Study on high velocity impact response of aramid fibers-epoxy/aluminum laminate composites toughened by ZrO 2 and SiO 2 nanoparticles

Abstract

The present study investigates the improvement in high-velocity impact response of fiber metal laminates through modification of epoxy using different percentages (0, 1, 3, and 5 wt.%) of SiO₂ and ZrO₂ nanoparticles. To ensure a good distribution of nanoparticles into epoxy resin, the nanoparticles were dispersed by a high-speed shear mixer followed by an ultrasonic device. By using the hand lay-up technique followed by a mold pressing process, FML samples were made of 2024-T3 aluminum sheets (0.5 mm thick) and woven Kevlar fabric impregnated with modified epoxy. The high-velocity impact test on FML samples was conducted to determine the influence of epoxy modification on their specific energy absorption. The study revealed that the modification of epoxy increased the specific energy absorption up to 130% and 91% at samples with 3 wt.% of SiO₂ and 5 wt.% of ZrO₂, respectively. It was also observed from scanning electron microscopy analysis that incorporation of ceramic nanoparticles changed the delamination failure mechanism of matrix cracking to fiber breakage. Furthermore, finite element simulation (FES) was additionally conducted with Abaqus to predict the residual velocity and model impact response. The simulation results agree well with experimental data.

Introduction

In recent years, the requests for materials with advanced mechanical properties have been increasing, especially in the aviation industry in which lightweight materials with high strength properties are needed.^1,2 In recent decades, composite materials are frequently utilized due to their advantages such as weight saving, high strength, fatigue, and corrosion resistance. ³ Furthermore, bio-based composites are also eco-friendly and cost-saving with acceptable mechanical properties ⁴ ; however, all composites are weak in terms of toughness and moisture resistance. ⁵

Therefore, widespread modifications have been conducted among which sandwich-structured composites have emerged as an alternative since they overcame those limitations and possessed acceptable toughness. This type of composite was fabricated by covering the central section with two stiff skins.^6,7 One of the most important families of this class was fiber metal laminates (FMLs). ⁸ These multilayer metal-fibers were made of thin laminates of metal and polymer-based composite.

Aramid reinforced aluminum laminate (ARALL) was the first class of FMLs, introduced in the 1980s. Its special characteristic was fatigue resistance ⁹ . In airplane design, studies indicated that ARALL was a favorite material in the lower wing and the skin of a fuselage where fatigue resistance is extremely important. Weight savings of more than 20% were easily attainable^10,11; in addition to fatigue resistance and weight reduction, ARALL also represented high damage tolerance, corrosion resistance, and good flame resistance.^12–15 These properties made ARALL the ideal material for the aviation industry; however, since aircraft were always exposed to high-velocity (50–1000 m/s ¹⁶ ) impacts, improving the energy absorption capacity was also required. Thus, many studies on improvement in the energy absorption capacity and toughness of ARRAL against high velocity have been started. ¹³

While in many investigations the influence of many parameters, including different numbers of alternating layers, different types of aluminum alloy, and different aluminum/composite thickness ratios, were analyzed, only small improvements were observed in the energy absorption.^17–19

The main reason for the low energy absorption of ARALL is generally attributed to the polymer matrix. The most widely used polymer matrix, epoxy resin, suffers from major disadvantages such as low toughness, poor crack resistance, brittle nature at room temperature, and low impact resistance. Considerable efforts have been made to improve the toughness of epoxy resin, one of which was the incorporation of dispersed nanoparticles.^20–22 The inclusion of a small amount of the nanofillers (e.g. 5 wt.%), because of crack deflection and the toughening mechanism of void formation, led to a significant increase in the toughness of the epoxy resin. ²² Many nanofillers including rigid nanoparticles such as TiO₂, ZnO₂, CaSiO₃, BN, Al₂O₃, and SiO₂ successfully enhanced epoxy toughness and tensile strength; these promising results lead to test these modified epoxy in FMLs structures including ARALL.^21,23,24

Eslami-Farsani et al.^25–28 conducted investigations on improving the properties of FMLs by using nanofillers. In these investigations, nanofillers with high stiffness such as graphene, graphene oxide, carbon nanotube, TiO₂, and zirconia were dispersed in the polymer matrix. The results indicated many improvements in properties of FMLs, such as fracture toughness, tensile strength, electrical conductivity, wear resistance, water resistance, and flammability resistance. Kaboodvand et al. ²⁹ studied the effect of multiwalled carbon nanotubes on the tensile strength of FMLs. The results showed that the tensile strength improved 14% by 0.3 wt.% of carbon nanotubes. Gurusideswar et al. ³⁰ studied the effect of using nanoclay on the tensile behavior of glass/epoxy composites. The results showed that the elastic modulus and tensile strength of the epoxy/clay nanocomposites are improved by 16% and 9%, respectively.

