A parametric study on the behavior of FMLs based on UHMWPE composite under high velocity impact loading

Abstract

Numerical parametric study is performed to investigate ballistic impact performance of a novel fiber metal laminate (FML) based on ultra-high molecular weight polyethylene (UHMWPE) fiber composite and aluminum 2024-T3 layers. A finite element modeling is developed and validated with experimental tests. A user-defined material subroutine based on continuum damage mechanics is used to define damage constitutive model of UHMWPE composite. High velocity impact simulations shows similar modes of failure to that observed in experiments. The effect of various parameters such as metal thickness, composite core thickness, metal volume fraction (MVF), and lay-up sequence on ballistic limit velocity, absorbed energy and specific perforation energy (SPE) of samples has been investigated. The results show that increasing the number of composite layers increases the SPE while increasing the thickness of metal layers decreases the SPE. Although, as the core thickness increases, the growth of SPE decreases. Changes in the lay-up sequence do not have much effect on ballistic velocity and absorbed energy. Whereas, the MVF is an important parameter in the high velocity impact performance of the PERALL specimens. In addition, with equal MVF, stacking sequence change has no significant effect on the ballistic limit velocity. Finally, a simple linear equation is suggested to describe the relationship between MVF and specific perforation energy.

Keywords

Thermoplastic matrix cohesive contact equivalent plastic strain mechanisms of failure delamination

Introduction

The hybridization of thin sheets of metal and fiber-reinforced composite laminates is known as FMLs, which with theirs combined properties, have many applications in various industries.¹ The most common FMLs are glass-reinforced aluminum laminates (GLARE), aramid reinforced aluminum laminate (ARALL), and carbon reinforced aluminum laminate (CARAL). Combining valuable properties of metals such as ductility and good impact resistance with the advantages of fiber-reinforced composites such as light weight, high strength and fatigue resistance, FMLs are a suitable choice for use in air vehicles.^2,3 Investigating the impact behavior of FMLs as one of their advantages has always been of interest to researchers. Also, due to their advantages and applications, the production of new FMLs has recently been considered. For example, the fabrication of FMLs using basalt fiber,⁴ self-reinforced polypropylene fiber,⁵ with 3D printed glass fiber composite,⁶ and carbon fibers with different aluminum alloys⁷ are a part of recent works in this field.

Various fibers have been used in composite cores of FMLs. UHMWPE fiber is a fiber with unique properties such as low density and high strength; and its combination with thermoplastic polymer matrices makes a composite with low weight, and high strength and impact resistance.^8,9 The unique properties of UHMWPE composite have led to it being used as a component in hybrid structures in recent research. Some researchers have studied the ballistic behavior of hybrid composites made from UHMWPE fibers and other fibers such as carbon¹⁰ and basalt.¹¹ Li et al.¹² fabricated FML with titanium metal layers and UHMWPE composite laminate as a core, and performed high velocity impact tests on the samples. Their observations showed that FMLs with UHMWPE fibers performed better than FMLs with carbon fibers and titanium face sheets. Recently, Mansoori et al.¹³ introduced a FML based on UHMWPE fibers and aluminum layers and experimentally investigated its behavior under ballistic impact. Results showed that the new FML has a good performance against high velocity impact compared to GLARE specimen.

High velocity impact failures is the main form of damage in aerospace structures. Conical projectile is used as a common type of impactor in high velocity impact tests for a variety of composite and FML materials. Zhu et al.¹⁴ experimentally investigated a UHMWPE composite plate under high velocity impact with conical projectile. Their observations showed that the fiber failure and lateral displacement of fibers occurred at impact zone. Zarei et al.¹⁵ investigated the ballistic behavior of GLARE impacted with conical and flat projectiles. Results show that the ballistic limit of GLARE with conical projectile is less than flat projectile and there is no plug in targets impacted with conical projectile. Xu et al.¹⁶ experimentally investigated CARAL specimens under high velocity impact with conical, hemispherical, and flat projectile. The lowest ballistic limit was observed for specimens impacted with conical projectile compared with hemispherical and flat projectile.

Ballistic and high velocity impact experiments are expensive and time-consuming. Finite element method (FEM) has been widely used because of its less limitation and capability for modeling the damage mechanisms and penetration process during impact period. One of the most important parts of numerical simulation of FMLs is the simulation of the composite core. Haque et al.^17,18 introduced a model for UHMWPE composite laminates with a shell model that provides deformation mechanisms similar to the experiment. Lässig et al.¹⁹ proposed a non-linear orthotropic hydro-code model and simulated the hypervelocity impact on UHMWPE composite. The results provided good predictions of the residual velocity. This model was developed by Nguyen et al.²⁰ considering a sub-laminate to better predict the ballistic limit and back-face deflection (BFD). Sub-laminates were considered as an orthotropic material with orthotropic elastic–plastic strength, failure criteria and directional hardening; and connected by tied contacts in ANSYS Autodyn software. Hazzard et al.²¹ recently modeled UHMWPE composite laminate with a similar sub-laminate approach for a range of loading conditions in LS-DYNA software. MAT162 (material model) was used for modeling the sub-laminates as fabric composite. The literature review shows that no numerical study has been performed to simulate the ballistic behavior of UHMWPE composites impacted with conical projectile.

During the impact process, several failure modes occur, such as fiber/matrix tension, fiber/matrix compression, fiber shear punch, fiber crush, and matrix shear. Therefore, for numerical simulations, it is essential to choose a model that correctly considers the modes of damage. Continuum damage mechanics (CDM) with considering different damage modes and introducing damage variables is an effective approach for impact modeling. The CDM predict damage initiation using failure criteria, and then stiffness is degraded with different methods until complete failure. The ABAQUS/Explicit is capable of modeling composite laminate under impact load. Many researchers have modeled the low velocity^22–24 and the high velocity impact^25,26 in ABAQUS software by writing subroutines based on Hashin’s criterion²⁷ and CDM. Delamination or inter-laminar damage is an important damage mode under impact loading for laminated composites. There are two methods for modeling the delamination during impact loading based on Cohesive Zone Model (CZM): (1) using cohesive elements and (2) applying surface-based cohesive contact model. Both methods have been used in previous researches for simulation the delamination in ABAQUS software under low and high velocity impact.^28–32

Due to the mentioned properties of UHMWPE, this composite can be a good candidate for hybridization with aluminum alloys and making a light weight FML with special properties for aerospace applications. The main purpose of this paper is to numerically investigate the effect of different geometric parameters as well as the type of aluminum alloy on ballistic behavior of polyethylene reinforced aluminum laminate (PERALL) specimens. Progressive damage modeling includes the 3D strain-based model for fabric composite with fiber failure modes such as compressive, tensile, punch shear and crush; and matrix failure modes such as in-plane shear and through thickness delamination. Inter-laminar damage is simulated utilizing the CZM method based on cohesive contact model between composite layers as well as composite and metal interfaces. The ballistic impact with a conical projectile is simulated, and modes of failure and residual velocity against conical projectile are verified using experimental results. The effect of various parameters on the ballistic limit velocity, absorbed energy, and specific perforation energy (SPE) of the samples is investigated.

