Conventional Superalloys Research Articles

Hierarchical ferrous medium entropy with heterogeneous precipitates embedded in core-shell grain structure for superior mechanical properties

Superalloys designed for high-temperature applications, featuring a face-centered cubic matrix and L12 precipitates, have shown excellent tensile properties at both room and elevated temperatures. However, the substantial Ni and Co, necessary for generating a high fraction of the ordered L12 phase within the matrix, results in high mass density and cost, subsequently limiting their widespread industrial application. It is important to increase Fe content over Ni and Co while preserving outstanding mechanical properties at ambient and high temperatures. In this study, we propose a novel approach to introduce a hierarchical structure in a 60-at%-Fe-based medium entropy alloy. The heterogeneous nano-precipitates embedded in harmonic (core-shell) grain structure reinforce mechanical contrast between soft and hard domains, achieving an excellent heterostructure. The present alloy incorporates hierarchical heterogeneity at multi-scales, combining heterogeneous grain at micrometers, precipitates at tens of nanometers, and elemental fluctuation at nanometers. This hierarchical structure shows superior mechanical properties at room and high temperatures comparable to those of conventional superalloys. Further, the high content of Fe in this alloy system shows excellent performance in alloy cost and mass density. This work suggests the unique hierarchical heterostructure to overcome the trade-off dilemma in alloy cost, mass density, and mechanical properties in room/elevated temperatures.

Novel Ni-Co-Cr-Al eutectic high-entropy superalloys with superb mechanical properties

Eutectic high-entropy alloys (EHEAs) with superior castability and mechanical properties are attractive for high-temperature applications. In this work, the novel Ni70-xCo10Cr20Alx eutectic high-entropy superalloys (EHESs) that have attained a ∼13 % reduction in density compared to the conventional superalloys, with the outstanding balance between mechanical properties and density were reported. These EHESs possess a lamellar heterogeneous structure consisting of face-centered cubic (FCC) and ordered body-centered cubic (B2) phases with L12 and BCC nano-precipitates, respectively. Moreover, the EHESs exhibit superb tensile properties at ambient and high temperatures, e.g. Ni52Co10Cr20Al18 alloy exhibited a yield and ultimate tensile strength and elongation of ∼787 MPa, ∼1133 MPa and ∼7.0 % respectively at ambient temperature; a yield and ultimate tensile strength of ∼563 MPa and ∼618 MPa at 750 ℃, which is even higher than those of the reported EHESs and traditional nickel-based superalloys at 700 ℃. It is revealed that the excellent combination of strength and plasticity originated from the synergic effects of the solid solution strengthening of Al, back stress hardening of finer eutectic lamellar structure, and precipitation strengthening of high-density nano-precipitates. Besides, deformation twins, superlattice stacking faults, and the anti-phase boundaries in the FCC(L12) phase further improved high-temperature strength and strain-hardening ability.

Study of phase equilibrium of refractory high-entropy alloys using the atomic size difference concept for turbine blade applications

Abstract In the pursuit of advancing turbine blade materials, refractory high-entropy alloys (RHEAs) have emerged as promising candidates, offering superior performance at elevated temperatures compared to conventional superalloys. With the plateauing of melting temperatures in Ni-based superalloys, the demand for innovative material systems capable of substantial performance enhancements in turbines has increased. The expansive compositional space of high-entropy alloys (HEAs) presents a rich yet underexplored realm, particularly concerning the intricate phase equilibria pivotal for alloy stability at high temperatures. This research purpose is to elucidate the phase formation dynamics within the W–Re–Ni–Co–Mo HEA system across varying atomic percentages of each constituent element. Employing two-dimensional mapping methodology for correlating atomic size difference and enthalpy mix parameters, enabling the differentiation between intermetallic (IM) phase and single-phase formations in the non-equimolar W–Re–Ni–Co–Mo system across numerous atomic percentages of each element. Major findings indicate distinct phase formations based on elemental compositions, with elevated nickel and rhenium percentages favouring single-phase solid solution (SPSS) structures, while diminished concentrations yield alternative configurations such as (IM + SPSS). Similarly, variations in tungsten and molybdenum concentrations influence phase stability. The ability to assess phases for diverse atomic percentages of elements in the W–Re–Ni–Co–Mo system will facilitate to analyse HEA systems for high-temperature turbine blades.

