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 (Al_20.4-Mo_10.5-Nb_22.4-Ta_10.1-Ti_17.8-Zr_18.8), EF-BCC-Cr20-Ti20 (Ti₂₀-Zr₂₀-Hf₂₀-Nb₂₀-Cr₂₀), ONS-BCC-Ti27.9 (Al_11.3-Nb_22.3-Ta_13.1-Ti_27.9-V_4.5-Zr_20.9), ONS-BCC-Ti27.7 (Al_5.2-Nb_23.4-Ta_13.2-Ti_27.7-V_4.3-Zr_26.2), 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 (Al_20.4-Mo_10.5-Nb_22.4-Ta_10.1-Ti_17.8-Zr_18.8) 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.

Keywords:
High-entropy alloys; aeroengine; turbines; multiple-attribute decision making

1. Introduction and Background

The estimated passenger growth forecast for air travel in 20 years is 4 to 8 billion¹. Around 40,000 new aircraft are projected to meet the demand, which is estimated to be about $16 trillion in aircraft purchases and maintenance^2-4. 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^7-10. 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^11-13. Aeroengine turbines demand lightweight, strong, high temperature materials supported by high reliability and durability in extreme service environment¹⁴; 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^15-26, 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 718^29-31). 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, etc³². 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 predetermined³³. 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^33-40. 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 unity³³.

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.

2. Methods

Figure 1 presents the flowchart of the novel methodology for data-driven sorting and selection of Ti-containing high-entropy 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:

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

2.1. 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^15-26. 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.

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.

