# Shrinkage Optimization in Talc- and Glass-Fiber-Reinforced Polypropylene Composites

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Sample Preparation

#### 2.3. Shrinkage Measurements

#### 2.4. Distribution of Reinforcements

#### 2.5. Design of Experiments

#### 2.6. Optimization Methods

## 3. Results and Discussion

#### 3.1. Effect of the Reinforcement on Shrinkage

^{−6}1/C) had a lower thermal expansion coefficient than talc (10

^{−5}1/C) [29].

#### 3.2. Shrinkage as a Function of Location

#### 3.3. Distribution of Reinforcement

#### 3.4. Analysis of Variance (ANOVA)

#### 3.5. The Taguchi Method

#### 3.6. Regression Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Shrinkage of talc-reinforced polypropylene composites (PP/T) and glass-fiber-reinforced polypropylene composites (PP/GF) in the flow direction, depending on the reinforcement type.

**Figure 9.**Shrinkage in the flow direction, as a function of the measurement location: (

**a**) PP/T and (

**b**) PP/GF.

**Figure 10.**Shrinkage in the transverse direction, as a function of the measurement location: (

**a**) PP/T and (

**b**) PP/GF.

**Figure 17.**Interaction plot for the mean (

**a**) shrinkage in the flow direction, (

**b**) shrinkage in the transverse direction, and (

**c**) differential shrinkage.

**Figure 18.**Regression analysis plot for the shrinkage of PP/T: (

**a**) Shrinkage in the flow direction, and (

**b**) shrinkage in the transverse direction.

**Figure 19.**Regression analysis plot for the shrinkage of PP/GF: (

**a**) Shrinkage in the flow direction, and (

**b**) shrinkage in the transverse direction.

Level | Controllable Factor | Noise Factor | |
---|---|---|---|

Reinforcement Type | Reinforcement Content (wt %) | Reinforcement Size | |

1 | Talc | 5 | Big |

2 | Glass fiber | 10 | Small |

3 | 15 | ||

4 | 20 |

Number | Reinforcement Type | Reinforcement Content (wt %) | Reinforcement Size |
---|---|---|---|

1 | - | 0 | - |

2 | Talc | 5 | Big |

3 | Talc | 5 | Small |

4 | Talc | 10 | Big |

5 | Talc | 10 | Small |

6 | Talc | 15 | Big |

7 | Talc | 15 | Small |

8 | Talc | 20 | Big |

9 | Talc | 20 | Small |

10 | Glass fiber | 5 | Big |

11 | Glass fiber | 5 | Small |

12 | Glass fiber | 10 | Big |

13 | Glass fiber | 10 | Small |

14 | Glass fiber | 15 | Big |

15 | Glass fiber | 15 | Small |

16 | Glass fiber | 20 | Big |

17 | Glass fiber | 20 | Small |

Factor | Degrees of Freedom | Sum of Squares | Mean Square | F-Ratio (%) | p-Value |
---|---|---|---|---|---|

Reinforcement type | 1 | 22.197 | 22.197 | 919.82 | 0.000 |

Reinforcement content | 3 | 1.678 | 0.5593 | 1.90 | 0.137 |

Reinforcement size | 1 | 0.0026 | 0.0026 | 0.01 | 0.927 |

Factor | Degrees of Freedom | Sum of Squares | Mean Square | F-Ratio (%) | p-Value |
---|---|---|---|---|---|

Reinforcement type | 1 | 10.866 | 10.866 | 366.91 | 0.000 |

Reinforcement content | 3 | 2.036 | 0.6788 | 4.63 | 0.005 |

Reinforcement size | 1 | 0.0237 | 0.0237 | 0.14 | 0.709 |

Factor | Degrees of Freedom | Sum of Squares | Mean Square | F-Ratio (%) | p-Value |
---|---|---|---|---|---|

Reinforcement type | 1 | 0.8248 | 0.8248 | 423.83 | 0.000 |

Reinforcement content | 3 | 0.04670 | 0.01557 | 1.27 | 0.290 |

Reinforcement size | 1 | 0.004117 | 0.004117 | 0.33 | 0.567 |

Factor | Degrees of Freedom | Sum of Squares | Mean Square | F-Ratio (%) | p-Value |
---|---|---|---|---|---|

Reinforcement type | 1 | 22.197 | 22.197 | 9652.18 | 0.000 |

Reinforcement content | 3 | 1.6778 | 0.5593 | 243.19 | 0.000 |

Reinforcement typeⅹcontent | 3 | 0.0389 | 0.0130 | 5.64 | 0.002 |

Factor | Degrees of Freedom | Sum of Squares | Mean Square | F-Ratio (%) | p-Value |
---|---|---|---|---|---|

