A study on protective performance of bullet-proof helmet ...
Investigation of Bullet-Proof Helmet Protective Efficacy
2.1 Selection of Ballistic Helmet Model
For this research, the ACH medium-size bullet-proof helmet was selected due to its effectiveness against 7.62 mm rounds from Type 54 pistols within a distance of 5 meters, a standard utilized by the United States Army (see Fig. 1(a)). In accordance with guidelines established by the US National Institute of Justice [8] and the Department of Defense’s V50 ballistic limit tests [9], non-essential components within the helmet, including internal linings and attachments, were extracted to focus solely on the helmet shell for the finite element modeling process.
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The initial step involved scanning the helmet using a 3D scanner, resulting in detailed geometric data saved in STL file format (Fig. 1(b)). This data underwent further processing using Geomagic software to develop a precise surface model (Figs. 1(c)-(f)). Following this, the model transitioned into a solid format and was meshed using HyperMesh software, culminating in the establishment of the helmet’s 3D finite element model (Figs. 1(f)-(g)). LS-DYNA software facilitated the subsequent simulation, analysis, and calculations. A flow-chart depicting the study process is provided in Fig. 1.
The finite element model consisted of eight-node hexahedrons, comprising a total of units and nodes, designed with unit sizes of 2 mm and a thickness of 7.5 mm, classified as Solid (SectSld).
2.2 Bullet and Equivalent Body Armor Plate Modelling
To facilitate simulation and validation alongside the NIJ-.01 standard testing [10], two distinct types of bullets were modeled: a steel ball, measuring 14.2 mm and weighing 11.9 g, and a 9 mm bullet weighing 8 g. The eight-node hexahedron formed the finite element representation of the 14.2 mm ball, encompassing units and nodes, with each unit measuring 2 mm (Fig. 2(a)). Similarly, the finite element model for the 9 mm pistol bullet was established as an eight-node hexahedron with units and nodes of equal measurement (Fig. 2(b)). Both the spherical steel projectile and the 9 mm bullet adhered to the Solid (SectSld) element type.
To allow for a comparative analysis between the helmet and bullet-proof plates, a corresponding equivalent plate was modeled based on helmet geometrical attributes (thickness of 7.5 mm, unit size of 2 mm, consisting of nodes and units). The equivalent plate took on the dimensions of 220×250×7.5 mm, matching the helmet's surface area. Utilizing the eight-node hexahedron once again, the finite element model for the equivalent bullet-proof plate included nodes and units, retaining a unit size of 2 mm (Fig. 2(c)).
Fig. 1Finite Element Modelling Procedure for Bullet-Proof Helmet and Associative Impact Protective Performance Evaluation
Illustrations include a) modeling of the bullet-proof helmet with finite element simulation regarding bullet impact, b) research process flow-chart for the current investigation.
2.3 Material Parameters and Constitutive Model
The bullet is composed of elastic steel, while the bullet-proof helmet utilizes Kevlar material [11]. The bullet-proof plate employs equivalent material parameters to the helmet. The assessment of material performance employed the constitutive model referencing the Chang-Chang failure criterion, which outlines fiber breakage, matrix cracking, and overall matrix material failure [12, 13]. This criterion adheres to established stress failure principles. The Chang-Chang criterion differentiates between fiber and matrix failures categorized as tensile or compressive, including fiber rupture and matrix cracking within tensile failures. Complementary composite failure criteria [14] were also applied to accurately predict matrix cracking, compression, shear-out, and fiber breakage occurrences.
Fig. 2Modeling of Bullets and Equivalent Bullet-Proof Plate: a) 14.2 mm steel projectile, b) 9 mm pistol projectile; c) equivalent bullet-proof plate.
Table 1Material Properties of Bullets Utilized in the Study
Bullet types: Spherical steel projectile, 9 mm pistol bullet.
Table 2Material Attributes of the Ballistic Helmet and Its Equivalent Plate [14, 15]
Property parameters include density, tensile elasticity, shear modulus, yield stress, etc.
The fiber failure index, e1, correlates as follows:
1e1=σ11/Xt2+τ12,...
The matrix cracking failure criterion is defined as:
3e2=σ22/Yt2+τ12,...
The matrix compression failure criterion can be articulated as:
4ecomp=σ22...
The success of the Chang-Chang criterion necessitates that all elastic constants of failed laminae are nullified once the conditions are satisfied.
