**1. Introduction and Background**

The selection of materials for aeroengine applications to meet the stringent requirements of high specific strength, good creep and fatigue resistance, high fracture toughness, oxidation and corrosion resistance, and so forth, is a challenge. To explore suitable materials for applications, including compressor blades, at temperatures of up to ~500 ◦C, an effort to select materials using Cambridge Engineering Selector (CES) software was attempted by maximizing several material performance indices, such as resistance to bending, fatigue, specific stiffness, and so on [1]. The analysis revealed titanium (Ti) alloys provide the best performance in temperatures of up to ~500 ◦C considering the cost and other trade-offs among the other competing alloy systems, viz., low alloy steels, stainless steels, nickel-based superalloys, etc. However, once the selection is zoomed down to Ti alloys, as per the analyses in [1], it is imperative to focus on the choice of apt Ti alloys for applications where strength-efficient structures and corrosion resistance are immanent, including aeroengines [2].

Since the beginning of the historical evolution in 1954, the high-temperature conventional Ti alloys, also known as near-*α* Ti alloys [3–8], are the choice class among the five different categories of Ti alloys for applications in compressor components in temperatures of up to ~600 ◦C in aeroengines [9,10]. The most advanced current commercial near-*α*

**Citation:** Canumalla, R.; Jayaraman, T.V. Decision Science Driven Selection of High-Temperature Conventional Ti Alloys for Aeroengines. *Aerospace* **2023**, *10*, 211. https://doi.org/ 10.3390/aerospace10030211

Academic Editor: Sebastian Heimbs

Received: 10 February 2023 Revised: 22 February 2023 Accepted: 22 February 2023 Published: 24 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Ti alloys are IMI834 and Ti-1100, with the capability for applications up to ~600 ◦C [11,12]. However, several investigations have shown that low tensile ductility at room temperature is a concern, which is attributed to various reasons, such as the precipitation of silicides, silicides aided by Ti3Al, Ti3Al aided by silicides, Ti3Al, etc. [3]. Therefore, alternative thermomechanical processing (TMP) and stability of the microstructures in service conditions are currently being investigated to mitigate the low tensile ductility at room temperature (that is designer specific) in near-*α* Ti alloys, which is critical for compressor components in aeroengines. The standard processing condition for the most current commercial alloy (IMI 834), suitable for up to ~600 ◦C, is typically considered the benchmark. However, generating creep, fatigue, fracture toughness, etc., obtaining data for the intended application/s on every one of those alternatives and variations become time-consuming, tedious, and expensive. Thus, to advance research and perform testing in a limited, faster, less expensive, and more sensible way, it is necessary to sort and select a few alloys, among the several alternative alloys available in the current literature, based on the important and easy to obtain room temperature tensile properties, by adopting decision science driven methods.

Material selection, a holistic approach of selecting an optimal material from a list of materials that is best suited for a given design and application, typically involves compromises between various material properties (mechanical, physical, chemical, etc.), cost, availability, environmental effects, to name a few [13]. The most common approach to material selection is Ashby's material-selection approach—popularly referred to as the materials property chart approach [13–15]. The less common techniques include multiple attribute decision making (MADM) [16–23], cost per unit property method [15,24], Paretooptimal solutions [15], and artificial intelligence methods (e.g., neural networks) [15,25,26]. MADM refers to making preference decisions over the available alternatives (list of materials) characterized by multiple, usually conflicting attributes (i.e., properties) [22,23]. MADM techniques find applications widely in various industries, including but not limited to logistics, management, manufacturing, and so on [27]. In this paper, we compile, evaluate, sort, and select near-*α* Ti alloys in the current literature for high-temperature applications in aeroengines, driven by decision science integrating MADM and principal component analysis (PCA). A combination of 12 MADM methods ranks a list of 105 alloy variants based on the TMP conditions of 19 different near-*α* Ti alloys (the majority are 'research' alloys). PCA, a powerful tool that transforms a multi-dimensional dataset into two dimensions [28–30], consolidates the ranks from various MADMs and identifies the ten top-ranking alloy variants for the intended applications.

#### **2. Methods**

Figure 1 presents a flowchart of the decision science driven selection of near-*α* Ti alloys from the literature for applications in compressor parts in aeroengines. The literature data comprises 105 variants (based on the TMP routes) of 19 distinct near-*α* Ti alloys. The method consists of three key routines: (i) Literature data (compilation of the near-*α* Ti alloys), (ii) Ranking (ranking by MADM methods), and (iii) Analyses (rank consolidation by PCA and interpretation).

**Figure 1.** The flowchart of decision science driven analyses of the near-*α* Ti alloys. It comprises three routines: literature data, ranking, and analyses.

## *2.1. Literature Data*

We compiled a list of near-*α* Ti alloys (alternatives) and their room-temperature mechanical properties (attributes) from the literature. Table A1 (in Appendix A) presents the alternatives, the near-*α* Ti alloys, screened for the current study primarily from peerreviewed journals and conference proceedings [31–52]. The table presents the nominal chemistry, processing conditions, and imminent microstructure. Eleven of the above 19 alloys are 'research' alloys (viz., WJZ-Ti, KIMS, JZ1, JZ2, JL, LD-Ti423, TMC-Ti213, TKT-1, TKT-2, TKT-3, and PC), implying they were fabricated and processed on a laboratory scale (under development) followed by characterization and testing. Eight of the 19 are current commercial alloys (IMI685, IMI829, IMI834, Ti-1100, Ti6242S, TA19, TA29, and Ti60). We identified room temperature % elongation (*%EL*), yield strength (*YS*), and ultimate tensile strength (*UTS*) as the properties (attributes) for the current investigation. For a targeted application, such as the compressor blade, the material needs to satisfy the desired room-temperature attributes (i.e., *%EL*, *YS*, and *UTS*) before examining the other important attributes, namely, the high-temperature properties, including creep resistance, oxidation resistance, and corrosion resistance to optimize the alloy. In the parlance of MADM, all of the identified attributes (*%EL*, *YS*, and *UTS*) are maximizing (or beneficial) attributes, suggesting, for most applications, that the alloys ought to have the following combination: high *%EL*, high *YS*, and high *UTS*. Table A2 (in Appendix A) is the decision matrix comprising the alternatives (near-*α* Ti alloys) and attributes (properties *%EL*, *YS*, and *UTS*) in the literature [31–52].
