Figure 1 shows the produced ginger leaves particles in different particle sizes.

The mean and S/N ratio for bending modulus of elasticity, modulus of rupture, and the impact energy are presented in Table 3. The S/N ratio for the three effects was calculated based on the higher the better criteria represented with Equation 1.

Table 3

Mean and S/N Ratio of Bending Modulus of Elasticity, Modulus of Rupture, and Impact Energy

SN | GLP Size (µm) | GLP Content (wt. %) | MOE | MOR | IE |

**Mean (MPa)** | **S/N (dB)** | **Mean (MPa)** | **S/N (dB)** | **Mean (J)** | **S/N (dB)** |

1 | 420 | 30 | 2340 | 67.3843 | 10.51 | 20.4321 | 1.1 | 0.8279 |

2 | 420 | 35 | 2450 | 67.7833 | 11.70 | 21.3637 | 1.9 | 5.5751 |

3 | 420 | 40 | 2400 | 67.6042 | 11.58 | 21.2742 | 2.8 | 8.9432 |

4 | 420 | 45 | 1700 | 64.6090 | 10.05 | 20.0433 | 3.4 | 10.6296 |

5 | 420 | 50 | 900 | 59.0849 | 7.37 | 17.3493 | 2.6 | 8.2995 |

6 | 520 | 30 | 2370 | 67.4950 | 10.63 | 20.5307 | 1.3 | 2.2789 |

7 | 520 | 35 | 2470 | 67.8539 | 11.90 | 21.5109 | 2.2 | 6.8485 |

8 | 520 | 40 | 2410 | 67.6403 | 11.62 | 21.3041 | 3.0 | 9.5424 |

9 | 520 | 45 | 1950 | 65.8007 | 10.25 | 20.2145 | 3.8 | 11.5957 |

10 | 520 | 50 | 950 | 59.5545 | 7.59 | 17.6048 | 2.8 | 8.9432 |

11 | 710 | 30 | 2330 | 67.3471 | 10.80 | 20.6685 | 2.0 | 6.0206 |

12 | 710 | 35 | 2490 | 67.9240 | 11.65 | 21.3265 | 2.9 | 9.2480 |

13 | 710 | 40 | 2400 | 67.6042 | 11.52 | 21.2290 | 3.3 | 10.3703 |

14 | 710 | 45 | 2280 | 67.1587 | 9.50 | 19.5545 | 4.1 | 12.2557 |

15 | 710 | 50 | 2100 | 66.4444 | 6.12 | 15.7350 | 3.1 | 9.8272 |

| | Mean | 2102.67 | 66.0859 | 10.186 | 20.00941 | 2.687 | 8.0804 |

Where MOE is the bending modulus of elasticity, MOR is the modulus of rupture and IE is the impact energy. The general mean for the MOE, MOR, and IE are 2102.67MPa, 10.186MPa, and 2.687J respectively and their S/N ratios are 66.0859dB, 20.00941dB, and 8.0804dB respectively. The response table for the means and S/N ratios of the MOE, MOR, and IE are presented in Table 4. Each is derived from averaging the measured responses of the factors at each level. Such that:

$${S}_{Pi}=\frac{\sum _{n=1}^{9}{\eta }_{in}}{l}$$

4

Where \({S}_{Pi}\) represents the average response of factor P(A, B) at level i; \(n\) is the experiment number; \({\eta }_{in}\) is the result of the S/N ratio or mean at level \(i\) appearing within the number of runs; \(l\) is the number of levels.

Table 4

Response Table for Means and S/N Ration of MOE, MOR, and IE in Respect to Particle Size and Particle Content.

| MOE | MOR | IE |

**Level** | **Particle** **Size** | **Particle** **Content** | **Particle** **Size** | **Particle** **Content** | **Particle** **Size** | **Particle** **Content** |

**Mean (MPa)** | **S/N (dB)** | **Mean (MPa)** | **S/N (dB)** | **Mean (MPa)** | **S/N (dB)** | **Mean (MPa)** | **S/N (dB)** | **Mean (MPa)** | **S/N (dB)** | **Mean (J)** | **S/N (dB)** |

1 | 1958 | 65.29 | 2347 | 67.41 | 10.242 | 20.09 | 10.647 | 20.54 | 2.360 | 6.855 | 1.467 | 3.042 |

2 | 2030 | 65.67 | 2470 | 67.85 | 10.398 | 20.23 | 11.750 | 21.40 | 2.620 | 7.842 | 2.333 | 7.224 |

