Ti-containing High-Entropy Alloys for Aeroengine Turbine Applications

Abstract Sustained research in high-entropy alloys (HEAs) has presented opportunities for relatively lighter alloys, specifically the Ti-containing HEAs, having an excellent combination of properties, and a great potential to replace heavier superalloys. We adopted a novel data-driven methodology to sort and select Ti-containing HEAs from the literature for their potential applications in aeroengine turbines by applying multiple-attribute decision-making (MADM). The ranks of the alloys evaluated by diverse MADMs were consistent. The data-driven methodology identified the following top five Ti-containing HEAs: ONS-BCC-Ti17.8 (Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8), EF-BCC-Cr20-Ti20 (Ti20-Zr20-Hf20-Nb20-Cr20), ONS-BCC-Ti27.9 (Al11.3-Nb22.3-Ta13.1-Ti27.9-V4.5-Zr20.9), ONS-BCC-Ti27.7 (Al5.2-Nb23.4-Ta13.2-Ti27.7-V4.3-Zr26.2), and ONS-BCC-Ti20 (Nb20-Cr20-Mo10-Ta10-Ti20-Zr20); the methodology provides directives for further development of the identified Ti-containing HEAs for potential replacement of legacy superalloys in aeroengine turbines. The top-ranked alloy (Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8) is lighter than the current industry benchmark, Inconel 718, by ~13%. All the top five Ti-containing HEAs have configurational entropy greater than ~13.3 J/mol K and body-center cubic crystal structure. The potency of the methodology could further be tapped by choosing appropriate weights of the properties for specific aeroengine turbine applications.


Introduction and Background
The estimated passenger growth forecast for air travel in 20 years is 4 to 8 billion 1 .Around 40,000 new aircraft are projected to meet the demand, which is estimated to be about $16 trillion in aircraft purchases and maintenance [2][3][4] .About 30% of this business is in aeroengine.Skyrocketing jet fuel costs and environmental concerns demand fuel-efficient engines to sustain this growth.In addition, fuel-efficient engines require a reduction in the weight of the engines and the entire aircraft.Further, alternate zero-emission fuel aircraft are also under development 5,6 .Irrespective of the fuel type, the efforts to reduce the weight of the aeroengines by using lighter, stronger, and corrosion-resistant materials are imminent.The use of conventional titanium alloys with low density (about half that of steel and superalloys), good mechanical properties both at room and elevated temperatures (up to about 600°C), corrosion resistance, and forgeability, have gone up from about 0% in 1950 to beyond 30% in various aeroengine fan and compressor (shafts, discs, blades, casings, etc.) parts [7][8][9][10] .In low-pressure turbine blades, the intermetallic TiAl alloys (Ti-48Al-2Cr-2Nb and other variants) with even lower density and superior elevated temperature properties compared to the conventional Ti alloys have replaced heavier superalloys [11][12][13] .Aeroengine turbines demand lightweight, strong, high temperature materials supported by high reliability and durability in extreme service environment 14 ; the combination of material properties significant for the application is low density, high elevated-and room-temperature yield, ultimate tensile, and fatigue strengths, and high temperature oxidation and creep resistance.
With growing interest in replacing the heavier superalloys, the sustained research over more than a decade in the new class of alloys, the high-entropy alloys (HEAs), has presented opportunities for relatively lighter Ti-containing high-entropy alloys [15][16][17][18][19][20][21][22][23][24][25][26] , having an excellent combination of properties with great potential 27,28 .Therefore, it is imperative to sort Ti-containing high-entropy alloys in the literature and compare them with the current industry benchmark (e.g., Inconel 718 [29][30][31] ).Subsequently, identify and focus on a few top-ranked high-entropy alloys with equivalent or superior properties compared to the benchmark and pursue further development for the intended applications.Material selection is a holistic approach to selecting an optimal material from a list of materials, which typically involves trade-offs between various properties, cost, availability, environmental effects, etc 32 .Multiple criteria decision making (MCDM) is a popular branch of decision making that has two distinct sub-branches: multi-objective decision making (MODM) and multi-attribute decision making (MADM).MODM centers on decision problems in which the decision space is continuous-mathematical programming problems with multiple objective functions-while, MADM focusses on problems with discrete decision spaces-where the set of decision alternatives has been predetermined 33 .Multiple attribute decision making (MADM) finds wide applications in many industries, including manufacturing, logistics, construction, transportation and material selection, which involves making preference decisions over the available alternatives characterized by multiple and usually conflicting attributes expressed in a matrix format [33][34][35][36][37][38][39][40] .The decision matrix comprises alternatives that is evaluated in terms of attributes, while the importance of each attribute is assigned weights and the sum of the weights of all the attribute equals unity 33 .
The paper applies MADM to rank the Ti-containing high-entropy alloys in the literature for aeroengine turbine applications.Subsequently, it consolidates the ranks evaluated by diverse MADMs by basic and advanced statistical techniques.Lastly, it identifies the top five Ti-containing high-entropy alloys and recommends alloys for further development for the potential replacement of legacy superalloys in aeroengine turbine applications.