Although in many investigations incorporation of nanoparticles improved mechanical properties of epoxy resin, the influence of using modified epoxy on the high-velocity impact response of ARALL has not yet been clarified. In the present study, ARALL panels, stiffened by using modified epoxy, are investigated to define the improvement in energy absorption capacity. SiO₂ and ZrO₂ nanofillers with the concentration of 1, 3, and 5 wt.% are incorporated into epoxy resin to reinforce the ARALL panel. Subsequently, high-velocity impact tests are carried out on these ARALL plates. Damaged areas are investigated to define the mechanisms that affect energy absorption capacity. Since the incorporation of SiO₂ nanoparticles yields more promising results, finite element simulation (FES) technique is carried out for samples containing SiO₂ nanoparticles to predict the residual velocity and model impact response.

Experimental procedure

Materials

In this study, the ARALL samples were made up of 0.5 mm thick rolled sheets of the aluminum 2024-T3 alloy (130 × 130 mm²). The reinforcing element of FMLs was Kevlar-29 fibers in form of woven Kevlar fabric (HM1500D-P220). Adhesive was the mixture of epoxy resin (Ker828, Kumho P&B chemicals) and amine hardener by the weight ratio of 100:10. SiO₂ and ZrO₂ nanoparticles (from Nanosany Co.) were used with an average size of 20–30 nm and purity of +99%. NaOH solution was utilized in degreasing and final etching treatment on the aluminum sheets was done by the mixed solution of sulfuric acid (98%) and potassium chromate (K₂CrO₄) powder. The specifications of Kevlar-29 and woven Kevlar fabric are given in Tables 1 and 2, respectively.

Table 1.

The specifications of Kevlar-29.

Material	Molecular formula	Density (kg/m3)	Tensile yield strength (MPa)	Modulus of elasticity (GPa)	Elongation (%)
Kevlar-29	C14H14N2O4	1.44	3600	83	3

Table 2.

The Specifications of woven Kevlar fabric.

Model no	Type	Surface density (denier)	Weave	Weight (g/m2)
HM1500D-P220	HM (high module)	1500	Plain	220

Preparation and fabrication of samples

Nanoparticles by values of 1, 3, and 5 wt.% of each SiO₂ and ZrO₂ separately were added in epoxy resin. To distribute these nanoparticles, a high-speed shear mixer at the rate of 2000 r/min was used for 1 h. Then, the ultrasonic device with 24 kHz and 120 W dispersed the nanoparticles for 90 min while the epoxy was kept in an ice-water bath to stop the temperature from rising. Next, to remove the bubbles, formed in the previous step, a vacuum oven was used to degas the mixture. Finally, it was mixed with an amine hardener by the weight ratio of 100:10 followed by stirring gently to avoid the formation of bubbles for 5 min.

In order to ensure good adhesion between the aluminum sheets and the composite layer, a series of mechanical and chemical surface treatments were conducted on aluminum sheets. In the first step, mechanical treatment, after aluminum sheets were degreased with acetone, they were polished by sandpaper (No. 40). Then, the sheets were steeped in boiling water for 20 min so that OH⁻ and H⁺ agents were generated on their surfaces. Finally, aluminum sheets were washed again in acetone to ensure a perfectly clean surface. To degrease sheets before performing a chemical treatment, they were pre-etched n 100 g/L NaOH solution at 60°C for 1 min.

In the second step, the chemical process, the Forest Products Laboratory (FPL) etch process, producing microscopic scratches on the sheets, was performed. Aluminum sheets were soaked in an acidic FPL etch solution, a mixture of 33 vol.% sulfuric acid and 3.3 vol.% K₂CrO₄ solution, at 62 °C for 30 min. Then, they were rinsed in tap water at 20°C. Finally, to dry them, sheets were kept in an oven at 40°C for 30 min.

