Low-velocity Impact Response And Residual Flexural Behavior Of Composite Sandwich Structures Isope 2018

Proceedings of the Twenty-eighth (2018) International Ocean and Polar Engineering Conference Sapporo, Japan, June 10-15, 2018 Copyright © 2018 by the International Society of Offshore and Polar Engineers (ISOPE) ISBN 978-1-880653-87-6; ISSN 1098-6189

www.isope.org

Low-velocity Impact Response and Residual Flexural Behavior of Composite Sandwich Structures with Corrugated Core Wentao He1*, Shuqing Wang1, Jingxi Liu2, De Xie2 and Zhe Tian1 1

College of Engineering, Ocean University of China Qingdao, China 2 School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology Wuhan, China.

2016; He, Liu, Tao, Xie, Liu and Zhang, 2016; Xiong, Ma, Wu, Liu and Vaziri, 2011). Corrugated core sandwich structures exhibit extremely anisotropic behavior, so they have good application prospects in the field of shipbuilding and ocean engineering as beam components (Zhou, Guan and Cantwell, 2016; Liu, He, Xie and Tao, 2017; Park, Jung and Kim, 2016). Composite structures are vulnerable to suffer from impact damage from foreign objects, and their residual strengths have significant reduction, possibly causing catastrophic failure (Liu, Zhang and Li, 2017). Therefore, it is necessary to investigate the impact response and resulting damage state, evaluating the post-impact flexural properties of the structure.

ABSTRACT: A lightweight sandwich structure is fabricated with carbon fiber reinforced polymer (CFRP) face sheets and aluminum alloy corrugated core. This hybrid design enables such structures to maximize the stiffness/strength-to-weight ratios and improve impact resistance properties. The impact damage and residual flexural strength of such structures are systematically investigated by experimental and numerical methods under various impact energy levels. The lowvelocity impact tests are carried out to evaluate the impact-induced damage resistance and tolerance with respect to impact load and failure mode. Subsequently, three-point bending tests are performed to assess the residual bearing ability of sandwich beams. Simultaneously, a progressive damage model involving damage initiation and damage evolution of composite laminates is implemented in ABAQUS/Explicit by using user subroutine VUMAT to simulate low-velocity impact response and residual flexural behavior of the composite sandwich structure. Comparing the experimental measurements and numerical predictions, reasonably good agreement is achieved in terms of failure modes and damage mechanisms for the impact response and postimpact flexural behavior of such structures. These studies reveal that the impact-induced damage is closely related to the impact energy level. For the lower impact energy case (10 J), delamination is the predominant damage pattern; as the impact energy level increases, fiber breakage and matrix cracking gradually become the dominant damage modes. The top face sheet fracture is crucial to determining ultimate load carrying capacity. There is a drastic reduction in residual flexural strength and stiffness even though the impact energy is lower (10 J), which indicates that impact damage is very sensitive to the residual flexural behavior of corrugated sandwich structures.

Regarding composite structures with impact-induced damage, the residual compressive (Abir, Tay, Ridha and Lee, 2017), tensile (Zhang, Wang, Ma, Xiong and Wu, 2013) and flexural properties (Zhang and Richardson, 2007) are used to evaluate the residual load-bearing capacity of a structure. Most studies have been conducted on the compression properties after impact, while fewer studies concern the residual tensile and flexural properties. With respect to residual compression properties, many researchers have performed a great deal of work to assess the influence of skin/core thickness, impact energy, impact site, impactor size on the impact response and compressionafter-impact (CAI) behavior (González, Maimí, Camanho, Turon and Mayugo, 2012; Rozylo, Debski and Kubiak, 2017). For example, Davies, Hitchings, Besant, Clarke and Morgan (2004) presented a comparative study on the CAI strength of honeycomb sandwich structures with various face sheet and core thickness. It was found that the energy absorption was related to the core thickness values. Zhang, Wang, Ma, Xiong, Yang and Wu (2013) studied the impact damage and CAI strength of pyramidal truss core sandwich structures under various impact energy levels. Wang, Waas and Wang (2013) and Wang, Wang, Chen, Huang and Liu (2017) investigated the impact damage and CAI strength of woven polymer-based foam-core sandwich panels. They pointed out there was a complex relationship between CAI strength and the possible relevant parameters. As another measuring standard of the impact-damaged composite laminates and structures, the residual tensile response has been investigated by several researchers (Liu, Lin, Zong, Sun and Li, 2013; Wang and Callinan, 2014). Wang, Wu and Ma (2010) studied the impact response and the