Ultrahigh intermediate-temperature strength and good tensile plasticity in chemically complex intermetallic alloys via lamellar architectures

As a newly emerged class of materials, chemically complex intermetallic alloys (CCIMAs) with exceptional thermal and mechanical properties are a promising candidate for high-temperature structural use. However, serious intergranular embrittlement at intermediate temperatures (600∼800 °C) is frequently found in those CCIMAs, obstructing their large-scale engineering applications. In this study, through deliberately tailoring thermomechanical processing, we designed a lamellar-structured (LS) L12-type Co-Ni-Al-Ti-Ta-Nb-B-based CCIMA that effectively overcomes this critical issue. The LS-CCIMA exhibits an excellent yield strength (YS) of ∼1.0 GPa with a large tensile elongation of ∼17% at room temperature. More prominently, it also presents an anomalous YS of ∼1.2 GPa combined with an acceptable tensile elongation of ∼10% at intermediate temperatures ranging from 600 to 800 °C, outperforming those of many other simple ordered intermetallics and conventional superalloys. Such superb immediate-temperature strengths primarily originate from the high anti-phase boundary energy caused by the addition of multiple alloying elements (Ti, Ta, and Nb) and the pile-ups of geometrically necessary dislocations. Moreover, we attribute the acceptable tensile plasticity to the increased plastic deformation capacities from the activation of various deformation-induced substructures (e.g., dislocation pairs at 600 °C and superlattice intrinsic stacking faults at 800 °C) and the inhibiting mechanisms of the lamellar structures on oxygen-induced grain boundary damage and microcrack's propagation. This work provides a new pathway for the innovative design of strong-yet-ductile heat-resistant CCIMAs.

Ultrastrong High‐Ductility Ni35Co35Fe10Al10Ti8B2 High‐Entropy Alloy Strengthened with Super‐High Concentration L12 Precipitates

L12 phase hardening alloys with excellent mechanical properties are of great significance for structural applications. However, low volume fractions of L12 precipitates in conventional alloys (nearly lower than 60%) tend to limit their practical usage, while the strengths of the alloys generally increase with L12 precipitation contents. Herein, a novel high‐entropy alloy (HEA) Ni35Co35Fe10Al8Ti10B2 with ultrahigh concentration L12 precipitates is successfully designed aided by the calculation of phase diagrams (CALPHAD). The volume fraction of L12 precipitates in this HEA is up to 75% and outperforms that of most of traditional superalloys. The novel L12‐strengthened Ni35Co35Fe10Al8Ti10B2 has an ultrahigh tensile yield strength of ≈1.45 GPa, ultimate tensile strength of ≈1.9 GPa, and great ductility of ≈23% at room temperature. The desirable strength–ductility combination is superior to most of conventional superalloys and reported HEAs, mainly due to the presence of ultrahigh concentration L12 precipitates that act as dislocation obstacles and the formation of numerous stacking faults and deformation twining. This work is expected to provide guidance for developing new high‐performance HEAs with an excellent combination of strength and ductility.

A L12 precipitation strengthened Co-free medium-entropy alloy with superior high-temperature performance

In present work, the superior high-temperature properties in a novel (Ni, Cr, Fe)3(Al, Ti, Cr)-γʹ (L12) type precipitation-strengthened Co-free medium-entropy alloy (MEA) was systematically evaluated. Experimental results indicate that this γʹ-strengthened alloy demonstrates excellent structure thermal stability and no other brittle intermetallic phases formed at grain boundaries or grain interior during long-term thermal exposures. The γʹ phase in this Co-free MEA exhibits an extraordinary sluggish coarsening rate, which is much lower than most conventional superalloys and recently developing γʹ-strengthened high/medium-entropy alloys (HEAs/MEAs). This γʹ-strengthened alloy also exhibits a good combination of high γʹ-solvus temperature (1068 °C) and low mass density (7.79 g/cm3). More significantly, this γʹ-strengthened MEA shows excellent high-temperature tensile strength, especially outstanding specific strength, which is superior to most Ni/Co-based superalloys. Our present work provides a useful illustration for designing advanced high-temperature alloys based on γʹ(L12)-strengthened HEAs/MEAs, rather than Ni-based/Co-based superalloys.