After preparing epoxy and aluminum sheets, the hand lay-up technique was applied to fabricate the ARRAL samples. By the weight ratio of 50:50, three layers of woven Kevlar fabric were covered manually by prepared epoxy. Oriented in the same direction, three impregnated layers of woven Kevlar fabric were sandwiched between two aluminum sheets to form the stacking sequence of AL/K/K/K/AL. Finally, fabricated laminate was cured using a compression mold technique with the application of pressure (500 bar) and temperature (25°C) for 48 h. Figure 1 shows the steps of fabricating ARALL samples.

Figure 1.

The steps of fabricating ARALL samples.

Mechanical testing and characterization

To conduct an impact test, a gas gun, as shown in Figure 2, was used to fire an aluminum cylindrical projectile with a spherical head. The outer diameter and the length were 21.5 and 40 mm, respectively. The cylinder weighed 26.85 g. The initial velocity of the projectile was 117 m/s to be assured of complete penetration. Samples were square (130 × 130 mm²). The predominant mechanism of failure on the damaged area was defined using the field emission scanning electron microscope (FESEM, model MIRA3TESCAN-XMU).

Figure 2.

A gas gun machine setup.

Experimental results and discussion

High-velocity impact results

To ensure the complete target perforation, tests were conducted at the initial velocity of 117 m/s. The residual velocity of the projectiles for each test was recorded and ballistic limit velocity (V₅₀), the velocity at which there is a 50% probability of penetration, is calculated using equation (1)

$${\text{V}}_{50}^2{=\text{ V}}_{\text{i}}^2-{\text{ V}}_{\text{r}}^2$$

(1)

V_i and V_r are the initial and residual velocity of the projectile before the impact and after perforating the sample, respectively. The experimental results are presented in Table 3.

Table 3.

Experimental results of high-velocity impact test on FMLs samples.

Mass (kg)	Nanoparticle (wt.%)	V50 (m/s)	Vr (m/s)	Vi (m/s)
0.06963	0%	55.50	103	117
0.06975	1% SiO2	69.66	94	117
0.06999	3% SiO2	84.43	81	117
0.07023	5% SiO2	80.40	85	117
0.0697	1% ZrO2	62.35	99	117
0.06985	3% ZrO2	73.54	91	117
0.07017	5% ZrO2	77.10	88	117

Figure 3, shows ballistic limit velocity as a function of nanoparticles content in the ARRAL samples. The samples with 3 wt.% SiO₂ and 5 wt.% ZrO₂ have the highest ballistic limit velocity by 84.43 and 77.10 m/s, respectively.

Figure 3.

The effect of the nanoparticles loading (wt.%) on the ballistic limit velocity of ARALL samples.

The experimental energy absorption (E_b) can be determined from ballistic limit velocity (E_b) using equation (2)

$${\text{E}}_{\text{b}}=\frac{1}{2}\hspace{0.17em}{\text{M}}_{\text{b}}(\text{V}{\hspace{0.17em}}_{50}){\hspace{0.17em}}^2$$

(2)

Where M_b is the mass of projectile. To exclude the influence of wight variation on energy absorption capacity, the specific energy absorption (SEA) is determined according to equation (3)

$$\text{SEA}=\frac{1}{2}\frac{{\text{M}}_{\text{b}}}{{\text{M}}_{\text{s}}}{\text{V}}_{{\hspace{0.17em}}^{50}}$$

(3)

Where M_s is the mass of specimen.

Figure 4 illustrates the variation of specific energy absorption as a function of nanoparticles loading in the ARALL samples.

Figure 4.

The effect of the nanoparticles loading on the specific energy absorption of ARALL samples.

As can be seen in Figures 3 and 4, the enhancement in limit velocity and specific energy absorption values is clearly observed with the incorporation of SiO₂ and ZrO₂ nanoparticles. The highest improvement of 130% and 91% in specific energy absorption was achieved by the incorporation of 3 wt.% SiO₂ and 5 wt.% ZrO₂ nanoparticles, respectively, compared to ARALL sample with neat epoxy. The saturation point of SiO₂ nanoparticles is 3 wt.% after which the specific energy absorption decreases. This is because modified epoxy with rigid nanoparticles suffers mainly from the agglomeration, triggering a brittle response because of stress concentration and void formation. ³¹ The saturation level of ZrO₂ nanoparticles could be 5 wt.% or more which is higher than the saturation level of SiO₂. The higher saturation point of ZrO₂ is attributed to its better distribution behavior. Zirconia nanoparticles show less agglomeration in general. ³²

