# Ballistic Impact Performance of SiC Ceramic-Dyneema Fiber Composite Materials

Authors: Kai-Kuang Wu; Yu-Liang Chen; Jau-Nan Yeh; Wei-Lun Chen; Chia-Shih Lin
Journal: Advances in Materials Science and Engineering
 (2020)

---

## Abstract

This study investigated the ballistic resistance of a composite target plate fabricated by combining SiC ceramic with the Dyneema fiber. To achieve a light-weight target plate that conforms to the US National Institute of Justice level four (NIJ IV) standards, minimal areal density analysis was conducted to obtain the optimal SiC ceramic-Dyneema fiber thickness combination. This study used energy absorption to analyze the ballistic resistance of the target plates. To drastically reduce experimental costs, most of this work employed ANSYS/LS-DYNA software to conduct finite element numerical simulations. First, ballistic experiments that conformed to NIJ IV standards were conducted to verify the simulation parameter configurations. Subsequently, the correlation function of the relationship between the combined thickness of the composite material and its ballistic resistance was determined through the experimental design, which effectively reduced the simulation analysis time. According to simulation experiments and regression analysis, the equation for the relationship between the combined thickness of the composite material and its ballistic resistance wasEAhc,hf=−6276.5+500.6hc+1512.6hf+30.7hchf−8.1hc2−113.6hf2, though there were limitations to its application. From the numerical analysis results, 8.1940 mm SiC ceramic and 6.9637 mm Dyneema fiber were determined to constitute the optimal thickness combination for a composite that features a minimal areal density and which conforms to NIJ IV standards. The combination was verified to be consistent with the numerical simulation analysis results.


---

## Body

## 1. Introduction

Protective measures on battlefields commonly have a wide range of applications for personnel, vehicles, ships, planes, and buildings. The latest protection technologies are generally used on tanks (armored vehicles) and protective clothing. The continuous enhancement of weapons with the progress of science and technology required the constant development of protective materials and structures. The most widely applied protective materials are currently ceramic composites, which use ceramic as front plates and fiber, metal, or other tough materials as the back plate. This combination is called the ceramic composite (Figure1).Figure 1
Schematic diagram of the ceramic composite.Ceramic is extremely hard and wear-resistant, which enables the passivation, erosion, and shattering of projectiles, increasing the impacted area between projectiles and armors and dissipating impact load. Furthermore, shattered ceramics cause mutual erosion with projectiles, producing lateral and reverse impact flow and preventing further penetration [1]. Fiber has greater tenacity, specific strength, specific modulus, fatigue resistance, wear resistance, and shock absorption compared with the metal. When used as the back plate material for ceramic composite bulletproof target plates, fibers can delay tensile failure in ceramics, causing projectiles to fully erode the target plate and dissipate kinetic energies, providing support and absorbing the kinetic energy of projectiles and ceramic shards [2].Therefore, composite materials that combine ceramic and fiber are currently the most widely applied bullet-resistant material. The results of a review of the literature on ceramic composites and ballistic protection were as follows.Reviewing studies on the ballistic resistance of ceramic composites before 2008, Hou et al. [3] concluded that findings on the effects of the penetration resistance of ceramic composites had been inconsistent. He proposed that future research should shift from the application of clay-metal composites to clay-fiber composites.In a study on the ballistic resistance of ceramic composite target plates that combined ceramic (Al2O3) with different materials such as steel, aluminum, and spectra fiber as the back plate, Sherman [4] concluded that the ceramic plate was the main factor in resisting bullet penetration.Du et al. [5] analyzed the ballistic resistance of an Al2O3-Kevlar fiber composite target plate using the modified hydrodynamics of Alekseevsky–Tate, maximum strain failure theory, and the law of conservation of energy. Du discerned a three-phase mode for the process of shooting a bullet at a target plate and established mathematical equations to present the energy loss in each phase and estimate the ballistic limit (V50) of the target plates. After conducting firing tests using 7.62 mm armor-piercing (AP) incendiary ammunition, Du concluded that increasing the thickness or surface density of the target plate can improve its ballistic resistance, with ceramic plates showing more significant improvements than fiber plates. In addition, increasing the length-diameter ratio of the bullets greatly decreased the ballistic limit (V50) of the target plates.In a study involving ceramic composite target plates with a combination of fiber layer-ceramic plate-fiber layer-aluminum alloy, Li et al. [6] conducted a qualitative analysis on the ballistic resistance of the plates using theoretical models such as stress wave, restraint mechanism, back-force effect, and shock absorption. The results indicated that to improve ballistic resistance, the transmitted wave intensity had to be decreased and the reflected wave intensity had to be increased. This caused the edge of the shell crater to collapse and reduced its perforation size, hindering bullet movement because of the increased thickness of the fabric layer.Hsieh et al. [7] investigated whether the addition of ceramic plates to aromatic polyamide fabric would alter the fabric’s ballistic resistance. Their results indicated that 6 mm ceramic plates were able to effectively disperse the impact energy of bullets, and the addition of ceramic plates was able to increase the bullet attrition rate.Chen et al. [8] studied the resistance of ceramic-low carbon steel composite target plates to the impact of 7.62 mm AP ammunition. The study employed a numerical simulation that combined finite element and smoothed particle hydrodynamics methods, whereby a mathematical relation of ballistic limit (V50) constituting the ratio between the thickness and surface density of ceramics and low carbon steel was established. This relation was applicable to the ballistic limit (V50) of 400 m/s–800 m/s and a ceramic-low carbon steel thickness ratio of 1.5–6.0.Ömer et al. [9] studied a GFRP composite material milled to experimentally minimize the damages on the machined surfaces, using two, three, and four flute end mills at different combinations of cutting parameters. Experimental results showed that the damage factor increased with increasing cutting speed and feed rate; on the contrary, it was found that the damage factor decreased with increasing depth of the cut and number of the flutes. In addition, analysis of variance (ANOVA) results clearly revealed that the feed rate was the most influential parameter affecting the damage factor in end milling of GFRP composites.Erkan et al. [10] studied a series of machining operations done for data collection by varying the flute number, feed rate, depth of cut, and cutting speed. The relationship between the cutting parameters of end milling operations and the surface roughness of the machined surface was studied. For the analysis of the data and selection of the optimal cutting parameters, Taguchi method and genetically optimized neural network systems (GONNs) were used.Gökhan and Ömer [11] indicated that it is possible to improve the whole quality by reducing the delamination which occurs in the drilling of carbon fiber-reinforced plastic (CFRP) composite plates. For the study, carried out under dry machining conditions, the parameters included three different cutting speeds, three different feed rates, and drill geometry involving three different point angles.This study conducted finite element method numerical simulations using ANSYS/LS-DYNA software to drastically lower live firing costs and simultaneously reduce the number of experiments using the factor combination of the experimental design. In addition, the study used regression analysis to obtain empirical functions and effectively reduce simulation time.The present study used ballistic-resistant composite target plates composed of silicon carbide ceramic (SiC) and Dyneema fiber, analyzing their ballistic resistance through energy modes. Ballistic resistance was defined as the kinetic energy difference and the absorptive power of the ceramic composite plate when the bullet penetrated it. Ballistic experiments conforming to the US National Institute of Justice level four (NIJ IV) standards were conducted to verify the simulation parameters; factor combinations were planned using the experimental design. Further data regression was conducted to obtain the correlation function between the thickness combination of the ceramic composite ballistic-resistant plate and its ballistic resistance. The optimal combined thickness of ceramic and fiber for a light-weight, bullet-resistant ceramic composite target plate with minimal surface density was achieved through the derivation of the aforementioned correlation function. Finally, the optimal combination was verified through ballistic experiments and simulations.