3 | 2320 | 67.30 | 2403 | 67.62 | 9.918 | 19.70 | 11.573 | 21.27 | 3.080 | 9.544 | 3.033 | 9.619 |

4 | | | 1977 | 65.86 | | | 9.933 | 19.94 | | | 3.767 | 11.494 |

5 | | | 1317 | 61.69 | | | 7.027 | 16.90 | | | 2.833 | 9.023 |

Delta | 362 | 2.00 | 1153 | 6.16 | 0.480 | 0.53 | 4.723 | 4.50 | 0.720 | 2.689 | 2.300 | 8.451 |

Rank | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 |

Table 4 shows the MOE, MOR, and IE of the GLP-HDPE composite at different levels of particle size and particle content. The ranking shows that the particle content has more effect on the bending modulus of elasticity, modulus of rupture, and the impact energy as they have the best rank. These effects are depicted graphically in Figures 2, 3, and 4.

Figure 2(A) shows the effect of particle size on the Bending Modulus of Elasticity of the GLP-HDPE composite. There was a constant rise of the bending modulus of elasticity with an increase in particle size. It shows that the highest mean Bending Modulus of Elasticity of 2320MPa at means and 67.30dB at S/N ratio on the particle size of 710µm and the lowest Bending Modulus of Elasticity at 420µm particle size. Tensile modulus and internal bonding strength measurements are among the most important indicators of strength in the material and are the most widely specified property (Idris et al., 2011). Tensile modulus is an indication of the relative stiffness of a material; it is a measurement of the property of a material to withstand forces that tend to pull it apart and to determine to what extent the material stretches before breaking. The improvement in tensile modulus was noticed with the developed particleboards. These indicate that the use of ginger leaves particles and RHDPE in the production of the particleboards improved the load-bearing capacity of the board. Increased particle size is indicative of a reduced number of particles, reducing the possibility of fibrillation (initiation of fracture or crack from the interfaces of fiber and matrix adhesion).

The effect of particle content on the Bending Modulus of Elasticity properties is shown in Figure 2(B). It shows an increase in Bending Modulus of Elasticity with the increase in the amount of ginger leaf particle in the composite within a particle content of 30-35% beyond which there is a drop in the bending modulus of elasticity and the downward trend continues with increasing the particle content of the ginger leaves. The increase in Young’s modulus with increasing GLP is expected since the addition of GLP to HDPE increases the stiffness as stated by Bartczak et al. (1999). The presence of a polar group in the HDPE may contribute to electrostatic absorption between HDPE and the agro particles. The reverse trend at 35% may be attributed to the over-saturation of composite with the GLP leading to particle compaction, and therefore uneven distribution of the particles within the composites. Similar observations have been reported by Adewuyi *et al.* (2017), Orsar (2004), and Wasylciw (1999). In addition, the developed composite deform less until maximum load, which gives a higher tensile modulus.

Figure 3 (A) shows the effect of particle size on the Modulus of Rupture of the GLP-HDPE composite. There was a constant rise of the Modulus of Rupture with an increase in particle size from 420µm to 520µm. Beyond 520µm, the bending modulus of rupture reduced. Implying that increasing the particle size of the ginger leaves beyond 520µm will reduce the Modulus of rupture. It is also observed that the highest mean Modulus of Rupture of 10.398MPa at means and 20.23dB at S/N ratio on with particle size of 520µm and lowest Modulus of Rupture at 710µm particle size.

The effect of particle content on the Modulus of Rupture properties is shown in Figure 3 (B). It depicts an increase in Modulus of Rupture with the increase in the amount of ginger leaf particle in the composite within a particle content of 30-35% beyond which there is a drop in the Modulus of Rupture and the downward trend continues with increasing the particle content of the ginger leaves. This is in agreement with the observation of Rajak et al. (2019).

Figure 4 (A) shows the effect of particle size on the Impact Energy of the GLP-HDPE composite. There was a linear rise of the Impact Energy with an increase in particle size. It also shows that the highest mean Impact Energy of 3.080J at means and 9.544dB at S/N ratio on the particle size of 710µm and lowest Impact Energy at 420µm particle size. A similar observation was made by Orsar (2014) with the steep increase in the impact strength of the produced GLP-HDPE composite attributed to the presence of particles well bonded by the HDPE binder.

