# Machine Learning Study of the Effect of Process Parameters on Tensile Strength of FFF PLA and PLA-CF

^{*}

## Abstract

**:**

^{2}value of 91.75% for ultimate tensile strength, 94.08% for Young’s modulus, and 88.54% for strain at break. The genetic algorithm successfully identified optimal parameter values for the desired mechanical properties. For optimal ultimate tensile strength, PLA-CF was used at 222.28 °C, 0.261 mm layer, 40.30 mm/s speed, yielding 41.129 MPa. For Young’s modulus: 4423.63 MPa, PLA-CF, 200.01 °C, 0.388 mm layer, 40.38 mm/s. For strain at break: 2.249%, PLA, 200.34 °C, 0.390 mm layer, 45.30 mm/s. Moreover, this work is the first to model the process–structure property relationships for an additive manufacturing process and to use a multi-objective optimization approach for multiple mechanical properties, utilizing ensemble learning-based algorithms and genetic algorithms.

## 1. Introduction

_{2}on the mechanical properties of 3D-printed ABS matrix composites. They found that ABS reinforced with TiO

_{2}at a 5% weight ratio showed the highest ultimate tensile strength. Aissa et al. [12] experimented with reinforced polyamide (RPA) as the printing material and used printing speed, extrusion temperature, and layer thickness as FFF process parameters. They found that extrusion temperature and layer thickness had a more significant impact on tensile strength than printing speed. Mushtaq et al. [13] used ABS as a printing material and focused on part properties like flexural strength, tensile strength, surface roughness, print time, and energy consumption. The process parameters were layer thickness, printing speed, and infill density. Using a full central composite design, twenty specimens were tested. Layer thickness was shown to be critical for achieving the optimum surface roughness and print time, while infill density was critical for mechanical qualities. Zhang et al. [14] developed a data-driven predictive modeling approach to understand the structure–property relationship of FFF-fabricated continuous carbon fiber-reinforced polymers (CCFRP). The ensemble learning algorithm combined eight base learners: multiple linear regression, least absolute shrinkage and selection operator (lasso), multivariate adaptive regression splines (MARS), generalized additive model (GAM), K-nearest neighbors (KNN), support vector machine (SVM), extra-trees, and extreme gradient boosting (XGBoost). Their study concluded that the predictive model accurately predicted the flexural strength of CCFRP specimens, with a minimum RMSE of 9.87%, a minimum RE of 7.75%, and a maximum R

^{2}of 96.99%.

## 2. Machine Learning

#### 2.1. Machine Learning Regression Models

#### 2.1.1. Multiple Linear Regression

_{0}+ β

_{1}x

_{1}+ ⋯ + β

_{p}x

_{p}

_{0}is the value of y when the independent variables are equal to zero, and {β

_{1}, …, β

_{p}} are the estimated regression coefficients.

#### 2.1.2. Decision Tree Regression

#### 2.1.3. Least Absolute Shrinkage and Selection Operator (Lasso)

_{0}and β

_{j}represent the coefficients for the least squares estimates, and λ denotes the tuning parameter that regulates the penalty effect on the estimation of coefficients. The lasso offers an advantage over traditional least squares approaches as the penalty term facilitates managing the trade-off between variance and bias.

#### 2.1.4. Ridge Regression

_{1}, x

_{2}, x

_{3}, …, x

_{p}via the linear relationship:

#### 2.2. Ensemble Learning Methods

#### 2.2.1. Bagging and Boosting

_{i}is the step size, and −${\nabla}_{f{m}_{i-1}}L\left(f{m}_{i-1}\right)\left(.\right)$ denotes the opposite of the current fitting error relative to the existing model.

_{i}and ${\widehat{y}}_{i}$ are the actual label and the predicted label, respectively, f

_{i}is the weak learner, and Ω is the regulation term (Equation (10)), which is defined as:

#### 2.2.2. Stacking

#### 2.2.3. Blending

#### 2.3. Performance Metrics

#### 2.3.1. Root Mean Squared Error (RMSE)

#### 2.3.2. Coefficient of Determination (R^{2})

^{2}, also known as the coefficient of determination, represents the difference between 1 and the ratio of the sum of residual squares to the total sum of squares [28], as shown in Equation (12):

^{2}score of 1.0 signifies a perfect fit of the model to the data, while an R

^{2}value of 0.0 suggests that the predicted values are constant and equal to the mean value of the training data. A negative R

^{2}score implies that the model’s performance is exceptionally poor.