## 2. Ballistic Experiments

### 2.1. Definition of Ballistic Resistance

To acquire test data that enabled calculation and analysis, a plate penetration experiment was conducted, and the residual velocity of the bullet was determined, from which the kinetic energy difference was obtained. Thus, the study defined ballistic resistance as the kinetic energy difference of the bullet when it penetrated the target plate, i.e., the absorptive energy of the plate (equation (1)). A higher absorptive energy meant the plate possessed a higher ballistic resistance. Because it was difficult to collect the bullets that had penetrated the plates during the ballistic experiments, the mass of the bullet was assumed to remain constant throughout the test:(1)EA=12mvi2−12mvr2,where EA (J) represents the ballistic resistance of the plates; m (kg) represents the bullet weight; vi (m/s) represents the initial velocity of the bullet; and vr (m/s) represents the residual velocity of the bullet after it penetrated the plate.


### 2.2. Target Plate Fabrication

The ballistic-resistant ceramic composite target plate mainly consisted of silicon SiC ceramic and a Dyneema (unidirectional structure) fiber back plate. The ceramic plate was hexagonal with side lengths of 60 mm each, fabricated by sintering SiC ceramic powder under atmospheric pressure at a temperature of 2050°C. A 200 mm × 200 mm piece of Dyneema fabric was cut and hot-pressed into the plate at a temperature of 115°C. The ceramic and fiber plates were then bound together using epoxy resin and compressed under a 10 kg weight for 24 h to ensure they were firmly joined.


### 2.3. Ballistic Test Arrangement

This study conducted ballistic test in accordance with the NIJ IV standard, using 0.30″ AP ammunitions, with the amount of gunpowder adjusted to achieve an initial velocity of 868 m/s ± 15 m/s. Photoelectric screens were used to measure the velocity of the bullet, whereby two screens were placed 1 m apart to separately measure the initial and residual velocities of the bullet by transmitting the photoelectric signals to the oscilloscope. The smallest measured scale was 10−6 sec. Figure 2 shows a schematic diagram of the ballistic experiments.Figure 2
Schematic diagram of ballistic test.


### 2.4. Ballistic Test Results

To reduce the influences of factors such as temperature and humidity on the results, the experiment was completed within the same day and conducted in triplicate to ensure its accuracy. To verify the parameter settings of the finite element numerical simulation, 6 mm silicon carbide ceramic and a 6 mm Dyneema fiber were bound and used as the ceramic composite target plate, which was then used to conduct the target plate penetration experiment under the NIJ IV standard using 0.30″ AP ammunitions. The initial and residual velocities of each bullet after it penetrated the plate were measured to calculate the absorptive energy of the plate, as shown in Table1. The bullet mass (m) was measured as 10.6 g and was held constant throughout the experiment.Table 1
Correctness of experimental.
No.
v
i (m/s)
v
r (m/s)
Absorptive energy of the target plate (J)
1
871
536
2,498
2
875
542
2,501
3
882
553
2,502Despite minor variations in the initial velocity, it still fell within the range of NIJ IV standards with a difference of less than 1.263%, evidence that this experiment was well controlled. The measured absorptive energy of the target plate also varied, but the difference was less than 0.164%, indicating the stability and consistency of this experiment. Therefore, the influence of the initial velocity difference of the bullet on the absorptive energy of the target plate could be disregarded.The second set of data from the ballistic test was compared with the analysis results to verify the finite element numerical simulation. To completely eliminate the influence of the initial velocity difference of the bullet on the absorptive energy of the target plate, the initial velocity was set as 875 m/s during the finite element simulation analysis.


## 2.1. Definition of Ballistic Resistance

To acquire test data that enabled calculation and analysis, a plate penetration experiment was conducted, and the residual velocity of the bullet was determined, from which the kinetic energy difference was obtained. Thus, the study defined ballistic resistance as the kinetic energy difference of the bullet when it penetrated the target plate, i.e., the absorptive energy of the plate (equation (1)). A higher absorptive energy meant the plate possessed a higher ballistic resistance. Because it was difficult to collect the bullets that had penetrated the plates during the ballistic experiments, the mass of the bullet was assumed to remain constant throughout the test:(1)EA=12mvi2−12mvr2,where EA (J) represents the ballistic resistance of the plates; m (kg) represents the bullet weight; vi (m/s) represents the initial velocity of the bullet; and vr (m/s) represents the residual velocity of the bullet after it penetrated the plate.


## 2.2. Target Plate Fabrication

The ballistic-resistant ceramic composite target plate mainly consisted of silicon SiC ceramic and a Dyneema (unidirectional structure) fiber back plate. The ceramic plate was hexagonal with side lengths of 60 mm each, fabricated by sintering SiC ceramic powder under atmospheric pressure at a temperature of 2050°C. A 200 mm × 200 mm piece of Dyneema fabric was cut and hot-pressed into the plate at a temperature of 115°C. The ceramic and fiber plates were then bound together using epoxy resin and compressed under a 10 kg weight for 24 h to ensure they were firmly joined.


## 2.3. Ballistic Test Arrangement

This study conducted ballistic test in accordance with the NIJ IV standard, using 0.30″ AP ammunitions, with the amount of gunpowder adjusted to achieve an initial velocity of 868 m/s ± 15 m/s. Photoelectric screens were used to measure the velocity of the bullet, whereby two screens were placed 1 m apart to separately measure the initial and residual velocities of the bullet by transmitting the photoelectric signals to the oscilloscope. The smallest measured scale was 10−6 sec. Figure 2 shows a schematic diagram of the ballistic experiments.Figure 2
Schematic diagram of ballistic test.