Numerical simulation

Finite element modeling

Finite element (FE) model is established based on ABAQUS/Explicit to analyze the behavior of FML specimens under impact loading with conical projectile. For modeling the UHMWPE laminate, a cross-ply sub-laminate homogenization approach has been used. Each ${[0 / 90]}_{2}$ is considered as a sub-laminate and meshed using single elements in thickness according to refs.^20,21. The 2/1 and 3/2 stacking sequence FML targets with dimension 110 × 110 mm and different thicknesses are built from UHMWPE sub-laminates and aluminum 2024-T3 metal layers. Figure 1 shows a schematic of the FMLs with different configurations. Cohesive contact model is introduced at the interfaces between aluminum and composite layers; and between the sub-laminates as composite-composite interface to simulate the delamination under impact loading.

Figure 1.

Schematic of FMLs (a) 2/1 lay-up sequence configuration, (b) 3/2 lay-up sequence configuration.

Deformation and damage mainly take place in the contact area and around it in high velocity impact simulation. Therefore, the biased mesh with increasing element size approaching the edge of the layer are used. A mesh study with different element numbers was conducted and a mesh independency was observed at number of 100 elements across edge with an aspect ratio of five for each layer. Aluminum layers, composite sub-laminates, and projectile are created using hourglass controlled eight-node 3D reduced elements (C3D8R). also Two clamps are established in the model as a rigid body for boundary condition and meshed with C3D8R elements, considering the material properties as: ρ = 7800 kg/m³, E = 210 GPa, and υ = 0.33. The FE model of FML under impact loading with conical projectile is displayed in Figure 2. For the bottom clamp, all nodes are fixed and for the top clamp, the nodes along 1 and 2-directions are fixed. A pressure of 2 MPa is applied to the front surface of top clamp to simulate the clamping pressure imposed in the experiments.

Figure 2.

Finite element model of FML under high velocity impact with conical projectile.

Damage model of metals

For simulation metals in the impact and rate-dependent problems, Johnson–Cook model³³ embedded in ABAQUS is commonly used. Johnson–Cook model is an empirically based model with material parameters including A, B, C, m, and n as follows³⁴

σ = [A + B {(\bar{ε_{pl}})}^{n}] [1 + C ln (\frac{{\dot{\bar{ε}}}_{pl}}{{\dot{\bar{ε}}}_{0}})] [1 - T^{* m}]

(1)

where

\bar{ε_{p l}}

is the equivalent plastic strain,

{\dot{\bar{ε}}}_{0}

and

{\dot{\bar{ε}}}_{p l}

are the reference strain rate and equivalent plastic strain rate, respectively. In the above equation non-dimensional temperature T^* is defined by

T^{*} = \frac{T - T_{r}}{T_{m} - T_{r}}

(2)

Where T is the material temperature, T_r and T_m are the room temperature and the material melting temperature, respectively. In order to determine the structural damages in the model, strain at failure

{({\bar{ε}}_{p l})}_{f}

is calculated as

{({\bar{ε}}_{pl})}_{f} = [D_{1} + D_{2} e^{(D_{3} σ^{*})}] [1 + D_{4} ln (\frac{{\dot{\bar{ε}}}_{pl}}{{\dot{\bar{ε}}}_{0}})] (1 + D_{5} T^{*})

(3)

where

σ^{*}

is the mean stress normalized by the equivalent stress and D₁, D₂, D₃, D₄, and D₅ are material constants, which can be obtained from the experimental test. Failure occurs when the damage parameter D reaches the unity. The parameter D is determined by

D = \sum^{​} (\frac{Δ {\bar{ε}}_{pl}}{{({\bar{ε}}_{pl})}_{f}})

(4)

where

Δ {\bar{ε}}_{p l}

is the increment of equivalent plastic strain during an increment of loading.

Similarly, the steel projectile is considered as elastic-plastic metals because of plastic deformation during high velocity impact. All the properties and material constants in the Johnson–Cook model required for modeling the aluminum sheets and projectile are summarized in Table 1.

Table 1.

Required parameters for the Johnson-Cook material model.

Name	Al 2024-T3²⁵	Al 7075-T6 ⁷	4340H steel²⁰
A Parameter (MPa)	369	546	1030
B Parameter (MPa)	684	678	477
n parameter	0.0083	0.024	0.18
C Parameter	0.73	0.71	0.012
m parameter	1.7	1.7	1
Melt temperature (K)	775	775	1763
Effective strain rate (s⁻¹)	1	1	1
Specific Heat (J/kg.K)	875	875	477
D₁ parameter	0.112	−0.068	3
D₂ parameter	0.123	0.451	0
D₃ parameter	1.5	−0.952	0
D₄ parameter	0.007	0.036	0
D₅ parameter	0	0	0

Damage model of UHMWPE composite

Due to various failure modes during the ballistic impacts, damage evolution of composite laminates is rather complicated. For simulating damage initiation and progress under impact loading, appropriate failure criteria should be used. Damage initiation criteria are selected to model the behavior of the homogenized sub-laminates as fabric similar to those in Ref³⁵. Based on this theory, five failure criteria for UD composites and seven failure criteria for fabric composites are utilized to model different damage modes in composite laminates. Damage initiation criteria for sub-laminates have been presented in Table 2, where

X_{T}

and

X_{c}

are the longitudinal tensile and compressive strengths in direction 1;

Y_{T}

and

Y_{c}

are the transverse tensile and compressive strengths in direction 2;

S_{F S}

S_{F c}

, and

S_{3 T}

are fiber mode shear strength, crush strength, and through thickness tensile strength;

S_{12}

S_{23}

, and

S_{31}

are the matrix mode shear strength in direction 12, 23, and 31, respectively. In the last equation, s is delamination scaling factor, and r_7–13 are damage thresholds.³⁶ The modulus and strength values are given in Table 3.

Table 2.

Failure criteria for composite sub-laminates.