Methods
Figure 1 presents the flowchart of the novel methodology for data-driven sorting and selection of Ti-containing highentropy alloys from the literature.The method consists of three distinct routines: (i) Literature data (compile literature data), (ii) Ranking-apply multiple attribute decision making (MADM) methods to rank the alloys, and (iii) Statistical analyses (consolidate the ranks by basic and advanced statistical techniques); subsequently, identify/recommend potential Ti-containing high-entropy alloys having a superior combination of properties compared to the legacy alloys in aeroengine turbine applications.The distinct routines in the context of the current investigation is explained in more details below:

Literature data
The first routine (Figure 1) is compilation of the literature data.We compiled a list of Ti-containing high-entropy alloys (alternatives) and their properties (attributes) from the literature, including conference proceedings and peer-reviewed journals [15][16][17][18][19][20][21][22][23][24][25][26] .Table 1 presents the alloy chemistry (in at.%), processing conditions, imminent microstructures of the alloys, and unique identifier assigned for the current study-alloy designation, while Table 2 presents their properties.The properties identified for the investigation were density (ρ), yield strength at room temperature (0.2% YS-RT), and yield strength at 800°C (0.2% YS-800°C).For the targeted aeroengine turbine applications, a combination of low density and high yield strengths at ambient and elevated temperatures is desirable.Hence, in the parlance of MADM, ρ is a minimizing attribute (lower the better), while 0.2% YS-RT and 0.2% YS-800°C are maximizing attributes (higher the better).Thus, the alternatives (Alloy designation) and the attributes (ρ, 0.2% YS-RT, and 0.2% YS-800°C) form the data matrix for the study.

Ranking
The second routine (Figure 1) is evaluation of ranks by applying MADM methods.We evaluated the ranks of the decision matrix (columns Alloy designation, ρ, 0.2% YS-RT, and 0.2%YS-800 °C in Table 2) by several MADM methods.Making preference decisions over the available alternatives that are often characterized by multiple and usually conflicting attributes is MADM 33,34 .Distinct components of MADM are (i) the decision matrix, which comprises alternatives and attributes, and (ii) attribute weights that quantify the relative importance of the attributes 33,34,41 .The attribute weights are of two types: (a) objective-that applies a mathematical model to quantify the relative weights of the attributes;

Statistical analyses
The third and the last routine (Figure 1) is consolidation of the ranks by evaluating mean and by applying principal component analysis (PCA).Each MADM method applies a unique mathematical aggregation procedure to rank the alternatives; consequently, the ranks evaluated by the methods are likely to deviate.We evaluated Spearman's correlation coefficients to quantify the similarities (or differences) among the ranks from the ten MADMs 65,66 .The ranks obtained by various MADMs were consolidated by basic and advanced statistical techniques.In the former, ranks were consolidated by taking the mean (average), while in the latter, the ranks were consolidated by principal component analysis (PCA) [67][68][69] .PCA, a multivariate technique, reduces the dimensionality of the data set consisting of several variables to a new set of variables by orthogonal transformation.The new set of variables, commonly termed principal components (PC), are ordered such that the first few PCs (usually one or two) retain most variations in the original data.The statistical analyses were carried out on a commercial software Minitab® 20.

