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Article

Strategic Selection of Refractory High-Entropy Alloy Coatings for Hot-Forging Dies by Applying Decision Science

by
Tanjore V. Jayaraman
1,*,† and
Ramachandra Canumalla
2,*,†
1
Department of Mechanical Engineering, United States Air Force Academy, CO 80840, USA
2
Weldaloy Specialty Forgings, Warren, MI 48089, USA
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Coatings 2024, 14(1), 19; https://doi.org/10.3390/coatings14010019
Submission received: 21 November 2023 / Revised: 11 December 2023 / Accepted: 17 December 2023 / Published: 24 December 2023
(This article belongs to the Special Issue New Insights of High Entropy Alloys and Its Applications)
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Abstract

:
We compiled, assessed, and ranked refractory high-entropy alloys (RHEAs) from the existing literature to identify promising coating materials for hot-forging dies. The selection methodology was rigorously guided by decision science principles, seamlessly integrating multiple attribute decision making (MADM), principal component analysis (PCA), and hierarchical clustering (HC). By employing a combination of twelve diverse MADM methods, we successfully ranked a total of 22 RHEAs. This analytical technique unveiled the top five RHEAs: Ti20-Zr20-Hf20-Nb20-Cr20, Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8, Ti20-Zr20-Hf20-Nb20-V20, Al11.3-Nb22.3-Ta13.1-Ti27.9-V4.5-Zr20.9, and Al7.9-Hf12.8-Nb23-Ta16.8-Ti18.9-Zr20.6 pertinent for generating data on other significant properties, including wear resistance, fatigue (both thermal and mechanical), bonding compatibility with the substrate die material, oxidation resistance, potential reactions with the workpiece, cost-effectiveness, fabricability, and more. The three highest-ranked RHEAs share key characteristics, including a body-centered cubic (BCC) crystal structure, thermal conductivity below ~70 W/mK, and impressive yield strength at ambient and elevated temperatures, surpassing 1100 MPa. Moreover, they exhibit a remarkable ~73% similarity among themselves. The decision science-driven analyses yield sound metallurgical insights and provide valuable guidelines for developing RHEA coatings tailored for hot-forging dies. The strategy for designing RHEA-based coating materials for hot-forging dies should focus on compositions featuring a substantial presence of refractory metals while maintaining a BCC crystal structure. This combination is likely to deliver the desired blend of thermal and mechanical properties, rendering these coatings exceptionally well-suited for the demanding requirements of hot-forging operations.

