Simulation Study on the Performance of Kevlar Fibre Reinforced Composites Under the Penetration of Fragment

Aiming at the problem of Kevlar fibre reinforced composite target anti penetration of wedge-shaped fragment, the finite element models of Kevlar fibre reinforced composite targets with different thickness and the fragments are established. The simulation calculation of Kevlar fibre reinforced composite target against penetration of different velocity fragments is carried out. The anti-ballistic V50 of Kevlar fibre reinforced composite target with different thickness is obtained, and the damage failure mode of the Kevlar fibre reinforced composite target in the process of anti fragment penetration is analyzed, and the simulation results are verified by experiments. This simulation provides scientific basis and data support for the optimization design of composite structure armor and armor lining.


Introduction
In addition to high specific strength, high specific modulus and strong designability compared with traditional metal materials, fibre-reinforced composite materials also have outstanding advantages, such as anti-penetration and anti-fragmentation [1] . Therefore, fibre-reinforced composite materials are widely used in the field of armor protection, such as armor lining, bulletproof vest, bulletproof helmet and so on [2] . In the battlefield environment, fibre-reinforced composites are faced with various kinds of high-speed kinetic energy projectile and high-speed fragment penetration, so it is of great significance to study the dynamic response of fibre-reinforced composites under penetration [3][4][5] . In this paper, the failure mode and mechanism of Kevlar composite target under the fragment penetration are studied by the method of simulation calculation and test verification, which is of great guiding significance for the design of composite structure armor and composite armor lining. In this paper, a three-dimensional finite element model of Kevlar fibre reinforced composite target against wedge-shaped fragment penetration is established, and the solid164 (a three-dimensional 8-node solid element) is selected for solid mesh generation. There are three kinds of algorithms commonly used in dynamic simulation software: Lagrangian algorithm, Euler algorithm and ALE (arbitrary Lagrangian Euler) algorithm. Generally speaking, Lagrangian algorithm has high accuracy and efficiency, but it is not suitable for extreme deformation. ALE algorithm and Euler algorithm are suitable for solving large deformation problems, but the complexity of the algorithm increases, the computational efficiency decreases accordingly, the material interface is not clear, it is unable to accurately simulate the material thermodynamic behaviour related to history and strain rate, and the computational accuracy is usually lower than Lagrangian algorithm. In this paper, The simulation mainly focuses on the anti penetration performance of composite materials, considering the calculation accuracy and efficiency, and the penetration problem does not involve great deformation, so Lagrangian explicit integration algorithm is adopted.

Constitutive model of fibre-reinforced composite
Orthotropic constitutive model is currently the most widely used composite material model. When the composite structure was simulated under high overload conditions, it will present diversity and complexity due to different failure criteria [6] . The failure of fibre-reinforced composite materials is generally considered to be a progressive failure process [7] . Chang-Chang proposed a progressive failure model for predicting the ultimate strength of laminates with open holes under the tensile load in 1987. The Chang-Chang criterion is mainly described by five material strength parameters: S1, S2, S12 and C2 are obtained from material strength measurement,  is defined by material shear stress-strain measurements [8][9] .
In plane stress, the strain expressed by stress as:  (1) The matrix cracking failure criteria is determined from v are set to 0.
(2) The compression failure criteria is given as where failure is assumed whenever comp F >1. If comp F >1, then the material constants 2 The final failure mode is due to fibre breakage.

Construction of finite element model
A finite element model was established for the process of the fragment penetrating the Kevlar fibre reinforced composite, as shown in Figure 1. According to the actual situation, a series of specific solution methods and boundary conditions were established. For example, multi-node parallel computing is set up, and the calculation starts from the fragment approaching the target; non-reflective boundary conditions are applied to avoid the impact of stress wave reflection; surface-to-surface erosion contact is defined to describe penetration; the destructive behaviour of the material is described by the two failure criteria of equivalent stress and principal strain.

