In the current study, AZ31 magnesium alloy (Si-0.10, Zn-1.20, Fe-0.22, Mn-0.28, Al-3.20, and Mg-Balance) and WC nanoparticles (80 nm, HSN 28499020, 99.9% purity, Hongwu International Group Ltd.) are taken as base alloy and reinforcement, respectively. The SEM micrograph of WC nanoparticles is shown in Figure 1. AZ31-WC nanocomposites are successfully synthesized using an ultrasonic vibrator-associated stir casting setup. Illustration of the casting setup is presented in Figure 2. Initially, the furnace temperature is fixed at 750°C, and ingots are melted by being placed inside the crucible. The melt temperature is monitored by K-type thermocouple. Simultaneously, nanoparticles and permanent die are preheated in a particle preheating furnace and heater, respectively. Preheating helps to remove moisture content while die heating is necessary to avoid defects. Afterwards, mechanical stirring (500 rpm) is started when alloy gets melted. Mechanical stirring generates a vortex, and particles are continuously impinged into that generated vortex. After particle pouring is finished, the speed of the mechanical stirrer is enhanced to 600 rpm and continues for 6–8 min. After that, the horn of the ultrasonic vibrator is put into melt, and vibration (20 kHz) is applied for 3–5 min. Then molten slurry is streamed out by bottom pouring arrangement into the die in vacuum circumstances (10^–2 mbar). A similar process is followed for all nanocomposites. Inert gas supply is maintained for all experiments in the furnace (argon: SF₆ = 9:1). Afterwards, the solidified sample is removed from the die and machined properly to produce desired samples.

Microstructural characterization helps to understand the presence of different phases, particle distribution, and composition of developed material. It also helps us understand whether the samples are successfully developed or not. In the current study, samples are initially polished and etched properly before characterization. Samples are polished with different grades of SiC abrasive paper. Then samples are further polished in cloth. Next samples are etched in acetic picric solution (4 g picric acid, 10 ml acetic acid, 70 ml ethanol, and 10 ml H₂O). An optical microscope (LEICA) is used to observe different phases and interfacial bonding of developed nanocomposites. A scanning electron microscope (JEOL, Japan) is employed to find the particle distribution of nanocomposites. EDAX (JSM-6360, Japan) is used to study compositional details of the nanocomposites.

Design of experiment is a typical methodical proposition to accomplish maximum indisputable statistics from minimum process specifics. This statistical methodology proposes features of the experimental technique to achieve suitable particulars, which can be further analyzed and validate. A proper design for experiment typically servers as a guide to achieve change in any variable with respect to another one and guides the interaction between parameters for the least number of experiments. Interpretation of interaction data between different input parameters is also very pivotal and explains the methodology to control parametric arrangement so that optimality can be achieved. The Box–Behnken design approach is one such methodology. Box–Behnken is a typical union of factorial pattern and fragmentary block design, which can limit the total number of trials. It also fulfills the rotability criterion, which suggests that variance is co-related with the distance of the central point. This methodology is also very useful for the quadratic model and found to be less expensive. Accordingly, in the current study, the Box–Behnken design criterion is considered. In this study, three input factors (wt.% of WC, load, and speed) and three levels of each factor are considered. Control factors and their levels are shown in Table 1.

A mathematical model connecting output factors with input factors is developed by performing statistical modeling. The response is established based on RSM and corresponding regression analysis. Analysis of variance (ANOVA) is also performed to find significant parameters. Interaction criterion and quadratic terms are also included in the model so that the second-order model can be generated. As a consequence, curvature or any sort of nonlinearity can be taken under consideration. For a second-order mathematical model, depending on response surface, the following generalized equation (Eq. 1) is considered to analyze parametric supremacy on output. Finally, a confirmation study is also conducted by investigating the optimal predicted result with the experimental result. y u =   b 0 +   ∑ i = 1 p b i x i u +   ∑ i = 1 n b i i x i u 2 +   ∑ i < j b i j x i u x j u +   e u … … … … … … … . (1) where linear, square, and cross-product terms are x_iu for surface y_u; b_i, b_ii, and b_ij are the intercept of the plane for second-order regression; and e_u is noise.

