Statistical Analysis and Optimization of the Experimental Results on Performance of Green Aluminum-7075 Hybrid Composites

: The present study assessed the potential of engaging response surface analysis in the experimental design, modeling, and optimization of the strength performance of aluminum-7075 green composite. The design of the experiment was carried out via the Box–Behnken method and the independent variables are rice husk ash (RHA) at 3–12 wt.%, glass powder (GP) at 2–10 wt.%, and stirring temperature (ST) at 600–800 ◦ C. Responses examined are yield, ultimate tensile, flexural, and impact strengths, as well as microhardness and compressive strength. ANOVA analysis revealed that the input factors had consequential contributions to each response, eventually presenting regression models statistically fit to represent the experimental data, further affirmed by the diagnostic plots. The result of the optimization envisaged an optimal combination at 7.2% RHA, 6.2 GP, and 695 ◦ C with a desirability of 0.910. A comparison between the predicted values for the responses and the values of the validation experiment revealed an error of <5% for each response. Consequently, the models are certified adequate for response predictions at 95% confidence, and the optimum combination is adequate for the design of the composite.


Introduction
Modern-day engineering applications have centered on the use of aluminum alloys owing to their light weight, strength, and excellent corrosion properties. Aluminum metal matrix composites (AMMCs) are often preferred to unreinforced base aluminum metal because of their superior strength, hardness, and wear resistance. These have made AMMCs more attractive for engineering applications than unreinforced ones. In recent times, hybrid AMMCs containing two or more reinforcing fillers have been preferred over single AMMCs because of their superior mechanical performance [1,2]. These sets of composites are engaged in defense, aerospace, automobiles, trains, and other forms of application. Various studies have been engaged in the fabrication of hybrid AMMCs using synthetic reinforcement [3][4][5][6][7][8][9][10].
Owing to high cost of these reinforcing particles and for the purpose of developing sustainable hybrid aluminum composite, bio-and industrial wastes are often reprocessed in powdered form and applied as supplements alongside synthetic fillers in aluminum matrixes. For instance, in Vijayakumar et al. [11], aluminum-5083 was hybridized with SiC and fly ash via stir casting. While fly ash was held constant at 2 wt.%, SiC was varied at 3, 5, and 7 wt.%. Tensile strength and hardness were reported to improve as SiC dosage

Experimental Program
The experimental program entails the design of experiment, and statistical analysis of experimental results on AA-7075/RHA/GP composite.

Design of Experiment (DoE)
Box-Behnken design, often known as BBD, is an approach to the response surface technique that was employed in the experiment's design. The independent factors include the quantity of rice husk ash (A), the amount of glass powder (B), and the temperature at which the mixture is being stirred (C). Through the use of mathematical and statistical approaches [26][27][28], the response surface approach investigates the interactions that may take place between a number of different variables and a number of different responses. In order to analyze the interactions, several approaches are used. The contributions of Design-Expert 13 were essential for both the initial stage of preparing the experiment and the subsequent phase of analyzing the outcomes. In all, there were fourteen (14) distinct experimental runs that were conducted and assessed with reference to the many varied response parameters. In Table 1, the three levels of the experimental components that were incorporated into the design of the experiment are shown, and in Table 2, fourteen different combinations of the variables that were investigated are displayed. A is rice husk ash proportion, B is glass powder dosage, C is casting temperature. Table 1 details the chemical makeup of the 7075-T6 aluminum ingot that was acquired for the experiment. Glass powder was produced by shattering collected and discarded glass into tiny fragments, then grinding and milling the fragments into powder. Procured rice husk was initially washed, dried, and heated in a muffle furnace at 700 • C for 6 h to obtain the ash, which was then crushed and sieved to 23 microns. The procured AA-7075 billet was charged into a graphite crucible (dimensions 100 mm in diameter and 175 mm in height), which was initially preheated to 500 • C. Prior to the casting procedure, RHA and GP were preheated to 500 • C.

A Brief on Composite Development and Examined Properties
The temperature was raised to the specified levels ( Table 2). The melt was stirred at 300 revolutions per minute, and preheated fillers (RHA and GP) were introduced into the resulting vortex. The filler discharge rate was kept at a rate of 2.5 g/min. Each mixture was stirred for 10 min at 300 rpm. Subsequently, the molten liquid of the composites was poured at a rate of 2.4 cm 3 /s into metal molds, and the solidification rate was kept constant at 100 K/s. The resulting specimens were tested with tensile, flexural, hardness, impact, and compression tests as per ASTM E 8/E8M-21 [29], ASTM A 370 [30], ASTM E 384-11 [31], ASTM E 311 [32], and ASTM E09-9 [33], respectively. Obtained experimental results were recorded against each experimental run as presented in Table 3.

