Ballistic Response of a Glass Fiber Composite for Two Levels of Threat
Abstract
:1. Introduction
2. Materials and Methods
3. Results of the Simulation
3.1. The Model
- Macro, with the target being one body, made of a single equivalent material, used especially for metallic shields [41];
- Meso, implying the layers as a continuous body with equivalent properties determined experimentally [27] and paying attention to modeling the bonding between them, being applied the cohesive zone model [42,43,44,45,46,47,48,49], as the designer wanted to have the thickness of the entire panel as small as possible; in this group, we can include fabrics modeled with yarns. This model is difficult to calibrate, taking into account the statistical response of such a multitude of bodies;
3.2. Material Models of the Bodies Involved in the Model
3.3. Analysis of the Simulation Results
4. Analysis of the Failure Mechanisms after Actual Tests
- Micro, including glass fibers and resin damage;
- Meso, here including delamination and failure of the projectile;
- Macro, including qualification of the composite and partial or total penetration, evidenced by photos taken of the entire panel or large areas or sections of it.
- (a)
- Top view of the penetration hole produced by the 9 mm FMJ;
- (b)
- Detail of the surface that the projectile was stopped on (fragments of the projectile are not in this image, but there are glass fiber fragments);
- (c)
- Shear cut of a glass fiber (up), typically for impacted glass fibers, meaning a cut surface almost perpendicular to the fiber axis;
- (d)
- Top view of the penetration hole produced by the 0.357 Magnum. On the bottom the flattened projectile is visible, less fragmented compared to the 9 mm FMJ;
- (e)
- Detail in cross section, with flattened projectile and hole, not very cylindrical due to the different orientation of the yarns in each sub-layer;
- (f)
- Detail of cut fibers and the aspect of delamination, revealing the detaching of the fibers of different orientation and other fibers remaining in the matrix.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Layer | Yarn Orientation | Fiber Type | Area Weight |
---|---|---|---|
1. | 0° | 600 Tex | 283 g/m2 |
2. | 45° | 300 + 600 Tex | 300 g/m2 |
3. | 90° | 600 Tex | 307 g/m2 |
4. | −45° | 300 + 600 Tex | 300 g/m2 |
Stitch | 76 Dtex | 10 g/m2 | |
Total surface weight: 1200 g/m2 (±%3) |
Element Average (wt. %) (9 Measurement on Cross Section of Fibers on the Same Yarn) | |||||||||||||
B | C | O | Na | Mg | Al | Si | S | Cl | K | Ca | Ti | Fe | Zn |
29.3 | 24.7 | 9.0 | 0.3 | 0.4 | 3.5 | 14.2 | 1.7 | 0.2 | 0.2 | 8.8 | 0.5 | 2.1 | 4.4 |
Element Average (Wt. %) (4 Measurement on External Surface of Fibers on the Same Yarn) | |||||||||||||
30.8 | 24.6 | 9.7 | 0.5 | 0.6 | 3.1 | 10.6 | 1.5 | 0.2 | 0.5 | 7.8 | 1.0 | 2.8 | 5.6 |
Characteristics | Resin (A) Biresin® CR82 | Hardener (B) Biresin® CH80-2 | |
Mixing ratio, parts by weight | 100 | 27 | |
Viscosity at 25 °C, mPa·s | ~1.600 | ~80 | |
Density at 25 °C, g/mL | 1.11 | 0.99 | |
Mixture | |||
Potlife, 100 g/RT (approx.), minutes | ~80 | ||
Mix viscosity, 25 °C (approx.), mPa·s | 800 | ||
Characteristics | Tested According to | Units | Resin Biresin® CR82 (A) with hardener CH80-2 |
Tensile strength | ISO 527 | MPa | 85 |
Tensile elasticity modulus | ISO 527 | MPa | 3250 |
Elongation at break | ISO 527 | % | 5.0 |
Flexural strength | ISO 178 | MPa | 125 |
Flexural E-Modulus | ISO 178 | MPa | 3200 |
Compressive strength | ISO 604 | MPa | 107 |
Density | ISO 1183 | g/cm3 | 1.16 |
Shore hardness | ISO 868 | - | D 84 |
Impact resistance | ISO 179 | kJ/m2 | 21 |
Typical thermal properties of fully cured neat resin | |||
Heat distortion temperature | ISO 75A | °C | 77 |
Glass transition temperature | ISO 11357 | °C | 89 |
Panel | Fabrics Mass | Panel Mass | Resin Mass * | Mass Ratio Fabrics/Panel ** | Surface Density *** | Thickness in 4 Points | ||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | Average | ||||||
