Experimental and numerical study on compression-after-impact behavior of composite panels with foam-filled hat-stiffener

Ocean Engineering 198 (2020) 106991

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Experimental and numerical study on compression-after-impact behavior of composite panels with foam-filled hat-stiffener Da Liu a, Ruixiang Bai a, **, Zhenkun Lei a, *, Jingjing Guo a, Jianchao Zou a, Wen Wu a, Cheng Yan b a b

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, 4001, Australia

A R T I C L E I N F O

A B S T R A C T

Keywords: Low-speed impact Compression-after-impact Composite stiffened panel Foam-filled hat-stiffener

Compression-after-impact tests were used to investigate the impact resistance of composite panel with hatstiffener filled with foam via good energy absorption. The low-speed impact tests were conducted on three different locations, and then fringe projection profilometry was used to measure the full-field deflection of composite panels during compression. The experimental results show that local buckling occurs during compression of the free-impacted panels, and material compression damage of the impacted panels is caused by impact damage. The residual compressive strength of the stiffened panels is different because of damage of the stiffened panels at different impact locations. Finally, finite element simulation was performed to analyze the damage propagation in the compression-after-impact and the effect on the ultimate failure. The strain history, full-field deflection and numerical simulation results are of reference significance for the impact resistance design of hat-stiffened composite panels.

1. Introduction Fiber reinforced resin composites are commonly used in the marine industry due to their better corrosion resistance, higher specific strength and design freedom compared to metal or wood (Kolanu et al., 2016; Tarfaoui and El Moumen, 2018; Tran et al., 2018). The composite panel with foam-filled hat-stiffener (FFHS) is suitable for marine engineering structures (Sutherland, 2018a). The hat stiffener geometric features are fully enclosed, with many geometric parameters and large optimization space (Jin et al., 2015). It is expected to improve the structure impact resistance via using the good energy absorption of soft foam materials, which is widely used in the composite industry (Zhang et al., 2013; Ismail et al., 2019; Cantwell and Morton, 1991; Bibo and Hogg, 1996). A low-speed impact (such as tool drop during maintenance, floating objects impact) is one of the most common threats for conventional �lu et al., composite panels used in marine and ship structures (Balıkog 2018; Zenkert, 2009). If the FFHS composite panel was impacted by objects, there would be a small permanent indentation in the skin, and the stiffness of the impacted panel would decrease (Sutherland and Soares, 2012; Abrate, 2005, 2011; Richardson and Wisheart, 1996). In

particular, the composite panel with local damage will have more complex buckling and post-buckling phenomenon, which will cause local large deformation, including fiber fracture, matrix cracking, delamination, debonding and stiffener/skin separation, and finally lead to structure sudden failure (Li and Chen, 2016; Cestino et al., 2016; Ouyang et al., 2018). Therefore, it is important to study the mechanical behavior of foam core hat-stiffened composite panel under low-speed impact and the residual strength under compression-after-impact (CAI). Many scholars have performed experiments and numerical studies on impact and CAI behaviors of composite laminates to investigate the mechanism of impact damage propagation and its effect on residual compression strength. Wang et al. (2019) established an analysis model using the energy principle and variational method in applied mechanics. As a result, the residual strength of synthetic foam sandwich panels with lattice webs was predicted. Yang et al. (2015) manufactured foam-filled sandwich panels using six types of face sheets including pure carbon fiber, glass fiber, and mixed fiber via a vacuum-assisted resin injection process. The impact response and residual strength of different sandwich panels were then studied via CAI experiments. Although the numerical model can be used to analyze and optimize the design of the CAI

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (R. Bai), [email protected] (Z. Lei). https://doi.org/10.1016/j.oceaneng.2020.106991 Received 20 September 2019; Received in revised form 15 December 2019; Accepted 18 January 2020 Available online 30 January 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved.

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projector respectively. Q represents a point on the object surface to be measured; Pr and Cr are projections of the line PQ and CQ on the reference plane respectively. Without considering the influence of nonlinear error, standard sinusoidal fringes are projected from the projector and reflected by the surface of the measured object, which are then captured by the camera. The intensity of the signal acquired by the camera can be expressed as follows:

composite structure and the buckling characteristics can be accurately predicted, a large number of experimental data are needed to strictly verify the correctness of the numerical models (Sutherland and Soares, 2005; Sutherland, 2018b). Moreover, it is necessary to reveal and confirm the CAI failure mechanism, especially the similarities and dif­ ferences of failure mechanisms at different impact locations have not been fully considered (Feng et al., 2016; Sun et al., 2018a). The development and evolution of buckling modes are the basic characteristics of marine stiffened panel deformation. By establishing a numerical model to analyze and optimize the design of CAI composite structures, their buckling characteristics can be accurately predicted. The key aspect is to use an abundance of experimental data to strictly verify the correctness of the numerical model. Advanced experimental measurement techniques can be used to effectively monitor the defor­ mation process of composite stiffened panels (Cucinotta et al., 2016). Fringe projection profilometry (FPP) has the advantages of non-contact, full-field measurement (Zhang, 2018; Van der Jeught and Dirckx, 2016). Moreover, this approach facilitates the monitoring of the deflection characteristics of whole composite stiffened panels in the process of compression buckling, and allows for the effective analysis of the compression buckling behavior of composite stiffened panels based on experimental data. The buckling behaviors of stiffened panels under the load of shear or compression were studied using the FPP (Bai et al., 2017, 2018; Lei et al., 2012, 2016; Liu et al., 2019) and the CAI behavior of composite foam core sandwich panels using digital image correlation (Bai et al., 2019). In contrast, the FPP is more suitable for the study of the CAI behavior of the composite stiffened panel with discontinuous surface. In order to investigate the CAI behavior of FFHS composite panel, in this study, the impact tests with different low-speeds and locations, and the CAI tests of the FFHS composite panels were performed. The FPP was used for full-field deflection detection of the panels. According to the strain gauges and optical measurement, the buckling evolution behavior of the panels during CAI testing is analyzed and the effect of different impact damage locations on the compression residual strength is dis­ cussed. Finally, a finite element model was established to determine the damage propagation mode and ultimate failure modes of the panel during compression testing after impact at different locations, and the numerical results were compared to the experimental data.

Ii ðx; yÞ ¼ I0 ðx; yÞ þ Im ðx; yÞsin½φðx; yÞ þ iδ� ;

(1)

where I0 is the direct current component and is susceptible to ambient light. Im is the fundamental frequency modulation amplitude and is susceptible to the reflectivity of the surface. When the standard sinu­ soidal fringes are twisted by the object’s surface, the phase value ϕ contains the height information of the point Q. If the N-step phaseshifting method is used, then δ ¼ 2π/N is the phase-shifting quantity, and i (¼1, 2, …, N) corresponds to each step of the phase-shift. The expression for the phase value ϕ is obtained by the least square method as follows: PN Ii ðx; yÞcosðiδÞ ϕw ðx; yÞ ¼ arctan Pi¼1 : (2) N i¼1 Ii ðx; yÞsinðiδÞ The wrapped phase ϕw 2 [-π, π] is obtained this arctangent function, which is related to ϕ as follows: ϕ ¼ ϕw þ 2kπ,

(3)

where k is a positive integer, and the process of solving for k is called “phase unwrapping”. There have been numerous studies on the related phase unwrapping algorithm. We choose a dual-frequency unwrapping algorithm (Yu et al., 2017) here that can be used to measure the surface morphology of discontinuous objects stably. Using the same method to measure the reference plane, the phase ϕ0 can be obtained. Therefore, the phase difference Δϕ can be obtained as, Δϕ ¼ ϕ-ϕ0.

(4)

For a linear FPP system (Zhang et al., 2018) with CP//PrCr, as shown in Fig. 1, the height h at the point Q is obtained by using the triangular similarity relation ΔCPQ ∽ ΔCrPrQ, which is related to the phase dif­ ference Δϕ of the point as

2. Principle of FPP

h¼

To analyze the failure modes of the composite stiffened panels after impact at different locations, the FPP was used to measure their full-field buckling during compression experiments. Fig. 1 shows a typical FPP optical layout. C and P represent the location of the camera and

lpΔφ ; 2πd þ pΔφ

(5)

where l and d are the distances from the camera to the reference plane and the projector respectively, and p is the pitch of the fringes. They are invariants in the measurement, so they can be inversely solved via calibration. Subsequently, the morphology of the object can be recon­ structed by solving for the phase difference Δϕ. In the experiment, the wrapped phase was obtained using a four-step phase-shifting method and the unwrapped phase was then obtained using a multi-frequency unwrapping algorithm. The gamma error was eliminated using an inverse phase method (Lei et al., 2015). Before the experiment, a calibration block was used to calibrate the system and the relationship between the height and phase difference was obtained by least square fitting. After completion of the calibration process, the out-of-plane displacement of the measured object was obtained using Eq. (5). 3. Experiment 3.1. Sample description Four single hat-stiffened composite panel specimens with dimensions of 440 mm � 260 mm were used. The shape and specific size of the sections are shown in Fig. 2(a). The skin and stiffener was made of