As can be seen, at the same mass concentration, higher ballistic limit velocity and specific energy absorption capacity values were achieved in the sample containing SiO₂ nanoparticles in comparison to the sample containing ZrO₂ nanoparticles. To explain this phenomenon, it must be mentioned that incorporating nanoparticles increases the toughness of epoxy since every nanoparticle in the epoxy matrix acts as an obstacle deflecting a crack tip. Therefore, the crack front tilts and twists when it encounters the particles and hence passes around them. ³³ Both SiO₂ and ZrO₂ nanoparticles, used in this study, were similar in shape and size so these factors were not related to this phenomenon. However, the density of ZrO₂ nanoparticle is higher than SiO₂. Therefore, in the same mass concentration, numbers of ZrO₂ nanoparticles are fewer than SiO₂ nanoparticles, which means fewer sites to pin or deflect a crack. ³⁴

A typical fractography

ARALL samples are made of three different layers of aluminum, epoxy, and Kevlar fabric. Since in current investigation only properties of epoxy are modified by incorporation of nanoparticles, the increase in energy absorption is mainly related to change in the failure mechanism of the epoxy layer which is defined as delamination. Delamination is a crack that runs in the resin-rich area between different plies. ³⁵ The high-velocity impact results in localized damage which induces high transverse shear stress between all layers; This parameter in addition to the bending stiffness mismatch of aluminum and Kevlar fabric put huge stress on their resin-rich interface causing delamination.

To define the change in delamination mechanism leading to change in energy absorption capacity, samples with the lowest and the highest energy absorption, which are 0 and 3 wt.% SiO_2, respectively, were selected for microscopic study (FESEM). For each sample, micrographs from the debonded face of Kevlar fabric and aluminum sheet, on the damaged area are taken. Based on observations, a schematic model of the interlaminar fracture mechanism is developed to represent the damage mechanism in the epoxy layer. Figure 5, illustrates schematically interlaminar failure and FESEM micrographs of aluminum sheet and Kevlar fabric in the sample containing neat epoxy.

Figure 5.

Interlaminar failure of the sample containing neat epoxy, (a) Schematic representation, (b) Cross section of debonded aluminum, (c) and (d) Debonded face of Kevlar fabric.

As can be seen in Figure 5a, the crack propagated predominantly through the epoxy matrix leaving on both surfaces of the aluminum and Kevlar fabrics an epoxy covering. Figure 5b shows the cross section of aluminum on the damaged area. A smooth epoxy covering on the aluminum surface suggests a brittle fracture in the epoxy layer. Figure 5c, shows the surface of Kevlar fabric; while on the center a smooth epoxy covering also demonstrates a brittle fracture in the epoxy layer, on the sides, fibers are bare, with no epoxy covering. The lack of epoxy resin on fibers, as can be seen in Figure 5d, could be related to both poor wet-out in the hand lay-up process and poor interfacial adhesion between aramid fibers and neat epoxy resin ³⁶ due to mismatch of thermal expansion coefficient in the curing process. ³⁷ Therefore, in the sample containing neat epoxy, the main mechanism of interlaminar failure is the matrix cracking which is the result of the low strength and brittle nature of neat epoxy. However, in the sample containing 3 wt.% SiO₂, large number of fractured fibers are observed on the delaminated Kevlar fabric, as can be seen in Figure 6.

Figure 6.

Fractured fibers on the surface of delaminated Kevlar fabric in sample containing 3 wt.% SiO₂.

Figure 7 illustrates schematically interlaminar failure and FESEM micrograph of aluminum sheet and Kevlar fabric in the sample containing 3 wt.% SiO₂.

Figure 7.

Interlaminar failure of the sample containing 3 wt.% SiO₂, (a) Schematic representation, (b) Cross section of debonded aluminum, (c) Debonded face of Kevlar fabric.

As can be seen in Figure 7a, in some areas the crack propagated through the Kevlar fabrics and cut fibers. This leaves an epoxy layer, including some broken fibers, on the aluminum surface as can be seen in Figure 7b. The torn-out fibers on the Kevlar fabric surface can be seen clearly in Figure 7c.

It must be mentioned that a crack propagates through the weakest regions. In the sample containing neat epoxy, the brittle matrix of epoxy is the weakest part; therefore, the crack can propagate easily in the epoxy matrix, leaving a smooth layer of epoxy resin on the surface of aluminum and Kevlar fabric. However, the incorporation of nanoparticles in epoxy enhanced the strength of the epoxy matrix, making the crack shift its path into Kevlar fabrics. Breaking the fibers makes an increase in the level of energy consumption during crack propagation.