The effect of particle content on the Impact Energy properties is shown in Figure 4 (B). It depicts an increase in Impact Energy with the increase in ginger leaf particles in the composite within a particle content of 30-45% beyond which there is a drop in the Impact Energy with increasing the particle content of the ginger leaves. The increase in Impact Energy with increasing GLP is expected since the addition of GLP to ginger leaves particles increases the stiffness of the GLP-HDPE composite material. The reverse trend at 45% particle size may be attributed to the over-saturation of the composite with the GLP leading to particle compaction, increasing the brittleness. Therefore the highest impact energy is obtained at a ginger leaf particle size of 45% weight content.

Interaction Effects

Interaction effects between the considered factors were studied. The interaction effect is shown in Figure 5 (A-C).

Figure 5 (A) shows the Bending Modulus of Elasticity effect of the interaction between the particle size and the particle content. In agreement with Figure 1(A, B), the highest bending modulus of elasticity is obtained at regions with a combination of low particle content and the content and any particle size. The lowest bending modulus of elasticity was observed at regions of high particle content and low particle sizes. This implies that irrespective of the particle size, to obtain maximum bending modulus, GLP should be kept at lower percentage composition in the composite.

Figure 5 (B) shows the interaction effect between the particle size and the particle content on the Modulus of Rupture. In agreement to Figure 3(A, B), the highest Modulus of Rupture is obtained at regions with a combination of low particle content and the content and any particle size (32-42%). The lowest Modulus of Rupture was observed at regions of high particle content and low particle sizes. This implies that irrespective of the particle size, to obtain maximum Modulus, GLP should be kept at lower percentage composition in the composite.

Figure 4 (C) shows the Impact Energy effect of the interaction between the particle size and the particle content. In agreement with Figure 4(A, B), the highest Impact Energy is obtained at regions with a combination of high particle content and larger particle size. The lowest Impact Energy was observed at regions of low particle content and low particle sizes. Also, the reduction in impact energy is observed at particle content greater than 45%. This implies that the best impact energy is obtained at the region of 40-48% particle content and particle sizes greater than 500µm.

Analysis of Variance

The analysis of variance (ANOVA) is used to determine the significance of each factor considered on the effect measured. That is, the ANOVA was used to determine the significance of particle size and particle content on the MOE, MOR, and IE of the GLP-HDPE composites. The analysis of variance of means for the MOE, MOR, and IE is presented in Table 5-7 respectively.

Table 5

Analysis of Variance for MOE Means and S/N Ratio

Source | DF | SS: Mean | SS: SN | MS: Mean | MS: SN | P: Mean | P: SN | % Cont. Mean (%) | % Cont. S/N (%) |

Particle Size (µm) (A) | 2 | 367213 | 11.33 | 183607 | 5.665 | 0.194 | 0.234 | 9.54 | 9.69 |

Particle Content (wt.%) (B) | 4 | 2755627 | 79.66 | 688907 | 19.915 | 0.008 | 0.015 | 71.61 | 68.15 |

Residual Error | 8 | 725453 | 25.90 | 90682 | 3.237 | | | 18.85 | 22.16 |

Total | 14 | 3848293 | 116.89 | | | | | | |

Table 5 shows the analysis of variance of the Bending modulus of elasticity for the different factors considered. At 95% confidence interval, the particle size on the S/N and mean had an insignificant effect with a P-value of 0.234 and 0.194 (P>0.005). Implying that the particle size has no significant effect on the bending modulus of elasticity. Also, the ginger leaf particles content in the composite showed a significant effect on the Bending Modulus of Elasticity properties of the GLP-HDPE composite with a P-value of 0.015 at S/N ratio and 0.008 at means which is less than 0.005 (P<0.005). The percentage contribution of the particle size and particle content was shown by the analysis of variance of the S/N ratio and Bending Modulus of Elasticity means as depicted in Table 5 to be 9.69%, 9.54%, and 68.15%, 71.61% respectively. Implying that the particle content has a higher percentage contribution to the Bending Modulus of Elasticity properties. A change in the particle content has more tendency to affect the Bending Modulus of Elasticity property of the GLP-HDPE Composite.