1. Introduction and Background

In the aerospace industry, hot forging is widely adopted due to its reliability and cost-effectiveness in shaping metal parts. The service life of hot-forging dies is pivotal in ensuring the quality of the forged products and the overall efficiency of the forming process. Achieving an extended die lifespan involves selecting the most suitable die material and optimizing die design to enhance thermal fatigue and wear resistance and minimize plastic deformation and surface fracture [1,2]. The selection of conventional hot forge dies with improved die life and performance is based on several factors, including alloy composition, heat treatment, cleanliness, and forging conditions. Accordingly, conventional die steels, for example, H13, Finkl, 4340, and Uddeholm Dievar; specialty steels, including maraging steels; and superalloys like A286, 718, 720, Waspaloy, Hastelloy, and Stellite are common, depending on the application and the stringent requirements of the forging parts [3,4,5,6,7]. The performance requirements of hot-forging dies typically include good (a) hardenability, (b) toughness and ductility, (c) temper resistance, (d) hardness and strength at room and elevated temperatures, (e) wear resistance, (f) oxidation and corrosion resistance, (g) thermal conductivity, (h) thermal and mechanical fatigue, and some other requirements [3,4,5,6,7,8,9].
A noticeable decline in die performance is apparent upon assessing the conventional die materials for factors like hardness, strength, wear resistance, and oxidation resistance over a range of elevated temperatures. To illustrate [3,4,5,6,7], in H13 and Uddeholm Dievar, the yield strength diminishes significantly, dropping from ~1250 MPa (at room temperature) to ~1000 MPa at ~427 °C (800 °F) and further to about ~825 MPa at ~538 °C (1000 °F). Given the external forces in the forging process that typically fall within the range of 500 to 1000 MPa, it is evident that the die material is likely to undergo deformation when exposed to temperatures exceeding ~427 °C (800 °F) [10,11]. These die materials are also susceptible to thermal and mechanical fatigue due to transformational stresses and the nature of the forging process, respectively [12]. During the hot-forging process, dies are preheated to mitigate the chilling effect on the workpiece, which reduces the need for repeated reheating of the workpiece and enhances the thermomechanical processing of the forged products, thus improving their quality at the expense of softening the die during its service [13,14]. Furthermore, the performance of these materials hinges on the localized temperature at the interface between the die and the forging stock. This issue is exacerbated in press operations with prolonged dwell times and higher contact pressures, potentially impacting die longevity [3,10,11,12,13,14]. In scenarios involving the forging of steel, superalloys, and titanium alloy products that require hot forming temperatures of up to ~1205 °C (2200 °F), surface temperatures on the die exceeding ~650 °C (1200 °F) can be reached. This causes the die to soften, resulting in distortion and damage [3,13,14]. Consequently, these elevated temperatures have a detrimental effect on the longevity of these die materials. To address these challenges, the industry, along with research and development labs and academia, has been consistently striving to enhance the lifespan of these cost-effective base/substrate conventional hot-forging die materials. Various surface coating materials and technologies have been explored to shield them from exposure to temperatures above ~427 °C (800 °F) [3,5,15,16,17].
While the industry has been diligently working to enhance die lifespan and, consequently, the quality of forged products using various techniques and methodologies as previously discussed, significant efforts have also been directed toward a relatively new class of materials, “High-entropy Alloys (HEAs)” or “Complex Concentrated Alloys (CCAs)” over the past two decades [18,19]. HEAs/CCAs are multi-element equiatomic alloy systems comprising five or more elements with high configurational entropies that stabilize the phase(s). This development represents a groundbreaking advancement in material design, with a multitude of alloys currently under exploration for various applications across different industries [18,19,20]. There is considerable promise in utilizing these materials as coatings for conventional hot-forging die substrates, surpassing the highly coveted superalloys and aluminides in performance. Die coatings can be categorized into three main groups [18,19,21]: metallic coatings (comprising transition metals, refractory metals, and lightweight metals), ceramic coatings (encompassing oxides, borides, carbides, and nitrides), and composite coatings (involving ceramic-reinforced and hybrid coatings). Upon careful evaluation, it becomes evident that refractory HEAs (RHEAs) exhibit exceptional suitability as coatings for conventional hot forge die materials, offering a remarkable combination of properties ideally suited for their intended application as coatings on hot forge dies, employing various coating techniques [19,21,22,23,24,25,26,27].
RHEAs exhibit favorable properties [18,20], such as strength at both room and elevated temperatures up to ~800 °C (1472 °F), alongside excellent ductility, toughness, wear resistance, and outstanding oxidation resistance. Delving deeper into their potential, one can strategically select RHEAs with low thermal conductivity [25] and high strength characteristics to safeguard the integrity of low-cost base/substrate conventional hot-forging die materials at elevated temperatures. This, in turn, helps prevent deformation or distortion during forging operations, considering the temperatures and press loads involved. Additionally, there is the option to explore the implementation of a multi-material gradient layer [1] between the RHEA and the substrate die material. This layer/s can be designed to have low thermal conductivity while promoting better bonding between the substrate and the RHEA, should the need arise. Coating these low-cost base/substrate conventional hot-forging die materials with RHEAs offers several advantages. These include reducing cycle times (minimizing the need for re-heats, decreasing wear, mitigating failures, reducing repair, refurbishing frequency, etc.), improving thermomechanical processing, and influencing the desired microstructure and properties of the forged products. Ultimately, this approach enhances the products’ quality in hot-forging operations.
In this investigation, the focus is narrowed down to examining RHEAs as promising candidates for high-temperature, high-strength coatings on hot-forging dies. It is crucial to emphasize that generating data on all the properties (such as wear resistance, strength, fatigue properties, fabricability, coating methods, bonding characteristics, the necessity of a multi-material gradient layer, etc.) for every available RHEA in the current literature is a time-consuming, laborious, and costly endeavor [28]. Moreover, not all the properties mentioned above are documented for every RHEA in the literature; only a few common properties of most RHEAs are reported. Therefore, the overarching approach in this endeavor is to employ decision science to sort and rank the RHEAs based on readily accessible essential properties in the current literature: thermal conductivity and ambient and 800 °C yield strength. Following this strategy, the top-ranked RHEAs, resulting from the decision science-driven ranking, can be subjected to a more thorough evaluation encompassing all other properties pertinent to their intended functional application cost-effectively and expediently. Our approach involves compiling, evaluating, sorting, and selecting RHEAs from the existing literature, focusing on coating hot-forging dies, guided by decision science principles. This process involves integrating twelve multiple attribute decision making (MADM) methods to rank a list of 22 RHEAs. Principal component analysis (PCA), a powerful analytical tool that reduces multidimensional data into a more manageable format, plays a key role in consolidating rankings from various MADM techniques. Furthermore, hierarchical clustering (HC) helps identify similarities among the RHEAs and suggests potential alternatives that could potentially replace the top-ranked choices.

