Tribological Study of Multi-Walled Carbon Nanotube-Reinforced Aluminum 7075 Using Response Surface Methodology and Multi-Objective Genetic Algorithm

Abstract

Aluminum metal matrix composites (AlMMCs) are widely employed in the aerospace and automotive industries due to their greater qualities in comparison to the base alloy. Adding nanocomposites like multi-walled carbon nanocomposites (MWCNTs) to aluminum enhances its mechanical properties. In the current research, aluminum 7075 with MWCNT particles was prepared and characterized to study its tribological behaviors, such as its hardness and specific wear rate. The experiment was designed with varying weight percentages of MWCNTs of 0.5, 1.0, and 1.5, and these were fabricated using powder metallurgy, employing compacting pressures of 300, 400, and 500 MPa and sintering temperatures of 400, 450, and 500 °C. Further, the experimental setup was designed using Design-Expert V13 to examine the impact of influencing parameters. A second-order mathematical model was developed via central composite design (CCD) using a response surface methodology (RSM), and the performance characteristics were analyzed using an analysis of variance (ANOVA). The hardness (HV) and specific wear rate (SWR) were measured using a hardness tester and pin-on-disk apparatus. From the results thus obtained, it was observed that an increase in compacting pressure and sintering temperature tends to increase the hardness and specific wear rate. An increasing weight percentage of MWCNTs increased their hardness, while the SWR was less between the weight percentages 0.9 and 1.3. A multi-objective genetic algorithm (MOGA) was trained and evaluated to provide the best feasible solutions. The MOGA suggested sixteen sets of non-dominated Pareto optimal solutions that had the best and lowest predicted values. The confirmatory analytical results and predicted characteristics were found to be excellent and consistent with the experiential values.

1. Introduction

Aluminum metal matrix composites (AlMMCs) are lightweight, corrosion-resistant, and highly durable materials compared to their base metals. In light of these characteristics, AlMMCs have a wide range of applications in the aerospace, automotive, and marine industries. Moreover, the introduction of a ceramic material into the matrix produces a composite material with an attractive combination of physical and mechanical properties that cannot be obtained with monolithic alloys. An MWCNT is an allotrope of carbon (i.e., graphene) and is one of the most durable materials, being highly resistant to chemicals, incapable of generating heat, and highly conductive, as well as emitting electricity, despite the fact that it is used in applications such as membranes and filters for water filtration, batteries and solar cells, automobile parts, semiconductor materials, etc.

Studies [1] that aim to provide insights into optimizing manufacturing processes to enhance the wear characteristics of Al 7075 carbon nanotube (CNT) composites demonstrate that appropriate CNT addition enhances the Al matrix’s wear resistance. Still, the effectiveness of this process depends heavily on achieving a uniform CNT dispersion and strong interfacial bonding. The authors of [2] studied the impact of MWCNT reinforcement on Al 7075 alloy composites synthesized through mechanical milling to analyze the tensile strength, yield strength, elongation, and hardness of the composite materials based on the proportion of nanotubes, and their distribution and size, in the microstructure. The results indicate that MWCNT reinforcement can significantly enhance the mechanical characteristics of Al alloys. This experiment was designed using the Taguchi technique [3] to investigate the wear behavior and microstructural properties of AA7075 reinforced with MWCNTs manufactured using the friction stir processing (FSP) process, using rotational speed, traverse speed, and the number of passes as the input parameters. The ANOVA approach revealed that the number of passes had a substantial effect on the wear resistance.

Using the Taguchi approach [4], we explored the impact of the wear resistance and coefficient of friction on Al 7075 MMC reinforced with varying weight percentages of MWCNTs and fabricated using stir casting, where the results showed that increasing the amount of reinforcement reduces the wear rate. Experimental work was conducted to calculate the mechanical characteristics of the alloy, which were then compared to those of MWCNTs/Al7075, Al 7075 alloy, and the Al 7075-O alloy. The results showed that MWCNTs/Al7075 displayed a higher microhardness due to an increased reinforcement content but a reduced ductility as reinforcement material was added [5]. We investigated the effects of Cu coating on the MWCNTs’ dispersion and interfacial bonding within the Al matrix and how this impacts the composite’s mechanical properties, including its wear and hardness [6]. The researchers of [7] examined the material removal rate (MRR), coefficient of friction, microhardness, tensile strength, and wear rate of Al 7075 composites reinforced with MWCNTs produced using the liquid-state method. The results showed that at a sliding speed of 3 m/s, the wear rate and coefficient of friction decreased by 39 and 48 percent, respectively, while the microhardness and tensile strength increased by 6 and 25 percent. Although the surface roughness rose by 38 percent, the MRR decreased by 40 percent [8]. The research reported in [9] focused on material characterization, including the wear rate, frictional force, and coefficient of friction, and optimization of a functionally graded material composed of carbon-nanotube-reinforced AA7075 and processed using ultrasonic cavitation.