Table 6

Analysis of Variance for MOR Means and S/N Ratio

Source | DF | SS: Mean | SS: SN | MS: Mean | MS: SN | P: Mean | P: SN | % Cont. Mean (%) | % Cont. S/N (%) |

Particle Size (µm) (A) | 2 | 0.5995 | 0.7548 | 0.2998 | 0.3774 | 0.162 | 0.211 | 1.32 | 1.76 |

Particle Content (wt.%) (B) | 4 | 43.8847 | 40.5095 | 10.9712 | 10.1274 | 0.000 | 0.000 | 96.39 | 94.54 |

Residual Error | 8 | 1.0419 | 1.5857 | 0.1302 | 0.1982 | | | 2.29 | 3.70 |

Total | 14 | 45.5262 | 42.8500 | | | | | | |

Table 6 shows the analysis of variance of the modulus of rupture concerning the particle size and particle content. At 95% confidence interval, the particle size on the S/N and mean had an insignificant effect with a P-value of 0.211 and 0.162 (P>0.005). Implying that the particle size has no significant effect on the Modulus of Rupture. Also, the ginger leaf particles content in the composite showed a significant effect on the Modulus of Rupture properties of the GLP-HDPE composite with a P-value of 0.000 at S/N ratio and 0.000 at means which is less than 0.005 (P<0.005). The percentage contribution of the particle size and particle content was shown by the analysis of variance of the S/N ratio and Modulus of Rupture means as shown in Table 6 to be 1.76%, 94.54%, and 1.32%, 96.3968% respectively. Implying that the particle content has a higher percentage contribution to the Modulus of Rupture properties so that a change in the particle content has more tendency to affect the Modulus of Rupture property of the GLP-HDPE Composite.

Table 7

Analysis of Variance for Impact Energy Means and S/N Ratio

Source | DF | SS: Mean | SS: SN | MS: Mean | MS: SN | P: Mean | P: SN | % Cont. Mean (%) | % Cont. S/N (%) |

Particle Size (µm) (A) | 2 | 1.3293 | 18.508 | 0.66467 | 9.2542 | 0.000 | 0.004 | 12.98 | 12.51 |

Particle Content (wt.%) (B) | 4 | 8.7640 | 123.060 | 2.19100 | 30.7651 | 0.000 | 0.000 | 85.61 | 83.20 |

Residual Error | 8 | 0.1440 | 6.346 | 0.01800 | 0.7933 | | | 1.41 | 4.29 |

Total | 14 | 10.2373 | 147.915 | | | | | | |

Table 7 shows the analysis of variance of the impact energy means and S/N ratio in respect to the variable considered. At 95% confidence interval, the particle size on the S/N and mean had a significant effect with a P-value of 0.004 and 0.000 (P>0.005). Implying that the particle size has a significant effect on the Impact of Energy. Also, the ginger leaf particles content in the composite showed a significant effect on the Impact Energy properties of the GLP/HDPE composite with a P-value of 0.000 at S/N ratio and 0.000 at means which is less than 0.005 (P<0.005). The percentage contribution of the particle size and particle content was shown by the analysis of variance of the S/N ratio and Impact Energy means depicted in Table 7 to be of 12.51%, 12.98%, and 83.20%, 85.61% respectively. Implying that the particle content has a higher percentage contribution to the Impact Energy properties. A change in the particle content has more tendency to affect the Impact Energy property of the GLP/HDPE Composite.

From Table 4, the optimum levels at which MOE, MOR, and IE are at the maximum are determined from the highest values of means or S/N ratio. The optimum MOE, MOR, and IE of the GLP-HDPE composite material are predicted using Equation 5.

$${T}_{opt}={T}_{m}+\sum _{k=1}^{{k}_{n}}\left[{\left({T}_{ik}\right)}_{max}-{T}_{m}\right]$$

5

The optimum of these effects are presented in Table 8 and it is compared with the rest of a confirmation test carried out with the optimum combination.

Table 8

Predicted and Confirmation of the Optimal Properties of the GLP-HDPE polymer composites

| MOE | MOR | IE |

Optimum Combination | A3B2 | A2B2 | A3B4 |

Predicted Mean | 2687J | 11.962MPa | 4.16J |

Confirmed Mean | 2490 | 11.90MPa | 4.1J |

Percentage Error (%) | 7.33 | 0.52 | 1.4 |

Regression Analysis

A mathematical model for the combination of particle size and particle content was derived from regression analysis carried out using the Minitab® 19 statistical software which is used for the prediction of the MOE, MOR, and IE of the developed composite. The regression analysis models are presented in Equations 6-8.

MOE = 8158 - 7.30 A - 169.1 B + 0.2145 A*B (6)

MOR = 12.28 + 0.0094 A - 0.034 B - 0.000267 A*B (7)

Impact Energy = -3.82 + 0.00577 A + 0.1287 B - 0.000082 A*B (8)

The mathematical models have an R-square value of 73.11%, 56.55%, and 64.5% for the MOR, MOR or IE respectively. This is high when compared to the R-Square values of other studies on the modeling of the mechanical properties of fiber reinforced polymer composites.

Figure 6 (A, B, and C) shows the comparison between the predicted and experimental effects.