## 2.4. Ballistic Test Results

To reduce the influences of factors such as temperature and humidity on the results, the experiment was completed within the same day and conducted in triplicate to ensure its accuracy. To verify the parameter settings of the finite element numerical simulation, 6 mm silicon carbide ceramic and a 6 mm Dyneema fiber were bound and used as the ceramic composite target plate, which was then used to conduct the target plate penetration experiment under the NIJ IV standard using 0.30″ AP ammunitions. The initial and residual velocities of each bullet after it penetrated the plate were measured to calculate the absorptive energy of the plate, as shown in Table1. The bullet mass (m) was measured as 10.6 g and was held constant throughout the experiment.Table 1
Correctness of experimental.
No.
v
i (m/s)
v
r (m/s)
Absorptive energy of the target plate (J)
1
871
536
2,498
2
875
542
2,501
3
882
553
2,502Despite minor variations in the initial velocity, it still fell within the range of NIJ IV standards with a difference of less than 1.263%, evidence that this experiment was well controlled. The measured absorptive energy of the target plate also varied, but the difference was less than 0.164%, indicating the stability and consistency of this experiment. Therefore, the influence of the initial velocity difference of the bullet on the absorptive energy of the target plate could be disregarded.The second set of data from the ballistic test was compared with the analysis results to verify the finite element numerical simulation. To completely eliminate the influence of the initial velocity difference of the bullet on the absorptive energy of the target plate, the initial velocity was set as 875 m/s during the finite element simulation analysis.


## 3. Finite Element Numerical Simulation Analysis

### 3.1. ANSYS/LS-DYNA Finite Element Simulation Software

The LS-DYNA simulation software facilitates numerical analysis on high-speed impact and penetration experiments. It is among the most powerful software programs involving dynamic finite element analysis and is widely applied in the defense and civil sectors. The software mainly operates using an explicit integral algorithm, with a minor integral algorithm acting as a supplementary mode. It also has three numerical description methods: Lagrangian, Eulerian, and arbitrary Lagrangian–Eulerian and is suitable for static load analysis as well as studying brief or instantaneous dynamic behaviors with short action times, large deformations, nonlinear structural impacts, and complicated contact impacts [12].


### 3.2. Procedure of the Finite Element Method Numerical Simulation

The finite element method numerical simulation procedure in this study was divided into two parts. First, the ANSYS program was used as a preprocessor to establish high-speed impact numerical analysis models for the bullet and the target plate. This included model drawing, meshing, defining material properties, selecting material models, and configuring the contact mode, as well as control parameters and boundary conditions, which in turn produced the keyword file.Next, the keyword file was input into the LS-DYNA software solver to determine the solution and was further processed by the LS-PrePost to analyze the penetration and destruction mode of the target plate, as well as evaluate the residual velocity of the bullet.


### 3.3. Material Model Construction

The bullet model was based on a 0.30″ AP ammunition (Figure3), and its dimensions are shown in Figure 4; its exterior material and interior materials are copper and steel, respectively. A 1/4 scale symmetrical model was constructed, whereby the reflect function was used to present the full bullet figure during analysis; material model 3 (Mat_Plastic_Kinematic) is suited to model isotropic material, therefore was chosen to describe the steel component of the bullet in this study. The mechanical properties of the steel are shown in Table 2. Material model 10 (Mat_Elastic_Plastic_Hydro) allows the modeling of an elastic-plastic hydrodynamic material, and the characteristics of copper are suited to use this model. The mechanical properties of copper are shown in Table 3.Figure 3
0.30″ AP model.Figure 4
0.30″ AP bullet dimensions.Table 2
Mechanical properties of material model 3 (Mat_Plastic_Kinematic).
Materials
ρ (g/cm3)
E (Mbar)
ν
SIGY (Mbar)
Steel
7.89
2.02
0.3
0.0107Table 3
Mechanical properties of material model 10 (Mat_Elastic_Plastic_Hydro).
Materials
ρ (g/cm3)
SIGY (Mbar)
EH (Mbar)
G (Mbar)
Cu
8.93
0.0012
0.00288
0.477The target plate model was divided into SiC ceramic and Dyneema fiber (Figure5). Material model 110 (MAT_Johnson_Holmquist_Ceramics) is useful for modeling ceramics [13], therefore was chosen to describe SiC ceramic. Mechanical properties of SiC are shown in Table 4. Dyneema fiber was described using material model 22 (MAT_Composite_Damage), in which an orthotropic material with optional brittle failure for composite can be defined. Mechanical properties of Dyneema are shown in Table 5. The aforementioned material parameter setting is referred to the paper presented by Fawaz et al. [14]. In addition, the “Contact_Eroding_Surface_To_Surface” contact model in LS_DYNA was chosen to describe the dynamic behavior between bullet and SiC ceramic as well as bullet and Dyneema fiber. After the fiber board was damaged by the bullet, the fiber will generate layer-stripped phenomenon, and the layers will delaminate. Among those “Contact” commands, we chose the “Contact_Tied_Surface_To_Surface” to describe the dynamic behavior among the layers of the Dyneema fiber. In this contact mode, the nodes are stuck together before the fiber board was damaged. When the material of the fiber is subjected to external force, damage will occur in accordance with the failure criterion. The failure criterion is shown as equation (2), controlled by tensile failure stress and shear failure stress.(2)σnNFLS2+σsSFLS2≥1,where NFLS is the tensile failure stress and SFLS is the shear failure stress.Figure 5
Target plate model.Table 4
Mechanical properties of SiC.
ρ
3.1 (g/cm3)
G
1.79 (Mbar)
A
0.96 [8, 14]
B
0.35 [8, 14]
C
0.0 [8, 14]
M
1.0 [8, 14]
N
0.65 [8, 14]
T
0.001275 (Mbar)
HEL
0.03738 (Mbar)
P
hel
0.0174 (Mbar)
D
1
0.48 [8, 14]
D
2
0.48 [8, 14]
K
1
2.09 (Mbar)Table 5
Mechanical properties of Dyneema.
E
11,22 (GPa)
E
33 (GPa)
G
12 (GPa)
G
23,31 (GPa)
ν
22
ν
31,32
X
t (GPa)
Y
t (GPa)
X
c (GPa)
Y
c (GPa)
ρ (g/cm3)
30.7
1.97
1.97
0.67
0.008
0.044
3.0
3.0
0.95
0.95
0.97
E
ij: Young’ modulus, Gij: shear modulus, νij: Poisson’s ratio, ρ: density, 1–3: x-, y-, and z-axis directions of materials, Xt, Xc: maximum tensile and compressive strength of x-axis directions, and Yt, Yc: maximum tensile and compressive strength of y-axis directions.The mesh type used in the simulation model is hexahedron (3D_Solid_164), and the mesh size is as follows (length ∗ width ∗ height):(a)
Steel: 0.021 ∗ 0.021 ∗ 0.04 (cm)(b)
Cu: 0.025 ∗ 0.025 ∗ 0.04 (cm)(c)
Ceramic: 0.086 ∗ 0.1 ∗ 0.1 (cm)(d)
Fiber: 0.1 ∗ 0.1 ∗ 0.05 (cm)Because only a quarter of the target plate and the bullet model were established, the boundary conditions of the numerical simulation in this study are set as the BOUNDARY_SYMMETRY_FAILURE model to allow the simulation results to map out the remaining three-quarters of the model and avoid unreasonable damage and physical phenomena; theX-, Y-, and Z-axis movement and rotation direction of all nodes on the symmetry axis and plane should be restrained according to the actual situation. The all sides of the back plate were set fixed.


