A study on protective performance of bullet-proof helmet under impact loading

2.1. Ballistic helmet model

The ACH (medium size) was chosen as the bullet-proof helmet for the current study. It can resist 7.62 mm bullets from type 54 of pistols within 5 m, and it is widely used in the United States Army (Fig. 1(a)). For the current study, according to the US National Institute of Justice standards [8] and the Department of Defense Test Standards V50 ballistic limit test [9], the inside and outside components of the helmet were removed, such as interior decorations and objects in suspension. Thus, only the helmet shell itself was used for developing the finite element model.

Firstly, the helmet was scanned using a 3D scanner, and its geometry information was obtained and saved in STL files (Fig. 1(b)). Then, the STL files were handled in point cloud format using the Geomagic software, and the accurate surface model was obtained (Fig. 1(c)-(f)). Subsequently, the model was changed into a solid entity; and after being meshed using hypermesh software, it was finally developed into the helmet’s 3D FE model (Fig. 1(f)-(g)). In addition, for simulation, analysis and calculation using this model, the LS-DYNA software was used. The flow-chart of the whole research process of the current study was shown in Fig. 1.

The finite element model was developed with the eight-node hexahedron, with the total numbers of 97874 units and 112992 nodes, and with each unit being 2 mm in size and 7.5 mm thickness. The element type of the helmet is Solid (SectSld).

2.2. Modelling of bullets and the equivalent body armour plate

For the purposes of simulation, verification and NIJ-0106.01 standard test simulation [10], modelling was carried out for two kinds of bullets. One is a steel ball with 14.2 mm and 11.9 g, the other one is a bullet with 9 mm and 8 g. The finite element of the ball was modelled in an eight-node hexahedron, in which there are 3375 units and 4143 nodes, with each unit being 2 mm in size (Fig. 2(a)). Also, the finite element model of the pistol bullet was developed by an eight-node hexahedron, which has 19965 units and 21663 nodes, with each unit being 2 mm in size (Fig. 2(b)). The element types of the 14.2 mm spherical steel projectile and the 9 mm pistol bullet are Solid (SectSld).

In order to compare and analyze the protective performance of the helmet and bullet-proof plates, according to the geometry and finite information of the helmet (thickness 7.5 mm, each unit 2 mm in size, including 112992 nodes and 97874 units), the current study used a bullet-proof plate which was equivalent to the helmet. The equivalent plate was a rectangular body with the size of 220×250×7.5 mm, with the same surface square as the helmet. The finite element model of the equivalent bullet-proof plate also used the eight-node hexahedron, with 110000 nodes and 94612 units and each unit being 2 mm in size (Fig. 2(c)). The element type of the equivalent bullet-proof plate is Solid (SectSld).

Fig. 1The finite element (FE) modelling process of a bullet-proof helmet and evaluation research process of its protective performance under impact loading

a) The bullet-proof helmet modelling process and the finite element simulation of bullet impact

b) The research process flow-chart of the current study

2.3. Constitutive model and material parameters

The ball is made of elastic steel, and the bullet is made of elastic-plastic steel (with material parameters being shown in Table 1). The material of helmet is Kevlar [11]. For the bullet-proof plate, the same material parameters were chosen as for the helmet. For evaluating material performance, the constitutive model was used, which refers to failure criterion of chang-chang defining the fiber breakage, matrix cracking and matrix material failure and so on [12, 13]. The standard is based on stress failure rules. The chang-chang criterion classifies the failures of fiber and matrix into tension and compression failures, with the tensile failure including the fiber fracture and matrix cracking. In addition, previously developed composite failure criteria [14] were utilized to predict failures in matrix cracking, matrix compression, fiber-matrix shear-out and fiber breakage.