Sl#	Alloy chemistry in at.%	Processing Step 1	Processing Step 2	Microstructure	Alloy designation	Ref.
1	Ni47.9-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 microstructure	Solution Treated (ST) at 1210°C/10h to Homogenize; Aging at 800°C/20h	γ +γ' - L12 -Ni3(Ti,Al) (69% 290nm avg. size)	TKT-HESA1-FCC-Ti5.8	Gaber15, Tsao et al.16
2	Al6.25-C1-Co15-Cr13-Fe4.5-Mo1.75-Nb0.6-Ni48-V5-Ti5	Vac. arc melting (5 times) and suction casting	ST 1175°C/2h-850°C/8h-650°C/8h-Water Quenched (WQ)	60% vol. fraction of γ' - L12 ; 450nm sized γ'	KWG-HESA2-FCC-Ti5	Gaber15
3	Al10-Co25-Cr8-Fe15-Ni36-Ti6	Vac. induction melted and solidified directionally	Homogenized at 1220°C/20h/Furnace Cooled (FC)-900°C/5h/Air Cooled (AC)	L12 γ' Ni3 (Ti,Al) (45% Vf/450nm) in γ FCC solid sol. & B2/NiAl (needle like -up to 50μm long) (< 5% Vf) precipitates	HMD-HESA3-FCC-Ti6-5H	Daoud et al.17
4	Al10-Co25-Cr8-Fe15-Ni36-Ti6	Vac. induction melted and solidified directionally	Homogenized at 1220°C/20h/FC-900°C/50h/AC	L12 γ'-Ni3(Ti,Al)(46% Vf/460nm) in γ FCC solid sol. & B2/NiAl (needle like, up to 50μm long) (<5% Vf) ppts	HMD-HESA3-FCC-Ti6-50H	Daoud et al.17
5	Al20.4-Mo10.5-Nb22.4-Ta10.1-Ti17.8-Zr18.8	Vac. arc melting-remelted 5 times	AC, Hot Isostatic Pressing (HIP) at 1400°C/207 MPa/2h, 1400°C/24 in Ar	BCC1+BCC2; 75 μm avg. grain size; nanolamellar structures of the two phases	ONS-BCC-Ti17.8	Senkov et al.18,19
6	Al21.9-Nb32-Ta9-Ti26.7-Zr10.3	Vac. arc melting-remelted 5 times	AC, HIP at 1400°C/207 MPa/2h, 1400°C/24h in Ar	BCC; 2000 μm avg. grain size; nanophases	ONS-BCC-Ti26.7	Senkov et al.18,19
7	Al7.9-Hf12.8-Nb23-Ta16.8-Ti18.9-Zr20.6	Vac. arc melting-remelted 5 times	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h in Ar	BCC; 140 μm avg. grain size; nanophases	ONS-BCC-Ti18.9	Senkov et al.18,19
8	Al5.7-Nb23.5-Ta17.6-Ti27.2-Zr26	Vac. arc melting-remelted 5 times	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h in Ar	BCC1+BCC2; 200 μm avg. grain size; nanolamellar structures of the two phases	ONS-BCC-Ti27.2	Senkov et al.18,19
9	Al5.2-Nb23.4-Ta13.2-Ti27.7-V4.3-Zr26.2	Vac. arc melting-remelted 5 times	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h in Ar	BCC; 180 μm avg. grain size; nanophases	ONS-BCC-Ti27.7	Senkov et al.18,19
10	Al11.3-Nb22.3-Ta13.1-Ti27.9-V4.5-Zr20.9	Vac. arc melting-remelted 5 times	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h in Ar	BCC1+BCC2; 100 μm avg. grain size; nanolamellar structures of the two phases	ONS-BCC-Ti27.9	Senkov et al.18,19
11	Al26.6-Nb23.8-Ti25.1-V24.5	Vac. arc melting - remelting 5 times - and casting	Homogenized at 1200°C/24h	BCC SS (300 to 400 μm grain size)	NDS-BCC-Ti25.1	Stepanov et al.20
12	Nb20-Cr20-Mo10-Ta10-Ti20-Zr20	Vac. arc melting and re-melted 5 times and casting	AC, HIP at 1450°C/207 MPa/3h	BCC1 (67% Vf) +BCC2 (16% Vf)+Laves (FCC) (17% Vf)	ONS-BCC-Ti20	Senkov and Woodward21
13	Nb28.3-Ti24.5-V23-Zr24.2	Vac. arc melting and re-melted 5 times and casting	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h	BCC+submicron ppts	DBM-BCC-Ti24.5	Senkov et al.22,23
14	Nb22.6-Ti19.4-V37.2-Zr20.8	Vac. Arc Melting and re-melted 5 times and casting	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h	BCC1+BCC2+BCC3	DBM-BCC-Ti19.4	Senkov et al.22,23
15	Cr24.6-Nb26.7-Ti23.9-Zr24.8	Vac. arc melting and re-melted 5 times and casting	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h	BCC+Laves (ordered FCC)	DBM-BCC-Ti23.9	Senkov et al.22,23
16	Cr20.2-Nb20-Ti19.9-V19.6-Zr20.3	Vac. arc melting and re-melted 5 times and casting	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h	BCC+Laves (ordered FCC)	DBM-BCC-Ti19.9	Senkov et al.22,23
17	Hf20-Mo20-Nb20-Ti20-Zr20	Vac. arc melting and re-melted 5 times and casting	AC, Homogenized at 1100°C/10h/SC	BCC (dendritic)-no ordered phases	NNG-BCC-Ti20	Guo et al.24
18	Ta19.68-Nb18.93-Hf20.46-Zr21.23-Ti19.7	Vac. arc melting and casting	AC, HIP at 1200°C/207 MPa/2h, 1200°C/24h (only homogenized)	BCC (dendritic and nonuniform); equiaxed grains about 100μm bottom to 200 μm at the top	ONS-BCC-Ti19.7	Senkov et al.25
19	Ti20-Zr20-Hf20-Nb20-V20	Vac. induction melting and cast	As-Cast	BCC+U (unknown intermetallic phase)	EF-BCC-V20-Ti20	Fazakas et al.26
20	Ti20-Zr20-Hf20-Nb20-Cr20	Vac. induction melting and cast	As-Cast	BCC+Laves (L1+L2)	EF-BCC-Cr20-Ti20	Fazakas et al.26

Table 2
The properties—density (ρ), yield strength (0.2% strain offset) at room temperature (0.2% YS-RT), and yield strength (0.2% strain offset) at 800 °C (0.2% YS-800 °C)—of the Ti-containing high-entropy alloys (from the literature) identified for the data-driven analyses.

