# A New Uniaxial Tensile Model for Foam Metal/Epoxy Interpenetrated Phase Composites

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## Abstract

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## 1. Introduction

_{2}O

_{3}/Al polydimethylsiloxane IPC and Al

_{2}O

_{3}/Ni polydimethylsiloxane IPC by employing octagonal cells and Kelvin cells, calculated the compression and bending effects with COMSOL Multiphysics software and compared them with experimental results. Yuan et al. [16] proposed a finite element model of decahedra (six orthotetragonal and eight orthohexagonal) to simulate foam aluminum prisms in foam aluminum/polymer (polypropylene and acetal) IPC and calculated the strength of IPC under tensile loading. Chaturvedi et al. [17] also studied foam nickel/rubber IPC by the decahedral finite element model.

## 2. Tensile Mesoscopic Model

#### 2.1. Subsection

- The representative volume element is isotropic in mechanical properties; the matrix phase damage is isotropic.
- As the load is in the far-field z-direction, the direction is parallel to the direction normal to the upper surface of the representative volume element.
- Neither the matrix phase nor the reinforced phase undergoes volume change, and Poisson’s ratio is 0.5 in the plastic deformation stage, so the plastic spherical strain is zero in the calculation. The plastic deformation follows the conditions of total strain theory, and the loading mode is simple loading with small deformation.
- Both the reinforcement phases and matrix phases follow the von Mises yielding criterion.

#### 2.2. Deterioration Process Analysis of Mechanical Properties under Tensile Loading

#### 2.3. Damage Variables

## 3. Tensile Intrinsic Characterization

#### 3.1. Intrinsic Equation of the Representative Volume Element

#### 3.2. Damage Evolution Equation

## 4. Tensile Test

#### 4.1. Specimens of Epoxy Resins and IPC

#### 4.2. Test Instruments and Methods

#### 4.3. Test Results and Analysis

#### 4.4. Tensile Testing of Ni-Fe Alloys

## 5. Verification

## 6. Conclusions

- The force characteristics of the foam metal/epoxy IPC are analyzed under uniaxial tensile loading, and a microscopic mechanical model of the tensile representative volume element for the foam metal/epoxy IPC is established. The stress–strain relationships of representative volume elements are derived for foam metal/epoxy IPC in elastic and plastic deformation phases based on the assumptions of equal stress and equal strain; the damage evolution equations of IPC are determined with the effective area of the matrix phase as the damage parameter.
- The uniaxial tensile strengths of PPI20, PPI30, and PPI40 Ni-Fe/epoxy interpenetrated phase composites and their constituent phases (epoxy and Ni-Fe alloy) were tested in three groups each. The results show that the combination of three-dimensional networks interpenetrating does not significantly improve the tensile strength of the composites since the presence of weak interfaces.
- The damage evolution equations of PPI20 and PPI30 IPC are determined from the measured data of PPI40 Ni-Fe/epoxy composites, geometric data, and the constitutive phase Ni-Fe and epoxy intrinsic relationships, and then the intrinsic equations of PPI20 and PPI30 Ni-Fe/epoxy IPC are predicted. Satisfactory results are obtained in comparison with experimental data, thus verifying the accuracy and applicability of the representative volume element tensile model.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**The computational model for representative volume elements and uniaxial tensile of metal/polymer IPC.

**Figure 2.**Dimensional diagram of the reinforcing phase prisms in representative volume elements of metal/polymer IPC.

**Figure 4.**Microscopic defect diagram of Ni-Fe/Epoxy IPC tensile morphology (

**a**) initial defect (

**b**) process damage.

**Figure 7.**Diagram of tensile loading process of foam Ni-Fe/epoxy composite: (

**a**) original specimen; (

**b**) damaged specimen.

**Figure 10.**Stress–strain curve of tensile specimen: (

**a**) fixture force-displacement curve; (

**b**) epoxy resin; (

**c**) composite PPI20; (

**d**) composite PPI30; (

**e**) composite PPI40; (

**f**) comparison of epoxy and composites.

**Figure 14.**Comparison of predicted and measured results of intrinsic structure curves for Ni-Fe/EP IPC (

**a**) PPI20 and (

**b**) PPI30.

Material Type | Apparent Density (g·cm ^{−3}) | Ni-Fe Alloy Density (g·cm ^{−3}) | Young’s Modulus of Ni-Fe Alloy (MPa) |
---|---|---|---|

Ni-Fe foam(PPI20) | 0.18 | 8.23 | 22,847 |

Ni-Fe foam(PPI30) | 0.21 | 8.23 | 22,847 |

Ni-Fe foam(PPI40) | 0.26 | 8.23 | 22,847 |

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**MDPI and ACS Style**

Wang, X.; Zhang, L.; Zhao, Y.; Li, H.
A New Uniaxial Tensile Model for Foam Metal/Epoxy Interpenetrated Phase Composites. *Polymers* **2023**, *15*, 812.
https://doi.org/10.3390/polym15040812

**AMA Style**

Wang X, Zhang L, Zhao Y, Li H.
A New Uniaxial Tensile Model for Foam Metal/Epoxy Interpenetrated Phase Composites. *Polymers*. 2023; 15(4):812.
https://doi.org/10.3390/polym15040812

**Chicago/Turabian Style**

Wang, Xiaoxing, Lixin Zhang, Yu Zhao, and Huijian Li.
2023. "A New Uniaxial Tensile Model for Foam Metal/Epoxy Interpenetrated Phase Composites" *Polymers* 15, no. 4: 812.
https://doi.org/10.3390/polym15040812