Dry sliding tribological tests are conducted in a pin-on-disk multi-tribotester (Ducom, India) following ASTM G99-05 in normal room temperature. A pin sample (Ф6 mm, L = 30 mm) made from an as-cast bar is placed in the attachment of the tribotester where an EN8 steel disk acts as a counterface. In this study, the track diameter is taken as 40 mm, and each test is conducted for 10 min. A computerized system controls the whole operation, and load is put in by enforcing dead weight on the loading pan, which is coupled to a loading lever. Effective load and frictional forces are properly measured with the help of a load sensor and frictional force sensor, respectively. Frictional force is directly obtained from the computerized setup, and wear is computed from mass loss of sample. Wear rate is computed considering load, speed, and mass loss. Wear of counterface can be neglected as it possesses high hardness compared to the sample. Finally, worn surface is observed under SEM to investigate wear mechanisms.

Basic characterizations of synthesized nanocomposites are very important to justify the successful development. Figures 3A,B depicts an optical illustration of Mg-1WC and Mg-2WC nanocomposites. Figure 3 illustrates the presence of α-Mg and β-phase. The framework of β-phases is plate like and positioned near grain boundaries, which helps to reduce grain growth, resulting in reduced grain size. The presence of WC helps in recrystallization and generates almost equiaxed grains. Optical micrographs also divulge a superior interfacial bonding connecting base and reinforcement. Figures 4A,B shows SEM images of Mg-1WC and Mg-2WC nanocomposites. Nanocomposites show a close-packed composite layout. Reinforced nano-sized WC particles are almost homogeneously spread out over the matrix. No notable agglomeration is distinguished in SEM micrographs. Furthermore, the composition of Mg-2WC is scrutinized using EDAX analysis. The EDAX spectrum of Mg-2WC is presented in Figure 5. Compositional details of the base alloy and all nanocomposites are presented in Table 2. The EDAX result shows that all constituents of AZ31 are available along with W, O, and C. Therefore, incorporation of WC is completely apprehended.

It is essential to build connectivity between input and output factors so that process behavior can be clearly understood. In this regard, the Minitab software is used to develop the mathematical model, and corresponding parametric analysis is performed to achieve optimal results. In the current study, a similar approach is taken to minimize wear and coefficient of friction (COF) of Mg-WC MMNCs. Therefore, the response surface model is generated, and the mathematical model between input and output factors is established. Two models are generated to connect two output parameters to three process variables. Mathematical models (quadratic) consist of linear, squared, and interaction terms. The quadratic form of the model is considered so that all data can fit as precisely as possible. Experiments are carried out according to the response surface-based Box–Behnken design. Experimental results along with the uncoded design is shown in Table 3. Furthermore, the mathematical model of output factors, i.e., wear rate and COF, are obtained as in Eq. 2 and Eq. 3. W e a r = 9.58 − 4.46 A − 0.2451 B + 0.0477 C + 2.603 A × A + 0.005304 B × B + 0.000099 C × C − 0.0402 A × B − 0.03334 A × C − 0.000022 B × C (2) C O F = 0.8665 − 0.4150 A + 0.00005 B + 0.002610 C + 0.2100 A × A + 0.000085 B × B − 0.000011 C × C − 0.008800 A × B + 0.000140 A × C + 0.000021 B × C (3)