2. Methods

Figure 1 presents a flowchart of the strategic selection of RHEAs for coating hot-forging dies by applying decision science. The decision science-driven selection methodology is similar to the selection of Ti-containing high-entropy alloys for aeroengine turbine applications and the selection of high-temperature conventional Ti alloys for aeroengines [20,28]. It consists of three key routines: (i) literature data (compilation of refractory high-entropy alloy-based coatings for hot-forging dies); (ii) ranking (ranking by MADM methods); and (iii) analyses (rank consolidation by PCA and interpretation). The three routines in the flow chart are presented in detail in the following sections:

2.1. Literature Data

We compiled a comprehensive list of RHEAs suitable for coating hot-forging dies, along with their pertinent mechanical and thermal properties, all sourced from various references. Table 1 showcases the RHEAs (alternatives) meticulously screened for this study, primarily drawn from peer-reviewed journals and conference proceedings [29,30,31,32,33,34,35,36,37,38,39,40]. In the table, information on the nominal chemical composition, processing conditions, and resulting microstructures of these RHEAs is presented as well.
Our focus in this investigation centers around three key attributes: thermal conductivity (κ), ambient temperature yield strength (AT-YS), and elevated temperature yield strength (ET-YS). These attributes are of paramount importance for the specific application targeted here, namely, coating for hot-forging dies. To optimize the selection of RHEA-based coatings, it is imperative that these materials exhibit a desirable combination of properties: low κ (thermal conductivity), high AT-YS, and high ET-YS. Only after satisfying these criteria will it be pertinent to delve into the examination of other significant attributes, including wear resistance, fatigue (both thermal and mechanical), bonding compatibility with the substrate die material, oxidation resistance, potential reactions with the workpiece, cost-effectiveness, fabricability, and more. In the context of multiple attribute decision making (MADM) [41,42], κ serves as a minimizing (the lower the better to mitigate heat transfer to the substrate and shield it) attribute, whereas both AT-YS and ET-YS are regarded as maximizing (the higher the better to resist deformation to the external loads during forging) attributes. Thus, Table 2 functions as a decision matrix, bringing together the array of alternatives (RHEA-based coatings for hot-forging dies) and the critical attributes, i.e., properties (κ, AT-YS, and ET-YS), culled from the existing literature.

2.2. Ranking

We assessed the decision matrix in Table 2, employing various MADM methods. MADM involves making informed decisions by systematically evaluating and prioritizing alternatives based on multiple attributes [41,42,43]. Within the MADM framework, two key elements play a significant role: Firstly, there is the decision matrix, a comprehensive representation encompassing both the alternatives and the attributes under scrutiny. Secondly, we address attribute weights, which are essential within the MADM theory. These weights provide a quantitative expression of the relative importance of each attribute within the decision-making process [41,42]. For this study, we opted for an equitable distribution of weights, allocating 33.33% to each attribute. This decision was made with a deep understanding of these materials and their intended application.
We identified and applied twelve MADM methods to assess the data matrix and rank the RHEAs. These methods include the additive ratio assessment method (ARAS) [44], complex proportional assessment (COPRAS) [45], measurement of alternatives and ranking according to compromise solution (MARCOS) [46], multi-attribute utility theory (MAUT) [47], multi-objective optimization on the basis of ratio analysis (MOORA) [48], operational competitiveness ratio (OCRA) [49], preference selection index (PSI) [50], range of value method (ROVM) [51], simple additive weighting (SAW) [52], technique of order preference by similarity to ideal solution (TOPSIS) [45,53], multi-criteria optimization and compromise solution (VIKOR) [45,54] (known as vIse kriterijumska optimizacija kompromisno resenje in Serbian), and weighted euclidean distance-based approach (WEDBA) [55]. This comprehensive set of methods enables a thorough evaluation of the RHEAs and facilitates a robust ranking based on their suitability for the intended application. The MADM methods were soft-coded in Microsoft Excel (Version 2311) [28].

2.3. Analyses

Each MADM approach possesses its own unique mathematical aggregation method for ranking alternatives, contributing to creating a robust array of ranks. As expected, the rankings generated by these distinct methods may exhibit variations. Nonetheless, the correlation between the outcomes from different techniques enhances the overall reliability of the results. The entire process was implemented in Microsoft Excel, aligning with the formulations detailed in the respective references of the MADM methods. The rankings generated by the diverse MADM methods were then subjected to a correlation analysis. We employed Spearman’s correlation coefficients [56] to assess the degree of correlation among the rankings produced by the twelve MADM methods. To consolidate these rankings derived from various MADM methods, we computed their mean (i.e., average) and conducted principal component analysis (PCA) [57,58]. PCA, a powerful multivariate technique, reduces the dimensionality of a dataset consisting of interrelated variables. It accomplishes this by transforming the data into new principal component (PC) variables. These PCs are uncorrelated and arranged so that the initial few PCs, usually one or two, capture most of the variation present in the original data. The results of this PCA analysis (rank evaluation) are presented visually through a score plot. Furthermore, we explored the relative similarities among the RHEAs by applying hierarchical clustering [59]. This method allows us to identify groupings or clusters based on similarity criteria. All the analyses were conducted using the commercial software Minitab® 21 [28].