Alloy designation	ΔSconfig/R (mol-1)	Density (ρ) (g/cm3)	0.2% YS-RT (MPa)	0.2% YS-800 °C (MPa)	Test type	Ref.
TKT-HESA1-FCC-Ti5.8	1.60	7.44	875	800	Tensile	Gaber15, Tsao et al.16
KWG-HESA2-FCC-Ti5	1.66	7.60	1000	700	Compressive	Gaber15
HMD-HESA3-FCC-Ti6-5H	1.60	7.38	568	535	Tensile	Daoud et al.17
HMD-HESA3-FCC-Ti6-50H	1.60	7.38	596	581	Tensile	Daoud et al.17
ONS-BCC-Ti17.8	1.75	7.21	2000	1597	Compressive	Senkov et al.18,19
ONS-BCC-Ti26.7	1.50	6.74	1280	728	Compressive	Senkov et al.18,19
ONS-BCC-Ti18.9	1.74	8.86	1841	796	Compressive	Senkov et al.18,19
ONS-BCC-Ti27.2	1.51	7.91	1965	362	Compressive	Senkov et al.18,19
ONS-BCC-Ti27.7	1.60	7.49	1965	678	Compressive	Senkov et al.18,19
ONS-BCC-Ti27.9	1.67	7.27	2035	796	Compressive	Senkov et al.18,19
NDS-BCC-Ti25.1	1.39	5.46	1020	685	Compressive	Stepanov et al.20
ONS-BCC-Ti20	1.76	8.19	1595	983	Compressive	Senkov and Woodward21
DBM-BCC-Ti24.5	1.38	6.50	1105	187	Compressive	Senkov et al.22,23
DBM-BCC-Ti19.4	1.35	6.44	918	240	Compressive	Senkov et al.22,23
DBM-BCC-Ti23.9	1.39	6.66	1260	300	Compressive	Senkov et al.22,23
DBM-BCC-Ti19.9	1.61	6.53	1298	615	Compressive	Senkov et al.22,23
NNG-BCC-Ti20	1.61	8.62	1575	825	Compressive	Guo et al.24
ONS-BCC-Ti19.7	1.61	9.79	929	535	Compressive	Senkov et al.25
EF-BCC-V20-Ti20	1.61	8.00	1170	1148	Compressive	Fazakas et al.26
EF-BCC-Cr20-Ti20	1.61	8.00	1375	1325	Compressive	Fazakas et al.26

2.2. 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; and (b) subjective—that takes experts' opinions (sound judgement based on the intended application) and designers' opinions (design constraints) to quantify the relative weights of the attributes. We adopted both objective and subjective attribute weights in this investigation. The objective attribute weights were evaluated by Shannon's entropy method⁴²; on the other hand, equal weights (1/3) were assigned to each of the attributes (ρ, 0.2% YS-RT, and 0.2% YS-800°C) for subjective weights. The ten MADM methods identified for the investigation are as follows: Simple additive weighting (SAW)^33,34,43,44, Simple multi-attribute rating technique (SMART)^33,45,46, Multiplicative exponent weighting (MEW)^33,41,47, Technique of order preference by similarity to ideal solutions (TOPSIS)^33,41,48,49, Weighted Euclidean distance-based approach (WEDBA)^34,50,51, Multi-objective optimization on the basis of ratio analysis (MOORA)^52,53, Operational competitiveness ratio (OCRA)^54-56, Multi-criteria optimization and compromise solution (VIKOR, a Siberian abbreviation)^57-59, Additive ratio assessment method (ARAS)^60-62, and Range of value method (ROVM)^63,64. The modus operandi of the MADMs was soft-coded in Microsoft Excel. While there are numerous MADMs available in the literature, we chose the above ten MADMs owing to the diverse applications of the methods across industries^33,35.

2.3. 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)^67-69. 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.