Reinforcement type | 1 | 10.866 | 10.866 | 3827.91 | 0.000 |

Reinforcement content | 3 | 2.0363 | 0.6788 | 239.12 | 0.000 |

Reinforcement typeⅹcontent | 3 | 0.0693 | 0.0231 | 8.13 | 0.000 |

Factor | Degrees of Freedom | Sum of Squares | Mean Square | F-Ratio (%) | p-Value |
---|---|---|---|---|---|

Reinforcement type | 1 | 0.8249 | 0.8249 | 708.69 | 0.000 |

Reinforcement content | 3 | 0.0467 | 0.01557 | 13.37 | 0.000 |

Reinforcement typeⅹcontent | 3 | 0.0213 | 0.0071 | 6.10 | 0.001 |

No. | A | B (wt %) | Shrinkage (%) | S/N Ratio (dB) | |||||
---|---|---|---|---|---|---|---|---|---|

1 | Talc | 5 | N1 | 1.664 | 1.618 | 1.644 | 1.587 | 1.598 | −4.394 |

N2 | 1.705 | 1.700 | 1.654 | 1.700 | 1.710 | ||||

2 | Talc | 10 | N1 | 1.592 | 1.577 | 1.577 | 1.582 | 1.592 | −3.835 |

N2 | 1.526 | 1.516 | 1.526 | 1.547 | 1.511 | ||||

3 | Talc | 15 | N1 | 1.414 | 1.373 | 1.419 | 1.414 | 1.399 | −3.021 |

N2 | 1.419 | 1.444 | 1.434 | 1.439 | 1.404 | ||||

4 | Talc | 20 | N1 | 1.296 | 1.317 | 1.307 | 1.296 | 1.327 | −2.164 |

N2 | 1.251 | 1.256 | 1.251 | 1.261 | 1.266 | ||||

5 | GF | 5 | N1 | 0.531 | 0.531 | 0.618 | 0.541 | 0.597 | 3.684 |

N2 | 0.740 | 0.730 | 0.750 | 0.740 | 0.704 | ||||

6 | GF | 10 | N1 | 0.541 | 0.500 | 0.556 | 0.531 | 0.536 | 6.374 |

N2 | 0.434 | 0.393 | 0.398 | 0.413 | 0.459 | ||||

7 | GF | 15 | N1 | 0.286 | 0.265 | 0.286 | 0.311 | 0.271 | 10.351 |

N2 | 0.316 | 0.316 | 0.296 | 0.332 | 0.347 | ||||

8 | GF | 20 | N1 | 0.271 | 0.276 | 0.260 | 0.260 | 0.250 | 11.358 |

N2 | 0.260 | 0.306 | 0.281 | 0.281 | 0.255 |

No. | A | B (wt %) | Shrinkage (%) | S/N Ratio (dB) | |||||
---|---|---|---|---|---|---|---|---|---|

1 | Talc | 5 | N1 | 1.595 | 1.551 | 1.572 | 1.545 | 1.551 | −4.041 |

N2 | 1.602 | 1.595 | 1.636 | 1.639 | 1.633 | ||||

2 | Talc | 10 | N1 | 1.511 | 1.507 | 1.507 | 1.507 | 1.511 | −3.489 |

N2 | 1.470 | 1.460 | 1.497 | 1.487 | 1.484 | ||||

3 | Talc | 15 | N1 | 1.328 | 1.328 | 1.345 | 1.355 | 1.352 | −2.668 |

N2 | 1.379 | 1.386 | 1.372 | 1.386 | 1.362 | ||||

4 | Talc | 20 | N1 | 1.264 | 1.254 | 1.264 | 1.261 | 1.264 | −1.861 |

N2 | 1.210 | 1.213 | 1.230 | 1.200 | 1.227 | ||||

5 | GF | 5 | N1 | 0.848 | 0.852 | 0.865 | 0.845 | 0.875 | 0.463 |

N2 | 1.034 | 1.021 | 1.048 | 1.031 | 1.021 | ||||

6 | GF | 10 | N1 | 0.821 | 0.818 | 0.804 | 0.794 | 0.825 | 2.252 |

N2 | 0.737 | 0.696 | 0.710 | 0.754 | 0.744 | ||||

7 | GF | 15 | N1 | 0.510 | 0.453 | 0.470 | 0.446 | 0.460 | 4.997 |

N2 | 0.629 | 0.632 | 0.673 | 0.652 | 0.629 | ||||

8 | GF | 20 | N1 | 0.466 | 0.466 | 0.480 | 0.470 | 0.470 | 6.621 |

N2 | 0.450 | 0.483 | 0.463 | 0.443 | 0.473 |

No. | A | B (wt %) | Shrinkage (%) | S/N Ratio (dB) | |||||
---|---|---|---|---|---|---|---|---|---|

