2.1. Preparation of samples

Si₃N₄-hBN composites prepared with 0, 4, 8, 12 and 16% vol. of hBN mixed in Si₃N₄. The mixing of Si₃N₄ and hBN is performed with a ball mill. The pin samples were prepared at uniaxial hot-pressing at 30 MPa, 1600 ^◦C and 60 min dwell time with polyvinyl alcohol as an additive. The pin dimensions were 10 mm diameter and 15 mm long. Tables 1 and 2 shows the properties of sintered specimens and a steel disc, respectively.

2.2. DoE-Taguchi methodology

The Taguchi method was developed by Genichi Taguchi for planning experiments and to investigate how different factors affect the mean and variance of a process characteristic. Orthogonal arrays, the experimental design proposed by Taguchi, helps to organize the factors influencing the process and the levels at which they should be varied; it contributes to collect the necessary data to determine which factors most affect product quality with a minimum amount of experimentation, thus saving time and resources. The proper orthogonal array can be selected with knowledge of the number of factors and their levels. The experiments were carried out to analyze the influence of testing parameters on the wear rate of composite made of Si₃N₄ and hBN. The factors and corresponding levels are illustrated in Table 3.

Load and % volume hBN are two factors selected at five levels as shown in Table 3. Therefore L₂₅ orthogonal array selected, in total 25 experiments were carried out; each experiment repeated twice to maintain consistency, with the aim of relating the influence of load and % volume of hBN on wear rate.

2.3. Wear test procedure

The wear tests were conducted on a Ducom TRLE-PMH400 pin-on-disc tribometer having a maximum normal load capacity of 200 N. Figure 1(a) shows a schematic arrangement of loading used for testing and Figure 1(b) shows the experimental setup used for testing. Tests were performed according to ASTM F732 standards (^{ASTM F732-00, 2011}). During test composite used as pin specimen loaded through a vertical specimen holder against a flat steel disc as counterface rotating at a speed of 200 rpm for a 20-min duration. Before tests, the flat surface of the pin was abraded with grit paper. Tests were conducted in a dry environment without lubricant and at atmospheric condition. Table 4 shows the average value of wear rate for all 25 experiments.

Fig. 1 (a) Schematic arrangement of loading and (b) experimental setup. 

2.4. Taguchi-SA approach for modelling and analysis of wear behaviour

Integrated Taguchi-SA approach used for modelling, analysis, and optimization of wear behaviour of the Si₃N₄-hBN composite. Figure 2 presents the steps of the integrated Taguchi-SA approach applied for optimization.

Fig. 2 Integrated Taguchi-SA approach. 

3.1. Signal-to-noise (S/N) ratio analysis

Experiments were performed on a pin-on-disc tribometer with two input parameters and wear rate of a specimen as output. Wear rate calculated for sliding distance covered by pin during 20 min duration and speed of disc 200 rpm at corresponding wear track diameter. Taguchi recommended the use of signal-to-noise (S/N) ratio measured by the deviations of characteristics from the target value. The experimental results are further transformed into signal-to-noise (S/N) ratio. The significance of the controllable factor is investigated using S/N ratio approach. A smaller of wear rate is expected to extend joint life. Therefore, in this study a S/N ratio with a smaller-the-better methodology was used for wear rate and calculated as follows:

where y ₁, y ₂ and so on = experimental results/observation, n = number of experiments (i . . . n).

Irrespective of the category of the performance characteristic, the higher value of S/N ratio corresponds to a better performance (^{Kamaruddin, Khan, & Foong, 2010}). The maximization of S/N ratio signifies maximization of the desired effect (minimization of wear rate) against noise factor. Observation of the response table of the S/N ratio gives an optimal combination of input parameters for the required output characteristic. From Table 4, expt. 13 offers an optimal combination of 15 N load and 12% vol. of hBN for a minimum wear rate of 0.013 mm³/m with a maximum S/N ratio of 37.98933 dB.

3.2. Response plot

The interaction plot represents the interaction effect of control factors on performance characteristics, showing the minimum value of wear rate at the interaction of 15 N load and 12% vol. of hBN in Figure 3 and the maximum value of S/N ratio at the same combination in Figure 4 prepared with Minitab 17.

Fig. 3 Interaction plot for wear rate (mm³/m). 