KEYWORDS: Corrugated core sandwich structure; Low-velocity impact; Residual flexural strength; Impact response; Flexural behavior INTRODUCTION Sandwich structures have been widely used for lightweight constructions in the aerospace, automotive and marine fields due to their specific bending stiffness/strength and good energy-absorbing capability (Schneider, Kazemahvazi, Russell, Zenkert and Deshpande,

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post-impact tensile strength of carbon/epoxy composite beams. Caprino and Teti (1994) studied residual tensile behavior of foam core sandwich panels. It pointed out that residual strength was closely related to the impact damage. Wang, Wu, Ma and Feng (2011) studied the impact response and the residual tensile behavior of composite lattice core sandwich structures.

material is described in Fig. 2, and its mechanical properties are given in Table 1. The CFRP panels are manufactured from T700/3234 carbon fiber/epoxy prepregs, with the stacking sequence [0o/90o/0o/90o]s. The material properties of the unidirectional laminate are listed in Table 2. Face sheets and the core are bonded together by using a two-part epoxy adhesive under a certain pressure. The prepared sandwich beam is displayed in Fig. 1(a).

Although post-impact flexural behavior is not as common as compression for residual strength assessment, it is necessary to evaluate the residual flexural properties, particularly for sandwich structures intended to be used as beams. With respect to the residual flexural strength assessment of composites, most research so far has focused on impact damaged composite laminates, while few studies involved sandwich structures after impact. Santiuste, Sánchez-Sáez and Barbero (2010) investigated the impact damage and the residual flexural strength of glass/polyester composite beams under various impact energy levels. They stated that the residual flexural strengths were related to the impact damage. Sarasini, Tirillò, D'Altilia, Valente, Santulli, Touchard and Gaudenzi (2016) studied the impact response and residual flexural behavior of carbon/flax composite beams. They pointed out that hybridization can improve impact performance. Klaus, Reimerdes and Gupta (2012) studied the impact response and residual flexural behavior of composite foldcores sandwich structures. It was found that the bending strength depended on impact damage. Vachon, Brailovski and Terriault (2013) presented a comparative study on the post-impact flexural properties among three different carbon/epoxy structures. Hart, Chia, Sheridan, Wetzel, Sottos and White (2017) studied the impact response and residual flexural behavior of the woven fiber-reinforced composites. They pointed out that the latter had larger reduction than the former under the impact loading. However, to the best knowledge of the authors, only a few research efforts focus on bending behavior after impact (Xu, Yang, Zeng, Cheng and Wang, 2016; Boorle and Mallick, 2016), but a study on the residual flexural strength regarding corrugated core sandwich structures has not yet been reported.

(a)

(b)

Short span

Long span

Web member

Fig. 1 (a) Corrugated sandwich structure. (b) Configuration of the trapezoidal core cell. 500

True stress (MPa)

400 300 200 100 0

0

0.03

0.06 0.09 True strain

0.12

0.15

Fig. 2 True stress-strain curve of core material. Table 1. Material properties of 2A12-T4 aluminum.

This paper aims to investigate the low-velocity impact response and residual flexural strength behavior of sandwich structures consisting of CFRP face sheets and aluminum alloy corrugated cores. This hybrid design enables such structures to maximize the stiffness/strength-toweight ratios and improve impact resistance properties. The impact damage and residual flexural strength of such structures are systematically investigated by experimental and numerical methods under various impact energy levels. The low-velocity impact tests are carried out to evaluate the impact resistance and three-point bending tests are conducted to assess the residual bearing ability of sandwich beams. Simultaneously, a progressive damage model involving damage initiation and damage evolution of composite laminates is implemented in ABAQUS/Explicit by using user subroutine VUMAT to simulate low-velocity impact response and residual flexural behavior of the composite sandwich structure. Finally, based on the experimental and numerical results, the failure modes and damage mechanisms of the impact response and residual flexural behavior of such structures are elucidated in detail.

