a non-IHT heating schedule in which controlling the heating and cooling rate allows modification of the supersaturation matrix and the precipitate critical size, directly impacting the mechanical strength of Al-Zn-Mg alloy.

Table 1. The non-IHT cases are discussed in the literature.

Materials	Methods	Remarks	Ref.
Fe-2Cu	Experimental & modeling	Non-IHT’s yield strength improved by 8% more than IHT	²³
Al-Zn-Mg	Experimental & modeling	Non-IHT increases the precipitate phase fraction	²⁴

Al 7050	Experimental	Non-IHT’s yield strength is ~5% more than IHT, shortened aging time	²⁷

Furthermore, Jiang et al. ²⁷ investigated the Al 7085 alloy with varying HT conditions and found a non-IHT route with a higher yield strength of ~ 5% and shortened aging time than the IHT condition. These observations show that the number of possible experiments/tests is limited to experimentally determining the optimal time and HT temperatures for these alloys. Another critical reason is that it has been exceedingly challenging to investigate a large number of candidates' HT scheduling. Obviously, such optimization is time-consuming and costly with traditional methods due to HT multidimensionality ^2,26,28,29. As a result, it is challenging to determine whether the best solution has been found experimentally.

In the literature, there is no report on HT scheduling in Ni-based superalloys. In addition, we didn’t find suitable methodologies in Ni-based superalloys or another alloy system. From a practical point of view, it could be combined with other statistical modules or tools to eliminate the manual search for optimized cost/performance solutions. We should establish a way to design the non-IHTs in a huge design searching space of HT conditions such as annealing temperature and holding time.

In this paper, we would like to introduce AI-inspiring methodologies and report our attempt to address this problem for a Ni-Al binary alloy with the γ/γ' two-phase microstructure, which is a model for the Ni-based superalloys ³⁰. Recently, we have developed the computational workflow for high throughput prediction of 0.2% proof stress with different HT scheduling ³¹, which is implemented in our original material design system, MInt ^32,33. Herein, we are trying to design non-IHTs with supreme 0.2% proof stress to that obtained by IHTs by connecting the prediction workflow with the AI algorithm for efficient searching of non-IHTs. We specifically utilize Monte Carlo tree search (MCTS) ³⁴, which is a data-driven iterative design algorithm that has demonstrated efficiency in several materials inverse design problems ³⁵. Taking advantage of the use of computerized prediction methods ^36–44, we deeply analyze the microstructure evolution associated with heat treatments and examine the essence of AI-found HTs based on expertise in materials science. Based on the specified essence, we finally propose a new concept of HT design to optimize the high-temperature strength for the Ni-base two-phase alloys, which concept can be called AI-inspired one.

Setup for the searching conditions. In this section, we discussed the setup for the searching space conditions. For example, we set the annealing time of the total HT as 10 mins. In other words, we would like to design the non-IHTs which outperformed the IHT for 10 mins. It is noteworthy to mention that the annealing time of 10 min is enough to obtain a reasonable size of γ' at mild temperatures as the diffusion kinetics in the binary alloys is relatively higher than in the more complicated alloy system. It should be noted that the non-IHT is designed for a total fixed time of 10 mins with a time frame of 1 min each (i.e., a total number of 10 microstructures for each case, one microstructure for each minute). For example, 700 ℃ for 1^st min, 550 ℃ for 2^nd min, 575 ℃ for 3^rd min … up to 10 mins. Therefore, the fixed time of 10 mins is considered for comparing the 0.2% proof stress with IHT and non-IHTs schedules. In addition, prior to annealing HT, the initial state microstructure was tuned through isothermally heat treatment at 1000 ℃ for 32 s, followed by rapid cooling to obtain the supersaturated microstructure in the alloy ³¹.

Here, the digitization parameters employed are described in detail. The entire searching space for digitalized conditions is (i.e., 3,486,784,401). For instance, the considered temperature range for scheduling is 500 – 700 ℃ with 25 ℃ intervals for the further optimal solution search for HT schedule. As a result, the total considered temperature for scheduling is 9 (for example, 500, 525, 550, 575 ℃…...700 ℃) and the total considered time interval is 10 (i.e., 1, 2, 3 min ……10 min). Therefore, the optimized HT schedules are obtained from a huge search space by the MCTS algorithm (discussed in Section 2.3).

Fig. 1a illustrates the coarse-tuned digitalized parameters (i.e., temperature interval and time step size) that the MCTS algorithm utilized to choose the starting temperature during the HT schedule. For example, the annealing temperature input parameter for starting temperature is set to be in the range of 600 – 800 ℃ with an interval of 50 ℃ and for the fixed time of 10 mins, as shown in Fig. 1a. After coarse tuning for the starting temperature, the annealing temperature range is considered for the fine-tuning to find the optimal solution, as illustrated in Fig. 1b. Finally, in this fine-tuned step, the candidates of the HT reached up to ~ 3 billion.