Fig. 1. A typical model for FPP. 2

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composite material ZT7G/LT-03A, the single layer thickness was 0.125 mm, and the specified length direction of the stiffened panel was 0� . Among them, the skin thickness was 2 mm, the laying layer was [45/90/ 0/-45/0/-45/45/0]s; the hat-stiffener thickness was 0.5 mm, the laying layer was [-45/90/45/0], and the outermost layer of the hat-stiffener is 0� . The core material is PMI-B75-X foam, and the panel-panel adhesive is LWF-2B adhesive film. The core of the hat-stiffener was filled with foam core and the filler was filled in the R-region at the bottom of the foam core (the filler is a ZT7G/LT-03A one-way belt wrapped by one layer of LWF-2B adhesive film). Fabrication of the panels was performed using the glue-bonding and co-curing process. In this approach, the skin initially solidifies and subsequently, glue-bonding and co-curing are performed using the foam and the stiffener. The end of the sample was strengthened using glass fiber laminates. An image of the specimen is shown in Fig. 2(b).

of artificial visual inspection of impact pit, namely, the impact pit was invisible to the naked eye at a distance of 1.5 m, which was regarded as the principle of no maintenance. For the three impact locations in this study, the corresponding crit­ ical impact energy needed to be determined through three impact ex­ periments, in other words, three identical stiffened composite panels were tested for each impact location. Three specimens (D, E and F) had the same impact location at the skin in non-foam core region (♠, as shown in Fig. 4(a)). Three specimens (G, H and I) had the same impact location at the center of the skin back of the hat-stiffener (◆, as shown in Fig. 4(b)). Three specimens (J, K and L) had the same impact location at the center of the convex surface of the hat-stiffener (♣, as shown in Fig. 4(c)). The impacted specimen photos corresponding to above three locations are shown in Fig. 4(d–f). By comparison, three specimens (A, B and C) were the intact stiffened panels without impact damage. The impact test results of these stiffened panels were summarized in Table 1. It can be seen from Table 1 that for the impact location ♠, when the impact energy is 29.5 J (Specimen D), the corresponding impact pit depth is 1.85 mm, which is visible to the naked eye at the distance of 1.5 m. Decreasing the impact energy to 25 J (Specimen E), the corre­ sponding impact pit depth is 1.48 mm, which is slightly visible to the naked eye at the distance of 1.5m. The repeated impact test with the impact energy of 25 J (Specimen F), the corresponding impact pit depth is 1.33 mm, which is also slightly visible. Therefore, for the impact location ♠, the critical impact energy can be determined to be 25 J through the above three impact tests. Similarly, for other impact loca­ tion ◆, the critical impact energy can be determined as 25 J (Specimen I), and the corresponding impact pit depth is 1.56 mm. Especially, to investigate the repeatability of impact tests for the impact location ♣, the critical impact energy can be determined as 7 J for three specimens (J-L). The corresponding impact pit depth is close to 1.55 mm. For simplicity and comparison, Specimens A, E, I and L were selected as the representatives in the study base on the fact that the pit depths of each of the three repeat tests of each type were sufficiently similar. The shape of

3.2. Impact tests The impact test was carried out on the composite stiffened panel via the impact testing machines (BTF2000), as shown in Fig. 3(a). In the impact test, the drop hammer with known mass was lifted to a known height and released. The drop hammer fell freely through two guide rails, and the steel impact bar with hemispherical end fixed on the drop hammer impacted the specimen. After the rebounded of the drop hammer, the pneumatic cylinder of the testing machine was raised to limit the position of the hammer to prevent the secondary impact. Meanwhile, the specimen clamping fixture was designed according to ASTM D7136 standard. As shown in Fig. 3(b), the four corners of the specimen were clamped with point contact to ensure that the stiffened panel was not producing any displacement during the impact test. The diameter of the hemispherical impact bar is 12.7 mm, as shown in Fig. 3 (c). In the impact tests, the impact energy was obtained by calculating the product of drop weight mass and height. In this study, the selection of impact energy was considered as follows: according to the experience

Fig. 2. (a) Structure dimensions of stiffened panel and (b) specimen image. 3

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Fig. 3. (a) Setup of impact test, (b) specimen clamping fixture and (c) hemispherical impact bar.

Fig. 4. Schematic of impact location on (a) skin in non-foam core region, (b) center of the skin back of the hat-stiffener and (c) center of the convex surface of the hatstiffener, (d–f) impacted specimen photos corresponding to above three locations.

the impact pits was recorded by the optical images, as shown in Fig. 5. In the actual impact test, the depth of impact pit decrease with the decrease of impact energy. When the impact energy is lower than a threshold value, there is no pit, but once the pit appears, the depth will exceed 1 mm. In the impact test, the electronic depth micrometer was used to measure the pit depth. The micrometer head adopts a hemi­ sphere with a diameter of 3 mm, the depth range is 0–25.4 mm, and the

resolution is 1 μm. Before the measurement of the pit depth, the micrometer was pressed against a flat surface and set to zero. Then, the micrometer was pressed against the upper surface of the impact pit. Meanwhile, the micrometer was moved back and forth along the directions of 0� , 45� , 90� and 135� respectively to ensure that the whole pit area was covered. Finally, the maximum depth was recorded as the pit depth. 4

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Table 1 Determination of critical energy value by impact tests. Impact location

Used in the study

Specimen No.