ρ 2700 kg/m3

E 70 GPa

v 0.3

Su 460 MPa

Table 2. Material properties of composite laminates. E11

E22

E33

v12, v13

v23

123 GPa

8.4 GPa

8.4 GPa

0.32

0.3

G12, G13

G23

Xt

Xc

Yt

4 GPa

3 GPa

2100 MPa

800 MPa

25 MPa

Yc

Zt

S12, S13, S23

ρ

120 MPa

50 MPa

40 MPa

1560 kg/m3

Impact tests

EXPERIMENTAL METHODOLOGY

Impact testing is conducted using a drop hammer impact test equipment, as depicted in Fig. 3(a). A rebound system is used to avoid multiple impacts. The specimens are clamped by pneumatic clamping fixture with 75 mm diameter testing area. A clamping pressure of 0.02MPa is imposed by the steel panels of the pneumatic clamping fixture. The drop hammer weighs 13.2 kg with a hemispherical tip of 12 mm impactor tip. A force sensor with a maximum loading capacity of 10 kN is used to record the impact load-time response. Three impact energy levels (10 J, 20 J and 70 J) are chosen to impact the specimens.

Materials and specimens The sandwich beam with 3 unit cells is fabricated with an aluminum alloy trapezoidal corrugated core and two CFRP face sheets, as shown in Fig. 1(a). The core walls are made of 0.5 mm thick 2A12-T4 aluminum and its configuration is depicted in Fig. 1(b), with L1=7 mm, L2=25 mm and ω=55o. The true stress-strain response of the core

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Xiong, 2015; Zhang, Lu and Zhang, 2013) can be written using the failure factor, R, and is given below: Fiber tensile failure:

Three-point bending tests Three-point bending testing is carried out to evaluate the residual flexural properties after impact tests, as depicted in Fig. 3(b). The cylindrical indenter and both cylindrical supports are 20 mm in diameter and the support span between the cylindrical supports is 200 mm. The applied speed for the indenter is 1 mm/min on the impacted side of the specimen. Similarly, non-damaged specimens are also tested to give the baseline strength for the sandwich beams. Briefly, the specimen impacted on the short span under the impact energy of 10J is marked as S-SS-10J.

 R 2ft   11  X  T

2      12      S12

2

      13        S13 

2

11  0

(2)

Fiber compressive failure: 







 R 2fc   11   X  C

2

11  0

(3)

Matrix tensile failure: 2      2 33    1 Rmt   22    Y  S 2 T    23

    2 E 22 E33  22 33    12    23  2   S  G23   12 

Matrix compressive failure:

Specimen



 E   E33 33 2   22 22 Rmc   2G12 S12 

Support

2       2 33   13 Rld     Z   S  T   13

where 

d

1

2

2

   S12 , S13 and S 23 are the shear strain strength components, and ZT is

the tension strain strength in thickness direction. The failure factor (i = ft, fc, mt, mc, ld) denotes the levels of failure. The strain strength components are written as:

The ductile damage model is adopted to describe failure initiation and damage evolution of core material. In this model, the damage initiation occurs once the following is satisfied, pl pl D ( ,  ) pl

 22   33   0

strengths in the longitudinal and transverse directions, respectively;

Damage model for aluminum core



2

     23  (6)  33  0        S 23  Where, X T , X C , YT and YC are the tension and compression strain

NUMERICAL SIMULATION

D 

2

    13          S13 

2 2      1     1       S 23    （5

） Yeh delamination failure:

(b)

Fig. 3. Test setups: (a) Impact Testing Machine; (b) Tensile testing machine.

pl

2       E Y    22  33   22 C        Y C     2G12 S12

   E 22 E33  2   12     22 33  23     2 G 23    S12

Pneumatic clamping fixture

(a)

