Experimentally Predicted Optimum Processing Parameters Assisted by Numerical Analysis on the Multi-physicomechanical Characteristics of Coir Fiber Reinforced Recycled High Density Polyethylene Composites

This paper presents the analysis of processing parameters in the fabrication of coir fiber recycled high density polyethylene composite through experimental data and Taguchi grey relational analysis. Three processing parameters; fiber conditions, fiber length, and fiber loading with mixed level design, having orthogonal array L32 (2**1 4**2) were employed in the preparation of polymer composite. Numerical analysis assisted by Taguchi design was conducted on the experimental multi-physicomechanical characteristics of the polymer composite for optimum processing parameters. The optimum grey relational grade was gotten to be 0.8286 and was experimentally validated with 95% confidence interval. The optimum processing parameters were discovered to be a treated fiber having 8 mm length at 30% loading. Although, other processing parameters are significant, but fiber loading is the most significant parameter. Correspondingly, the contribution of residual error on the overall multi-physicomechanical characteristics is insignificant having 2.43% of contribution.

Polymer matrix impregnated with natural fiber of high strength is a natural fiber polymer composites (NEPC) [5].
Moreover, recycled HDPE is a potential material with a suitable matrix. It is abundant globally, due to the fact that it is relatively cheap, easy to be processed and have some desirable properties [6]. Because HDPE is a disposable container, it is easier to be recycled, coupled with the fact that it is very much compatible with fiber reinforcement. Its low melting point makes it less susceptible to degradation, even though some reports have shown that it degrades, especially when it is crosslinked, but it can be mitigated through some treatment processes such as alkali treatment [7]. Surface treatment is essential when it comes to improving natural fiber/plastic bonds, but majority of its techniques employed expensive equipment and chemicals [8]. However, some techniques, for instance, alkali treatment of natural fibers, salane coupling, etc. are not expensive. Hence, in this work, we employed alkali treatment technique to improve the coconut fiber's properties for better mechanical and water absorption competence, which can make it suitable for some load bearing applications.
Natural fibers have variations in their chemical components depending on the type of natural fiber, its maturity, source and processes. In addition, the combination of natural fiber and processing method makes it essential to find effective parameter setting to obtain high-performance composites. This is to attain a guide for manufacturers and an acceptable standard for highperformance coir fiber composite production. Hence, this study seeks to employ effective optimization technique in finding the best process parameter values for coir fiber recycled high density polyethylene composite production [9].
Taguchi approach is employed in this study for the optimization because it is robust and cost effective. In classical process parameter design, a large number of experiments has to be carried out as the number of the processing parameters increases; making it complex and not easy to use. Taguchi's approach provides an efficient and systematic approach for conducting experiments to determine the optimum setting of design parameters for performance and cost. The Taguchi method uses orthogonal arrays to study a large number of variables using a small number of experiments [10]. The conclusions made from small size experiments are valid over an entire experimental region spanned by the factors and their settings. Taguchi approach can reduce research and production costs by simultaneously studying a large number of parameters. By applying the Taguchi parameter design technique, product and process designs performance can be improved.
Grey relational analysis is augmented with Taguchi design method for multiple performance characteristics of the polymer composite. The Grey relational analysis procedure is used to combine all the considered performance characteristics into a single value that can be used as the single characteristic in optimization problems. Thus, the study will explore simplifying optimization of the complicated multiple performance characteristics of the process using the Taguchi-grey relational analysis. Different studies have been conducted using Taguchi-grey relational analysis to optimize processing factors for multiple performance characteristics. Abifarin [10] employed Taguchi-grey relational analysis to optimize multiple mechanical characteristics of natural hydroxyapatite. Stalin et al. [11] used Taguchi-grey relational analysis and ANN-TLBO algorithm to optimize wear parameters for silicon nitride filled AA6063 matrix composites. Pawade & Joshi [12] optimized multi-objective surface roughness and cutting forces in high-speed turning of Inconel 718 with the help of Taguchi-grey relational analysis. Tzeng et al. [13] optimized multiple performance characteristics of turning operations using Taguchi-grey relational analysis.
In this study, the effect of one surface modification, five levels of fiber loading and five level of fiber lengths on multiple response of coir fiber recycled high density polyethylene composites were investigated. For experiment that has multiple responses, the input factors combination that gives high value in a particular performance characteristic might not be desirable for another. Thus there is a need to find a factor combination that will give desirable values for all the considered performance characteristics, and was done through multi-response optimization using Taguchi gray relational analysis.