Failure mode	Criterion
Fiber tension/shear in direction 1	${(\frac{E_{1} ε_{1}}{X_{T}})}^{2} + {(\frac{G_{31} ε_{31}}{S_{F S}})}^{2} = r_{7}^{2}$
Fiber tension/shear in direction 2	${(\frac{E_{2} ε_{2}}{Y_{T}})}^{2} + {(\frac{G_{23} ε_{23}}{S_{F S}})}^{2} = r_{8}^{2}$
Fiber compression in direction 1	${(\frac{E_{1} ε_{1}^{'}}{X_{c}})}^{2} = r_{9}^{2}; ε_{1}^{'} = - ε_{1} - ε_{3} \frac{E_{3}}{E_{1}}$
Fiber compression in direction 2	${(\frac{E_{2} ε_{2}^{'}}{Y_{c}})}^{2} = r_{10}^{2}; ε_{2}^{'} = - ε_{2} - ε_{3} \frac{E_{3}}{E_{2}}$
Fiber crush in direction 3	${(\frac{E_{3} - ε_{3}^{}}{S_{F c}})}^{2} = r_{11}^{2}$
Matrix shear in direction 12	${(\frac{G_{12} ε_{12}}{S_{12}})}^{2} = r_{12}^{2}$
Matrix delamination	$s^{2} {{(\frac{E_{3} ε_{3}}{S_{3 T}})}^{2} + {(\frac{G_{23} ε_{23}}{S_{23}})}^{2} + {(\frac{G_{31} ε_{31}}{S_{31}})}^{2}} = r_{13}^{2}$

Table 3.

Material properties and parameters for UHMWPE composite laminate^20,21.

Property	Symbol	Value	Units
Density	ρ	0.00097	g/ $m m^{3}$
Young’s modulus 1 and 2	E₁ = E₂	34,257	MPa
Young’s modulus 3	E ₃	3620	MPa
Poisson’s ratio 21	$ν_{21}$	0	—
Poisson’s ratio 31	$ν_{31}$	0.013	—
Poisson’s ratio 32	$ν_{32}$	0.013	—
Shear modulus 12	$G_{12}$	173.8	MPa
Shear modulus 31	$G_{31}$	547.8	MPa
Shear modulus 23	$G_{23}$	547.8	MPa
Longitudinal tensile and compressive strength	$X_{T} = X_{c}$	1250	MPa
Transverse tensile and compressive strength	$Y_{T} = Y_{c}$	1250	MPa
Crush strength	$S_{F C}$	1250	MPa
Fiber mode shear strength	$S_{F S}$	625	MPa
Matrix mode shear strength12	$S_{12}$ = $S_{23} = S_{13}$	1.8	MPa
Delamination scale factor	s	1	—
Eroding axial strain	E_LIMIT	0.06	—
Eroding compressive volume strain	ECRSH	0.05	—
Eroding tensile volume strain	EEXPN	4	—

After obtaining the values of r, the effect of these values on the tensile and shear modulus must be examined. For this purpose, the matrix q is used that determines the effect of the failure on the modulus. This matrix has seven columns and six rows, in which each column represents a damage mode threshold value (r_7–13), and each row represents one of the loading directions (damage variable). The q matrix for fabric is³⁵

q_{i j} = [\begin{matrix} \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{matrix} \end{matrix} \begin{matrix} \begin{matrix} 0 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 1 \end{matrix} \end{matrix}]

(5)

According to Matzenmiller et al. ,³⁷ the growth rate of damage variables is defined by the exponential evolution law. It was shown that the exponential evolution damage model is more accurate compared to experimental observations than the linear evolution damage model ³⁸ The damage function $φ$ indicating the stiffness degradation for each damage mode; and a set of damage parameters $ω_{i}$ with i = 1… 6 to relate the maximum damage variable as the module reduction parameter, are calculated as follows:

ω_{i} = m a x {φ_{j} q_{i j}}; i = 1.2 \dots .6

(6)

φ_{j} = 1 - e^{\frac{1}{m} (1 - r_{j}^{m})}; r \geq 1 & j = 1.2 \dots .7

(7)

where

r_{j}

is the relevant damage threshold. The parameter

m

is known as the softening parameter related to damages under various loading conditions, including

(1) Fiber damage in the direction one $(m_{1} = 20)$

(2) Fiber damage in the direction two $(m_{2} = 20)$

(3) Fiber crush damage $(m_{3} = 20)$

(4) Matrix and delamination fd8damage $(m_{4} = - 0.8)$

After calculating the values of $ω_{i}$ , new stiffness constants are obtained. Then the compliance matrix S is calculated as equation (8).

S = {\begin{matrix} \begin{matrix} \frac{1}{E_{1} (1 - ω_{1})} & - \frac{ν_{21}}{E_{2}} & - \frac{ν_{31}}{E_{3}} \\ - \frac{ν_{12}}{E_{1}} & \frac{1}{E_{2} (1 - ω_{2})} & - \frac{ν_{32}}{E_{3}} \\ - \frac{ν_{13}}{E_{1}} & - \frac{ν_{23}}{E_{2}} & \frac{1}{E_{3} (1 - ω_{3})} \end{matrix} & 0 \\ 0 & \begin{matrix} \frac{1}{G_{12} (1 - ω_{4})} & 0 & 0 \\ 0 & \frac{1}{G_{23} (1 - ω_{5})} & 0 \\ 0 & 0 & \frac{1}{G_{31} (1 - ω_{6})} \end{matrix} \end{matrix}}

(8)

This matrix is used to calculate the strain in orthotropic materials. Having the matrix S, the stiffness matrix C is obtained and the stresses are calculated as $σ = C ε$ .

The material model and failure criteria are implemented with a user-defined subroutine (VUMAT) in ABAQUS/Explicit. The local stiffness reduction in the material due to internal damage can lead to element distortion and divergence during problem solving. To remove the damaged elements, the maximum strain criterion is implemented in the VUMAT subroutine based on the strain value exceeding the specified values in two directions one and two. This maximum value is presented in Table 3 as E_LIMIT. In addition, the volume strain criterion is utilized such that when tensile relative volume strain (ratio of current volume to initial volume) is greater than a specified limit, the element is eliminated. Also, when compressive relative volume strain is smaller than a specified limit, the corresponding element is eliminated. The specified values are marked with EEXPN and ECRSH in Table 3, respectively.

