# Computer Simulation of Composite Materials Behavior under Pressing

^{1}

^{2}

^{3}

^{4}

^{5}

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## Abstract

**:**

## 1. Introduction

_{2}O

_{3}by the discrete element modeling. All technological stages were analyzed for obtaining composite materials, experimental results for the hot pressing were received, and microscopic studies of the NiAl–Al

_{2}O

_{3}interface were conducted.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Technological Process of Obtaining Composite Materials

#### 2.2.1. Pressing

#### 2.2.2. Sintering

## 3. Numerical Method

#### 3.1. Construction of a Solid-State Model of a Composite Material

_{i}from 10 to 50 μm. Straight circular cylinders with diameters d

_{i}from 8 μm to 10 μm and length l

_{i}from 0.70 μm to 0.87 μm were taken for the short cylindrical filler.

#### 3.1.1. The Spherical Filler

_{i}in the range from 10 μm to 50 μm, respectively, and the position of the center (x

_{i}; y

_{i}; z

_{i}) in the range from d

_{i}/2 μm to a − d

_{i}/2 μm, which made it possible not to consider the issue of modeling the dissected filler. In addition, the condition of non-intersection of filler balls is imposed, which is mathematically formulated:

#### 3.1.2. The Short Cylindrical Filler

_{i}in the range from 8 μm to 10 μm, respectively, the length l

_{i}from 0.70 μm to 0.87 μm, the position of the center (x

_{i}; y

_{i}; z

_{i}) in the range from d

_{i}/2 μm to a − d

_{i}/2 μm, and direction cosines (a

_{xi}; a

_{yi}; a

_{zi}). Since d

_{i}>> li, two conditions are considered in the simulation:

_{ij}is the distance between the centers of mass of the cylinders.

#### 3.2. Construction of a Finite Element Model of a Composite Material

#### 3.2.1. Micromechanical Approach

#### 3.2.2. Macromechanical Approach

## 4. Results and Discussion

#### 4.1. Model Simulation Results

#### 4.2. Verification of the Results of the Micromechanical Approach (First Stage)

#### 4.3. Verification of the Results of the Macromechanical Approach (Second Stage)

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Graph of the real process of pressing PTFE-composition by the MS-500 press: I — pressure rise, II — endurance at maximum pressure, III — pressure relief.

**Figure 3.**The true stress–strain curve for industrial PTFE at 25 °C, provided that the speed of linear elongation deformations does not exceed 500 μm/s.

**Figure 6.**A solid-state model of composite materials randomly reinforced with spherical (

**a**) and short cylindrical (

**b**) inclusions.

**Figure 7.**The deformation state of the finite element micromechanical model of composite materials randomly reinforced with spherical (

**a**) and short cylindrical inclusions (

**b**) with applied boundary conditions with undeformed model.

**Figure 8.**Finite element micromechanical models of fillers with spherical (

**a**) and short cylindrical (

**b**) inclusions.

**Figure 9.**Macromechanical scheme of composite materials during compression pressing: 1 — matrix; 2, 6 — upper and lower punches; 3 — mandrel; 4 — powder weight; 5 — compressed tablet: experimental setup (

**a**); solid-state simulation model (

**b**).

**Figure 10.**Equivalent von Mises stress, Pa (

**a**) and equivalent plastic strain (

**b**) with spherical filler at the moment of loss of bearing capacity (first stage).

**Figure 11.**Equivalent stresses according to von Mises stress, Pa for matrix (

**a**) and filler (

**b**) and equivalent plastic strain (

**c**) with short cylindrical filler at the moment of loss of bearing capacity (first stage).

**Figure 12.**Stress– plastic strain (

**a**) and stress– total strain (

**b**) curves for composite with spherical filler (first stage).

**Figure 13.**Stress– plastic strain (

**a**) and stress– total strain (

**b**) curves for composite with short cylindrical filler (first stage).

**Figure 14.**Equivalent stresses according to von Mises stress (

**a**) and residual (plastic) relative linear strains (

**b**) for composite with spherical filler at the moment of full compression (second stage).

**Figure 15.**Equivalent stresses according to von Mises stress (

**a**) and residual (plastic) relative linear strains (

**b**) for composite with short cylindrical filler at the moment of full compression (second stage).

Designation | Material | Size, μm | Density, kg·m^{−3} | Modulus of Elasticity, MPa | Poisson’s Ratio |
---|---|---|---|---|---|

Matrix | PTFE | 50–500 | 2200 | 686.5 | 0.45 |

Spherical inclusions | Coke | 10–50 | 1730 | 500 | 0.30 |

Short cylindrical inclusions | Kaolin | up to 10 | 2350 | 92000 | 0.18 |

**Table 2.**Characteristics of strength and elastic-plasticity for simulation models of composite materials with a micromechanical approach (first stage).

Composition (Matrix/Filler) | Mass/Volume Fractions of Matrix and Filler | The Shape of the Filler | Ultimate Strength Simulation/Experiment, MPa | Average Ultimate Total Strain, % | Average Ultimate Plastic Strain, % | Poisson’s Ratio |
---|---|---|---|---|---|---|

PTFE + coke | 80:20/75.88:24.12 | spherical | 19.72/18.6 | 88.34 | 73.55 | 0.406 ± 0.005 |

PTFE + kaolin | 98:2/98.13:1.87 | short cylindrical | 17.86/17.8 | 28.49 | 18.18 | 0.445 ± 0.005 |

**Table 3.**Strain capacity of composite materials after mechanical processing based on simulations and experimental data for materials after heat treatment.

Composition (Matrix/Filler) | After Mechanical Processing (Simulation Data) | After Heat Treatment (Experimental Data) | ||
---|---|---|---|---|

Average Total Strain under 35 MPa Pressure, % | Average Plastic Strain under 35 MPa Pressure, % | Total Strain Capacity after Unloading, % | Total Strain Capacity, % | |

PTFE + coke | 5.9844 | 2.8021 | 88.34 − 2.80 = 85.54 | 115 |

PTFE + kaolin | 1.4363 | 0.20061 | 28.49 − 0.20 = 28.29 | 432 |

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**MDPI and ACS Style**

Berladir, K.; Zhyhylii, D.; Brejcha, J.; Pozovnyi, O.; Krmela, J.; Krmelová, V.; Artyukhov, A.
Computer Simulation of Composite Materials Behavior under Pressing. *Polymers* **2022**, *14*, 5288.
https://doi.org/10.3390/polym14235288

**AMA Style**

Berladir K, Zhyhylii D, Brejcha J, Pozovnyi O, Krmela J, Krmelová V, Artyukhov A.
Computer Simulation of Composite Materials Behavior under Pressing. *Polymers*. 2022; 14(23):5288.
https://doi.org/10.3390/polym14235288

**Chicago/Turabian Style**

Berladir, Khrystyna, Dmytro Zhyhylii, Jiří Brejcha, Oleksandr Pozovnyi, Jan Krmela, Vladimíra Krmelová, and Artem Artyukhov.
2022. "Computer Simulation of Composite Materials Behavior under Pressing" *Polymers* 14, no. 23: 5288.
https://doi.org/10.3390/polym14235288