Multi-objective parametric optimization process of hybrid reinforced titanium metal matrix composite through Taguchi-Grey relation analysis (TGRA)

Hybrid titanium metal matrix composites (HTMMCs) are advanced composite materials that can be tailored to a variety of applications. Because of their decreased fuel consumption and cost, they are popular in the transportation industry. Using multi-objective optimization and Taguchi-based Grey relational analysis (TGRA), this study investigates the impact of hybrid reinforced HTMMCs synthesized using powder metallurgy on their physic mechanical properties. The research investigates reinforcements such as B 4 C, SiC, ZrO 2 , and MoS 2 at various compaction pressures, milling durations, and sintering temperatures. The best


Introduction
Metal Matrix Composites (MMCs) are important in a variety of sectors due to their strength, low weight, and resistance to wear and corrosion.They are widely used in the automotive and aviation sectors because of their reliability and durability, minimal carbon emissions, and good mechanical qualities.MMCs also minimize energy/ fuel consumption, manufacturing costs, and industrial waste [1].
Titanium is a popular and sophisticated engineering material due to its low density, biocompatibility, and high strength, but it poses production issues due to its limited wear resistance, high price, and brittle nature.Researchers are studying thermomechanical methods to minimize manufacturing costs while increasing performance, with the ultimate goal of creating titanium and its alloys at cheap prices, notably in transportation, by employing nanoparticles as a new ultrafine reinforcing material [2,3].
Pure titanium grade 5 is currently the most desirable metallic material for aerospace applications due to its low density (4.43 g/cm 3 ), high strength-to-density ratio, and exceptional corrosion resistance.Titanium and its alloys exhibit poor wear resistance [4,5] are difficult to manufacture into useable products and machines [2], and are prohibitively expensive [6].Titanium oxide is formed at all processing temperatures, and its concentration is mostly determined by temperature.The oxide layer, made of TiO 2 , generates a multi-layered porous structure with linear oxidation kinetics.Titanium's oxygen affinity causes it to react with oxygen in the air, generating a TiO 2 layer on the surface that shields the substrate from further oxidation and corrosion in a variety of hostile situations [7].
Titanium is brittle and readily broken down at ambient temperature, but it may be reinforced using thermomechanical processes like substitution and interstitial addition.Its mechanical qualities are restricted, rendering it ineffective for mechanical applications.Temperature influences its behavior, with brittleness at room temperature and ductility at higher degrees [3,8].
Titanium metal matrix composites (TMMCs) are popular because of their exceptional combination of mechanical and physical qualities, such as enhanced strength, low weight, high stiffness, amazing elastic modulus, great strength-to-weight ratio, and high wear resistance.These composite materials are made by integrating two or more materials to improve mechanical qualities such as tribological, structural, thermal, wear, chemical, and corrosion resistance [9,10].Composite combinations and amalgamations provide superior properties [11].
Traditional methods like squeeze casting, stir casting, spray casting, and compo casting are used to create composites [24].When compared to machining, casting, and forging with Powder Metallurgy (PM), PM is an energy-saving, environmentally friendly advance that allows for more complex shapes.PM is vital for the mass manufacture of automotive components because it has better yield strength, tensile strength, compressive strength, and elongation than casting parts.PM consists of three operations: milling, compaction, and sintering.Milling introduces mixed particles and sizing, compaction processes combine powder particles to a green body, and sintering methods encourage and enhance amalgamation and densification [25].
Recent research investigates several methodologies for creating monolithic/hybrid reinforcements in multi-modulus composites (MMCs), including Taguchi, ANOVA, response surface approach, full factorial, and DOE [26,27].The constraints of singleobjective optimization, which is frequently employed for TMMCs, are that it only offers the most appropriate process parameters.By determining the optimal input parameter value, multi-objective optimization addresses all major objectives [28].The paper suggests that porosity, wear rate, and density be reduced while compressive strength and hardness be increased.Temperature, particle size, compaction pressure, and particle concentration may all be adjusted to optimize outcomes.The density, porosity, hardness, compression strength, and tensile toughness of synthesized hybrid reinforcement MMCs were investigated using the TGRA technique [29].
The current study is focused on the development of Hybrid Titanium Metal Matrix Composites (HTMMCs) with superior physical and mechanical properties by mixing SiC, ZrO 2 , MoS 2 , and B 4 C ceramics to pure Ti grade 5 matrixes.Additionally, to optimize the physic mechanical properties, control components such as powder metallurgical process parameters and hybrid reinforcement weight percentage were adjusted using Taguchi and GRA approaches.