Fig. 2Finite element modeling of bullets and the equivalent bullet-proof plate: a) a 14.2 mm spherical steel projectile, b) a 9 mm pistol bullet, c) an equivalent bullet-proof plate

a)

b)

c)

The fiber breakage failure criterion is defined as follows:

where $e_1$ is the failure index for fiber fracture, $X_t$ is the longitudinal tensile strength, ${\sigma }_{11}$ is normal stress (${\sigma }_{11}\ge$0), and $\ddot{\tau }$ is given as follows:

In Eq. (2), $G_{12}$ is the shear modulus, ${\sigma }_{12}$ is shear stress, $S_c$ is the longitudinal shear strength, and ${\alpha }_1$ is a nonlinear shear stress parameter defined by the material’s shear stress-strain measurements, which should have a value between 0 and 0.5 [13].

The matrix cracking failure criterion is defined as follows:

where $e_2$ is matrix cracking failure index, $Y_t$ is the transverse tensile strength. ${\sigma }_{22}$ is normal stress (${\sigma }_{22}\ge$0).

The matrix compression failure criterion is defined as follows:

where, $Y_c$ is the transverse compressive strength, and ${\sigma }_{22}$ is normal stress (${\sigma }_{22}<$0).

When the failure criterion of chang-chang was used, all the same kinds of the fiber composite materials could not imitate the compression failures and fiber delamination.

When the Eq. (1) is satisfied ($e_1\ge$1), all of the elastic constants of the failed lamina are set to zero (i.e., $E_{11}=E_{22}=G_{12}={\nu }_{12}={\nu }_{21}=$0).

When the matrix cracking failure criterion in Eq. (3) is satisfied ($e_2\ge$1), all of the elastic constants except for the fiber modulus $E_{11}$ are set to zero.

2.4. Validation

To verify the effectiveness of the bullet-proof helmet FE model, experimental data were obtained and used from studies of C. Y. Tham [7] and B. T. Long [16], where the front/side impact tests were conducted with a ballistic helmet prototype and with a ballistic gas gun. The experiments were designed to evaluate the protective performance of ballistic helmets under frontal and lateral impacting. Experimental data primarily contained the launcher unit, gun barrel and target chamber. The emitting device was a type of high-pressure air chamber, and it was connected to a gas cylinder. A high-pressure gas was pumped into the gas chamber, and then the chamber was opened by valves. The pressure of the released air had the ability of pushing the projectile (the steel ball) of 11.9 g and 14.2 mm. The helmet was placed on a steel platform and fixed by three constraint points as shown (Fig. 3). The steel ball was launched at a speed of 205 m/s to 220 m/s from the trajectory. The helmet was impacted in the front and by the side by the high-speed steel ball. The speed of the steel ball was measured by a speedometer, and meanwhile, the rebounding of the bullet was caught by a high-speed camera, when the bullet shot the helmet.

In the finite element simulation, the helmet’s freedom of movement was limited to 6 directions ($X$, $Y$, and $Z$ three directions of movement and rotation). The front face of the helmet was impacted by the steel ball with all the nodes loaded with the speed of 205 m/s, and the lateral impact by the steel ball with all the nodes loaded with the speed of 220 m/s. The contact between the bullet and helmet was defined as contact-eroding-surface-surface, the helmet itself contact was defined as contact-automatic-single-surface. The coefficients of static and dynamic friction were set to 0.3 and 0.28, respectively.

2.5. Evaluation of protective performance of the bullet-proof helmet

After verifying the effectiveness of the helmet FE model, this model was used to evaluate the bullet-proof helmet’s protective performance upon impact by a non-penetrating bullet. The work had two parts that were carried out by simulation. The first part was the finite element simulation of the bullet-proof helmet, the other part was a simulation of the equivalent bullet-proof plate. Both the helmet’s and equivalent plate’s finite element models were loaded the same impact pressure. These simulations enabled obtainment of the inside surface’s maximum relationships between deformation with time, the impact force with time, the impacting energy with time, the internal energy conversion with time, and the stress with strain.