The authors of [10] employed sensor-assisted techniques to ascertain the wear rate and MRR of an AA7075 MMC reinforced with MWCNTs and pulverized fuel ash. The input variables that had an impact on its characteristics were optimized using Taguchi’s DOE technique, and the input factors’ contribution to its wear behavior was analyzed using an ANOVA. The research investigated different synthesis methods, using optical and scanning electron microscopy (SEM), to optimize the results of MWCNTs reinforced with aluminum matrix. The result was an increase in the CNT percentage, as well as increases in the Young’s modulus, tensile strength, hardness, and ductility [11]. The authors of [12] assessed the hardness, wear rate, and coefficient of friction of LM 9 aluminum reinforced with varying MWCNT weight percentages and processed using a stir casting machine, which resulted in increases in both the hardness of the composites and the weight fraction of MWCNTs. The experimental study by [13] was conducted to establish a relationship between the processing parameters, microstructure, tensile strength, and wear resistance properties of the AA7075/CNT composites. The study also looked into the efficiency of the process in producing a homogeneous composite powder with a uniform distribution of MWCNTs within the Al7075 matrix. The decreased particle size caused by the inclusion of MWCNTs was validated using X-ray diffraction (XRD) patterns and the Williamson-Hall model [14]. The authors of [15] investigated the machinability characteristics such as the cutting force, surface roughness, flank wear, crater wear, and chip morphology of Al7075 reinforced with silicon carbide, graphene, and carbon nanotubes. A review article examined the mechanical properties of aluminum-based metal matrix composites (MMCs) reinforced with graphene/carbon nanotubes [16].

The goal of the study reported in [17] was to determine the best MWCNT reinforcement percentage needed to improve the mechanical characteristics of the composite while limiting potential negative consequences such as low ductility. The findings were intended to help improve the design and optimization of high-performance AA7075-MWCNT composites. The study by [18] also looked at the microstructure, hardness, and tensile strength of MWCNTs reinforced with Al 7075, which was fabricated employing a casting process. The optical microscopy (OM) and SEM methodologies were utilized to investigate the samples, and the findings showed that hardness and tensile strength increased with increasing weight percentage. Microstructural research was carried out to determine the mechanical characteristics of Al 7075 reinforced with MWCNTs. The findings demonstrated that the flexural strength and hardness were reduced owing to nanotube agglomeration and the creation of clusters in the microstructure of the nanocomposites [19]. The authors of [20] conducted an experimental study to investigate the mechanical and creep parameters of A356 Al alloy reinforced with different percentages of MWCNTs produced by stir casting. The results demonstrated increased yield stress, ultimate tensile strength, hardness, and maximum elongation. The experimental work reported in [21] was performed to compute the structural, morphological, and crystallographic properties of MWCNT-reinforced Al7075 composite powders by using Raman spectroscopy, SEM, high-resolution transmission electron microscopy (HR-TEM), and XRD analysis. The study examined the influence of hardness and wear rate on aluminum reinforced with MWCNTs and graphene, taking into consideration various processing parameters such as stirring speed, die and melt temperature, and percent reinforcement. The study was conducted using the Taguchi–Criteria Importance Through Intercriteria Correlation (CRITIC)–Multi-Objective Optimization on the basis of Ratio Analysis (MOORA)–Grey relational analysis (GRA) method [22], which resulted in increased hardness and decreased wear rate. The study reported in [23] investigated the effect of mechanical milling on different weight percentages of MWCNTs reinforced with AA7075 that were fabricated using powder metallurgy. The goal was to achieve a uniform distribution of MWCNTs within the AA7075 matrix so that the mechanical properties in the final composite material were improved.

