Keywords

1 Introduction

The percentage and configuration of composite parts used are important parameters indicating aircraft performance [1, 2]. Because of their high strength, design flexibility, and resistance to fatigue failure, as well as their ability to be manufactured in large integral (i.e., one-piece) parts, advanced composite materials are widely used in the integral tank structure to effectively reduce structure weight [3, 4]. Nevertheless, composites are associated with their own issues. For example, during use composite parts may occasionally experience impacts by foreign objects, such as birds, stones (on the runway), or tools (accidentally dropped during repairs). Such impacts can cause matrix cracking, delamination, fiber rupture, or other damage modes in composite structures. This damage severely affects the structural safety of an aircraft and, thus, has been extensively investigated. The residual mechanical properties (under tension, compression, and shear) of composite structures after a low-energy impact are a major current topic of research [5, 6]. In addition, the structures adjacent to the fuel tank work under substantial bending loads due to fuel pressure and can deform considerably [7, 8]. Therefore, the out-of-plane bending properties of these structures and the residual bending performance after impact must be considered in the structural design.

The previous research were mainly focused on the bending of composite plate and sandwich structure. The typical structures adjacent to the fuel tank were seldom studied [9]. Luo Liang studied the compression after impact performance for T300/NY9200Z, T300/QY8911 and T700S/5228. Fracture mechanics behavior by means of mechanical numerical simulation The research results indicated that there are homologous knee points in these curves and these points which the damage mechanisms change significantly [10, 11]. Gong Xiaohui the studied low-velocity impact properties and three-point bending properties of the composite foamed-sandwich foam composites. The bending strength and stiffness of the foam sandwich composite board can be effectively improved, and the bending performance of the sandwich structure is effectively improved because of stiffeners [12]. Meng Xiangyao studied the three-point bending damage evolution and fracture mechanics behavior by means of mechanical numerical simulation [13]. The present study investigated the post-impact bending characteristics of typical structures (spar cap) adjacent to the fuel tank. The spar cap specimens (under two conditions) were subjected to four-point bending, the test results shown that it was consistent with the working conditions of an actual structure adjacent to the fuel tank under condition 1. Progressive failure analysis was performed based two-dimensional Hashin failure for intralaminar failure model and bilinear traction separation constitutive model is adopted for interlaminar failure model. The results shown that the appearance and internal damage morphology obtained by the simulation are consistent with experimental results.

2 Four-Point Bending

2.1 Structure of Test Specimens

Structures adjacent to the fuel tank experience high loads generated by the fuel pressure and, thus, can deform considerably. The out-of-plane bending properties of these structures are important considerations in the structural design of aircraft. Here, two typical structures adjacent to the tank, a spar cap and a spar web, were studied (Fig. 1).

Samples were prepared using prepregs fabricated from carbon fiber fabric and unidirectional tapes. Prepregs were plied and cured in an autoclave (SCHOLZ, Germany; diameter: 4 m, temperature departure: ±3 ℃, ramp: 0–3 ℃/min, cooling: 0–5 ℃/min).

The spar cap layer:

  • P1: [±45/02/ ± 45/02/±452/02/±45/02/±45] (thickness: 2.427 mm);

  • P2: [±45/02/±452/0/±452/02/±45] (thickness: 2.545 mm).

Please note that the first paragraph of a section or subsection is not indented. The first paragraphs that follows a table, figure, equation etc. does not have an indent, either. Subsequent paragraphs, however, are indented.

Fig. 1.
figure 1

Schematic representation

Full size image

The materials used for preparation of test specimens are domestic carbon fiber fabric 5224/CF3052 and unidirectional tape 5224/U3160; the mechanical properties of these materials are shown in Table 1.

Table 1. Mechanical properties of composite materials
Full size table

2.2 Spar Cap Bending Testing

Considering the spar cap deforms considerably under the bending load during operation, we tested the bending properties of this structure using a four-point bending test (ASTM D 7264) under two constraint conditions (Fig. 2). Under Condition 1 (Figs. 2a and 3a), two supporting pins (6 mm) were placed on a horizontal plane, and the distance between the pins (support span) was adjusted and fixed to 44 mm (±0.1 mm). The sample was allowed to straddle the pins, and a U-shaped loading head was inversely placed on the sample. The head contacted the sample via its round ends (6.0 ± 0.1 mm). Then a compressive load was applied at 7.5 m/min, and the sample was allowed to flatten and widen freely. Under Condition 2 (Figs. 2b and 3a), two protruding bars were engineered on the plane to prevent the sample from widening during compression; other parameters were identical to Condition 1.

