# Ballistic Impact Resistance of Bulletproof Vest Inserts Containing Printed Titanium Structures

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}of the area [14]. Thanks to continuous progress of material engineering [15,16,17] and production technologies, more efficient bulletproof vests may be developed. Current research projects in the field of personal protection [18], are focused on increasing the protected area and reducing areal density of vests related to the v

_{50}ballistic limit.

## 2. Materials and Methods

#### 2.1. Materials Insert Configurations

^{3}and had the form of a grid consisting of many loosely intertwined repeatable components (uniform cells). The whole structure was additively manufactured in one technological operation by sintering powder with laser or electron beam. The grid made in this way may use cells of different geometry (Figure 1). The ratio of empty space between the cells to the total volume of the layer may be within the range of 5–60%. All of the analyzed variants of structures had the same areal density (m

_{s}= 18.0 kg/m

^{2}) which made it easier to compare their effectiveness.

#### 2.2. Construction of the 3D Printed Structures

#### 2.3. 9 mm FMJ Parabellum Projectile

_{k}= 600 J. During the analyses the 9 mm projectile with a mass of 8.0 g, muzzle velocity of 360 m/s and initial energy E

_{k}~ 518 J was used [38].

#### 2.4. Determination of Material Characteristics for Numerical Modeling

## 3. Numerical Investigations

#### 3.1. Assumptions Adopted for Modeling

_{0}= 360 m/s. Scheme of the analyzed phenomenon is shown in Figure 9.

#### 3.2. Numerical Models

#### 3.2.1. General Assumptions

#### 3.2.2. Projectile Model

#### 3.2.3. Ballistic Clay Model

#### 3.2.4. Fabric Model

_{s}= 0.18, dynamic coefficient of friction µ

_{d}= 0.19) and between the fabric and the other components of the simulation (fabric-projectile: µ

_{s}= 0.38, µ

_{d}= 0.5; fabric-titanium structure: µ

_{s}= 0.5, µ

_{d}= 0.5; fabric-ballistic clay: µ

_{s}= 0.9, µ

_{d}= 0.9) was modelled [49]. The contacts used the * CONTACT-ERODING_SURFACE_TO_SURFACE algorithm [43].

_{L}—constitutive matrix defined in terms of the material constants of the orthogonal material axes, {a, b, c}.

_{L}for the orthotropic case was defined as [44]:

_{i}—Young moduli in principal material directions, ν

_{ij}—Poisson ratios and G

_{ab}, G

_{bc}and G

_{ca}—shear moduli.

#### 3.2.5. Titanium Structures Model

- 316,080 elements for S1 structure;
- 113,152 elements for S2 structure;
- 199,680 elements for S3 structure;
- 352,560 elements for S4 structure.

_{s}= 0.36, µ

_{d}= 0.3) as well as between the structures and the other components of simulation (structure-ballistic clay: µ

_{s}= 0.9, µ

_{d}= 0.9; structure-projectile: µ

_{s}= 0.36, µ

_{d}= 0.27) [49] were modelled with the *CONTACT-ERODING_SURFACE_TO_SURFACE algorithm [43]. The elastic-viscoplastic material model *MAT_224-TABULATED_JOHNSON_COOK [44] was used to describe behavior of titanium structures. In the model plastic heating causes adiabatic temperature increase and material softening. Plastic failure strain can be defined as a function of triaxiality, strain rate, temperature and element size. The user has the ability of direct input of parameters defining curves. The Ti-6Al-4V titanium alloy used in the simulations was defined with the following curves:

- LCK1: effective stress–effective plastic strain curves for different strain rates (1.0 × 10
^{−4}–5.0 × 10^{4}(s^{−1}); - LCKT: effective stress–effective strain curves for different temperature values (223–2500 K);
- LCF: curves that define plastic failure strain as a function of the triaxiality parameter;
- LCG: curves that define plastic failure strain as a function of plastic strain rate;
- LCH: curves that define plastic failure strain as a function of temperature;
- LCI: curves that define plastic failure strain as a function of element size.

