# The Influence of Cork and Manufacturing Parameters on the Properties of Cork–Rubber Composites for Vibration Isolation Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation of Samples

#### 2.2. Characterization of Samples

^{2}.

#### 2.3. Statistical Analysis

^{2}factorial analysis of variance (ANOVA) (function aov from R package stats). The cork–natural rubber samples analyzed were collected from compounds C, D, E and F. Regarding this study, all mechanical properties described in the previous section were analyzed. When assumptions of the factorial ANOVA failed to be accomplished, the alternative method consisted of using a robust two-way factorial ANOVA based on trimmed means (function t2way from R package WRS2) [44]. A level of trimming of 20% was chosen, as recommended by Wilcox [44].

#### 2.4. Regression Models

^{2}) and adjusted coefficient of determination (R

^{2}

_{adj}) were determined.

## 3. Results and Discussion

#### 3.1. Effect of Cork Granules

#### 3.1.1. Addition of Cork Granules

#### 3.1.2. Granulometry and Quantity

#### 3.2. Effect of Vulcanization Parameters

#### 3.2.1. Molding Pressure

#### 3.2.2. Vulcanization Temperature

#### 3.3. Application of Regression Models

^{2}equal to 44.50%. A summary of the regression analysis including the coefficients of the regression model and respective confidence intervals are presented in Table 6. The model obtained is not appropriate to conduct predictions about the value of apparent compression modulus, since the cork quantity only explains 44.50% of the variation of the apparent compression modulus.

^{2}and R

^{2}

_{adj}values was selected with quadratic and interaction terms included. After conducting a multiple linear regression using the ordinary least squares method, the assumption of residuals normally distributed was found not to be accomplished. As an alternative, a robust regression using Huber M-estimator was applied instead, using the same model terms. The coefficients obtained for each regression model (OLS and robust) are shown in Table 7. The robust regression model is presented in Figure 10. The value of the coefficient of determination, R

^{2}, obtained for the robust regression model was 94.71%, which makes it a useful model to predict the expected dynamic behavior of cork–rubber composites according to its cork quantity and compression conditions (apparent compression modulus and stress imposed).

## 4. Conclusions

^{2}) was below 45%, indicating a low prediction capacity. More data must be collected, and the existence of more influential variables should be examined in order to achieve a good prediction model for cork–rubber compounds. However, the developed model to predict the ratio between dynamic and apparent compression modulus according to the stress imposed and cork quantity, resulted in a useful tool for a product’s improvement with an R

^{2}value above 90%.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Effect of the addition of cork granules on the ratio between dynamic and static stiffness across different compression stress levels.

**Figure 2.**Results of cork analysis: (

**a**) Hardness Shore A; (

**b**) Static compression stress at 10% strain.

**Figure 3.**Results of cork analysis: (

**a**) Natural frequency at 1.5 MPa; (

**b**) Ratio between dynamic and static stiffness at different loads.

**Figure 4.**Results of cork analysis: interaction plots of: (

**a**) Hardness Shore A; (

**b**) Stress obtained at 10% compression strain; (

**c**) Natural frequency when loaded at 1.5 MPa.

**Figure 5.**Results from cork analysis: interaction plots of: (

**a**) Compression set; (

**b**) Tensile strength; (

**c**) Elongation at break; (

**d**) Tear strength; (

**e**) Rebound.

**Figure 6.**Results of vulcanization temperature analysis: (

**a**) Hardness Shore A; (

**b**) Static compression stress at 10% strain.

**Figure 10.**Experimental results and surface representing the regression model applied to predict the ratio between dynamic and apparent compression moduli.

Compound | A | B | C | D | E | F |
---|---|---|---|---|---|---|

Cork granulometry | − | Type 1 | Type 1 | Type 1 | Type 2 | Type 2 |

Cork quantity (phr ^{1}) | 0 | x | x/2 | 2x | x/2 | 2x |

^{1}phr—Parts per hundred rubber; x—standard cork granules quantity.