Finite element simulation

In this section, the FES technique is applied to simulate the response of the composite structure to the high-velocity impact experiment. FES model is established for the aluminum, Kevlar fabric, epoxy layer, and impactor in Abaqus/CAE 2020. All geometries, boundary conditions, and material properties are taken into consideration as near as experimental setup. Analyses are performed in a dynamic explicit framework.

Simulation condition and setup

Geometrical modeling

The FE model was assembled of the ARALL sheet and impactor. The hemispherical impactor was modeled as a rigid body with a mass of 26.58 g. An illustration of the FE model of the impactor is shown in Figure 8.

Figure 8.

The FE model of the impactor, designed from the projectile in the experimental test.

The experimental dimension of the ARALL plate was 130 × 130 mm². However, since an area of 1.5 mm wide all around the plate was fixed with a high-pressure loading in the experiment, it was modeled with the size of 100×100 mm². The ARALL plate with 1.24 mm thickness was composed of two layers of aluminum, three layers of Kevlar fabric, and four layers of epoxy resin. As in experimental analyses, a Ply thickness of 500 μm was assigned to the aluminum layer. Also, since the weight ratio of Kevlar to epoxy is 50:50 and their density is almost the same, their thickness ratio was considered 50:50. Therefore, the thickness of 120 μm were assigned to four layers of epoxy, 30 μm for each layer; similarly, the thickness of 120 μm were assigned to three layers of Kevlar fabric, 40 μm for each layer.

Boundary conditions

To simulate the real condition, the six freedoms of the edges of the ARRAL plate except for the epoxy layers, which were modeled as the cohesive film, were fixed to limit all displacement and rotation. Also, the initial velocity of 117 m/s is given to the projectile in the negative Z-direction.

To calculate common interactions and simulate the contact behavior, a general contact algorithm, using the penalty and “hard” contact methods, was applied in Abaqus/Explicit. Also, defining a true friction coefficient was of great importance since it can change the transferred forces in contact surfaces. The friction coefficient for general contact was set at 0.2. ³⁸ Figure 9 shows the model and boundary condition of the ARALL specimen.

Figure 9.

The model and boundary condition of ARALL specimen.

Material model

Since the ARRAL plane is composed of three different materials with different behavior in high-velocity impact, different mechanical properties and failure criteria were assigned to them. The Johnson-Cook, cohesive zone models (CZM), and Hashin criteria were assigned to aluminum, epoxy, and Kevlar fabric, respectively. Aluminum sheets are made of aluminum 2024-T3; its main mechanical properties are presented in Table 4.

Table 4.

Mechanical properties of aluminum 2024-T3. ³⁹

Density, ρ (kg/m3)	Poisson’s ratio, ν	Modulus of elasticity, E (MPa)
2770	0.33	73,084

The J-C material model was chosen to represent its plastic behavior in the numerical model. It is used to describe the response of 2024-T3 aluminum sheets. This model is expressed by equation (4)

$$\text{σ }=\left[\text{A }+\text{ B}{\left({\text{ε}}_{\text{p}}\right)}^{\text{n}}\right]\hspace{0.17em}\left[1+\text{C}\hspace{0.17em}\text{ln}\left({\dot{\epsilon }}^{\ast }\right)\right]\hspace{0.17em}\left[1-{\left(\frac{\text{T}-{\text{T}}_{\text{room}}}{{\text{T}}_{\text{melt}}-{\text{T}}_{\text{room}}}\right)}^{\text{m}}\right]$$

(4)

where σ is effective stress, ${\epsilon }_p$ is an effective plastic strain, and ${\dot{\epsilon }}^{\ast }$ is normalized effective plastic strain rate (typically normalized to a strain rate of 1.0 s⁻¹). Also, A, B, n, and m are the material constants, C defines the sensitivity to the strain rate, T_melt is the melting point, and T_room is the ambient temperature. In Table 5, Johnson-Cook parameters of aluminum 2024-T3 are presented. ³⁹

Table 5.