Lightweight, ultrastrong and high thermal-stable eutectic high-entropy alloys for elevated-temperature applications

Eutectic high-entropy alloys (EHEAs) that combine the advantages of HEAs and eutectic alloys are promising candidates for high-temperature applications. However, currently developed EHEAs still exhibit high densities and low high-temperature strengths, which limit their usage. Here we propose a strategy to design lightweight, strong, and high thermal-stable EHEAs by introducing an extremely stable Heusler-type ordered phase (L21 phase) containing a high-content of low-density elements and constructing a low lattice misfit eutectic-phase interface, which can lead to generate ultrafine and stable lamellar structures and high-density of coherent nanoprecipitates. As a manifestation of this strategy, a novel bulk Al17Ni34Ti17V32 EHEA was designed to consist of L21 and body-centered-cubic (BCC) phases (interlamellar spacing ∼ 320 nm) with a lattice misfit only 2.4%. This alloy has one of the lowest densities (∼ 6.2 g/cm3) among all EHEAs reported previously and exhibits much higher high-temperature hardness and specific yield strengths than most reported refractory HEAs (RHEAs), lightweight HEAs (LWHEAs), EHEAs, and conventional superalloys. This work paves the way to develop light EHEAs with excellent high-temperature properties.

Inhibiting creep in nanograined alloys with stable grain boundary networks.

Creep, the time-dependent deformation of materials stressed below the yield strength, is responsible for a great number of component failures at high temperatures. Because grain boundaries (GBs) in materials usually facilitate diffusional processes in creep, eliminating GBs is a primary approach to resisting high-temperature creep in metals, such as in single-crystal superalloy turbo blades. We report a different strategy to inhibiting creep by use of stable GB networks. Plastic deformation triggered structural relaxation of high-density GBs in nanograined single-phased nickel-cobalt-chromium alloys, forming networks of stable GBs interlocked with abundant twin boundaries. The stable GB networks effectively inhibit diffusional creep processes at high temperatures. We obtained an unprecedented creep resistance, with creep rates of ~10^-7 per second under gigapascal stress at 700°C (~61% melting point), outperforming that of conventional superalloys.

Mechanical and thermal behaviors of Ti36-Al16-V16-Fe16-Cr16 high entropy alloys fabricated by spark plasma sintering: An advanced material for high temperature/strength applications

Conventional superalloys possess high strength, high oxidation resistance and high creep resistance. Nonetheless, some lose strength at elevated temperatures, while others suffer high temperature oxidation and creep. This work was aimed at developing high entropy alloy (HEA) of Ti36-Al16-V16-Fe16-Cr16 at near equi molar configuration using spark plasma sintering technique which would be able to address the challenges of conventional superalloys. The powders were mixed with Turbular mixer at 69 rpm for 10 h. The sintering was carried out with the same sintering pressure of 40 MPa, time of 10 min, heating rate of 100°C/mins on all the samples. Only the sintering temperature was varied. The temperatures used included 700°C, 800°C, 900°C, 1000°C and 1100°C, respectively. The powders and sintered samples were characterized with Scanning electron microscopy connected to Energy Dispersive Spectroscopy and X-ray diffractometer. The mechanical properties were tested with Nano indenter using ASTM D785 standard; while the thermal stability was investigated with thermogravimetric analyzer. Results showed that HEA sintered at 1000°C possessed the best nanomechanical, thermal and microstructural properties while that sintered at 700°C had the weakest properties. The best developed alloy had an improved elastic modulus of 671.17 ± 50 GPa and 930.12 ± 38 GPa at darker flakey phase and white phase, respectively. It had creep resistance of 1.82%, densification of 98.96% and porosity of 1.04%. It was concluded that the developed alloy can perform much better than most superalloys in high temperature and high strength and applications.

Metal-carbide eutectics with multiprincipal elements make superrefractory alloys.

Materials with excellent high-temperature strength are now sought for applications in hypersonics, fusion reactors, and aerospace technologies. Conventional alloys and eutectic multiprincipal-element alloys (MPEAs) exhibit insufficient strengths at high temperatures due to low melting points and microstructural instabilities. Here, we report a strategy to achieve exceptional high-temperature microstructural stability and strength by introducing eutectic carbide in a refractory MPEA. The synergistic strengthening effects from the multiprincipal-element mixing and strong dislocation blocking at the interwoven metal-carbide interface make the eutectic MPEA not only have outstanding high-temperature strength (>2 GPa at 1473 K) but also alleviate the room-temperature brittleness through microcrack tip blunting by layered metallic phase. This strategy offers a paradigm for the design of the next-generation high-temperature materials to bypass the low–melting point limitation of eutectic alloys and diffusion-dominated softening in conventional superalloys.

