Multi-response optimization of process and reinforcement parameters of hybrid reinforced Al matrix composites using Taguchi- Grey relational analysis

The cost of the particulate-reinforced composites (SiC, Al₂O₃, and Gr) is less than the fiber-reinforced composites, due to the lower cost of particles [44]. Moreover, the physicomechanical, tribological, and corrosion properties of particulates are generally isotropic. In this research work, four different particulates, namely; SiC, Al₂O₃, Gr, and SCBA (see figure 1) are used as reinforcement materials. Table 1 provides the raw materials' physicomechanical properties and the rationale for their selection in order to create HAMC materials, which may exhibit superior characteristics to those of the individual components and are anticipated to be a potential candidate material for use in aerospace, automotive, marine, and biomedical applications [26].

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Hybrid reinforcements outperform double reinforcements, which in turn exhibit greater qualities than single reinforcements. Additionally, the two secondary reinforcements, SCBA and Gr, play a part in lowering the cost and weight while enhancing the necessary qualities. While SCBA is the greatest replacement material for cost and weight reduction as well as enhancing other material qualities including strength, hardness, wear, corrosion, and other features, Gr offers the new HAMC materials a self-lubricating capability [26].

Bagasse is defined as the dry pulpy residue left after the extraction of juice from sugar cane [26]. The sugar extracted from sugarcane left behind sugarcane bagasse, when grid powdered to ash, is called sugarcane bagasse ash (SCBA). SCBA is an agro-industrial waste material constitutes mainly silicon dioxide. SCBA is one of the most inexpensive and low-density reinforcements available in large quantities as an agro-industrial waste by-product during the combustion of waste sugarcane [26]. Equipment used in the preparation of SCBA are Crucible, 45 μm size Sieve, Becker, sample holder, drying oven, and muffle furnace. The synthesis of SCBA is shown in figure 2 below.

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The largest proportion of the primary components (SiO₂ + Al₂O₃ + Fe₂O₃) in the solid waste SCBA is 86.2% (see table 2), making it a suitable secondary reinforcement for the creation of innovative MMC materials. Furthermore, XRD measurements of SCBA calcined at 850 °C verified the existence of SiO₂ and Al₂O₃, with strong SiO₂ peaks and low Al₂O₃ peaks. Figure 3 depicts the phase identification of SCBA using XRD. As a result, the obtained SCBA fine powder can be used as an effective secondary reinforcing material in the fabrication of novel tetra hybrid reinforced HAMC materials [25].

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The PM process is one of the most cost-effective techniques for producing near-net particle-reinforced MMCs, offering improved flexibility, cheaper manufacturing costs due to shorter machining times, and fewer scrap losses [45, 46]. The PM processing method gives greater uniformity in reinforcing material distribution, which eliminates clustering and enhances mechanical properties. The three critical processes in PM operation are powder mixing, powder compaction, and the sintering process. The phases of the PM fabrication process are explained in detail in our previously published article [26].

The Taguchi approach is one of the most powerful and successful ways for developing high-quality HAMC systems using L₁₆ OAs [47]. L₁₆ (or 4^5) orthogonal arrays indicate that there are five parameters such as milling time, compaction pressure, sintering temperature, wt% of Gr, and wt% of SCBA, and there are four levels for each of the five factors, resulting in 16 experiments (table 3). Taguchi's experimental design focuses on minimizing the number of iterations. It also allows for the best results in a short period of time. This powerful tool analysis was performed using the Minitab Statistical Software (version 20.3) to simulate experimental runs.

The number of comparisons made between process parameters to determine the better level is referred to as the Degree of Freedom (DoF). This is used to determine the smallest number of experiments necessary to investigate the observed factors. Equation (1) gives the DoF value, and table 4 shows the overall DoF of experimental factors in this study.