Impact energy (J)

Naked eye observation on impact pit at a distance of 1.5 m

Pit depth (mm)

None

✓ / /

A B C

None

/

/

Skin in non-foam core region (♠)

/ ✓ /

D E F

29.5 25 25

Clearly visible Slightly visible Slightly visible

1.85 1.48 1.33

Center of the skin back of the hat-stiffener (◆)

/ / ✓

G H I

28 26 25

Clearly visible Clearly visible Slightly visible

3.27 2.87 1.56

Center of the convex surface of the hat-stiffener (♣)

/ / ✓

J K L

7 7 7

Slightly visible Slightly visible Slightly visible

1.48 1.56 1.55

Fig. 5. External surface impact damage of the specimens.

Fig. 6. (a) Schematic diagram and (b) image of compressive setup and (c) FPP setup.

3.3. CAI tests

testing machine was then carefully adjusted to slowly come into contact with the upper end of the specimen. A digital micrometer was used to position the specimen vertically and the upper end of the specimen was fixed to limit all displacements except for the displacement in the compression direction, as shown in Fig. 6(a). Then, the wedge-shape blocks of the fixture were adjusted by the

The design of compression experiment is based on the standard ASTM D 7137. After assembling the lower fixture and two pairs of wedge-shape blocks, the upper-pressure head was assembled to the testing machine. The specimen was placed vertically in the fixture. The 5

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bolts to contact with the both sides of the specimen in a simplysupporting contact condition, as show in Fig. 6(b). The off-plane dis­ placements of the sides of the specimen were limited, but the off-plane rotations of the sides of the specimen were not affected. In this study, strain gauges were used to monitor the deformation state of specimens. To ensure that the gauges stuck firmly to the speci­ mens, their surface was polished by 100, 200, 220, 320 mesh sandpapers in order to increase the surface roughness. Then, the specimen surface was cleaned using ethanol and the gauges were subsequently pasted at the front and back of the panels in pairs, as shown in Fig. 2. For example, positions 5/5’ represent the corresponding pasted position at the front (No. 5) and the back (No. 50 ) of the panel respectively. Finally, white paint was uniformly sprayed on the front of the stiffened panel for FPP optical measurement. Before the formal test, a pre-loading test (less than 10% of the limit load) was performed to make sure that the strain on the symmetrical positions of the specimen was similar after adjustment of the fixture and specimen position. The results of the pre-loading test confirmed that the clamp, test machine controller, and strain gauge measurement compo­ nents were all in good working order and that the load can be transferred smoothly. The universal testing machine (CCS20T) was used to apply compression load during the test and the displacement control mode was adopted, which maintained the displacement loading rate as 0.5 mm/ min until the specimen failed. During the experiment, groups of multifrequency fringes were projected onto the specimen using a projector (TLP-X2000) at a speed of 4 fps. The fringes were captured by a digital camera (F–080B) and the acquired data was post-processed and subse­ quently analyzed. The experiment setup is shown in Fig. 6(c).