Property Responses of Composites
Rice husk ash proportion is denoted by the letter A, glass powder dosage by the letter B, casting temperature by the letter C, yield strength by the letter Y, ultimate tensile strength by UTS, flexural strength by FS, microhardness by Hv, impact strength by IS, and compressive strength by CS (MPa).

Statistical Analysis of Experimental Outcome
An analysis of variance (ANOVA), computational analysis, validation of the model, response surface analysis, and optimization were all performed on the obtained experimental data.

Analysis of Variance (ANOVA)
In order to have an idea of whether or not the differences that were found in the data are statistically significant, analyses of variance were carried out. The assessment was carried out at a degree of confidence of 95% and a level of significance of 5%. To serve as the foundation for establishing the relevance of a particular parameter or interaction, a probability value, denoted by p, was selected. If the p-value is less than 0.05, this implies that the contribution is significant. When the value is more than 0.05, on the other hand, the contribution is considered to be negligible.
The findings of the ANOVA on the responses are summarized in Table 4. The p-values for the models of the response variables are less than 0.05, indicating that the models adequately capture the data. The residual coefficient of correlation for the models is 0.9905, which is more than 0.95, indicating that there is a good connection between the models and the corresponding data. As a result, the models have a reliability of more than 95% to describe the data with a standard deviation of less than 5%. In addition to this, the p-values for the mismatch are higher than 0.05. As a consequence of this, the models exhibit a high level of fitting in relation to the residuals. The discrepancy between the modified R 2 and the expected R 2 is less than 0.2 (which is less than 20 percent), which provides more evidence that the model is statistically fit. The fact that the value of the adequacy accuracy for the responses is greater than 4 indicates that the models may be used to navigate the design space. According to the results shown in Table 4, factor A (RHA) has a substantial impact on the responses TS, UTS, HD, and CS (p < 0.05), while it has only a marginal impact on FS (p > 0.05). The p-value for component B (GP) is less than 0.05, while the p-value for factor C (temperature) is also less than 0.05. The contributions of RHA and temperature to all of the responses are important, as the conclusion suggests. As the p-values for the cross interactions between the factors (AB, AC, and BC) are all greater than 0.05 for each of the attributes, it can be deduced that the contributions of the cross interactions to the responses are not significant. With the exception of microhardness, the square interaction A 2 had a substantial influence on all of the responses of the attributes. B 2 had a substantial effect on all of the responses, with the exception of the microhardness and compressive strength measurements. It has been shown that the influence of interaction C 2 is significant for each and every response (p-value less than 0.05).

