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Oblique penetration mechanism of hybrid composite laminates

  • Meng Han EMAIL logo , Chuwei Zhou , Vadim V. Silberschmidt , Xindong Ma , Mao Liu , Wenan Jiang and Qinsheng Bi
Published/Copyright: October 25, 2021
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Science and Engineering of Composite Materials
From the journal Science and Engineering of Composite Materials Volume 28 Issue 1

Abstract

Hybrid fiber composites are widely used to improve the anti-penetration performance. Carbon/Kevlar hybrid composites are used in aircrafts and safety devices, thanks to the strong toughness of Kevlar fibers and high strength of carbon fibers. In the present work, the contact force of hybrid composites under oblique impact is derived. The viscoelastic constitutive model of Kevlar layer is investigated and the dissipation energies of composites for different high velocity oblique impacts are simulated. The results show that hybrid composites have good bullet-proof performance, the contact forces are fluctuant in short time and the frictional dissipation energy allows us to prevent penetration.

Keywords: contact force; dissipation energy; hybrid composite; oblique penetration

1 Introduction

Composite materials are widely used in the aircraft structures, which should be of certain impedance capability for a variety of complex loads. Due to the high specific strength, low weight, and good resistance, hybrid composites have been widely used [1]. In particular, their behavior under high impact loads is paid more attention in aerospace engineering. There are a lot of experimental and simulated studies in the literature on hybrid composites under high velocity impact tests. Heydari et al. studied, both experimentally and numerically, the elastic modulus of polymers reinforced with nanoclay [2], but the interfacial debonding between matrix and nanoclay was not considered. Xu et al. [3] studied the high velocity penetration resistance of carbon fiber reinforced polymeric (CFRP) and CFRP_aluminum laminates through experimental tests and showed that the carbon fiber reinforced aluminum laminate (CRALL) targets had better penetration resistance to the three shapes of nose projectiles than CFRP in terms of both ballistic limits and energy absorption performance, due to the strain rate hardening effect. Sayer et al. studied the impact response and damage process of hybrid composite plates under low velocity impact [1]. Naresh et al. experimentally and theoretically studied the tensile properties of glass/epoxy, carbon/epoxy, and hybrid (glass-carbon/epoxy) composites [4] influenced by strain rate and showed that failure strain changed with the increase in strain rate. Tirillo et al. investigated the effect of basalt fiber hybridization in carbon/epoxy laminates on high velocity impacts through experiments [5] and showed that the stacking sequence affected the ballistic limit, with the intercalated [(B2/C2)3/B2/C]S configuration exhibiting the highest value among all hybrids. Xie et al. [6] described the correlations between the mechanical performances and different impact factors on the structural integrity of advanced carbon–carbon composites for high temperature through impact tests on heated composite samples. Tao et al. [7] proposed a method to identify crack tip elements with a virtual fatigue damage variable and simulated the delamination in composite materials under fatigue loads using extended cohesive interface elements. Yao et al. [8] experimentally and numerically investigated the successive impact response and accumulated damage of fiber metal laminates under oblique successive impacts. Srivatsava et al. [9] assessed experimentally the dynamic mechanical properties of carbon, Kevlar, hybrid, and sandwich configuration composites and showed that sandwich and hybrid fiber composites exhibited superior damping properties at higher frequencies. Woo and Kim [10] showed that the high strain rate induced failure characteristics in a carbon/Kevlar hybrid composite subjected to high strain rate compressive loading using a novel SHPB-AE coupled test.

Only a few theoretical research studies on the hybrid composite under the high velocity impact are available in the literature. Sanchez-galvez et al. presented an improved analytical model which considered oblique impact [11], which is able to predict with high accuracy both the ballistic limit and the residual velocity. The analytical model has been worked to analyze also the impact on hybrid composite material targets [12].

Oblique impact is common in the flight accidents, such as bird impact, hail impact, and aero-engine fan released blade impact. Carbon/Kevlar hybrid composite is the optimal material with impact resistance potential, and the research on high velocity oblique impact over 200 m/s is scarce. In this article, the contact force of hybrid composites under oblique impact is derived based on the cavity expansion theory, and the strain rate-dependent property of Kevlar, the stress distribution, damage dissipation, and frictional dissipation energies are simulated, in order to reveal the mechanism of oblique penetration and provide suggestions for the design of protective equipment.