Coir fiber
The coir fiber used was obtained from coconut husk (From Lagos state, Nigeria). The outer layer shell or the mesocarp of the coconut was where the fiber was extracted from. The coconut was gathered from the Arecaceae family of palm, particularly cocus nucifera. Retting process was used for extraction. This process involves allowing the fibers to be separated from the woody core by controlled degradation of the husk [14]. The Coconut Husk were soaked in water for 3 months, to decompose the pulp on the shell, after which the fibers were extracted by pulling them out and the fibers then washed again to remove the embedded dirt between the fibers were then combed were air dried for 48 as posited by Gu [15]. These fibers were cut into varying lengths of 2mm, 4mm, 6mm and 8mm. These cut fibers were treated in 5% NaOH of analytical grade obtained from DOW Chemicals. The fibers were soaked and left for 10 hrs at room temperature. The fibers were then rinsed in distilled water until it was no longer slippery. The fibers were then neutralized with 1% acetic acid. The fibers were dried in open air for 24 hours and placed in an oven at a temperature of 60 degrees Celsius to ensure proper drying.

High density polyethylene (recycled)
The high density polyethylene used in this work was obtained from the empty yoghurt bottles from a particular company simply referred to as SAN yoghurt in the main campus of Ahmadu Bello University, Zaria, Nigeria. They have the monopoly of yogurts sale on campus and therefore have high patronage. This also implies that the bottles are littered everywhere within the school surrounding. The bottles were obtained from their campus depot, washed properly with mild detergent and dried in open air, away from the sun. The dried containers are cut into smaller sizes manually before shredding inti smaller bits using a Worthy Crust Machines, which has a capacity of 81kg, Rev/min of 1440 at a frequency of 50hertz.

Taguchi DOE
Taguchi recommends Orthogonal Array (OA) to carry out experiments. Three processing parameters with mixed levels design were considered on the resultant mechanical and physical properties of fiber reinforced HDPE composite. The Table 1a below highlight the experimental design: The orthogonal array L32 (2**1 4**2) selected as shown in Table 1b having 32 rows. The considered orthogonal array was based on the design in Table 1a, and was generated in the Minitab, given in Table 1b.

Composite Formulation
The matrix and the fiber were blended using the two roll mill. The machine was heated for 30-45 minutes to attain a temperature of 180°C. The rear and front rolls co-rotate. The front roller is responsible for the shear force so it rotates faster. It squeezed the material at the nip of the rollers, forming it into a band After the HDPE had melted the filler was added to it. The two-roll mill rotated at 70rpm for 5 minutes. Under this condition, a uniform dispersion and distribution of fibers can be achieved in recycled HDPE. The shredded HDPE is first of all filled in the heated mixing cavity while the rolls are under constant rotational speed. After 4 minutes, the fibers were carefully added into the already melted HDPE and the mixing process was continued for another 2minutes. The rolls are then stopped and the composites removed from the heated roll of the two-roll mill, and cut in a non-uniform sizes which are wide enough to fit into the mold to be used for compression with a little extra. A fiber loading ranging from 10-50% was used. The 8 station compression molding machine was used for this process. It was heated for 40minutes to 1hour to raise the temperature to about 170 °C, a temperature lower than the one used during melting. This is to prevent degradation of the compound. Here, heat and pressure is applied. Before the sample was placed into the machine. The compounded material was then pressed into a 130 by 130 by 3.2 mm mold and the mold was placed in the machine. The sample been molded was held for 1 minute at that temperature under compression before been cooled at room temperature.