Heat Transfer, Thermal Stress and Failure Inspection of a Gas Turbine Compressor Stator Blade Made of Five Different Conventional Superalloys and Ultra-High-Temperature Ceramic Material: A Direct Numerical Investigation

Heat Transfer, Thermal Stress and Failure Inspection of a Gas Turbine Compressor Stator Blade Made of Five Different Conventional Superalloys and Ultra-High-Temperature Ceramic Material: A Direct Numerical Investigation

A microstructure-based creep model for additively manufactured nickel-based superalloys

Creep fracture is a general failure mode for nickel-based superalloy components made by additive manufacturing (AM). However, the existing creep models originally built for conventional superalloys cannot explain the creep rate acceleration caused by fast cavitation, which relates to the AM-specific microstructural features, in particular the porosity, columnar grain structure and compositional inhomogeneity. In this work, a microstructure-based creep model is developed for additively manufactured Ni-based superalloys that specifically considers the correlation between cavity formation kinetics and creep deformation behaviour. The applications to IN718 and IN738LC demonstrate the model can well simulate the creep process at all stages and the creep lifetime for a wide range of microstructures. After calibration, the effects of the aforementioned AM-produced microstructure features on creep performance were discussed. The simulated data in cooperation with experimental results shows a significant increment in creep rate and a decrement in lifetime due to fast cavitation. The application of the model can simulate the creep performance of AM alloys and provide a quantitative method to estimate the influence of AM-produced microstructure features on creep performance. Moreover, the time-consuming creep testing procedure can be reduced once the model is calibrated with experimental data.

Superior High-Temperature Strength in a Supersaturated Refractory High-Entropy Alloy.

Refractory high-entropy alloys (RHEAs) show promising applications at high temperatures. However, achieving high strengths at elevated temperatures above 1173K is still challenging due to heat softening. Using intrinsic material characteristics as the alloy-design principles, a single-phase body-centered-cubic (BCC) CrMoNbV RHEA with high-temperature strengths (beyond 1000MPa at 1273 K) is designed, superior to other reported RHEAs as well as conventional superalloys. The origin of the high-temperature strength is revealed by in situ neutron scattering, transmission-electron microscopy, and first-principles calculations. The CrMoNbV's elevated-temperature strength retention up to 1273 K arises from its large atomic-size and elastic-modulus mismatches, the insensitive temperature dependence of elastic constants, and the dominance of non-screw character dislocations caused by the strong solute pinning, which makes the solid-solution strengthening pronounced. The alloy-design principles and the insights in this study pave the way to design RHEAs with outstanding high-temperature strength.

Recent advances of high entropy alloys for aerospace applications: a review

PurposeThis study aims to review the recent advancements in high entropy alloys (HEAs) called high entropy materials, including high entropy superalloys which are current potential alternatives to nickel superalloys for gas turbine applications. Understandings of the laser surface modification techniques of the HEA are discussed whilst future recommendations and remedies to manufacturing challenges via laser are outlined.Design/methodology/approachMaterials used for high-pressure gas turbine engine applications must be able to withstand severe environmentally induced degradation, mechanical, thermal loads and general extreme conditions caused by hot corrosive gases, high-temperature oxidation and stress. Over the years, Nickel-based superalloys with elevated temperature rupture and creep resistance, excellent lifetime expectancy and solution strengthening L12 and γ´ precipitate used for turbine engine applications. However, the superalloy’s density, low creep strength, poor thermal conductivity, difficulty in machining and low fatigue resistance demands the innovation of new advanced materials.FindingsHEAs is one of the most frequently investigated advanced materials, attributed to their configurational complexity and properties reported to exceed conventional materials. Thus, owing to their characteristic feature of the high entropy effect, several other materials have emerged to become potential solutions for several functional and structural applications in the aerospace industry. In a previous study, research contributions show that defects are associated with conventional manufacturing processes of HEAs; therefore, this study investigates new advances in the laser-based manufacturing and surface modification techniques of HEA.Research limitations/implicationsThe AlxCoCrCuFeNi HEA system, particularly the Al0.5CoCrCuFeNi HEA has been extensively studied, attributed to its mechanical and physical properties exceeding that of pure metals for aerospace turbine engine applications and the advances in the fabrication and surface modification processes of the alloy was outlined to show the latest developments focusing only on laser-based manufacturing processing due to its many advantages.Originality/valueIt is evident that high entropy materials are a potential innovative alternative to conventional superalloys for turbine engine applications via laser additive manufacturing.

