Numerical investigation of impact-induced damage of auxiliary composite fuel tanks on Korean Utility Helicopter

Composites Part B 165 (2019) 301–311

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Numerical investigation of impact-induced damage of auxiliary composite fuel tanks on Korean Utility Helicopter

T

Dong-Hyeop Kima, Sang-Woo Kima,∗ a

Department of Mechanical Engineering, Hankyong National University, Anseong-si, Gyeonggi-do, 17579, Republic of Korea

ARTICLE INFO

ABSTRACT

Keywords: A. Laminates B. Impact behavior C. Finite element analysis (FEA) C. Damage mechanics

This study analysed the impact-induced damage on the auxiliary composite fuel tank of a Korean Utility Helicopter. A coupled Eulerian–Lagrangian method was applied to consider the sloshing of fuel inside the tank. The composite damage modes were contemporarily considered by applying the Hashin failure criteria. We found that the degraded area due to the large and global deformation of the fuel tank generally decreases as the amount of fuel increases. However, the completely failed area due to the large and global deformation was altered by the strengths dominantly reflected into Hashin failure criteria. Meanwhile, the local damage and failure near the impact point generally increase due to the repulsive force induced by the inertia of the fuel as the amount of fuel increases. Accordingly, the impact behavior and damage according to the amount of the fuel will be used to build the basic data for bird strike tests and safety assessment of liquid-filled composite tanks.

1. Introduction Aircraft composite structures, including fuel tanks used in the aerospace industry, are exposed to low-velocity impacts, such as bird strikes, as illustrated in Fig. 1. In reality, a bird strike is substantially critical and detrimental to structural safety. In the United States, bird strikes annually cost the aviation industry $495 million in damage. Bird strikes also caused 47 fatal accidents, which killed 242 people from 1912 to 2004 [1–3]. Evidently, structural safety and its validation should be assessed to minimize damage cost, as well as prevent fatal failures [1–3]. Moreover, a bird strike test for evaluating the structural safety of aircrafts is not only inevitable, but also important in flight certification and validation. However, it is time consuming and expensive. Thus, several studies [4–8] have been conducted to reduce the time and cost required for impact tests by minimizing the number of test trials through numerical analysis prior to the tests. Lannuchi et al. [4] analysed bird strikes on a composite plate by modeling it using a new woven glass failure model. Shmotin et al. [5] modeled the bird based on the smoothed particle hydrodynamics (SPH) method and performed the impact analysis of the bird strike on the fans of a turbofan engine. Thereafter, they compared the results of SPH method with those of the Lagrangian method. Belega et al. [6] and Ugrčić et al. [7] also modeled the birds based on SPH method and simulated the bird strike on aircraft wing structures having an isotropic behavior. Smojver et al. [8] modeled the birds based on coupled

∗

Eulerian-Lagrangian (CEL) method and investigated the effect of bird strike on composite aircraft wing structures. Among aircraft components, the damage on fuel tanks because of explosions or fire resulting from external impacts can directly cause injury and affect passenger life and safety. Consequently, the safety of these tanks are critical components in the safety certification of aircrafts. Thus, the structural safety of fuel tanks should be thoroughly examined. Yang et al. [9] investigated the coupled behavior between fluids and structures by the drop impact test for helicopter fuel tanks. Kim et al. [10] and Cheng et al. [11] numerically analysed the safety and validity of external auxiliary fuel tanks of the rotorcraft for crash impact tests. Kim et al. [12] also analysed the influence of the amount of internal fuel in bird strike tests on the external auxiliary fuel tank of the rotorcraft. However, previous researchers [4–12] have not investigated the effect of bird strikes on damage modes and the extent of damage on composite fuel tanks considering the sloshing effect of liquid fuel. For a fact, the structural behavior and damage of liquid-filled auxiliary fuel tanks made of composite materials are considerably complex as the liquid fuel in the tank unstably fluctuates because of the impact made by external objects. Moreover, the occurrence and propagation of damage in composite materials with anisotropic properties are complicated and dissimilar to isotropic materials. Meanwhile, the currently operating transport utility helicopter (KUH) of Surion Derivatives developed by the Korea Aerospace Industry, Ltd. will be equipped with auxiliary composite fuel tanks.

Corresponding author. E-mail address: [email protected] (S.-W. Kim).

https://doi.org/10.1016/j.compositesb.2018.11.117 Received 25 March 2018; Received in revised form 11 November 2018; Accepted 27 November 2018 Available online 29 November 2018 1359-8368/ © 2018 Elsevier Ltd. All rights reserved.

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Fig. 1. Risk of low-velocity impacts on helicopter fuel tanks.