### 3.4. Comparison of Numerical Simulation and Ballistic Test Results

The ballistic test result in this study was compared with that of numerical simulation analysis. Excluding the construction of material models, the required computational time was 2 hours.Constructed from a combination of 6 mm SiC ceramic and 6 mm Dyneema fiber plates, the ceramic composite target plate in this study underwent ballistic experiments and numerical simulation on plate penetration. Through the initial velocity of the bullet and the residual velocity measured after the bullet penetrated the plate, it was estimated that the absorptive energy of the plate was 2,501 J. In addition, assuming the initial velocity of the bullet was the same with the ballistic experiments, the numerical simulation analysis indicated that the residual velocity of the bullet after it penetrated the target plate was 532 m/s, and the absorptive energy of the target plate was estimated to be 2,558 J. The results indicated a difference of 2.276% between the numerical simulation analysis and the ballistic experiments (Table6), which verifies that the LS-DYNA model and parameter settings can be used to simulate and analyze the actual bullet impact phenomenon.Table 6
Comparison of target plate absorptive energy in the numerical simulation and ballistic tests.
Ballistic experiments
Numerical simulation
Target plate absorptive energy difference (%)
v
i (m/s)
v
r (m/s)
v
i (m/s)
v
r (m/s)
875
542
875
532
2.276


## 3.1. ANSYS/LS-DYNA Finite Element Simulation Software

The LS-DYNA simulation software facilitates numerical analysis on high-speed impact and penetration experiments. It is among the most powerful software programs involving dynamic finite element analysis and is widely applied in the defense and civil sectors. The software mainly operates using an explicit integral algorithm, with a minor integral algorithm acting as a supplementary mode. It also has three numerical description methods: Lagrangian, Eulerian, and arbitrary Lagrangian–Eulerian and is suitable for static load analysis as well as studying brief or instantaneous dynamic behaviors with short action times, large deformations, nonlinear structural impacts, and complicated contact impacts [12].


## 3.2. Procedure of the Finite Element Method Numerical Simulation

The finite element method numerical simulation procedure in this study was divided into two parts. First, the ANSYS program was used as a preprocessor to establish high-speed impact numerical analysis models for the bullet and the target plate. This included model drawing, meshing, defining material properties, selecting material models, and configuring the contact mode, as well as control parameters and boundary conditions, which in turn produced the keyword file.Next, the keyword file was input into the LS-DYNA software solver to determine the solution and was further processed by the LS-PrePost to analyze the penetration and destruction mode of the target plate, as well as evaluate the residual velocity of the bullet.


## 3.3. Material Model Construction

The bullet model was based on a 0.30″ AP ammunition (Figure3), and its dimensions are shown in Figure 4; its exterior material and interior materials are copper and steel, respectively. A 1/4 scale symmetrical model was constructed, whereby the reflect function was used to present the full bullet figure during analysis; material model 3 (Mat_Plastic_Kinematic) is suited to model isotropic material, therefore was chosen to describe the steel component of the bullet in this study. The mechanical properties of the steel are shown in Table 2. Material model 10 (Mat_Elastic_Plastic_Hydro) allows the modeling of an elastic-plastic hydrodynamic material, and the characteristics of copper are suited to use this model. The mechanical properties of copper are shown in Table 3.Figure 3
0.30″ AP model.Figure 4
0.30″ AP bullet dimensions.Table 2
Mechanical properties of material model 3 (Mat_Plastic_Kinematic).
Materials
ρ (g/cm3)
E (Mbar)
ν
SIGY (Mbar)
Steel
7.89
2.02
0.3
0.0107Table 3
Mechanical properties of material model 10 (Mat_Elastic_Plastic_Hydro).
Materials
ρ (g/cm3)
SIGY (Mbar)
EH (Mbar)
G (Mbar)
Cu
8.93
0.0012
0.00288
0.477The target plate model was divided into SiC ceramic and Dyneema fiber (Figure5). Material model 110 (MAT_Johnson_Holmquist_Ceramics) is useful for modeling ceramics [13], therefore was chosen to describe SiC ceramic. Mechanical properties of SiC are shown in Table 4. Dyneema fiber was described using material model 22 (MAT_Composite_Damage), in which an orthotropic material with optional brittle failure for composite can be defined. Mechanical properties of Dyneema are shown in Table 5. The aforementioned material parameter setting is referred to the paper presented by Fawaz et al. [14]. In addition, the “Contact_Eroding_Surface_To_Surface” contact model in LS_DYNA was chosen to describe the dynamic behavior between bullet and SiC ceramic as well as bullet and Dyneema fiber. After the fiber board was damaged by the bullet, the fiber will generate layer-stripped phenomenon, and the layers will delaminate. Among those “Contact” commands, we chose the “Contact_Tied_Surface_To_Surface” to describe the dynamic behavior among the layers of the Dyneema fiber. In this contact mode, the nodes are stuck together before the fiber board was damaged. When the material of the fiber is subjected to external force, damage will occur in accordance with the failure criterion. The failure criterion is shown as equation (2), controlled by tensile failure stress and shear failure stress.(2)σnNFLS2+σsSFLS2≥1,where NFLS is the tensile failure stress and SFLS is the shear failure stress.Figure 5
Target plate model.Table 4
Mechanical properties of SiC.
ρ
3.1 (g/cm3)
G
1.79 (Mbar)
A
0.96 [8, 14]
B
0.35 [8, 14]
C
0.0 [8, 14]
M
1.0 [8, 14]
N
0.65 [8, 14]
T
0.001275 (Mbar)
HEL
0.03738 (Mbar)
P
hel
0.0174 (Mbar)
D
1
0.48 [8, 14]
D
2
0.48 [8, 14]
K
1
2.09 (Mbar)Table 5
Mechanical properties of Dyneema.
E
11,22 (GPa)
E
33 (GPa)
G
12 (GPa)
G
23,31 (GPa)
ν
22
ν
31,32
X
t (GPa)
Y
t (GPa)
X
c (GPa)
Y
c (GPa)
ρ (g/cm3)
30.7
1.97
1.97
0.67
0.008
0.044
3.0
3.0
0.95
0.95
0.97
E
ij: Young’ modulus, Gij: shear modulus, νij: Poisson’s ratio, ρ: density, 1–3: x-, y-, and z-axis directions of materials, Xt, Xc: maximum tensile and compressive strength of x-axis directions, and Yt, Yc: maximum tensile and compressive strength of y-axis directions.The mesh type used in the simulation model is hexahedron (3D_Solid_164), and the mesh size is as follows (length ∗ width ∗ height):(a)
Steel: 0.021 ∗ 0.021 ∗ 0.04 (cm)(b)
Cu: 0.025 ∗ 0.025 ∗ 0.04 (cm)(c)
Ceramic: 0.086 ∗ 0.1 ∗ 0.1 (cm)(d)
Fiber: 0.1 ∗ 0.1 ∗ 0.05 (cm)Because only a quarter of the target plate and the bullet model were established, the boundary conditions of the numerical simulation in this study are set as the BOUNDARY_SYMMETRY_FAILURE model to allow the simulation results to map out the remaining three-quarters of the model and avoid unreasonable damage and physical phenomena; theX-, Y-, and Z-axis movement and rotation direction of all nodes on the symmetry axis and plane should be restrained according to the actual situation. The all sides of the back plate were set fixed.


