Investigation of energy absorption mechanisms in a soft armor panel under ballistic impact

Abstract

This study aims to identify different contributions of each layer to ballistic resistance and energy absorption distribution in a soft armor panel under ballistic impact. Different ballistic responses of each fabric layer and energy absorption mechanisms of a multilayer panel were investigated through finite element (FE) analysis using Abaqus. FE models were created to simulate transverse impact of a projectile onto multilayer panels before clay. FE results show that fabric layers in front, middle and back of the panel exhibit different extents of transverse deformation and stress distribution characteristics. Energy absorption in each layer is increased from the front layer to the peak value at the last perforated layer and then gradually decreased in following back layers of the panel. This pattern remains the same regardless of increasing total number of layers in the panel. When increasing the impact velocity, the position of the peak value of energy absorption with the last perforated layer is shifted towards back of the panel. These fundamental understandings contribute to the hybrid design of soft armor panel.

Keywords

energy absorption distribution soft armor panel finite element analysis transverse deformation stress distribution

With the development of sophisticated weaponry and the invention of new firearms, there is an ever-increasing demand for further improvement of ballistic performance and weight reduction of soft body armor. Although ballistic performance of soft armor panel is highly dependent on material properties, it needs to be noted that the construction of the armor panel also has a great influence. Before new types of ballistic materials are put into use, optimizing the construction of the soft body armor with available materials will be an efficient and feasible option in current situation.

The panel of soft body armor is usually constructed by layering multiple same fabric layers. However, such construction may not be the most mass efficient method for achieving ballistic performance.¹ According to previous studies, energy absorption of a multilayer panel has been found less than the sum of energy absorption of an individual fabric layer with the same number of layers.^2–4 This indicated that each layer in a panel plays different roles in energy absorption. Cunniff concluded that such a deleterious system effect of the panel is due to possible constraint of the transverse deflection by subsequent layers on the front layers.² The interference between layers may prevent the stacked layers from achieving the amount of energy absorption by individual layers. Karahan et al. speculated that in a non-perforated panel most of energy was absorbed by the first fabric layers.⁵ Lim et al. found that the ratio of energy absorbed in the double-ply system to that of the single-ply system has been influenced by the impact velocity and projectile geometry.⁶ For the sharp-nosed projectile, the energy absorption of layered system was better than spaced systems. Wang et al. found that four layers of loose fabrics possess higher energy absorption than that of three layers of tight fabrics at the same total areal weight.⁷ They explained that a tight fabric with large crimp is prone to form high stress at the edge of the projectile and lower stress wave velocity in comparison with that of the loose fabric. This results in higher energy absorption at unit area density of the fabric with low crimp of yarns.

The contribution of each layer in a panel has also been investigated in many studies. Joo and Kang numerically investigated energy absorption of each layer in a multilayer panel.⁸ In the non-perforation case, the absorbed energy is the highest for the first layer followed by the subsequent layers. When the perforation occurs, the sequence is reversed. Chen et al. reported that the front layers of fabric in a multilayer panel are more likely to be broken in shear,^9,10 and the back layers of fabric tend to fail in tension. As a result, energy absorption of each layer is increased from front to back in the panel. Cunniff concluded that the material near the impact face has little influence on ballistic performance of an armor panel when the impact velocity is much higher than the ballistic limit.¹¹ Novotny et al. reported that decrease of the strain along the thickness of the panel results in less energy absorption by back layers at the early stages of the impact before penetration.³ Prosser reported that the work of penetration through each interior layer of a nylon panel is essentially constant,¹² but is different from the impact layer and back layer. In these studies, due to different impact conditions and limited total number of layers in the panel, the general energy absorption mechanism in a soft armor panel under ballistic impact still has not been identified.

This study aims to identify the different contributions of each layer to ballistic resistance and energy absorption distribution in a soft armor panel under ballistic impact. Finite element (FE) simulation is employed to reveal ballistic responses of each layer in a soft armor panel. To reveal the general pattern of energy absorption distribution in a panel, some factors including the total number of layers and the impact velocity are taken into account. This result is important for the construction design of soft armor panel in order to achieve the improvement of ballistic performance and weight reduction.