## 3. Methodology

#### 3.1. Choice of Material

#### 3.2. Design of the Experiment

#### 3.3. Data Collection and Modeling

^{2}score for the prediction of ultimate tensile strength was 91.75%, the R

^{2}score for Young’s modulus was 94.08%, and the R

^{2}score for strain at break was 88.54% (Figure 4). The RMSE values were also relatively low, indicating that the models have a good predictive accuracy.

#### 3.4. Influence of the Features Studied on the Mechanical Properties of the Part

#### 3.4.1. Feature Importance

#### 3.4.2. Analysis of the Response Surfaces

#### 3.5. Optimization of the Process Parameters

#### 3.5.1. Genetic Algorithm

#### 3.5.2. Optimization of the Process Parameters

- 1.
- Ultimate tensile strength (UTS)—the optimum solution has a value of 41.129 MPa. The optimal parameters for achieving this value are:
- Printing temperature: 222.28 °C;
- Layer thickness: 0.261 mm;
- Printing speed: 40.03 mm/s;
- Material: PLA-CF.

- 2.
- Young’s modulus—the optimal value is 4423.63 MPa, and the optimal parameters are:
- Printing temperature: 200.01 °C;
- Layer thickness: 0.388 mm;
- Printing speed: 40.038 mm/s;
- Material: PLA-CF.

- 3.
- Strain at break—the optimal solution has a value of 2.249%. The parameters for achieving this value are:
- Printing temperature: 200.34 °C;
- Layer thickness: 0.39 mm;
- Printing speed: 45.30 mm/s;
- Material: PLA.

## 4. Conclusions and Prospects

- UTS increases when layer thickness and printing speed decrease, with maximum values at printing temperatures between 210 °C and 225 °C;
- Young’s modulus increases with increasing layer thickness and printing speed and decreasing printing temperature;
- Strain at break increases with increasing printing temperature and decreasing printing speed, with maximum values for layer thicknesses between 0.375 mm and 0.425 mm.

- Both UTS and Young’s modulus increase when all studied process parameters (printing temperature, printing speed, and layer thickness) increase;
- Strain at break increases when printing temperature decreases, with maximum values for layer thicknesses between 0.375 mm and 0.425 mm, and printing speeds between 45 mm/s and 55 mm/s.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

PLA Run | Ultimate Tensile Strength | Modulus of Elasticity | Strain at Break | PLA- CF Run | Ultimate Tensile Strength | Young’s Modulus | Strain at Break |
---|---|---|---|---|---|---|---|