Results and Discussion
Table 3 presents the descriptive statistics of the Ticontaining high-entropy alloys in the literature.Inconel 718, current benchmark for aeroengine turbine applications, is a conventional alloy (not a high-entropy alloy) whose ΔS config /R, ρ, 0.2% YS-RT, and 0.2% YS-760°C are ~1.30mol -1 , 8.28 g/cm 3 , 1034 MPa, and 758 MPa (at 760°C), respectively [29][30][31] .Comparing the properties of the Inconel 718 with the descriptive statistics of the literature data of Ti-containing high-entropy alloys reveal that the mean of ρ (~7.43 g/cm 3 ) is less than the benchmark, and the 0.2% YS-RT (~1319 MPa) is greater than the 0.2% YS-RT of the benchmark.The yield strength for Inconel 718 (~758 MPa) at a relatively lower temperature of 760 °C is greater than the mean of 0.2% YS-800°C (~721 MPa) of the literature data, which is at a higher temperature, i.e., 800°C.Thus, it is reasonable to assume that 0.2% YS for Inconel 718 at 800°C is likely to be similar to the mean of the 0.2% YS-800°C of the Ti-containing high-entropy alloys.Hence the combination of properties of certain Ti-containing high-entropy alloys is likely to be better than the benchmark.
Figure 2 presents the objective and subjective weights of the attributes (properties).The objective weights of the properties-data-driven based on Shannon's entropy method-were evaluated as 0.05 for ρ, 0.33 for 0.2% YS-RT, and 0.62 for 0.2% YS-800°C.The objective weights appear skewed for the intended aeroengine application!However, all the three properties (ρ, 0.2% YS-RT, and 0.2% YS-800°C) are equally important; hence, the subjective weights were assigned 0.33 each for ρ, 0.2% YS-RT, and 0.2% YS-800°C.Consequently, we adopted the subjective weights to evaluate ranks by MADMs.
Figure 3 shows the ranks of the alloys evaluated by the ten MADMs.The alloys ranked 1, 2, and so on are considered top or best alloys.Since each MADM method applies a unique mathematical aggregation procedure to sort the alternatives, the ranks evaluated by various methods are likely to deviate, as evident from the figure.For example, all the MADMs identify ONS-BCC-Ti17.8as the top-ranked alloy (rank#1).On the contrary, the rank evaluated by the various MADMs to NDS-BCC-Ti12.5 differs significantly.Table 4 unravels the Spearman's correlation coefficients (S ρ ) that quantify the similarities (or differences) among the ranks evaluated by the ten MADMs.For example, the correlation between SMART and SAW is 0.941-a strong correlation.On the other hand, S ρ between WEDBA and OCRA is 0.617.Over all S ρ ranges from 0.617 to 1, which is expected since each MADM method applies a unique mathematical aggregation procedure to rank the alternatives; consequently, the ranks evaluated by the methods are likely to deviate.Such a wide range in S ρ also makes the analyses robust.Nevertheless, of the 45 combinations, ~80% have S ρ ≥ 0.8, and the rest have S ρ ≥ 0.6; such a strong correlation of ranks elicits that it is reasonable to consolidate the ranks from the various MADMs.
Figure 4a elucidates the mean-based consolidation of the ranks of Ti-containing high-entropy alloys from the ten MADMs.The consolidated rank of the alloys is superimposed (solid yellow points and dotted green lines) over the individual MADM ranks as in Figure 3.The five top-ranked alloys are: ONS-BCC-Ti17.8(Rank#1), EF-BCC-Cr20-Ti20 (Rank#2), ONS-BCC-Ti27.9(Rank#3), ONS-BCC-Ti27.7,and ONS-BCC-Ti20 (both ranked#4).i.e., ranks from ten MADMs) into a two-dimensional space.Table 5 presents the eigenvalues (and their proportion) that capture the variation of the distribution of each principal component.The new axes capture ~99% of the variation in the original data.Thus, this way of presentation qualifies to be called a rank chart.The first principal component (PC1) captures ~90% of the variation or scatter in the original data, while the second principal (PC2) describes ~9% of the variation.Since PC1 captures nearly 90% of the variation in the initial ten dimensions (i.e., sets of ranks), it approximates the consolidated ranks of Ti-containing high-entropy alloys.) (currently rank#9) could emerge as a top-ranked alloy that has properties comparable to the Inconel 718 but with significantly lower density (by 34%).The potency of the data-driven methodology could further be tapped by effectively and appropriately choosing the weights of the properties for specific aeroengine turbine applications.Miracle and Senkov 27 have classified the high-entropy alloys for high-temperature structural applications into 3d transition-metal complex concentration alloys (CCAs) and refractory metal CCAs.The Ti-containing high-entropy alloys in the current investigation fall under refractory metal CCAs.Some alloys exhibit superior room and elevated temperature strength than the current benchmark Inconel 718 and others.Moreover, the literature data is predominantly cast alloys subjected to thermal treatments (to reduce chemical segregation), and only a limited few were thermomechanically processed for microstructure evolution.Wrought microstructures with grain refinement and other strengthening mechanisms should be investigated to further improve properties in a targeted way.Additionally, most of the data in the literature are for compression testing; however, tensile data is required, especially for a clearer picture of the ductility.Further, creep, fatigue, fracture toughness, and oxidation resistance studies are also desirable.Some studies on understanding the solid solution strengthening 70 have agreed with adjustments made to classical hardening concepts.While there is a lot of data that is desired, the present effort would assist in selecting the top-ranked alloys using the ranking methodology and thus, one could concentrate on some selected alloys for generating extensive data in the desired direction.The investigation identifies a few Ti-containing high-entropy alloys that match the current benchmark, recommends the potential of the HEAs to substitute legacy alloys in aeroengine, and provides guidelines and directives to focus on the further development of the identified Ti-containing high-entropy alloys.

