Experimental and numerical investigation on damage behavior of honeycomb sandwich panel subjected to low-velocity impact

Journal Pre-proofs Experimental and numerical investigation on damage behavior of honeycomb sandwich panel subjected to low-velocity impact Zhang Xiaoyu, Xu fei, Zang Yuyan, Feng Wei PII: DOI: Reference:

S0263-8223(19)33022-3 https://doi.org/10.1016/j.compstruct.2020.111882 COST 111882

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

9 August 2019 24 November 2019 3 January 2020

Please cite this article as: Xiaoyu, Z., fei, X., Yuyan, Z., Wei, F., Experimental and numerical investigation on damage behavior of honeycomb sandwich panel subjected to low-velocity impact, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct.2020.111882

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Experimental and numerical investigation on damage behavior of honeycomb sandwich panel subjected to low-velocity impact Zhang Xiaoyu1*, Xu fei1*, Zang Yuyan1 and Feng Wei1 1

School of Aeronautics, Northwestern Polytechnical University, Xi'an, China

Abstract: This paper presents the low-velocity impact behavior of sandwich panel with carbon fiber reinforced plastic (CFRP) composite facesheet and Nomex honeycomb core through experimental and numerical methods. Experiments were carried out on two thickness of honeycomb core at various impact energy levels. The dynamic response including contact force history and energy absorption as well as contact duration was recorded. The damage modes were obtained through non-destruction inspection (NDI) C-scan and microscopic observation. A refined three-dimensional finite element model combined with continuum damage mechanics(CDM) was developed with composite plies and detailed honeycomb core. Physically-based Puck’s composite failure criteria and energy based progressive damage model were used to capture the intralaminar damage initiation and evolution, respectively. The interlaminar damage of facesheet and debonding of facesheet/core interface were predicted using cohesive element. The hexagonal honeycomb cells were characterized in FE model with an elasto-plastic constitutive model and damage criterion in detail during impact. The simulation results show good agreements with experiments and the model can be used to predict the low-velocity impact response and impact damage effectively. More detailed responses, such as internal damage details, damage modes and evolution, are observed and discussed with the numerical model proposed.

Keywords: sandwich structure; low-velocity impact; continuum damage mechanics; physically-based failure criteria.

F

Gibbs free energy density

E1, E2, E3

young’s modulus of lamina in material coordinates

G12, G23, G13

shear modulus of lamina in material coordinates

υ12, υ13, υ23

Poisson’s ratio

𝝈, 𝜎𝑖𝑗

stress tensor and components of lamina

𝜺, 𝜀𝑖𝑗

strain tensor and components of lamina

𝑫, 𝑑𝑖

damage tensor and components of damage variable

𝑑

compliance tensor with damage in terms of engineering constants of lamina

𝑑

𝑪

stiffness tensor with damage in terms of engineering constants of lamina

Xt, Xc

tensile and compressive strength of lamina in fiber direction

Yt, Yc

tensile and compressive strength of lamina in matrix direction

𝑆𝑖𝑗

shear strength of lamina

𝑺

Gft, Gfc

fracture toughness of lamina in fiber direction

Gmt, Gmc

fracture toughness of lamina in matrix direction

𝑡 𝑐 𝐹11 , 𝐹11

fiber damage initiation criteria

𝑡0 𝑐0 𝜀11 , 𝜀11

critical strain corresponding to fiber damage initiation

𝑡𝑓 𝜀11 ,

fiber failure strain

𝑐𝑓 𝜀11

𝑙𝑐

characteristic length of element

𝐹𝐸 (𝜃)

stress exposure factor for matrix damage initiation

𝜎𝑛 (𝜃), 𝜎𝑛𝑡 (𝜃), 𝜎𝑛𝑙 (𝜃)