The authors of [24] reported experimental observations of the wear behavior of eutectic Al-7075 composites reinforced with carbon nanotubes (CNTs) and graphite, which were produced utilizing a two-stage stir and squeeze casting procedure. The objective was to understand the individual and combined effects of the graphene nanoplatelets (GNPs) and MWCNT-reinforced AA7075 matrix, aiming to identify optimal reinforcement strategies for enhancing specific material properties; the results showed that a small amount of nanocarbon significantly increases the toughness and hardness [25]. A study’s goal was to establish the optimal MWCNT concentration for improving tribological performance in AA7075, considering the trade-off between improved wear rates, reduced coefficient of friction, and potential negative effects on other material characteristics [26]. The wear processes were investigated using surface and subsurface characterization techniques to create a high-performance AA7075 hybrid composite with improved wear resistance by systematic adjustment of the reinforcement mix and FSP processing parameters, to assess the suitability of the improved composite for wear-critical applications [27]. The investigation by [28] assessed the corrosion, mechanical, and microstructural characteristics of aluminum 7075–CNT nanocomposites for robotic applications in corrosive environments. The research also looked into the machinability of Al7075 MMC reinforced with nano-silicon carbide, boron carbide, graphene, and MWCNTs. Authors [29] concluded that the B₄C-based composite exhibited the highest flank wear, while the graphene-based composite showed the lowest. A study evaluated the mechanical and tribological characteristics of surface composites produced by FSP on AA7075-T6 aluminum alloy reinforced with silicon carbide and MWCNTs [30]. The study’s goal was to establish the most effective MWCNT coating concentration for improving the fatigue crack growth resistance and other mechanical characteristics of Al 7075-T6 thin plates, consequently assisting in the creation of high-performance lightweight components with longer fatigue life [31].

The above highlights of the literature indicate that there is limited research on improving the hardness and specific wear rate on Al 7075 reinforced with MWCNTs utilizing RSM and MOGA, considering compacting pressure, sintering temperature, and MWCNT weight percent. This study recognizes the need for the prediction of the hardness, specific wear rate, and the parameters influencing Al 7075/MWCNTs. To overcome these obstacles and address these critical concerns with industrial specialists, experiments were conducted to forecast hardness and specific wear rates.

2. Materials and Methods

A composite was manufactured using Al 7075 material as base metal and MWCNTs as a reinforcement. The chemical composition of Al 7075 (The Coimbatore Metal Mart, Tamilnadu, India) is shown in

Table 1. Chemical composition of Al 7075.

Al 6061	Mg	Si	Fe	Mn	Cu	Cr	Zn	Ti	Al
Weight	2.1–2.9	0.4	0.50	0.30	1.2–2.0	0.18–0.28	5.1–6.1	0.20	Remainder

. MWCNTs were used as reinforcement (Shilpent, Maharashtra, India) according to the data from Shilpent with a purity of 99%, diameter of 5–20 nm, and length of 10 µm.

Response surface experiments typically use a central composite design, which includes center and star points. Parameters such as compacting pressure, sintering temperature, and wt.% of MWCNTs and their ranges were set.

Table 2. Process parameters and their levels.

Sl. No.	Parameters	Unit	Factorial Levels
			−1	0	+1
1	Compacting pressure (P)	MPa	300	400	500
2	Sintering temperature (T)	°C	400	450	500
3	Wt.% of MWCNTs (W)	%	0.5	1	1.5

shows that the highest and lowest factorial levels for all three variables are +1 and −1, respectively. Interpolation was used to determine the intermediate levels (0 for all variables). The hardness and specific wear rate are the output response. The hardness was measured using a Vickers hardness tester (Fine Manufacturing Industries, Maharashtra, India), and the specific wear rate (Saini Scientific Industry, Ambala, India) was measured using a three-factor CCD with 15 coded conditions, as illustrated in

Table 3. Experimental values with responses.