These tanks should achieve the airworthiness certification, as well as pass the impact simulation and bird strike tests. Accordingly, we numerically investigated the impact behaviors of the auxiliary composite fuel tanks on the KUH series to save the time and costs as a part of the preparation for achieving the airworthiness certification prior to the bird strike tests. A finite element analysis (FEA) was performed using a finite element simulator, ABAQUS/Explicit. We examined the effect of the amount of liquid fuel (i.e., 50 and 100 vol%) on impact behaviors and absorption energy by considering the sloshing effect of the liquid fuel using the CEL method. The damage modes and failure tendencies of the composite fuel tanks were further investigated based on the Hashin failure criteria.

from conventional isotropic materials and complicated in their tendencies in relation to damage and failure. Moreover, the damage in composite materials are generally initiated without significant plastic deformation. The Hashin failure criteria are mainly used for the prediction of damage in orthotropic and brittle composite materials [15,16]. This study applied the Hashin failure criteria to progressive damage analysis so as to predict the failures of four composite damage modes, given in Eqs. (1)–(4), as follows:

F ft =

11 Xt

2. Coupled Eulerian–Lagrangian method

F fc =

11 Xc

Fig. 2 shows the schematic explanation of the Lagrangian and Eulerian models. In the Lagrangian method, the movement of the continuum is specified as a function of time and material coordinates. Thus, the nodes of the Lagrangian mesh are deformed together with the material. This means that the interface between the two parts is precisely tracked and defined [13]. However, the errors of the Lagrangian method increase when it is used for the excessive distortion of elements in the large deformation analysis. The Eulerian method complements the vulnerability of the Lagrangian method. In the Eulerian method, the movement of the continuum is specified as a function of time and spatial coordinates. Nodes of the material freely move through Eulerian meshes. Consequently, elements are not distorted. This study used the CEL method, which is mainly employed in a large deformation analysis to consider both the sloshing effect of the liquid fuel and structural behavior because of the bird strike. It is an analytical method with the coupled advantages of the Lagrangian (mainly applied to solid mechanics) and Eulerian (mainly applied to fluid mechanics) methods. The Eulerian parts in ABAQUS/Explicit is executed by the Eulerian volume fraction (EVF) in the CEL analysis. For elements fully filled with materials, EVF is 1.0, whereas for those that are completely empty, EVF is 0.0 [13,14].

Fmt =

Fmc =

22

Yt

22 2S T

2

2

for

2

+

2

+

2

12 SL

+

11

for

11

0,

(1)

< 0,

12

SL

2

(2)

for

YC 2S T

0,

22

2

1

22 Yc

(3)

+

12 SL

2

for

22

< 0,

(4)

where σij is the principal stress, and τij is the shears stress. Here, the subscripts, ‘‘ij’’ (i, j = 1, 2), “f”, and “m” indicate the respective principal directions of the material, fiber, and matrix, respectively. Moreover, F, X, Y, and S denote the failure modes, strengths in two respective directions of the material, and shear strengths, respectively. The superscripts, “c”, “t”, “T”, and “L” mean compressive, tensile, transverse, and longitudinal, respectively. The contribution of the shear stress to the fiber tensile initiation criterion is expressed as α. Equations (1)–(4) represent the Hashin failure criteria for four damage modes, specifically fiber tension, fiber compression, matrix tension, and matrix compression. The status of the material for each mode is regarded to be fully failed if the value calculated in Eqs. (1)–(4) is 1. Unidirectional composite materials show several damage modes (fiber breakage, matrix cracks, etc.) according to direction. If damage is considered in Hooke's law in the constitutive model, the relationship between the true stress matrix (σ) and strain matrix (ε) can be rearranged by applying degradation parameters (d), as given in the following equation [17]:

3. Progressive damage and failure model Composite materials have orthotropic properties that are different

Fig. 2. Concepts of the Lagrangian and Eulerian models [13].

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Table 1 Material properties of water.

= Cd (1 =

d f ) E1

1 (1 df )(1 D E2 0

dm )

(1 12

df )(1 (1

dm )

21 E1

0

d m ) E2 0

0 (1

,

ds ) GD (5)

where σ, ε, Cd, Ek, νkl, and G are stress, strain, stiffness matrix with damage, Young's modulus, Poisson's ratio, and shear modulus, respectively. The parameter D is given as:

D=1

(1

df )(1

dm) v12 v21.

Properties for equation of state (EOS)

Value

Unit

Speed of sound Slope of Us-Up relation Grüneisen ratio Density Dynamic viscosity

1450 0 0 996 1E-6

m/s – – kg/m3 m2/s

Table 2 Mechanical properties and Hashin damage parameters of the composite material.

(6)

The subscripts, “d”, “f”, “m”, “kl” (k, l = 1, 2) denote damage, fiber, matrix, and principal directions of the material, respectively. The stiffness matrix with damage has a similar form with the stiffness matrix without damage. However, material properties in the stiffness matrix with damage are reduced by degradation parameters. Their value is between 0 (for undamaged state) and 1 (for completely degraded state).