2

 22   33   0 （4）

Indenter Impactor

2

    13          S13 

X T  X T / E11 ,

（1）

is the equivalent plastic strain, pl is the equivalent plastic

  X /E XC 11 C

YT  YT / E 22 ,

YC  YC / E 22 ,

Z T  Z T / E33

  S /G , S12 12 12

  S /G , S13 13 13

  S /G S 23 23 23

(7)

when the failure factor Ri  1 , the damage initiates and the material stiffness degrades based on the corresponding failure modes. Therefore, the damage variable d i is defined to characterize the damage evaluation according to the failure factor,

strain rate and  Dpl is the equivalent plastic strain at the onset of damage; is the stress triaxiality. When damage initiation criterion is met at an integration point, the stress-strain response of the aluminum alloy is softened according to the exponential damage evolution law, and thus the material stiffness at that point is degraded. Once the stiffness degradation at any one integration point reaches a critical value, the elements are removed from the finite element model.

di  1 

1 Rin

Ri  1,

n  1; i  ft , fc , mt , mc , ld 

(8)

where d ft , d fc , d mt , and d mc are the damage variables in the tension and compression modes for the fiber and matrix, respectively; d ld is the damage variable for delamination. The parameter n=1 is adopted to control material damage according to the trial.

Damage model for composite face sheets In order to simulate the damage of composite laminate, a progressive damage model including 3D Hashin failure criteria and Yeh delamination failure criteria is implemented in ABAQUS/Explicit through an user-defined VUMAT subroutine. The progressive damage model involves five damage modes, namely fiber tension and compression, matrix tension and compression, and delamination. Strain-based failure criteria are used to characterize impact damage because they are more continuous and smoother than stresses. The strain-based damage initiation (Huang and Lee, 2003; Yu, Wu, Ma and

Once strains of the element satisfy the Hashin or Yeh failure criteria in the calculation process, material failure occurs and the stiffness of the structure is degraded. Therefore, the stress values of the element are also updated in the next calculation iteration. The stiffness degradation of material is associated with the damage parameter i (i=1…6), and therefore the stress-strain relations of the laminate can be expressed as following,

529

Once the impact simulation is completed, the impact boundary conditions are replaced by the new boundary conditions of three-point bending simulation. The rate of loading for the indenter is 1 mm/ms in order to save time. Similarly with the impact case, material properties and general contact are employed in the bending process.

 11       22         33       12       23       13 

RESULTS AND DISCUSSIONS Low-velocity impact characterization (a) 4

(9)

12

where the damage parameter i (i=1…6) is expressed as follows,

S-SS-10J

  2  max0.0, d f , d m , 3  max0.0, d f , d d      6  max0.0, d f , dd   max0.0, d ft , d fc , d m  max0.0, d mt , d mc , d d  max0.0, dld 

1  max 0.0, d f , df

Impact load (kN)

4  max 0.0, d f , d m , 5  max 0.0, d f , d d ,

(10)

Finite element model This simulation is performed in three steps, namely the impact step, the step of changing boundaries and the bending step. The finite element models of the sandwich beam for low-velocity impact simulation and three-point bending simulation are illustrated in Fig. 4. Face sheets and core are all meshed with 8-node linear brick reduced integration elements, with finer meshes around the impact region. During the testing process, there is only limited debonding failure at the face sheetcore interfaces of the specimens, so interface elements are not used between the interfaces. Instead, surface-based tie constrains are employed at the interfaces. In the whole model, general contact is used as the contact condition. Two plates are established to simulate the clamping boundary and a uniform pressure of 0.02 MPa is applied on the top clamp. The impactor is allowed to move only in 3-direction and its mass is defined by the reference point of the impactor. Impact energies are also defined by assigning the initial velocity to the reference point. The impactor and pneumatic clamps are modeled as rigid bodies. (a)

3

9

2

6

1

0

3

Simulation Experiment 0

3

(b) 6

Energy (J)

                  

6 Time (ms)

9

0 12 24

Impact load (kN)

S-SS-20J 4

16

2

6 Simulation Experiment

0 0

3

6 Time (ms)

9

(c) 6

Impactor

Energy (J)