Tensile test
Tensile strength was carried out according to ASTM D 638-06 on dumbbell shaped specimens using Universal Testing machine. The testing condition used were crosshead speed 10 mm/min, gauge length of 60 mm and load cell 1 KN. The recorded value is the average of 3 results. Besides the ultimate tensile strength (UTS), percentage of elongation was also obtained from the tensile testing machine [16].

Flexural strength test
Flexural strength is the ability of the composite material to withstand bending forces applied perpendicular to its longitudinal axis. The 3-point flexural test was conducted with a universal testing machine (model 4240). Flexural testing was carried out in accordance with ASTM D790-08 with a span length of 60mm. The dimensions of the specimen in each case was 100 by 30 by 3mm. The flexural strength and flexural modulus of the composite specimens and will be determined using the following equations;

Impact strength test
The impact strength of a material provides information regarding the energy required to break a specimen of a given dimension, the magnitude of which reflects the material's ability to resist a sudden impact [17]. Three specimens were tested and an average of these results taken. The test was performed in accordance to ASTM E23.

Hardness test
Hardness is the resistance of a material to deformations, indentations or scratching. The method was based on the rate of penetration of a specified indenter forced into the material, under specified conditions. Each sample was subjected to 3 hardness readings at different positions on the sample bases and the average taken. ASTM D2240 (Shore D) was used [18,26,27].

Water absorption test
Coir/HDPE composite being bio-based have the tendencies of absorbing water and so it is important to study their water absorption properties with relation to time. This is crucial for optimum utilization [19]. Water absorption is troublesome because it can lead to matrix cracking, dimensional instability, and inferior mechanical properties of the fiber-reinforced polymer composite [20]. Water absorption test was done by taking the difference between the mass of the samples before and after water immersion at intervals according to ASTM standard D 570-98. The measurement was taken every day for the period of 29 days. The formula used to calculate the values is shown in equation 3 [21]: Where, 1 = weight of sample before immersion and 2 = weight of sample after immersion Figure 1 shows the experimental procedure for the fabrication of coir fiber reinforced recycled high density polyethylene composite.

Numerical Analysis
The numerical analysis considered in this study was grey relational analysis. The first step of the grey relational analysis is the grey relational generation. During this step, the responses will be normalized in the range between zero and one. Next, the grey relational coefficient will be calculated from the normalized data to express the relationship between the desired and the actual responses. Then, the grey relational grade will be computed by averaging the grey relational coefficient corresponding to each performance characteristic. Overall evaluation of the multiple performance characteristics is based on the grey relational grade. As a result, optimization of the complicated multiple performance characteristics can be converted into optimization of a single grey relational grade. The optimal level of the process parameters is the level with the highest grey relational grade. Furthermore, a statistical analysis of variance (ANOVA) is performed to find which process parameters are statistically significant. With the grey relational analysis and statistical analysis of variance, the optimal combination of the process parameters can be predicted. Finally, a confirmation experiment is conducted to verify the optimal process parameters obtained from the analysis. These steps were obtained from Abifarin [10], Lin [24] & Achuthamenon et al. [25] 3.0 Results and Discussion

Grey Relational Analysis for the Multiple Performance Characteristics
A linear data preprocessing method employed in this study for the eight performance characteristics is the higher the-better and is expressed as: Where xi (k) is the value after the grey relational generation, min yi (k) is the smallest value of yi (k) for the kth response, and max yi (k) is the largest value of yi (k) for the kth response.
Where Δ ( ) = ∥xo (k) − xi (k)∥= difference of the absolute value between * (k) and * (k); = distinguishing coefficient (0∼1), but it is generally set at 0.5 to allocate equal weights to every parameter; and * (k) and * (k) refer to reference and compatibility sequences, respectively. Δ and Δ are the minimum and maximum deviations of each response variable. The grey relational coefficient results for the experimental layout are shown in Table 4a and 4b.   As shown in equation (6), a composite grey relational grade (GRG), is then computed by averaging the GRC of each response variable, according to Abifarin [10]: (6) Where = the value of GRG determined for the ith experiment, n is the aggregate count of the performance characteristics. Table 5 shows the GRG: Optimization of the 8 multiple performance characteristics can be converted into optimization of a single grey relational grade. The mean of the grey relational grade for each level of the considered processing parameters, and the total mean of the grey relational grade is summarized in Table 5. Figure 2 shows the grey relational grade graph, where the dashed line reflects the total mean of the grey relational grade. The higher value of the grey relational grade represents the stronger relational degree between the reference sequence x0(k) and the given sequence xi(k). The reference sequence x0(k) is the best process response in the experimental layout. The highest value of the grey relational grade means that the corresponding processing parameters is closer to optimal. Meaning, optimization of the complicated multiple performance characteristics can be converted into optimization of a single grey relational grade. The mean of the grey relational grade for each level of factors, and the total mean of the grey relational grade is summarized in Table 6. Figure 2 is the grey relational grade graph, where the dashed line shows the total mean of the grey relational grade.