Thermal Barrier Coating Deposited Using the PS-PVD Method on TiAl-Nb-Mo Intermetallic Alloy with Different Types of Bond Coats

TiAl intermetallics can be considered an alternative for conventional nickel superalloys in the high-temperature application. A TBC (Thermal Barrier Coatings) with ceramic topcoat with columnar structure obtained using EB-PVD (electron beam physical vapour deposition) is currently used to protect TiAl intermetallics. This article presents the new concept and technology of TBC for TiAl intermetallic alloys. Bond coats produced using the slurry method were obtained. Si and Al nanopowders (70 nm) were used for water-based slurry preparation with different composition of solid fraction: 100 wt.% of Al, 50 wt.% Al + 50 wt.% Si and pure Si. Samples of TNM-B1 (TiAl-Nb-Mo) TiAl intermetallic alloy were used as a base material. The samples were immersed in slurries and dried. The samples were heat treated in Ar atmosphere at 1000 °C for 4 h. The outer ceramic layer was produced using the new plasma spray physical vapour deposition (PS-PVD) method. The approximately 110 μm thick outer ceramic layers contained yttria-stabilised zirconium oxide. It was characterised by a columnar structure. Differences in phase composition and structures were observed in bond coats. The coatings obtained from Al-contained slurry were approximately 30 μm thick and consisted of two zones: the outer contained the TiAl3 phase and the inner zone consisted of the TiAl2 phase. The second bond coat produced from 50 wt.% Al + 50 wt.% Si slurry was characterised by a similar thickness and contained the TiAl2 phase, as well as titanium silicides. The bond coat formed from pure-Si slurry had a thickness < 10 μm and contained up to 20 at % of Si. This suggests the formation of different types of titanium silicides and Ti-Al phases. The obtained results showed that PS-PVD method can be considered as an alternative to the EB-PVD method, which is currently applied for deposition a columnar structure ceramic layer. On the other hand, the use of nanopowder for slurry production is problematic due to the smaller thickness of the produced coating in comparison with conventional micro-sized slurries.

Design, phase equilibria, and coarsening kinetics of a new [formula omitted] precipitation-hardened multi-principal element alloy

Multi-principal element alloys (MPEAs), with dispersed nanometric precipitates in a ductile matrix, are attracting a considerable amount of literature’s attention. Understanding the coarsening kinetics and potential properties of such alloys is crucial for future developments in the field. In the present study, we report a new precipitation-hardened multi-principal element alloy, Cr29.7Co29.7Ni35.4Al4.0Ti1.2 (at%), developed with the aid of the CALPHAD method. The alloy has a tough Cr-Co-Ni FCC matrix and nanometric L12 precipitates. After standard heat treatments, the alloy was aged at 850 °C for different aging times and the coarsening kinetics was investigated. The evolution of mechanical properties as a function of aging time was evaluated through microhardness tests. An increment of 106 HV 0.5 was observed compared to the sample in the solution-treated condition. This hardness increment was higher than that of conventional superalloys with a similar volume fraction of precipitates. Experimental data indicate that particle growth during coarsening is governed by diffusion controlling mechanism. The coarsening rate constant was lower than that of traditional wrought superalloys aged at the same temperature, indicating better thermal stability of the current MPEA. Furthermore, experimental particle size distributions show a good correlation with the curve predicted by the Lifshitz–Slyozov–Wagner (LSW) theory. Deviations and the applicability of this theory for MPEAs are discussed.

ATI 20-25+Nb

Abstract ATI 20-25+Nb is an austenitic stainless steel intended primarily for elevated-temperature service. This alloy fills a performance gap between conventional heat-resistant stainless steels and nickel-base superalloys, providing high performance with an economical composition. This datasheet provides information on composition, physical properties, elasticity, and tensile properties as well as creep. It also includes information on high temperature performance as well as forming, heat treating, machining, and joining. Filing Code: SS-1331. Producer or source: ATI.