Fig. 4 Interaction plot of S/N ratio for wear rate. 

From the interaction plot, for wear rate and S/N ratio, it is clear that wear is affected by the interaction of load and % volume of hBN. The interaction plot also presents an optimal combination of 15 N load and 12% vol. of hBN for minimum wear rate of 0.013 mm³/m.

3.3. Analysis of variance (ANOVA)

ANOVA standard statistical technique used to interpret experimental results. The analysis of variance is used to study the parameter combinations which significantly influence the output response, i.e., wear rate. The study was conducted at 90% of confidence level. The results of the variance analysis are given in Table 5.

In the ANOVA table (^{Ghalme, Mankar, & Bhalerao, 2016}):

● The degree of freedom (DF) is a measure of amount independent information available from the given set of data. DF for concerning factor is less than the number of levels.

● The sequential sum of squares (Seq SS) of factor measures the variability in data contributed by that factor. Total SS is the sum of SS of an individual factor and SS of error.

where y¯ _i - is the mean of observation at ith factor level, y¯ - mean of all observation, y _ij value of jth observation at theith factor level, n _i - number of observation for ith factor level.

● Adjusted mean square (AdjMS) or variance is given by:

● Percentage contribution signifies individual contribution of a factor on the mean response. It is calculated by:

From the analysis of variance, it can be concluded that the interaction of load and % volume of hBN has the greatest contribution of 51.89% followed by 35.04% of % volume of hBN and 13.06% of the load on the wear rate of silicon nitride.

3.4. Morphology of worn surface

Worn surface of the composite material was examined using scanning electron microscope and energy dispersive spectroscopy (SEM-EDS) so as to understand the mechanism of wear. These micrographs were obtained after the tribological test at 200 rpm and a normal load of 15 N. SEM micrographs along with EDS are given in Figure 4. The mechanism of wear of the examined composite material is adhesive wear. In Figure 5, a consequence of adhesive wear can be observed because there was a pulling material from the contact area of the composite material. It was concluded by the visible traces in the form of cavities of irregular shapes and depth on the surface.

Fig. 5 SEM micrograph and EDS analysis of sample 1-5. 

4.1. Mathematical modelling

A second-order polynomial equation used to fit the experimental data using Minitab 17 statistical software. A quadratic model which includes the linear model can be described as:

where y is the response modelled as a function of constant, linear, interaction and quadratic terms formed from two predictor variables x ₁ and x ₂ , β ₀ is the model intercept coefficient, β _i (i = 1. . .5) are the coefficients of linear, interaction and quadratic terms, respectively, and ε is random error (^{MATLAB Stat Guide, 2010}). From the experimental data obtained from Taguchi orthogonal array experimentation the final equations obtained in terms of coded factors-load and % volume of hBN for wear rate (WR) as follows:

ANOVA is used to evaluate the variability between predicted data by model and experimental data.

In ANOVA table:

● Variance ratio (F value): commonly called as F-statistics, is the ratio of variance due to the individual factor and variance due to the error term.

Table 6 presents ANOVA for model calculated at 90% confidence level.

From F statistic table (Table 7) it is clear that the F-value calculated for the model is more than the F-value obtained from the design and analysis table (^{Ross, 2005}) indicating that the model is significant.

4.2. Optimization using simulated annealing

Simulated annealing (SA), name and inspiration come from the annealing process in metallurgy, a technique involving heating and controlled cooling of the material to increase the size of its crystal and reduce their defects. Simulated annealing is a technique for finding an optimal (not necessarily perfect) solution to an optimization problem. If you are in a condition to find the maximum or minimum of something, your problem can likely be tackled with simulated annealing. The first use or idea of SA is derived from a paper by ^{Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953)} in 1953. The Metropolis algorithm simulates the cooling process for a system by gradually lowering the temperature of the system until the system converges to a steady, frozen state.

The algorithm for SA as follows (^{Kirkpatrick, Gellat, & Vechhi, 1983}; ^{Rao, 2009}):

Using this algorithm code developed and simulated with MATLAB for Eq. (8), objective function wear rate to be minimized. The upper and lower bound of control factors are given in Eqs. (10) and (11). Results of the optimum value of the individual factors are shown in Table 8 with the best fitness plot illustrated in Figure 6.

Fig. 6 Best fitness plot.