_{𝑦}expressed as a function of plastic strain 𝜀

_{𝑝}, plastic strain rate ${\dot{\epsilon}}_{p}$ and temperature 𝑇 have the following form (using curves LCK1, LCKT) [44]:

_{𝑣𝑚}, lode parameter, plastic strain rate ${\dot{\epsilon}}_{p}$, temperature 𝑇 and initial element size 𝑙

_{c}(volume over maximum area for solids) by [44]:

_{𝑝𝑓}and is obtained by accumulation over time:

_{R}—room temperature, β—dissipation factor, C

_{p}—specific heat and $\rho $—density.

## 4. Results and Discussion

#### 4.1. Results of Ballistic Impact Simulations

- Final deformations of the phenomenon components;
- Distribution of plastic strain in the 3D printed titanium structures;
- Volumes, shapes and dimensions of characteristic deformation parameters of the ballistic clay;
- Plots of kinetic energy of the projectile versus time.

#### 4.2. Mesh Sensitivity Study

## 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.**Variants of 3D printed titanium structures chosen for analyses: (

**a**) structure of the S1 type; (

**b**) structure of the S2 type; (

**c**) structure of the S3 type and (

**d**) structure of the S4 type.

**Figure 3.**Example of additively manufactured cell interlacing: 1—cells forming the grid structure; 2—internal circuit of the adjacent grid structure element; 3—external circuit of the adjacent grid structure element.

**Figure 4.**Microstructure of the Ti-6Al-4V titanium alloy after the selective laser melting (SLM) process (scanning microscopy). Distribution of α’-phase lath martensite on the background of the β-phase.

**Figure 5.**Microstructure of the Ti-6Al-4V titanium alloy after the SLM process (light microscopy) etched with Kroll’s reagent.