## 3.4. Comparison of Numerical Simulation and Ballistic Test Results

The ballistic test result in this study was compared with that of numerical simulation analysis. Excluding the construction of material models, the required computational time was 2 hours.Constructed from a combination of 6 mm SiC ceramic and 6 mm Dyneema fiber plates, the ceramic composite target plate in this study underwent ballistic experiments and numerical simulation on plate penetration. Through the initial velocity of the bullet and the residual velocity measured after the bullet penetrated the plate, it was estimated that the absorptive energy of the plate was 2,501 J. In addition, assuming the initial velocity of the bullet was the same with the ballistic experiments, the numerical simulation analysis indicated that the residual velocity of the bullet after it penetrated the target plate was 532 m/s, and the absorptive energy of the target plate was estimated to be 2,558 J. The results indicated a difference of 2.276% between the numerical simulation analysis and the ballistic experiments (Table6), which verifies that the LS-DYNA model and parameter settings can be used to simulate and analyze the actual bullet impact phenomenon.Table 6
Comparison of target plate absorptive energy in the numerical simulation and ballistic tests.
Ballistic experiments
Numerical simulation
Target plate absorptive energy difference (%)
v
i (m/s)
v
r (m/s)
v
i (m/s)
v
r (m/s)
875
542
875
532
2.276


## 4. Optimal Thickness Combination of the Ceramic Composite

### 4.1. Experimental Design

To effectively lower the time required for material model construction and numerical computation, this study formulated factor combinations to reduce the number of experiments required. The empirical function was then obtained through regression analysis to shorten the simulation time.Based on previous experiences with ballistic experiments, a composite target plate is deemed to meet the NIJ IV standards if it is 15 mm thick and the ceramic part is 10 mm thick. To acquire the ballistic resistance value of the plate, the experiment was designed as a penetration test. Therefore, the thickness of the test plate should not exceed 15 mm, and the thickness of the ceramic plate should not exceed 10 mm.Based upon face-centered cubic composite design, the thickness of the SiC ceramic plate (hc) and thickness of the fiber plate (hf) were used as experimental factors, and the absorptive energy of the target plate (EA) was the reaction value. The factor combination was formulated using the 2-factor-3-level model (Table 7). The unit for hc and hf was mm, and the unit for EA was J.Table 7
Experimental design.
No.
h
c (mm)
h
f (mm)
1
5
4
2
5
6
3
5
8
4
6
4
5
6
6
6
6
8
7
7
4
8
7
6
9
7
8


### 4.2. Test Results

The bullet mass was assumed to remain constant throughout the experiment, and the initial velocity of the bullet was controlled at 875 m/s. Through numerical analysis following the construction of material models, the residual velocity of the bullet after penetrating the plate was obtained, whereinEA was calculated based on the dynamic values of the bullet velocity (Table 8).Table 8
Test data.
No.
h
c (mm)
h
f (mm)
v
i (m/s)
v
r (m/s)
E
A (J)
1
5
4
875
768
932
2
5
6
875
641
1,880
3
5
8
875
612
2,073
4
6
4
875
719
1,318
5
6
6
875
532
2,558
6
6
8
875
488
2,796
7
7
4
875
632
1,941
8
7
6
875
412
3,158
9
7
8
875
347
3,420Next, the adaptive quadratic reaction surface method was conducted usinghc and hf as operational variables, with EA as the reaction value. This could also be viewed as the energy function (equation (3) whereupon the adaptive function could be obtained following analysis equation (4)):(3)EAhc,hf=k+ahc+bhf+chchf+dhc2+ehf2,(4)EAhc,hf=−6276.5+500.6hc+1512.6hf+30.7hchf−8.1hc2−113.6hf2.


### 4.3. Analysis Results

#### 4.3.1. Regression Function Limitations

According to equation (3), when the values of both hc and hf were 0, the value obtained for EA was less than 0, which was clearly inconsistent with real-world physics. Thus, there were limitations to the application of equation (3).Because the quadratic coefficients ofhc and hf were both smaller than 0, it was clear that the target plate thickness had maximal influence on EA. Therefore, the maximal operational variable of the energy function could be acquired by subjecting hc and hf in equation (2) to differentiation (equation (5)).(5)∂EA∂hc=0⟶a+chf+2dhc=0∂EA∂hf=0⟶b+chc+2ehf=0⟹hcmax=−2ae+bc4de−c2hfmax=−2bd+ac4de−c2.