Johnson-Cook parameters of aluminum 2024-T3. ³⁹

Static yield limit, A (MPa)	Strain hardening modulus, B (MPa)	Strain hardening exponent, N	Strain rate coefficient, C	Thermal softening exponent, M	Reference temperature, Troom (K)	Melting temperature, Tmelt (K)
265	426	0.34	0.015	1	294	775

Damage in the J-C model is based on a cumulative damage law which is defined by equation (5)

$$\text{D}={\displaystyle \sum }\frac{\mathrm{\Delta }\mathrm{\epsilon }}{{\mathrm{\epsilon }}_{\text{f}}}$$

(5)

In which Δε is the increment of effective plastic strain and ε_f is the effective plastic strain at failure which is expressed by equation (6)

$${\text{ε}}_{\text{f}}=\left[{\text{D}}_1+{\text{D}}_2\exp \left({\text{D}}_3{\text{σ}}^{\text{*}}\right)\right]\left[1+{\text{D}}_4\ln {\text{ε}}^{\text{*}}\right][1+{\text{D}}_5{\text{T}}^{\text{*}}]$$

(6)

Where σ^* is the ratio of pressure to effective stress and ε* is the dimensionless strain rate. The parameters D1-D5 are fracture constants. Failure of elements is assumed to occur when D from equation (5) reaches one. Fracture constants of aluminum 2024-T3 are given in Table 6. ³⁹

Table 6.

Johnson-Cook fracture constants of aluminum 2024-T3. ³⁹

Fracture constant 1, D1	Fracture constant 2, D2	Fracture constant 3, D3	Fracture constant 4, D4	Fracture constant 5, D5
0.13	0.13	−1.5	0.011	0

As was mention before, one of the main reasons for high energy absorption in FMLs was delamination. In this simulation, delamination was considered as the failure of the adhesive bond. Also, the adhesive bond simulation was based on the method (CZM) using uncoupled traction. Details are described in the Abaqus manual. ⁴⁰

Damage initiation was predicted by using quadratic nominal stress (QUADS Damage). Also, the damage evolution law, describing the degradation of material stiffness, was modeled based on the displacement of the interface in combination with a tabular softening. Material Properties of epoxy with different percent of SiO₂ nanoparticles, calculated from literature, ⁴¹ are presented in Table 7.

Table 7.

Properties of epoxy with different SiO₂ nanoparticles loading (wt.%). ²⁶

Sample	Density, ρ (kg/m3)	Young module, E (MPa)	Shear module, G (MPa)	Nominal stress, σn (MPa)	Shear stress, τ (MPa)
Neat epoxy	1160	2500	960	40	24
Epoxy-2% SiO2	1160	2750	1050	50	30
Epoxy-3.5% SiO2	1160	3000	1150	75	45
Epoxy-5% SiO2	1160	3000	1150	45	27

Since in Abaqus a failure prediction of a composite is limited to two-dimensional unidirectional composite, to simulate a three-dimensional woven Kevlar fabric a VUMAT user subroutine was applied. Woven Kevlar fabric, simulating a three-dimensional state, was assumed to be orthotropic. ⁴² Its properties are presented in Table 8.

Table 8.

Properties of woven Kevlar fabric. ⁴²

Density, ρ (kg/m3)	Poisson’s ratio, ν12	Poisson’s ratio, ν13	Poisson’s ratio, ν23	Longitudinal modulus of elasticity, E1 (MPa)	Transverse modulus of elasticity, E2 (MPa)
1220	0.03	0.03	0.03	22,400	22,400
Transverse modulus of elasticity, E3 (MPa)	In-plane shear module of elasticity, G12 (MPa)	Transverse shear module of elasticity, G13 (MPa)	Transverse shear module of elasticity, G23 (MPa)	Damping factor, β (ms)	—
1500	1800	500	500	1e-9	—

A modified 3D Hashin criteria, implemented in a VUMAT user subroutine, predicted the failure of Kevlar fabric. Damage criteria of this modified Hashin 3D model, including six different failure modes, are presented in Table 9.

Table 9.