Parameters

Symbol

Value

Unit

Mechanical properties

E1 E2 , E3 v12 , v13 v23 G12 , G13 G23

143.4 9.27 0.31 0.52 3.8 3.2

GPa GPa mm/mm mm/mm GPa GPa

4. Finite element analysis

Hashin damage parameters

Xt Xc Yt Yc

2.945 1.650 54 240 106.8

GPa GPa MPa MPa MPa

Fig. 3 shows the calculation model for the composite fuel tank. Fig. 3(a) and (b) present geometries of the calculation model and stacking sequence of composite parts, as well as the load and boundary conditions in the simulation. The calculation model of FEA primarily consists of four parts: fuel, composite tank, impactor, and jigs. The liquid fuel was created as an Eulerian model, whereas the others were built as Lagrangian models.

SL ST

106.8

MPa

4.1.2. Composite tanks and others Carbon fiber and epoxy resin were used as laminates for the composite fuel tank. The mechanical properties and Hashin damage parameters similar to the actual composites used in the composite fuel tank of KUH are listed in Table 2. The predesigned stacking sequence of S#1([(0°/90°/45°/135°)3]s) was basically applied to the composite tank, as shown in Fig. 3(a). Meanwhile, the additional impact analysis was performed for the other stacking sequence of S#2([(0°/45°/90°/135°)3]s) to investigate the effect of ply angle on the impact behavior of the composite fuel tank. The thickness of each ply and all plies are 0.1 and 2.4 mm, respectively. A three-dimensional (3D) shell element (S4R) was applied to represent the composite tank, with a total number of nodes and elements of 48,371 and 48,364, respectively. The gravity refueling cap made of aluminum and positioned at the top of the tank has a Young's modulus of 71.7 GPa, and Poisson's ratio of 0.33. Moreover, the general mechanical properties of steel, i.e., Young's modulus of 207 GPa and Poisson's ratio of 0.266, and 3D four-node element (C3D4) were applied to the jigs. Their total number of nodes and elements are 17,951 and 58,031, respectively. The impactor has a Young's modulus of 7 GPa and

4.1. Simulation model 4.1.1. Fuel Fuels of 50 and 100 vol% were designated as Eulerian reference parts in order to investigate the impact absorption energy according to the amount of fuel, as shown in Fig. 3(a). Here, 100 vol% of fuel corresponds to the position of the surface of the fuel, which is 42.4 mm away from the gravity refueling cap installed on top of the tank. The dimensions of the Eulerian part are 1130 mm × 670 mm × 880 mm, which are larger than the dimensions of the tank. The Eulerian brick element (EC3D8R) was used, and the total number of nodes and elements were set as 46,368 and 42,525, respectively. A kerosene-based jet fuel, JP-8, is utilized for the transport utility helicopter of Surion Derivatives. However, the material properties of water generally used in the dropping impact tests of helicopter fuel tanks [9] were applied in the simulation instead of the properties of JP8 as a conservative approach. The material properties of water used in the Eulerian reference parts are summarized in Table 1 [9,13].

Fig. 3. Geometries of calculation models and basic stacking sequence of composite parts. 303

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Poisson's ratio of 0.4. Its material properties were determined by referring them to the properties of a bird's beak [18] as conservative approaches. The impactor is a sphere with a radius of 50 mm and mass of 0.99 kg, corresponding to the mass of a typical bird. A 3D eight-node element (C3D8R) is applied to represent the impactor with a total number of nodes and elements of 3,991 and 3,416, respectively.

nodes instantaneously increased at approximately 0.7 and 0.6 ms (slightly varying with respect to stacking sequence) for the fuel with 50 and 100 vol%, respectively. The sudden pressure increase in the 100 vol % fuel was ahead of the pressure increase in the 50 vol% fuel because the relatively small cavity in the tank containing the former suppressed the motion of the liquid fuel, resulting in an immediate increase of the internal pressure. Thereafter, the internal pressures of the fuel steadily decreased, varying up to a time of 3.0 ms. In the case of the S#1, the maximum pressures of 11.62 (11.57 for S#2) and 27.25 (27.7 for S#2) MPa were calculated for the fuel with 50 and 100 vol%, respectively. Consequently, it was found that the maximum internal pressure increases as the amount of fuel increases. Thus, we expected that the amount of fuel can substantially affect the sloshing of the fuel, as well as the structural behavior and safety of the composite tank at impact. Fig. 5 shows the structural behavior of the composite fuel tank according to the amount of fuel and stacking sequence during the impact, and the detailed values are illustrated in Table 4. As shown in Fig. 5 and Table 4, the differences of impact behaviors (deflection, contact force, absorption energy) of the composite fuel tank according to stacking sequence were not clearly observed. The contact force-time curve is illustrated in Fig. 5(a) for investigating the contact forces between the impactor and composite fuel tank according to the amount of fuel during the impact. The maximum contact forces increased from 113.2 to 188.7 kN (slightly varying with respect to stacking sequence) as the amount of fuel increased from 50 to 100 vol%. The increase in the internal pressure, which depends on the amount of fuel, increased the maximum contact force between the impactor and composite fuel tank. For all cases, the contact forces suddenly decreased due to the fiber failure in tension of the composite fuel tank. After then, the contact forces increased again until reaching to the maximum contact force. This means that the composite plies of the fuel tank still retained their load-carrying capacity although the equivalent stiffness significantly decreased. Fig. 5(b) represents the deflection curve according to time during impact. Generally, the maximum deflection increases as the maximum contact force increases [19–21]. However, in this analysis, the deflection decreased with the increase of the contact force because of the fuel; for the S#1, the maximum deflections of the fuel tank for 50, and 100 vol% fuels are approximately 31.6 (31.6 for S#2), and 18.2 (18.1 for S#2) mm, respectively. This is because the repulsive forces of the fuel, added to the internal pressure of the fuel, were applied to the surface of the composite tank during the impact, as shown in Fig. 4. This reduced the deflection of the composite tank with the increase in the volume of fuel even though their contact forces increased. Concurrently, the contact force-deflection curves were derived, and their closed areas were contemporarily estimated to examine the absorption