#### 4.3.2. Minimal Target Plate Thickness

Equation (6) shows hc being arranged in a series of descending power. The target plate thickness (θ = hc + hf) was used as the analysis parameter and was held constant. When hf was substituted with target plate thickness (θ) and hc, EA was a function of θ and hc:(6)EAθ,hc=−c+d+ehc2+a−b+θc−2ehc+k+bθ+eθ2=P1hc2+Q1θhc+R1θ=P1hc+Q1θ2P12+R1θ−Q12θ4P1⟹R1θ−Q12θ4P1≥EAθ,hc⟹EAθ,hcmax=R1θ−Q12θ4P1P<0.According to equation (5), EA had a maximal value when θ remained a fixed value. In other words, when EA was a known value, the minimal target plate thickness (θmin) as well as the optimal thickness combination of the SiC ceramic plate and Dyneema fiber plate could be inversely calculated. Thus, when the value of EA was 0, the minimal value of θ and hc could be inversely calculated according to the following equation:(7)θmin=hcmax+hfmax−24de−c2−c+d+ea2e+b2d−abc−4de−c2k,hcmin=hcmax+c−2e4de−c2a2e+b2d−abc−4de−c2k−c+d+e.


#### 4.3.3. Minimal Areal Density

This study sought to design a light-weight ballistic-resistant target plate under the NIJ IV standard. Hence, areal density (Ψ) was used as the analysis parameter (equation (8)):(8)Ψhc,hf=ρchc+ρfhf⟹Ψρf=ρcρfhc+hf⟹α=βhc+hf,where the volume densities of SiC ceramic (ρc) and Dyneema fiber were 3.1×10−3 (g/mm3) and 0.97×10−3g/mm3, respectively; α is the ratio of Ψ over ρf, and β is the ratio of ρc over ρf.Equation (9) shows hc being arranged in a series of descending power. The value of target areal density (Ψ = ρchc + ρfhf) remained constant, and hf was substituted with Ψ and hc. EA was thus a function of α and hc:(9)EAα,hc=−cβ+d+eβ2hc2+a−bβ+αc−2eβhc+k+bα+eα2=P2hc2+Q2αhc+R2α=P2hc+Q2α2P22+R2α−Q22α4P2⟹R2α−Q22α4P2≥EAα,hc⟹EAα,hcmax=R2α−Q22α4P2P2<0.According to equation (9), EA had a maximal value when the value of Ψ was held constant. In other words, minimal Ψ and the optimal combined thickness of SiC ceramic and Dyneema fiber could be inversely calculated when EA was a known value. Therefore, when the value of EA was 0, the minimal value of Ψ and hc could be inversely calculated as follows:(10)Ψmin=ρchcmax+ρfhfmax−2ρf24de−c2−cβ+d+eβ2a2e+b2d−abc−4de−c2k,hcmin=hcmax+c−2eβ4de−c2a2e+b2d−abc−4de−c2k−cβ+d+eβ2.


#### 4.3.4. Optimal Combination

To completely absorb the kinetic energy of the bullet using the SiC ceramic and Dyneema fiber composite target plate, the optimal combination ofhc and hf could be obtained through the aforementioned numerical analysis (Figures 6 and 7).Figure 6
Absorptive energy corresponded to minimization of thickness and areal density of the target.Figure 7
Optimal thickness combination of the composite materials.


### 4.4. Experimental Verification

#### 4.4.1. Energy Function Verification

The energy function of the ballistic-resistant target plate was obtained through experimentally designed regression analysis, wherein the target plate thickness was maintained between 9 mm and 15 mm. Hence, four sets of target plate thickness combinations were chosen from the range and were subjected to numerical simulations to verify the energy function (Table9). The results indicated that the optimal combination featuring minimal target plate thickness (θmin) which corresponded to the energy function and satisfied the NIJ IV standards was consistent with that obtained from the numerical simulation analysis.Table 9
Verification of the energy function.
Energy function
Numerical simulation
Difference (%)
θ
min mm
(hc)opt mm
(hf)opt mm
(EA)1 J
v
i m/s
v
r m/s
(EA)2 J
E
A
1
/
E
A
2
−
1
9.0
4.2949
4.7051
946.5579
875.0
762.0
980.3993
−3.451
12.5
7.2564
5.2436
2,905.6687
875.0
467.0
2901.9408
0.13
14.7
9.1179
5.5821
4,080.7837
875.0
0.0
4,057.8125
0.57
15.0
9.3717
5.6283
4,237.6600
875.0
0.0
4,057.8125
4.43


#### 4.4.2. Verifying the Optimal Combination

This study aimed to develop light-weight ballistic-resistant target plates while conforming to NIJ IV standards. Therefore, the energy function was verified using the optimal combination with minimal areal density (Ψmin) (Table 10). The results indicated that, in the estimation of the absorptive energy of the target plate, the energy function fits the numerical simulation analysis.Table 10
Verification of the optimal combination.
Energy function
Numerical simulation
Ψmin g/mm2
(hc)opt mm
(hf)opt mm
(EA)1 J
v
i m/s
v
r m/s
(EA)2 J
0.032
8.1940
6.9637
4,057.8
875.00
0.00
4,057.8


## 4.1. Experimental Design

To effectively lower the time required for material model construction and numerical computation, this study formulated factor combinations to reduce the number of experiments required. The empirical function was then obtained through regression analysis to shorten the simulation time.Based on previous experiences with ballistic experiments, a composite target plate is deemed to meet the NIJ IV standards if it is 15 mm thick and the ceramic part is 10 mm thick. To acquire the ballistic resistance value of the plate, the experiment was designed as a penetration test. Therefore, the thickness of the test plate should not exceed 15 mm, and the thickness of the ceramic plate should not exceed 10 mm.Based upon face-centered cubic composite design, the thickness of the SiC ceramic plate (hc) and thickness of the fiber plate (hf) were used as experimental factors, and the absorptive energy of the target plate (EA) was the reaction value. The factor combination was formulated using the 2-factor-3-level model (Table 7). The unit for hc and hf was mm, and the unit for EA was J.Table 7
Experimental design.
No.
h
c (mm)
h
f (mm)
1
5
4
2
5
6
3
5
8
4
6
4
5
6
6
6
6
8
7
7
4
8
7
6
9
7
8


## 4.2. Test Results

The bullet mass was assumed to remain constant throughout the experiment, and the initial velocity of the bullet was controlled at 875 m/s. Through numerical analysis following the construction of material models, the residual velocity of the bullet after penetrating the plate was obtained, whereinEA was calculated based on the dynamic values of the bullet velocity (Table 8).Table 8
Test data.
No.
h
c (mm)
h
f (mm)
v
i (m/s)
v
r (m/s)
E
A (J)
1
5
4
875
768
932
2
5
6
875
641
1,880
3
5
8
875
612
2,073
4
6
4
875
719
1,318
5
6
6
875
532
2,558
6
6
8
875
488
2,796
7
7
4
875
632
1,941
8
7
6
875
412
3,158
9
7
8
875
347
3,420Next, the adaptive quadratic reaction surface method was conducted usinghc and hf as operational variables, with EA as the reaction value. This could also be viewed as the energy function (equation (3) whereupon the adaptive function could be obtained following analysis equation (4)):(3)EAhc,hf=k+ahc+bhf+chchf+dhc2+ehf2,(4)EAhc,hf=−6276.5+500.6hc+1512.6hf+30.7hchf−8.1hc2−113.6hf2.