The loading standards for the current study (Fig. 3) used those of the V50 ballistic limit test [17]. The V50 simulation experiment was carried out with the NIJ-0106.01 standard (Table 3). The helmet was fixed on a steel platform by three constraint points. Its freedom of movement was limited to 6 directions ($X$, $Y$, and $Z$ three directions of movement and rotation). The helmet was impacted respectively at the front (Fig. 3(a)), the back (Fig. 3(b)), the left (Fig. 3(c)) and the right (Fig. 3d) sides. The equivalent bullet-proof plate was also fixed on a steel platform and the freedom of movement was limited to 6 directions ($X$, $Y$, and $Z$ three directions of movement and rotation). It was impacted directly at the front and the constraint condition as shown in Fig. 3(e). During the test, the distance between gun and the object was 5 meters. The 9 mm pistol bullet was launched from the gun and struck the object at the speed of 426±15 m/s. Since the study’s focus was on the bullet-proof protective performance, the bullet speed of 426 m/s was chosen.

After comparing results from the FE simulation of the ballistic helmet with those from bullet-proof equivalent plate impact simulation, the helmet’s bullet-proof performance was evaluated.

Fig. 3Bullet-proof helmet and equivalent bullet-proof ballistic plate performance studies

3.1. Validation of the bullet-proof helmet finite element model

The current study has developed a 3D finite element (FE) model of a bullet-proof ballistic helmet based on the process as shown in Fig. 1. For the purposes of simulation, verification and evaluation of the ballistic bullet-proof helmet performance, FE modelling was also developed for two kinds of bullets (a steel ball and a pistol bullet) as shown in Fig. 2. To verify the effectiveness of this model of bullet-proof helmet, simulation was carried out with this FE ballistic helmet model, and deformation and damage data were compared between the ballistic tests in C. Y. Tham’s study [7], reported simulated data [16], and our helmet’s finite element simulation (Fig. 3 and Table 3).

While the steel ball did not penetrate the helmet, the helmet was damaged to some extents. Indentation was obvious in the affected area of the helmet, with the maximum deformation area found in the impacting center of the bullet and helmet (Fig. 4 and Table 4). In the front of the bullet-proof helmet, a permanent damage area was apparent with a diameter of 42 mm in the ballistic test, of 32 mm in the literature, and of 28 mm in our finite element simulation. In the side test, the damage area diameter was 32 mm, 32 mm and 42 mm, respectively. In addition, deformation values of the inside surface of the bullet-proof helmet were 15 mm in the front ballistic test, 6.4 mm reported in the literature, and was 6.5 mm in our finite element simulation; and similarly, the inside surface deformation values were 18.7, 10.4, and 9.6 mm, respectively in the side test, in the literature and in our simulation. For the maximum energy absorption, the values were 251.3 J in the frontal ballistic test, 284.4 J reported in the literature, and 250.0 J in our finite element simulation; and these values were 285.3, 278.9, and 287.9 J in the lateral ballistic test, in the literature and in our finite element simulation. These comparisons suggest that, while there are some numerical differences between the prototype ballistic test and finite element simulation, the data from the literature are more similar to the results of our simulation. Thus, the finite element model of the bullet-proof helmet is effective to a good extent.

Fig. 4Ballistic helmet prototype test [7] and helmet deformation finite element simulation

3.2. The bullet-proof performance

Simulation results of the inside surface maximum deformations of the helmet at different locations are shown in Table 5 together with those of the equivalent bullet-proof plate under 9 mm bullet impacts at 426 m/s. Among the five locations of the helmet, while the maximum deformation at the front was 11.2 mm, deformation at the left and right sides was 8 to 9 mm. On the other hand, deformation of the equivalent bullet-proof plate reached 14 mm. These results demonstrate that inside surface deformation of the bullet-proof helmet varies at different locations with the left and right sides having the smallest deformations, and that deformation of the bulletproof equivalent plate was larger than those of the helmet.

The relationship of the inside surface deformation with time was presented at Fig. 5 comparing different locations of the bullet-proof helmet and the equivalent plate. It can be seen that, once the bullet made the contact, the helmet and plate transformed rapidly. In particular, they deformed faster in the first 0.05 ms, and then slowed down between 0.05-0.12 ms.