4.2. Calculation conditions The kinematic couplings between the jigs and the tank were applied using tie constraints provided in ABAQUS. The constrained regions (tied surfaces) are indicated by the oblique pattern in red, as illustrated in Fig. 3(b). The end points of the jigs were constrained by the pinned condition, as follows:

U1 = U2 = U3 = UR2 = UR3 = 0 and UR1

0,

(7)

where Un and URn are translational and rotational degree of freedom (DOF), respectively. The subscripts, represented by ‘‘n’’ (n = 1, 2, 3), indicate the principal axes for the DOF. The impactor was struck with 71.7 m/s along the x-axis at the center of the fuel tank, as shown in Fig. 3(b). The velocity was determined by considering the relative and standard velocities of the helicopter and bird. The dynamic analyses were performed during 6 ms using ABAQUS/Explicit. 5. Results 5.1. Impact behavior and absorption energy Table 3 presents the sloshing behavior of the fuel in the composite tank, and Fig. 4 shows the pressure of the fuel acting on the composite tank according to the amount of fuel and stacking sequence. The suddenly applied impact force generated waves at the surface of the fuel, as shown in Table 3. We found that the sloshing behavior of the fuel did not depend on the given stacking sequences but the amount of the fuel. The sloshing of 50 vol% fuel generated waves larger than those of the fuel with 100 vol% because the inertia of the latter, which has more mass, is larger than that of the former with less mass. Moreover, a relatively large cavity in the tank with 50 vol% fuel allows for the sloshing to be easily generated. Fig. 4(a)–(b) and 4(c)–(d) show pressure histories with respect to time during the impact for the internal fuel with 50 and 100 vol%, respectively. Fig. 4(a) and (c) show pressure histories for the stacking sequence of S#1, and Fig. 4(b) and (d) illustrate those of S#2. The pressure histories did not also depend on the given stacking sequence, similarly to sloshing of the fuel. The pressures calculated at the Eulerian

Table 3 Sloshing behavior of fuel in the composite tank caused by impact.

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Fig. 4. Pressure history of fuel according to the amount of fuel and stacking sequence during the impact.

Fig. 5. Structural behavior of the composite fuel tank due to the impact.

of the failed area was evaluated. It is only 3.72% and 3.87% of the failed area for S#1 and S#2, respectively. The tendency of failed region for S#1 and S#2 was also very similar each other. For the fiber damage mode in tension and the matrix damage mode in compression, the locally failed area near the impact point was clearly observed when the fuel tank had 100 vol% fuel. The fuel tank with 100 vol% fuel did not relatively experience the large and global deformation as well as the corresponding high stresses making the fiber (with high longitudinal tensile strength (Xt)) or matrix (with high transverse compressive strength (Yc)) to be broken, compared to the fuel tank with 50 vol% fuel. Therefore, the wide range of fiber damage in tension and matrix damage in compression was not observed in the fuel tank with 100 vol% fuel. However, it experienced the severe local stress which makes the reinforced fiber and matrix to be broken due to the high maximum contact forces and the repulsive force induced by the fuel. The fuel tank with 50 vol% fuel suffered global deformation and thus the large and wide degraded region was observed although the completely failed area was small due to the high longitudinal tensile strength (Xt) and transverse compressive strength (Yc) of the composite. In the cases of the fiber damage mode in compression and the matrix damage mode in tension, the effect of the global deformation on the structural failures was clearly observed because the longitudinal compressive strength (Xc), transverse tensile strength (Yt) are relatively

Table 4 Results of structural behaviors of the composite fuel tank. Amount of fuel