stress components on the potential fracture plane

𝐴 𝐴 𝑅⊥𝑡 , 𝑅⊥⊥ , 𝑅⊥∥

three strengths on the fracture plane

𝑡 𝑝⊥⊥ , 𝑡 𝑝⊥𝜑 ,

𝑐 𝑝⊥⊥ , 𝑐 𝑝⊥𝜑

𝑡 𝑝⊥∥ ,

𝑐 𝑝⊥∥

inclination parameters inclination parameters at any angle 𝜑

𝐴 𝑅⊥𝜑

strengths against a resultant shear stress

𝐺𝑚𝑡 , 𝐺𝑚12 , 𝐺𝑚23

critical energy release rate under tension and shear stress on fracture plane

𝐺

critical energy release rate for matrix failure

𝜀𝑒𝑞

equivalent strain

0 𝜀𝑒𝑞 ,

𝑓 𝜀𝑒𝑞

equivalent damage initiation and failure strain on fracture plane

𝜎𝑒𝑞

equivalent stress

𝑜 𝜎𝑒𝑞

0 equivalent stress corresponding to 𝜀𝑒𝑞

N, S, T

interface strength in normal and shear direction

𝑡𝑛 , 𝑡𝑠 , 𝑡𝑡

the traction force in normal and shear direction of interface

𝐺𝑛 , 𝐺𝑠, 𝐺𝑡

interface energy release rate for mode I, II and III

𝐺𝐼𝑐 ,

interface critical energy release rate of mode I, II and III

𝐺𝐼𝐼𝑐 ,

𝑐 𝐺𝐼𝐼𝐼

1. Introduction Composite sandwich structures are increasingly used in various applications ranging from energy and aerospace applications due to their high stiffness-to-weight ratio, energy absorption properties and corrosion resistance[1-5]. However, sandwich structures are also susceptible to low-velocity impact events from foreign object. Such impact events can be caused by tool drop, hail and debris impact during manufacture, maintenance and service life. The impact damage can result in the reduction of properties especially compressive strength which can lead to catastrophic failure during whole life. Therefore, it is necessary to investigate the complicated impact resistance and damage mechanism of sandwich structures under low-velocity impact[6,7]. Sandwich structures focused in this paper consist of two thin composite facesheet and a relatively soft Nomex honeycomb core[8]. Recently, composite structure are becoming more attractive to metals because of advantageous properties such as high strength-to-weight ratio[9-12]. And Nomex honeycomb can also be a suitable choice thanks to good flammability, environment resistance and low dielectric properties[13-18]. Low-velocity impact can induce different damage modes on facesheet, core material and facesheet/core interface. These damage behaviors depend on various factors including impact energy, material properties, geometric parameters and boundary conditions. Typical failure modes on laminate facesheet mainly contain intralaminar(fiber breakage, matrix cracking) and interlaminar(delamination) damage[19-23]. Localized core crushing with irreversible deformation always appear in the impact region due to indentation. Meanwhile, global deformation of sandwich structure can cause core shear.

The damage mechanism of composite sandwich structures is significantly complicated than conventional laminates[24]. It is mainly due to the interaction of facesheet damage and core deformations. Experimental, numerical and theoretical methods have been employed to investigate the mechanical behavior of sandwich structures under low-velocity impact[25-28]. Many researchers obtained the dynamic response and material damage directly through impact experiments and inspection methods. Theoretical investigation is convenient to get the dynamic response with reductions in the cost and time. But some details can hardly be obtained due to assumptions and simplifications. Numerical finite element method (FEM) combined with fracture models has become a common method to analyze and predict the impact procedure. Simulation can obtain extra important information such as internal damage details with appropriate time-consuming and cost-intensive. In practice, researchers tend to use a combination of these methods to investigate impact behavior to improve the designable and predictable capability. Morada et al[7] investigated the damage resistance of sandwich panel with ATH/epoxy core under low-velocity impact. The viscoplastic-damage model was used to present the mechanical behavior of ATH/epoxy core. It was found that the primary failure mode is indentation instead of fiber breakage, delamination and facesheet/core debonding. Chen et al[29] investigated the low-velocity impact response of composite sandwich panel through finite element modelling and experiment. The model included facesheet damage, core crushing as well as facesheet/ core debonding. Klaus et al[30] investigated the residual strength after impact of sandwich panels experimentally and numerically. They obtained the residual strength through 4-point bending after impact with different energy. It is observed that the damage and deformations caused by impact test had great influenced on the bending strength of the damaged specimen. And the numerical has also been established to present the impact and bending test with a good agreement. Besant et al[31] established a finite element model to study the low-velocity impact behavior of composite sandwich panels. The metal honeycomb is regarded as an anisotropic elasto-plastic material and the yield criteria are based on combined shear and compression experiment. They observed that the honeycomb absorb energy well through a combination of local crush and shear yielding. Menna et al[32] studied the impact behavior of composite honeycomb sandwich structures numerically. They concerned the damage model, the strain-rate effect and energy absorption capacity. The material parameters were calibrated based on fundamental experiments in order to obtain more reliable simulation results. Feng and Aymerich[33] concerned the development of a FE tool for predicting the damage response of composite foam sandwich structures under low-velocity impact. They proposed the detailed simulation of intralaminar and interlaminar damage. Experiments were performed to observe material damage and calibrate simulations. Qualitative agreement was obtained between FE results and experiment in terms of dynamic response and damage modes. Ivañez et al[34] developed a 3D finite element model to predict the dynamic flexural behavior of composite sandwich beams with foam core. In the FE model, they present the failure damage of woven composite facesheet by using Hou criteria. The results indicated that the compressive properties of foam core greatly influenced failure of sandwich beams directly even though composite facesheet has high strength. Wang et al[35] studied the impact behavior of foam-core sandwich panels subjected to low-velocity impact using experimental and numerical methods. They investigated the influence of the facesheet thickness, core thickness, impact energy and impactor size on the dynamic response and material damage of sandwich plates. When the facesheet thickness increase, the percent of absorbed energy and impact duration decrease, while the peak load increase. Lacy and Hwang[36] established a three-dimensional FE model to analyze the residual compressive strength after impact of sandwich composite structure. They determined several parameters of impacted plate including dent depth, damage area and core crushing zone throughout