$\begin{eqnarray}&&{\rm{Degree}}\,{\rm{of}}\,{\rm{Freedom}}={\rm{number}}\,{\rm{of}}\,{\rm{levels}}\,\mbox{--}\,1\,\end{eqnarray} \tag{ 1 }$

Table 5 depicts an L16(4^5) OA, where L16 represents the maximum number of rows (experiments), 4 represents the number of levels, and 5 represents the number of columns (factors).

Signal - to -noise (S/N) ratio is a communication and engineering quality that is defined as the ratio of the signal's power (μ²) to the noise's power (σ²) expressed in decibels (dB) [48]. The S/N ratio has been used as a quality criterion, with smaller values indicating better quality, larger values indicating better quality, and nominal values indicating the best quality. Table 6 displays the signal-to-noise ratio functions and their practical application during multi-response optimization.

Table 6. Types of problems and respective signal-to-ratio function.

S/N function	S/N formula	Usage when the goal is to...
Smaller the better	${\boldsymbol{S}}/{\boldsymbol{N}}=-10\,\mathrm{log}\left[\displaystyle \frac{1}{3}\displaystyle {\sum }_{{\boldsymbol{i}}=1}^{3}{{\boldsymbol{y}}}_{{\boldsymbol{i}}}^{2}\right]$	Minimizing the responses: for instance, in this study, minimizing the response of
		• Exp. density
		• Porosity
Nominal the better	${\boldsymbol{S}}/{\boldsymbol{N}}\,=\,10\,\mathrm{log}\,\tfrac{{{\boldsymbol{\mu }}}^{2}}{{{\boldsymbol{\sigma }}}^{2}}$	Target the response and want to base the S/N ratio on means and standard deviations
Larger the better	${\boldsymbol{S}}/{\boldsymbol{N}}\,=-10\,\mathrm{log}\left[\displaystyle \frac{1}{{\boldsymbol{n}}}\displaystyle {\sum }_{{\boldsymbol{i}}=1}^{{\boldsymbol{n}}}\tfrac{1}{{{\boldsymbol{y}}}_{{\boldsymbol{i}}}^{2}}\right]$	Maximize the response: for instance, in this study, maximizing the response of
		• Vickers' microhardness, and
		• Compressive strength

This study attempts to determine and optimize physicomechanical parameters with the following two goals in mind: (1) to minimize density, porosity, and (2) to maximize the micro-Vickers hardness, compressive, and ultimate tensile strength of a new HAMC material fabricated using a powder metallurgical process. As a result, it's an instance of multi-response optimization, as opposed to single-performance characteristic optimization [41]. When one performance feature has a greater S/N ratio, another could have a lower S/N ratio. As a result, for the optimization of numerous performance aspects, an overall evaluation of the S/N ratio is necessary. GRA is a measurement of the absolute value of the data difference between two sequences that can be used to determine the approximate correlation between them. The GRA is a technique for determining the absolute value of a data difference between two sequences, as well as an estimated correlation between them. It's a good way to look at the relationship between sequences with a small amount of data and it can look at a lot of different things. The Taguchi-based Grey Relational Analysis (TGRA) is well-known for tackling issues involving many input parameters and response variables that have inter-functional relationships. The wt% of SCBA and Gr, milling time, compaction pressure, and sintering temperature are all factors to consider. In this work, sixteen separate sets of tests are carried out, which are then improved using GRA. The responses considered during this study are density, porosity, hardness, compressive strength, and ultimate tensile strength. Estimating Grey Relational Grade (GRG) was used to convert these physicomechanical property outputs into a single common dataset. The combination with the greatest GRG value is considered to be the most influential and is ranked accordingly. GRG was calculated for each set of data values, and it was utilized to determine the most significant levels of input parameters which results in better outcomes. The GRG is the average of the grey relational coefficients added together. The main steps in GRA are depicted in figure 4 below.