## 4.3. Analysis Results

### 4.3.1. Regression Function Limitations

According to equation (3), when the values of both hc and hf were 0, the value obtained for EA was less than 0, which was clearly inconsistent with real-world physics. Thus, there were limitations to the application of equation (3).Because the quadratic coefficients ofhc and hf were both smaller than 0, it was clear that the target plate thickness had maximal influence on EA. Therefore, the maximal operational variable of the energy function could be acquired by subjecting hc and hf in equation (2) to differentiation (equation (5)).(5)∂EA∂hc=0⟶a+chf+2dhc=0∂EA∂hf=0⟶b+chc+2ehf=0⟹hcmax=−2ae+bc4de−c2hfmax=−2bd+ac4de−c2.


### 4.3.2. Minimal Target Plate Thickness

Equation (6) shows hc being arranged in a series of descending power. The target plate thickness (θ = hc + hf) was used as the analysis parameter and was held constant. When hf was substituted with target plate thickness (θ) and hc, EA was a function of θ and hc:(6)EAθ,hc=−c+d+ehc2+a−b+θc−2ehc+k+bθ+eθ2=P1hc2+Q1θhc+R1θ=P1hc+Q1θ2P12+R1θ−Q12θ4P1⟹R1θ−Q12θ4P1≥EAθ,hc⟹EAθ,hcmax=R1θ−Q12θ4P1P<0.According to equation (5), EA had a maximal value when θ remained a fixed value. In other words, when EA was a known value, the minimal target plate thickness (θmin) as well as the optimal thickness combination of the SiC ceramic plate and Dyneema fiber plate could be inversely calculated. Thus, when the value of EA was 0, the minimal value of θ and hc could be inversely calculated according to the following equation:(7)θmin=hcmax+hfmax−24de−c2−c+d+ea2e+b2d−abc−4de−c2k,hcmin=hcmax+c−2e4de−c2a2e+b2d−abc−4de−c2k−c+d+e.


### 4.3.3. Minimal Areal Density

This study sought to design a light-weight ballistic-resistant target plate under the NIJ IV standard. Hence, areal density (Ψ) was used as the analysis parameter (equation (8)):(8)Ψhc,hf=ρchc+ρfhf⟹Ψρf=ρcρfhc+hf⟹α=βhc+hf,where the volume densities of SiC ceramic (ρc) and Dyneema fiber were 3.1×10−3 (g/mm3) and 0.97×10−3g/mm3, respectively; α is the ratio of Ψ over ρf, and β is the ratio of ρc over ρf.Equation (9) shows hc being arranged in a series of descending power. The value of target areal density (Ψ = ρchc + ρfhf) remained constant, and hf was substituted with Ψ and hc. EA was thus a function of α and hc:(9)EAα,hc=−cβ+d+eβ2hc2+a−bβ+αc−2eβhc+k+bα+eα2=P2hc2+Q2αhc+R2α=P2hc+Q2α2P22+R2α−Q22α4P2⟹R2α−Q22α4P2≥EAα,hc⟹EAα,hcmax=R2α−Q22α4P2P2<0.According to equation (9), EA had a maximal value when the value of Ψ was held constant. In other words, minimal Ψ and the optimal combined thickness of SiC ceramic and Dyneema fiber could be inversely calculated when EA was a known value. Therefore, when the value of EA was 0, the minimal value of Ψ and hc could be inversely calculated as follows:(10)Ψmin=ρchcmax+ρfhfmax−2ρf24de−c2−cβ+d+eβ2a2e+b2d−abc−4de−c2k,hcmin=hcmax+c−2eβ4de−c2a2e+b2d−abc−4de−c2k−cβ+d+eβ2.


### 4.3.4. Optimal Combination

To completely absorb the kinetic energy of the bullet using the SiC ceramic and Dyneema fiber composite target plate, the optimal combination ofhc and hf could be obtained through the aforementioned numerical analysis (Figures 6 and 7).Figure 6
Absorptive energy corresponded to minimization of thickness and areal density of the target.Figure 7
Optimal thickness combination of the composite materials.


## 4.3.1. Regression Function Limitations

According to equation (3), when the values of both hc and hf were 0, the value obtained for EA was less than 0, which was clearly inconsistent with real-world physics. Thus, there were limitations to the application of equation (3).Because the quadratic coefficients ofhc and hf were both smaller than 0, it was clear that the target plate thickness had maximal influence on EA. Therefore, the maximal operational variable of the energy function could be acquired by subjecting hc and hf in equation (2) to differentiation (equation (5)).(5)∂EA∂hc=0⟶a+chf+2dhc=0∂EA∂hf=0⟶b+chc+2ehf=0⟹hcmax=−2ae+bc4de−c2hfmax=−2bd+ac4de−c2.


## 4.3.2. Minimal Target Plate Thickness

Equation (6) shows hc being arranged in a series of descending power. The target plate thickness (θ = hc + hf) was used as the analysis parameter and was held constant. When hf was substituted with target plate thickness (θ) and hc, EA was a function of θ and hc:(6)EAθ,hc=−c+d+ehc2+a−b+θc−2ehc+k+bθ+eθ2=P1hc2+Q1θhc+R1θ=P1hc+Q1θ2P12+R1θ−Q12θ4P1⟹R1θ−Q12θ4P1≥EAθ,hc⟹EAθ,hcmax=R1θ−Q12θ4P1P<0.According to equation (5), EA had a maximal value when θ remained a fixed value. In other words, when EA was a known value, the minimal target plate thickness (θmin) as well as the optimal thickness combination of the SiC ceramic plate and Dyneema fiber plate could be inversely calculated. Thus, when the value of EA was 0, the minimal value of θ and hc could be inversely calculated according to the following equation:(7)θmin=hcmax+hfmax−24de−c2−c+d+ea2e+b2d−abc−4de−c2k,hcmin=hcmax+c−2e4de−c2a2e+b2d−abc−4de−c2k−c+d+e.


