# Experimental and Numerical Analysis of a Car Body Shield Loaded with a Ballistic Impact

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{®}or Twaron

^{®}type, composites with ultra-high molecular weight polyethylene (UHMWPE) of the Spectra

^{®}or Dyneema

^{®}type, and composites combined with ceramics. In addition to their high energy-intensive properties, another benefit is the high availability of these materials on the European market, and the possibility of obtaining them artificially [4,5,6].

## 2. Materials and Methods

#### 2.1. Shield Material and Its Characteristics

#### 2.1.1. Aramid Laminate

#### 2.1.2. Magnetic Foil

_{i}is principal stretches.

#### 2.2. Gun Fire and Car Body Material Characteristics

#### 2.3. Laboratory Tests

#### 2.4. Numerical Analysis

_{d}reaches the value 1. The parameter W

_{d}is defined by the equation:

_{1}, d

_{2}, d

_{3}, d

_{4}and d

_{5}are material parameters, σ* is a dimensionless ratio expressed as the pressure P and

**σ**is the effective stress (von Mises equivalent stress), $\dot{\epsilon}$ is the strain rate corresponding to a car body sheet metal, ${\dot{\epsilon}}_{0}$ is the reference strain and T* is the homologous temperature (dimensionless temperature value). Between the homologous temperature (T*) and melt temperature (T

_{m}), the following relationship exists:

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Examples of ad hoc applications of ballistic protection reinforcement: (

**a**) protection of the interior of the vehicle cabin; (

**b**) use of spall liner; (

**c**) explosion-proof reinforcement of the vehicle floor; (

**d**) possibility of protecting the seats with a flexible ballistic shield. Source: Developed based on advertising materials from Scanfiber Composites A/S.

**Figure 4.**Stand for strength tests: (

**a**) strength machine MTS, (

**b**) specimen, (

**c**) specimen after breaking, (

**d**) selected stretching curve for LIM 1 laminate specimen.

**Figure 8.**General view of the ammunition: (

**a**) 9 × 19 mm FMJ Parabellum, (

**b**) bullet, (

**c**) bullet cross section.

**Figure 9.**General view of the door from the Ford Focus car: (

**a**) from the front, (

**b**) from the inside.

**Figure 10.**General view of the tests: (1) fired from the position, (2) samples position, (3) light lamp, (4) place for data camera recorded, (5) computer system.

**Figure 12.**Door after shooting: bullet hole marked with red circles, deflection zones marked with green circles and the yellow marked zone represents the area not covered by the shields.

**Figure 13.**Discrete models: (

**a**) bullet jacket, (

**b**) bullet core, (

**c**) car door sheets and ballistic laminate.

**Figure 15.**Comparison of numerical and experimental deformation modes: (

**a**) numerical simulation, (

**b**) deformation of laminate plate, (

**c**) experimental bullet deformation, (

**d**) experimental bullets deformation.

**Figure 16.**Scheme adopted for numerical analyses of the protective system of the vehicle door surface.

**Figure 18.**Numerical and experimental deformation analysis view: (

**a**) numerical simulation of the deformation of the shield mounted on the tape; (

**b**) estimated dynamic deformation from FEM; (

**c**) one of the selected ballistic laminate layers.

Specification | Unit | LIM 1 Laminate | Single Fabric of Aramid | Matrix |
---|---|---|---|---|

Laminate thickness | [mm] | 4.8 | 0.6 | 0.2 |

Areal density | [g/cm^{2}] | 520 | 46 | 2.0 |

Density ρ | [g/cm^{3}] | 1.14 | 0.766 (66 thread on 10 cm) | 1.25 |

Binder type | - | - | - | Neoprene WRT |

Percentage of fibers | [%] | 70.8 | - | - |

Young’s modulus E | [GPa] | 7.46 | 7.5 | - |

Tensile strength R_{m} | [MPa] | 319 | 466.7 ^{1} | - |

Yield strength R_{e} | [MPa] | 318.5 | 500 | |

Elongation to break | [%] | 17 | 11 |

^{1}sample was 50 mm wide.

Constants | μ_{i} | μ_{i} |
---|---|---|

1 | −355.9176616 | 1.81890242 |

2 | 151.800249 | 2.21739197 |

3 | 210941268 | 1.37908823 |

Round Mass | Bullet Weight | Muzzle Velocity | Jacket Type | Core Type |
---|---|---|---|---|

12 g | 8.0 g | 360 ± 10 m/s | FMJ (brass M 90) | Lead (lead alloy Pb1 antimony) |

**Table 4.**Material data assumed in the J-C model [23].

Parameter | Unit | Brass M90 | Lead Alloy Pb1antimony | Steel | LIM 1 |
---|---|---|---|---|---|

ρ | kg/m^{3} | 8730 | 11,300 | 7800 | 1440 |

E | MPa | 100,000 | 115,000 | 210,000 | 7500 |

v | [-] | 0.34 | 0.42 | 0.34 | 0.30 |

Model J-C | |||||

A | MPa | 90 | 24 | 275 | 270 |

B | MPa | 292 | 40 | 350 | 319 |

n | [-] | 0.31 | 0.50 | 0.10 | 0.10 |

C | s^{−1} | 0.025 | 0.1 | 0.003 | 0.001 |

Parameter | Brass M90 | Lead | Metal Sheet |
---|---|---|---|

d_{1} | 0.54 | - | 1.40 |

d_{2} | 4.89 | - | 0.08 |

d_{3} | −3.03 | - | −0.04 |

d_{4} | 0.014 | - | 0.00 |

d_{5} | 1.12 | - | 0.00 |

Tm [K] | 1189 | 760 | 1800 |

${\dot{\epsilon}}_{0}$ [s^{−1}] | 0.0005 | 0.0005 | 0.0005 |

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**MDPI and ACS Style**

Mamys, M.; Pyka, D.; Kurzawa, A.; Baocian, M.; Barsan, N.; Jamroziak, K.
Experimental and Numerical Analysis of a Car Body Shield Loaded with a Ballistic Impact. *Machines* **2024**, *12*, 88.
https://doi.org/10.3390/machines12020088

**AMA Style**

Mamys M, Pyka D, Kurzawa A, Baocian M, Barsan N, Jamroziak K.
Experimental and Numerical Analysis of a Car Body Shield Loaded with a Ballistic Impact. *Machines*. 2024; 12(2):88.
https://doi.org/10.3390/machines12020088

**Chicago/Turabian Style**

Mamys, Maciej, Dariusz Pyka, Adam Kurzawa, Mirosław Baocian, Narcis Barsan, and Krzysztof Jamroziak.
2024. "Experimental and Numerical Analysis of a Car Body Shield Loaded with a Ballistic Impact" *Machines* 12, no. 2: 88.
https://doi.org/10.3390/machines12020088