Finite element modeling of the armor panel

An FE model of a woven panel before clay under ballistic impact of a projectile was created using Abaqus/Explicit. According to previous ballistic tests,¹³ Twaron® plain fabric can be used to construct multilayer panels. The specifications of the fabric are shown in Table 1. The fabric layer has square shape with a size of 240 × 240 mm². A steel right circular cylinder (RCC) projectile is used to impact the armor panel, which has the diameter and height of 5.5 mm, and 1 g in mass. In order to stop the projectile, a multilayer panel usually contains more than 24 fabric layers. All fabric layers are packed together to construct a panel without space. The panel is placed before clay with two elastic tapes fixed. Four edges of the panel are set free.

Table 1.

Specifications of Twaron fabric

Material	Yarn count (tex)		Yarn density (ends/cm)		Thickness (mm)
Material	Warp	Weft	Warp	Weft	Thickness (mm)
Twaron	93	93	11	11	0.2

Three FE models of multilayer panels with 24, 36, and 48 layers were created, namely 11F₂₄, 11F₃₆, and 11F₄₈, to satisfy the non-perforation case. The influence of the impact velocity was also investigated with three different impact velocities of 300 m/s, 500 m/s, and 600 m/s.

Geometrical modeling

A three-dimensional (3D) continuum FE model is adopted in this study. In a non-perforation ballistic case, an FE model is composed of a projectile, an armor panel, and clay as shown in Figure 1(a). Only one-quarter of the armor system with a size of 75 × 75 mm² is modeled due to the symmetry of the system.

Figure 1.

Finite element (FE) modeling. (a) FE model of a multilayer panel before clay under transverse impact; (b) the mesh of a single layer of fabric under ballistic impact; (c) fine mesh in a primary yarn; (d) coarse mesh in a secondary yarn.

In the FE model, the armor panel is layered up by a certain number of woven fabrics. A woven fabric is modeled at the yarn level as shown in Figure 1(b). According to our previous observation of a single yarn in fabric, the cross-section displays a lenticular shape due to little twists assembled on filaments.¹³ Therefore, a single yarn is represented as a 3D solid with a lenticular cross-section and defined crimp wave in the FE model, as shown in Figure 1(c) and (d). The schematic of yarn cross-section is shown in Figure 2. According to the fabric thickness and the weave density of the fabric, the yarn geometry can be calculated according to

L = \frac{1}{P}

(1)

R_{m}^{2} = (\frac{L}{2})^{2} + (R_{m} - \frac{h}{4})^{2}

(2)

R_{i} = R_{m} - \frac{h}{4}

(3)

\frac{W / 2}{L / 2} = \frac{R_{i} - \frac{h}{4}}{R_{i}}

(4)

where P is the weave density (ends/cm), L is the half crimp wave length (m), h is the fabric thickness (m), R_m and R_i are the middle and inner radius of crimp arc of yarn (m), respectively, and W is the width of yarn cross-section (m).

Figure 2.

Schematic of yarn cross-section.

It is calculated that the width of the yarn cross-section is 0.0881 cm and the length of the crimp wave is 0.1832 cm. This is assigned to the FE model of a single yarn. The same yarns are assembled in warp and weft directions to construct the plain fabric. The multilayer panel is created by copying a single layer of fabrics.

The clay at the back of the panel is modeled as a 3D solid continuum block with a size of 75 × 75 × 50 mm³. The right cylindrical projectile with a height of 5.5 mm and a radius of 2.75 mm is modeled as a rigid body, due to no obvious deformation produced in previous ballistic tests.¹³

In ballistic tests, a free boundary condition is applied for an armor panel. This means there is no constraint applied on fabric edges in the FE model. The other two edges crossing at the impact point are applied symmetry conditions. For the clay in a container, the constraint boundary conditions are assigned for the outer edges and the back of the clay. The symmetry conditions are applied for the other two edges crossing at the impact area. The general contact algorithm and simple coulomb friction is used for all contact surfaces in the FE model. The friction coefficient of yarns is assumed to be 0.2 according to Rao’s tests results.¹⁴ Three impact velocities of 300 m/s, 500 m/s, and 600 m/s are assigned to the projectile perpendicular to the armor plane.