Monte Carlo tree search. MCTS is an iterative, guided, random best-first tree search algorithm that systematically explores a space of candidates to determine the optimal solution to a problem. In this work, we have used a combination of the MInt system and an AI-based search algorithm, MCTS, to design non-IHTs schedules. To design the non-IHTs, a Python implementation of MCTS named MDTS was used as it automatically and adaptively balances the search exploration vs. exploitation hyperparameter ⁴⁵. In the case of MCTS design, the candidates for HT schedules are represented using a shallow tree, where each node in the tree is a possible end temperature assignment for a single step in the schedule, as illustrated in Fig. 2. A full path from the root to a leaf in the maximum depth represents a full HT schedule. In the beginning, the tree has no nodes. The search starts with random rollout selection, and then the tree expands gradually towards the promising area of the search space using previous observation. The tree is traversed iteratively from the root, following the path with the most promising path using the Upper Confidence Bound score (UCB) ³⁴. In each iteration, 4 steps are conducted, selection using UCB score, expansion where a new node (possible HT schedule step is added in the tree), simulation, where the route in the tree is completed using random roll out and the obtained schedule is evaluated using Mint system, finally, in the backpropagation step, tree information is updated for a more informed decision in the next iteration (see Fig. 2). We also computed the case of conventional isothermal heating (i.e., IHT) and specified the best temperature to obtain the highest 0.2% proof stress at a service temperature. It is important to highlight that schedules obtained from the MCTS design are compared with the benchmark obtained from the IHT conditions.

Simulation system, MInt. In this section, we introduce the MInt system, which is used for the forward calculation in these alloys. MInt system is a computational workflow that we developed to simulate the microstructure evolution and evaluate the high-temperature strength for different alloys ^32,33. The detailed architecture of the MInt module system can be referred to in reference ^31,33. The module was built as part of the Cross-ministerial Strategic Innovation Promotion Program (SIP) project on materials integration (MI) ³². It consists of the microstructure prediction at different conditions using phase-field simulation ⁴⁶ for simulated microstructure image analysis, which includes γ' size (the mean diameter of a circle of equal projection area for γ'-precipitate) as well as volume fraction and the performance prediction (i.e., 0.2% proof stress) ^19,47, as schematically shown in Fig. 3.

Isothermal heat treatment benchmark. In this section, the IHT benchmark has been obtained from the calculated 0.2% proof stress of the Ni- 9.8 wt.% Al alloy with g-g’ two-phase as a function of the annealing temperature using the MInt system, as shown in Fig. 4. These calculations have been performed for temperatures from 500 to 900 ℃ with the temperature interval of 25 ℃ for fixed 10 minutes. It is apparent that the 0.2% proof stress increases with annealing temperature until it reaches its maximum value (i.e., peak-aged state) and then gradually drops, as illustrated in Fig. 4a. The benchmark (i.e., highest 0.2% proof stress) for IHT condition at a service temperature (i.e., 725 ℃) with a fixed time of 10 minutes was obtained; the best isothermal annealing temperature was 642 ℃. The obtained benchmark 0.2% proof stress is found to be 784.48 MPa. This condition is further referred to as IHT benchmark. It should be noted that the obtained benchmark value is examined up to a narrow range of 1 ℃, as shown in Fig. 4b.

It is essential to show the simulated microstructural evolution for these conditions. A clear and distinguishing feature of the microstructural evolution of γ' precipitates as a function of annealing temperature at the fixed aging time of 10 mins in Ni-Al binary alloy is illustrated in Fig. 5. One can notice that the annealing temperature heavily influences the microstructures. Finally, it is evident from the microstructures that coarsening of γ' precipitates is significantly promoted after heat treatment at temperatures more than 650 ℃, as highlighted in Figs. 5h – 5p. In addition, the coarsening kinetics of the γ' precipitates accelerate (see Fig. 5) as the precipitation hardening slows as the annealing temperature increases to 850 °C, resulting in a considerable (around 200 MPa) decrease in the 0.2% proof stress (refer to Fig. 4a). This may be related to the drop in number density of precipitates during the rapid coarsening (i.e., increase in interparticle spacing), which directly minimizes the obstruction to the dislocations by the precipitates in the system. It is noteworthy to mention that the critical size of γ' is found to be around 40 nm (Fig. S1, see online supplementary material), over which the over-aging occurred. The microstructures presented in Fig. 5 are zoomed-in images of simulated phase-field microstructures. It should be noted that the phase-field simulation is performed under periodic boundary conditions. Therefore, no inconsistencies are observed at the edges of microstructures. The detailed quantitative analysis of the microstructure evolution of Fig. 5 (Fig. S1) and contour plots (Fig. S2) as a function of annealing temperature is given in the supplementary material.