3. Results and Discussion

Table 3 presents the descriptive statistics of the Ti-containing 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 ~1.30 mol^-1, 8.28 g/cm³, 1034 MPa, and 758 MPa (at 760°C), respectively^29-31. 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/cm³) 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.

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

Attribute	Minimum	Maximum	Range	Mean±stdev
ΔSconfig/R (mol-1)	1.35	1.76	0.41	1.58±0.12
ρ (g/cm3)	5.46	9.79	4.33	7.47±0.98
0.2% YS-RT (MPa)	568	2035	1467	1319±464
0.2% YS-800 °C (MPa)	187	1597	1410	721±351

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

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-Ti17.8 as 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 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.

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

	SAW	SMART	MEW	TOPSIS	WEDBA	MOORA	OCRA	VIKOR	ARAS
SMART	0.941
MEW	0.872	0.741
TOPSIS	0.950	0.844	0.923
WEDBA	0.877	0.965	0.618	0.770
MOORA	0.985	0.916	0.907	0.974	0.845
OCRA	0.877	0.728	0.965	0.956	0.617	0.919
VIKOR	0.941	1.000	0.741	0.844	0.965	0.916	0.728
ARAS	0.979	0.910	0.920	0.973	0.836	0.995	0.929	0.910
ROVM	0.941	1.000	0.741	0.844	0.965	0.916	0.728	1.000	0.910

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). Figure 4b shows the PCA-based consolidation (score plot) of the ranks of Ti-containing high-entropy alloys from the ten MADMs. The score plot presents the first two components (PC1 and PC2), post-reduction of the data dimension (10, 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. An imaginary reference line (perpendicular to PC1) traversing from left to right (-5 to 5) indicates the overall ranks of the alloys. The alloys ONS-BCC-Ti17.8 (Al_20.4-Mo_10.5-Nb_22.4-Ta_10.1-Ti_17.8-Zr_18.8), EF-BCC-Cr20-Ti20 (Ti₂₀-Zr₂₀-Hf₂₀-Nb₂₀-Cr₂₀), ONS-BCC-Ti27.9 (Al_11.3-Nb_22.3-Ta_13.1-Ti_27.9-V_4.5-Zr_20.9), ONS-BCC-Ti27.7 (Al_5.2-Nb_23.4-Ta_13.2-Ti_27.7-V_4.3-Zr_26.2), and ONS-BCC-Ti20 (Nb₂₀-Cr₂₀-Mo₁₀-Ta₁₀-Ti₂₀-Zr₂₀) are the top five alloys in that order. The five top-ranked alloys by PCA-based consolidation are strikingly similar to the top-ranked alloys by mean-based rank consolidation. Additionally, the PCA-based rank consolidation refines the ranks of ONS-BCC-Ti-27.7 and ONS-BCC-Ti20 to rank#4 and rank#5, respectively, both of which were tied at rank four by mean-based rank consolidation. All the top five Ti-containing high-entropy alloys have configurational entropy greater than 13.3 J/K mol and body-center cubic crystal structure. Specifically, the alloy ONS-BCC-Ti17.8 (Al_20.4-Mo_10.5-Nb_22.4-Ta_10.1-Ti_17.8-Zr_18.8) (rank#1) has significantly superior properties to the benchmark it is lighter than the current industry benchmark, Inconel 718, by ~13%. By assigning higher weightage to density (in the Ranking routine) compared to the other properties, the alloy NDS-BCC-Ti25.1 (Al_26.6-Nb_23.8-Ti_25.1-V_24.5 ) (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.

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 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.

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10
Eigenvalue	8.9787	0.8556	0.0752	0.0357	0.0232	0.0156	0.0119	0.0030	0.0000	0.0000
Proportion	0.898	0.086	0.008	0.004	0.002	0.002	0.001	0.000	0.000	0.000
Cumulative	0.898	0.984	0.991	0.995	0.997	0.999	1.000	1.000	1.000	1.000

Miracle and Senkov²⁷ 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 strengthening⁷⁰ 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.