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The Taguchi-based Grey Relational Analysis (TGRA) was employed in the multi-response optimization process [50–52]. To find the ideal values of process variables, the Taguchi technique was utilized for designing and performing the experiment, while grey relational analysis was used to analyze the outcomes of matrix experiments [52]. Because it was a problem-solving tool that improved the performance of the product, process design, and system. The following response data are measured for each of the HAMCs that were tested using the Taguchi method. Table 7 shows the responses of density and porosity, in which the quality characteristic feature must be minimized and the S/N ratio must be smaller to be better, while table 8 shows the responses of Vickers hardness, compressive strength, and ultimate tensile strength, in which the quality characteristic feature must be maximized and, as a result, the S/N ratio of these responses must be larger the better.

To use the Vickers micro-hardness results from this study to predict tensile properties, previously-published correlations were used [53–55]. The ultimate tensile strength of HAMCs upon a hardness measurement was calculated using the following equation.

$\begin{eqnarray*}&&{\sigma }_{UTS}=\left(\displaystyle \frac{Hv}{2.9}\right){\left(\displaystyle \frac{n}{0.217}\right)}^{n}\end{eqnarray*}$

Vickers hardness is strongly related to tensile and yield strength. However, using these relationships as a predictive tool for processes where strain-hardening behavior is poorly understood may be impractical [56]. The measured hardness values were higher than predicted for a given yield or tensile strength, with the strain hardening exponent ranging from 0 to 1, with 0 implying a perfectly plastic solid and 1 implying a perfectly elastic solid. Many of the most of these metals have n-values ranging between 0.10 and 0.50. Since, the strain hardening exponent of aluminum and its alloys is in the range of 0.2–0.3 [56], let us assume n = 0.25 for aluminum in all of the calculations using above equation.

The ultimate tensile strength of HAMCs could be estimated as follows; First, change the measured Vickers hardness number (HVN) into MPa using the following conversions [55, 57].

• ⇒  
  In order to convert HV to MPa, multiply it by 9.807.
• ⇒  
  In order to convert HV to GPa, multiply it by 0.009807.

For instance; for S1 of first trial (HV-1);

HV-1 = 155.900 HVN =155.900*9.807 = 1528.9113 MPa.

Taguchi's technique is sufficient for determining the best process parameter settings for a single response characteristic. Multi-response optimization utilizing GRA is the recommended strategy when there are two or more replies with different quality attributes [58]. Grey relational grade is used to reduce a multi-objective problem to a single objective [52]. The scope of this study was to identify the optimal combination of process parameters that concurrently minimize the density and porosity and maximize the Vickers microhardness, compressive strength, and ultimate tensile strength. For resolving interrelationships among multiple responses, grey relational analysis is performed. A grey relational grade is generated in this method for analyzing the relationship degree of multiple responses [59]. Multiple performance criteria can be optimized into a single grey relational grade in this research [48]. For grey relational analysis, the following steps are examined.

Step 1. Using the relevant equations for the kind of quality characteristic feature, convert the original response data into S/N ratio (η). For each response, there are three replications. The data must now be translated into a S/N ratio. Because Vickers hardness (HV), compressive strength (CS), and Ultimate tensile strength (UTS) must all be maximized, the type of quality characteristic utilized is larger—the better. As a result, the S/N ratio for the larger—the better-quality characteristic feature is calculated using equation (2) given below:

$\begin{eqnarray}&&{\boldsymbol{S}}/{\boldsymbol{N}}\,{\boldsymbol{ratio}}\,({\boldsymbol{\eta }})=-10\,\mathrm{log}\left[\displaystyle \frac{1}{{\boldsymbol{n}}}\displaystyle \sum _{{\boldsymbol{i}}=1}^{{\boldsymbol{n}}}\displaystyle \frac{1}{{{\boldsymbol{y}}}_{{\boldsymbol{i}}}^{2}}\right]\end{eqnarray} \tag{ 2 }$

Where; n is the number of repetitions of the experiment, y_i is the observed response value

The second performance measure (response) is smaller—the better type utilized for experimental density (ED) and porosity (P) and its S/N ratio is computed using equation (3), as follows:

$\begin{eqnarray}&&{\boldsymbol{S}}/{\boldsymbol{N}}\,{\boldsymbol{ratio}}\,\left({\boldsymbol{\eta }}\right)=-10\,\mathrm{log}\left[\displaystyle \frac{1}{{\boldsymbol{n}}}\displaystyle \sum _{{\boldsymbol{i}}=1}^{3}{{\boldsymbol{y}}}_{{\boldsymbol{i}}}^{2}\right]\end{eqnarray} \tag{ 3 }$

Similarly, the following S/N ratio for observed responses is calculated using the appropriate equations (2) and (3) shown in table 9.