1    11    12  13 0 0 0 E 22 E 33    E11 1  1     1    22    12  23 0 0 0    E 22 E 22 1  1  E 22      1     13  23 0 0 0  33   E 33 E 22 E 33 1   3    1    0 0 0 0 0  12   G12 1   4     1    0 0 0 0 0  23   G 23 1   5     1    0 0 0 0 0  13   G13 1   6  

12

0

90 S-SS-70J

3 2 1

(b)

Specimen

4

60 Energy (J)

Impact load (kN)

Clamps

Simulation Experiment 2

30

Indenter

0 0

Impacted specimen

4

8 Time (ms)

12

0 16

Fig. 5. Impact response of specimens (a) 10 J; (b) 20 J; and (c) 70 J. 3

The low-velocity impact responses of specimens under three representative impact energy levels are described in Fig. 5. For all impact load curves, a small drop emerges once the load reaches the first peak point, which is predominately attributed to the plastic buckling of web members when the contact force reaches to 2.6 kN. It is found that the maximum contact force increases as the impact energy increases before the top face sheet is subjected to serious damage. For the 10 J

2 1

Support

Fig. 4. Finite element model (a) Impact simualtion; (b) Bending simulation.

530

and 20 J cases, the top face sheets and cores are not perforated; the damage images are described in Fig. 6. For the 10 J case, a barely visible indentation can be found in the top surface of the specimen, but the cracks take place around the impact zone. As the impact energy increases, the indentation and the plastic buckling of web members become more and more apparent accompanied with the intricate damage in the top face sheet. For the 70 J case, face sheets and the core are perforated and the impact load curve exhibits a sudden load drop where the core is perforated completely. The primary damage modes for the composite laminates are intricate, in the form of fiber breakage, matrix cracking and delamination. For all cases, the buckling of core members only appears in the impact zone, and no visible debonding is found in the interfaces between the face sheets and the cores. This shows that there is a strong bonding for the specimens even though they are subjected to impact loading.

energy levels. To gain a better knowledge of the damage mechanisms, the simulation for the impact response under various impact energy levels has been conducted. The predicted impact load and absorbed energy curves are consistent with the experimental results, as shown in Fig. 5. However, the predicted initial stiffness of the load curve before the plastic buckling occurs is slightly overestimated compared to the experiment measure. This is primarily due to manufacturing defects of the specimens and slight debonding of the interfaces between the face sheets and the core, which are not considered in the numerical simulation. The numerical damage representations for the composite laminates are also depicted in Fig. 7. The rainbow colors represent solution dependent variables of failure modes for the composite laminates. For the 10 J case, no element is deleted from the laminate. From the numerical and experimental results, it is clearly found that the dominant failure mode for this lower impact energy is delamination. As the impact energy increases (20 J case), the elements around the impact zone are removed, which indicates that the face sheet suffers serious damage. The primary failure mode becomes fiber damage, which is consistent with the experimental results. For the 70 J case, the specimen is completely penetrated, leaving a hole with almost the same diameter in the face sheets and the core. The intricate failure modes can be found from the numerical simulation, in the forms of fiber breakage and matrix damage. Generally, the predicted damage state is similar to the experimental result, including the profile and size of the composite damage.

Post-impact flexural behavior 8

Fig. 6. Impact damage of specimens under various impact energy levels.

0J 10 J 20 J 70 J

Load (kN)

6

4

2

0

0

2

4 6 Displacement (mm)

8

10

Fig. 8. Load-displacement curves in the bending process. The residual flexural strength is investigated for the specimens subjected to low-velocity impact. In addition, non-impacted specimen testing is also conducted to provide the baseline strength. The typical load-displacement curves are shown in Fig. 8. For such structures, the ultimate load-bearing capability (maximum contact force) can be considered as the residual flexural strength. Obviously, the residual flexural strength for damaged specimens is about 5.2kN no matter how much impact energy is applied to the specimens. Although only slight damage can be produced by the low impact energy (10 J case), it leads to a dramatic reduction in residual flexural strength. As the impact energy increases, the residual bending strength exhibits no significant reduction until the specimen is penetrated (70 J case). However, the initial bending stiffness decreases significantly even though the