impact experiment. The damaged facesheet is presented by degraded stiffness meanwhile the constitutive law of intact and damaged core, which is considered as springs, is also different. Leijten et al[37] experimentally investigated the primary sandwich structures under low-velocity impact by considering the influence of different impact energy, materials and geometric sizes on the behavior of impact and compression after impact. They found that damage is more local for thicker core whereas global damage tended to appear for thinner core. The planar damage is influenced obviously by core thickness and density(but not by facesheet). The residual strength mainly depended on the facesheet damage instead of core damage. McQuigg et al[38,39] studied the low-velocity impact and compression after impact behavior of honeycomb core sandwich panels with thin composite facesheet and had new understanding of damage tolerance for these materials. Refined numerical models can provide sufficient detailed information of failure mechanism and damage evolution. Many literatures have focused simulation based on different methods containing several categories: failure criteria, fracture mechanics, damage mechanics and plastic theories[40,41]. FEM simulations based on continuum damage mechanics(CDM) are often utilized with composite failure criteria as damage initiation and followed by stiffness degradation as damage evolution. Despite of complication and interaction of sandwich damage, the material model of composite facesheet and honeycomb core can be considered in FE model individually. On the one hand, the precision of simulation results depends on the failure criteria of composite laminate. Many researchers have investigated low-velocity impact of conventional composite laminates numerically[42-46]. On the other hand, honeycomb core can also influence the facesheet damage apparently. Early researches regard honeycomb cell as equivalent continuum material using solid element to improve calculation efficiency[47-48]. However, these approaches might neglect the real behavior of cell walls especially at post-buckling stage. Three-dimensional FE models with detailed cell walls revealing accurate deformation damage progression are becoming more attractive[49-52]. Honeycomb cell walls are considered as isotropic, orthotropic or further multilayer shells with plasticity. As outlined above, this paper focuses on the description of low-velocity impact damage resistance of sandwich panels with CFRP facesheet and Nomex honeycomb core. In order to investigate the damage modes and sequence under different impact levels for two core thickness, a series of low-velocity impact tests on two different core thickness were performed through drop weight tower. The impact dynamic response of impacted sandwich panels was characterized in terms of peak force history, energy absorption and contact duration. Failure modes of specimens were observed subsequently through non-destructive inspection (NDI) ultrasonic C-scan and destructive methods. In addition, a refined three-dimensional finite element model was established with intralaminar and interlaminar damage of composite facesheet. Geometrical and material conditions of cell walls of honeycomb core were also considered by using the detailed meso-scale model. The intralaminar damage initiation and evolution of facesheet were predicted with physically-based composite failure criteria and energy-based progressive damage, respectively. While the interlaminar damage including facesheet delamination and facesheet/core debonding was simulated by means of cohesive element. This refined FE model is shown to be able to reproduce the damage of sandwich structures as well as the failure mechanism under low-velocity impact. An objective of the paper is, therefore, to figure out the impact damage with two core thickness under different impact energy levels. This research also aims to develop an available virtual testing model to provide thorough understanding of the damage characterization. Consequently, it can be used on new sandwich designs with wide range of possible configurations before manufacturing for reducing costs and timeconsumption. Furthermore, the present FE model can be used to predict residual properties of pre-impact