Optimizing the non-IHTs schedules using AI. In order to promote solid solution hardening and age hardening, the starting temperature plays a vital role. For instance, a higher starting temperature causes γ' particles to coarsen more rapidly and with less tendency to nucleation than at lower temperatures ^2,30. However, an optimum starting temperature is required for the pronounced precipitation hardening effects with aging time. At the same time, we adjust the starting temperature range from 600 to 800 ℃ with an interval of 50 ℃ between each temperature selection (as discussed in Fig. 1a). Fig. 6 shows the variation of maximum 0.2% proof stress with the number of iterations as a function of starting temperature.

It should be mentioned that each data point of the heat-treated sample in the plot corresponds to a non-IHT condition which was heat treated for a fixed time of 10 minutes. Therefore, the relationship between 0.2% proof stress and the number of iterations has been established. The results revealed that a starting temperature of 700 ℃ (green curve) has superior 0.2% proof stress (after the 20^th iterations) to the IHT benchmark, as shown in Fig. 6. In contrast, the 650 ℃ (blue curve) achieved the 0.2% proof stress value after 2 iterations but it is less than 700 ℃. Hence, we selected 700 ℃ as the starting temperature for further non-IHT scheduling routes.

Fig. 7 shows the more fine-tuned non-IHT searching of HT scheduling to obtain the optimum 0.2% proof stress at the starting temperature of 700 ℃ for a fixed time of 10 mins by the MCTS design. For instance, the total 12 independent MCTS trees are considered with a larger number of iterations of 135 for each tree. We plotted the iteration curve for the case finding the best five candidates. It is noteworthy to mention that all these five trees have multiple candidates which outperformed the IHT benchmark, as shown in Fig. 7. The plot also demonstrates how the AI explored a huge searching space to select the best non-IHT cases.

The results also showed that the AI discovered the non-IHT schedule (tree 1, red curve) in fewer than 5 iterations, outperforming the IHT benchmark (grey dotted curve). In the case of tree 4, it achieves the non-IHT benchmark that outperforms the IHT benchmark after 20 iterations. In this way, most of the trees find the supreme 0.2% proof stress case in the very early stage. In contrast, depending on the trees, sometimes after 50 – 60 iterations, AI cannot find the non–IHT schedule that performs better. MCTS discovered substantially better examples as a result of these incubations. Interestingly, we successfully obtained 110 non-IHT schedules out of 1620 non-IHTs that outperformed the IHT benchmark.

Furthermore, by using the 10 time frames of 1 minute each, the MCTS discovered several non-IHTs that outperformed the best IHT, leading to the higher 0.2% proof stress by tuning the combination of heating and cooling rates (for example, cooling from 700 ℃ to 550 ℃, the cooling rate is ) in each time frame, as illustrated in Fig. 8a. Fig. 8b – d compare the microstructure characteristics (for example, γ' phase fraction and size) as well as 0.2% proof stress of best five outperformed non-IHT by the best IHT. For instance, the precipitation hardening process during IHT and non-IHT as a function of annealing time up to 10 min is demonstrated in Fig. 8d.

For the example of IHT, it can be noticed that the 0.2% proof stress increases steadily as the annealing time increases from time 0 to 10 mins (see grey dotted line in Fig. 8d). In contrast, when an alloy is subjected to 700 ℃ for one minute for the case of non-IHT, the 0.2% proof stress increases significantly within the first 2 minutes (i.e., 1 min at 700 ℃ from starting temperature of 700 ℃ and 1 min during cooling from 700 ℃ to lower temperatures such as 550 ℃), as shown in Fig. 8d. It can be attributed to the increase in γ' precipitate size to ~ 40 nm within 2 minutes of HT, as illustrated in Fig. 8c. The phase fraction also rises remarkably during this stage and higher phase fraction of ~ 56 % is obtained in this time period. Following that, the size nearly stabilizes and the fraction increases from 56% to 57.7% (see Fig. 8b).