with results reported in references (Feng et al., 2016; Sun et al., 2018a). 4.2. Strain-time curves The strain history of the four stiffened panels obtained via the compression tests is shown in Fig. 8. For Specimen A without impact damage, the strain curve is shown in Fig. 8(a), the strain gauge pairs 6/ 60 , 7/70 , 8/80 data bifurcate at 60 s, and 1/10 , 4/40 , 9/90 bifurcate at 90 s. The bifurcated strain gauge pairs (6/60 , 7/70 , and 8/80 ) data then ac­ celerates the separation process. It shows that the non-damage com­ posite stiffened panel presents the different local buckling mode under different loads, which is consistent with the observation results in reference (Ghelli and Minak, 2011). For the stiffened panels with impact damage (Specimen E and Specimen I), the strain curves are shown in Fig. 8(b) and (c). The overall trend is similar to that of Specimen A. The strain curve bifurcation phenomenon indicates the initiation of local buckling in the stiffened panels. It is noteworthy that for Specimen E, the strain gauge pairs 7/70 , 9/9’ and the strain gauges 5, 8 change abruptly when approaching 80 s. Moreover, for Specimen I, the strain gauges 4, 5, 6, 7, 9 change abruptly when approaching 92 s. This phenomenon results from load redistri­ bution caused by delamination of the damaged panels (Li and Chen, 2016; Ghelli and Minak, 2011; Tan et al., 2018). In addition, for Spec­ imen I, almost all the strain gauge pairs change abruptly when ap­ proaches 170 s, which implies that the stiffener damage leads to the load redistribution. According to the characteristics of strain bifurcation, the initial buckling load in the compression experiment can be determined. The compression buckling load of non-destructive stiffened panel (Specimen A) is 91.2 kN, which is significantly higher than that of the stiffened panel with impact damage (72.3 kN for Specimen E and 71.3 kN for Specimen I). It is noted that for Specimen E and Specimen I, although the impact damage locations on the panels are different, there are similar compression buckling loads. Especially for Specimen L with impact damage at the stiffener convex side, the fluctuation of the strain curves is shown in Fig. 8(d). The trend of the strain gauge data is consistent without bifurcation, which in­ dicates that no obvious local buckling is evident until the stiffener damage occurs. In several reports (Tuo et al., 2019a; Rhead et al., 2017), it has been shown that local buckling induces and guides the delamination damage. It was shown also in reference (Ouyang et al., 2018) that the delami­ nation damage also contributes to local buckling. However, in reference (Sun et al., 2018b), it was shown that the CAI stiffener panel failure process is progressive because the failure of the impacted stiffener re­ sults in the overall bending of the panel and the delamination growth between the stiffener and the panel. In this study, the experimental re­ sults show that Specimens E and Specimen I that were impacted on their panel experienced an abrupt change in the strain data. This indicates the occurrence of delamination growth in the panels. The failure of Spec­ imen L before buckling indicates that the impact damage at the stiffener convex side is fatal to the hat-stiffened panel. This is because the impact does not only damage the stiffener fiber that bears a significant component of the load but also introduce pre-bending, resulting in the advanced instability of the panel.

4. Results and discussion 4.1. Load-displacement curves The load-displacement curves of the four stiffened panels that were obtained via compression experiments are shown in Fig. 7. It is evident that Specimen A without impact damage has the highest bearing ca­ pacity of approximately 106 kN. In contrast, the specimens with impact damage in different regions exhibited a significant decrease in the re­ sidual compression bearing capacity. The ultimate loads for Specimen E, I, and L were 85.8 kN, 93.91 kN, and 40.6 kN, respectively. It is evident that even with a similar impact pit depth, the damage associated with different impact positions result in different residual compression bearing capacities. For Specimen L in particular, the impact at the center of the stiffener has the greatest effect on the carrying ca­ pacity, while the impact in other regions has less effect. This is consistent

4.3. Full-field buckling results The evolution of the buckling modes is the basic characteristics of the stiffened panel structure deformation, and the FPP measurement result of Specimen A is shown in Fig. 9(a). There is significant buckling waveform on the panel on either side of the stiffener, which has four almost symmetric peaks and troughs distributed at the left and right sides. This phenomenon is consistent with the observation results in reference (Feng et al., 2016) and the strain trend shown in Fig. 8(a). For the stiffened panels with impact damage at different locations (Specimen E and Specimen I), their buckling modes are consistent with

Fig. 7. The load-displacement curves for different stiffened panels. 6

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Fig. 8. Strain-time curves for (a) Specimen A, (b) Specimen E, (c) Specimen I and (d) Specimen L.

that of the non-impact panel (Specimen A), as shown in Fig. 9(b and c). The corresponding strain curves as shown in Fig. 8(b–c) are also consistent with that of Fig. 9(a). However, the degree of local buckling is more severe than that of the non-impact panel (Specimen A), which indicates that the impact damage at different positions on the panel does not change the buckling mode of the stiffened panel, but will aggravate the buckling of the panel, which results in the decrease of the residual strength of the damaged stiffened panel. It is worth noting that for Specimen L with impact damage at the stiffener convex side, as shown in Fig. 9(d), there is no obvious local buckling because the stiffness of the damaged stiffener is reduced. This induces delamination failure as the load increases and results in bending of the entire panel. The buckling result is also consistent with the strain curves shown in Fig. 8(d). From this analysis, it is evident that the full-field displacement dis­ tribution can effectively visualize the local buckling mode and its evo­ lution, which is helpful in explaining the structural deformation corresponding to the strain curves.

