Taguchi grey relational analysis on the mechanical properties of natural hydroxyapatite: effect of sintering parameters

Previous studies have reported the synthesis and mechanical properties of natural hydroxyapatite (HA), but optimization of the measured hardness and compressive strength has not been examined. This paper presents optimization of HAp mechanical characteristics (hardness and compressive strength), using Taguchi grey relational analysis design. In the design, three factors with mixed levels (2 and 3) were employed with the consideration of sintering parameters (0 and 500 Pa compaction pressure, and 900, 1000, and 1100°C sintering temperature), reported in the previous study. The orthogonal array L18 having 18 rows corresponding to the number of tests and the required columns was selected. Results obtained show that HA with better hardness and compressive strength is feasible with little or no compaction pressure. An optimum grey relational grade (GRG) of the synthesized HA is 0.7171 and has an experimental value within 95% confidence interval. The optimum sintering parameters are gotten to be 500 Pa compaction pressure and 1100°C sintering temperature. The result shows that sintering temperature having 99.90 percentage of contribution is the most significant factor, while compaction pressure and residual error are insignificant on the overall hardness and compressive strength of the synthesized HA.


Introduction
Ca 5 (PO 4 ) 3 (OH, F, Cl) is the chemical formula of apatite. It is a basic component of bone, which encapsulates fluoroapatite, chlorapatite, and hydroxyapatite. Hydroxyapatite (HA) is the steadiest type of calcium phosphate, and it is considered quite possibly the most utilized material in bone recovery, in light of its liking to bone tissues. It has exceptionally close comparability to the normal bone mineral [1]. The pros of HA over other material is the simplicity of fitting its crystallinity and microstructure to suite explicit applications. Also, HA is biocompatible; i.e., it is non-toxic, non-inflammatory, and enhanced immunologic responses [2][3][4][5]. In recent studies, HA has been derived from natural sources [3][4][5].
HA is a bio-ceramic material, and it can be synthesized through different techniques, such as compaction processing and extrusion techniques [6]. The most predominant forming technique in fabricating porous ceramic is the compaction process. This technique has to do with the application of uniaxial loading to increase the density of the dry powder starting material. Sintering temperature in the fabrication of the final ceramic scaffold is also a critical factor that significantly affects the microstructure and mechanical properties of the finishing material scaffold [7]. A careful combination of levels of the main sintering parameters (compaction pressure and sintering temperature) will lead to a mechanically improved HA bio-ceramic scaffold.
The Taguchi design experiment (DOE) is a systematic and efficient methodology which brings out the optimum combination of processing parameter [8][9][10]. Taguchi method is advantageous because it simplifies experimental design and study of possible interaction between different parameters. Many researchers have worked with the Taguchi technique [9][10][11][12][13][14]. Taguchi is also known as the best method to optimize the design, performance, and costing issue [15]. The main objective of this paper is to optimize the sintering parameters for better mechanical properties by using Taguchi (L18) orthogonal array.
The theory of the grey system considers each stochastic variable as a grey quantity that differs within a fixed area and within a specific frame of time and refers to each stochastic process as a grey process [16]. Literature has shown the possibility of applying grey theory on small samples [17,18]. The term grey is gotten from grey-box in engineering, a partly arranged box within black-box and white-box [19]. In this context, the term grey means incompleteness; hence, a parameter between two extreme parameters is referred to as a grey parameter and the grey process is a process accompanying these grey parameters [20]. For instance, in fuzzy theory, the theory of grey system is a possible mathematical technique to analyze systems associated with incomplete information [20]. In engineering, grey relational analysis (GRA) is a prevalent method to optimize multiple performance characteristics and evaluate process parameters. Jiang et al. [18] employed machine vision-based grey relational theory applied to marking inspections. Kumar et al. [21] used Taguchi GRA on the optimization of multiple mechanical properties of silica fly ash-filled polyester composites. Pervez et al. [22] employed Taguchi DOE combined with GRA to optimize injection molding parameters in the fabrication of HDPE/TiO2 nanocomposites. Ajibade et al. [23] used GRA to optimize wear parameters of dual filler epoxy composites. Roy et al. [24] used Taguchi GRA to optimize multiple performance characteristics of nanosecond pulsed laser micro grooving of hydroxyapatite bioceramic. Gandhi and Rahul [25] used Taguchi GRA to optimize process parameters on the investigation of wet chemical machining of SS 316L stainless steel. Aslantas et al. [26] used the Taguchi GRA technique to optimize process parameters in micro-milling Ti-6Al-4V alloy.
These are a few out of many researches that have employed the GRA technique. Evaluation of quantitative and qualitative relationships between processing parameters associated with insufficient information is a unique and distinguishing characteristic of GRA compared to other conventional statistical techniques [27].
In previous studies, reports have been made on the synthesis and mechanical properties of natural HA [3,4]. However, optimization of sintering parameters has not been reported for better mechanical properties, which is very paramount in determining carefully optimized HA suitable for the load-bearing application. Taguchi grey relational analysis (GRA) design is capable of optimizing multiple performance characteristics of HA. Among many DOE analysis tools, GRA is one of the foremost design methods employed when having incomplete or uncertain information [28]. Literature reveals that no studies have been conducted on the use of Taguchi GRA for the optimization of sintering parameters on HA multiple mechanical characteristics. In this study, the Taguchi GRA technique will be employed to investigate the quantitative effect of sintering parameters on hardness and compressive strength of natural HA. Sintering parameter level suitable for better mechanical properties will be determined and validation of the predicted result with the experimental result using confirmation analysis will also be made.