Stacking sequence

Max. deflection

Max. contact force

Absorption energy

50 vol%

S#1∗ S#2∗∗ S#1 S#2

31.6 mm 31.6 mm 18.2 mm 18.1 mm

113.2 kN 114.5 kN 188.7 kN 183.2 kN

2.346 kJ 2.330 kJ 1.732 kJ 1.697 kJ

100 vol%

∗ ∗∗

S#1: [(0°/90°/45°/135°)3]s S#2: [(0°/45°/90°/135°)3]s

energy of the impact with respect to the amount of fuel [22], as shown in Fig. 5(c). We found that the absorption energy decreased by 614–633 J (slightly varying with respect to stacking sequence) as the amount of fuel increased from 50 to 100 vol%. This is similar to the results presented by Razaghi et al. [23]. Moreover, the failed area affected by the amount of the fuel was estimated by assessing the elements that were removed, satisfying the Hashin failure criteria. Table 5 shows the degraded region and failed area for four composite damage modes with respect to the amount of fuel and stacking sequence. They were not significantly affected by the given stacking sequences but the amount of fuel. For the matrix damage mode in tension with 50 vol% fuel, 152 cm2 of the maximum difference 305

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S#2

54.0 cm2

103 cm2

S#1

47.6 cm2

118 cm2

Matrix compression

D.-H. Kim, S.-W. Kim

lower than the longitudinal tensile strength (Xt), transverse compressive strength (Yc) of the composite. Of course, the structural failures induced by the local stress near the impact point were also observed in the fiber damage mode in compression and the matrix damage mode in tension. Therefore, both the wide and local damages near the impact point simultaneously occurred as the fuel tank was globally more deformed with a decrease of the amount of fuel. Consequently, the increase in the amount of fuel reduces the absorption energy, and negatively affects the failure of local area near the impact point. However, the degraded area due to the large and global deformation generally decreases as the amount of fuel increases. Of course, the completely failed area due to the large and global deformation was altered by the strengths dominantly reflected into Hashin failure criteria.

2,346 cm2 2,447 cm2 495 cm2

152 cm2

346 cm2

167 cm2

346 cm2

921 cm2

5.2.1. A composite tank with 50 vol% fuel 5.2.1.1. Fiber failure. Fig. 6 shows the fiber damage modes in tension (Fig. 6(a)) and compression (Fig. 6(b)), and Fig. 7 presents the stress (σ11) distribution (Fig. 7(a)) and fiber damage in tension and compression on the composite plies with 0°, 90°, 45°, and 135° fiber direction (Fig. 7(b)) at 1 ms after the impact. The failure of the fiber tension near the impacted region primarily occurred at the lower part, referred from the fuel surface, as shown in Fig. 6(a). Because of the inertia of the fuel, the repulsive force, generated at the relatively narrow impacted region, led to the severe damage of the relatively narrow region. The fibers in tension were damaged along the fiber direction, as shown in Fig. 6(a). Under the equal strain condition, the stress along the fiber direction during the impact is relatively greater than that along the transverse direction of the fiber because the former is stiffer than the latter based on their material properties and Hooke's law. As shown in Fig. 7(a), the fiber damage in tension for the fuel tank with 50 vol% fuel can be explained by the longitudinal tensile stress (σ11 > 0) distribution. This is because the longitudinal tensile stress (σ11 > 0) is dominantly reflected in the equation of the fiber damage in tension (Eq. (1)) among the Hashin failure criteria. Therefore, the tendency of the tensile stress (σ11 > 0) distribution (Fig. 7(a)), was similar to that of the fiber damage in tension (Fig. 7(b)). The stress (σ11 > 0) distribution was converged to the center of the impact point from the outermost ply (Ply 1) to the innermost ply (Ply 24) in the outof-plane direction, as shown in Fig. 7(a). Thus, the distribution of the corresponding degraded region for fiber damage in tension on each ply was also converged to the center of the impact point from the outermost ply to the innermost ply in the out-of-plane direction, as shown in Fig. 7(b). The fiber damage in compression primarily occurred at the upper part, referred from the fuel surface as shown in Fig. 6(b) because the upper part of the fuel tank without the fuel was more deformed during the impact than the lower part filled with the fuel. Moreover, the deformation at the upper part negatively affects to the failure of the fiber in compression of the fuel tank due to the relatively lower longitudinal compressive strength (Xc). However, the local failure of the fiber in compression at the impacted region more rapidly progressed in the lower part filled with fuel due to the narrow compression of the impactor, as shown in Fig. 7(b). The fibers in compression were damaged along the transverse direction of the fiber during the impact, as shown in Fig. 6(b), whereas the tensile failure occurred along the fiber direction, as illustrated in Fig. 6(a). The fiber failure in compression is explained by the structural

100 vol%

50 vol%

The damage mode and tendency of the fuel tank according to the amount of fuel were investigated. However, the stacking sequence of the composite fuel tank was not considered anymore because it has little effect on the impact behavior of the fuel tank during the impact, as mentioned above section 5.1.

500 cm2

4,081 cm2 890 cm2

S#1 S#2 S#1 S#1

S#2

Fiber compressizon Fiber tension

Degraded region and failed area Amount of fuel

Table 5 The degraded region and failed area with respect to the amount of the fuel and stacking sequence.