ANOVA is usually conducted to statistically analyze experimental results. Significant terms (at 1% and 5% significant levels) are obtained from the ANOVA table. The F-value and P-value of the ANOVA table help to validate the generated regression model. Typically, the obtained F-value must be superior to the critical F-value. ANOVA tables of wear rate and COF are shown in Tables 4, 5, respectively. Table 4 shows that the obtained F-values of all factors except B, (B × C) interaction, and lack of fit are superior to the corresponding critical F-value (95% confidence level). Typically, if the P-value of a parameter is less than 0.05, then that parameter is significant, while p < 0.01 suggests that the parameter is highly significant. Hence, it can be concluded from Table 4 that A, C, A², B², and (A × C) are highly significant while C² and (A × B) are significant parameters. Table 5 reveals that the obtained F-values of all factors except C, (A × C) interaction, and lack of fit are superior to the corresponding critical F-value (95% confidence level). Table 5 also discloses that A, B, A², C², (A × B), and (B × C) are highly significant while C and B² are significant parameters.

Minimum wear rate and COF are essential for maximum tribological systems to maintain the quality and longevity of components. The effect of WC wt.% and load on wear is presented in Figure 6A when sliding speed remains steady at 150 rpm. It is clear from Figure 6A that the wear value shrinks with a rise in wt.% of WC. Usually, the presence of hard ceramic WC particles in the Mg matrix helps to increase both load-bearing capability and work-hardening capability. As a result, a nanocomposite having a higher amount of WC possesses superior wear resistance. Figure 6A also reveals that wear initially decreases and then modestly increases with the increase in load. Initially, hard WC particles resist the penetration of asperities of the counter-surface and delay the thermal effect of frictional heating. But repeated loading creates thermal softening, causing an increase in wear rate. A similar conclusion was drawn by Banerji et al. (2013). Therefore, to achieve the best wear resistance, the wt.% of WC is to be kept at the highest level, keeping load at the moderate level, within experimental limit.

The integrated outcome of important input factors like load and sliding speed on wear rate is presented in Figure 6B. In this case, the wt.% of WC is fixed at 1.5%. It is observed that wear initially decreased and then modestly increased with the increase in load. Meanwhile, wear increases linearly with an increase in sliding speed within the experimental limit. Frictional heating increases with an increase in speed. Such increased frictional heating initiates thermal softening. As a result, wear increases with an increase in speed. A similar trend of WC wt.% and sliding speed is also present in the literature (Habibnejad-Korayem et al., 2010; Selvam et al., 2014). Figure 6C reveals a combined consequence of WC wt.% and speed while load remains fixed at 30 N. The wear rate contracted continuously with increased wt.% of WC, and wear rate increases linearly with increase in sliding speed. Usually, an increasing amount of particles resists penetration of the counter-surface, resulting in reduced wear rate. On the other hand, increasing speed ignites frictional heating, which results in the thermal softening of the material surface. Thermal softening results in increased wear rate. However, Figure 6C also discloses that the slope of increase in wear rate for Mg-1WC is steeper compared to Mg-2WC nanocomposites.

The combined effect of parameters A and B on COF is presented in Figure 7A, while speed remains at 150 rpm. Figure 7A discloses a moderate change in COF with respect to wt.% of WC. Moreover, COF increases slightly as wt.% of WC enhances. For increased wt.% of WC, more amount of ceramic particles come in contact with asperities of the counterface. As a result, a larger friction force develops, resulting in an increase in COF. Similar results are also available in the literature (Nguyen et al., 2015; Kaviti et al., 2018). Figure 7A also reveals that COF values decrease continuously with enhancement in load for Mg-2WC nanocomposites. This decline in COF may be ascribed to the typical softening of the contact surface due to frictional heating. The widely accepted model of Bowden and Tabor (1964)’s clearly describes friction as a force which needs to be repressed to conquer bonding of asperities from interacting with the contact surface. With increasing load, overheating occurs due to frictional heating. Overheating generates bulk softening in the contact surface. As a result, asperities of counter-disk may go through conveniently in the sample surface, resulting in reduced COF. Figure 7B presents a combined effect of load and speed on COF, while wt.% of WC is constant at 1.5%. In this case, COF decreases with the increasing load. COF initially increases but a further increase in speed leads to reduction. However, a change in COF is moderate for the experimental range. These effects are mainly due to frictional heating. Greater frictional heating generates progressive local hot spots, which lead to easier shearing of contact zones. Consequently, COF shows a declining trend. Moreover, the effect of wt.% of WC and speed is presented in Figure 7C. The COF value initially increases and then decreases with enhanced speed. Moreover, the COF value shrinks initially with enhanced wt.% of WC up to 1.5% and then tends to increase moderately.