To reduce the number of elements and ensure the accuracy of calculation, different mesh sizes are used for the yarn model in this study. Fine mesh is adopted for primary yarns with 10 elements in the yarn cross-section and 12 elements in the yarn wavelength, as shown in Figure 1(c). Coarse mesh is used for orthogonal yarns with four elements were used in the cross-section and four elements in the yarn wavelength, as shown in Figure 1(d). In this manner, the FE model of a single layer fabric with hybrid mesh only has 77,368 elements. This leads to 83.3% reduction of mesh elements in comparison with that of the FE model with the uniform size of fine mesh. In addition, energy absorption of a single layer fabric model with hybrid mesh does not show any difference, due to the majority of impact energy deposited in primary yarns.

For the clay model, in the central part around the impact point (25 × 25 × 20 mm³), a fine mesh of size 0.446 × 0.446 × 0.455 mm³ is used. In other regions, a coarse mesh size (from 0.446 × 0.455 × 1.505 mm³ to 1.329 × 3.000 × 6.020 mm³) is adopted. Eight-node hexahedron elements (C3D8R) were used for yarns, projectile, and clay in the model.

Material properties

Although a yarn contains numerous fibers, it is impossible to take the fibers into account explicitly. In this FE model, a single yarn is assumed to be the basic unit with a 3D continuum body. Homogeneous and isotropic assumption were used for yarn material properties in some previous studies in order to simplify the simulation.^7,10,15 Such an assumption leads to acceptable results with small inaccuracies of approximately 2.4% in energy absorption. Therefore, in this study the yarn model is assumed to have homogeneous and isotropic properties.

Material properties of Twaron yarns, which were obtained from the product properties supplied by Teijin Company, are listed in Table 2. Under impact force, the yarn can be assumed to reach the tightest structure with little void between fibers. The mass density of Twaron yarns was assumed to be the same as that of fibers (1440 kg/m³). Although the yarn-level modeling has some difference from the actual yarn structure, such assumption can represent material properties of Twaron fibers, which is very important for the dynamic problem in FE simulation. Correspondingly, the amount of materials of fabric is inevitably increased. However, the influence of areal density increase of each fabric layer in a panel on energy absorption can be negligible when every layer is in the same case.

Table 2.

Material properties of FE model

Material properties	Projectile	Twaron	Clay¹⁷
Yield stress (GPa)	Rigid body	3.6	6 × 10⁻⁵
Fracture strain (%)	Rigid body	4.0	/
Young’s modulus (GPa)	206.8	90	6.58 × 10⁻³
Poisson’s ratio	0.3	0.35	0.496
Mass density (kg/m³)	7800	1440	1539
Angle of internal friction (^o)	/	/	61
Flow stress ratio	/	/	1.0
Dilation angle (^o)	/	/	0

The material behavior under impact is defined as linear elastic-plastic. Ductile damage is assumed and applied in the model. The damage evolution law is specified in terms of the fracture energy. Fracture energy is defined as the energy required opening a unit area of crack. The damage evolution law can be specified in terms of fracture energy dissipation. For the high performance fibres, the fracture energy is assumed to be 1000 J.¹⁶ The softening is defined as of exponential form.

The clay (Roma Plastilina No.1) is used at back of panels to record the configuration of the indentation in its surface after impact. According to material tests by Pamukcu et al.,¹⁷ remolded clay behaves more like the von Mises material model. It displays no volume change upon yield. The elastic and yield properties of the clay are strain-rate dependent. Therefore, in this study, the clay is modeled as an isotropic, homogeneous, and also elastic-plastic material. Material properties and the hardening response of clay, which were obtain from the results of Pamukcu et al.’s tests, are listed in Tables 2 and 3.

Table 3.