Effect of strain rate

The tensile properties of UHMWPE composite are highly dependent on strain rate.^39,40 Hence, in this study, the effect of strain rate on the modulus as well as the strength of UHMWPE composite was considered. Russell et al.³⁹ proposed a method for testing the tensile response of UHMWPE composite for the strain rates between $10^{- 4}$ and $10^{3} s^{- 1}$ . They reported that the tensile performance of this material is highly sensitive to strain rate when subjected to rates of less than $10^{- 1} s^{- 1}$ . This is consistent with the published results of Kromm et al.⁴⁰ who tested UHMWPE fibers at the range of strain rates between $10^{- 5}$ and $10^{- 2} s^{- 1}$ . At strain rates more than $10^{- 1} s^{- 1}$ , the tensile strength and modulus of elasticity are not sensitive to the applied load.³⁹ Hence, the elastic modulus and strength of the UHMWPE composite are ascending at low strain rates and constant at high strain rates.³⁹

Using available experimental data from,³⁹ Mansoori and Zakeri⁴¹ introduced a hyperbolic function to properly model the effect of strain rate on the properties of UHMWPE composite as follows⁴¹

S E F = {[A \times \tanh (\log (\frac{\dot{ε}}{{\dot{ε}}_{0}}) + B)] + C}

(9)

where the parameter

\dot{ε}

is the strain rate. A, B, and C are constants obtained using experimental data. SEF is the ratio of the dynamic to static coefficient whose relations to the new modulus of elasticity and the new strength are

{S_{R T}} = {S_{0}} \times S E F; {E_{R T}} = {E_{0}} \times S E F

(10)

which

S_{R T}

is the updated strength,

E_{R T}

is the updated modulus,

S_{0}

and

E_{0}

are the initial strength and modulus at the reference strain rate

{\dot{ε}}_{0}

. The constant values of A, B, and C in equation (9) are presented in Table 4.

Table 4.

Values of parameters A, B and C in equation (9) for SEFs.⁴¹

Material property	Constant parameter
Strength	$A_{s} = 0.1$	$B_{s} = 2.1$	$C_{s} = 1.1$
Modulus	$A_{m} = 0.25$	$B_{m} = 2.7$	$C_{m} = 1.25$

Damage model of the interface

Delamination is a common mode of damage between composite layers as well as between metal-composite interfaces in FMLs. ABAQUS software uses a traction-separation law in the CZM technique for simulating the delamination. Two failure criteria are required for interface damage modeling (including damage initiation and final damage). For damage initiation, a quadratic nominal stress criterion can be used as follows⁴²

{(\frac{σ_{n}}{N})}^{2} + {(\frac{σ_{s}}{S})}^{2} + {(\frac{σ_{t}}{T})}^{2} = 1

(11)

where

σ_{n}

is the nominal stress in the normal mode and

σ_{s}

and

σ_{t}

are nominal stresses in the first and second shear direction, respectively. N is the tensile strength, and S and T are shear strengths of the interface.

The final damage is estimated based on a power-law criterion⁴².

(\frac{G_{I}}{G_{I C}}) + (\frac{G_{I I}}{G_{I I C}}) + (\frac{G_{I I I}}{G_{I I I C}}) = 1

(12)

where

G_{I}

G_{I I}

and

G_{I I I}

are the energy release rates of mode I, II, and III fracture, while

G_{I C}

G_{I I C}

and

G_{I I I C}

are the critical fracture energies in the mentioned fracture modes, respectively. As already mentioned, for FML samples, also a cohesive layer between the metal layer and the composite sub-laminate must be considered. Table 5 presents the cohesive interface parameters for two areas.

Table 5.

Required parameters for CZM modeling.

Property	Symbol	Sub-laminate²¹	Epoxy²⁸
Mode-I normal strength (MPa)	$N$	1.2	20
Mode-II shear strength (MPa)	$S$	2.6	60
Mode-III shear strength (MPa)	$T$	2.6	60
Mode-I fracture energy ( $N / m m^{}$ )	$G_{Ic}$	0.544	0.24
Modes-II and III fracture energy ( $N / m m^{}$ )	$G_{IIc}$ = $G_{IIIc}$	1.088	2.59

Results and discussion

Verification with experimental results

To verify the finite element model used, the numerical results predicted for targets affected by high velocity conical projectiles are compared with experimental data from Ref. ¹³. Six types of samples were fabricated using UHMWPE composite plies and Al 2024-T3 sheet, with dimensions of 110×110 mm and lay-up sequences of 2/1 and 3/2 (Figure 1). For brevity, each sample is introduced with a code. Lay-up configuration 2/1 is marked with A and 3/2 is marked with B at the beginning of the code. For the second part of this code, the decimal number of the metal thickness is considered. For example, 5 referring to 0.5 mm thick and 8 to 0.8 mm thick. The total number of [0/90] cross-ply composite layers comes after the P. For example, the specimen B5P8 has 3/2 configuration and 0.5 mm thick aluminum layers, and eight cross-ply layers including two

{[0 / 90]}_{4}

laminated cores. The Configuration and thickness of PERALL test samples are presented in Table 6. The projectiles used for the test were made of hard steel (Rc 60) with a conically shaped tip, with an overall length of 30 mm and a shank of 15 mm. The projectile has a diameter of 8.70 mm and about 9.74 g weight. A comparison between the experimental results and the simulations is presented in Table 7. As can be seen, the numerical results for the residual velocity are in good agreement with the experimental data. Damage pattern are described and compared in the next section.

Table 6.

Configuration and thickness of PERALL test specimens ¹³.

Configuration	Specimen code	Total thickness (mm)
$[A l / {(0 / 90)}_{4} / A l]$	A5P4	1.54
$[A l / {(0 / 90)}_{8} / A l]$	A5P8	2.09
$[A l / {(0 / 90)}_{12} / A l]$	A5P12	2.64
$[A l / {(0 / 90)}_{4} / A l / {(0 / 90)}_{4} / A l]$	B5P8	2.60
$[A l / {(0 / 90)}_{6} / A l]$	A8P6	2.42
$[A l / {(0 / 90)}_{12} / A l]$	A8P12	3.24

Table 7.

Summary of numerical and experimental (average) results using conical projectile.

Specimen code	Average impact velocity (m/s)	Residual velocity (m/s)
Specimen code	Average impact velocity (m/s)	Numerical result	Experimental result¹³
A5P4	184.1	163.6	166.8
A5P4	163.2	141.4	143.9
A5P8	184.3	158.4	157.2
A5P8	163.4	134.5	132.6
A5P12	184.2	146.3	147.4
B5P8	184.1	147.2	149.1
A8P6	184.3	149.6	153.7
A8P12	184.1	137.8	141.1

Failure mechanisms

The samples were exposed to conical projectiles at two velocities of about 163 m/s and 184 m/s. In all specimens, the projectile penetrated the target completely and a hole about the size of the projectile was created in the target. The results for the damage pattern show a good correlation between experimental observations and numerical simulation. In all targets, the front and back metal layers failed through plugging and petalling, respectively (as in Figure 3).