3. Results and Discussion

Figure 2 provides a visual representation of the rankings assigned to RHEA-based coatings for hot-forging dies. These rankings are discrete in nature, and for enhanced visual clarity, thin dotted lines connect the points assessed by each of the different MADM methods. Despite the unique mathematical aggregation procedures employed in these various MADM methods, there are instances where the peaks and troughs in the rankings somewhat align. For instance, several MADM methods assign similar ranks to ONS-BCC-1597, as indicated by the green shading. However, it is important to note that the rank assigned by different MADM methods to most RHEAs varies significantly, as seen with the RHEAs designated as ONS-BCC-846 (orange shading).
Table 3 presents the Spearman rank correlation coefficient (Sρ) that quantifies the rank correlations among the twelve MADM methods. For example, Sρ values exceeding 0.90, such as those between MARCOS and ARAS, MOORA and MAUT, or WEDBA and ROVM, indicate strong correlations. Conversely, Sρ values below 0.5, as observed between OCRA and COPRAS or VIKOR and PSI, are expected due to the distinct mathematical aggregation approaches in these various MADM methods. Out of the 66 possible combinations of MADM pairs, approximately 54% exhibit rank correlations equal to or above 0.90, while around 72% have rank correlations exceeding 0.55. These findings underscore the robustness and validity of the RHEA rankings. Given the diversity in the correlations across various MADM methods, it becomes imperative to consolidate these rankings. Based on the Sρ values obtained from various combinations of MADM methods, consolidating the rankings from all twelve MADM evaluations is a practical approach. Consequently, the consolidated rank, based on the arithmetic mean, is presented in Figure 3. Notably, the top five ranked data points in Figure 3 are EF-BCC-1325, ONS-BCC-1597, EF-BCC-1148, ONS-BCC-796-2, and ONS-BCC-796-1, listed in that order.
Figure 4 illustrates a score plot showcasing the consolidated rankings of RHEA coatings for hot-forging dies using principal component analysis (PCA). This plot represents the first two components, denoted as PC1 and PC2, derived after reducing the dimensionality of the data, which originally consisted of rankings from twelve different MADM methods. Table 4 provides insight into the eigenvalues and their respective proportions, which capture the distribution of variation within each principal component. Notably, the first principal component, PC1, accounts for approximately 80% of the variation or scatter present in the original data, while the second principal component, PC2, explains approximately 17% of the variation. Given that PC1 captures nearly 80% of the variance initially present across twelve dimensions (sets of ranks), it effectively approximates the overall ranking of RHEA coatings. In the score plot, an imaginary reference line perpendicular to PC1 extends from left to right, ranging from −5 to 5. This line serves as an indicator of the overall rankings of the RHEAs. The top five data points, corresponding to the RHEAs EF-BCC-1325, ONS-BCC-1597, EF-BCC-1148, ONS-BCC-796-2, and ONS-BCC-796-1 (enclosed within the box in Figure 4), are consistently ranked as the highest by PCA-based consolidation and align with the mean-based consolidation of ranking. This alignment with the top-ranked RHEAs determined through mean-based consolidation underscores the consistency and reliability of the ranking results.
Figure 5, presenting the hierarchical clustering (HC) dendrogram of RHEA coatings for hot-forging dies, unveils intriguing insights. Specifically, it reveals that the top five RHEAs—EF-BCC-1325, ONS-BCC-1597, EF-BCC-1148, ONS-BCC-796-2, and ONS-BCC-796-1—share a similarity of ~64% with each other. Further, the top three RHEAs, EF-BCC-1325, ONS-BCC-1597, and EF-BCC-1148, exhibit a notably high similarity of 73%. The observed similarity among the top five RHEA coatings centers around certain common attributes. These coatings boast configurational entropy exceeding ~13.34 J/K mol, possess a body-centered cubic (BCC) crystal structure, and exhibit thermal conductivity below ~70 W/mK. Moreover, the chemistry of the top three RHEAs is characterized by the presence of low thermal conductivity elements such as Ti, V, Mo, Hf, Zr, Ta, and others. This elemental composition seems to promote high configurational entropy and the formation of BCC phases. The correlation between the top five RHEAs and the BCC crystal structure hints at high hardness, translating into low wear rates [26]. These findings strongly support the idea that the top-ranked RHEAs excel in wear resistance, making them highly suitable for use as coating materials for hot-forging dies, which is evident in the WMoTaNb RHEA, which has a BCC crystal structure and exhibits a relatively high wear resistance (or low wear rate) at ambient and elevated temperatures [60]. The strengthening mechanisms elucidated in general in HEA coatings by Nair et al. [61] provide good insights into understanding the strengthening of RHEAs in the present effort. However, it is worth noting that the top-ranked RHEA, EF-BCC-1325 (Ti20Zr20Hf20Nb20Cr20), has a relatively expensive element Hf, introducing cost considerations. Nevertheless, the five top-ranked RHEAs: Ti20-Zr20-Hf20-Nb20-Cr20 (EF-BCC-1325), Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8 (ONS-BCC-1597), Ti20-Zr20-Hf20-Nb20-V20 (EF-BCC-1148), Al11.3-Nb22.3-Ta13.1-Ti27.9-V4.5-Zr20.9 (ONS-BCC-796-2), and Al7.9-Hf12.8-Nb23-Ta16.8-Ti18.9-Zr20.6 (ONS-BCC-796-1) are pertinent for generating data for other significant attributes, including wear resistance, fatigue (both thermal and mechanical), bonding compatibility with the substrate die material, oxidation resistance, potential reactions with the workpiece, cost-effectiveness, fabricability, and more.
In essence, the decision science-driven methodology offers valuable insights into the alloy design strategy for RHEA-based coating materials for hot-forging dies. RHEAs with a significant presence of refractory metals and a BCC crystal structure tend to exhibit the desired combination of thermal and mechanical properties, making them excellent choices for hot-forging die coatings, which is evident in the WMoTaNb RHEA, whose BCC crystal structure exhibits a relatively high wear resistance at ambient and elevated temperatures [60]. The optimization of property weights in this context could further enhance the efficacy of this decision science-driven analysis. As far as the fabrication methods for RHEAs’ coating are concerned, individual components in powder form could be mixed to make the required top-ranked RHEAs, or its alloy powders atomized from alloys made per the methods in Refs. [29,30,31,32,33,34,35,36,37,38,39,40] could be laser cladded or by any other method onto the substrate (hot forging dies) and then evaluated and then used for the intended application. Lastly, the alloy preparation [29,30,31,32,33,34,35,36,37,38,39,40], atomization into powders, methods of cladding or coating, and the like [21], and the fact that some of the components in these alloys are highly reactive in powder form and could be challenging in handling and making them into alloys and coatings, and how these aspects would evolve with more research and efforts, are outside the scope of the present objective.