Matrix tension

S#2

3,929 cm2

5.2. Structural damage of the composite fuel tank

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Fig. 6. Fiber damage modes in tension and compression (50 vol%; 6 ms).

behavior, i.e., the compressive stress (σ11 < 0) in the fibers occurred because of the compressive deformation as an effect of the in-plane Poisson’ ratio when the deformation in the transverse direction of the fibers toward the center of the impact was generated during the impact, as shown in Fig. 7(a). This compressive stress (σ11 < 0) induced the fiber failure in compression, as shown in Fig. 7(b). In the case of each ply of the composite fuel tank, the fiber damage in compression occurred because of the compressive stress (σ11 < 0), as shown in Fig. 7(a); it is dominantly reflected in the Hashin failure criteria for fiber damage in compression (Eq. (2)). Therefore, the tendency of the compressive stress (σ11 < 0) distribution, as shown in Fig. 7(a), was similar to the tendency of the fiber damage in compression illustrated in Fig. 7(b). For each ply of the composite fuel tank, the stress distribution (σ11 < 0) in the region subjected to compression spread to the region far from the impact point, from the outermost ply to the innermost ply in the out-of-plane direction, as shown in Fig. 7(a). Therefore, the distribution of the corresponding degraded region for fiber compression on each ply also spread to the region far from the impact point, from the outermost ply to the innermost ply in the out-ofplane direction, as shown in Fig. 7(b).

matrix, two failure modes in tension and compression were observed. For the matrix damage in tension, the tensile deformation in the fiber direction was suppressed by the reinforced fibers with a relatively higher stiffness. However, the tensile deformation in the transverse direction was easily generated because of the relatively lower stiffness of the composites (with comparable mechanical properties of matrix) in the transverse direction. Therefore, the matrix failure and damage in tension were suppressed in the fiber direction and primarily occurred in the transverse direction of the fiber as shown in Fig. 8(a). The matrix failure in tension occurred at the upper part as well as the lower part, referred from the fuel surface, regardless of the amount of fuel, as shown in Fig. 8(a). It is different to the fiber damage modes. The failure of fiber tension was dominantly affected by the local stress during the impact rather than by the large and global deformation. However, the large and global deformation as well as the local stress during the impact was sufficient to cause the matrix failure in tension due to the low transverse tensile strength (Yt) of the composite. Actually, the matrix degradation and failure in tension, induced by the wide and large deformation, contributed to the increase of the relatively large energy absorption for 50 vol% fuel, as mentioned above in section 5.1. Meanwhile, the matrix barely experienced the failure in compression compared to the matrix damage in tension. Moreover, the degradation of the tensile stiffness of the matrix more rapidly progressed than that of the compressive stiffness. This is because the transverse

5.2.1.2. Matrix failure. Fig. 8 presents the matrix damage modes in tension (Fig. 8(a)) and compression (Fig. 8(b)) for all composite plies when the composite fuel tank contains 50 vol% fuel. In the case of the

Fig. 7. Stress (σ11) distribution and fiber damage for 0, 90, 45 and 135° plies (50 vol% fuel; 1 ms). 307

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Fig. 8. Matrix damage modes in tension and compression (50 vol%; 6 ms).

tensile strength (Yt) is substantially lower than the transverse compressive strength (Yc) of the composite, as summarized in Table 2. Thus, the tensile failure of the matrix occurred earlier and was considerably severe than its compressive failure; the former and the latter occurred at 0.7 and 0.82 ms, respectively. Therefore, the matrix failure in compression was barely observed, when compared with its tensile failure, as shown in Fig. 8(b).

the distribution on the outermost ply (Ply 1) was converged to the center of the impact point on the innermost ply (Ply 24), as shown in Figs. 9(a) and 10(b). This tendency was also similar to the tendency of the composite tank with 50 vol% fuel. As shown in Fig. 9(a), different tendencies of damage were also observed in the composite fuel tank with 100 vol% fuel, i.e., unexpected damage was generated. For the 20th and 24th plies of the composite fuel tank, fiber failure in tension occurred at the left side of the region that sustained the impact because of the geometric effect. The local stress concentration was generated because of the significant change in geometry, i.e., the small radius of curvature. Moreover, the greater repulsive forces because of the 100 vol% fuel further accelerated the stress concentration. This region subjected to fiber failure can be regarded as a structurally vulnerable area. The fiber damage in compression for the composite fuel tank with 100 vol% fuel was similarly observed in that having 50 vol% fuels, i.e., the fibers were damaged along the transverse direction of fibers, as shown in Fig. 9(b). As mentioned in section 5.2.1.1, the compressive stress (σ11 < 0) induced by the compressive deformation was generated by the structural behavior due to the in-plane Poisson's ratio, as shown in Fig. 10(a), when a composite layup suffered the tensile deformation in the transverse direction of fibers during the impact. In the case of each ply, the compressive stress (σ11 < 0) induced the fiber damage in compression, as shown in Fig. 10(a) because it was dominantly applied as reflected in the Hashin failure criteria (Eq. (2)). Therefore, the compressive stress (σ11 < 0) distribution (Fig. 10(a)) was similar to the distribution of the fiber damage in compression (Fig. 10(b)). Moreover, the distribution of the region subjected to the compressive stress (σ11 < 0) in the out-of-plane direction of the 100 vol% fuel was similar to that of the 50 vol% fuel; it spread to the region far from the impact point, from the outermost ply (Ply 1) to the innermost ply (Ply 24), as shown in Fig. 10(a). Therefore, in all the plies, the distribution of the corresponding degraded region under fiber compression was also spread to the region far from the impact point, from the outermost ply to the innermost ply, as shown in Fig. 10(b). As shown in Fig. 9(b), for the 1st, 3rd, 4th, and 5th plies, the fiber