1 | Talc | 5 | N1 | 0.069 | 0.067 | 0.072 | 0.043 | 0.046 | 23.038 |

N2 | 0.103 | 0.104 | 0.018 | 0.060 | 0.077 | ||||

2 | Talc | 10 | N1 | 0.082 | 0.070 | 0.070 | 0.075 | 0.082 | 23.958 |

N2 | 0.056 | 0.056 | 0.029 | 0.059 | 0.027 | ||||

3 | Talc | 15 | N1 | 0.086 | 0.045 | 0.074 | 0.058 | 0.047 | 24.676 |

N2 | 0.040 | 0.059 | 0.062 | 0.054 | 0.042 | ||||

4 | Talc | 20 | N1 | 0.032 | 0.063 | 0.043 | 0.036 | 0.063 | 26.755 |

N2 | 0.040 | 0.042 | 0.020 | 0.061 | 0.039 | ||||

5 | GF | 5 | N1 | 0.318 | 0.321 | 0.248 | 0.304 | 0.278 | 10.559 |

N2 | 0.294 | 0.291 | 0.297 | 0.291 | 0.316 | ||||

6 | GF | 10 | N1 | 0.280 | 0.318 | 0.248 | 0.263 | 0.289 | 10.600 |

N2 | 0.303 | 0.303 | 0.312 | 0.340 | 0.284 | ||||

7 | GF | 15 | N1 | 0.225 | 0.188 | 0.184 | 0.135 | 0.189 | 11.576 |

N2 | 0.312 | 0.316 | 0.377 | 0.321 | 0.282 | ||||

8 | GF | 20 | N1 | 0.196 | 0.191 | 0.220 | 0.210 | 0.220 | 14.092 |

N2 | 0.189 | 0.177 | 0.182 | 0.162 | 0.218 |

No. | Talc (wt %) | GF (wt %) | Shrinkage in FD (%) | Shrinkage in TD (%) | Differential Shrinkage (%) |
---|---|---|---|---|---|

1 | 20 | 0 | 1.290 | 1.245 | 0.045 |

2 | 19 | 1 | 1.308 | 1.274 | 0.034 |

3 | 18 | 2 | 1.313 | 1.292 | 0.021 |

4 | 17 | 3 | 1.307 | 1.300 | 0.006 |

5 | 16 | 4 | 1.290 | 1.300 | 0.009 |

6 | 15 | 5 | 1.265 | 1.291 | 0.026 |

7 | 14 | 6 | 1.231 | 1.274 | 0.043 |

8 | 13 | 7 | 1.190 | 1.249 | 0.059 |

9 | 12 | 8 | 1.142 | 1.218 | 0.076 |

10 | 11 | 9 | 1.089 | 1.181 | 0.092 |

11 | 10 | 10 | 1.030 | 1.137 | 0.108 |

12 | 9 | 11 | 0.965 | 1.088 | 0.123 |

13 | 8 | 12 | 0.897 | 1.034 | 0.137 |

14 | 7 | 13 | 0.824 | 0.974 | 0.150 |

15 | 6 | 14 | 0.747 | 0.910 | 0.163 |

16 | 5 | 15 | 0.667 | 0.842 | 0.175 |

17 | 4 | 16 | 0.583 | 0.769 | 0.186 |

18 | 3 | 17 | 0.497 | 0.693 | 0.196 |

19 | 2 | 18 | 0.407 | 0.612 | 0.205 |

20 | 1 | 19 | 0.315 | 0.528 | 0.214 |

21 | 0 | 20 | 0.220 | 0.441 | 0.221 |

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**MDPI and ACS Style**

Ryu, Y.; Sohn, J.S.; Kweon, B.C.; Cha, S.W.
Shrinkage Optimization in Talc- and Glass-Fiber-Reinforced Polypropylene Composites. *Materials* **2019**, *12*, 764.
https://doi.org/10.3390/ma12050764

**AMA Style**

Ryu Y, Sohn JS, Kweon BC, Cha SW.
Shrinkage Optimization in Talc- and Glass-Fiber-Reinforced Polypropylene Composites. *Materials*. 2019; 12(5):764.
https://doi.org/10.3390/ma12050764

**Chicago/Turabian Style**

Ryu, Youngjae, Joo Seong Sohn, Byung Chul Kweon, and Sung Woon Cha.
2019. "Shrinkage Optimization in Talc- and Glass-Fiber-Reinforced Polypropylene Composites" *Materials* 12, no. 5: 764.
https://doi.org/10.3390/ma12050764