Fig. 2.
figure 2

Diagrams showing four-point bending tests

Full size image

Table 2 shown that all samples fractured at the middle of the curved part under Condition 1, which was consistent with the working conditions of an actual structure adjacent to the fuel tank. Under Condition 2, most samples failed at the regions contacting the loading head, exhibiting a local shearing failure mode. This was inconsistent with the out-of-plane bending condition experienced by a typical structure adjacent to the fuel tank.

Figure 3 shown the load-displacement curve at condition 1, and Fig. 4 shown the load-displacement curve at condition 2. It can be seen that the samples exhibited only one failure mode under Condition 2: local shearing failure at the loading head-sample contact region, and the load at failure was 4–5 times higher than those tested under Condition 1 (out-of-plane bending). Additionally, comparison of results obtained from different ply arrangements (P1 versus P2) indicates that increasing the proportion of 0° plies (P1) also significantly increased the bending strength.

Table 2. Bending test results of spar cap samples
Full size table
Fig. 3.
figure 3

Load-displacement curve at condition 1

Full size image
Fig. 4.
figure 4

Load-displacement curve at condition 2

Full size image

3 Bending Failure Analysis

3.1 Interlaminar Failure Model

The damage constitutive relations of Interlaminar behavior include bilinear, trapezoid, Parabola and exponential models [14, 15]. Considering the damage of adhesive layer is elastic-brittle, the bilinear constitutive model is chosen. σn, σs and σt are used to describe the normal traction stress and shear stress respectively, and the stress-strain relationship of the adhesive interface behavior is [15,16,17]:

$$ {{\varvec{\upsigma}}} = {\mathbf{K}} \cdot {{\varvec{\updelta}}} $$
(1)

where, \({\mathbf{K}} = \left[ {K_{nn} ,K_{ss} ,K_{tt} } \right], \cdot {{\varvec{\upsigma}}} = \left[ {\sigma_{n} ,\sigma_{s} , \cdot \sigma_{t} } \right],{{\varvec{\updelta}}} = \left[ {\delta_{n} ,\delta_{s} ,\delta_{t} } \right]\). \({\mathbf{K}}\) is the elastic stiffness coefficient of the adhesive interface in each stress direction, \({{\varvec{\updelta}}}\) is the opening displacement in each stress direction [15].

When the adhesive interface is damaged, the material shows the softening stage of damage, and the constitutive relation is [15]:

$$ {{\varvec{\upsigma}}} = (1 - {\mathbf{D}}){\mathbf{K}} \cdot {{\varvec{\updelta}}} $$
(2)

where, \({\mathbf{D}}\) is the damage state variable, \({\mathbf{D}}\) = 0, the adhesive layer is not damaged, \({\mathbf{D}}\) = 1, which means that the adhesive is completely failure [15].

According to the description of the properties of the interface adhesive, two criteria are needed to determine the final failure of the adhesive layer [15]: The second Nominal stress Criterion (Quadratic Nominal stress Criterion) is used to determine whether the plastic layer begins to fail; B-K criterion is used to determine whether a rubber layer unit is completely failed and destroyed as the damage propagation criteria [15, 18, 19].

$$ \left( {\sigma_{n} /N_{\max } } \right)^{2} + \left( {\sigma_{s} /S_{\max } } \right)^{2} + \left( {\sigma_{t} /T_{\max } } \right)^{2} = 1 $$
(3)

where, \(N_{\max } ,S_{\max } ,T_{\max }\) are the strength of the interface in each orthogonal direction [15, 18, 19].

$$ G_{IC} + \left( {G_{IIC} - G_{IC} } \right)\left( {G_{{\text{Shear }}} /G_{T} } \right)^{\eta } = G_{TC} $$
(4)
$$ G_{T} = G_{I} + G_{{\text{Shear }}} ;G_{{\text{Shear }}} = G_{II} + G_{III} $$
(5)

where, \(G_{TC}\) is the total release energy; \(G_{I}\), \(G_{II}\) and \(G_{III}\) are the fracture toughness respectively of Type I, Type II and Type III; \(G_{I}\), \(G_{II}\) and \(G_{III}\) are the critical energy release rates of Type I, Type II and Type III; \(G_{{\text{Shear }}}\) is the shear energy release rates; the η is a constant relative to the material (η = 1.45) [15, 18, 19].