Fig. 5The time-dependent inside surface deformations at different locations of the bullet-proof helmet in comparison with the equivalent bullet-proof plate under 9 mm bullet impacts at 426 m/s

Correspondingly, the maximum contact force of the helmet or plate with the impacting bullet occurred at the maximum deformation in the current impacting simulation test (Fig. 6). At the peak force of the contact, the maximum contact force with the equivalent plate was around 60 KN, and the peak force with the bullet-proof helmet (around 68KN) was similar on all sides. However, in the latter half of the impact, the contact force’s rates of decline on the left and right sides were slower than the front and back directions.

Fig. 6Contact force – time relationship at different locations of the bullet-proof helmet in comparison with the equivalent bullet-proof plate under 9 mm bullet impacts at 426 m/s

Fig. 7 shows charts of the kinetic energy and internal energy conversion for the bullet impacting different locations of the helmet and the equivalent plate. The total energy was 700 J; and when the helmet or plate was impacted by the bullet, the kinetic energy declined, and internal energy rose. The kinetic energy of the bullet from 0-0.10 ms was quickly converted to internal energy, as after 0.1 ms most of the kinetic energy had been absorbed and the energy transformed relatively flat. Since that point, the deformation was small, and the bullet began to rebound. Since the left and right sides of the contact and deformation were bigger than those of the front and back of the helmet, the left and right sides showed a stronger resistance to deformation and consequently a bigger contact stiffness performance than the front and back. It is known that the greater the contact stiffness, the slower the kinetic energy and internal energy are converted. Therefore, the bigger contact stiffness and thus a slower conversion between kinetic energy and internal energy led to a bigger contact force in the left and right sides than the front and back. For the equivalent plate, due to the larger deformation, its contact stiffness and contact force were lower, and kinetic energy and internal energy conversion was faster.

Fig. 7Impact energy and internal energy conversion – time relationship at different locations of the bullet-proof helmet in comparison with the equivalent bullet-proof plate under 9 mm bullet impacts at 426 m/s

The stress-strain simulation results of the helmet and the equivalent plate following the bullet impact are presented in Fig. 8. Results indicate that the 7.5 mm equivalent plate was not defeated (penetrated) by the 9 mm 426 m/s bullet. The maximum stress of the helmet was 1988 MPa in the front, 1609 MPa in the back, 1837 MPa in the left side, and 1704 MPA in the right side. Comparatively, the maximum pressure on bullet-proof equivalent plate was 1392 MPa. These results indicate that impacting stress was the biggest at the front and lowest at the bullet-proof equivalent plate, suggesting that the geometric shape of helmet confers a certain influence on the bullet-proof performance.

3.3. Characteristics of bullet deformations

In the above simulations of the helmet or the equivalent bullet-proof plate being impacted by the bullet, the bullet was also shown to have large deformations, the characteristics of which are shown in Fig. 9(a)-(d). It can be seen that, after the high-speed impacting, the bullet’s deformations have some certain characteristics and patterns. At the initial stage, it was elastic deformation. When the material property of the bullet reached the yield strength, the bullet showed a large plastic deformation followed by an elastic deformation. In addition, all deformations were shown to occur in the direction towards the top of the helmet, and the stress force of the bullet also shifted toward the direction of the helmet with a smaller curvature (Fig. 9(a)-(d)). Furthermore, during the impact process, the bullet deformation caused some slipping movement on the helmet; and this movement would consume a certain amount of impact energy, which would increase the absorption of energy and thus reduce the inside surface deformation of the helmet to a certain extent.

In the simulation of the equivalent bullet-proof plate being impacted by the bullet, the deformation form was mainly elastic at the initial stage. But when it reached the yield limit, the bullet began to become larger in volume, until the bullet's kinetic energy was absorbed and the deformation stopped (Fig. 9(e)).

Fig. 8Comparisons of the simulation stress-strain results between the helmet at different locations: a) front, b) rear, c) left, d) right and e) bullet-proof equivalent plate under 9 mm bullet impacts at 426 m/s

Fig. 9The deformation characteristics of the 9mm bullet after impacting at 426 m/s at different locations of the bullet-proof helmet or the equivalent bullet-proof plate