Summary and Conclusions
Sustained research in the new class of alloys over a decade-the high-entropy alloys (HEAs)-has presented opportunities for relatively lighter alloys, specifically the Ti-containing high-entropy alloys, having an excellent combination of properties, and a great potential to replace heavier superalloys.We adopted a novel data-driven methodology to sort and select Ti-containing high-entropy alloys from the literature for their potential applications in aeroengine turbines by applying multiple-attribute decisionmaking (MADM).The ranks of the alloys evaluated by diverse MADMs were consistent; basic and advanced statistical techniques consolidated the ranks.The data-driven methodology identified the following top five Ti-containing high-entropy alloys: ONS-BCC-Ti17.

Figure 1 .
Figure 1.The flowchart of data-driven sorting and selection of Ti-containing high-entropy alloys.

Figure 2 .
Figure 2. The pie chart of the (a) objective and (b) subjective weights of the attributes (properties).

Figure 3 .
Figure 3.The ranks of Ti-containing high-entropy alloys (HEAs) evaluated by the ten multiple attribute decision making (MADM) methods.For example, all the MADMs assign similar rank #1 (green ellipse) to the alloy ONS-BCC-Ti17.8.On the other hand, MADMs allot diverse rank (pink ellipse) to the alloy NDS-BCC-Ti25.1.

Figure 4 .
Figure 4.The rank consolidation by (a) mean and (b) principal component analysis (PCA) of Ti-containing high-entropy alloys evaluated by the ten multiple attribute decision making (MADM) methods.The ranking of the top five alloys by both methods matches.

Table 1 .
Ti-containing high-entropy alloys from the literature; includes alloy chemistry/composition, processing conditions, imminent microstructures, and unique identifier assigned for the current study.

Table 3 .
Descriptive statistics of the properties of the Ti-containing high-entropy alloys from the literature.

Table 5 .
The eigenvalues (and their proportion) by principal component analysis (PCA) of the ranks of the Ti-containing high-entropy alloys evaluated by the ten multiple attribute decision making (MADM) methods.

Table 4 .
The Spearman rank (S ρ ) correlation among the ten multiple attribute decision making (MADM) methods.