Sl. No.	Compacting Pressure	Sintering Temperature	Wt.% of MWCNTs	Hardness (HV)	SWR × 10−4
	MPa	°C	%	HV	mm3/Nm
1	500	500	0.5	161.5	1.4
2	300	400	0.5	140.4	2.4
3	400	400	1	148.6	2.1
4	500	400	1.5	164.5	1.2
5	300	450	1	142.7	2.3
6	400	500	1	162.6	1.3
7	400	450	1	154.5	1.8
8	500	450	1	166.9	1.1
9	400	450	1	154.4	1.7
10	400	450	1	156.1	1.7
11	300	500	1.5	146.8	2.2
12	400	450	1	157.2	1.6
13	400	450	0.5	147.3	2.1
14	400	450	1	155.4	1.8
15	400	450	1.5	160.2	1.6

.

2.1. Fabrication of Al7075-MWCNT Composite

The sample was prepared using a solid-state powder metallurgy fabrication technique by compacting the mixed powder via a hydraulic press. Weight compositions of 0.5 to 1.5% of MWCNTs were added as reinforcing materials in different proportions, while Al7075, as a base metal, was kept at a constant volume percentage throughout the production process. Firstly, the high-energy mill machine, shown in Figure 1a, was used to form fine powders, where the powders were uniformly mixed by using uniform-size zirconium balls with a powder ratio of 2:1 to synthesize Al7075–MWCNTs into nanocomposite powders according to the design of the experiment. Secondly, the compaction process was performed using a mounting press as shown in Figure 1b after the powder was poured into the mold and uni-axially loaded under a hydraulic press at different compaction pressures. All the samples were prepared as per the DoE with a diameter of 20 mm and height of 30 mm as shown in Figure 1c. Thirdly, the sintering process was performed to improve the product’s mechanical strength, density, and translucency while lowering sample oxidation. The technique was carried out while taking the environment into account. During the sintering process in a high-temperature box furnace, heat was supplied at a rate of 15 °C/min under varied degrees of sintering temperature over a one-hour continuous period. Because the technique did not require liquefaction of the material, the sintering temperature was set to be lower than the base metal’s melting point.

The particle distribution, morphology, phase, and microstructure of Al 7075 and MWCNTs were considered for experimentation purposes using optical microscopy, SEM, and energy-dispersive spectroscopy (EDS) as shown in Figure 2, Figure 3, Figure 4 and Figure 5. The presence of Al, Mg, Zn, Fe, Cu, and Si in the EDS images shown in Figure 4 confirms the presence of Al7075 alloy, while the C presence confirms MWCNTs.

2.2. Measurement of Mechanical Properties

To investigate the effect of the Al 7075 alloy reinforced with MWCNTs and its weight compositions (0.5, 1.0, and 1.5), with compacting pressure and sintering temperature as input parameters, mechanical tests, i.e., hardness measurement and specific wear rate, were performed.

2.2.1. Hardness Measurement

The hardness measurements of the Al 7075/MWCNT samples were performed on a Vickers hardness testing machine as shown in Figure 6 using a square-base diamond pyramid as an indenter. The sum of the angles between the pyramid’s opposite faces was 136°, and a 20 kgf force was applied gradually for 10 s at varied places. Then, the load was divided by the surface area of the indentation, which resulted in the diamond-pyramid hardness number (DPH), also referred to as the Vickers hardness number (VHN). The resulting indent mark was then inspected visually at 10× magnification to find the lengths of the diagonals to establish the hardness value.

2.2.2. Specific Wear Rate

The specific wear rate (SWR) is defined as the volume or mass lost per unit force per unit distance. Figure 7 depicts the specimens examined under dry sliding circumstances on a pin and disk machine. It was delicately cleaned with a brush to remove loose wear debris, and the pin was weighed using a digital scale with an accuracy of 0.0001 g. The test was conducted first by inserting the disk perpendicularly to the holding device and inserting the pin specimen securely in its holder. Then, the specimen was adjusted to 61° to the disc surface. The appropriate mass was added to the system lever, the motor was started, and the process parameters (load, rpm, and distance) were set. Finally, the specimen was reweighed to the closest 0.0001 g. The wear rate and specific wear rate were estimated using Equation (1) [32].

$$\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{r} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}={\displaystyle \frac{\mathrm{V}}{\mathrm{\rho }\mathrm{D}}}$$

(1)

$$\mathrm{S}\mathrm{W}\mathrm{R}={\displaystyle \frac{\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{r} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}}{\mathrm{L}}}({\mathrm{mm}}^3/\mathrm{N} \mathrm{m})$$

(2)

where SWR is the specific wear rate, $\mathrm{\rho }$ is the density of the material, V is the weight loss, D is the sliding distance, and L is the applied load.