Step 2. To prevent the effect of using various units and to reduce variability, normalize η_ij as Z_ij (0 $\leqslant$ Z_ij $\leqslant \,$1) using equations (4) and (5). Normalization is a transformation that is applied to a single input to uniformly distribute and scale the data so that it may be analyzed further. Taguchi's approach yields S/N ratios that are normalized between 0 and 1, a process is known as grey relational generation [28, 60]. The calculation technique 'higher the better' was used because maximizing the Vickers microhardness, compressive strength, and ultimate tensile strength of the HAMCs were intended, while for density and porosity 'lower the better' were used because minimization of the density and porosity of the HAMCs was intended [61].

For the S/N ratio with Larger the better manner, normalization of the S/N ratio is performed using equation (4)

$\begin{eqnarray}&&{Z}_{ij}=\,\displaystyle \frac{({\eta }_{ij})-\,{\rm{\min }}({\eta }_{ij})}{\max ({\eta }_{ij})-\,{\rm{\min }}({\eta }_{ij})}\end{eqnarray} \tag{ 4 }$

While for S/N ratio with smaller the better manner, normalization is performed using equation (5) given below.

$\begin{eqnarray}&&{Z}_{ij}=\,\displaystyle \frac{{\rm{\max }}({\eta }_{ij})-({\eta }_{ij})}{\max ({\eta }_{ij})-\,{\rm{\min }}({\eta }_{ij})}\end{eqnarray} \tag{ 5 }$

where, Z_ij = Normalized value for i_th experiment for j_th dependent variable/response, ${{\rm{\eta }}}_{ij}\,$is the S/N ratio value to be normalized, and max (η_ij) and min(η_ij) are the maximum and minimum values of η_ij, respectively. Larger normalized results correspond to better performance, according to Deng, and the best normalized result should equal one [62]. The grey relational coefficients are then computed to represent the link between the ideal (best) and actual experimental findings.

Table 10 displays the normalized S/N ratio values obtained from the S/N ratio in table 9 using the above-mentioned equations (4) and (5).

Step 3. Calculation of the deviation sequences (Δ_ij) in both quality features is similar, and the equation is as follows; ${\rm{\Delta }}$ = absolute difference between ${{\rm{Z}}}_{{\rm{ij}}}^{0}$ and ${{\rm{Z}}}_{{\rm{ij}}}$ which is a deviation from the target value and can be treated as a quality loss. The Deviation sequence for the respective of the normalized S/N ratios (η) has been shown in table 11.

$\begin{eqnarray}&&{{\boldsymbol{\Delta }}}_{{\bf{i}}{\bf{j}}}={{\boldsymbol{Z}}}_{{\boldsymbol{ij}}}^{0}-{{\boldsymbol{Z}}}_{{\boldsymbol{ij}}}\end{eqnarray} \tag{ 6 }$

Where, Δ_ij is the deviation sequence, and ${Z}_{ij}^{0}\,$is usually equal to one (${Z}_{ij}^{0}=1$).

Step 4. Calculation of the Grey relational coefficients (GRCs): Calculation of the grey relational co-efficient for the normalized S/N ratio values is based on the following equation

$\begin{eqnarray}&&GR{C}_{ij}=\displaystyle \frac{{{\rm{\Delta }}}_{\min }+\lambda {{\rm{\Delta }}}_{\max }}{{{\rm{\Delta }}}_{ij}+\lambda {{\rm{\Delta }}}_{\max }}\,\left\{\,\begin{array}{c}i=1,2,3,\ldots ,16\,experiments\\ j=1,2,3,4,\,and\,5\,responses\end{array}\right.\end{eqnarray} \tag{ 7 }$

λ is the distinguishing coefficient, which is defined in the range 0 ≤λ ≤1 (the value may be changed depending on the system's actual needs). λ is also called as the coefficient of identification, ranging between 0 and 1. According to [47, 63, 64], λ = 0.5 is commonly chosen for λ since using 0 or 1 has no effect on the ranking order of the parameters. Table 12 displays the GRC values obtained using equation (7).