4. Summary and Conclusions

In this comprehensive study, we compiled, assessed, ranked, and ultimately selected a set of RHEAs from the existing literature to serve as promising coating materials for hot-forging applications. This selection process was rigorously guided by decision science principles, seamlessly integrating multiple attribute decision making (MADM), principal component analysis (PCA), and hierarchical clustering (HC). By employing a combination of twelve diverse MADM methods, we successfully ranked a total of 22 RHEAs. Subsequently, we leveraged PCA to consolidate the rankings obtained from various MADM approaches. This analytical technique unveiled the top five RHEAs: Ti20-Zr20-Hf20-Nb20-Cr20 (EF-BCC-1325), Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8 (ONS-BCC-1597), Ti20-Zr20-Hf20-Nb20-V20 (EF-BCC-1148), Al11.3-Nb22.3-Ta13.1-Ti27.9-V4.5-Zr20.9 (ONS-BCC-796-2), and Al7.9-Hf12.8-Nb23-Ta16.8-Ti18.9-Zr20.6 (ONS-BCC-796-1) pertinent for generating other significant data attributes, including wear resistance, fatigue (both thermal and mechanical), bonding compatibility with the substrate die material, oxidation resistance, potential reactions with the workpiece, cost-effectiveness, fabricability, and more. Notably, the top-ranked RHEAs identified through PCA-based consolidation mirror those identified through mean-based consolidation, underscoring the robustness and reliability of our findings. The three highest-ranked RHEAs share key characteristics, including a body-centered cubic (BCC) crystal structure, thermal conductivity below ~70 W/mK, and impressive yield strength at both ambient and elevated temperatures, surpassing 1100 MPa. Moreover, they exhibit a remarkable ~73% similarity among themselves. Our decision science-driven analyses not only yielded sound metallurgical insights but also provided valuable guidelines for the development of RHEA coatings tailored for hot-forging dies. In essence, the strategy for designing RHEA-based coating materials for hot-forging dies should focus on compositions featuring a substantial presence of refractory metals while maintaining a BCC crystal structure, which corroborates with the previous research. This combination is likely to deliver the desired blend of thermal and mechanical properties, rendering these coatings exceptionally well-suited for the demanding requirements of hot-forging operations.