Hardening properties of clay.¹⁷

Yield stress (kPa)	Plastic strain
60	0.0
72	0.000119
96	0.000128
120	0.000159
144	0.000188
240	0.000263
360	0.000343
479	0.000462

Results and discussions

Validation of FE model

When the panel 11F₂₄ is impacted by a projectile with the velocity of 500 m/s, the projectile is stopped by the armor panel and an indentation is left in the clay. During the impact process, the projectile penetrates through the panel layer by layer. According to the FE result, the front seven layers of the panel 11F₂₄ are perforated. This is in the range of our previous ballistic test results of the panel 11F₂₄ with 7–10 perforated layers due to variability of ballistic tests.¹³

After it penetrates through the front seven layers, the projectile will not stop at once. It will continue to produce transverse deflection out of fabric panel until all kinetic energy of the projectile is dissipated. As a result, an indentation is left in the clay. In the FE model, the indentation in clay also shows the same configuration as that of ballistic test result, as shown in Figure 3. The back-face signature (BFS) and the width of the indentation are both in the range of actual values in ballistic test results.¹³ Therefore, the FE model at the non-perforation case is valid and can be used to identify ballistic responses of each layer in an armor panel.

Figure 3.

Indentation in clay behind the panel 11F₂₄: (a) FE model of clay; (b) clay for ballistic test; (c) measurement of back-face signature in clay.

Transverse deformation

When the panel is impacted, fabric layers in the panel will produce a transverse deflection out of fabric and deformation in the plane of fabric. Each layer displays different extents of transverse deformation. The maximum transverse deformation of each layer occurs at different moments. For the perforated layers, the maximum transverse deformation was produced at different fracture time of this layer. For the non-perforated layers, they can continue to produce the transverse deformation until the stopping moment of the projectile.

According to the FE results, the profile of the deformed central primary yarn in each layer that produces the maximum transverse deformation is plotted against the distances from the impact point to the edge of the fabric, as shown in Figure 4.

Figure 4.

FE results of the maximum transverse deflection of each layer in the panel 11F₂₄.

For the front few layers (ply−1, −2, and −3), the transverse deformation area in fabric is localized around the edge of the projectile. The middle layers close to the last perforated layer exhibit a wider transverse deformation area. In back layers, the transverse deformation area ceases to increase. Ballistic test results in our previous studies also confirm such findings from FE results,¹³ as shown in Figure 5. The last middle layer (ply-10) has an obvious large transverse deformation area compared with that of the first layer (ply-1) and the last layer (ply-24). This indicates that in the non-perforation case the materials in the middle position close to the last perforated layer possess the largest deformation area that is in strain under impact stress wave.

Figure 5.

Transverse deformation of some layers in the post-impact panel 11F₂₄.¹³

Stress distributions

When a projectile impacts on a woven fabric it produces transverse deflection in the primary yarns and generates longitudinal stress waves that propagate down the axis of the yarn. The transverse deformation proceeds until the stress at the impact point reaches a breaking stress. Figure 6 shows the von Mises stress distribution contours along the center of one primary yarn in fabric layers of the panel 11F₂₄. The stress distribution in the front, middle, and back layers exhibits different characteristics.

Figure 6.

FE results of stress distribution on some layers in the panel 11F₂₄: (a) front layers; (b) middle layers; (c) back layers.

In the front few layers, such as the front three layers, high stress concentrates in the contact area around the edge of the projectile, as shown in Figure 6(a). The stress is increased sharply during less than 10 µs. When the stress exceeds the yield stress of the material, the primary yarns are fractured. Due to the front layers being perforated quickly, the stress cannot propagate out of the impact area.

The middle perforated layers have longer interaction time to the impact from 10 µs to 21.5 µs. Therefore, the stress wave has enough time to propagate over a wider area from the impact point to the edge of fabric, as shown in Figure 6(b). This results in more fabric materials involved in the transverse deformation area before fabric fracture.

For back layers, they have a much longer interaction time with the projectile during the impact process. The stress wave on back layers can propagate to the edge of the fabric, as shown in Figure 6(c). Due to the lower stress magnitude than the yield stress in back fabric layers, the back layers cannot be perforated and just produces transverse deformation until the projectile stops.

Energy absorption distribution

When an armor panel is impacted by a projectile at high impact velocity, the impact energy of the projectile is mainly converted into the kinetic energy, strain energy and the frictional energy in fabric.^15,18 Due to the fact that the frictional energy dissipation only accounts for a very small portion of the total energy absorption in fabric,¹⁹ only the kinetic energy and strain energy of each layer are taken into account in FE results.