5.2.2. A composite tank with 100 vol% fuel For the fuel tank with 100 vol% fuel, the symmetrical tendency of failure of the four failure modes with respect to the impact point was observed in all composite plies, which is different from the tendency of the failure modes of the composite fuel tank with 50 vol% fuel. 5.2.2.1. Fiber failure. Fig. 9 shows the fiber damage modes in tension (Fig. 9(a)) and compression (Fig. 9(b)), and Fig. 10 presents the stress (σ11) distribution (Fig. 10(a)) and fiber damage in tension and compression on the 0°, 90°, 45°, and 135° plies (Fig. 10(b)) at 1 ms after the impact. The tendency of the fiber damage in the tank containing 100 vol% fuel was different from that of the 50 vol% fuel. For the 100 vol% fuel, the failure of the fiber symmetrically occurred with reference to the impact point, as shown in Fig. 9(a) and (b). This means that the effect of the presence of fuel on the damage direction of the structure is negligible because of the approximately symmetric condition of the fuel with reference to the impact point when the tank is filled with 100 vol% fuel. In tension, the fibers were similarly damaged as that of the composite fuel tank with 50 vol% fuel, which means that they were broken along the fiber direction, as shown in Fig. 9(a). For each ply, the fiber damage in tension was primarily determined by the longitudinal tensile stress (σ11 > 0) because it was dominantly reflected in the Hashin failure criteria for fiber damage in tension (Eq. (1)). Thus, the tendency of the tensile stress (σ11 > 0) distribution, as shown in Fig. 10(a), was similar to that of the fiber damage in tension, as illustrated in Fig. 10(b). Moreover, the distribution of the degraded region for fiber tension in the out-of-plane direction was investigated. For all the plies, 308

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Fig. 9. Fiber damage modes in tension and compression (100 vol%; 6 ms).

damage in compression also occurred at the left side of the impacted region because of the stress concentration. The reason for the generation of the local stress concentrations in compression is the same as that in the generation of the stress concentration in tension, which is because of the significant change in geometry and repulsive forces, as mentioned above. This region can also be regarded as a structurally vulnerable area.

mechanical properties of the matrix. Moreover, the matrix failure in tension widely occurred as shown Fig. 11(a), whereas the matrix failure in compression was barely observed, as shown in Fig. 11(b). This is because the tensile stiffness of the matrix was degraded earlier than its compressive stiffness because the transverse strength in tension (Yt) was considerably lower than the transverse strength in compression (Yc), as mentioned above in section 5.2.1.2. The tensile failure of the matrix occurred earlier than its compressive failure, i.e., the former and the latter occurred at 0.71 and 0.78 ms, respectively. Moreover, the degradation of the matrix stiffness in compression evolved along the fiber direction, where the matrix failure in tension was suppressed by the reinforced fibers. Therefore, the matrix damage in compression was slightly observed along the direction of the reinforcement, when compared with those in tension, as shown in Fig. 11(b).

5.2.2.2. Matrix failure. Fig. 11 presents the matrix damage modes in tension (Fig. 11(a)) and compression (Fig. 11(b)) in all composite plies when the composite fuel tank contains 100 vol% fuel. For the 100 vol% fuel, the failure of the matrix symmetrically occurred, measured from the impact point, as shown in Fig. 11(a) and (b). This was because of the approximately symmetric condition of the fuel, referred from the impact point, when the tank is filled with 100 vol% fuel. As shown in Fig. 11(a), the direction of the tensile failure of the matrix for the composite fuel tank with 100 vol% fuel was similar to that with 50 vol% fuel. For the matrix failure in tension, the tensile deformation in the fiber direction was suppressed by the reinforced fibers. This is because the reinforced fibers in the longitudinal direction are stiffer than those in the transverse direction, and dependent on the

6. Conclusion We studied the impact-induced damage of the auxiliary composite fuel tank of KUH caused by bird strike. The four failure modes of the composite plies were examined by applying the Hashin failure criteria,

Fig. 10. Stress (σ11) distribution and fiber damage for 0, 90, 45 and 135° plies (100 vol% fuel; 1 ms). 309

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Fig. 11. Matrix damage modes in tension and compression (100 vol%; 6 ms).