composite sandwich structures with different core thickness. 2. Experiment procedure 2.1 Sandwich panel The sandwich plates are manufactured with unidirectional CFRP composite facesheet and Nomex hexagonal cell honeycomb core. The material system used for the facesheet is T300/Epoxy in this study. The front and back-up composite facesheet bonded with honeycomb are quasi-isotropic laminate with a stacking sequence of [45/0/-45/90]s. The nominal thickness of facesheet is 1mm with each ply of 0.125mm. The sandwich plates were cut into specimens with the geometry of 100mm×150mm using a diamond coated blade. The core was made of Aramid/Resin honeycomb with nominal single cell thickness of 0.1mm. The specimens focused in this paper contain two different core thickness of 8mm and 16mm. The longitudinal direction is along the length of sandwich plate. 2.2 Drop weight impact tests The low-velocity impact tests were carried out by using Instron Dynatup 9250HV Drop Weight Impact Testing Machine. The steel hemispherical impactor guided by two guide columns is adopted for all the impact tests with a diameter of 16mm and mass of 5.607kg. A data acquisition system is used to collect the contact force between the impactor and specimen, and a pneumatic-laser system is equipped to avoid secondary impact(Fig. 1). The displacement and velocity history can be calculated through numerical integration of the acceleration and velocity history. The rectangular impact support fixture shown in Fig. 1 with a cutout of 125mm×75mm and four clamps with rubber tips are used to restrain specimens during impact. The impact energy levels of 3J, 6J and 10J are conducted by setting different impact velocity, as show in Table 1.

Fig. 1. Impact test setups Impact force, displacement and energy absorption time histories are obtained from the measurements and calculations during impact procedure. Dent depth is measured after the impact test immediately for each specimen. And the damage area of facesheet is also measured by ultrasonic C-scan equipment. Table 1 Sandwich specimens and test matrix Panel

Number of

Facesheet

ID

specimen

thickness(mm)

Stacking sequence

Core

Impact

thickness(mm)

energy(J)

2 S1

S2

3

3 1.0

[45/0/-45/90]s

16.0

6

3

10

2

3

3 3

1.0

[45/0/-45/90]s

8.0

6 10

3 Experimental results and discussion 3.1 Impact dynamic response

Fig. 2 shows typical contact force history and impact force-displacement curve of plates with 16mm thickness core in different impact energy. Fig. 2a illustrates that the shape of contact force history with small and large energy are different thanks to different damage mechanism. In small impact energy(3J), the curve is close to sine function with nearly smooth process whereas the other two with larger impact energy are not. At the beginning of the impact, the impact force increase to more than 0.6kN over a short period of time at which both facesheet and honeycomb core remain in elastic stage. After that, impact contact force with lower rate continue increasing up to peak value. The reason for the change might be that the honeycomb core crushing resulting to smaller foundation stiffness under facesheet lower its support to facesheet and impactor. For the impact energy of 6J and 10J, sudden load drops followed by a continued load increase with fluctuation are observed. As we can see, the maximum force with impact energy of 6J and 10J are larger than one with energy of 3J, obviously. It can be attributed to the catastrophic facesheet damage dominated by fiber breakage which was not appeared under 3J impact. From Fig. 2, it can be seen that the change of slope of force-displacement curves indicates stiffness degradation due to various damage modes. For these levels of impact energy, the curve before the maximum contact force are almost identical. However, the final and maximum displacement increase with the increase of impact energy.