Analysis of Variance
The essence of ANOVA is to investigate the factors level combination that significantly affects the overall performance characteristics. This was done by separating the total variability of the grey relational grades, which is measured by the sum of the squared deviations from the total mean of the grey relational grade, into contributions by each factor and the error. First, the total sum of the squared deviations SST from the total mean of the grey relational grade can be calculated using equation (4).
Where p= number of experiments in the orthogonal array, and j= mean of the grey relational grade for the jth experiment. The total sum of the squared deviations SST is decomposed into two sources: the sum of the squared deviations SSd due to each factor and the sum of the squared error SSe. The percentage contribution by each factor combination to the total sum of the squared deviations SST can be used to evaluate the importance of the factor combination change on the performance characteristics. In addition, the F test, named after Fisher [22] can also be used to determine which factor combination have a significant effect on the performance characteristic. Usually, the change of the factor combination has a significant effect on the performance characteristic when the F value is large. Results of the ANOVA (Table 7) indicate that fiber loading is the most significant factor affecting the multiple performance characteristics, followed by fiber length and treatment. The contribution of error, i.e. noise is insignificant based on the computed % contribution 0f 2.43%

Confirmation Test
After the determination of optimal level of the factors, the final step is to predict and very the quality characteristics as shown in equation (8): [23] = Where 0 represents the maximum of average GRG at the optimal level of factors and represents the mean GRG. The quantity q means the number of factors affecting response values.
From equation (8), the predicted grey relational grade using the optimal factor parameters was computed. From response table in Table 5, using equation (8), the predicted response is 0.8286, compared with the experimental values, which is 0.9921, and it is the experimental number 32.
To investigate closeness of experimental result is to the predicted result, confidence interval (CI) is used in equation (9)  The predicted optimal grey relational grade is: = 0.8286 The 95% confidence interval of the predicted optimal grey relational grade as posited by Abifarin [10] is given in equation 11: The experimental grey relational grade, which is for the experimental number 32 was found to be 0.9921. This value is within the confidence interval (95 %) of the predicted optimal grey relational grade.

Conclusions
The experimental investigations on the analysis of eight multiple performance characteristics (Impact strength, hardness, tensile strength, percentage of elongation, tensile modulus, flexural strength, flexural modulus and water absorption capacity) of coir fiber reinforced recycled HDPE composites have been conducted. From Taguchi grey relational analysis of the experimental results, the following conclusions can be made: i. Fabrication of coir fiber reinforced recycled HDPE composite with relatively low volume of fibers is feasible by simple hand lay-up technique. ii. The fiber reinforced HDPE composite has an optimum grey relational grade of 0.8286 and the validated experimental value was within 95% confidence interval. iii. The optimal control factors (fiber condition, fiber length, fiber loading) are set at (treated fiber (TF), 8mm and 30%wt) or (level 2, level 4, level 4). iv.
Fiber loading is the most significant factor affecting the multiple performance characteristics, followed by fiber length and treatment. v. The contribution of error, i.e. noise is insignificant based on the computed % contribution 0f 2.43%

Declaration
Funding: This research did not receive any funding

Conflicts of interest/Competing interests:
The authors declare no conflict of interest