4. 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 decision-making (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-Ti17.8 (Al_20.4-Mo_10.5-Nb_22.4-Ta_10.1-Ti_17.8-Zr_18.8), EF-BCC-Cr20-Ti20 (Ti₂₀-Zr₂₀-Hf₂₀-Nb₂₀-Cr₂₀), ONS-BCC-Ti27.9 (Al_11.3-Nb_22.3-Ta_13.1-Ti_27.9-V_4.5-Zr_20.9), ONS-BCC-Ti27.7 (Al_5.2-Nb_23.4-Ta_13.2-Ti_27.7-V_4.3-Zr_26.2), and ONS-BCC-Ti20 (Nb₂₀-Cr₂₀-Mo₁₀-Ta₁₀-Ti₂₀-Zr₂₀) in that order; and recommends them for further development for the potential replacement of legacy superalloys in aeroengine turbine applications. The top-ranked alloy Al_20.4-Mo_10.5-Nb_22.4-Ta_10.1-Ti_17.8-Zr_18.8 is lighter than the current industry benchmark, Inconel 718, by ~13%. All the top five Ti-containing high-entropy alloys have configurational entropy greater than ~13.3 J/K mol and body-center cubic crystal structure. The investigation provides directives and guidelines to focus on further developing the identified Ti-containing high-entropy alloys. The potency of the methodology could further be tapped by effectively and appropriately choosing the weights of the properties for specific aeroengine turbine applications.

5. Acknowledgements

The corresponding author Ramachandra Canumalla thanks the Weldaloy Specialty Forgings management for all the support (R&D account# 8860.00). The other corresponding author T. V. Jayaraman thanks the College of Engineering and Computer Science (grant# 049150) and the Institute of Advanced Vehicle Systems (grant# 052349) at the University of Michigan-Dearborn for the support.