(a)

(b)

(c)

Fig. 2. Impact response of sandwich plates under different energy: (a) impact force history, (b) impact force-displacement curve and (c) energy absorption. 3.2 Non-destructive C-scan inspection Delamination damage is particularly significant to evaluate the impact damage resistance. Fig. 3 demonstrates the typical delamination area obtained through ultrasonic C-Scan under different impact energy. Delamination is detected in the facesheet of impact side and larger C-scan damage area appears for higher impact energy. For the small impact energy of 3J, the projected shape is irregular with delamination in different interface. For larger impact energy, the projected delamination is nearly elliptical with obviously larger areas. It can be observed that delamination mainly occurs in bottom position of upper facesheet.

Fig. 3. Ultrasonic C-scan damage: (a)S1-3J, (b)S1-6J, (c)S1-10J, (d) S2-3J, (e) S2-6J and (f) S2-10J. 3.3 Impact damage 3.3.1 Visible damage and indentation The visible inspections of the damaged specimens are presented to observe the damage modes and regions. The facesheet damage including fiber and matrix damage occurred on facesheet of impact side.

Fig. 4 shows the facesheet damage of specimen with thick core under different impact energy.

(a)

(b)

(c)

Fig. 4. Impact damage of facesheet: (a)3J, (b)6J and (c)10J. From Fig. 4, it is observed that the impact-induced damage area increases with the increase of impact energy. For the impact energy of 3J, facesheet damage cannot be observed. The size in Fig. 4a is used to show the small dent after impact instead of facesheet damage. The facesheet damage occurs for larger impact energy. And the damage area of specimens with thin core is similar to what is shown in

Fig. 4. The details of upper facesheet damage area are illustrated in Fig. 5. Impact damage under 6J and 10J is shown in this paper. It can be observed that the impact-induced damage includes fiber breakage and matrix cracking in different regions and the damage is more severe for specimen under impact energy of 10J. Fiber and matrix damage results from bending and membrane stress of top facesheet.

(a)

(b)

Fig. 5. Details of impact-induced damage: (a) impact energy of 10J and (b) impact energy of 10J. 3.3.2 Section inspection Section inspection was performed for a typical specimen under 6J impact as shown in Fig. 6. The intralaminar and interlaminar damage can be observed in digital microscope images. Fiber breakage and extensive matrix cracking were caused mainly by tensile stress appeared under impactor. Meanwhile, the delamination is also obvious in the damage region and larger area. Matrix cracking can grow diagonally in several off-axis plies and connected with interface cracks. It can be indicated that initiation and propagation of matrix cracking and delamination interacted with each other during impact process. Similar characteristics were reported in ref[53]. In addition, the core curshing appeared under damaged facesheet with buckling of cell walls. It is worth noting that shear cracking can be seen in several cell walls of honeycomb core outer the impact location for specimen with thinner thickness of core, as shown in Fig. 6b. It is expected that the specimen subjected to impact loading with thinner core are more flexible and have larger shear stress in honeycomb core. Thus the shear cracking appeared in thinner honeycomb core while no shear cracking can be observed in thicker core.

(a)

(b) Fig. 6. Section inspection for material damage: (a) thicker core and (b) thinner core. 3.4 Influence of impact energy and core thickness The peak contact force, displacement and impact duration under different impact energy are shown in Fig. 7(a)-(c). The relationship between maximum contact force and impact energy is not linear. The peak force combined with load drop indicates the catastrophic failure of facesheet as shown in aforementioned discussion. As a result, the peak value barely increased after impact energy of 6J due to the fiber breakage resulting in the loss of load capacity. It is mentioned that peak force for specimens with thinner core is smaller than that for thicker ones with lower flexibility, especially under 3J impact.