elements with zero thickness were inserted into gaps between the joint parts because the use of traditional shell elements together with cohe­ sive elements proved to be the fastest method and the relative error of the CAI strength was less than 4% (Soto et al., 2018). In this study, the SC8R continuous shell element was used for the stiffener and skin modeling, while the C3D8R solid element was used for the foam and R-zone filler. The COH3D8 solid element was used for the rubber layer and the C3D8R solid element was used for the impact head. The hat-stiffener was filled with foam core of which the bottom was filled with R-zone filler. A “tie” binding connection was adopted between different parts. Fig. 10(a) shows the finite element model of the non-impact stiffened panel. The boundary condition under low-velocity impact is quadrilateral clamping. To ensure the accuracy and compu­ tational efficiency of the finite element numerical simulation results, the grid was denser near the impact center and relatively sparse at a certain distance from the impact center. Abaqus/Explicit was adopted to simulate the failure process of the stiffened panel under low-speed impact. The required impact velocity was determined according to the impact energy, the impact locations including the center of the back of the stiffener in the foam core region, the center of the stiffener convex side in the foam core region, and the intersection of the stiffened panel longitudinal symmetric line and the unilateral panel symmetric line, as shown in Fig. 4(a–c). In the finite element software ABAQUS, the restart method was used to introduce the panel impacted results as the initial state into the CAI finite element simulation. The boundary condition of CAI is that the two sides of the panel apply a normal constraint, the bottom end is fixed, and the upper end applies a displacement compression load as shown in Fig. 10(b). The mesh division is consistent with the impact model.

4.4. Finite element simulation The stiffened panel consists of the skin, stiffener, foam, and filler. The stacking sequence of skin is [45/90/0/-45/0/-45/45/0]s and that of the stiffener is [-45/90/45/0]. The ply thickness of the skin and stiffener is 0.125 mm in both cases and their mechanical properties are shown in Tables 2 and 3. In the ABAQUS software, the low-velocity impacts for different en­ ergies and impact positions on the stiffened panels were respectively simulated and the integrated modeling method was adopted. Cohesive 7

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Fig. 9. FPP measured buckling results under different loads for (a) Specimen A, (b) Specimen E, (c) Specimen I and (d) Specimen L.

8

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Table 2 Elastic constants of the composites. EX/GPa

EY/GPa

GXY/GPa

PRXY

129

9.42

4.02

0.278

Table 4 Hashin failure criterions. Failure mode Matrix tension Matrix compression

Table 3 Strength constants of the composites.

Fiber tension

Xt/MPa

Xc/MPa

Yt/MPa

Yc/MPa

S/MPa

1832

1118

49.6

164

111

Fiber compression

(1) Buckling mode The eigenvalue method is a linear buckling analysis method based on the linear elastic theory of small displacement and small strain. Its buckling load is determined by the linear generalized eigenvalue equation, namely λKσ Þq ¼ 0 :

(6)

Because of the eccentricity of loading, manufacturing defects, anisotropy of composite materials and other factors, the eigenvalue method for solving linear buckling is not valid. Therefore, it is necessary to model the practical composite panels considering the nonlinear effect and large deflection via nonlinear buckling theory. According to the nonlinear buckling theory, the equilibrium equa­ tion needs to be built on the structure with constant deformation, and the incremental equation to be solved is KT ðqÞΔq ¼ ΔZðqÞ :

�

�2 � 1; ðσ22 � 0Þ L S "� # � �2 � � �2 σ22 2 YC σ22 σ12 FV2 ¼ þ 1 þ � 1;ðσ22 < 0Þ T T C 2S 2S Y SL � �2 � �2 σ11 σ12 FV3 ¼ þα L � 1; ðσ11 � 0Þ T S � X �2 σ11 FV4 ¼ � 1; ðσ11 � 0Þ XC

FV1 ¼

σ22 YT

�2

�

þ

σ12

incremental displacement vector. Based on the nonlinear buckling theory, the aforementioned nu­ merical model was established to predict the compressive buckling characteristics of the damaged composite stiffened panel and the cor­ rectness of the prediction model was evaluated by comparison with the FPP measurement results. For the non-impact stiffened panel, as shown in Fig. 11(a), the nu­ merical simulation predicted panel compressive buckling (left) and the FPP measurement results (right) both show the alternation form of the wave packet/trough but the number of troughs is different. For Specimen E, as shown in Fig. 11(b), although the smooth region on the other side of the panel was not impacted, it still exhibited a symmetric buckling distribution. For Specimen I, as shown in Fig. 11(c), its buckling region is widely distributed on both sides of the panel. In contrast, for Specimen L, as shown in Fig. 11(d), the buckling region is concentrated near the stiff­ ener and the impact damage is mainly distributed on the stiffener. The much lower value of the compressive bearing capacity of Spec­ imen L compared to that of Specimen I can be explained from the panel buckling failure mode because the stiffener determines the compressive bearing capacity of the stiffened panel. For the specimens with impact damage (Specimens E, I and L), as shown in Fig. 11(b–d), it can be determined that the local buckling re­ gion is generally connected. This indicates that there is delamination in the panel damage mode resulting in buckling extension, which is consistent with the results in reference (Ouyang et al., 2018). It is evident from Fig. 12(c–d) that the local buckling starts from the affected region and propagates along the width direction to the two outer boundaries, which is consistent with the observation results in reference (Tuo et al., 2019b). By comparing the buckling distribution of finite element simulation and the FPP measurement results, some differences are observed. In addition, the buckling mode of the stiffened panel that is compressed after impact in the non-foam core region exhibits a symmetry that is inconsistent with the asymmetric damage mode, indicating that the ef­ fect of invisible impact damage on the smooth sides is limited.