2 Contact force analysis of hybrid composite

High velocity impact is a penetration process, so the cavity expansion theory [13,14] needs to be employed to analysis. The normal stress σ n of projectile nose [15], which is penetrating into the target, is equal to the radial stress σ r :

(1) σ n = σ r .

The frictional stress σ τ is obtained by:

(2) σ τ = μ σ r .

The normal resistance σ z n and tangential one σ z τ can be calculated as:

(3) σ z n = σ r cos θ + σ t sin θ = σ r ( cos θ + μ sin θ ) , σ z τ = σ r sin θ − σ t cos θ = σ r ( sin θ − μ cos θ ) ,

where μ is the sliding friction coefficient, θ is the angle between the curvature radius of tip and dotted line (d) paralleled with axial direction of projectile, and α is the angle between axis of projectile and horizontal plane of target, as shown in Figure 1.

Figure 1 Penetration diagram of hybrid fiber laminates.
Figure 1

Penetration diagram of hybrid fiber laminates.

The normal force and axial resistance force of the projectile nose can be obtained as [16]:

(4) d F n = 2 π s 2 ( sin θ − sin θ 0 ) σ n d θ , d F z = 2 π s 2 ( sin θ − sin θ 0 ) σ z d θ , d F z τ = 2 π s 2 ( sin θ − sin θ 0 ) σ z τ d θ ,

where θ 0 is the angle between the line (oa) and the dotted line (d) paralleled with axis of the projectile, as shown in Figure 1; point “o” is the tip node of projectile, point “a” is the intersection node between local reference system of projectile and surface of target, and “s” is the length of line (oa).

According to equations (1), (3), and (4), the following equations can be obtained:

(5) d F n = 2 π s 2 σ r ( sin θ − sin θ 0 ) d θ , d F z = 2 π s 2 σ r ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) d θ , d F z τ = 2 π s 2 σ r ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) d θ .

So the force components in the global coordinate system of target are calculated as:

(6) d F z ′ = d F z sin α + d F z τ cos α , d F x ′ = d F z cos α − d F z τ sin α .

The radial stress on the surface of the projectile nose can be calculated with the velocity and angle as follows [17]:

(7) σ r ( V z , θ ) / Y = 2 3 1 + 2 E 3 Y n ∫ 0 1 − ( 3 Y − 2 E ) ( − ln x ) n 1 − x + 3 2 [ ( ρ t / Y ) 1 / 2 V z cos θ ] 2 ,

where ρ t and Y are the density of plate material and the yield strength of plate material, respectively, A and B are constants related to the characteristics of the plate materials, and V z is the impact velocity of the projectile.

According to equations (5)–(7), the contact force of target can be obtained as:

(8) F z ′ = 2 π s 2 sin α ∫ θ i θ j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A Y + B ρ t V z 2 cos 2 θ ) d θ + cos α ∫ θ i θ j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A Y + B ρ t V z 2 cos 2 θ ) d θ F x ′ = 2 π s 2 cos α ∫ θ i θ j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A Y + B ρ t V z 2 cos 2 θ ) d θ − sin α ∫ θ i θ j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A Y + B ρ t V z 2 cos 2 θ ) d θ .

Because the hybrid composite plate has lots of layers with different fibers, the penetration process can be considered to contain different stages.

At the initial stage, the projectile has not contacted the target, F z ′ = F x ′ = 0 . When the projectile nose contacts the top surface of the target, it is supposed that the effective displacement z is the initial value zero. The total thickness and the number of layers of target are L t and m , respectively.

  1. Before the nose wholly penetrates into the target ( 0 < z sin α ≤ L h ) , the contact force can be calculated as:

    (9) F z ′ = 2 π s 2 sin α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ + cos α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ F x ′ = 2 π s 2 cos α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ − sin α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ ,

    where the total layers penetrated of target n = floor ( z sin α / h ) and n ≤ m ; L h is the thickness of each layer; A k and B k are the constants related to the characteristics of the k layer; Y k and ρ t k are the yield strength and density of the k layer, respectively; and V z k is the impact velocity of projectile on the k layer.