Step 5. Compute the grey relational grade (GRG_i): after calculating the GRC_ij, the GRG_i can be obtained as follows;

$\begin{eqnarray}&&GR{G}_{i}=\displaystyle \frac{1}{m}\displaystyle \sum GR{C}_{ij}\end{eqnarray} \tag{ 8 }$

where m is the number of responses (or the number of performance characteristics), and is equal to 5 since there are five responses, (namely; ED, P, HV, CS, and UTS). The grey grade values are generated in the same way for all of the trials and are listed in table 12.

Step 6. Determine the most appropriate factor and its level combinations. The larger the grey relational grade, the superior the quality of products; hence, the factor influence may be evaluated and the best level for each controllable component can be found using the grey relational grade [48]. This can be done using two ways; (1) using Minitab software, it is possible to find out the optimal parameter settings, or (2) it can be computed by averaging the GRG values manually. The following is the process for determining the average grey relational grade [28]:

• 1.  
  Grouping of the grey relational grades by factor level for each column in the orthogonal array.
• 2.  
  Taking the average of grey relational grades.
• 3.  
  Calculation of grade values for each experiment of the L₁₆ orthogonal arrays.

Table 11. Deviation sequence for the respective of the normalized S/N ratios (η).

	Deviation Sequence (Δij has the same formula for all)
Exp. No.	ED	AP	HV	CS	UTS
1.	0.0000	0.8336	0.9080	0.1775	0.9080
2.	0.0534	0.7320	0.4084	0.1711	0.4084
3.	0.3277	0.8149	0.0000	0.4359	0.0000
4.	0.4145	0.2793	1.0000	0.3754	1.0000
5.	0.5021	0.0000	0.6129	0.6645	0.6129
6.	0.4973	0.1391	0.7011	0.0185	0.7011
7.	0.1052	1.0000	0.6118	0.0795	0.6118
8.	0.3916	0.5129	0.9965	0.1149	0.9965
9.	0.6382	0.1315	0.7103	1.0000	0.7103
10.	0.4873	0.2110	0.5531	0.6692	0.5531
11.	0.4527	0.5138	0.1133	0.0000	0.1133
12.	0.4438	0.9231	0.0790	0.1770	0.0790
13.	0.3769	0.6710	0.8355	0.1005	0.8355
14.	1.0000	0.0800	0.6558	0.0677	0.6558
15.	0.9698	0.0524	0.1220	0.1002	0.1220
16.	0.6680	0.4544	0.3295	0.1296	0.3295
${{\rm{\Delta }}}_{\min }$	0.0000	0.0000	0.0000	0.0000	0.0000
${{\rm{\Delta }}}_{\max }$	1.0000	1.0000	1.0000	1.0000	1.0000

To determine the effect of factor I, for example, the average of grade values (AGV) for each level j has been calculated, represented as AGV_ij, and then the effect, E_i, is defined as:

$\begin{eqnarray}&&{E}_{i}=\,\max \left(AG{V}_{ij}\right)-\,\min \left(AG{V}_{ij}\right)\end{eqnarray} \tag{ 9 }$

If the factor i is controllable, the best level j*, is determined by

$\begin{eqnarray}&&{j}^{* }=\,{\rm{\max }}(AG{V}_{ij})\end{eqnarray} \tag{ 10 }$

Where, MT is Milling time (hrs.), CP is compaction pressure (MPa), ST is sintering temperature (°C), Gr is graphite content (wt%), and SCBA is sugar cane bagasse ash content (wt%), and bolded results show optimal parameters setting values.