While the difference is less apparent under higher impact energy. In addition, the larger flexibility of thin specimen due to larger maximum displacement and impact durations from Fig. 7(b) and (c). It can be concluded that the local facesheet breakage determined the maximum value of contact force under higher impact energy.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7. Comparison between thick and thin specimen: (a) peak force, (b) maximum displacement, (c) impact duration, (d) normalized absorbed energy, (e) indentation depth and (f) delamination area. The energy absorption ratio, indentation depth and delamination area are also shown in Fig. 7(e)(f). An increasing impact energy leads to more energy absorption ratio, permanent indentation depth and projected delamination area. Nevertheless, the normalized absorbed energy did not show a linear relationship with impact energy. Obviously, the impact energy was absorbed mainly through facesheet damage and honeycomb crushing. Thus, the energy absorption ratio had more significantly growth from 3J to 6J impact due to the appearance of fiber breakage of facesheet. The permanent indentation depth of thick specimens was slight larger than thin ones. In addition, the delamination area of facesheet with thick specimens was apparently higher than that of thin specimens. 4 Material modelling 4.1 Constitutive model In this research, a three-dimensional FE model based on continuum damage mechanics (CDM) combined with failure criteria was implemented for the prediction of intralaminra damage of composite facesheet under low-velocity impact. The damage of composite laminates of facesheet contains two procedure[54]: damage initiation and damage evolution. The damage initiation indicates the happening of damage determined by damage initiation criteria. Damage evolution is a process up to final failure following the damage initiation. Composite lamina is considered orthotropic material. The damage tensor is adopted for orthotropic material, which is defined by the following equation 3

𝑫 = ∑ 𝐷𝑖 𝒏𝑖 ⨂𝒏𝑖 𝑖

(1)

where Di and ni are the principal value and direction of damage tensor D, respectively. The damage of lamina is derived based on Gibbs free energy density, which can be represented as[55]: 𝐹=

2 2 2 2 2 𝜎11 𝜎22 𝜎33 𝜎12 𝜎13 + + + + 2𝐸1 (1 − 𝑑1 ) 2𝐸2 (1 − 𝑑2 ) 2𝐸3 (1 − 𝑑3 ) 2𝐺12 (1 − 𝑑12 ) 2𝐺13 (1 − 𝑑13 ) 2 𝜎23 𝜐12 𝜐13 𝜐23 + − 𝜎11 𝜎22 − 𝜎11 𝜎33 − 𝜎 𝜎 2𝐺23 (1 − 𝑑23 ) 𝐸1 𝐸3 𝐸2 22 33

(2)

where the di(i=1, 2, …) is the components of damage variable referring to material coordinate of composite lamina. The constitutive relationship with damage can be derived following the thermodynamics potential 𝜺=

𝜕𝐹 = 𝑺𝑑 ∶ 𝝈 𝜕𝝈

(3)

where σ and  are the stress and strain tensor, respectively. Sd is compliance tensor with damage in terms of engineering constants of composite lamina. The stiffness tensor Cd with damage can be obtained from the inversion of compliance tensor Sd 𝑪𝑑 = (𝑺𝑑 )−1

(4)

Therefore, the constitutive law with damage expressing the relationship between stress and strain is 𝝈 = 𝑪𝑑 ∶ 𝜺

(5)

For composite lamina, shear nonlinearity significantly influences the mechanical behavior under low-velocity impact and other conditions. Various forms of shear nonlinearity were proposed. The nonlinear shear model as following was adopted 𝜏𝑖𝑗 = 𝑆𝑖𝑗 [1 − 𝑒

𝐺𝑖𝑗 𝛾𝑖𝑗 − 𝑆𝑖𝑗

]

(6)

where the 𝛾𝑖𝑗 is shear strain components. 4.2 Intralaminar damage model 4.2.1 Fiber damage model The maximum strain criterion is used to predict the fiber tensile and compressive damage initiation. 2

𝜀11 𝑡 𝐹11 = ( 𝑡0 ) ≥ 1 𝜀11

𝜀11 ≥ 0 (7)

2

𝑐 𝐹11

𝜀11 = ( 𝑐0 ) ≥ 1 𝜀11

𝜀11 ≤ 0

𝑡0 𝑐0 where 𝜀11 and 𝜀11 is critical strain corresponding to damage initiation for fiber tension and

compression, respectively. The expression is 𝐼0 𝜀11 =

𝑋𝐼 𝐸11

(𝐼 = 𝑡, 𝑐)

(8)

The progressive degradation model is selected to present the damage status. The damage variable for fiber tension and compression can be presented as 𝑡𝑓

𝑡 𝑑11 =

𝑐 𝑑11

=

𝑡0 ) 𝜀11 (𝜀11 − 𝜀11 𝑡𝑓 𝑡0 ) 𝜀11 (𝜀11 − 𝜀11 𝑐𝑓 𝑐0 𝜀11 (𝜀11 − 𝜀11 )