Author Contributions

Conceptualization R.C. and T.V.J.; methodology, T.V.J.; software, T.V.J.; validation, R.C. and T.V.J.; formal analysis, T.V.J. and R.C.; investigation, T.V.J. and R.C.; data curation, R.C.; writing—original draft preparation, R.C. and T.V.J.; writing—review and editing, T.V.J. and R.C.; visualization, T.V.J.; supervision, R.C. and T.V.J.; project administration, R.C. and T.V.J. All authors have read and agreed to the published version of the manuscript.

Funding

This work received no external funding. Weldaloy Specialty Forgings R&D#8860.00.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Acknowledgments

The author, T. V. Jayaraman, thanks the Department of Mechanical Engineering, United States Air Force Academy, for all the support. The author, R. Canumalla, thanks the Weldaloy Specialty Forgings management for all the support.

Conflicts of Interest

The authors Tanjore V. Jayaraman and Ramachandra Canumalla of the respective organizations namely United States Air Force Academy and Weldaloy Specialty Forgings declare that the research was conducted in the absence of any commercial or financial relationships or any other that could be construed as a potential conflict of interest.

Distribution Statement

Approved for public release: distribution unlimited (PA# USAFA-DF-2023-775).

Disclaimer/Authors’ Note

The views expressed in this article are those of the authors and do not necessarily reflect the official policy or position of the United States Air Force Academy, the Air Force, the Department of Defense, or the U.S. Government. The views expressed in this article are those of the authors and do not necessarily reflect the official policy or position of Weldaloy Specialty Forgings, Warren, MI.