Under transverse impact, each fabric layers in the panel is under high stress. The yarns are stretched and fabric produces transverse deformation until the fracture moment for those perforated layers. Therefore, in FE results the maximum energy absorption of perforated layers is corresponded to the fracture moment. However, the projectile will not stop at once until all kinetic energy is dissipated. This is related to yarn pull-out, yarn bowing, transverse deformation of fabric and other failure mechanisms. Therefore, the maximum energy absorption of those non-perforated layers is corresponded to the stop moment of the projectile for the FE results.

Energy absorption of each layer in the panel 11F₂₄ is shown in Figure 7. It is the sum of the kinetic energy and strain energy of each layer. For a given impact velocity of 500 m/s, the front seven layers are perforated. The last perforated layer (the seventh layer) has the highest energy absorption. This is due to the last perforated layer can sustain long time in high stress before fracture, which allows more fabric material to be involved in energy absorption. For the front few layers (the front three layers) and some back layers (the back 10 layers), energy absorption is much lower. This is due to the high stress concentration on the front few layers and lower stress magnitude on back layers. On the whole, energy absorption by each layer is increased from the front layer to the maximum value by the last perforated layer and then decreased gradually in the following back layers.

Figure 7.

Energy absorption of each layer in the panel 11F₂₄ at an impact velocity of 500 m/s.

This pattern of energy absorption distribution in the non-perforated panel remains the same in the panels 11F₃₆ and 11F₄₈, as shown in Figures 8 and 9. Both of these two panels have seven perforated layers and the last perforated layer always has the highest energy absorption among layers in a panel. The total amount of areal weight of the whole panel has no influence on the pattern of energy absorption distribution in a non-perforated case.

Figure 8.

Energy absorption of each layer in the panel 11F₃₆ at an impact velocity of 500 m/s.

Figure 9.

Energy absorption of each layer in the panel 11F₄₈ at an impact velocity of 500 m/s.

Influence of the total number of layers

With the increase of the total number of layers, the total amount of energy absorption in an armor panel is improved. According to the FE results shown in Table 4, in comparison with the panel 11F₂₄, when the total amount of material in the panel is increased 50% from 24 layers to 36 layers, the total energy absorption is just increased 17.95%. With 100% increase of the total amount of the panel from 36 to 48 layers, energy absorption is only increased 4.56%. With more layers added in the multilayer system, the growth rate of energy absorption in the panel will become less and less. This indicates that the energy absorption efficiency of additional layers decreases significantly.

Table 4.

Energy absorption (EA) of multilayer panels at the impact velocity of 500 m/s

Multilayer system	Total number of layers	Total EA (J)	EA of front 24 layers (J)	The number of broken layers	BFS (mm)
Twaron Woven Panel	24	57.79	57.79	7	8
	36	70.43	50.57	7	7.12
	48	73.64	47.26	7	5.27

In addition, it is found that energy absorption of front 24 layers in the panel decreases with more additional layers in the panel, as shown in Figure 10. In comparison with the panel 11F₂₄, energy absorption of front 24 layers in the panel 11F₃₆ and 11F₄₈ decreases 12.49% and 18.22% respectively. Energy absorption of front layers is constrained and decreased by additional layers. These results indicated that it is not effective to achieve further improvement of energy absorption by adding more layers in a non-perforated panel at the current testing condition in this study.

Figure 10.

Energy absorption in three panels at an impact velocity of 500 m/s.

Although the increasing number of layers in the panel contributes little to energy absorption, it has a great influence on minimizing BFS behind the panel, as shown in Table 4. In comparison with the panel 11F₂₄, BFS behind the panel 11F₃₆ and 11F₄₈ decreases 11.2% and 25.92%, respectively. With more layers added in the non-perforated panel, BFS behind panels decreases more significantly. It can be inferred that when a panel is added by numerous fabric layers, there would be no indentation in clay, due to little transmitted energy through the panel.

Influence of the impact velocity

According to previous studies, ballistic responses of an armor panel have been greatly influenced by the impact velocity.^20–22 Therefore, energy absorption distribution in the armor panel has also been investigated by FE simulation at different impact velocities in detail, including a low impact velocity of 300 m/s and a high impact velocity of 600 m/s. Figures 11 and 12 shows energy absorption of each layer in the panel 11F₂₄ at these two impact velocities.

Figure 11.