(9)

𝑐𝑓

𝑐0 ) 𝜀11 (𝜀11 − 𝜀11 𝑡𝑓

𝑐𝑓

where the 𝜀11 and 𝜀11 are the failure strain for fiber tension and compression, respectively. The failure strain is expressed by fiber fracture toughness Gf

𝐼𝑓

𝜀11 =

2𝐺𝑓𝐼 𝑋𝐼 𝑙𝑐1

(10)

where 𝑙𝑐1 is characteristic length which can reduce the mesh sensitivity. The residual strength of fiber can be considered assuming equal to matrix compressive strength to account for the interaction of fragment fiber under compression. The schematic diagram of bilinear damage evolution models for fiber are shown in Fig. 8. The damage evolution law in fiber

Fig. 8. The damage evolution law in fiber direction 4.2.2 Matrix damage model A large amount of literature focusing on the failure criteria for unidirectional composite materials has been developed[56-58]. According to WWFE[59], failure criteria proposed by Puck and Schurmann[60] show good prediction in certain condition especially for matrix failure mode. Puck’s criteria were used to predict the matrix cracking. The matrix crack in Puck’s criteria lead to straight crack on a potential fracture planes paralleled to fiber direction called action plane, as shown in Fig. 9. The

action plane and fracture angle.

Fig. 9. The action plane and fracture angle The stress of action plane including normal and shear stress determine matrix cracking. In the case of tension stress on action plane (𝜎𝑛 > 0), matrix crack is promoted combined with two shear stress components whereas fracture is counteracted through compressive normal stress (𝜎𝑛 < 0). The criteria are illustrated as follows 2

2 2 𝑡 𝑡 𝑝⊥𝜑 𝑝⊥𝜑 1 𝜏𝑛𝑡 (𝜃) 𝜏𝑛𝑙 (𝜃) 𝐹𝐸 (𝜃) = √[( 𝑡 − 𝐴 ) ∙ 𝜎𝑛 (𝜃)] + ( 𝐴 ) + ( ) + 𝐴 𝜎𝑛 (𝜃) ≥ 1 𝑅⊥∥ 𝑅⊥ 𝑅⊥𝜑 𝑅⊥⊥ 𝑅⊥𝜑

𝜎𝑛 (𝜃) ≥ 0

(11) 2

𝐹𝐸 (𝜃) = √(

2

2

𝑐 𝑐 𝑝⊥𝜑 𝑝⊥𝜑 𝜏𝑛𝑡 (𝜃) 𝜏𝑛𝑙 (𝜃) ) + ( 𝐴 𝜎𝑛 (𝜃)) + 𝐴 𝜎𝑛 (𝜃) ≥ 1 𝐴 ) +( 𝑅 𝑅⊥⊥ 𝑅⊥𝜑 𝑅⊥𝜑 ⊥∥

𝜎𝑛 (𝜃) ≤ 0

where 𝑡,𝑐 𝑝⊥𝜑 𝐴 𝑅⊥𝜑

=

𝑡,𝑐 𝑡,𝑐 𝑝⊥∥ 𝑝⊥⊥ 2 2 ∙ cos 𝜑 + 𝐴 𝐴 ∙ sin 𝜑 𝑅⊥⊥ 𝑅⊥∥

(12)

𝐴 𝑅⊥⊥ =

𝑅⊥𝑐 𝑐 ) 2(1 + 𝑝⊥⊥

cos2 𝜑 =

2 (𝜃) 𝜏𝑛𝑙 2 (𝜃) 2 (𝜃) 𝜏𝑛𝑙 + 𝜏𝑛𝑡

and the stress components on action plane shown in Fig. 9 are 1 1 𝜎𝑛 (𝜃) = (𝜎2 + 𝜎3 ) + (𝜎2 − 𝜎3 ) ∙ cos 2𝜃 + 𝜏23 ∙ sin 2𝜃 2 2 1 𝜏𝑛𝑡 (𝜃) = − (𝜎2 − 𝜎3 ) ∙ sin 2𝜃 + 𝜏23 ∙ cos 2𝜃 2

(13)