Mathematical Models
The mathematical models for yield strength, ultimate tensile strength, microhardness, flexural strength, impact strength, and compressive strength are represented by Equations (1)-(6), respectively. The models show that the coefficients of components A and C both have a positive value. This indicates that factors A (RHA) and C (temperature) have a consequentially constructive impact (one that is synergistic with the responses). The only instance in which component B has a negative coefficient is in the context of microhardness; this indicates that factor B acts in a manner that is hostile to microhardness. The ensuing effects of square interaction A 2 exhibited a negative impact on YS, UTS, FS, and CS, but a good contribution to HD. It can be deduced from the models that the contributions of B 2 and C 2 are in opposition to all of the responses. When it comes to the cross interactions, AB is antagonistic to YS, UTS, and HD, while it has a synergistic relationship with FS, IS, and CS. When it comes to interaction AC, the contribution is antagonistic toward UTS, HD, FS, and IS, but synergistic in terms of YS and CS. Due to this, factor BC had a consequent posi-tive effect on the variables YS, UTS, and HD, while it had a resultant negative contribution to the variables FS, IS, and CS. The effect of the interaction between rice husk ash and glass powder on the yield tensile strength, ultimate tensile strength, flexural strength, microhardness, impact strength, and compressive strength is showcased in Figure 1a-f, respectively. As observed in Figure 1a-d, the blend of 3-7.5% RHA and 2-6% GP sparked improvement in the responses. The strength increase observed from 3-7.5% RHA and 2-6.0% GP is similar to the findings of Ahamed et al. [34], in which progressive enhancement of strength was noticed with 3-9 percent RHA. Likewise, Adediran et al. [35] reported an increment in tensile strength when glass particulate was introduced into Al-6061 melt in a similar manner, with these findings between 2 and 6 percent GP in this study. Adediran et al. [35]; Ahamed et al. [34] linked the increased strength to the coexistence of the two types of particulates as well as good adhesion with the matrix via particle strengthening mechanisms. Moderate viscosity resulting from moderate casting temperature was linked to the improved tensile strength of the composite when temperature was between 600 and 700 • C [36].
On the other hand, the combination of 7.5-12% RHA and 6-10% GP (Figure 1a-f) led to strength reduction. The reduction in strength is associated with the high density of the particles and the resulting clustering of particles within the matrix, as reported by Roether and Boccaccini [37]. Virkunwar et al. [38] associated the findings to poor wettability existing between particulates, and they observed a decrease in tensile strength when RHA exceeded 8 percent in their study. In Figure 1d, a progressive improvement in hardness is shown when 3-12% RHA is combined with 2-10% GP in the matrix at a constant temperature of 700 • C. Mishra et al. [39] revealed the significance of RHA in the improvement of the hardness of aluminum alloy composites. Verma and Vettivel [40] carried out response surface optimization of Al-7075 reinforced with RHA and B 4 C. Interaction between 1-5% RHA and 1-5% B 4 C engendered progressive improvement in microhardness. The surface plot of the interaction between RHA and B 4 C in the study is in sync with the result of the surface plot depicted for the interaction between GP and RHA in the present study. The accretion recorded is connected to an increment in particulate presence and the improved cohesion between particles. Saravanan and Senthilkumar [41] validated the use of GP in this study, as similar accretion in hardness with progressive assimilation of GP was reported.
compressive strength of the Al-Si LM6 alloy. The authors Ali and Motgi [44] demonstrated the potential of RHA in improving the compressive strength of the AlSi 10 Mg matrix by assimilation of 2-12% RHA in the matrix. However, the same dosage of RHA combined with 6-10% GP triggers strength reduction. The deterioration occurred due to the brittle nature of the particulate. Akinwande et al. [23] claimed that at higher particle densities for glass powder, there is a tendency for the brittle nature of the particulate to take dominance, leading to a reduction in density.  The 3-12% RHA blended with 2-6% GP is responsible for the improvement in compressive strength as indicated in Figure 1f. The improvement in compressive strength is attributable to compaction and reduced interparticle distance based on the even dispersion of the particles within the matrix, resulting in increased dislocation density and consequently improved strength. In addition, such an improvement in strength is attainable on account of reduced interparticle distance within the composite structure, consequently improving compaction. Senapati et al. [42] reported a progressive rise in the compressive strength of aluminum composites prepared with 2-12 wt.% RHA. The blend of fly ash and RHA, as reported by Saravanan and Kumar [43], has considerable input in improving the compressive strength of the Al-Si LM6 alloy. The authors Ali and Motgi [44] demonstrated the potential of RHA in improving the compressive strength of the AlSi 10 Mg matrix by assimilation of 2-12% RHA in the matrix. However, the same dosage of RHA combined with 6-10% GP triggers strength reduction. The deterioration occurred due to the brittle nature of the particulate. Akinwande et al. [23] claimed that at higher particle densities for glass powder, there is a tendency for the brittle nature of the particulate to take dominance, leading to a reduction in density.

Assessment of Effect of the Interaction between Rice Husk Ash and Temperature on Responses When Maintaining GP at 6% Constant Dosage
The influence of the interaction between rice husk ash and stirring temperature (maintaining GP at 6%) on the yield tensile strength, ultimate tensile strength, flexural strength, microhardness, impact strength, and compressive strength is illustrated in Figure 2a-f, respectively. The response plots portrayed in Figure 2a-f show that the responses were improved with the introduction of 3-7.5% RHA at 600-700 • C. This study revealed that 600-700 • C favors improvement of impact strength whereas 700-800 • C is detrimental to the strength. The influence of temperature on the strength performance of aluminum composites elucidated in Mathur and Barnawal [45] showed that an increase in temperature between 700 and 725 • C was beneficial to the strength property evaluated, while between 725 and 750 • C, the strength value declined. The observation substantiates the findings of this study as regards how temperature affects strength. The decline in strength is associated with particulate coagulation and the possible storage of residual stress.
were improved with the introduction of 3-7.5% RHA at 600-700 °C. This study revealed that 600-700 °C favors improvement of impact strength whereas 700-800 °C is detrimental to the strength. The influence of temperature on the strength performance of aluminum composites elucidated in Mathur and Barnawal [45] showed that an increase in temperature between 700 and 725 °C was beneficial to the strength property evaluated, while between 725 and 750 °C, the strength value declined. The observation substantiates the findings of this study as regards how temperature affects strength. The decline in strength is associated with particulate coagulation and the possible storage of residual stress.  [46]. At lower viscosity, the reinforcing particles have lower mobility within the melt, causing segregation, agglomeration, and clustering. If the viscosity is high due to a high temperature, particles possess a high amount of kinetic energy with the possibility of even dispersion. At much higher  Figure 3a-e that a dosage of 2-6% GP at stirring temperature of 600-700 • C ensured enhancement of the strength response. The viscosity of a metal melt is dependent on casting temperature, and it influences the properties of the developed composite [46]. At lower viscosity, the reinforcing particles have lower mobility within the melt, causing segregation, agglomeration, and clustering. If the viscosity is high due to a high temperature, particles possess a high amount of kinetic energy with the possibility of even dispersion. At much higher temperatures, there is a tendency for gas entrapment. However, determining the moderate casting temperature for even casting is not an easy task. In this study, temperatures between 600 and 700 • C seem moderate, beyond which there is strength reduction.
In Figure 3d,f for microhardness and compressive strength, 2-10% GP engendered improvement of hardness at 600-700 • C stirring temperature, while the same proportion of GP at 700-800 • C is detrimental. According to Mathur and Barnawal [45], temperatures between 700 and 725 • C were favorable to hardness and compressive strength, while temperatures between 725 and 750 • C caused a decrease in the response values due to the likely presence of defects such as microcracks, surface microporosity, and weakened bonds in the matrix. In this study, the temperature range of 600 and 700 • C favors enhancement of hardness and compressive strength, while the temperature range of 700-800 • C is detrimental to the properties.
In Figure 3d,f for microhardness and compressive strength, 2-10% GP engendered improvement of hardness at 600-700 °C stirring temperature, while the same proportion of GP at 700-800 °C is detrimental. According to Mathur and Barnawal [45], temperatures between 700 and 725 °C were favorable to hardness and compressive strength, while temperatures between 725 and 750 °C caused a decrease in the response values due to the likely presence of defects such as microcracks, surface microporosity, and weakened bonds in the matrix. In this study, the temperature range of 600 and 700 °C favors enhancement of hardness and compressive strength, while the temperature range of 700-800 °C is detrimental to the properties.