## 4.3.3. Minimal Areal Density

This study sought to design a light-weight ballistic-resistant target plate under the NIJ IV standard. Hence, areal density (Ψ) was used as the analysis parameter (equation (8)):(8)Ψhc,hf=ρchc+ρfhf⟹Ψρf=ρcρfhc+hf⟹α=βhc+hf,where the volume densities of SiC ceramic (ρc) and Dyneema fiber were 3.1×10−3 (g/mm3) and 0.97×10−3g/mm3, respectively; α is the ratio of Ψ over ρf, and β is the ratio of ρc over ρf.Equation (9) shows hc being arranged in a series of descending power. The value of target areal density (Ψ = ρchc + ρfhf) remained constant, and hf was substituted with Ψ and hc. EA was thus a function of α and hc:(9)EAα,hc=−cβ+d+eβ2hc2+a−bβ+αc−2eβhc+k+bα+eα2=P2hc2+Q2αhc+R2α=P2hc+Q2α2P22+R2α−Q22α4P2⟹R2α−Q22α4P2≥EAα,hc⟹EAα,hcmax=R2α−Q22α4P2P2<0.According to equation (9), EA had a maximal value when the value of Ψ was held constant. In other words, minimal Ψ and the optimal combined thickness of SiC ceramic and Dyneema fiber could be inversely calculated when EA was a known value. Therefore, when the value of EA was 0, the minimal value of Ψ and hc could be inversely calculated as follows:(10)Ψmin=ρchcmax+ρfhfmax−2ρf24de−c2−cβ+d+eβ2a2e+b2d−abc−4de−c2k,hcmin=hcmax+c−2eβ4de−c2a2e+b2d−abc−4de−c2k−cβ+d+eβ2.


## 4.3.4. Optimal Combination

To completely absorb the kinetic energy of the bullet using the SiC ceramic and Dyneema fiber composite target plate, the optimal combination ofhc and hf could be obtained through the aforementioned numerical analysis (Figures 6 and 7).Figure 6
Absorptive energy corresponded to minimization of thickness and areal density of the target.Figure 7
Optimal thickness combination of the composite materials.


## 4.4. Experimental Verification

### 4.4.1. Energy Function Verification

The energy function of the ballistic-resistant target plate was obtained through experimentally designed regression analysis, wherein the target plate thickness was maintained between 9 mm and 15 mm. Hence, four sets of target plate thickness combinations were chosen from the range and were subjected to numerical simulations to verify the energy function (Table9). The results indicated that the optimal combination featuring minimal target plate thickness (θmin) which corresponded to the energy function and satisfied the NIJ IV standards was consistent with that obtained from the numerical simulation analysis.Table 9
Verification of the energy function.
Energy function
Numerical simulation
Difference (%)
θ
min mm
(hc)opt mm
(hf)opt mm
(EA)1 J
v
i m/s
v
r m/s
(EA)2 J
E
A
1
/
E
A
2
−
1
9.0
4.2949
4.7051
946.5579
875.0
762.0
980.3993
−3.451
12.5
7.2564
5.2436
2,905.6687
875.0
467.0
2901.9408
0.13
14.7
9.1179
5.5821
4,080.7837
875.0
0.0
4,057.8125
0.57
15.0
9.3717
5.6283
4,237.6600
875.0
0.0
4,057.8125
4.43


### 4.4.2. Verifying the Optimal Combination

This study aimed to develop light-weight ballistic-resistant target plates while conforming to NIJ IV standards. Therefore, the energy function was verified using the optimal combination with minimal areal density (Ψmin) (Table 10). The results indicated that, in the estimation of the absorptive energy of the target plate, the energy function fits the numerical simulation analysis.Table 10
Verification of the optimal combination.
Energy function
Numerical simulation
Ψmin g/mm2
(hc)opt mm
(hf)opt mm
(EA)1 J
v
i m/s
v
r m/s
(EA)2 J
0.032
8.1940
6.9637
4,057.8
875.00
0.00
4,057.8


## 4.4.1. Energy Function Verification

The energy function of the ballistic-resistant target plate was obtained through experimentally designed regression analysis, wherein the target plate thickness was maintained between 9 mm and 15 mm. Hence, four sets of target plate thickness combinations were chosen from the range and were subjected to numerical simulations to verify the energy function (Table9). The results indicated that the optimal combination featuring minimal target plate thickness (θmin) which corresponded to the energy function and satisfied the NIJ IV standards was consistent with that obtained from the numerical simulation analysis.Table 9
Verification of the energy function.
Energy function
Numerical simulation
Difference (%)
θ
min mm
(hc)opt mm
(hf)opt mm
(EA)1 J
v
i m/s
v
r m/s
(EA)2 J
E
A
1
/
E
A
2
−
1
9.0
4.2949
4.7051
946.5579
875.0
762.0
980.3993
−3.451
12.5
7.2564
5.2436
2,905.6687
875.0
467.0
2901.9408
0.13
14.7
9.1179
5.5821
4,080.7837
875.0
0.0
4,057.8125
0.57
15.0
9.3717
5.6283
4,237.6600
875.0
0.0
4,057.8125
4.43


## 4.4.2. Verifying the Optimal Combination

This study aimed to develop light-weight ballistic-resistant target plates while conforming to NIJ IV standards. Therefore, the energy function was verified using the optimal combination with minimal areal density (Ψmin) (Table 10). The results indicated that, in the estimation of the absorptive energy of the target plate, the energy function fits the numerical simulation analysis.Table 10
Verification of the optimal combination.
Energy function
Numerical simulation
Ψmin g/mm2
(hc)opt mm
(hf)opt mm
(EA)1 J
v
i m/s
v
r m/s
(EA)2 J
0.032
8.1940
6.9637
4,057.8
875.00
0.00
4,057.8


## 5. Conclusion

This study explored the relationship between the SiC ceramic and Dyneema fiber layers in a composite target plate and its ballistic resistance. To achieve a light-weight target plate that conforms to NIJ IV standards, an analysis of the minimal areal density was conducted to obtain the optimal SiC ceramic-Dyneema fiber thickness combination.This study analyzed the ballistic resistance of the target plate using energy modes. To substantially reduce the experimental costs, ANSYS/LS-DYNA software was used to conduct finite element method numerical simulations and to obtain the correlation function of the target plate ballistic resistance. The ballistic resistance, which is also the function of the absorptive energy of the target plate, was obtained using simulations and regression analysis. From the numerical analysis results, 8.1940 mm SiC ceramic and 6.9637 mm Dyneema fiber were determined to be the optimal thickness combination for a composite that features a minimal areal density and which conforms to NIJ IV standards. The combination was found to be consistent with the numerical simulation analysis results.



---

*Source: 9457489-2020-01-22.xml*