(σ) | (E) | (ϵ) | (σ) | (E) | (ϵ) | ||

1 | 26.66 | 1746.67 | 1.79 | 1 | 33.61 | 3754.25 | 1.42 |

2 | 25.92 | 1744.65 | 1.84 | 2 | 34.17 | 3356.07 | 1.44 |

3 | 27.34 | 1505.78 | 2.00 | 3 | 34.44 | 3497.39 | 1.55 |

4 | 24.50 | 1543.07 | 1.95 | 4 | 37.93 | 4391.66 | 1.16 |

5 | 26.85 | 1202.43 | 2.31 | 5 | 38.14 | 4174.61 | 1.30 |

6 | 25.93 | 1482.00 | 1.96 | 6 | 37.61 | 4581.69 | 1.10 |

7 | 31.41 | 1812.83 | 2.08 | 7 | 35.85 | 4125.07 | 1.08 |

8 | 29.42 | 1891.01 | 1.89 | 8 | 35.74 | 4132.72 | 1.10 |

9 | 24.30 | 1258.48 | 2.18 | 9 | 31.13 | 3984.64 | 0.92 |

10 | 27.23 | 1556.10 | 1.96 | 10 | 39.60 | 3505.53 | 1.56 |

11 | 30.20 | 2143.89 | 1.97 | 11 | 37.34 | 3986.06 | 1.30 |

12 | 31.21 | 1629.61 | 2.06 | 12 | 37.39 | 3853.34 | 1.38 |

13 | 28.87 | 1809.15 | 1.92 | 13 | 38.53 | 4153.85 | 1.44 |

14 | 28.39 | 1762.37 | 1.94 | 14 | 36.99 | 4000.50 | 1.30 |

15 | 27.16 | 1617.90 | 2.024 | 15 | 36.31 | 4060.63 | 1.22 |

16 | 33.59 | 1801.88 | 2.15 | 16 | 35.57 | 3768.16 | 1.37 |

17 | 29.87 | 1756.94 | 1.83 | 17 | 35.88 | 3939.81 | 1.22 |

18 | 25.90 | 1625.23 | 1.717 | 18 | 34.43 | 4034.85 | 1.06 |

19 | 30.21 | 1895.71 | 2.054 | 19 | 31.40 | 3497.64 | 1.37 |

20 | 32.03 | 1755.01 | 2.39 | 20 | 34.65 | 4250.31 | 1.38 |

21 | 32.95 | 2094.29 | 1.90 | 21 | 34.88 | 3941.19 | 1.51 |

22 | 30.64 | 1958.45 | 1.82 | 22 | 35.05 | 3339.23 | 1.70 |

23 | 30.38 | 1881.98 | 1.80 | 23 | 34.24 | 3518.94 | 1.47 |

24 | 29.65 | 1922.06 | 1.79 | 24 | 34.53 | 3256.32 | 1.79 |

25 | 26.15 | 1897.19 | 1.45 | 25 | 32.76 | 3343.46 | 1.37 |

26 | 29.91 | 1931.47 | 1.85 | 26 | 33.24 | 3432.23 | 1.33 |

27 | 31.54 | 2011.35 | 1.85 | 27 | 34.89 | 3912.19 | 1.22 |

## Appendix B

**Figure A1.**Response surface 3D plots of the predicted ultimate tensile strength of PLA-CF: (

**a**) printing temperature vs. layer thickness, (

**b**) printing temperature vs. printing speed, and (

**c**) printing speed vs. layer thickness.

**Figure A2.**Response surface 3D plots of the predicted ultimate tensile strength of PLA: (

**a**) printing temperature vs. layer thickness, (

**b**) printing speed vs. printing temperature, and (

**c**) printing speed vs. layer thickness.

**Figure A3.**Response surface 3D plots of the predicted Young’s modulus of PLA-CF: (

**a**) printing temperature vs. layer thickness, (

**b**) printing temperature vs. printing speed, and (

**c**) printing speed vs. layer thickness.

**Figure A4.**Response surface 3D plots of the predicted Young’s modulus of PLA: (

**a**) printing temperature vs. layer thickness, (

**b**) printing speed vs. printing temperature, and (

**c**) printing speed vs. layer thickness.

**Figure A5.**Response surface 3D plots of the predicted strain at break of PLA-CF: (

**a**) printing temperature vs. layer thickness, (

**b**) printing temperature vs. printing speed, and (

**c**) printing speed vs. layer thickness.

**Figure A6.**Response surface 3D plots of the predicted strain at break of PLA: (

**a**) printing temperature vs. layer thickness, (

**b**) printing speed vs. printing temperature, and (

**c**) printing speed vs. layer thickness.

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**Figure 4.**Observed versus predicted mechanical properties: (

**a**) strain at break (%), (

**b**) ultimate tensile strength (MPa), and (

**c**) Young’s modulus (MPa).

**Figure 8.**The optimal solution for each iteration of the optimization process for the mechanical properties.

Reference | Material | Parameters Studied | Major Findings |
---|---|---|---|

Gebisa et al. [5] | ULTEM 9085 | Contours number Raster parameters Air gap | Raster angle had the greatest influence on mechanical properties. |

Claver et al. [6] | PLA, ABS | Layer height Infill density Layer orientation | Infill density highly impacted tensile strength; layer thickness had a smaller effect. |