6. References

• ¹
  IATA: International Air Transport Association. Tourism economics air passenger forecasts. 2020.
• ²
  Bickers C, Bergman P. Boeing forecasts $8.7 Trillion Aerospace and Defense Market through 2028. Boeing; 2019.
• ³
  Fischer T, Denden M. Airbus forecasts need for over 30,000 new aircraft in the next 20 years. Airbus; 2019.
• ⁴
  Scherer C. Global market forecast. Airbus; 2019.
• ⁵
  Norris G. What radical engine changes means for the aftermarket. Aviation Week Network; 11 sep 2020.
• ⁶
  Ambrose J. Airbus reveals plans for zero-emission aircraft fueled by hydrogen. The Guardian; 21 sep 2020.
• ⁷
  Eylon D, Fujishiro S, Postans PJ, Froes FH. High-temperature titanium alloys: a review. J Met. 1984;1:55-62.
• ⁸
  Gogia AK. High-temperature titanium alloys. Def Sci J. 2005;55(2):149-73.
• ⁹
  Rao MN. Materials for gas turbines: an overview. In: Benini E, editor. Advances in gas turbine technology. London: IntechOpen; 2010. p. 293-314.
• ¹⁰
  Canumalla R. On the low tensile ductility at room temperature in high temperature titanium alloys. SCIREA J Metall Eng. 2020;4(2):16-51.
• ¹¹
  Bewlay B, Nag S, Suzuki A, Weimer M. TiAl alloys in commercial aircraft engines. Mater High Temp. 2016;33(4-5):549-59.
• ¹²
  Janschek P. Wrought TiAl blades. Mater Today Proc. 2015;2(1):S92-7.
• ¹³
  Sallot P, Martin G, Knittel S. Implementation of γ-TiAl alloys for low pressure turbine blades: opportunities and new challenges. In: TMS 2017; 2017; San Diego, California. Proceedings. Pittsburgh: TMS; 2017.
• ¹⁴
  Boyer RR, Cotton JD, Mohaghegh M, Schafrik RE. Materials considerations for aerospace applications. MRS Bull. 2015;49(12):1055-66.
• ¹⁵
  Gaber KW. The design and characterization of HEA for high-temperature applications. New Mexico: New Mexico Institute of Mining and Technology; 2020.
• ¹⁶
  Tsao TK, Yeh AC, Kuo CM, Kakehi K, Murakami H, Yeh JW, et al. The high temperature tensile and creep behaviors of high entropy superalloy. Sci Rep. 2017;7(1):12658.
• ¹⁷
  Daoud HM, Manzoni AM, Wanderka N, Glatzel U. High-temperature tensile strength of Al10Co25Cr8Fe15Ni36Ti6 compositionally complex alloy (high entropy alloy). J Mater. 2015;67:2271-7.
• ¹⁸
  Senkov ON, Senkova SV, Woodward C. Effect of aluminum on the microstructure and properties of two refractory high entropy alloys. Acta Mater. 2014;68:214-28.
• ¹⁹
  Senkov ON, Woodward C, Miracle DB. Microstructure and properties of aluminum-contaning refractory high entropy alloys. J Mater. 2014;66(10):2030-42.
• ²⁰
  Stepanov ND, Shaysultanov DG, Salishchev GA, Tikhonovsky MA. Structure and mechanical properties of a lightweight AlNbTiV high entropy alloy. Mater Lett. 2015;142:153-5.
• ²¹
  Senkov ON, Woodward CF. Microstructure and properties of a refractory NbCrMo0.5Ta0.5TiZr. Mater Sci Eng A. 2011;529:311-20.
• ²²
  Senkov ON, Senkova SV, Woodward C, Miracle DB. Low-density refractory multi-principal element alloys of CrNbTiVZr system: microstructure and phase analysis. Acta Mater. 2013;61(5):1545-57.
• ²³
  Senkov ON, Senkova SV, Miracle DB, Woodward C. Mechanical properties of low-density refractory multi-principal element alloys of CrNbTiVZr system. Mater Sci Eng A. 2013;565:51-62.
• ²⁴
  Guo NN, Wang L, Luo LS, Li XZ, Su YQ, Guo JJ, et al. Microstructure and mechanical properties of refractory MoNbHfZrTi high entropy alloy. Mater Des. 2015;81:87-94.
• ²⁵
  Senkov ON, Scott JM, Senkova SV, Meisenkothen F, Miracle DB, Woodward CF. Microstructure and elevated temperature properties of a refractory TaNbHfZrTi alloy. J Mater Sci. 2012;47(9):4062-74.
• ²⁶
  Fazakas É, Zadorozhnyy V, Varga LK, Inoue A, Louzguine-Luzgin DV, Tian F, et al. Experimental and theoretical study of Ti₂₀Zr₂₀Hf₂₀Nb₂₀X₂₀ (X 1/4 V or Cr) refractory high entropy alloys. Int J Refract Hard Met. 2014;47:131-8.
• ²⁷