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Figure 1. The flow chart of strategic selection of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
Figure 1. The flow chart of strategic selection of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
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Figure 2. The ranks of refractory high-entropy alloys (RHEAs) for coating hot-forging dies evaluated by the multiple attribute decision making (MADM) methods. Several MADM methods assign diverse ranks to some alloys (e.g., ONS-BCC-846, orange-shaded) and similar ranks to others (e.g., ONS-BCC-1597, green-shaded).
Figure 2. The ranks of refractory high-entropy alloys (RHEAs) for coating hot-forging dies evaluated by the multiple attribute decision making (MADM) methods. Several MADM methods assign diverse ranks to some alloys (e.g., ONS-BCC-846, orange-shaded) and similar ranks to others (e.g., ONS-BCC-1597, green-shaded).
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Figure 3. Mean-based rank consolidation of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
Figure 3. Mean-based rank consolidation of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
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Figure 4. Principal component analysis (PCA)-based rank consolidation of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
Figure 4. Principal component analysis (PCA)-based rank consolidation of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
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Figure 5. Hierarchical clustering (HC) of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
Figure 5. Hierarchical clustering (HC) of refractory high-entropy alloys (RHEAs) for coating hot-forging dies.
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Table 1. Refractory high-entropy alloys (RHEAs) for coating hot-forging dies from the literature include alloy chemistry/composition, processing conditions, resulting microstructures, and a unique identifier assigned for the current study [29,30,31,32,33,34,35,36,37,38,39,40].
Table 1. Refractory high-entropy alloys (RHEAs) for coating hot-forging dies from the literature include alloy chemistry/composition, processing conditions, resulting microstructures, and a unique identifier assigned for the current study [29,30,31,32,33,34,35,36,37,38,39,40].
#Alloy Chemistry in at. %Processing
Step 1		Processing
Step 2		MicrostructureAlloy Designation
1Ni47.9-Al10.2-Co16.9-Cr7.4-Fe8.9-Mo0.9-Nb1.2-W0.4-C0.4-Ti5.8 Vac. arc melting followed by DS to produce columnar microstructureSolution treated (ST) at 1210 °C/10 h to homogenize; aging at 800 °C/20 hγ + γ’ - L12 - Ni3(Ti,Al)
(69% 290 nm avg. size)		TKT-FCC-800
2Al6.25-C1-Co15-Cr13-Fe4.5-Mo1.75-Nb0.6-Ni48-V5-Ti5 Vac. arc melting (5 times) and suction castingST at 1175 °C/2 h-850 °C/8 h-650 °C/8 h-water quenched (WQ)60% vol. fraction of γ’ - L12; 450 nm-sized γ’KWG-FCC-700
3Al10-Co25-Cr8-Fe15-Ni36-Ti6 Vac. induction melted and solidified directionallyHomogenized at 1220 °C/20 h/furnace cooled (FC)-900 °C/5 h/air cooled (AC)L12 γ’ Ni3 (Ti,Al) (45% Vf/450 nm) in γ FCC solid sol. and B2/NiAl (needle-like, up to 50 μm long) (<5% Vf) precipitatesHMD-FCC-535
4Al10-Co25-Cr8-Fe15-Ni36-Ti6 Vac. induction melted and solidified directionally Homogenized at 1220 °C/20 h/FC-900 °C/50 h/ACL12 γ’-Ni3(Ti,Al)(46% Vf/460 nm) in γ FCC solid sol. and B2/NiAl (needle-like, up to 50 μm long) (<5% Vf) pptsHMD-FCC-581
5Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8Vac. arc melting-remelted 5 timesAC, hot isostatic pressing (HIP) at 1400 °C/207 MPa/2 h, 1400 °C/24 in ArBCC1 + BCC2; 75 μm avg. grain size; nanolamellar structures of the two phasesONS-BCC-1597
6Al21.9-Nb32-Ta9-Ti26.7-Zr10.3Vac. arc melting-remelted 5 timesAC, HIP at 1400 °C/207 MPa/2 h, 1400 °C/24 h in ArBCC; 2000 μm avg. grain size; nanophasesONS-BCC-728
7Al7.9-Hf12.8-Nb23-Ta16.8-Ti18.9-Zr20.6Vac. arc melting-remelted 5 timesAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 h in ArBCC; 140 μm avg. grain size; nanophasesONS-BCC-796-1
8Al5.7-Nb23.5-Ta17.6-Ti27.2-Zr26Vac. arc melting-remelted 5 timesAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 h in ArBCC1 + BCC2; 200 μm avg. grain size; nanolamellar structures of the two phasesONS-BCC-362
9Al5.2-Nb23.4-Ta13.2-Ti27.7-V4.3-Zr26.2Vac. arc melting-remelted 5 timesAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 h in ArBCC; 180 μm avg. grain size; nanophasesONS-BCC-678
10Al11.3-Nb22.3-Ta13.1-Ti27.9-V4.5-Zr20.9Vac. arc melting-remelted 5 timesAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 h in ArBCC1 + BCC2; 100 μm avg. grain size; nanolamellar structures of the two phasesONS-BCC-796-2
11Al26.6-Nb23.8-Ti25.1-V24.5Vac. arc melting—remelting 5 times—and castingHomogenized at 1200 °C/24 hBCC SS (300 to 400 μm grain size)NDS-BCC-685
12Nb20-Cr20-Mo10-Ta10-Ti20-Zr20Vac. arc melting and re-melted 5 times and castingAC, HIP at 1450 °C/207 MPa/3 hBCC1 (67% Vf) +BCC2 (16% Vf) + laves (FCC) (17% Vf)ONS-BCC-983
13Nb28.3-Ti24.5-V23-Zr24.2Vac. arc melting and re-melted 5 times and castingAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 hBCC + submicron pptsDBM-BCC-187
14Nb22.6-Ti19.4-V37.2-Zr20.8Vac. arc melting and re-melted 5 times and castingAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 hBCC1 + BCC2 + BCC3DBM-BCC-240