Damage criteria of the Hashin 3D model. ⁴³

Failure mode	Criteria
Tensile failure in the x-direction	$d_{1t}$ = ${\left(\frac{{\mathrm{\sigma }}_{11}}{x_{1t}}\right)}^2$ + ${\mathrm{\alpha }}_{1t}{\left(\frac{\frac{{\tau }_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{12}^4}{\frac{s_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{12}^4}\right)}^2$ + ${\mathrm{\alpha }}_{1t}{\left(\frac{\frac{{\mathrm{\tau }}_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{13}^4}{\frac{s_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{13}^4}\right)}^2$
Compression failure in the x-direction	$d_{1c}$ = ${\left(\frac{{\mathrm{\sigma }}_{11}}{x_{1c}}\right)}^2$ + ${\mathrm{\alpha }}_{1c}{\left(\frac{\frac{{\mathrm{\tau }}_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{12}^4}{\frac{s_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{12}^4}\right)}^2$ + ${\mathrm{\alpha }}_{1c}{\left(\frac{\frac{{\mathrm{\tau }}_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{13}^4}{\frac{s_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{13}^4}\right)}^2$
Tensile failure in the y-direction	$d_{1t}$ = ${\left(\frac{{\mathrm{\sigma }}_{22}}{x_{2t}}\right)}^2$ + ${\mathrm{\alpha }}_{2t}{\left(\frac{\frac{{\mathrm{\tau }}_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{12}^4}{\frac{s_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{12}^4}\right)}^2$ + ${\mathrm{\alpha }}_{2t}{\left(\frac{{\mathrm{\tau }}_{23}}{s_{23}}\right)}^2$
Compression failure in the y-direction	$d_{1c}$ = ${\left(\frac{{\mathrm{\sigma }}_{22}}{x_{2c}}\right)}^2$ + ${\mathrm{\alpha }}_{2c}{\left(\frac{\frac{{\mathrm{\tau }}_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{12}^4}{\frac{s_{12}^2}{2G_{12}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{12}^4}\right)}^2$ + ${\mathrm{\alpha }}_{2c}{\left(\frac{{\mathrm{\tau }}_{23}}{s_{23}}\right)}^2$
Tensile failure in the z-direction	$d_{3t}$ = ${\left(\frac{{\mathrm{\sigma }}_{33}}{x_{3t}}\right)}^2$ + ${\mathrm{\alpha }}_{3t}{\left(\frac{\frac{{\mathrm{\tau }}_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{\mathrm{\tau }}_{13}^4}{\frac{s_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{13}^4}\right)}^2$ + ${\mathrm{\alpha }}_{3t}{\left(\frac{{\mathrm{\tau }}_{23}}{s_{23}}\right)}^2$
Compression failure in the z-direction	$d_{3c}$ = ${\left(\frac{{\mathrm{\sigma }}_{33}}{x_{3c}}\right)}^2$ + ${\mathrm{\alpha }}_{3c}{\left(\frac{\frac{{\mathrm{\tau }}_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathit{\alpha }}_s{\mathrm{\tau }}_{13}^4}{\frac{s_{13}^2}{2G_{13}}+\frac{3 }{4}{\mathrm{\alpha }}_s{s}_{13}^4}\right)}^2$ + ${\mathrm{\alpha }}_{3c}{\left(\frac{{\mathit{\tau }}_{23}}{s_{23}}\right)}^2$

Where ${\mathrm{\sigma }}_{ij}$ , ${\mathrm{\tau }}_{ij}$ , ${\text{X}}_{\mathit{i}}$ , $s_{ij}$ , and ${\mathrm{\alpha }}_i$ (i, j = 1, 2, 3) are the normal stress, shear stress, maximum normal strength, maximum shear strength, and shear contribution factors, respectively. Maximum normal and shear strength for modeling the failure of the woven Kevlar fibers plies are taken from previous relevant literature ⁴² and are given in Table 10.

Table 10.

Damage initiation properties of woven Kevlar fibers. ⁴²

Longitudinal tensile strength, X1t (MPa)	Longitudinal compressive strength, X1c (MPa)	Transverse tensile strength, X2t (MPa)	Transverse compressive strength, X2c (MPa)	Transverse tensile strength, X3t (MPa)
1000	200	1000	200	200
Transverse compressive strength, X3c (MPa)	Longitudinal shear strength, S12 (MPa)	Transverse shear strength, S23 (MPa)	Transverse shear strength, S13 (MPa)	Longitudinal shear strength, S12 (MPa)
200	200	200	200	200

Yuan Zhou et al. ⁴³ classify 3D Hashin into three types base on its shear contribution factors, presented in Table 11. The first type ⁴⁴ was used in this simulation.

Table 11.