A variety of failure criteria and damage evolution methods have been evaluated (Li et al., 2019), and Hashin criterion (Hashin, 1980), which has the advantages of a simple expression and conservative prediction, is recommended to analyze the low-speed impact failure and CAI behavior of composite panels, as shown in Table 4. Among them, σij is the stress component, α is a coefficient (0 � α � 1) that accounts for the shear stress σ 12 contribution to fiber breakage in tension criterion, X, XC are the longitudinal tensile and compression strength respectively, Y, YC are the transverse tensile and compression strength respectively, and ST, SL are the longitudinal and transverse shear strength respectively. If the stress component of the element satisfied any of the equations in Table 4, the corresponding failure mode was considered. Introducing a custom subroutine, the stiffness degradation criterion is adopted in the damage analysis of the stiffened panel; in which FV1 represents matrix tensile failure, FV2 represents the matrix compression failure, FV3 represents fiber tensile failure, and FV4 represents the fiber compression failure. When the aforementioned variable, i.e. FV1-4, arrives 1, it implies that the corresponding material damage and the structural begin to failure.

ðK0

Failure criterion

(7)

(2) Damage analysis

where KT is the tangent stiffness matrix of a certain incremental step in the calculation process, ΔZ is the unbalanced force component, Δq is the

Fig. 10. (a) FE model meshing of the conventional nondestructive stiffened panel for impacting simulation and (b) boundary conditions of stiffened panel for CAI simulation. 9

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Fig. 11. Full-field buckling comparison of FE simulation (left) and FPP measurement (right) under ultimate load for different stiffened panels of (a) Specimen A, (b) Specimen E, (c) Specimen I and (d) Specimen L.

Fig. 12. The failure mode for (a) Specimen A, (b) Specimen E, (c) Specimen I and (d) Specimen L.

Fig. 12 show the final compression failure photos of the stiffened panels with different impact locations. It can be seen that the ultimate failure parts of the panels are all in the middle of the stiffeners and all of the main failure modes are fiber fracture. According to the failure results of the stiffened panels, the different impact locations have minor effect on the ultimate failure mode of the stiffened panels. The buckling mode is closely related to the damage distribution and evolution in CAI stiffened panels (Tuo et al., 2019b; Abir et al., 2017). The damage development and distribution mode of CAI stiffened panels under different impact damages are shown in the following figures. When the stiffened panel without the impact damage (Specimen A) is loaded with the ultimate load, the maximum deformation is

concentrated in the middle region of the stiffener, indicating that the stiffener determines the bearing capability of the non-impact stiffened panel. As shown in Fig. 13, the failure regions are mainly concentrated on the stiffener and the edge of the panel. The main failure modes are the matrix tensile failure and fiber compression failure. Fig. 14 shows the CAI numerical simulation of the stiffened panel (Specimen E). There are mainly fiber compression failure and matrix tensile failure in the panel structure under the ultimate load. The panel bends toward the stiffener convex side during the compression process. The delamination caused by the impact damage extends in the smooth panel more easily, which leads to the extensive distribution of fiber compression, matrix compression, and matrix tensile damage. 10

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Fig. 13. Failure forms of the non-impact stiffened panel (Specimen A) under the ultimate load, (a) the distribution of the matrix tensile failure and (b) the dis­ tribution of the fiber compression failure.

Fig. 14. CAI Failure forms of the stiffened panel (Specimen E), (a) fiber compression damage, (b) fiber tensile damage, (c) matrix compression damage and (d) matrix tensile damage.