15Cr24.6-Nb26.7-Ti23.9-Zr24.8Vac. arc melting and re-melted 5 times and castingAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 hBCC + laves (ordered FCC)DBM-BCC-300
16Cr20.2-Nb20-Ti19.9-V19.6-Zr20.3Vac. arc melting and re-melted 5 times and castingAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 hBCC + laves (ordered FCC)DBM-BCC-615
17Hf20-Mo20-Nb20-Ti20-Zr20Vac. arc melting and re-melted 5 times and castingAC, homogenized at 1100 °C/10 h/SCBCC (dendritic)-no ordered phasesNNG-BCC-825
18Ta19.68-Nb18.93-Hf20.46-Zr21.23-Ti19.7Vac. arc melting and castingAC, HIP at 1200 °C/207 MPa/2 h, 1200 °C/24 h (only homogenized)BCC (dendritic and nonuniform); equiaxed grains about 100 μm bottom to 200 μm at the topONS-BCC-535
19Ti20-Zr20-Hf20-Nb20-V20Vac. induction melting and castingAs-castBCC + U (unknown intermetallic phase)EF-BCC-1148
20Ti20-Zr20-Hf20-Nb20-Cr20Vac. induction melting and castingAs-castBCC + laves (L1 + L2)EF-BCC-1325
21Mo20-Nb20-Ta20-V20-W20Vac. arc melting and castingAs-castBCC (dendritic)ONS-BCC846
22Mo25-Nb25-Ta25-W25Vac. arc melting and castingAs-castBCC (dendritic)ONS-BCC-552
Table 2. The properties—the ratio of configurational entropy and the ideal gas constant (ΔSconfig/R), density (ρ), thermal conductivity (κ), yield strength at ambient temperature (YS-AT), and yield strength at elevated temperature—800 °C (YS-ET)—of the refractory high-entropy alloys (RHEAs) for coating hot-forging dies (from the literature) identified for strategic selection by applying decision science [29,30,31,32,33,34,35,36,37,38,39,40]. Note that κ was evaluated as in [25].
Table 2. The properties—the ratio of configurational entropy and the ideal gas constant (ΔSconfig/R), density (ρ), thermal conductivity (κ), yield strength at ambient temperature (YS-AT), and yield strength at elevated temperature—800 °C (YS-ET)—of the refractory high-entropy alloys (RHEAs) for coating hot-forging dies (from the literature) identified for strategic selection by applying decision science [29,30,31,32,33,34,35,36,37,38,39,40]. Note that κ was evaluated as in [25].
Alloy DesignationΔSconfig/R
(mol−1)		ρ
(g/cm3)		κ
(W/mK)		YS-AT
(MPa)		YS-ET
(MPa)
TKT-FCC-8001.607.4492.74875800
KWG-FCC-7001.667.6090.481000700
HMD-FCC-5351.607.3892.46568535
HMD-FCC-5811.607.3892.46596581
ONS-BCC-15971.757.2167.6020001597
ONS-BCC-7281.506.7459.531280728
ONS-BCC-796-11.748.8643.441841796
ONS-BCC-3621.517.9145.451965362
ONS-BCC-6781.607.4943.541965678
ONS-BCC-796-21.677.2748.452035796
NDS-BCC-6851.395.4665.511020685
ONS-BCC-9831.768.1958.901595983
DBM-BCC-1871.386.5035.081105187
DBM-BCC-2401.356.4434.23918240
DBM-BCC-3001.396.6638.721260300
DBM-BCC-6151.616.5343.391298615
NNG-BCC-8251.618.6250.181575825
ONS-BCC-5351.619.7937.71929535
EF-BCC-11481.618.0029.7611701148
EF-BCC-13251.618.1726.3113751325
ONS-BCC-8461.6112.36102.871246846
ONS-BCC-5521.3913.75109.491058552
Table 3. The Spearman rank correlation of refractory high-entropy alloys (RHEAs) for coating hot-forging dies evaluated by the twelve multiple attribute decision making (MADM) methods.
Table 3. The Spearman rank correlation of refractory high-entropy alloys (RHEAs) for coating hot-forging dies evaluated by the twelve multiple attribute decision making (MADM) methods.
ARASCOPRASMARCOSMAUTMOORAOCRAPSIROVMSAWTOPSISVIKOR
COPRAS0.580
MARCOS0.9980.600
MAUT0.9150.2960.906
MOORA0.9880.5820.9910.907
OCRA0.4840.2760.4570.6080.440
PSI0.5290.1440.5050.5890.5020.932
ROVM0.9830.5870.9880.9160.9890.4170.453
SAW0.9980.6001.0000.9060.9910.4570.5050.988
TOPSIS0.9880.5920.9890.8940.9950.4530.5210.9830.989
VIKOR0.9830.5870.9880.9160.9890.4170.4531.0000.9880.983
WEDBA0.9950.6340.9970.8890.9890.4330.4900.9830.9970.9900.983
Table 4. The eigenvalues and their proportion by principal component analysis (PCA) of the ranks of refractory high-entropy alloys (RHEAs) for coating hot-forging dies by the twelve multiple attribute decision making (MADM) methods.
Table 4. The eigenvalues and their proportion by principal component analysis (PCA) of the ranks of refractory high-entropy alloys (RHEAs) for coating hot-forging dies by the twelve multiple attribute decision making (MADM) methods.
PC1PC2PC3PC4PC5PC6PC7PC8PC9PC10PC11
Eigenvalue8.7781.8620.2560.0590.0240.0140.0040.0020.0020.0000.000
Proportion0.7980.1690.0230.0050.0020.0010.0000.0000.0000.0000.000
Cumulative0.7980.9670.9910.9960.9980.9991.0001.0001.0001.0001.000
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Jayaraman, T.V.; Canumalla, R. Strategic Selection of Refractory High-Entropy Alloy Coatings for Hot-Forging Dies by Applying Decision Science. Coatings 2024, 14, 19. https://doi.org/10.3390/coatings14010019

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Jayaraman TV, Canumalla R. Strategic Selection of Refractory High-Entropy Alloy Coatings for Hot-Forging Dies by Applying Decision Science. Coatings. 2024; 14(1):19. https://doi.org/10.3390/coatings14010019

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Jayaraman, Tanjore V., and Ramachandra Canumalla. 2024. "Strategic Selection of Refractory High-Entropy Alloy Coatings for Hot-Forging Dies by Applying Decision Science" Coatings 14, no. 1: 19. https://doi.org/10.3390/coatings14010019

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