Chemical composition of reinforcement and matrix in hybrid TMMC synthesis
Powder metallurgy (PM) is used in the study to generate nanocomposites of grade 5 titanium, B 4 C, SiC, MoS 2 , and ZrO 2 nanoparticles with sizes of 90-100 nm, purity > 99%, and reinforcement purity of 99% acquired from Saveer Matrix Nano Pvt. Ltd., Uttar Pradesh, India.The study looks at the mechanical properties of powder metallurgybased processes for producing particle-reinforced MMCs, with an emphasis on powder blending, mixing, cold compression, and sintering.
Particulate-reinforced composites (SiC, B4C, ZrO2, and MoS2) are cheaper than fiberreinforced composites, and the physical, mechanical, tribological, and corrosion properties of particles are frequently isotropic [30,31].This study uses four different types of particles as reinforcing materials, with MoS2 potentially self-lubricating.Hybrid reinforcements outperform other reinforcements in terms of performance, cost, and weight reduction while improving material properties [32].

Synthesis and characterization HTMMCS
The researchers used pressure-less sintering to manufacture Ti-B 4 C, MoS 2 SiC, and ZrO 2 nanocomposites and investigated their mechanical properties such as microstructure, density, hardness, wear rate, and reinforced dimensions dependency and dispersion.The powder blend was made by combining grade 5 Ti powder with nanoparticle fortification of these powders.Sintered samples were 10.0 mm in diameter and 12 mm in height.
The materials' morphology was investigated using a Model JCM/6000Plus Bench Top SEM and the elemental phases present in the manufactured samples were analyzed using XRD in accordance with the XRD working principle: Bragg's law the XRD was performed on a fully computerized powder X-ray diffractometer (XRD7000 X-ray diffractometer, Shimadzu Corporation (Japan)) at 40 kV and 30 mA.The compressive strength was investigated using a Universal Testing Machine (UTM) model Bairo electro computer-controlled-hydraulic universal testing machine type HUT-600 from Beijing United Tester Co., Ltd., Beijing, China.A Digital Rockwell micro-hardness type HRS-150, Beijing United Tester Co., Ltd. of Beijing, China, was also used for micro-hardness measuring device testing, with a weight of 150 kgf and a holding time of 15 s.Archimedes' method was applied to test specimens to approximate their porosity, bulk density, actual density, and water absorption.The sintered weight of the specimen was first determined using a precision digital weighing balance (HR-250AZ, A&D Company Limited, Korea) with a 0.0001-gm accuracy.
HTMMCs were created using powder metallurgy, and the wear rate was measured using a pin-on-disc device.Tribological analysis and investigation were done under dry conditions, a 6-mm diameter and 12 mm height specimen was slid against an EN31 steel disc of 120 mm diameter and 65 HRC hardness utilizing POD equipment in accordance with ASTM: G 99 standards utilized DUCOM-TR-20 Micro model (Bangalore, India, DUCOM Instruments Company Pvt.Ltd.) Every specimen was subjected to additional tests with varying loads (10, 20, 30N) and sliding velocity (4,4.5, 5 m/s).Fig. 1 depicts the methodological design for the evaluation and characterization of the synthesis's HTMMCs.