The simulation results of Kevlar fibre reinforced composites anti penetration
According to the simulation results of different thickness Kevlar fibre reinforced composite target against wedge-shaped fragment penetration, the anti-ballistic V50, the damage failure mode of the target plate and the velocity variation law of the projectile body were obtained. The anti-penetration condition of fragment penetrate the Kevlar fibre reinforced composite target plate with a thickness of 3.7 mm is selected as an example for detailed analysis. Figure 2 shows the process of the wedge fragment penetrating the Kevlar composite target with an initial velocity of 540 m/s, and Figure 3 shows the plastic damage process of the Kevlar composite target. According to the figure, after the fragment hits the target at a higher velocity, the Kevlar composite target plate is directly crushed by impact and showed open pit damage, forming a cross-shaped damage on the front of the target plate Strain zone, with the continuous intrusion of the fragment, the erosion damage of the Kevlar composite target plate deepens, and there is obvious stamping shear damage inside the target plate, forming a punch hole equivalent to the diameter of the fragment, while the back of the target is convex, the composite material on the back of the target plate is stretched, at this time, the interior of the whole laminated target plate appears typical and significant inter-layer damage. With the reduction of the fragment's speed, the intrusive effect weakened, the damage between the layers of the composite target plate is more obvious, and finally in the back of the Kevlar composite target, form a back convex drum bag that is far beyond the diameter of the fragment.    Figure 4 shows the speed-time curve of the fragment in the process of invading the Kevlar composite target plate, it can be derived from the figure that as the invasion progresses, the speed of fragment is gradually decreased, and at about 70 μs moment, the bullet body speed began to rebound, at this moment the fragment has not yet run through the Kevlar composite target plate, there are still multiple layers of composite material can play a protective role. Subsequently, the fragment rebounded due to the last few layers of the target deformation rebound.  Figure 5 shows the process of the fragment penetrating the Kevlar composite target with an initial velocity of 560 m/s, and Figure 6 shows the plastic damage process of the Kevlar composite target. According to the figure, after the fragment hits the target at a higher velocity, the Kevlar composite target plate is directly crushed by impact and showed open pit damage, forming a cross-shaped shape on the front of the target plate. With the continuous intrusion of the fragment, the erosion and destruction of the Kevlar composite target plate is deepening, and there is obvious stamping shear damage inside the target plate, forming a punch hole equivalent to the diameter of the chip, while the back of the target is convex, the composite material on the back of the target plate is stretched, at this time, the interior of the whole laminated target plate appears typical and significant inter-layer damage. With the gradual decrease of the breaking speed, the intrusive effect gradually weakened, the damage between the layers of the composite material target plate is more obvious, and finally the composite target plate is run through, the damage between the layers is more significant, especially in the back of the Kevlar fibre composite target plate, the layering and stripping range of the laminate is much larger than the diameter of the fragment.     In order to verify the validity of the simulation method and the accuracy of the simulation results, the simulation results are compared with the test results. The statistics of simulation and test results are shown in Table 1, and the comparison of target damage and failure modes is shown in Figure 8. Through comparison, it is found that the speeds are very close, and the damage modes of the target are basically the same, which verifies the reliability of the calculation method and the accuracy of the simulation results.

Conclusion
In this paper, The simulation calculation of Kevlar fibre reinforced composite target against penetration of different velocity fragments is carried out. The anti-ballistic V50 of Kevlar fibre reinforced composite target is obtained, and the damage failure mode of the Kevlar fibre reinforced composite is analyzed, and the reliability and accuracy of the simulation calculation method are verified. It is found that with the increase of Kevlar sheet thickness, its anti-ballistic V50 continuously improved, but it is not linear. Under the effect of Penetration, the Kevlar composite target plate is crushed and showed open pit damage, with the continuous intrusion, the erosion and destruction of the Kevlar composite target is deepening, and there is obvious stamping shear damage inside the target, forming a punch hole with a diameter equivalent to the fragment, the back of the target is stretched, and the interior of the whole laminated target appears typical and significant inter-layer damage, and finally the composite target plate is run through, the damage between the layers is more significant,