Hardness Shore A | Stress at 10% Strain (MPa) | Nat. freq. at 1.5MPa (Hz) | |||||||
---|---|---|---|---|---|---|---|---|---|

Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. | |

Compound A | 52 | 52.1 | 0.652 | 1.336 | 1.322 | 0.052 | 20.86 | 20.89 | 0.096 |

Compound B | 57 | 56.3 (+8.1%) | 0.975 | 1.536 | 1.520 (+15%) | 0.041 | 20.43 | 20.50 (−1.8%) | 0.191 |

Properties | Significant Factors ^{1} | Test Statistic | Percentage Contribution ^{3} |
---|---|---|---|

Hardness | A | F(1,16) = 150.59, p-value < 0.001 | 47.25% |

B | F(1,16) = 150.59, p-value < 0.001 | 47.25% | |

Stress at 10% strain | AB | F(1,16) = 17.32, p-value < 0.001 | 11.50% |

Natural frequency at 1.5 MPa | AB | F(1,16) = 55.79, p-value < 0.001 | 9.54% |

Compression set 50% ^{2} | A | Q = 12.95, p-value = 0.017 | 8.92% ^{4} |

B | Q = 117.56, p-value < 0.001 | 81.00% ^{4} | |

Tensile strength | A | F(1,8) = 5.95, p-value = 0.041 | 5.93% |

B | F(1,8) = 85.08, p-value < 0.001 | 84.88% | |

Elongation at break | AB | F(1,8) = 7.78, p-value = 0.024 | 15.61% |

Tear strength ^{2} | B | Q = 16.17, p-value = 0.005 | 58.62% ^{4} |

Rebound | AB | F(1,20) = 7.40, p-value = 0.013 | 0.58% |

^{1}A—Cork type; B—Cork quantity; AB—Interaction between cork type and quantity;

^{2}Robust ANOVA using a 20%-level trimmed mean;

^{3}Percentage contribution as the ratio between factor sum of squares to total sum of squares;

^{4}Results of percentage contribution obtained from parametric two-factor ANOVA results.

**Table 4.**Descriptive statistics of samples collected from compound D vulcanized at different pressure levels.

Hardness Shore A | Stress at 10% Strain (MPa) | Nat. freq. at 1.5 MPa (Hz) | |||||||
---|---|---|---|---|---|---|---|---|---|

Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. | |

Low(5 MPa) | 57 | 57.3 | 0.447 | 0.91 | 0.91 | 0.024 | 21.0 | 21.0 | 0.203 |

High(20 MPa) | 56.5 | 56.3 | 0.274 | 1.00 | 1.00 | 0.012 | 20.6 | 20.6 | 0.209 |

Properties | Compound A | Compound B |
---|---|---|

Hardness | H (3) = 17.72, p-value < 0.001 ^{1} | F (3,16) = 87.98, p-value < 0.001 |

Stress (10% strain) | F (3,7.4) = 246.72, p-value < 0.001 ^{2} | F (3,16) = 395.50, p-value < 0.001 |

Natural frequency | F (3,16) = 367.37, p-value < 0.001 | F (3,16) = 86.31, p-value < 0.001 |

^{1}Kruskal–Wallis test;

^{2}Welch’s F test.

Term | Coefficients | 95% CI | t | p-Value |
---|---|---|---|---|

Intercept (β_{0}) | 13.260 | [13.005; 13.515] | 109.430 | <0.001 |

Cork quantity (β_{1}) | 0.040 | [0.018; 0.062] | 3.799 | 0.001 |

Term | Coefficients | Percentage Contribution ^{1} | |
---|---|---|---|

OLS | Huber M-Estimator | ||

Intercept (β_{0}) | 1.497 | 1.489 | − |

$\sigma $ (β_{1}) | 0.179 | 0.188 | 87.73% |

$c$ (β_{2}) | −0.049 | −0.048 | 0.55% |

${\sigma}^{2}$ (β_{3}) | 0.067 | 0.065 | 0.97% |

${c}^{2}$ (β_{4}) | 0.002 | 0.002 | 4.74% |

$\sigma c$ (β_{5}) | 0.006 | 0.005 | 0.73% |

^{1}Percentage contribution of each parameter as the ratio between factor sum of squares to total sum of squares (parametric ANOVA results).

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**MDPI and ACS Style**

Lopes, H.; Silva, S.P.; Carvalho, J.P.; Machado, J.
The Influence of Cork and Manufacturing Parameters on the Properties of Cork–Rubber Composites for Vibration Isolation Applications. *Sustainability* **2021**, *13*, 11240.
https://doi.org/10.3390/su132011240

**AMA Style**

Lopes H, Silva SP, Carvalho JP, Machado J.
The Influence of Cork and Manufacturing Parameters on the Properties of Cork–Rubber Composites for Vibration Isolation Applications. *Sustainability*. 2021; 13(20):11240.
https://doi.org/10.3390/su132011240

**Chicago/Turabian Style**

Lopes, Helena, Susana P. Silva, João Paulo Carvalho, and José Machado.
2021. "The Influence of Cork and Manufacturing Parameters on the Properties of Cork–Rubber Composites for Vibration Isolation Applications" *Sustainability* 13, no. 20: 11240.
https://doi.org/10.3390/su132011240