Powder metallurgy production method
The PM technique is a cost-effective way of making near-net particle-reinforced MMCs that provides adaptability, lower production costs, and less scrapping waste [32].By ensuring homogeneous reinforcing material dispersion by powder mixing, compaction, and sintering, PM processing enhances mechanical characteristics while preventing clustering.The earlier published paper [33] describes the steps of the PM manufacturing procedure in depth.

DOE utilizes the Taguchi approach
The Taguchi methodology is an optimization method that uses a modified L27 orthogonal array and is measured using the signal-to-noise ratio (S/N).It focuses on reducing repetitions and obtaining the greatest results as rapidly as possible.The experimental trial, which included 27 trials, was modeled using Minitab Statistical Software.Quality is measured by the S/N, which quantifies communication and engineering application efficiency.Depending on the needed features, upgrades, and applications, lower or higher values imply higher quality.Table 1 describes the experiment's process and reinforcement parts, as well as their quantities, as well as their specified variables and levels.
The selection of reinforcement weight percentage was made based on the most desirable outcome from a prior inquiry, the reputation of consistent mechanical qualities in various scholars' analyzed works, and extra enhancement of mechanical and physical properties.Moreover, the upper and lower levels of each parameter were selected based on the literature available in the field of study.
Previous study reveals that MoS 2 addition in a Ti metal matrix by 4%, yielded the best results which are compatible with the findings of many scholars' investigations.In this manuscript, therefore weight percentage of MoS2 is fixed at 4% for all specimen preparations.
Additionally in detailed list of experimentation trial L27 OA is shown in Table 2, where L27 signifies the maximum number of rows (experimentation trial repetition).

Grey relation analysis (GRA)
GRA outperforms other approaches due to its capacity to assess partial and restricted data while preserving trust and it's one of the most effective approaches [34].The Grey relational grade (GRG) is an approach that uses DOE considerations to examine data and determine the relevance of items in research.It ranks the evaluated features based on specified scores or ratings, highlighting the most important ones [35].In one research, GRA was utilized to examine densities, wear rates, porosities, hardness, and compressive strength in 27 sets of examinations.Fig. 2 depicts the calculation of the ideal variable level configurations for multiple responses of synthesized HTM-MCs material.

Data from experimentally measured results
In a multi-response optimization process, Taguchi-based Grey relational analysis (TGRA) was utilized to discover the most successful combinations of process variables [36].GRA was utilized for matrix analysis and the approach was employed for experiment design and execution.The findings revealed that raising desirable quality characteristics and S/N enhanced performance, consequently improving product design, manufacturing process, and system effectiveness.Table 3 illustrates the observed response statistics from the experiment findings.The GRG estimation approach merged many physic mechanical domain results into a single standard database, with the highest GRG score value deemed critical.The GRG is calculated for each data combination in order to find the most significant factors, resulting in better outcomes.