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2.4 Verification of Model
The bullet-proof helmet's finite element model underwent validation using experimental data sourced from studies by C. Y. Tham [7] and B. T. Long [16]. These investigations performed front/side impact tests on a ballistic helmet prototype utilizing a ballistic gas gun, aiming to assess protective performance under both frontal and lateral impacts. Experimental parameters outlined included launcher unit, gun barrel, and target chamber specifications to simulate the impact environment effectively. Projectiles were propelled from a high-pressure air chamber connected to a gas cylinder, with bullets measuring 11.9 g or 14.2 mm launched at speeds between 205 m/s and 220 m/s towards the helmet secured on a steel base via three anchor points (Fig. 3). High-speed cameras recorded bullet rebounds during impacts.
In the finite element simulation process, the helmet’s movement was restricted across six axes (X, Y, Z, rotational). Uniform high-velocity impacts were applied to helmet surfaces while setting appropriate contact parameters. Static and dynamic friction coefficients were established at 0.3 and 0.28, correspondingly.
2.5 Bullet-Proof Helmet's Protective Performance Evaluation
V50 ballistic limit testing standards [17] were employed for the current research (see Fig. 3). The helmet underwent varied impacts from four directions, namely front, back, left, and right, and comparable evaluations were conducted on the equivalent plate. The tests maintained a firing distance of 5 meters with a 9 mm bullet delivering impacts at a preset speed of 426±15 m/s, focusing the study on the protective efficacy against ballistic threats.
Results from the finite element helmet simulation were compared with corresponding data obtained from equivalent plate impacts to finalize the bullet-proof efficiency assessment.
Table 3NIJ-.01 Testing Standards [8]
3.1 Model Validation of Bullet-Proof Helmet
The development of the 3D finite element model for the bullet-proof helmet was conducted per the outlined process (Fig. 1). Additionally, FE modeling was coordinated for both steel ball and pistol bullet simulations (Fig. 2). To validate this model, simulation results were critically assessed against empirical data from C. Y. Tham’s ballistic tests [7] and other studies [16], encompassing information represented in Fig. 3 and Table 3.
While the helmet exhibited no penetration, damage manifested across its surface. Notably, areas subjected to impact presented significant deformation patterns, with clear distinctions observed across different impact zones (Table 4). Diameter measurements indicated that the frontal region sustained a permanent damage radius of 42 mm in ballistic trials, compared to 32 mm in the literature and 28 mm in simulation. Side impacts recorded consistent damage metrics, further validating model results.
Fig. 4Ballistic helmet prototype tests [7] and finite element simulation results regarding deformation.
3.2 Analysis of Bullet-Proof Capabilities
Simulation results from various locations of the helmet revealed the internal surface’s maximum deformation under 9 mm bullet strikes at 426 m/s (see Table 5). While front impacts yielded a maximum deformation of 11.2 mm, lateral impacts ranged from 8 to 9 mm, showcasing the helmet’s superior protective performance compared to the equivalent plate which experienced 14 mm deformation.
Fig. 5 visually elucidates the relationship between deformation and time across different locations on the ballistic helmet against the equivalent plate's response under identical bullet impacts. Data illustrates rapid initial deformation followed by deceleration in response dynamics post-impact.
Fig. 5Deformation verses time comparisons for different helmet locations and equivalent plate subjected to 9 mm bullet impacts at 426 m/s.
Table 5Illustrative values reveal internal surface deformations following impacts.
Additionally, maximum contact force evaluations indicated that peak forces experienced by helmet or plate closely matched maximum deformation instances (Fig. 6). The 68 KN face contact force on the helmet underscores its substantial impact resistance, while showing lesser decline rates compared to the plate.
Fig. 6Contact forces corresponding with time across varied impact locations on the helmet compared to the equivalent plate under 9 mm projectile impacts at 426 m/s.
Figures of kinetic energy transformations during impact illustrate significant energy absorption dynamics contrasting the contact stiffness metrics of different impacted regions.
Fig. 7Energy dynamics describing interrelated kinetic and internal energy behaviors upon bullet contact at specified helmet locations.
3.3 Deformation Characteristics of the Bullet
Insights regarding bullet deformation characteristics arising from helmet impacts reveal pronounced trends post-collision (Fig. 9(a)-(d)). Initial elastic deformation transitions to substantial plastic deformation at yield thresholds, influencing stress transfer directions toward helmet contours, thereby enhancing energy absorption.
For the equivalent bullet-proof plate impact scenarios, initial elastic responses swiftly transition to larger volumetric deformations until kinetic energy dissipation ceases (Fig. 9(e)).
Fig. 8Comparative stress-strain simulation results for helmet and equivalent plate under 9 mm impacts at 426 m/s.
Fig. 9Illustration of deformation traits experienced by 9mm projectiles due to high-speed interactions with helmet surfaces or equivalent ballistic plates.
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