The desirability approach is mainly an objective function which ranges between zero and one. The desirability function typically transmutes the approximated outcome to scale-free data. The basic objective is to achieve a minimized, maximized, or targeted value. In the current study, initially single-objective optimization tries to minimize wear rate and COF depending on the developed mathematical model (Eq. 2 and Eq. 3). Figures 8, 9 depict the optimized data of wear rate and COF, respectively. For wear rate, the linear desirability function (d) is found to be one for the experimental limit. The minimum wear rate is obtained as 4.9105 when wt.% of WC, load, and speed are 1.73%, 30 N, and 100 rpm, respectively. For COF, the desirability function is obtained as 1, and a minimum COF is 0.5625 when wt.% of WC, load, and speed are 1.79%, 40 N, and 100 rpm, respectively.

Multi-objective problems related to nonlinear programming are real-world problems. Due to the absence of a proper solution procedure, these problems are statistically converted into a single-objective one. In this regard, the desirability function approach is widely a employed technique considered by the industry for optimizing multi-response problems. Typically, it depends on the quality factor of the system. This method tries to predict the most desirable operating condition which provides optimized result. In the current study, analysis of tribological parameters (wear and COF) of AZ31-WC nanocomposites is conducted to explore multi-response optimization. The multi-response optimization result is shown in Figure 10. Optimized wear and COF are computed simultaneously in a single parametric setting. In Figure 10, each row contains a plot related to output parameters, while each column is associated with input parameters of the tribological study. Every cell of the plot discloses modification of the response variable while one parameter is in action, keeping other parameters constant. In the current parametric arrangement, composite desirability as well as independent desirability for wear and COF is also shown in Figure 10. It is observed that the composite desirability value is 0.9778 for the present study. The predicted minimum wear and COF values are 5.4540 and 0.5633, respectively. The predicted desirable condition is 1.73% WC, 40 N load, and 100 rpm speed.

The mathematical model is further verified by conducting experiments with a parametric setting obtained from optimized results. Those results are compared with predicted results, and percentage error is also computed.

Table 6 shows the confirmation table containing experimental results, predicted results, and percentage error. In the current investigation, the experimental value and predicted value are quite close (>5%), which is within the acceptable limit. The experimental result of the COF at optimal condition is illustrated in Figure 11.

Worn surface analysis is very important to observe the wear mechanism and justify the basic reasons behind wear and friction behavior. In the current study, worn surfaces of samples tested in optimal condition are examined, and possible wear mechanisms are discussed in detail. An SEM micrograph of samples tested at optimal wear condition is shown in Figure 12A. Figure 12A shows grooves parallel to the sliding direction. Indication of ploughing is present. Parallel trench and ploughing signify the occurrence of abrasion. Some delamination and plastic deformation are also present in the wear track. Consequently, it may be revealed that the basic wear mechanism for this sample is abrasion, delamination, and plastic deformation. Furthermore, the SEM micrograph of samples tested at optimal COF condition is shown in Figure 12B. In the SEM micrograph, some deep grooves are present, but plastic deformation and some sort of delamination are mainly observed. Plastic deformation occurs due to thermal softening, which helps to provide better COF. Hence, plastic deformation and delamination are the main wear mechanism for this condition. The SEM micrograph of samples tested at optimal condition for multi-objective optimization is presented in Figure 12C. In worn surface, deep abrasive grooves are observed along with plastic deformation and deformation. Signs of resolidified layers are also there. These layers protect the surface from severe wear, while thermal softening helps to lower the COF. As a result, the combined effect of wear and COF results in optimal conditions within the experimental range.