Multi-response optimized performance of stages within GRA
Taguchi's approach is used to find the best process parameter configurations for a given set of attributes.For several responses with various quality features, multiresponse optimization utilizing GRA is advised [37].The goal of this research was to find the best process parameter combination for lowering wear rate, porosity, and enhancing Rockwell microhardness type "C" and compressive strength.The method creates a GRG for measuring the degree of connection of several responses, merging various performance criteria into a single Grey relationship grade.Table 4 shows the S/N (η) ratio for the calculated values.The following stages are investigated for GRA.Stage 1: Convert original experimental result data into S/N ratio (η) using applicable formulae for quality characteristics, defining the larger the better-quality ratios using Eq. ( 1), and three for compression strength replications and eight for Rockwell hardness type "C" tests.whereas m is the number of replication tests performed and xi had a response that was values that were measured.
To convert the S/N ratio, use Eq. ( 2) and three repeats of each response, with smaller responses better desirable for porosity and wear rate.
The subsequent S/N ratio for generated outcomes is calculated in a resembling manner using the applicable Eqs. ( 1) and ( 2) provided and shown in Table 3.
Stage 2: Normalize ηij as Zij (0 ≤ Zij ≤ 1) using Eqs.( 4) and ( 5) to reduce variance and avoid using various units.Using a Grey relational generating strategy, Taguchi's method provides normalized S/N ratios between 0 and 1 [37].Greater values maximize compressive strength and Rockwell microhardness, whereas lower values reduce MMC porosity [38].Normalization of the S/N ratio is accomplished using Eq. ( 3), with bigger being better.
Normalization is accomplished using the formula (4) given below to calculate S/N ratios, where the lower the value scale the better.
where Zij is the normalized value for the ith experiment for the jth dependent factor/ response, ηij is the S/N ratio to be normalized, and max (ηij) and min(ηij) are the maximum and minimum values of ηij, correspondingly. (3 Table 5 Computed normalized S/N ratios of determined results Based on Julong's [39] investigation, larger normalized results equate to higher achievement, and the optimal normalized outcome should equal one.The GRC is then calculated to indicate the relationship between ideal (best) and actual examination outcomes.Table 5 figured out normalized S/N ratios of determined results computed from Table 4 calculated data utilized the above-mentioned formulae (3) and ( 4).

S. N S/N ratios normalized (η) for lower is better S/N ratios normalized (η) for higher is better S/N ratio of (P) S/N ratio of (WR) S/N ratio of (CS) S/N ratio of (H)
Stage 3. The computation of the deviation sequences ((Δij) in both quality characteristics is identical, and the equation is as follows; ∆ = absolute difference between Zij 0 and Zij, which is a variation from the desired level and may be considered a quality loss.Table 6 shows the Deviation sequence for the various normalized S/N ratios (η) as Eq. ( 5).
whereas Δij denotes the deviation series and Zij 0 is typically equal to one (Zij 0 = 1).
Stage 4: Computation of GRCs calculation: The following equation is used to calculate the GRC for normalized S/N ratio data.
(5 λ is the distinguishing coefficient, specified in the range 0 ≤ λ ≤ 1 (its value can be adjusted based on the system's real requirements).is also known as the identification coefficient, and it ranges between 0 and 1.According to [26,38,40], λ = 0.5 is typically used since choosing 0 or 1 has no influence on the value of the parameter rankings sequence.The GRC values derived from Eq. ( 6) are shown in Table 7.
Stage 5: Determine the GRGi: after determining the GRCij, the GRGi may be calculated as follows Eq. ( 7); whereas m denotes the total number of responses (or achievement attributes) and equals 4 due to the four responses (P, H, CS, and WR).Table 7 shows the GRCs and GRGs for all experimentations that were calculated in the similar way.
(6 Stage 6: Select the most optimally suited variable and level configurations.The higher the Grey relationship grade, the higher the product degree of excellence attribute; hence, the variable influence may be investigated, and the optimal amount level that satisfies every single one may be determined. The GRG was stated according to [41] can be used to identify controllable components.This may be accomplished in two methods: (1) utilizing Minitab software to determine the ideal parameter configurations, or (2) manually calculating the average of the GRG scores.The procedure for finding the average GRG [42] is as follows:(1) The GRGs are grouped by variable level for each of the columns in the OA; (2) taking the average of GRGs; (3) computation of grade scores for every single L27 OA examination according to DOE.
For the purpose of quantifying the influence of variable i, for instance, an overall mean of grade ratings (AGV) for each level j is found, which is written as AGVij, and its impact, Ei, may be defined as follows: If the variable i can be controlled, the optimal level j* is calculated by Eq. ( 8) Table 8 In the synthesis of HTMMC, the Taguchi method was utilized to compute the average grade of GRG for each level of powder metallurgy control parameters.The greater the GRG, the better the multi-achievement qualities [43].The optimal powder metallurgy control parameters for HTMMC synthesis were milling duration (MD) level 2, compaction pressure (CP) level 2, compaction duration (CD) level 2, sintering temperature (ST) level 3, and sintering duration (SD) level 2. It may be written as MD2CP2CD2ST3SD2.
Figure 3 depicts the influence of experiment parameters on the physical and mechanical properties of HMMCs.A straight line has little effect, but a highly slanted line has a large impact on process parameters.Compaction pressure and milling duration are critical, with factors influencing their rank of impact, whereas the variables CP > MD > ST > CD > SD had an impact based on their rank of impact.
In HTMMCs materials, compaction pressure and milling time have a considerable influence on compressive strength, microhardness, and porosity.Increased CP and MD reduce porosity while improving mechanical behavior and effectiveness.The Max-Min ratio is the most important factor in powder metallurgical MMC multiperformance characteristics [27].The final max-min value is 0.0525228, with CP and MD having the most influence on performance factors.In powder metallurgical MMC, compaction pressure and milling According to Fig. 3a, b, the optimum The properties of a powder metallurgy product depend on the process parameters such as compaction pressure, sintering temperature, sintering time, type and rate of reinforcement, size of matrix and reinforcing elements, etc. [45].Homogeneity in powder mixing, compaction pressure, and sintering temperature is critical for producing samples with higher mechanical qualities for novel HTMMCs required for engineering applications, including matrix and reinforcement weight percentages and attributes.The reinforcement and matrix weight percentage compositions were previously established in line with the experimental design employed in this study.Following optimization, the optimal sample weight percentage was used directly in this validation experiment.Powder metallurgy was mixed and combined reinforcing and matrix elements to create a green compact.The compacts are compressed at a certain pressure based on the required porosity.The green compacts are then heated to high temperatures to promote diffusion bonding.This process is called sintering, and the most important factors are the compaction pressure, holding temperature, and holding duration.These characteristics have a significant impact on the qualities of powder metallurgical products.Reinforcement materials have a substantial impact on composite material qualities since they are determined by the type and bonding of reinforcement materials to the matrix material.The % weight fraction of reinforcing materials is critical for manufacturing.The law of mixing determines the attributes of a composite material, which are always intermediate between the properties of the component elements [46].