Materials, synthesis, and sintering
Previous researches have reported materials, synthesis, sintering, and mechanical property evaluation of HA considered in this studies [3,4]. The mechanical synthesis is shown in Fig. 1 below:

Taguchi DOE
Taguchi recommends using orthogonal arrays (OA) for experiments. OA is the generalized Graeco-Latin square. The method of designing the experiment is to select the most appropriate OA and assign the parameters and interactions of interest to the appropriate columns. The two performance characteristics of Taguchi GRA to determine samples with better hardness and compressive strength were employed. Taguchi will help establish the optimum HA conditions; to estimate the contribution of various parameters and interactions, and to estimate the response under optimal conditions, three mixed levels of factors were selected, which were used in previous studies [4]. Table 1 shows the experimental design. The orthogonal array L18 selected as shown in Table 2 has 18 rows, corresponding to the number of tests with the required columns, which is a function L18 (2 ** 1 3 ** 1) suitable for design existing in Minitab.

Grey relational analysis
Grey grade generation is the first step to take in grey relational analysis. In this step, the response will be set between zero and one. From the set data, the grey coefficient will be computed to show how close the expected response is to the actual response. Then, the grey relational coefficient of all the performance characteristics corresponding to each sample treatment will be averaged to get the grey relational grade. Grey relational grade shows the overall assessment of all the multiple performance characteristics. In other words, the optimization of a single grey relational grade is the optimization of complex multiple performance characteristics. The highest grey relational grade level is the optimal level of the process parameter. Subsequently, statistical analysis of variance (ANOVA) is performed to determine the significance level of the employed process parameters. The best combination of the process parameters will be predicted with the help of grey grade analysis and ANOVA. Finally, a confirmation experiment is carried out to verify the best process parameters obtained from the analysis. GRA is applied with the following conditions: 1. GRA is used when there is incomplete information, and to optimize more than one performance characteristic. 2. The larger the better or the smaller the better is employed when estimating grey relational generation value. In this study, the larger the better is employed because higher hardness and compressive strength are desired (see Eq. (1)). 3. According to the literature [21-25, 29, 30], the distinguishing coefficient, ζ, is usually set to each parameter an equal weight of 0.5. Table 3 highlights the experimental results of the two performance characteristics.

Grey relational analysis for the multiple performance characteristics
A linear data preprocessing method employed in this study for hardness and compressive strength performance characteristics is the larger the better and is expressed as: where x i (k) is the grey relational generation value, min y i (k) is the littlest estimation of y i (k) for the response, kth, and max y i (k) is the biggest estimation of y i (k) for the response, kth. The grey relational generation sequences are shown in Table 4. An ideal sequence is x 0 (k) (k = 1 and 2) for hardness and compressive strength.
Grey relational grade is to show the relative degree of grey relation between the two sequences [xo (k) and xi (k), i = 1, 2 . . . 18; k = 1 & 2]. Equation (2) below is used to compute grey relational coefficient (GRC) ξ i (k): where Δ oi (k)= ∥x o (k)− x i (k)∥ = difference between the absolute value of x * o (k) and x * i (k); ζ = distinguishing coefficient (0∼1), but usually assign it to each parameter an equal weight of 0.5; and x * o (k) and x * i (k) allude to the reference and similarity arrangements, respectively. Δ min and Δ max are the   base and most extreme deviations of every reaction variable respectively. Table 5 shows the experimental layout of the grey relational coefficient and grade. As demonstrated in Eq. (3), the complex grey relational grade (GRG) is determined by averaging the GRC of every reaction variable: where γ i = the value of GRG determined for the ith experiment, and n is the aggregate count of the performance characteristics.
Optimization of hardness and compressive strength execution attributes is the maximum grey relational grade. Table 6 sums up the relational grade mean for each level of the utilized variables, and its complete mean. The grey relational grade diagram is shown in Fig. 2, where the middle line is the total grey relational grade mean. The highest value of grey relational grade addresses the more grounded relational degree between the reference sequence x 0 (k) and the given sequence x i (k). The reference sequence x 0 (k) is the best interaction reaction in the design of the experiment. The sintering parameter corresponding to the highest grey relational grade is the optimum parameter. This means optimization of the hardness and compressive strength execution attributes is when the grey relational grade is optimized.