3. Results and Discussion

Table 4. Predicted by RSM.

Sl. no	Compacting Pressure	Sintering Temperature	Wt.% of MWCNT	RSM Predicted Values
				Hardness (HVPred)	SWR × 10−4 (Ws Pred)
	MPa	°C	%	HV	mm3/Nm
1	500	500	0.5	161.48	1.40
2	300	400	0.5	140.38	2.40
3	400	400	1	148.64	2.10
4	500	400	1.5	164.48	1.20
5	300	450	1	142.74	2.30
6	400	500	1	162.64	1.30
7	400	450	1	155.49	1.72
8	500	450	1	166.94	1.10
9	400	450	1	155.49	1.72
10	400	450	1	155.49	1.72
11	300	500	1.5	146.78	2.20
12	400	450	1	155.49	1.72
13	400	450	0.5	147.34	2.10
14	400	450	1	155.49	1.72
15	400	450	1.5	160.24	1.60

shows the predicted values using RSM, while Figure 8a and b show the worn surface of Al7075 + MWCNTs with 2 µm and 20 µm magnification, respectively.

3.1. Analysis of Variance

3.1.1. ANOVA Analysis to Predict Hardness

DESIGN EXPERT V13 software was used for the analysis purpose, where the second-order quadratic model was designed to predict hardness. The model was verified for its competency using ANOVA as shown in

Table 5. Hardness (HV): ANOVA for quadratic model.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	889.87	9	98.87	90.18	<0.0001	significant
P: Compacting pressure	292.82	1	292.82	267.07	<0.0001
T: Sintering temperature	98.00	1	98.00	89.38	0.0002
W: Wt.% of MWCNT	83.20	1	83.20	75.89	0.0003
PT	22.41	1	22.41	20.44	0.0063
PW	50.43	1	50.43	45.99	0.0011
TW	7.68	1	7.68	7.00	0.0456
P2	1.12	1	1.12	1.02	0.3595
T2	0.0566	1	0.0566	0.0516	0.8293
W2	7.58	1	7.58	6.92	0.0465
Residual	5.48	5	1.10
Lack of Fit	0.0142	1	0.0142	0.0104	0.9238	not significant
Pure Error	5.47	4	1.37
Cor Total	895.35	14

. ANOVA was used to identify which actual measurements affect the specified values [33]. The F-value of 90.18 indicates that the model is significant. There is just a 0.01% probability that this huge F-value is caused by noise. p-values < 5% suggest that the model terms are significant, while values larger than 0.1000 imply that the model terms are not significant. The F-value of 0.01 indicates that the lack of fit is not statistically significant in comparison to the pure error. There is a 92.38% chance that the F-value will not be adjusted owing to noise. A non-significant lack of fit is beneficial for experimental purposes. The regression equation for the hardness was obtained by using design software and is expressed as follows (Equation (3)):

Hardness = +265.84314 − 0.318765 × P − 0.336941 × T − 65.87647 × W + 0.000820 × P × T + 0.123000 × P × W + 0.096000 × T × W − 0.000065 × P² + 0.000059 × T² − 6.81176 × W²

(3)

The computed value of the F-value exceeds the standard (tabulated) value of the F-value for hardness, as given in Table 5, which indicates that the model is appropriate for a required 95% level of confidence. In other words, the error discovered between the experimental and anticipated values is within acceptable limits.

3.1.2. ANOVA Analysis of Specific Wear Rate

The observed reading was accurately analyzed using the software. A second-order quadratic model was developed to forecast specific wear rates, and the model’s appropriateness was tested by ANOVA.