Figure 3.

Perforated damage surface of the specimen A5P4 subjected to impact with conical projectile: (a) front metal layer, (b) back metal layer.

Figure 4 illustrates the damage mode observed in cross sectional images for three samples obtained from numerical analysis and experiments. It can be seen that no significant deformation occurs in the aluminum layers except in the perforated area. A circular hole in the composite core has been generated by the projectile during perforation. Delamination is observed in UHMWPE composite core as well as interfacial debonding of metal and adjacent composite layers around the impact point. As shown in Figure 4, around the impact point, the composite core is deformed to fit the aluminum layer. Because at the same time as the tip of the projectile penetrates the target and the conical part of the projectile progresses, the fibers are pushed aside by the projectile. This mechanism in the composite core, after the removal of the aluminum layers, is shown in Figure 5(a). Due to the low inter-laminar shear strength of the UHMWPE composite laminate, delamination occurs around the impact point. In addition, the low content of polyurethane matrix in the pre-preg material and the ductile behavior of UHMWPE fibers cause the fibers to deform easily at the impact point. As shown in Figure 5(b), numerical simulation well predicts this mechanism. It should be noted that this mechanism is not seen in FMLs with brittle behavior of fibers, such as carbon reinforced aluminum laminate, exposed to conical projectile .¹⁶

Figure 4.

Damage morphologies and numerical predictions of samples subjected to impact test with conical projectile impacted at 184 m/s. (a) Specimen A5P4, (b) specimen A5P12, (c) specimen B5P8.

Figure 5.

Damage morphologies for the composite core of specimen A5P12 subjected to impact with conical projectile (a) experimental observation, (b) numerical simulation.

Figure 6 illustrates the penetration process (Figures 6(a)–(h)) and its associated contact force history (Figure 6(i)) for the specimen A5P12 under the impact. Penetration begins with a slight deformation and an increase in the contact force. By penetrating the projectile in the first layer of aluminum, the contact force decreases (Figure 6(a)) and then again by penetrating the projectile into the composite layers, the contact force increases until it reaches its maximum value (Figure 6(b)). The contact force drops sharply as the projectile tip penetrates the rear aluminum layer (Figure 6(c)). After that, the penetration continues to the end of the conical part of the projectile with the deformation of the core and the aluminum sheet and the contact force increases simultaneously until the deformation reaches its maximum value (Figure 6(d)). This deformation occurs elastically and with the gradual removal of the cylindrical part of the projectile, the deformation decreases and the contact force decreases with the penetration of the cylindrical section. At this point, the contact force is almost constant until the projectile penetrates completely (Figures 6(e) to (g)). Finally, the projectile completely loses contact with the target and the contact force becomes zero. The sample appears without bending deformation and only with damage in impact zone (Figure 6(h)).

Figure 6.

The simulated perforation process (a–h) and contact force history (i) for specimen A5P12.

Parametric study

In this section, the effect of different geometric parameters including composite core thickness, aluminum layer thickness, and lay-up sequence as well as the type of aluminum alloy on the impact behavior of PERALL specimens is investigated.

Effect of composite core thickness

To understand the effect of composite core thickness, ballistic limit velocity for PERALL specimens with four different core thicknesses was estimated and compared. Ballistic limit velocity is the maximum impact velocity that the projectile does not pass through the target. Targets were impacted with different impact velocities and complete penetrations against conical projectiles. At least three impact velocities with residual velocities were simulated to estimate the ballistic limit velocity using the Lambert–Jonas approximation⁴³

V_{R} = a {(V_{I}^{P} - V_{BL}^{P})}^{\frac{1}{P}}

(13)

where

V_{I}

and

V_{R}

are initial and residual velocity, respectively, and

V_{B L}

is the ballistic limit velocity.

V_{B L}

a

and

p

are determined from the least squares fit of the initial and residual velocity results. Figure 7(a) shows the residual velocity versus initial velocity curves plotted with Lambert–Jonas equation for targets with the same thickness of aluminum layers (0.5 mm) and different composite core thicknesses. As can be seen, the ballistic limit velocity increases with increasing core thickness. The ballistic velocity for the specimen A5P16 is about 60% higher than for the specimen A5P4. The ballistic velocity difference between A5P4 and A5P8 specimens is about 25%, between A5P8 and A5P12 is 15% and between A5P12 and A5P16 is 6%. This indicates that the ballistic velocity growth decreases with further increase of the composite layers.

Figure 7.

Numerical prediction of residual velocity with Lambert-Jonas $V_{B L}$ fit with parameters given in the legend as (a, p $V_{B L}$ ) for specimens with different thicknesses of (a) composite core, (b) aluminum face sheets.

Figure 8(a) shows the contact force history versus contact time for three specimens with different composite core thicknesses. The diagram consists of three parts. The first part is related to increasing the contact force until the projectile tip penetrates into the target and decreases the contact force. In the second part, the contact force increases again as the conical section progresses until the contact force decreases again with the penetration of the cylindrical section. In the third stage, it continues with an almost constant amount until the projectile penetrates completely. As seen in the Figure 8(a), with increasing core thickness, the force and contact time in the first and second parts increase sharply, especially in the first part, which involves the penetration of the projectile tip. In the first part, the contact force and contact time of specimen A5P12 is about two times that of specimen A5P4. This indicates an increase in the resistance to penetration of the targets by increasing the core layers due to the high strength of UHMWPE composite. In the second part, the increase in contact force is less than in the first part, because after the projectile tip penetrates the target, the projectile progresses by pushing the fibers aside. The third part of the diagram is almost the same for all specimens. Therefore, it can be concluded that increasing the core thickness has a significant effect on the sample resistance to penetration.

Figure 8.

Contact force history for targets exposed to conical projectile at impact velocity of 184 m/s (a) different core thickness, (b) different aluminum thickness, (c) different lay-up sequence.

Effect of thickness of aluminum face sheets

In this section, aluminum layers with a thickness of 0.3, 0.5, 0.6, and 0.8 mm are used to simulate and compare the results. Figure 7(b) shows the initial-residual velocity curves for targets with the same composite core thickness (consisting of 12 cross-ply layers) and four different aluminum layer thicknesses. The ballistic velocity increase for specimen A8P12 is about 28% higher than that of the specimen A3P12, 10% higher than that of the A5P12, and 6% higher than that of the A6P12. This indicates that the increase in ballistic velocity occurs in proportion to the increase in aluminum thickness and has almost the same trend.