Validation experimentations
The validation test for HTMMCS, a material used in biomedical equipment, vehicles, and aircraft components, used optimal process parameters, reinforcement, and matrix to investigate wear rate, porosity, Rockwell hardness, and compressive strength.The results validated TGRA's efficacy in multi-output optimization, predicting physic mechanical characteristics.The optimization technique is viable for developing innovative structural materials with improved experimental findings, demonstrating the material's potential for usage in a variety of applications.Figure 4 shows a digital display of experimental data from a Rockwell hardness type "C" testing equipment.Table 9 shows the improved process parameters, matrix, and reinforcements as a percentage of prior experimentally observed data.The validation examination findings generated by the confirmation test are shown in Table 10.

Microstructure analysis
Figure 5 exhibits micrographs illustrating the samples taken from an SEM shown below.SEM was used to examine the surface morphology of TMMC and base-Ti6Al4V specimens for themselves, exhibiting a coarse lamellar + morphology associated separation of   phases at elevated temperature sintering and consequently sluggish rate of cooling [33].SEM micrographs indicate that raising the percentages of ZrO 2 and B 4 C, decreasing SiC, and inserting MoS 2 particles into a Ti-based metal matrix reduces porosity and densifies the surface.In the produced sample SEM morphology observed in micrographs, ZrO2 reinforcement creates and source of agglomerations.
The insertion of course, columnar grains into a fine-grained microstructure would not be expected to improve mechanical strength; in fact, the most likely impact would be for that section of the component to lose strength [47].Optimum specimen (OS) has lower porosity boundaries between reinforcement particles and phases, and porosity rises as the number of reinforced particles increases.