Table 6. ANOVA results of specific wear rate for the quadratic model.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	2.25	9	0.2499	44.57	0.0003	significant
P: Compacting pressure	0.7200	1	0.7200	128.39	< 0.0001
T: Sintering temperature	0.3200	1	0.3200	57.06	0.0006
W: Wt.% of MWCNT	0.1250	1	0.1250	22.29	0.0052
PT	0.0300	1	0.0300	5.35	0.0687
PW	0.2133	1	0.2133	38.04	0.0016
TW	0.0133	1	0.0133	2.38	0.1837
P2	0.0014	1	0.0014	0.2582	0.6330
T2	0.0014	1	0.0014	0.2582	0.6330
W2	0.0418	1	0.0418	7.46	0.0412
Residual	0.0280	5	0.0056
Lack of Fit	0.0000	1	0.0000	0.0056	0.9439	not significant
Pure Error	0.0280	4	0.0070
Cor Total	2.28	14

displays the ANOVA analysis results of the specific wear rate. The model F-value of 44.57 indicates that the model is significant. There is just a 0.03% chance that an F-value of this size will occur owing to noise. Normally, p-values of less than 0.05 suggest that model terms are significant. The F-value of 0.01 indicates that the lack of fit is not statistically significant in comparison to the pure error. A lack of fit F-value of this magnitude, i.e., 94.39%, is likely to be caused by noise.

The regression equation for the specific wear rate obtained by using design software is as follows:

Specific wear rate = −3.95490 + 0.017382 × P + 0.016471 × T + 3.48824 × W − 0.000030 × P × T − 0.008000 × P × W − 0.004000 × T × W-0.000000235294 × P² − 0.000000941176 × T² + 0.505882 × W²

(4)

3.2. Interaction Effect

Using CCD by RSM of DoE, the following results were obtained using interaction effect analysis.

3.2.1. Interaction Effect on Hardness

This section discusses whether the process parameters interact with hardness. Figure 9a demonstrates the impact of compacting pressure and sintering temperature on hardness. It is verified that the increase in the compacting pressure has a significant effect and tends to increase the hardness. It is evidenced from the literature that increasing compacting pressure increases bulk hardness [34]. When compared to pressure, sintering temperature has less influence on increasing hardness. A rise in sintering temperature causes the metal powder to melt and join together, which increases hardness. Figure 9b shows the interaction effect between the wt.% of MWCNTs and sintering temperature over hardness. It is verified that the sintering temperature and wt. % of MWCNTs have less significant effects. The weight percentage of MWCNTs and the sintering temperature both influence the hardness of the composites [35]. Figure 9c shows the interaction effect between the wt.% of MWCNTs and the compacting pressure over hardness. It is verified that the compacting pressure and the wt.% of MWCNTs have significant effects, as discussed in the case of Figure 9a. As a result, hardness and density increase with compaction pressure and the weight % of MWCNTs [36]. Figure 9d shows the relationship between the predicted and the actual results from Design Expert software V13; both results are very close to the medium line.

3.2.2. Interaction Effect on Specific Wear Rate (SWR)

Figure 10a–c demonstrate the interaction impact of the machining settings on specific wear rates. In particular, Figure 10a shows the relation between compacting pressure and sintering temperature over SWR. The plot indicates that the compacting pressure has a significant impact on reducing the specific wear rate. Increasing compacting pressure leads to a decrease in SWR, and a similar tendency applies to sintering temperature over SWR. This is because higher sintering temperatures lead to greater consolidation of the powder and heat diffusion, which minimizes the number of damaged patches and rubble on the surface [37]. Additionally, raising the compaction pressure can lead to decreased surface values for all compositions [38].

Figure 10b depicts the relation between sintering temperature and wt.% of MWCNTs over SWR. As previously discussed, the same tendencies are observed in terms of sintering temperature. The graph demonstrates that the SWR decreases between 0.9 and 1.3 wt.%. This is because MWCNTs create a protective layer between the two levels, filling scratches and residing on friction surfaces to compensate for mass loss. The same trends, as shown in Figure 10c, are also attained as per the preceding discussion on the compacting pressure over SWR. A low wt.% of MWCNTs causes a low SWR since the increase in the percentage of reinforcement material tends to increase the wear rate [4]. Figure 10d depicts the relationship between anticipated and actual outcomes from the Design Expert program, which shows that both results are fairly near the medium line.