Figure 8(b) shows the contact force history of specimens A8P12 and A5P12. As can be seen, with increasing metal thickness, the force and contact time increase in all three parts of the curve. In the first part, the peak associated with penetration into the first layer of aluminum increases for specimen A8P12 with thicker metal layer. Although the contact force has increased by about 15%, the contact time has not changed much. In the second part, the contact time is significantly increased, which may be due to the petalling of the thicker layer of aluminum.

Effect of lay-up sequence

Figure 9(a) shows the initial-residual velocity curves for some targets with 2/1 and 3/2 configurations. Two pairs of specimens are considered: two samples with different metal volume fraction (MVF) and two samples with equal MVF, where MVF is considered as the ratio of the total thicknesses of the aluminum layers to the total thickness of FML sample⁴⁴

MVF = \frac{\sum^{​} t_{aluminum}}{t_{FML}}

(14)

Figure 9.

Numerical residual velocity prediction with Lambert-Jonas $V_{B L}$ fit with parameters given in the legend (a, p $V_{B L}$ ) for specimens with (a) different lay-up sequence, (b) different aluminum alloys type.

The ballistic velocity in specimen A5P12 does not increase significantly compared to specimen B5P8. The two samples are about the same thickness. However, the volume fraction of aluminum and composite is different: A5P12 has approximately 60% composite and 40% metal (MVF = 0.40), while MVF of B5P8 is close to 0.60.

On the other hand, the curves of specimens A6P12 and B4P12 with equal metal volume fraction (MVF = 0.43) show that the ballistic velocity of B4P12 is about 3.5% higher than that of A6P12, although as shown in the figure, the residual velocity difference between the two specimens becomes negligible at higher speeds. By reducing the number of composite layers, the ballistic velocity of specimen B4P8 is about 3% higher than that of specimen A6P8 (Table 8). It seems that the change in the lay-up sequence does not have much effect on the ballistic limit velocity against impact with a conical projectile. Figure 8(c) shows the contact force history for specimens B5P8 and A5P12. As can be seen, the force and contact time in the first part, which is related to the penetration of the projectile tip, is reduced for the B5P8 compared to A5P12. It seems that the 3/2 configuration causes a more rigid behavior of the sample; and the penetration of the projectile tip occurs earlier. However, the force and contact time have increased in the second part of the curve. It means that the presence of a middle layer of aluminum makes it more resistant to the penetration of the conical part of the projectile.

Table 8.

Energies calculated based on numerical results.

Specimen code	Total thickness (mm)	Areal density (kg/m²)	MVF	Ballistic velocity (m/s)	Absorbed energy, E (J)	SPE
A5P4	1.54	3.30	0.65	77.3	29.28	8.78
A8P4	2.14	4.84	0.75	95.4	44.5	9.2
A5P8	2.09	3.80	0.48	96.9	46.01	12.11
A5P12	2.64	4.38	0.38	111.9	61.36	14.01
A5P16	3.16	4.87	0.32	118.5	68.81	14.13
A6P12	2.82	4.90	0.43	116.5	66.50	13.57
A2P12	2.02	2.65	0.20	94.5	43.76	16.51
A3P12	2.22	3.23	0.27	98.3	47.35	14.66
B5P8	2.60	5.20	0.58	109.3	58.54	11.26
A8P6	2.42	5.24	0.66	103.5	52.49	10.02
A8P12	3.24	6.04	0.49	123.6	74.86	12.39
A6P8	2.28	4.38	0.53	100.6	49.59	11.32
B4P8	2.28	4.38	0.53	103.1	52.09	11.89
B4P12	2.82	4.90	0.43	120.5	71.15	14.52

Effect of aluminum alloys type

In order to investigate the effect of the type of aluminum alloy on ballistic behavior of the specimens, PERELL samples based on Al 7075-T6 aluminum alloy are modeled and the residual velocity is compared. Figure 9(b) shows the initial-residual velocity curves for specimens A5P12 and A8P12 with two aluminum alloys. The results show that the use of 7075-T6 aluminum alloy due to higher strength increases the ballistic velocity about 30–35%.

Energy absorption behavior

To evaluate the impact resistance of FMLs, energy absorption capacity is considered as one of the most important parameters. The projectile impact energy

E_{i} = \frac{1}{2} m V_{i}^{2}

(15)

where

V_{i} and m

are the impact velocity and projectile mass, respectively. Considering

V_{r}

as the residual velocity, the residual energy of the projectile

E_{r} = \frac{1}{2} m V_{r}^{2}

(16)

Then, the energy absorbed by the target is

E = \frac{1}{2} m V_{i}^{2} - \frac{1}{2} m V_{r}^{2}

(17)

V_{r} = 0

, then

V_{i} = V_{b l}

where

V_{b l}

is the ballistic limit velocity. In this case, the energy absorbed by the specimen is

E = \frac{1}{2} m V_{b l}^{2}

(18)

For all specimens, both the ballistic velocity and the weight increase with increasing thickness. Since weight gain is undesirable, the specimen should have a high ballistic velocity and optimal weight. Specific perforation energy (SPE) is defined as the absorbed energy at ballistic limit velocity over the areal density ( $ρ_{A} = m / A$ ) of the targets⁴⁵

S . P . E = \frac{E}{ρ_{A}}

(19)

Table 8 presents a comparison between ballistic limit velocity, absorbed energy, and specific perforation energy of the specimens. Figure 10(a) shows the absorbed energy and SPE of the targets with 2/1 configuration based on Al 2024-T3 sheets with a thickness of 0.5 mm. In these specimens, the number of cross-ply layers of the composite core has increased from 4 to 16. As can be seen, increasing the number of composite layers increases the energy absorbed. The absorbed energy for specimen A5P16 is about 135% higher than for specimen A5P4, 50% higher than for A5P8, and 12% higher than for A5P12. Also, the SPE increases with the number of composite layers. The SPE for specimen A5P16 is about 60% higher than for the specimen A5P4, 17% higher than for A5P8, and 1% higher than for A5P12. This indicates that the effect of increasing the number of composite layers on increasing energy absorption is more severe than weight gain. On the other hand, it can be seen that as the number of layers increases, the growth of SPE decreases to the extent that it is almost equal for A5P12 and A5P16.

Figure 10.

Comparison of absorbed energy and SPE for all specimens with: (a) different core thickness, (b) different thicknesses of aluminum layer.