  2. After the nose wholly penetrates into the target and before it is out through the bottom surface ( L h < z sin α ≤ L t ) , the contact force of the shank in the local coordinate system of projectile can be obtained as:

    (10) F z − shank = ∑ k = floor L h sin α h + 1 floor ( z − L h ) sin α h 2 a π Y k μ k h k .

    So the contact force of shank in the global coordinate system of target can be obtained as follows:

    (11) F z ′ − shank = F z − shank sin α F x ′ − shank = F z − shank cos α .

    The contact force of projectile of target can be calculated as:

    (12) F z ′ = 2 π s 2 sin α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ + cos α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ + ∑ k = floor L h sin α h + 1 floor ( z − L h ) sin α h 2 a π Y k μ k h k sin α , F x ′ = 2 π s 2 cos α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ − sin α ∑ k = 1 n ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ + ∑ k = floor L h sin α h + 1 floor ( z − L h ) sin α h 2 a π Y k μ k h k cos α .

  3. Before the nose is wholly out through the target ( L t < ( z sin α ) ≤ ( L t + L h ) < L ) , the contact force of nose in the global coordinate system of target can be obtained as:

    (13) F z ′ − nose = 2 π s 2 sin α ∑ k = floor L h − z + L target h sin α floor L target h sin α ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ + cos α ∑ k = floor L h − z + L target h sin α floor L target h sin α ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ F x ′ − nose = 2 π s 2 cos α ∑ k = floor L h − z + L target h sin α floor L target h sin α ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( cos θ + μ sin θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ − sin α ∑ k = floor L h − z + L target h sin α floor L target h sin α ∫ θ k i θ k j ( sin θ − sin θ 0 ) ( sin θ − μ cos θ ) ( A k Y k + B k ρ t k V z k 2 cos 2 θ ) d θ .

    The contact force of shank in the global coordinate system of target can be obtained as:

    (14) F z ′ − shank = ∑ k = 1 floor ( L h − z + L target ) sin α h 2 a π Y k μ k h k sin α , F x ′ − shank = ∑ k = 1 floor ( L h − z + L target ) sin α h 2 a π Y k μ k h k cos α .

    So the contact force of the whole projectile can be obtained as:

    (15) F z ′ = F z ′ − nose + F z ′ − shank F x ′ = F x ′ − nose + F x ′ − shank .

  4. After the nose penetrates out the target and before the end of shank penetrates into the target ( ( L t + L h ) < ( z sin α ) ≤ L ) , the contact force of nose equals to zero, so the contact force of projectile can be calculated as:

    (16) F z ′ = F z ′ − shank = F z − shank sin α = ∑ k = 1 m 2 a π Y k μ k h k sin α , F x ′ = F x ′ − shank = F z − shank cos α = ∑ k = 1 m 2 a π Y k μ k h k cos α .

  5. Before the end of the shank penetrates out of the target ( L < ( z sin α ) ≤ ( L + L t ) ) , some parts of shank stay in the target, so the contact force of projectile can be calculated as:

    (17) F z ′ − shank = F z − shank sin α = ∑ k = floor z − L h m 2 a π Y k μ k h k sin α , F x ′ − shank = F z − shank cos α = ∑ k = floor z − L h m 2 a π Y k μ k h k cos α .

  6. After the end of shank penetrates out of the target ( ( L + L t ) < ( z sin α ) ) , the contact force equals to zero.

3 Mechanical model

3.1 Constitutive model

It has been proved that the epoxy material has a viscoelastic behavior and the Kevlar/epoxy composite presents obviously strain rate-dependent property. The rate-dependent constitutive model of Kevlar fiber was based on a literature work [18], and it is used to investigate impact resistance performance of hybrid composite by employing the VUMAT subroutine of Abaqus.