Fig. 7. Predicted impact damage of specimens under various impact

531

fast to the center of face sheet. Except for the difference in crack initiation location of the top face sheet, failure mechanism for all samples remains similar in the bending process.

specimen is impacted by the 10 J impact energy. This is mainly due to the plastic buckling of the core members under the impact loading, which is very sensitive to bending response of the corrugated sandwich structures. For the 70 J case, the initial bending stiffness shows a dramatic reduction, which indicates that the entire specimen has suffered severe impact damage. However, from the load-displacement curves, there is a similar trend whether they are impacted or not, which indicates similar failure mechanisms for the sandwich structures in the bending process.

(a)

For a better indication of the influence of the impact damage on the residual properties, load-displacement curve and damage images of representative specimen S-SS-0J are selected to illuminate the failure mechanism, as shown in Fig. 9. Obviously, the bending process can be divided into three distinct stages. The first stage is the elastic deflection of the entire sandwich structure. In this section, the applied force curve is almost linear until the top face sheet initiates damage. With the loading increasing, the top face sheet begins to exhibit damage with the emergence of visible and audible signs of failure, which leads to a sudden load drop in the bending curve. The second stage is the compression fracture of the face sheet. As the compressive loading increases, the carrying capacity of the sandwich beam gradually decreases until a prolonged load plateau is reached. The first load drop is related to the initial damage of the composite laminate taking the form of matrix cracking and delamination. As the load increases, the failure modes are replaced by extensive fiber breakage, matrix cracking and delamination. The top face sheet continues to damage until the final rupture of the top face sheet. The third stage is the plastic deformation of the core. In this prolonged load plateau section, the plastic collapse of the core is the dominant failure mode, forming plastic hinges. Thus, the residual load-carrying capacity of such structure can be sustained by progressive plastic collapse of the core and further delamination of the face sheet. From the failure process of such structures under bending loading, the top face sheet fracture is crucial in determining ultimate load carrying capacity.

20mm

For a better understanding of the influence of the impact damage on the residual properties, the numerical simulation is conducted to evaluate the residual flexural strength. The predicted load-displacement curves for all cases are compared with the experimental results, as exhibited in Fig. 11. A generally good agreement can be achieved, except the prolonged load plateau section. In this stage, it seems that the numerical load values are overestimated when compared to the measured results. This is mainly attributed to the face that the interface debonding between face sheets and the core is not taken into account in predicted results, particularly after the face sheet fracture. The interface debonding leads to diminishing transfer of traction between the core and the top face sheet, which causes the subsequent decrease in the stiffness of the sandwich structure. However, the reduction in initial stiffness and the residual flexural strength can be well captured by the numerical simulation, which indicates that numerical simulation could be a promising tool for the bending strength evaluation. Because of the similar damage characteristics for all cases based on the measured results described above, a non-impacted specimen is selected to exhibit the deformation behavior and damage profile of the beam, as shown in Fig. 12. Obviously, the compressive stresses in the top face sheet and tensile stresses in the bottom face sheet can be generated in the bending process. In the preliminary stage of the bending, the damage appears in the contact area between the top face sheet and indenter, and spreads in the face sheet and the core as the compressive load increasing. Both global deformation and local deformation can be observed in the sandwich structure. The global displacement corresponds to the overall deformation of the beam, whereas the local deformation is dominate attributed to the core collapse. In fact, global deformation and local deformation are coupled together, which cripples the bending stiffness of such structure in the bending process. Similarly with the experimental observation, the local collapse of the core under the indenter speeds up after the final failure of the top face sheet.

6

Load (kN)

Fracture

4

2

Stage I

Stage II

2

Stage III

4 6 Displacement (mm)

8

20mm

Fig. 10. Damage image of the top face sheet: (a) Specimen S-SS-0J; (b) Specimen S-SS-20J.

Crack

0

Crack induced by compression

Damage induced by impact

8

0

(b)

Crack induced by compression

10

Fig. 9. Typical damage process of specimen S-SS-0J.