whereas the CEL method was applied to consider the sloshing of fuel. According to the damage mode, the damages of the fuel tank were generally propagated in the specific direction, and the degraded region was converged or spreads in the out-of-plane direction. We additionally found that the amount of fuel had a great impact on the damage and failure of the fuel tank. That is, the effect of the amount of fuel on the structural damage and failure varies according to damage mode and material property (especially the magnitude of strength) as follows:

1C1B2010417). This work was also supported by Korea Aerospace Industry, Ltd. Authors are grateful for their support. References [1] Eschenfelder C, Paul F. High speed flight at low altitude: hazard to commercial aviation? Birdstrike committee proceedings. Vancouver, July. 2005. [2] Working Paper WPII-3. Fatalities and destroyed civil aircraft due to bird strikes 2002 to 2004. Proceedings of IBSC27 conference. Athens, May. 2005. p. 65. [3] Cleary EC, Dolbeer RA, Wright SE. Wildlife strikes to civil aircraft in the United States 1990–2005. Birdstrike committee proceedings. Washington DC, june. 2006. [4] Lannuchi L, Donadon M. Bird strike modeling using a new woven glass failure model. 9th international LS DYNA users conference. 2006. [5] Shmotin YN, Chupin PV, Gabov DV, Ryabov AA, Romanov VI, Kukanov SS. Bird strike analysis of aircraft engine fan. 7th European LS-DYNA conference. 2009. [6] Belega BA. Impact simulation with an aircraft wing using SPH bird model. INCAS Bulletin 2015;7(3):51–8. [7] Ugrčić M, Maksimović SM, Stamenković DP, Maksimović KS, Nabil K. Finite element modeling of wing bird strike. FME Transactions 2015;43:82–7. [8] Smojver I, Ivančević D. Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach. Compos Sci Technol 2011;71(4):489–98. [9] Yang X, Zhang Z, Yang J, Sun Y. Fluid-structure interaction analysis of the drop impact test for helicopter fuel tank. SpringerPlus 2016;5(1):1573. [10] Kim HG, Kim SC. Numerical analysis of crash impact test for external auxiliary fuel tank of rotorcraft. Journal of the Korea Academia-Industrial cooperation Society (JKAIS) 2017;18(3):724–9. [11] Cheng LUO, Hua LIU, Yang J, LIU K. Simulation and analysis of crashworthiness of fuel tank for helicopters. Chin J Aeronaut 2007;20(3):230–5. [12] Kim HG, Kim SC. A numerical study on the influence of the amount of internal fuel in a bird strike test for the external auxiliary fuel tank of rotorcraft. Int J Crashworthiness 2017;12(14):1–15. [13] Abaqus Abaqus. Analysis user's manual, version 6.11. Dassault Systèmes 2011. [14] Qiu G, Henke S, Grabe J. Application of a Coupled Eulerian-Lagrangian approach on geomechanical problems involving large deformations. Comput Geotech 2011;38(1):30–9. [15] Hashin Z. Failure criteria for unidirectional fibre composites. J Appl Mech 1980;47(2):329–34. [16] Hashin Z, Rotem A. A fatigue failure criterion for fibre-reinforced materials. J Compos Mater 1973;7(4):448–64. [17] Matzenmiller A, Lubliner J, Taylor RL. A constitutive model for anisotropic damage in fibre-composites. Mech Mater 1995;20(2):125–52. [18] Soons J, Herrel A, Aerts P, Dirckx J. Determination and validation of the elastic

1. The degraded area due to the large and global deformation generally decreases as the amount of fuel increases. 2. However, the completely failed area due to the large and global deformation altered by the strengths dominantly reflected into Hashin failure criteria. 3. In case of two damage modes (fiber damage in compression and matrix damage in tension), the large failed area is estimated when the fuel tank has less fuel because the dominant strengths (Xc and Yt) affecting Hashin failure criteria are relatively low. 4. Meanwhile, the local damage and failure near the impact point generally increase due to the repulsive force induced by the inertia of the fuel as the amount of fuel increases. Therefore, we expect that the structural integrity and safety of the composite fuel tank with liquid fuel increased if the fiber with the strengthened compressive strength and matrix with the strengthened tensile strength are applied to the composite fuel tank. Furthermore, the impact behavior and damage, based on the amount of fuel in the tank, will be used as the basic data for bird strike tests, safety assessment, and airworthiness certification of the liquid-filled auxiliary composite tank of KUH. Acknowledgement This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NO. 2016R

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[21] Kim EH, Rim MS, Lee I, Hwang TK. Composite damage model based on continuum damage mechanics and low velocity impact analysis of composite plates. Compos Struct 2013;95:123–34. [22] Manikandan P, Chai GB. A Layer-wise behaveoral study of metal based interply hybrid composites under low velocity impact load. Compos Struct 2014;117:17–31. [23] Razaghi1 R, Sharavi M, Feizi MM. Investigating the effect of sloshing on the energy absorption of tank wagons crash. Trans Can Soc Mech Eng 2015;39(2):187–200.

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