Figure 11(b) shows the absorbed energy and SPE of samples with the same thickness of composite cores (12 layers) and different aluminum layer thicknesses. The absorbed energy increases with increasing thickness of aluminum sheets. The absorbed energy for specimen A8P12 is about 50% greater than for specimen A3P12, 22% higher than for A5P12, and 13% greater than for A6P12. As can be seen in Figure 10(b), among specimens with the same number of composite layers, specimen A3P12 with thinner aluminum sheets has a higher SPE. The SPE for specimen A3P12 is about 18% higher than the specimen A8P12, 8% higher than the specimen A6P12, and 5% higher than A5P12. In fact, although increasing the thickness of aluminum layers increases the absorbed energy, it can reduce the SPE due to the increase in specimen weight.

Figure 11.

Comparison of (a) absorbed energy, (b) SPE for specimens with different lay-up sequence.

Figure 11 shows the absorbed energy and SPE for the three sample pairs with 2/1 and 3/2 configurations. Two sample pairs with equal metal volume fractions (see Table 8) and one sample pair with different metal volume fractions are considered. The specimen A5P12 has approximately 60% composite and 40% metal, while the specimen B5P8 has approximately 40% composite and 60% metal, and both specimens are approximately the same thickness. The absorbed energy of the two samples is almost the same. However, the comparison between SPE shows that replacing part of the composite layers with aluminum layer leads to less efficiency. With equal total thickness, the SPE of specimen A5P12 is 24% greater than that of specimen B5P8 due to its lower weight. The energy absorption and SPE are very close for A6P12 and B4P12 samples, as well as specimens A6P8 and B4P8 with the same MVF. This shows that with the same metal volume fraction, the lay-up sequence does not have much effect on the energy absorption of the samples. In addition, comparing the B4P8 and B5P8 samples with 3/2 configuration and the same core thickness, it can be seen that sample B5P8 with higher metal thickness has approximately 12% more energy absorption and 5% less SPE than the B4P8 sample. The variation of the SPE with MVF based on the numerical results is shown in Figure 12. Due to the high strength and energy absorption, and low density of UHMWPE composite laminates, the SPE decreases with increasing MVF from 0.2 to 0.75. This indicates that MVF can be an important design parameter to increase SPE. Using linear curve fitting, the relationship between SPE and MVF can be described by equation (18):

Figure 12.

Variation of SPE with metal volume fraction for PERALL specimens.

Conclusions

In this research, a numerical study was performed to investigate the ballistic impact performance of PERALL samples using a sharp tip projectile. Damage model was used based on the CDM approach and exponential damage evolution law. Various modes of damage including fiber tension/shear, fiber compression, fiber crush, matrix shear, and matrix delamination were considered in the model. CZM technique was used to simulate the behavior of the interface. The simulation results were confirmed by experimental findings. The main results of this research can be summarized as follows:

(1) The results of high velocity impact simulation are in good agreement with the experimental tests. Failure mechanisms and residual velocity are similar to those observed in the ballistic impact experiments.

(2) The contact history diagram for targets impacted with conical projectile consists of three parts. The first of which deals with increasing the contact force until the projectile tip penetrates the target and decreasing the contact force. In the second stage, the contact force increases again with the progress of the conical section until the contact force decreases again with the penetration of the cylindrical section, and in the third stage, it continues with almost constant value until the projectile penetrates completely.

(3) The absorbed energy, also SPE, increases with increasing the number of composite layers of PERALL specimen. This indicates that the effect of increasing the number of composite layers on increasing energy absorption is more severe than weight gain. On the other hand, as the core thickness increases, the growth of SPE decreases.

(4) Although increasing the thickness of aluminum sheets in PERALL samples increases the absorbed energy, but due to the higher density of aluminum than UHMWPE, SPE decreases.

(5) A comparison between 2/1 and 3/2 configurations showed that with the same metal volume fraction, changes in the lay-up sequence do not have much effect on the ballistic velocity and energy absorbed in the samples.

(6) The MVF is an important parameter in the high velocity impact performance of the PERALL specimens. The result showed that with increasing MVF, SPE decreases. A simple linear equation was derived to describe the relationship between these two parameters.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Mahnaz Zakeri

References

Chai

Manikandan

. Low velocity impact response of fibre-metal laminates - A review. Compos Structures 2014; 107: 363–381, DOI: 10.1016/j.compstruct.2013.08.003.

Yang

J-M

. The mechanical behavior of GLARE laminates for aircraft structures. JOM 2005; 57: 72–79, DOI: 10.1007/s11837-005-0067-4.

Bikakis

Kalfountzos

Theotokoglou

. Elastic buckling of rectangular fiber-metal laminated plates under uniaxial compression. J Thermoplastic Compos Mater 2019; 33: 1629–1651. DOI: 10.1177/0892705719833123.

Bahari-Sambran

Eslami-Farsani

Arbab Chirani

. The flexural and impact behavior of the laminated aluminum-epoxy/basalt fibers composites containing nanoclay: An experimental investigation. J Sandwich Structures Mater 2018; 22: 1931–1951. DOI: 10.1177/1099636218792693.

Santiago

Cantwell

Jones

, et al. The modelling of impact loading on thermoplastic fiber-metal laminates. Compos Struct 2017; 189: 228–238, DOI: 10.1016/j.compstruct.2018.01.052.

Yelamanchi

MacDonald

Gonzalez-Canche

et al. The fracture properties of fiber metal laminates based on a 3D printed glass fiber composite. J Thermoplast Compos Mater 2020, https://doi.org/10.1177/0892705720976179.

Cai Yu

Zhi Wu

, et al. Low velocity impact of carbon fiber aluminum laminates. Compos Struct 2015; 119: 755–766.

Karbalaie

Yazdanirad

Mirhabibi

. High performance Dyneema fiber laminate for impact resistance/macro structural composites. J Thermoplastic Compos Mater 2011; 25(4): 403–414.

Haque

BZG

Gillespie

. Depth of penetration of Dyneema® HB26 hard ballistic laminates. J Thermoplast Compos Mater 2021, https://doi.org/10.1177/089270572110185.

10.

Zulkifli

Stolk

Heisserer

, et al. Strategic positioning of carbon fiber layers in an UHMWPE ballistic hybrid composite panel. Int J Impact Eng 2019; 129: 119–127.

11.

Yanga

Liu

Wang

, et al. Effect of fiber hybridization on mechanical performances and impact behaviors of basalt fiber/UHMWPE fiber reinforced epoxy composites. Compos Struct 2019; 229, DOI: 10.1016/j.compstruct.2019.111434.

12.