The two-term nonlinear spring-dashpot system model was employed [19], the constitutive model of Kevlar layers considered damage was investigated, and a new damage factor D 0 ε ̇ ε ̇ 0 a was proposed, reflecting the influence from strain rate. The constitutive model was written as follows:

(18) σ = 1 − D 0 ε ̇ ε ̇ 0 a E 0 ε + α ε 2 + β ε 3 + E 1 φ 1 ε ̇ 1 − exp − ε ε ̇ φ 1 + E 2 φ 2 ε ̇ 1 − exp − ε ε ̇ φ 2 ,

where φ 1 = η 1 E 1 , φ 2 = η 2 E 2 . The viscoelastic properties of Kevlar/epoxy are shown in Table 1 (Figure 2).

Table 1

Viscoelastic properties of Kevlar/epoxy

E 0 (GPa) E 1 (GPa) E 2 (GPa) η 1 (GPa s) η 2 (GPa s) D 0 a α β
409 387 351 8.5 16.89 0.70 0.052 −4,321 5,872
Figure 2 Nonlinear viscoelastic model.
Figure 2

Nonlinear viscoelastic model.

3.2 Failure criterion

Hashin’s failure criterion is widely used to predict the failure of component structures, and the failure modes are modified due to the effects from strain rate as follows [20]:

Tensile fiber mode, σ 11 ≥ 0 :

(19) σ 11 T 11 ⁎ 2 + λ τ 12 S 12 ⁎ 2 + λ τ 13 S 13 ⁎ 2 ≥ 1 .

Compressive fiber mode σ 11 < 0 :

(20) − σ 11 C 11 ⁎ ≥ 1 .

Tensile matrix mode σ 22 + σ 33 ≥ 0 :

(21) σ 22 + σ 33 T 22 ⁎ 2 + τ 23 2 − σ 22 σ 33 ( S 23 ⁎ ) 2 + τ 12 2 + τ 13 2 S 12 ⁎ ≥ 1 .

Compressive matrix mode σ 22 + σ 33 < 0 :

(22) σ 22 + σ 33 2 S 12 ⁎ 2 + ( σ 22 + σ 33 ) 2 4 ( S 23 ⁎ ) 2 + τ 23 2 − σ 22 σ 33 ( S 23 ⁎ ) 2 + τ 12 2 + τ 13 2 S 12 ⁎ ≥ 1 ,

where λ is the shear correction factor; T 11 ⁎ and C 11 ⁎ are longitudinal tension and compression strengths of unidirectional laminate in the corresponding strain rate, respectively; T 22 ⁎ and C 22 ⁎ are transverse tension and compression strengths of unidirectional laminate in the corresponding strain rate, respectively; and S 12 ⁎ , S 13 ⁎ , and S 23 ⁎ are the shear strengths in the corresponding strain rate, respectively.

4 Simulation

4.1 Simulation model

The oblique impact simulation model of carbon/Kevlar epoxy composite laminate was established, the thickness of target panel was 7.5 mm, the length and width were all 30 mm, carbon and Kevlar layers were alternant and orthogonally layered with [0°/90°], the bullet was rigid, and its radius was 25 mm, which impacted the hybrid composite laminate along 45° with the initial velocity. The target panel was meshed with 30,000 elements, as shown in Figure 3.

Figure 3 Oblique impact simulation model.
Figure 3

Oblique impact simulation model.

Abaqus/explicit subroutines were developed to define some variables and functions, in order to realize the rheological behaviors of Kevlar and hybrid composites, and to reappear the progressive penetration processes of targets on the serial velocity oblique impacts, and the flow chart of simulation is shown in Figure 4.

Figure 4 Flow chart of simulation in VUMAT.
Figure 4

Flow chart of simulation in VUMAT.

4.2 Simulation results

4.2.1 Stress distribution

The stress and progressive damage of oblique impact were simulated with Abaqus software. When the bullet impacted target first, stress concentration on the contact point appeared (Figure 5a), then the stress contour showed butterfly pattern on the back surface of target (Figure 5b). When the bullet penetrated the bottom of target, the area of high stress expanded and showed cross pattern (Figure 5c–g). When the bullet penetrated the target wholly, the range of stress concentration kept stable (Figure 5h and i).