Analysis of variance
The quintessence of ANOVA is to explore the variable level blend that fundamentally influences the general exhibition attributes. This was done by isolating the complete inconstancy of the grey relational grade, which is estimated by the amount of the squared deviations from the absolute mean of the grey relational grade, into commitments by each factor and the error. To start with, the absolute amount of the squared deviation SST from the total grey relational grade mean γ m can be determined using Eq. (4).
where p = experimental number in an orthogonal array and j = mean of the grey relational grade for the jth experiment. The absolute amount of the squared deviation SST deteriorates into two sources: the amount of the squared deviations SSd because of each factor and the amount of the squared error SSe. The commitment rate by each factor blend to the absolute amount of the squared deviation SST can be utilized to assess the significance of the factor mix change on the performance characteristics. Likewise, the F test, named after Fisher [31], can likewise be utilized to figure out which factor blend significantly affects the performance characteristics. Generally, the difference in the factor mix significantly affects the performance characteristics when the F value is enormous. Aftereffects of the ANOVA (Table 7) demonstrate that sintering temperature is the main factor influencing both hardness and compressive strength. Both compaction pressing factor and error (noise) are unimportant, having 0.05 and 0.06 percentage contribution, respectively.

Confirmation test
After the determination of the optimal level of the factors, the final step is to predict and vary the quality characteristics as shown in Eq. (5) [32]: where γ 0 represents the highest average value GRG at the optimal level of the sintering parameters and γ m represents the average of GRG. q is the number of the considered sintering parameters.
From Eq. (5), the predicted grey relational grade using the optimal factor parameters was computed. From the response table in Table 6, using Eq. (5), the predicted response is 0.7171, compared with the experimental values, which is 0.7127, and it is the average of experimental numbers 16, 17, and 18. To investigate the closeness of the experimental result to the predicted result, confidence interval (CI) is used in Eq. (6) [33]: F ∝ (1, f e ) = F ratio required for α; α = risk; f e = DOF of error; V e = variance of error; η eff = effective number of replications, which is Eq. (7) below: The predicted optimal grey relational grade is γ predicted = 0.7171.
The 95% confidence interval of the predicted optimal grey relational grade is: The experimental grey relational grade, 0.7127, is within the confidence interval (95%) of the predicted optimal grey relational grade.

Microstructural confirmation
It is important to show the microstructural characteristics of the materials as they elucidate more the effect of sintering temperature on the mechanical properties. Figure 3 shows the SEM micrographs of raw biowastes (RB) and the sintered HA at 900, 1000, and 1100°C [4]. The discrete nature morphology of RB compared to the sintered HA reflects the presence of organic materials [34]. The micrographs show that as the temperature is increased, the grain structures get closer to each other and the pores become narrower. This effect increases the mechanical properties of natural HA [4]. This assertion is confirmed in the employed Taguchi grey relational quantitative analysis.

Conclusions
Taguchi GRA technique on the optimization of sintering parameters for better hardness and compressive strength of natural HA has been employed. The obtained results revealed that sintering temperature has a 99.90 percentage of contribution to the overall mechanical properties, which shows that it is the only significant sintering parameter in the fabrication of natural HA. This suggests that a simple hand lay-up technique  [4] assisted with little or no compaction pressure is feasible in the fabrication of HA. The optimum and predicted GRG value was gotten to be 0.7171 and was validated by the experimental results within a 95% confidence interval. The optimum sintering parameters were obtained to be 500 Pa compaction pressure and 1100°C sintering temperature. Microstructural characteristics also confirm and validate the qualitative and quantitative effect of sintering temperature on the mechanical properties of natural HA. Further research can be conducted on the optimization of some other processing parameters, such as sintering dwell time, HA particle sizes, and varying compaction loads without zero compaction load on the mechanical properties of HA. GRA on the physical properties of HA, such as water absorption capacity, density, and porosity, can also be conducted.
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