Energy absorption of each layer in the panel 11F₂₄ at an impact velocity of 300 m/s.

Figure 12.

Energy absorption of each layer in the panel 11F₂₄ at an impact velocity of 600 m/s.

When the panel 11F₂₄ is impacted at the velocity of 300 m/s, the projectile only perforates one layer and is stopped before the panel due to low kinetic energy. The amount of energy absorption in each layer is lower than that of at the impact velocity of 500 m/s. The front layer has the highest energy absorption. In additional layers, energy absorption decreases gradually from front to back, as shown in Figure 11. At the impact velocity of 600 m/s, the projectile can perforate twelve layers due to the improved kinetic energy of the projectile, and is stopped in the panel at last. Energy absorption of each layer in the panel is increased in comparison with that of at the impact velocity of 500 m/s, as shown in Figure 12. Energy absorption distribution displays the same pattern as that of at the impact velocity of 500 m/s, as shown in Figure 7. It is increased from the front layer to the 12th layer (the last perforated layer) and then decreased in back layers.

If the panel is completely penetrated at even higher impact velocity, the last layer will have the highest energy absorption in a panel and energy absorption is increased from front to back layers in the panel. This has already been investigated numerically and experimentally in another paper.²³

According to above analysis, a general energy absorption distribution in the multilayer system at different striking velocities can be concluded. Energy absorption of each layer in the panel is increased from the front layer to the last perforated layer, and then decreased in back layers. Only the position of the peak value in energy absorption among layers is shifted towards the back of the panel with the increasing of the impact velocity.

In comparison with Joo and Kang’s study,⁸ their conclusions are consistent with findings in this study. However, due to the limited total number of layers in a panel (no more than 12 layers) and removing of clay, their FE results cannot represent a general case of ballistic impact. Such over-simplify of impact process for FE model also exists in Chen et al.’s study.^9,10 Their findings, as mentioned in the beginning of this paper, are the same as that of the perforation case in this study. Only the energy absorption mechanisms have been explained differently. However, it has not been confirmed in the non-perforation case. Therefore, their findings are not general energy absorption mechanisms in soft armor panel.

In all FE models in this study, the last perforated layer in a panel always has the peak value of energy absorption among all layers, as shown in the Figures 7, 11, and 12. In comparison with the seven perforated layers in panels 11F₂₄, 11F₃₆, and 11F₄₈ at the impact velocity of 500 m/s, there is one perforated layer at 300 m/s and 12 perforated layers at 600 m/s in the panel 11F₂₄. The number of perforated layers in a panel is highly dependent on the impact velocity rather than the total number of layers in the panel. These results indicates that for a given threat level and materials in an armor panel, the amount of fabric material that is required to dissipate the impact energy by fracture is constant. This means that the position of the last perforated layer can be exactly identified in a certain range of the panel. Therefore, the position of the peak value in energy absorption distribution in a panel can be determined correspondingly according to the threat level and materials in an armor panel.

Conclusions

In this study, different ballistic responses of each layer and energy absorption mechanisms in an armor panel were investigated in detail by FE simulation. It is found that ballistic responses of fabric layers are different in front, middle and back positions of a panel. The last perforated layer always has the maximum energy absorption among layers in the panel, due to large transverse deformation and wider stress distribution. As a result, in a multilayer panel, energy absorption of each layer is increased from front layers to the maximum value in the last perforated layer and then decreased gradually in the following back layers. This pattern of the energy absorption distribution remains the same, which is not affected by the total number of layers in the panel and the impact velocity. Only the peak value of energy absorption is shifted toward back of the panel with the increasing impact velocity.

With the increasing number of layers, energy absorption of a panel is increased but the growth rate decreases. Energy absorption of front layers is constrained and decreased by additional layers. Therefore, adding more layers in a panel in the non-perforation case contribute little to total amount of energy absorption, but it plays a significant role on minimizing BFS of the panel.

The findings in this paper improve the fundamental understanding of energy absorption distribution in soft armor panel, which is valuable for designers involved in development and elaboration of bulletproof vests.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is financially supported by Key Scientific Research Projects of High Education of Henan No.16A540007 and Research Fund for key laboratory of Technical Textile in Henan No.4600-32010017.

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