It is interesting to note that the higher 0.2% proof stress, which is more prominent than the 0.2% proof stress of the IHT benchmark value, is obtained in the case of non-IHT in just 2 minutes (refer to Fig. 8d). It is evident that many non-IHTs theoretically offer a 0.2% proof stress that is higher than the IHT benchmark (see the inset in Fig. 8d). For instance, the microstructural observations of one of the best non-IHT cases (i.e., having 0.2% proof stress of ~ 789 MPa) clearly illustrate the highly stable nature of γ' precipitate in microstructures in these alloys, shown in Fig. 9. The result indicates that the annealing temperature is relatively low in the later stages of non-IHT (see Fig. 8a), and the coarsening kinetics is expected to be weaker, as seen in Figs. 9c to 9j. At lower temperatures, the precipitate becomes much more stable. Thus, even though the fraction increases, the precipitate size does not vary significantly. However, this is shown to be a favorable factor for increasing strength.

A useful way of visualizing the correlations between γ' phase fraction and γ' size exhibited by this alloy is plotted in Fig. 10. It shows the statistical and comparative results of the γ' phase fraction and γ' size of the best five non-IHTs schedules, which performed better than IHT benchmark. The plot illustrates the statistical results of the IHT benchmark at 10 minutes which are similar to those at 2 minutes for non-IHT conditions. For instance, the average γ' precipitate size in non-IHT (shown by the orange symbol in the zoomed-in Fig. 10) is almost similar to the precipitate size in the IHT benchmark. As the annealing time for non-IHT grows from 2 minutes to 10 minutes, the phase fraction increases, followed by the non-IHT path, as shown in zoomed-in Fig. 10. The size of γ' precipitate increases first and then stabilizes as the annealing time increases. Therefore, optimum non-IHT scheduling routes are obtained, which provide a higher phase fraction (~ 57.7%) and critical γ' precipitate size (~ 40 nm). It is clearly observed that the upward path is followed by the non-IHT cycles (as indicated by the green arrows in Fig. 10).

The above analysis implies the essence of the non-IHTs, the top 5 non-IHTs found by AI have some common features, such as early high-temperature HT for a shorter time which quickly increases the γ' precipitate size to near critical size then, followed by the lower temperature annealing to increase the γ' phase fraction by keeping the γ' under the critical size. The early-stage high-temperature HT (in this case, 700 ℃) increases the γ' size near the critical size (~ 40 nm). It is essential to keep the duration of the high temperature short and immediately lower temperature. This is because if the size of γ' increases more than the critical size, the number density (i.e., distribution of precipitates in the microstructure) of γ' reduces, yielding an over-aging. According to Osada et al. ¹⁹ the number density of the secondary γ' within the trimodal distributed γ' (i.e., primary, secondary and tertiary γ' precipitates) in a Ni-based disk superalloy plays a significant role in precipitation strengthening. Furthermore, to increase the phase fraction of the γ' precipitates, a subsequent HT at a relatively lower temperature is also effective in enhancing the strength. The γ' is more stable at lower temperatures ^2,30 and thus, the volume fraction was assumed to slightly increase at the lower-temperature HT.

AI-Inspired expert-designed non-IHT. Based on the above-mentioned discussion, we can understand that the AI-found Top 5 non-IHTs commonly consists of two steps, as follows: Step 1. High-temperature, short-time annealing; and Step 2. Low-temperature, long-time annealing. The question arises whether the small and complex temperature changes in the Step 2 (see Fig. 8a) are not essentially necessary. In other words, we considered that it was possible to design a much more simple non-IHT and attain higher 0.2% proof stress by employing the essence from AI. Then, we designed a simple two-step HT consisting of 1-min isothermal HT at 700˚C, cooling down to a lower temperature and 8-min isothermal HT at the lower temperature. This newly proposed HT route can be referred to as AI-Inspired expert-designed non-IHT.

We here examined the optimal temperature for the second step in the range of 525 – 575 ℃ in order to attain the highest 0.2% proof stress with an efficient increase of the γ' phase fraction, as shown in Fig. 11a. We found that 555 ℃ is the optimal second-step temperature yielding the maximum 0.2% proof stress, as shown by the black dotted arrow in Fig. 11b. Note that our newly proposed two-step HT with the optimal second-step temperature outperformed not only the IHT benchmark (grey dashed lines) but also the AI-found best non-IHT (orange dotted lines). The results show the potential for collaborative creation between AI and experts in materials research. The comparison of proof stress values is also tabulated in Table 2.

Table 2. Different HT routes and their corresponding 0.2% proof stresses. (ST: starting temperature).