The typical predicted bending failure modes can be illustrated by the specimen S-SS-20J after impact, as shown in Fig. 13. The central damaged zone in the top face sheet is generated by the impact loading. The compression failure of the top face sheet and the plastic collapse of the core can be identified in the numerical results. The compressive damage of fiber and matrix and delamination are the primarily failure modes in the bending process. A crack appearing in the middle span is also successfully captured in the simulation analysis, which is generally in good agreement with experimental observation. After the final fracture of the face sheet, the plastic collapse of the core induced by the

From the observation of damage morphology for each sample, it is found that a crack with fiber breakage and delamination in the top face sheet spans the width of top skin. Damage images of specimen S-SS-0J and specimen S-SS-20J are shown in Fig. 10. Comparing damage morphologies, is can be seen that the crack initiation location in the face sheet is different between the impacted and non-impacted specimens. For the impacted case, the crack initiates at the impact damage zone, and grows towards the free edge; however, for the nonimpacted case, the crack originates at the free edge and extends very

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indentation can be identified clearly, as shown in Fig. 13(f). The red regions in the middle span (Fig. 13(g)) represent the local plastic hinges of the core, which are quite similar to those in the experiment in Fig. 12.

Fig. 11. Impact load and absorbed energy curves under various impact energy levels.

8 t=1.0 mm

S-SS-0J

Load (kN)

6

Simulation Experiment

t=2.7 mm

4 t=10.0 mm

2

0

0

2

4 6 8 Displacement (mm)

Fig. 12. Captured images and numerical prediction for various stages: t=1 mm, the elastic deflection stage; t=2.7 mm, the face fracture stage; t=10 mm, the core deformation stage.

10

5

(b)

(c)

(d)

(e)

(f)

S-SS-10J

4

Load (kN)

(a)

3 2 1 0

Simulation Experiment 0

2

5

4 6 8 Displacement (mm)

10

(g)

S-SS-20J

Load (kN)

4

Fig. 13. Numerically predicted failure modes on the top facesheet and the core for the residual flextual simulation. (a) Fiber tensile failure; (b) Fiber compressive failure; (c) Matrix tensile failure; (d) Matrix compressive failure; (e) delamination failure; and (f)(g) Core failure.

3 2

CONCLUSION Simulation Experiment

1 0

0

2

4 6 8 Displacement (mm)

This paper aims to investigate the low-velocity impact response and the residual flexural strength behavior of hybrid sandwich structures. The low-velocity impact tests are carried out to evaluate the impact resistance and three-point bending tests are conducted to assess the residual bearing ability of sandwich beams. Simultaneously, a progressive damage model is implemented in ABAQUS/Explicit by using user subroutine VUMAT to simulate low-velocity impact response and residual flexural behavior of the composite sandwich structure. Several major conclusions can be revealed:

10

5 S-SS-70J

Load (kN)

4 3

1. The contact force increases as the impact energy increases before the top face sheet and the core suffering serious damage. For the lower impact energy case (10 J), delamination is the predominant damage pattern; as the impact energy level increases, fiber breakage and matrix cracking gradually become the dominant damage modes.

2 Simulation Experiment

1 0 0

2

4 6 8 Displacement (mm)

2. Three distinct stages for the three-point bending response curve can be identified whether they are impacted or not: the elastic deflection of the whole structure, the compressive failure of the top face sheet and the local plastic collapse of the core. The top face sheet fracture is

10

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crucial to determining ultimate load carrying capacity.

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3. Impact damage and residual flexural strength are closely related to the impact energy level. There is a drastic reduction in residual flexural strength and stiffness even though the impact energy is lower (10 J), which indicates that impact damage is very sensitive to the residual flexural behavior of the corrugated sandwich structures. 4. A generally good agreement can be achieved between the numerical prediction and experimental observation in terms of the low-velocity impact response and the residual flexural strength behavior, which indicates that the numerical simulation could be a promising tool for the residual bending strength evaluation.

ACKNOWLEGEMENTS The present work is supported by the National Natural Science Foundation of China (Grant Nos. 51609089, 51579110 and 51079059).

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