Figure 5 depicts the primary effects of the various experimental conditions on the HAMCs' physical and mechanical characteristics. If the line for a given parameter in the main effect plot is near horizontal, the parameter has no meaningful influence. A parameter for which the line has the greatest inclination, on the other hand, has the most impact. The main effect plot revealed that the parameter CP (compaction pressure) was the most important, whereas the parameters ST, SCBA, MT, and MT had a lesser impact. This finding is also in line with the previous research by Wahyudie, I.A., et al [42] and Hlail, H.H. et al [65]. They conclude that based on the percentage contributions, the compaction pressure exhibited a strong effect in reducing porosity and increasing hardness. The increase in the compaction pressure caused less porosity and resulted in an improved material behavior, which in turn led to the improved tribological and corrosion performance of the HAMC materials [65, 66]. Table 13 shows the optimal parameter setting combination: optimal milling time, level 4; optimal compacting pressure, level 3; optimal sintering temperature, level 2; optimal wt% of Gr, level 1; optimal wt% of SCBA, level 3; and the optimal parameter setting combination, MT4 CP3 ST2 Gr1 SCBA3. Milling time (5 h.), compaction pressure (55 MPa), sintering temperature (450 °C), Gr content (0.5 wt%), and SCBA content (4.5 wt%) are the values of the optimal parameters setting, as shown in table 14. Table 13 also shows the gap between the grey relational grade's maximum and minimum values (Max–Min). The highest Max–Min ratio suggests that it is the most powerful element influencing multi-performance features [28, 65, 67]. In table 13, the maximum Max–Min value is 0.1578, and the related control factor, i.e., compacting pressure, has the greatest impact on various performance aspects. As shown in the rank given in table 13, the order of importance of the controllable factors to the multi-performance characteristics in the overall HAMC fabrication process, in sequence, can be listed as: factor CP > ST > SCBA > MT > Gr, i.e., 0.1578 > 0.1251 > 0.0553 > 0.0396 > 0.0225. The most controllable parameters in the development of powder metallurgical HAMC for multi-performance characteristics are compaction pressure and sintering temperature, which are significantly associated with prior investigations [31, 42, 65].

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Table 13. Response table of the average grey relational grade.

	Average grey relational grade by factor levels
Control Factors	1	2	3	4	Max-Min (${E}_{i}$)	Rank
MT	0.5962	0.5683	0.5986	0.6079	0.0396	4
CP	0.5310	0.5882	0.6887	0.5630	0.1578	1
ST	0.6252	0.6507	0.5693	0.5257	0.1251	2
Gr	0.6017	0.5959	0.5942	0.5792	0.0225	5
SCBA	0.5816	0.5710	0.6262	0.5922	0.0553	3

Table 14 indicates the optimum parameters which has obtained from table 13 for confirmation test.

Step 7. Confirmation experiments

The confirmation test was carried out using the optimal parameter settings to check experimental density, porosity, in which the quality feature needed to be lower is the better, and Vickers hardness, compressive strength, and ultimate tensile strength, in which their quality features needed to be higher is the better. Figure 6 depicts an optical micrograph of the Vicker hardness of the OS HAMC sample.

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Based on their respective quality features, the following results have been recorded;

Where;

• ⇒  
  Avg. ED is the average experimental density for three trials,
• ⇒  
  Avg. P is average porosity (%) for three trials,
• ⇒  
  Avg. HV Average Vickers hardness (MPa) for three trials,
• ⇒  
  Avg. CS is Average compressive strength of three trials, and
• ⇒  
  Avg. UTS is average ultimate tensile strength of three HV trials.

As shown in table 15 and figure 7, the OS HAMC sample produced at optimum parameters outperforms the 16 HAMC samples in terms of property outcomes. According to the confirmation results, TGRA is a very helpful method for performing multi-output optimization in order to predict physicomechanical properties for a variety of applications in biomedical devices, automotive, and aerospace components [28, 60].

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