Fig. 15 shows the CAI numerical simulation of the stiffened panel (Specimen I). It was determined that there is mainly fiber compression failure in the entire panel structure, and the failure parts concentrate on the stiffener. Fig. 16 shows the CAI numerical simulation of the stiffened panel (Specimen L). It was determined that mainly fiber compression and matrix compression failure occurred in the entire panel structure, and the failure parts concentrate on the middle of the stiffener. It was evident that the stiffener is the most vulnerable region of the stiffened panel, which is consistent with the conclusion in (Ye et al., 2019). The reason is that the stiffener was the main load-bearing structure in the panel resulting in the damage sensitivity. Secondly, the stiffness difference between the stiffener and the panel was prominent, and therefore the

bonding parts between them are prone to delamination damage. 4.5. Some considerations The geometric features of the hat-stiffener are fully enclosed, with many geometric parameters and large optimization space. The hatstiffened composite panel is widely used in the composite industry. If the form of hollow closed thin-wall panel was impacted by objects, the stiffness of the impacted panel would decrease which would lead to the mechanical properties of the structure deviated from the design. In this study, it is considered to fill the hat stiffener cavity with foam and take advantage of the good energy absorption of soft materials, so the impact resistance of the structure is expected to be improved. 11

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Fig. 15. CAI failure forms of the stiffened panel (Specimen I), (a) fiber compression damage and (b) fiber tensile damage.

Fig. 16. CAI failure forms of the stiffened panel (Specimen L), (a) fiber compression damage, (b) fiber tensile damage, (c) matrix compression damage and (d) matrix tensile damage.

Based on the idea of reinforcement element, this study designs and processes the single FFHS composite panel. Through the CAI experiment and FE simulation, the effectiveness of the measures to improve the impact resistance is investigated. The strain history, full-field deflection and numerical simulation are of reference significance for the impact resistance design of hat-stiffened composite panels. Some considerations can be obtained from the study.

compression strength, as shown in Fig. 7. For Specimen L in particular, the impact at the center of the stiffener has the greatest effect on the loading capacity, while the impact in other regions has less effect. (2) The strain bifurcation phenomenon means the occurrence of local buckling. It can be seen from the strain-time curve in Fig. 8 that the strain bifurcation phenomenon occurs in Specimens A, E and I, indicating that the local buckling and post-buckling behavior happened. By contrast, Specimen L hasn’t had buckling behavior. The experimental results show that Specimen E and Specimen I that were impacted on the skin experienced an abrupt change in the strain

(1) The impact location affects the residual compression strength of stiffened panels It is evident that even with a similar impact pit depth, the damage associated with different impact locations results in different residual 12

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data. It indicates the occurrence of delamination growth in the panels. The failure of Specimen L happened before buckling. It indicates that the impact damage at the stiffener convex side is fatal to the hatstiffened panel. This is because the impact does not only damage the stiffener fiber that bears a significant component of the load, but also introduce pre-bending, resulting in the advanced instability of the panel.

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(3) The impact location affects the delamination damage form in the CAI test. In Section 4.4, it gives the damage development and distribution of composite stiffened panels in the CAI test under different impact dam­ ages. The buckling mode of composite stiffened panels in the CAI test is closely related to their damage distribution and development. 5. Conclusions In this study, the CAI experiments for stiffened panels were per­ formed and the full-field optical measurements were conducted via the FPP. The damage evolution during the compression process and the damage influence on the ultimate failure were obtained. The main conclusions are summarized based on the experiment results and FE analysis as follows. (1) For the stiffened panel impacted at the center of the stiffener convex side, the buckling region was concentrated on the nearby stiffener. In contrast, for the stiffened panel impacted at the center of the backside of stiffener, its buckling region was widely distributed on both sides panel. Given that the stiffener de­ termines the compressive bearing capacity of the stiffened panel, the dramatic decrease of the compressive bearing capacity of the stiffened panel impacted at the center of the stiffener convex side can be explained from the panel buckling failure mode. (2) Damage of the CAI stiffened panel is prone to develop inside or near the stiffener, including the mode of fiber compression, ma­ trix compression and matrix tensile, while the fiber tensile damage can be ignored. The buckling mode of the stiffened panel impacted at the non-foam core region exhibited symmetry that was inconsistent with the damage mode. It indicated that the invisible impact damage on the smooth panel has a minor effect on the residual strength of the stiffened panel. Different impact locations could affect the quantity and mode of the local buckling in the compressed stiffened panel by delamination growth, but has a limited effect on the final failure mode of the stiffened panels. Author contribution Da Liu performed the impact tests, CAI tests and data analysis, and edited the manuscript. Jianchao Zou designed and assembled the experimental setups. Ruixiang Bai and Jingjing Guo conducted the FE simulations. Wen Wu gave some beneficial discussion on the revised manuscript. Cheng Yan conceived the study and gave some beneficial discussion on the manuscript. Zhenkun Lei conceived and designed the study, and reviewed the revised manuscript. All authors read and approved the revised manuscript. Acknowledgments The authors thank the National Natural Science Foundation of China (11772081, 11972106, 11635004), and Fundamental Research Funds for the Central Universities of China (DUT18ZD209，DUT2019TD37). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. 13

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