Zhang

Guo

, et al. Influence of fiber type on the impact response of titanium-based fiber-metal laminates. Int J Impact Eng 2018; 114: 32–42, DOI: 10.1016/j.ijimpeng.2017.12.011.

13.

Mansoori

Zakeri

Guagliano

. Energy absorption and damage mechanism of UHMWPE-aluminum composite sandwich laminate under impact loading: an experimental investigation. J Sandwich Struct Mater 2021; 24(1): 360–384, https://doi.org/10.1177/10996362211020459.

14.

Zhu

Huang

G-Y

Feng

S-S

, et al. Conical nosed projectile perforation of polyethylene reinforced cross-ply laminates: effect of fiber lateral displacement. Int J Impact Eng 2018; 118: 39–49, DOI: 10.1016/j.ijimpeng.2018.04.005.

15.

Zarei

Sadighi

Minak

. Ballistic analysis of fiber metal laminates impacted by flat and conical impactors. Compos Structures 2017; 161: 65–72.

16.

M-M

Huang

G-Y

Dong

Y-X

, et al. An experimental investigation into the high velocity penetration resistance of CFRP and CFRP/Aluminium laminates. Compos Structures 2018; 188: 450–460.

17.

Haque

Ali

Gillespie

. Modeling transverse impact on UHMWPE soft ballistic sub-laminate. J Thermoplastic Compos Mater 2017; 30(11): 1441–1483.

18.

Haque

BZG

Gillespie

. Perforation mechanics of UHMWPE soft ballistic sub-laminate and soft ballistic armor pack: a finite element study. J Thermoplast Compos Mater 2021, https://doi.org/10.1177/08927057211042058.

19.

Lässig

Nguyen

May

, et al. A nonlinear orthotropic hydrocode model for ultra-high molecular weight polyethylene in impact simulations. Int J Impact Eng 2015; 75: 110–122.

20.

Nguyen

Lässig

Ryan

, et al. A methodology for hydrocode analysis of ultra-high molecular weight polyethylene composite under ballistic impact. Composites A: Appl Sci Manufacturing 2016; 84: 224–235.

21.

Hazzard

Trask

Heisserer

, et al. Finite element modelling of dyneema composites: from quasi-static rates to ballistic impact. Composites Part A: Appl Sci Manufacturing 2018; 115: 31–45.

22.

Yao

Wang

, et al. Influence of impactor shape on low-velocity impact behavior of fiber metal laminates combined numerical and experimental approaches. Thin-Walled Structures 2019; 145: 106399, DOI: 10.1016/j.tws.2019.106399.

23.

Farooq

Myler

. Finite element simulation of damage and failure predictions of relatively thick carbon fibre-reinforced laminated composite panels subjected to flat and round noses low velocity drop-weight impact. Thin-Walled Structures 2016; 104: 82–105.

24.

Tie

Hou

, et al. An insight into the low-velocity impact behavior of patch-repaired CFRP laminates using numerical and experimental approaches. Compos Structures 2018; 190: 179–188.

25.

Zhu

Zhang

Curiel-Sosa

, et al. Finite element simulation of damage in fiber metal laminates under high velocity impact by projectiles with different shapes. Compos Structures 2019; 214: 73–82.

26.

Sharma

Mishra

Jain

, et al. Deformation behavior of single and multi-layered materials under impact loading. Thin-Walled Structures 2018; 126: 193–204.

27.

Hashin

. Failure criteria for unidirectional fiber composites. J Appl Mech 1980; 47: 329–334.

28.

Yademellat

Nikbakht

Saghafi

, et al. Experimental and numerical investigation of low velocity impact on electrospun nanofiber modified composite laminates. Compos Structures 2018; 200: 507–514.

29.

Zhang

. Simulating low-velocity impact induced delamination in composites by a quasi-static load model with surface-based cohesive contact. Compos Structures 2015; 125: 51–57.

30.

Higuchi

Okabe

Yoshimura

, et al. Progressive failure under high-velocity impact on composite laminates: Experiment and phenomenological mesomodeling. Eng Fracture Mech 2017; 178: 346–361.

31.

Saghafi

Ghaffarian

Salimi-Majd

, et al. Investigation of interleaf sequence effects on impact delamination of nano-modified woven composite laminates using cohesive zone model. Compos Structures 2017; 166: 49–56.

32.

Hou

Tie

, et al. Low-velocity impact behaviors of repaired CFRP laminates: effect of impact location and external patch configurations. Composites B: Eng 2019; 163: 669–680.

33.

Johnson

Cook

. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the Seventh International Symposium on Ballistics. The Hague 1983. p. 541–547.

34.

Mansoori

Zarei

. FSI simulation of hydrodynamic ram event using LS-Dyna software. Thin-Walled Structures 2019; 134: 310–318.

35.

Yen

C-F

. A ballistic material model for continuous-fiber reinforced composites. Int J Impact Eng 2012; 46: 11–22.

36.

Gama

. User Manual: A Progressive Composite Damage Model for Unidirectional and Woven Fabric, no. 215. Materials Sciences Corporation (MSC) & University of Delaware Center for Composite Materials (UD-CCM), 2015.

37.

Matzenmiller

Lubliner

Taylor

. A constitutive model for anisotropic damage in fiber-composites. Mech Mater 1995; 20: 125–152.

38.

Singh

Namala

Mahajan

. A damage evolution study of E-glass/epoxy composite under low velocity impact. Composites Part B: Eng 2015; 76: 235–248.

39.

Russell

Karthikeyan

Deshpande

, et al. The high strain rate response of ultra high molecular-weight polyethylene: from fibre to laminate. Int J Impact Eng 2013; 60: 1–9.

40.

Kromm

Lorriot

Coutand

, et al. Tensile and creep properties of ultra high molecular weight PE fibres. Polym Test 2003; 22(4): 463–470.

41.

Mansoori

Zakeri

. Strain-rate-dependent progressive damage modelling of UHMWPE composite laminate subjected to impact loading. Int J Damage Mech 2021; 31(2): 215–245, https://doi.org/10.1177/10567895211035480.

42.

Camanho

Dávila

. Mixed-mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials. NASA/TM- No., 2002.

43.

Lambert

Jonas

. Towards Standardization in Terminal Ballistic Testing: Velocity Representation. MD, USA: Ballistic Research Laboratories, 1976. DOI: 10.21236/ada021389.

44.

Vlot

Gunnink

(eds). Fiber metal laminates, an introduction. Dordrecht, the Netherlands: Kluwer Academic Publishers; 2001.

45.

Jones

. Structural Impact. Cambridge University Press, 1997.