XRD analysis
XRD with Bragg's law and a computerized powder X-ray diffractometer were used to analyze the elemental phases in manufactured samples.Miller indices were utilized to distinguish between atom planes and diffraction peaks.The phases were identified using ASTM X-ray diffraction data cards.Minor precipitate stages were personally validated and compared using JCPDS cards.Figure 6 shows an XRD pattern of HTMMCs composite powders milled prior to compaction and sintering, suggesting a strong interfacial chemical interaction between hybrid reinforcements.The hexagonal tightly packed crystal structure of the titanium grade 5 matrix samples has a density of 4.43 g/cm 3 .The existence of Ti, SiC, B 4 C, MoS 2 , ZrO 2 , and rutile (TiO 2 ) in the titanium metal matrix is connected to the presence of these phases.The B 4 C interacted mostly with the Ti the substrate as follows [19,44]: Due to the fact that 5Ti + B 4 C = TiC + 4TiB, in rare cases TiC maxima can also be discovered at 2Ɵ = 41.6 °, 44 °, and 76.0° angles, which coincide to crystal orientation (2000) and (222).TiB peaks (JCPDS: 0044598) may be found at 2Ɵ = 58.8°position orientations.As a result of this reaction, TiB and TiC phases are produced in the composite, as evidenced by XRD data.Because of the great hardness of the ceramics, this new phase has significantly improved the mechanical properties of synthesized optimal samples.

Conclusions
Titanium grade 5 MMCs were used to manufacture a Ti-B 4 C-SiC-MoS 2 -ZrO 2 nanocomposite for automotive and aerospace applications.The composites had a more desirable microstructure and enhanced particle dispersion homogeneously.The increase of reinforcement material lowered the wear rate, and matrix interfacial contact and adhesion impacted composite strength.The end effect is reduced porosity and wear rate while boosting Rockwell microhardness and compressive strength.The following are the manuscript's final remarks: Fig. 6 The XRD graph of optimal samples 1.The milling time was the most important parameter than ST, CP, SD, and CT which had a lesser impact.The increased compaction pressure resulted in decreased porosity and enhanced material behavior.2. The optimal levels' settings of powder metallurgy control in the synthesis of HTMMC control factors were milling duration (MD) at level 2 used 5 h, compaction pressure (CP) at level 1 used at 40 MPa, compaction duration (CD) at level 2 used 40 min, sintering temperature (ST) at level 3 used 1200 °C temperature, and sintering duration (SD) at level1 used 1 h.It may be stated simply as MD2CP-1CD2ST3SD1.3. The average density, porosity, hardness, compressive strength, and wear rate of 4.29 gm/cm 3 , 0.1178%, 71.53 RHN, 2782.36MPa, and 0.1519 mm 3 respectively have been obtained at optimal parameter settings.The study concludes that 4. The best outcomes are achieved by HTMMC material created at the determined optimum parameter values.
The dry sliding wear is investigated using a POD with load, sliding distance, and velocity parameters.It discovers that matrix materials have a homogeneous particle distribution, with nanoparticles such as B 4 C, SiC, ZrO 2 , and MoS 2 playing important roles in WR values.Composites produced with increased hardness have a reduced wear rate.Titanium grade 5 combines with reinforcements to produce TiB 2 and TiC, which improves hardness and compressive HTMMCS.The results of XRD and SEM demonstrate that matrix interfacial contact and adhesion have a direct influence on composite strength.

Fig. 2
Fig. 2 Development of synthesized HTMMCS optimization flow diagram

Fig. 3 a
Fig. 3 a Main effect graph of average GRGs.b Main effect graph for mean from Taguchi method

Fig. 4
Fig. 4 Optimal sample Rockwell hardness type "C" testing machine digital display

Table 1
Process and reinforcement factors and their levels

Table 2
List of L27 OA experimental designs S.

Table 3
Observed response statistics from the experiment findings S.

Table 4
The ratio S/N (η) for the determined values

Table 6
Deviation series progression for normalized S/N ratios (η)

Table 9
Optimal variable configuration for HTMMCs synthesis

Table 10
Validation examination outcomes