An investigation on thermodynamics and kinetics of η phase formation in Nb-modified iron-nickel base A286 superalloy

In this study, precipitation of η phase (Ni3Ti) in conventional and Nb-modified (Nb-A286) A286 superalloys was evaluated at different aging times and temperatures. The TTP curve of the η phase formation was plotted using thermodynamic analyses, kinetics and microstructural studies. Depending on temperature and heat treatment, the η phase precipitated at the grain boundaries or twin sites, as a result of the γ′ phase or matrix austenite transformation. Heat treatment of conventional A286 superalloy and Nb-A286 was performed within a temperature range of 650 to 900 °C for 2 to 30 h. The η phase transformation was evaluated by scanning electron microscope (SEM) which is equipped to energy dispersive X-ray spectroscopy (EDS) and optical microscopy (OM). In the analyses based on thermodynamic calculations, the interaction of the Gibbs free energy of η phase formation and the diffusion activation energy of the elements, especially titanium and niobium, was considered. The microstructural studies showed that increasing the heat treatment time results in increasing the volume fraction of the η phase. By increasing the aging temperature to 840 and 860 °C for conventional A286 superalloy and Nb-A286 superalloy, respectively, the η phase volume fraction increased, however, further increase led to volume fraction decrease. The results of the thermodynamic analyses showed the tip of the TTP diagrams at temperatures of 860 and 820 °C for the A286 and Nb-A286 alloys, respectively. Investigation of kinetics calculations showed that η phase transformation depends on the diffusion of titanium, nickel, and niobium.

Design of a low density refractory high entropy alloy in non-equiatomic W–Mo–Cr–Ti–Al system

A new refractory high entropy alloy (RHEA) with non-equiatomic composition of W10Mo27Cr21Ti22Al20 was designed based on empirical rules and CALPHAD approach. Calculated results showed that W10Mo27Cr21Ti22Al20 RHEA had lower density and higher melting temperature than that of equiatomic alloy. The designed alloy was prepared by vacuum arc melting then the crystal structure, microstructure, chemical composition, density, hardness and compressive strength had been evaluated. The alloy exhibited a BCC solid solution as major phase with typical dendritic microstructures. The experimental results confirmed calculated results, suggesting a BCC solid solution phase. The density of the alloy was 7.48 g/cm3, which was approximately close to the calculated value, 7.61 g/cm3. However, the measured hardness value (511 kg/mm2) was significantly higher than the calculated value (125 kg/mm2), indicating the effect of solid solution strengthening. This alloy had compressive yield strengths of 1245 MPa at room temperature, 510 MPa at 600 °C, 201 MPa at 1000 °C and 105 MPa at 1200 °C. Compressive strain of the alloy was limited at room temperature, but it increased significantly to above 60% at 1000 °C and 1200 °C. Comparing with four conventional superalloys Inconel 718, Waspaloy, Hastaloy X and Haynes 230, the studied RHEA shows lower density and superior high-temperature yield strength.

Composition effect on elastic properties of model NiCo-based superalloys**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFB0701502).

NiCo-based superalloys exhibit higher strength and creep resistance over conventional superalloys. Compositional effects on elastic properties of the γ and γ′ phases in newly-developed NiCo-based superalloys were investigated by first-principles calculation combined with special quasi-random structures. The lattice constant, bulk modulus, and elastic constants vary linearly with the Co concentration in the NiCo solution. In the selected (Ni, Co)3(Al, W) and (Ni, Co)3(Al, Ti) model γ′ phase, the lattice constant, and bulk modulus show a linear trend with alloying element concentrations. The addition of Co, Ti, and W can regulate lattice mismatch and increase the bulk modulus, simultaneously. W-addition shows excellent performance in strengthening the elastic properties in the γ′ phase. Systems become unstable with higher W and Ni contents, e.g., (Ni0.75Co0.25)3(Al0.25 W0.75), and become brittle with higher W and Co addition, e.g., Co3(Al0.25 W0.75). Furthermore, Co, Ti, and W can increase the elastic constants on the whole, and such high elastic constants always correspond to a high elastic modulus. The anisotropy index always corresponds to the nature of Young’s modulus in a specific direction.