  Miracle DB, Senkov ON. A critical review of high entropy alloys and related concepts. Acta Mater. 2017;122:448-511.
• ²⁸
  Jumaev E, Abbas MA, Mun SC, Song G, Hong SJ, Kim KB. Nano-scale structural evolution of quaternary AlCrFeNi based high entropy alloys by the addition of specific minor elements and its effect on mechanical characteristics. J Alloys Compd. 2021;868:159217.
• ²⁹
  Special Metals. INCONEL alloy 718 data dheet. Huntington, WV; 2007.
• ³⁰
  High Temp Metals. INCONEL 718 technical data [Internet]. 2015 [cited 2022 Apr 27]. Available from: https://www.hightempmetals.com/techdata/hitempInconel718data.php
  » https://www.hightempmetals.com/techdata/hitempInconel718data.php
• ³¹
  SAE International. Alloy bars, forgings, and rings, corrosion and heat resistant nickel base - 19Cr - 3.1Mo - 5.1(Cb + Ta) - 0.90Ti - 0.50Al solution and precipitation heat treated consumable electrode or vacuum induction melted AMS5663. Warrendale: SAE International; 2022.
• ³²
  Jahan A, Ismail MY, Sapuan SM, Mustapha F. Materials screening and choosing methods: a review. Mater Des. 2010;31(2):696-705.
• ³³
  Tzeng GH, Huang JJ. Multiple attribute decision making methods and applications. Boca Raton: CRC Press; 2011.
• ³⁴
  Rao RV. Decision making in the manufacturing environment, Using graph theory and fuzzy multiple attribute decision making methods. Berlin: Springer; 2007.
• ³⁵
  Zavadskas EK, Turskis Z, Kildiene S. State of art surveys of overviews on MCDM/MADM methods. Technol Econ Dev Econ. 2014;20(1):165-79.
• ³⁶
  Teraiya V, Jariwala D, Patel HV, Babariya D. Material selection of connecting rod using primary multi attribute decision making methods: a comparative study. Mater Today Proc. 2018;5(9):17223-30.
• ³⁷
  Kumar R, Singal SK. Penstock material selection in small hydropower plants using MADM methods. Renew Sustain Energy Rev. 2015;52:240-55.
• ³⁸
  Yang WC, Chon SH, Choe CM, Kim UH. Materials selection method combined with different MADM methods. J Artif Intell. 2019;1(2):89-99.
• ³⁹
  Yazdani M. New approach to select materials using MADM tools. Bus Syst Res. 2018;12(1):25-42.
• ⁴⁰
  Mahesh V, Joladarashi S, Kulkarni SM. A comprehensive review on material selection for polymer matrix composites subjected to impact load. Defence Technol. 2021;17(1):257-77.
• ⁴¹
  Jahan A, Edwards KL, Bahraminasab M. Multi-criteria decision analysis: for supporting the selection of engineering materials in product design. 2nd ed. Oxford: Butterworth-Heinemann; 2016.
• ⁴²
  Shannon ME. A mathematical theory of communication. Bell Syst Tech J. 1948;27(3):379-423.
• ⁴³
  Afshari A, Mojaahed M, Yusuff RM. Simple additive weighting approach to personal selection problem. Int J Innov Manag Technol. 2010;1(5):511-5.
• ⁴⁴
  Memariani A, Amini A, Alinezhad A. Sensitivity analysis of simple additive weighting method (SAW): the results of change in the weight of one attribute on the final ranking alternatives. J Indust Eng. 2009;4:13-8.
• ⁴⁵
  Siregar D, Arisandi D, Usman A, Irwan D, Rahim R. Research of simple multi-attribute rating technique for decision support. J Phys Conf Ser. 2017;930:012015.
• ⁴⁶
  Patel MR, Vashi MP, Bhatt BV. SMART-Multi-criteria decision-making technique for use in planning activities. In: New Horizons in Civil Engineering; 2017; Surat, Gujarat, India. Proceedings. New Haven: International Society for Industrial Ecology; 2017.
• ⁴⁷
  Budiharjo APW, Muhammad A. Comparison of weighted sum model and multi-attribute decision making weighted product methods in selecting the best elementary school in Indonesia. Int J Softw Eng Appl. 2017;11(4):69-90.
• ⁴⁸
  Triantaphyllou E, Shu B, Sanchez SN, Ray T. Multi-criteria decision making: an operations research approach. In: Webster HG, editor. Encyclopedia of electrical and electronics engineering. New York: John Wiley & Sons; 1998. p. 175. (vol. 15).
• ⁴⁹