Optimization and Validation
The response surface approach is a useful statistical and mathematical tool for optimizing multi-response parameters that have been specified by constraints, according to Awolusi et al. [46], and it has found application in a number of experimental and optimization analyses [47][48][49][50][51][52]. In the current investigation, Design-Expert software version 13 was applied for the purpose of conducting a multi-response optimization approach using the predetermined criteria shown in Table 5.

Optimization and Validation
The response surface approach is a useful statistical and mathematical tool for optimizing multi-response parameters that have been specified by constraints, according to Awolusi et al. [46], and it has found application in a number of experimental and optimization analyses [47][48][49][50][51][52]. In the current investigation, Design-Expert software version 13 was applied for the purpose of conducting a multi-response optimization approach using the predetermined criteria shown in Table 5. While the primary objective was to obtain the highest possible values for the strength parameters, the input variables A, B, and C were constrained to the ranges shown in Table 5.
The optimum experimental conditions for the multi-response optimization as predicted by the software are 7.24185~7.2 wt.% RHA, 6.21163~6.2 wt.% GP, and 695.126~695 • C for temperature (Figure 4). The predicted response values are presented in Table 6.
In the validation of the model, a confirmation experiment was carried out at optimum conditions of 7.2% RHA, 6.2% GP, 695 °C and triplicate samples were tested for each property. The experimental value obtained for each response is highlighted in Table 6. The estimated errors for each of the five responses are less than 5%, confirming the models to be statistically fit for the prediction of responses.

Conclusions
In this study, response surface analysis was engaged in the design of experiment, analysis of properties, modeling, and optimization of the mechanical performance of Al-7075 hybridized with green fillers (RHA and GP). According to our findings: 1. The results of the analysis of variance (ANOVA) showed that the three parameters, RHA proportion, GP dosage, and stirring temperature, had significant effects on yield, ultimate tensile, flexural, compressive and impact strengths, as well as microhardness. The probability value for each response was less than 0.05, indicating that the parameters' effects were significant.  In the validation of the model, a confirmation experiment was carried out at optimum conditions of 7.2% RHA, 6.2% GP, 695 • C and triplicate samples were tested for each property. The experimental value obtained for each response is highlighted in Table 6. The estimated errors for each of the five responses are less than 5%, confirming the models to be statistically fit for the prediction of responses.

Conclusions
In this study, response surface analysis was engaged in the design of experiment, analysis of properties, modeling, and optimization of the mechanical performance of Al-7075 hybridized with green fillers (RHA and GP). According to our findings:

1.
The results of the analysis of variance (ANOVA) showed that the three parameters, RHA proportion, GP dosage, and stirring temperature, had significant effects on yield, ultimate tensile, flexural, compressive and impact strengths, as well as microhardness. The probability value for each response was less than 0.05, indicating that the parameters' effects were significant.

2.
It was determined that the model that had been built for each response parameter was statistically significant and appropriate for use in the prediction of the responses.

3.
The surface plots which present the relation between the response variables and the input variables revealed that the trend of the properties is dependent on the input variables. 4.
The optimal experimental conditions for the multi-response optimization are a temperature of 598.06 In that case, the developed models were affirmed to be adequate for response predictions, and equally, the optimum condition that yielded the highest desirability is fit for desired composite development. Funding: The authors receive no funding from any organization. Data Availability Statement: All data generated or analyzed during this report are included in this published article.