[g] | [g] | [g] | [kg/m2] | [mm] | ||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 2500 | 3273 | 773 | 0.763 | 27.77 | 18.37 | 18.46 | 18.60 | 18.12 | 18.38 |
2 | 2510 | 3118 | 608 | 0.805 | 27.88 | 17.21 | 18.53 | 17.37 | 18.23 | 17.83 |
3 | 2460 | 3150 | 690 | 0.781 | 27.33 | 18.61 | 18.04 | 18.96 | 18.20 | 18.45 |
4 | 2460 | 3174 | 714 | 0.775 | 27.33 | 18.24 | 18.02 | 18.76 | 17.97 | 18.24 |
5 | 2450 | 3200 | 750 | 0.765 | 27.22 | 18.53 | 18.23 | 18.46 | 18.37 | 18.39 |
Average | 2476 | 3183 | 707 | 0.778 | 27.51 | 18.26 | ||||
Max | 2510 | 3273 | 773 | 0.805 | 27.88 | |||||
Min | 2450 | 3118 | 608 | 0.763 | 27.22 | |||||
Standard deviation | 24.17 | 52.51 | 57.17 | 0.015 | 0.266 | 0.225 |
Class | Type of Weapon | Caliber | Bullet | Test Condition | ||
---|---|---|---|---|---|---|
Type | Mass [g] | Test Range [m] | Bullet Velocity [m/s] | |||
FB2 | Hand gun | 9 mm Luger | FJ/RN/SC | 8.0 ± 0.1 | 5 ± 0.5 | 400 ± 10 |
FB3 | Hand gun | 0.357 Magnum | FJ/RN/SC | 10.2 ± 0.1 | 5 ± 0.5 | 430 ± 10 |
FJ—full metal jacket, RN—round-nose bullet, SC—soft core (lead). |
Property | Jacket (Brass) | Core (Lead Alloy) |
---|---|---|
Density [kg/m3] | 8450 * | 11350 * |
Specific heat at constant pressure [mJ/(kg °C)] | 380 | 1.288 × 105 |
Young modulus [MPa] | 90,000 * (115,000, [59]) | 16,000 [59] |
Poisson coefficient | 0.344 | 0.44 |
Temperature [°C] | 22 | 22 |
Constants for Johnson–Cook model | ||
Initial yield limit [MPa] | 90 [58] (80 [59]) | 1 [59] (0, [58]) |
Hardening constant [MPa] | 628 [58] | 55 [58] |
Hardening exponent | 0.72 [58] | 9.8 × 10−2 [58] |
Constant for strain rate | 0.266 [58] | 0.231 [58] |
Thermal softening exponent | 1 [58] | 1 [58] |
Quasi-static strain rate threshold (s−1) | 604 [59] | 221 [59] |
Melting temperature [°C] | 927 * | 327.5 * |
Equivalent plastic strain at break (EPS) | 0.75 * | 0.75 * |
Mechanical properties of a layer | ||
Property | Value | |
Density [kg/m3] | 1904 * | |
Specific heat at constant pressure [mJ/(kg °C)] | 6 × 105 * | |
Young modulus [MPa] | 50,000 [60] | |
Poisson coefficient | 0.3065 * | |
Temperature [°C] | 22 | |
Isotropic bilinear hardening model | ||
Initial yield limit [MPa] | 550 * (577 for 495 s−1, in [60]) | |
Tangent modulus [MPa] | 10,000 * | |
Temperature [°C] | 22 | |
Equivalent plastic strain at break (EPS) | 0.12 * |
Parameters for Modeling the Bilinear Strength in Interlaminar Delamination | |||||
Tempe-rature, °C | Maximum normal traction stress at the interface, MPa | Normal displacement jump at completion of debonding, mm | Maximum tangential traction stress at the interface, MPa | Tangential displacement jump at completion of debonding, mm | Ratio |
22 | 70 | 5 | 50 | 0.1 | 0.3 |
Parameters for Energy at Break in Interlaminar Delamination | |||||
Tempe-rature, °C | Maximum normal contact stress, MPa | Critical fracture energy for normal separation, J/m2 | Maximum equivalent tangential contact stress, MPa | Critical fracture energy for tangential slip, J/m2 | Artificial damping coefficient, s |
22 | 100 | 3000 [65] | - | - | 0.1 |
Case (Projectile) | Number of Broken Layers | |
---|---|---|
Experimental | Numerical | |
9 mm FMJ | 2–3 | 3 |
0.357 Magnum | 5 | 5 |
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Ojoc, G.G.; Chiper Titire, L.; Munteniță, C.; Pîrvu, C.; Sandu, S.; Deleanu, L. Ballistic Response of a Glass Fiber Composite for Two Levels of Threat. Polymers 2023, 15, 1039. https://doi.org/10.3390/polym15041039
Ojoc GG, Chiper Titire L, Munteniță C, Pîrvu C, Sandu S, Deleanu L. Ballistic Response of a Glass Fiber Composite for Two Levels of Threat. Polymers. 2023; 15(4):1039. https://doi.org/10.3390/polym15041039
Chicago/Turabian StyleOjoc, George Ghiocel, Larisa Chiper Titire, Cristian Munteniță, Cătălin Pîrvu, Simona Sandu, and Lorena Deleanu. 2023. "Ballistic Response of a Glass Fiber Composite for Two Levels of Threat" Polymers 15, no. 4: 1039. https://doi.org/10.3390/polym15041039