  Deng H, Yeh CH, Willis RJ. Inter-company comparison using modified TOPSIS with objective weights. Comput Oper Res. 2000;27(10):963-73.
• ⁵⁰
  Rao RV, Singh D. Evaluating flexible manufacturing systems using Euclidean distance-based integrated approach. Int J Risk Manag. 2012;3:32-53.
• ⁵¹
  Rao RV, Singh D. Weighted Euclidean distance-based approach as a multiple attribute decision making method for plant or facility layout design selection. Int J Indust Eng Comp. 2012;3:365-82.
• ⁵²
  Chakraborty S. Applications of the MOORA method for decision making in manufacturing environment. Int J Adv Manuf Technol. 2011;54(9-12):1155-66.
• ⁵³
  Dominguez LP, Mojica KYS, Pabon LCO, Diaz MCC. Application of the MOORA method for the evaluation of the industrial maintenance system. J Phys Conf Ser. 2018;1126:012018.
• ⁵⁴
  Chatterjee P, Chakraborty S. Material selection using preferential ranking methods. Mater Des. 2012;35:384-93.
• ⁵⁵
  Erdoğan S, Aydin S, Balki MK, Sayin C. Operational evaluation of thermal barrier coated diesel engine fueled with biodiesel/diesel blend by using MCDM method base on engine performance, emission and combustion characteristics. Renew Energy. 2020;151:698-706.
• ⁵⁶
  Darji VP, Rao RV. Intelligent multi-criteria decision making methods for material selection in sugar industry. Procedia Mater Sci. 2014;5:2585-94.
• ⁵⁷
  Gul M, Celik E, Aydin N, Gumus AT, Guneri AF. A state of the art literature review of VIKOR and its fuzzy extensions on applications. Appl Soft Comput. 2016;46:60-89.
• ⁵⁸
  Sayadi MM, Heydari M, Shahanaghi K. Extension of VIKOR method for decision making problem with interval numbers. Appl Math Model. 2009;33(5):2257-62.
• ⁵⁹
  Mohanty PP, Mahapatra SS. A compromise solution by VIKOR method for ergonomically designed product with optimal set of design characteristics. Procedia Mater Sci. 2014;6:633-40.
• ⁶⁰
  Zavadskas EK, Turskis Z. A new additive ratio assessment (ARAS) method in multicriterial decision making. Technol Econ Dev Econ. 2010;16(2):159-72.
• ⁶¹
  Zavadskas EK, Turskis Z, Vilutiene T. Multiple criteria analysis of foundation installment alternatives by applying additive ratio assessment (ARAS) method. Arch Civ Mech Eng. 2010;10(3):123-41.
• ⁶²
  Stanujic S, Jovanovic R. Measuring a quality of faculty website using ARAS method. In: International Scientific Conference Contemporary Issues in Business, Management and Education; 2012; Vilnius, Lithuania. Proceedings. Vilnius: Vilnius Gediminas Technical University; 2012. p. 545-54.
• ⁶³
  Madić M, Radovanovic M, Manic M. Application of the ROV method of selection of cutting fluids. Decis Sci Lett. 2016;5:245-54.
• ⁶⁴
  Jha GK, Chatterjee P, Chatterjee R, Chakraborty S. Suppliers selection in a manufacturing environment using a range of value method. Jixie Gongcheng Xuebao. 2013;3(3):16-22.
• ⁶⁵
  Levine DM, Ramsey PP, Smidt RK. Applied statistics for engineers and scientists. Upper Saddle: Prentice-Hall; 2001.
• ⁶⁶
  Navidi W. Statistics for engineers and scientists. 3rd ed. New York: McGraw-Hill Science/Engineering; 2010.
• ⁶⁷
  Rajan K. Materials Informatics. Mater Today. 2005;8(10):38-45.
• ⁶⁸
  Cadima J, Jolliffle IT. Principal component analysis: a review and recent developments. Philos Trans- Royal Soc, Math Phys Eng Sci. 2016;374(2065):20150202.
• ⁶⁹
  George L, Hrubiak R, Rajan K, Saxena SK. Principal component analysis on properties of binary and ternary hydrides and a comparison of metal versus metal hydride properties. J Alloys Compd. 2009;478(1-2):731-5.
• ⁷⁰
  Senkov ON, Scott JM, Senkova SV, Miracle DB, Woodward CF. Microstructure and room temperature properties of a high-entropy alloy TaNbHfzrTi alloy. J Alloys Compd. 2011;509(20):6043-8.

Publication Dates

• Publication in this collection
  06 Jan 2023
• Date of issue
  2023

History

• Received
  27 Apr 2022
• Reviewed
  21 Sept 2022
• Accepted
  30 Nov 2022