Figure 5 Simulated stress contours of 800 m/s oblique impact: (a) 5 μs, (b) 10 μs, (c) 15 μs, (d) 20 μs, (e) 25 μs, (f) 30 μs, (g) 35 μs, (h) 40 μs, and (i) 45 μs.
Figure 5

Simulated stress contours of 800 m/s oblique impact: (a) 5 μs, (b) 10 μs, (c) 15 μs, (d) 20 μs, (e) 25 μs, (f) 30 μs, (g) 35 μs, (h) 40 μs, and (i) 45 μs.

4.2.2 Contact force

The contact force vs time curves of carbon, Kevlar, and carbon/Kevlar hybrid composite laminates were plotted in different velocities (Figure 6). It showed that contact force of hybrid composite laminate was 11% lower than single composite laminate on the same velocity. That means the hybrid composite reduces the impact velocity effectively.

Figure 6 Contact forces of simulation: (a) carbon, (b) Kevlar, and (c) hybrid.
Figure 6

Contact forces of simulation: (a) carbon, (b) Kevlar, and (c) hybrid.

4.2.3 Damage dissipation energy

The damage dissipation energies of single and hybrid composite laminates on a series of impact velocities were investigated (Figure 7). It showed that damage dissipation energies of hybrid composite laminate were 16.6–40% lower than single composite laminate, and hybrid composite showed excellent damage resistance ability. Carbon/Kevlar hybrid composite combined the high strength of carbon and excellent toughness of Kevlar, so when the bullet impacted the target, the damage dissipation energy was reduced by combined actions from different composites. With the increase in initial impact velocity, the damage dissipation energy increased due to the failure of fibers. In the impact time, the damage dissipation energy showed three-stage non-linear characteristic. At the initial impact, the damage dissipation increased slowly before 5 μs, then it increased rapidly with impact at the range of 5–15 μs, because the most damages occurred in this stage. Increase rate of damage dissipation energy was gentle after 15 μs.

Figure 7 Damage dissipation energy of simulation: (a) carbon, (b) Kevlar, and (c) hybrid.
Figure 7

Damage dissipation energy of simulation: (a) carbon, (b) Kevlar, and (c) hybrid.

4.2.4 Frictional dissipation energy

The frictional dissipation energy also showed three-stage non-linear trend with impact (Figure 8). It increased rapidly for short time and reached stability in the end. Kevlar composite showed the superior absorption ability, so the hybrid composite target was produced with Kevlar to prevent the penetration.

Figure 8 Frictional dissipation energy of simulation: (a) carbon, (b) Kevlar, and (c) hybrid.
Figure 8

Frictional dissipation energy of simulation: (a) carbon, (b) Kevlar, and (c) hybrid.

Total dissipation energy of targets was calculated for different impact velocities (Figure 9). It showed “energy dissipation velocity effect”: dissipation energy was increased with the increase in impact velocity.

Figure 9 Simulated dissipation energy of composites.
Figure 9

Simulated dissipation energy of composites.

5 Conclusion

The oblique penetrations of hybrid composite target with bullet on the different velocities were investigated. The contact force of laminate was derived theoretically and plotted from simulation in impact process. The frictional dissipation energy was the action to prevent penetration. Damage and frictional dissipation energies both showed three-stage non-linear trend. Contact force of hybrid composite laminate was 11% lower than single composite laminate on the same velocity. Damage dissipation energies of hybrid composite laminate were 16.6–40% lower than single composite laminate, which showed the excellent damage resistance ability of hybrid composite. The results of this article suggested the design of engine case.

  1. Funding information: This work was partially supported by National Natural Science Foundation of China (Grant No. 12102152) and State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (Grant No. MCMS-E-0221Y02).

  2. Conflict of interest: Authors state no conflict of interest.

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Received: 2021-05-07
Revised: 2021-08-19
Accepted: 2021-09-24
Published Online: 2021-10-25

© 2021 Meng Han et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/secm-2021-0054
Keywords for this article
contact force; dissipation energy; hybrid composite; oblique penetration
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