4. Multi-Objective Optimization

In this study, a multi-objective genetic algorithm (MOGA) was used with regulated parameters. The constructed regression model was used in the genetic algorithm to optimize the best correlation between parameters and responses [39]. The optimization function’s purpose is to decrease hardness while increasing SWR. As a result, the procedure becomes complicated, and to find the ideal solution, one must examine a multi-objective function.

The goal of minimizing the hardness and maximizing the specific wear rate in a multi-objective optimization was formulated using the following objective functions:

Minimize hardness: HV (P, T, W)

(5)

Maximize specific wear rate: Ws (P, T, W)

(6)

where P (compacting pressure), T (sintering temperature), and W (wt.% of MWCNT) are optimization parameters, while the optimization constraints are stated as Ws ≤ Ws_limit and HV ≤ HV_limit. The lower and higher bounds of the optimization that must be met by responses are denoted by the HV_limit and the Ws_limit.

The optimization was conducted within the following parameter ranges:

300 ≤ P ≤ 500

(7)

400 ≤ T ≤ 500

(8)

0.5 ≤ W ≤ 1.5

(9)

The optimization settings used to obtain the best potential outcome were a population size of 100, crossover rate of 1.0, mutation rate of 0.1, Gaussian mutation function, and 1000 generations as a stopping criterion. Figure 11a shows the result of MOGA, while Figure 11b depicts the average distance between individuals in each generation, which is a helpful measure of the diversity of a population. The crowding distance for maintaining diversity in the selected population is also displayed in Figure 11c. Furthermore, Figure 11d shows the rank histogram used to forecast and diagnose the errors. The Pareto frontier distribution, which is the collection of solutions that are considered as optimum level points of MOGA for the responses, is represented by stars in Figure 12.

Table 7. MOGA analysis of sixteen sets of non-dominated Pareto optimum solutions.

Sl. No	Compacting Pressure (P)	Sintering Temperature (T)	Wt.% of MWCNTs (W)	MOGA Results
				Hardness (HVPred)	SWR × 10−4 (WsPred)
1	498.09	442.93	1.35	172.94	2.99
2	300.00	400.00	0.86	140.49	4.01
3	498.09	400.00	1.5	164.33	3.09
4	498.09	473.82	1.49	183.97	2.71
5	378.31	400.04	0.86	146.09	3.88
6	499.99	400.04	0.86	153.16	3.67
7	499.99	400.04	1.49	164.59	3.09
8	499.99	400.04	0.98	155.88	3.52
9	498.09	400.00	1.17	159.22	3.34
10	300	400.00	1.34	137.74	4.31
11	499.99	473.83	1.34	181.15	2.84
12	378.31	400.04	1.17	147.68	3.85
13	498.09	442.93	1.49	175.66	2.88
14	499.99	473.83	1.49	184.42	2.69
15	300	400.00	1.49	136.24	4.45
16	499.99	400.04	1.17	159.49	3.33

displays the input parameter grouping of sixteen sets of non-dominated Pareto optimum solutions based on the MOGA analysis. In this table, the entire range of parameters is displayed, with no partial obstruction detected on the upper or lower sides of the parameters, though performance measurements are contradicting in nature. All the MOGA-generated solutions are shown to have similarly good agreement. The physical parameters were additionally calibrated, and all the obtained results of the tribological characteristics of Al 7075 reinforced with MWCNTs and the error percentage are found to be within ±2%.

5. Conclusions

The experimental study reported in this article employed the CCD of RSM on Al7075/MWCNTs to predict hardness and specific wear rate. The impacts of the hardness and specific wear rate were investigated. A multi-objective genetic algorithm was used to optimize the parameters and the responses. Based on the obtained results, the following conclusions are drawn:

• An increase in compacting pressure has a significant effect of increasing hardness and decreasing the specific wear rate.
• Increasing sintering temperature has the least impact on hardness and specific wear rate.
• An increase in the weight percentage of MWCNTs reduces the hardness, but increases the specific wear rate. A lower SWR was observed for the MWCNTs in the range of 0.9 to 1.3 weight percentages.

Based on the multi-objective optimization using the MOGA, 16 non-dominated Pareto optimum solutions were obtained, and the confirmatory test was performed; the percentage error was in excellent agreement with the observed values.