Chokshi et al. [7] | PLA | Layer thickness Infill pattern Contours number | Layer thickness and contours number impact flexural strength. |

Othman et al. [8] | PLA | Layer thickness Infill pattern Contours number | Infill density, followed by layer thickness, have the highest influence on mechanical properties. |

Ning et al. [9] | ABS with carbon fibers | - | Carbon fibers enhanced tensile strength and Young’s modulus but reduced toughness and yield strength. |

Love et al. [10] | Polymers with carbon fibers | - | Carbon fibers increased strength, stiffness, thermal conductivity, and reduced distortion in FDM parts. |

Perez et al. [11] | ABS with fibers and TiO_{2} | - | ABS reinforced with TiO_{2} at a 5% weight ratio showed the highest ultimate tensile strength. |

Aissa et al. [12] | RPA | Printing speed Extrusion temperature Layer thickness | Extrusion temperature and layer thickness influenced tensile strength more than printing speed. |

Mushtaq et al. [13] | ABS | Layer thickness Printing speed Infill density | Layer thickness has a critical influence on achieving the optimum surface roughness and print time; infill density was critical for mechanical qualities. |

Zhang et al. [14] | CCFRP | - | The predictive model accurately determined the flexural strength of CCFRP specimens. |

Factors | Description | Value |
---|---|---|

Bed temperature (°C) | Used to heat the build platform | 60 |

Infill density % | The amount of material used in the inside of the print | 100 |

Infill pattern | The form or structure of the material within the component | Lines |

Number of contours | The number of contours surrounding the part | 1 |

Factors | Level 1 | Level 2 | Level 3 |
---|---|---|---|

Printing temperature (°C) | 200 | 215 | 230 |

Layer thickness (mm) | 0.25 | 0.35 | 0.45 |

Printing speed (mm/s) | 40 | 50 | 60 |

Property Predicted | R^{2} (%) | RMSE | Mean of Actual Values |
---|---|---|---|

Ultimate tensile strength (σ) (MPa) | 91.75% | 1.23 | 33.87 |

Young’s modulus (E) (MPa) | 94.08% | 278.00 | 3233.74 |

Strain at break (ϵ) (%) | 88.54% | 0.09 | 1.91 |

Ultimate Tensile Strength | Young’s Modulus | Strain at Break | |
---|---|---|---|

Material (PLA/PLA-CF) | 67.30% | 92.70% | 71.60% |

Printing temperature | 12.89% | 2.44% | 7.08% |

Layer thickness | 9.68% | 2.99% | 13.19% |

Printing speed | 10.11% | 1.85% | 8.12% |

Mechanical Property | Value | Material | Printing Temperature | Layer Thickness | Printing Speed |
---|---|---|---|---|---|

Ultimate tensile strength | 41.129 MPa | PLA-CF | 222.28 °C | 0.261 mm | 40.30 mm/s |

Young’s modulus | 4423.63 MPa | PLA-CF | 200.01 °C | 0.388 mm | 40.38 mm/s |

Strain at break | 2.249% | PLA | 200.34 °C | 0.390 mm | 45.30 mm/s |

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**MDPI and ACS Style**

Ziadia, A.; Habibi, M.; Kelouwani, S.
Machine Learning Study of the Effect of Process Parameters on Tensile Strength of FFF PLA and PLA-CF. *Eng* **2023**, *4*, 2741-2763.
https://doi.org/10.3390/eng4040156

**AMA Style**

Ziadia A, Habibi M, Kelouwani S.
Machine Learning Study of the Effect of Process Parameters on Tensile Strength of FFF PLA and PLA-CF. *Eng*. 2023; 4(4):2741-2763.
https://doi.org/10.3390/eng4040156

**Chicago/Turabian Style**

Ziadia, Abdelhamid, Mohamed Habibi, and Sousso Kelouwani.
2023. "Machine Learning Study of the Effect of Process Parameters on Tensile Strength of FFF PLA and PLA-CF" *Eng* 4, no. 4: 2741-2763.
https://doi.org/10.3390/eng4040156