Classification of shear contribution factors in the Hashin 3D model. ⁴³

Type	${\mathrm{\alpha }}_{1\mathit{t}}$	${\mathrm{\alpha }}_{1\mathit{c}}$	${\mathrm{\alpha }}_{2\mathit{t}}$	${\mathrm{\alpha }}_{2\mathit{c}}$	${\mathrm{\alpha }}_{3\mathit{t}}$	${\mathrm{\alpha }}_{3\mathit{c}}$	${\mathrm{\alpha }}_{\mathit{s}}$
First type	1	1	1	1	1	1	0
Second type	0	1	1	1	1	1	0
Third type	1	0	1	1	1	1	Constant

Discretization

The ARRAL plane was developed by using three types of an element. Shell element with reduced integration (S4R) was used for aluminum sheets. Also, the linear brick element with reduced integration (C3D8R) was used for Kevlar fabric. Finally, a brick-shaped CZE with eight noded (COH3D8) was assigned to the epoxy layers. To increase the accuracy of the numerical results, all layers were meshed by the intensive elements with the size of 300 μm. The number and types of elements allocated for each part are presented in Table 12. It is important to mention that this simulation required more than 160 h computational analysis using 3 GHz 8-core processor and 20 Gb of RAM.

Table 12.

The number and types of elements allocated for each part.

Part	Type of element	Number of elements
Aluminum plate	S4R	221,778
Projectile	C3D10M	20,246
Epoxy	COH3D8	438,244
Kevlar fabric	C3D8R	332,667

Model validation and discussion

Table 13 shows the detailed results obtained from the simulation. The numerical results of residual velocity are compared with the experimental ones to validate the finite element model. Figure 10 shows experimental and numerical residual velocity as a function of SiO₂ nanoparticles loading.

Table 13.

Simulation results of high-velocity impact test on ARALL samples with different SiO₂ nanoparticles loading (wt.%).

SiO2 nanoparticles (wt.%)	V50 (m/s)	Vr (m/s)	Vi (m/s)
0	59.059	101	117
2	74.75	90	117
3.5	82.46	83	117
5	66.88	96	117

Figure 10.

Residual velocity as a function of SiO₂ loading.

As can be seen, the numerical results are in good agreement with experiment results. However, there are differences in some results especially in samples with 5 wt.% SiO₂ nanoparticles. These differences can be related to the difference in materials, procedures of mixing, and curing conditions, which yield different amounts of nanoparticle agglomeration. Figure 11 shows the numerical prediction of stress distribution in each component of ARALL samples after complete perforation.

Figure 11.

The numerical prediction of stress distribution in each component of ARALL samples.

As can be seen, the most damaged parts are the epoxy layers placed between aluminum and Kevlar fabric. The reason is the bending stiffness mismatch between aluminum and Kevlar fabric which induces huge stress to their epoxy-rich interface. Also, the total damage in epoxy layers decreases as the nanoparticles’ loading increases in epoxy resin. This is because of an increase in the toughness of epoxy. However, in sample containing 5 wt.% SiO₂, because of agglomeration of nanoparticles, the toughness of epoxy decreases and so the total damage in the epoxy layers increases again.

Conclusions and further research

Conclusions

In this study, the influence of incorporation of ceramic nanoparticles (SiO₂ and ZrO₂) into epoxy resin on the high-velocity response of Kevlar fibers-epoxy/aluminum laminate composites was investigated. The high-velocity impact response of each sample was used to determine specific energy absorption and ballistic limit velocity. A typical fractography of samples was conducted to determine the interlaminar failure mechanism which affects energy absorption capacity. Five FESs of the high-velocity impact test on samples containing SiO₂ nanoparticles were also applied to predict the residual velocity and model the impact response. The results of the investigation were as follows:

1. In all samples containing modified epoxy, the specific energy absorption and ballistic limit velocity were higher than the sample containing neat epoxy.

2. The reason for an increase in energy absorption of ARALL samples is the change in the interlaminar failure mechanism from matrix cracking to fibers breakage.

3. The specific energy absorption and ballistic limit velocity of samples containing SiO₂ nanoparticles increased more than ZrO₂ nanoparticles. It attributes to a lower density of SiO₂.

4. The highest growth rates in specific energy absorption were at 3 wt.% SiO₂ and 5 wt.% ZrO₂ by 130% and 91%, respectively.

5. The FES results, including residual velocity, were in good agreement with the experimental analysis, verifying the simulation model.

Suggestions for future research

1. Limitations in the incorporation of nanoparticles within an epoxy matrix could be overcome by using the sol-gel process in the epoxy resin.

2. Surface modification of nanoparticles could also be applied to enhance specific energy absorption of ARALL to a higher extent.

3. Impact modeling of Kevlar fabric using the actual geometry of yarns would yield more promising results.