Design

HT schedule detail

0.2% proof stress

IHT benchmark

642 ℃ – 10 mins

784.48 MPa

max. non-IHT by AI

Optimum AI-Inspired expert-design non-IHT

ST 700 ℃→700 →550 →500 →500 →

550 →600 →525 →575 →600 →500 ℃

ST 700 ℃, 700 ℃ – 1 min, 700 ℃ → 555 ℃ (–2.416 ℃/s), 555 ℃ – 8 mins

788.50 MPa

789.53 MPa

It is also important to compare the microstructural evolution characteristics such as γ' phase fraction and size of the best performed AI-Inspired expert-designed non-IHT with the IHT benchmark and maximum non-IHT by AI. For instance, we heat treated the alloy at 700 °C for 1 min from the starting temperature of 700 ℃ (i.e., 1 min IHT at 700 ℃), then cooled it to 555 ℃ from 700 ℃ in 1 min (i.e., the cooling rate of 2.416 ℃/sec), and then maintained for 8 mins at the same temperature (i.e., IHT for 8 mins at 555 ℃). Figs. 12a, 12b, and 12c compare the AI-Inspired expert-designed non-IHT phase fraction, size, and 0.2% proof stress to those of the IHT benchmark and AI max. non-IHT route (i.e., non-IHT 1 in Fig. 8), respectively.

The results demonstrate that the AI-Inspired expert-designed non-IHT has a slightly higher γ' phase fraction than AI max. non-IHT, as shown in Fig. 12a. While the γ' size of the AI-Inspired expert-designed non-IHT is less (i.e., near to critical size ~ 40 nm) than AI max. non-IHT, as shown in Fig. 12b. Hence, it results in a higher magnitude of 0.2% proof stress, as illustrated in Fig. 12c. The difference in 0.2% proof stress is clearly shown in the insets of Fig. 12c. One may relate this to the best combination of γ' phase fraction and their size to achieve the optimum strength in the alloy. One hypothesis is that the early-stage high-temperature and later low-temperature heating may be able to bridge the best combination of γ' precipitate size and γ' phase fraction in these alloys. Therefore, early high-temperature heating helps in reaching the γ' precipitate size near critical size (i.e., ~ 40 nm) and later lower temperature HT increases the phase γ' fraction in these alloys.

We utilized Ni/Ni₃Al two-phase alloy as an example in this study. The fundamental ideas, nevertheless, are rather general and should be applicable to various precipitate-hardening systems. This work may be the first step in the development of various heating scheduling methods employing machine learning, MCTS, in order to enhance strength and design HT routes.

In conclusion, our study developed the pipeline to optimize the heat treatments to maximize 0.2% proof stress at 725 ℃ for the Ni-Al binary alloy with the γ - γ' two-phase microstructure. The pipeline consisted of the computational workflow predicting the 0.2% proof stress in MInt and the MCTS, the AI algorithm finding the HTs efficiently. The search space was defined as follows. That is, the heat treatment time was set to be 10 minutes, and the temperature was allowed to change in 25˚C steps in the range of 500 to 700 ˚C every minute. The number of HT candidates were huge, (i.e., 3,486,784,401). The MCTS found the 110 non-IHTs that outperformed the IHT benchmark in terms of 0.2% proof stress. The detailed analysis of the AI-found top 5 HTs revealed that they commonly consisted of two stages, as follows: early high-temperature HT for a shorter time to rapidly increase the γ' precipitate size to the near-critical size ~ 40 nm and the subsequent lower temperature annealing to increase the γ' phase fraction by keeping the γ' under the critical size. Based on the essence of the AI-found HTs revealed by the analysis, we proposed a new concept of two-step HT consisting of 1-min isothermal HT at 700˚C, cooling down to a lower temperature, and 8-min isothermal HT at the lower temperature. We found the optimum lower temperature for the second step to be 555°C and then confirmed that this heat treatment outperforms the AI-found best one. Both the design methodology using the AI-found solutions as a source of inspiration and the newly proposed two-step HT concept based on the methodology should be effective for Ni-base superalloys with a similar γ - γ' two-phase microstructure.

Supplementary material

See supplementary material for the details on the quantitative analysis of simulated microstructural evolution and 2D contour maps for γ' size, fraction and their 0.2% proof stress.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Acknowledgements: This work was supported by Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), Structural Materials for Innovation”, “Materials Integration” for Revolutionary Design System of Structural Materials (Funding agency: JST).

Author contributions

V.N., S.D., and M.D. developed the concept and performed the simulations and their analysis; M.D. supervised the conduct of this study; M.D., D.S.B., T.O., T.K., and S.M. contributed to the MInt system; All authors reviewed the manuscript.

Competing interests

The authors report that there are no competing interests to declare.

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No competing interests reported.

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Artificial Intelligence Inspired Design of Non-Isothermal Heat Treatments for γ - γ' Two-phase Ni-based Alloys

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