**Figure 6.**The 9 × 19 mm FMJ Parabellum bullet: (

**a**) single cartridge; (

**b**) projectile cross section; (

**c**) projectile and (

**d**) dimensions of projectile.

**Figure 7.**Experimental test of quasi-static penetration of Twaron CT 750 aramid fabric: (

**a**) test stand and (

**b**) example of results.

**Figure 8.**Deformations of the 9 mm FMJ Parabellum projectile obtained in the experiments and simulations: (

**a**) impact velocity of 100 m/s; (

**b**) impact velocity of 126 m/s and (

**c**) impact velocity of 143.8 m/s.

**Figure 11.**Discretization of Twaron CT 750 fabric: (

**a**) Schematic of a plain-woven and (

**b**) plain woven textile showing the warp and fill.

**Figure 12.**Discretization of the 3D printed structures made of Ti-6Al-4V titanium alloy: (

**a**) structure S1; (

**b**) structure S4; (

**c**) structure S2 and (

**d**) structure S3.

**Figure 13.**Results of simulation for S1 structure: (

**a**) location of the impact point; (

**b**) final deformation; (

**c**) distribution of effective plastic strain in the titanium structure; (

**d**) shape of the hollow in the ballistic clay and (

**e**) plot of the projectile energy against time.

**Figure 14.**Results of simulation for S2 structure: (

**a**) location of the impact point; (

**b**) final deformation; (

**c**) distribution of effective plastic strain in the titanium structure; (

**d**) shape of the hollow in the ballistic clay and (

**e**) plot of the projectile energy against time.

**Figure 15.**Results of simulation for S3 structure: (

**a**) location of the impact point; (

**b**) final deformation; (

**c**) distribution of effective plastic strain in the titanium structure; (

**d**) shape of the hollow in the ballistic clay and (

**e**) plot of the projectile energy against time.

**Figure 16.**Results of simulation for S4 structure: (

**a**) location of the impact point; (

**b**) final deformation; (

**c**) distribution of effective plastic strain in the titanium structure; (

**d**) shape of the hollow in the ballistic clay and (

**e**) plot of the projectile energy against time.

**Figure 17.**Variations of discretization used in the mesh sensitivity study: (

**a**) base size; (

**b**) mesh size 0.5–0.25 mm and (

**c**) mesh size 0.5–0.125 mm.

**Figure 18.**Results of simulations performed in the mesh sensitivity study: (

**a**) final deformation; (

**b**) distribution of effective plastic strain in the titanium structure; (

**c**) shape of the hollow in the ballistic clay and (

**d**) plot of the projectile energy against time.

**Table 1.**Properties of Twaron CT 750 aramid fabric [34].

Style | Type Warp/Weft | Weave | Set (per 10 cm) Warp/Weft | Areal Density (g/m^{2}) | Thickness (mm) | Minimum Break Strength (N/5 cm × 1000) Warp/Weft |
---|---|---|---|---|---|---|

CT 750 | 2000 | plain | 69/69 | 460 | 0.70 | 16.5/18.0 |

Specification | RO, (Tonnes) | E, (MPa) | PR, (-) | A, (MPa) | B, (MPa) | n, (-) | C, (-) | m, (-) | D1, (-) | D2, (-) | D3, (-) | D4, (-) | D5, (-) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Lead-Core | 1.01 × 10^{−8} | 18.4 × 10^{3} | 0.42 | 24 | 40 | 1.00 | 0.01 | 1.00 | 3 | 0 | 0 | 0 | 0 |

Brass-Jacket | 8.52× 10^{−9} | 11.5× 10^{4} | 0.31 | 206 | 899 | 0.42 | 0.01 | 1.68 | - | WC | 1414 | - | - |

Specification | RO, (Tonnes) | E, (MPa) | PR, (-) | K, (MPa) | N, (-) | SRC, (s ^{–1}) | SRP, (-) | SIGY, (MPa) | EPSF, (-) | VP, (-) | Source |
---|---|---|---|---|---|---|---|---|---|---|---|

Ballistic clay | 1878 | 14.2 | 0.49 | 0.24 | 0.014 | 0 | 0 | 0 | 2.5 | 1 | [48] |

Specification | RO, (Tonnes) | EA, (MPa) | EB, (MPa) | EC, (MPa) | PRBA, (-) | PRCA, (-) | PRCB, (-) | GAB, (MPa) | GBC, (MPa) | GCA, (MPa) | Source |
---|---|---|---|---|---|---|---|---|---|---|---|

Twaron CT 750 | 1.158 × 10^{−9} | 62,800 | 628 | 628 | 0 | 0 | 0 | 31,000 | 158 | 31,000 | [50,51,52] |

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**MDPI and ACS Style**

Zochowski, P.; Bajkowski, M.; Grygoruk, R.; Magier, M.; Burian, W.; Pyka, D.; Bocian, M.; Jamroziak, K.
Ballistic Impact Resistance of Bulletproof Vest Inserts Containing Printed Titanium Structures. *Metals* **2021**, *11*, 225.
https://doi.org/10.3390/met11020225

**AMA Style**

Zochowski P, Bajkowski M, Grygoruk R, Magier M, Burian W, Pyka D, Bocian M, Jamroziak K.
Ballistic Impact Resistance of Bulletproof Vest Inserts Containing Printed Titanium Structures. *Metals*. 2021; 11(2):225.
https://doi.org/10.3390/met11020225

**Chicago/Turabian Style**

Zochowski, Pawel, Marcin Bajkowski, Roman Grygoruk, Mariusz Magier, Wojciech Burian, Dariusz Pyka, Miroslaw Bocian, and Krzysztof Jamroziak.
2021. "Ballistic Impact Resistance of Bulletproof Vest Inserts Containing Printed Titanium Structures" *Metals* 11, no. 2: 225.
https://doi.org/10.3390/met11020225