3.2 Intralaminar Failure Model

Progressive failure analysis was performed based two-dimensional Hashin failure criteria for intralaminar failure model. Four different failure models are analyzed and processed for initiation mechanism: fiber stretching (FT), fiber compression (FC), matrix stretching (MT) and matrix pressure Shrink (MC).Two-dimensional Hashin failure criteria are as follows 15 [20, 21]:

$$ \begin{gathered} FT = \left( {\hat{\sigma }_{11} /X_{1}^{ + } } \right)^{2} + \left( {\hat{\tau }_{12} /S^{L} } \right)^{2} = 1,\left( {\hat{\sigma }_{11} \ge 0} \right) \hfill \\ FC = \left( {\hat{\sigma }_{11} /X_{1}^{ - } } \right)^{2} = 1,\left( {\hat{\sigma }_{11} < 0} \right) \hfill \\ MT = \left( {\hat{\sigma }_{22} /X_{2}^{ + } } \right)^{2} + \left( {\hat{\tau }_{12} /S^{L} } \right)^{2} = 1,\left( {\hat{\sigma }_{22} \ge 0} \right) \hfill \\ MC = \left( {\hat{\sigma }_{22} /2S^{T} } \right)^{2} + \left[ {\left( {Y^{c} /\left( {2S^{T} } \right)} \right)^{2} - 1} \right]\left( {\hat{\sigma }_{22} /X_{2}^{ - } } \right) + \left( {\hat{\tau }_{12} /S^{L} } \right)^{2} = 1,\left( {\hat{\sigma }_{22} < 0} \right) \hfill \\ \end{gathered} $$
(6)

where, \(X_{1}^{ + }\) \(X_{1}^{ - }\), \(X_{2}^{ + }\), \(X_{2}^{ - }\), \(S^{L}\) and \(S^{T}\) are longitudinal tensile strength, longitudinal compressive strength, and transverse tensile strength, transverse compression strength, longitudinal shear strength and transverse shear strength. \(\hat{\sigma }_{11}\), \(\hat{\sigma }_{22}\) and \(\hat{\tau }_{12}\) is the component of the effective stress tensor along the fiber direction, the transverse stress and in-plane shear stress., which can be calculated from the real stress \({{\varvec{\upsigma}}}\) and damage parameters \({\mathbf{\rm M}}\) [15, 20, 22].

$$ \hat{\user2{\sigma }} = {\mathbf{M}} \cdot {\varvec{\sigma}} $$
(7)
$$ {\mathbf{M}} = \left[ {\begin{array}{*{20}c} {1/\left( {1 - d_{f} } \right)} & 0 & 0 \\ 0 & {1/\left( {1 - d_{m} } \right)} & 0 \\ 0 & 0 & {1/\left( {1 - d_{s} } \right)} \\ \end{array} } \right] $$
(8)

where, \(d_{f}\), \(d_{m}\) and \(d_{s}\) are damage variables related to fiber, matrix and shear damage respectively. Typical curves of linear evolution were used for damage.

3.3 Numerical Simulation Results

The three-dimensional numerical simulation finite element model is established according to the size of the experimental specimen (shown in Fig. 1). The width of cap was 50 mm, and the two lengths of the angel clip were 40 mm. SC8R elements were used to simulation the fabric and unidirectional tape. The loading stick and supporting roller were simulated by the S4R shell elements and the loading stick and supporting roller were in contact with the upper surface and under surface of the specimen by Penalty function (Fig. 5). Cohesive interface contact behavior was defined to simulate the intralaminar failure model. The cohesive interface parameters of the adhesive bonding interface are shown in Table 3.

Fig. 5.
figure 5

Finite element model of bending failure analysis

Full size image
Table 3. Cohesive interface parameters [15]
Full size table

Figure 6 shown the damage photographs under condition 1. Figure 7 shown the Different failure modes: matrix tensile failure, matrix compression failure, fiber tensile failure and fiber compression failure under condition1. It can be seen that all samples fractured at the middle of the curved part. In the simulation, the load was applied and increased incrementally, up to an ultimate load of about 800 N. This was higher than the failure load measured experimentally, and the displacement is lower than load measured experimentally.

Figure 8 shown the load-displacement curves comparison between bending test and numerical simulation of four points bearing under condition 1.The results shown that the appearance and internal damage morphology obtained by the simulation were consistent with experimental results.

Fig. 6.
figure 6

The damage photographs under condition 1

Full size image
Fig. 7.
figure 7

Load-displacement curve at condition 2

Full size image
Fig. 8.
figure 8

Load-displacement curve at condition 2

Full size image

4 Conclusions

Representative composite structures adjacent to the fuel tank were studied for failure mode and strength under out-of-plane bending. Based on the results, the following conclusions are drawn:

  1. (1)

    The bending strengths of the spar cap samples were tested under two experimental conditions. Under Condition 2 (constrained lateral widening), the loading head caused local shearing failure, not satisfactorily simulating the loading pattern of this structure during actual use in an aircraft (out-of-plane bending by fuel pressure).

  2. (2)

    Progressive failure analysis was performed based two-dimensional Hashin failure for intralaminar failure model and bilinear traction separation constitutive model was adopted for interlaminar failure model.