𝜏𝑛𝑙 (𝜃) = 𝜏13 ∙ cos 𝜃 + 𝜏12 ∙ sin 𝜃 The stress exposure factor FE(θ) in failure criteria in Eq(11) depends on the action plane. Thus, when stress state is determined in material coordinates, the stress exposure factor can be considered a function in terms of the angle θ. The maximum value should be calculated and corresponding angle θ is the fracture angle θf. Actually, analytical solution can barely be obtained so that numerical method has to be utilized to get the solution. It is time consumed if the maximum value of FE(θ) is searched at an interval of 1°. Thus this paper employed the Selective Range Golden Section Search(SRGSS)[61,62] algorithm to obtained the maximum value of FE(θ). If the maximum of stress exposure factor equals to 1 or greater than 1, matrix damage occurs with the corresponding fracture angle θf. After the damage initiation of matrix crack, the damage variable will be also defined as bi-linear relationship with respect to the equivalent stress and strain, as presented in Eq(14). 𝑓

𝑑2 =

0 ) 𝜀𝑒𝑞 (𝜀𝑒𝑞 − 𝜀𝑒𝑞 𝑓 0 ) 𝜀𝑒𝑞 (𝜀𝑒𝑞 − 𝜀𝑒𝑞

(14)

The equivalent stress and strain can be defined as: 𝜀𝑒𝑞 = √〈𝜀𝑛 〉2 + (𝜀𝑛𝑙 )2 + (𝜀𝑛𝑡 )2 𝜎𝑒𝑞 = √〈𝜎𝑛 〉2 + (𝜏𝑛𝑙 )2 + (𝜏𝑛𝑡 )2

(15)

with 1 1 𝜀𝑛 = (𝜀2 + 𝜀3 ) + (𝜎2 − 𝜎3 ) ∙ cos 2𝜃 + 𝜀23 ∙ sin 2𝜃 2 2 𝜀𝑛𝑡 (𝜃) = −(𝜀2 − 𝜀3 ) ∙ sin 2𝜃 + 2𝜀23 ∙ cos 2𝜃 𝜀𝑛𝑙 (𝜃) = 2𝜀12 ∙ cos 𝜃 + 2𝜀13 ∙ sin 𝜃

(16)

𝑓 0 where the operator 〈∙〉 is McCauley operator. And the 𝜀𝑒𝑞 and 𝜀𝑒𝑞 are equivalent damage initiation

strain and equivalent damage failure strain on fracture plane, respectively. 𝑓

The 𝜀𝑒𝑞 is defined with respect to the fracture toughness and element characteristic length. The 𝑓

expression of 𝜀𝑒𝑞 is 𝑓

𝜀𝑒𝑞 =

2𝐺 𝑜 𝑙 𝜎𝑒𝑞 𝑐2

(17)

𝑜 0 where 𝜎𝑒𝑞 is equivalent stress corresponding to 𝜀𝑒𝑞 and 𝑙𝑐2 is element characteristic length.

It should be noted that the fracture toughness G can be defined under mixed-mode situation[63,64]. According to research from Ref[65], the power law mixed-mode criterion from interlaminar fracture can be used here as follows

2 𝛼

𝛼

1 − 2 𝛼 𝛼

0 𝑜 0 1 𝜎𝑛𝑜 𝜀𝑛0 2 1 𝜎 𝑜 𝜀𝑛𝑙 1 𝜎𝑛𝑡 𝜀𝑛𝑡 〈 𝑜 0 〉 ) +( ( 𝑛𝑙 ) ) +( ( 𝑜 0) ) ] 𝐺 = [( 𝑜 0 𝐺𝑚𝑡 𝜎𝑒𝑞 𝜀𝑒𝑞 𝐺𝑚12 𝜎𝑒𝑞 𝜀𝑒𝑞 𝐺𝑚23 𝜎𝑒𝑞 𝜀𝑒𝑞

(18)

where 𝐺𝑚𝑡 is critical fracture toughness for matrix tensile crack. 𝐺𝑚12 and 𝐺𝑚23 are critical fracture toughness under corresponding shear stress. The coefficient 𝛼 is set to 2. For both fiber and matrix damage, total damage was adopted in FE model as follows 𝑡 𝑐 }} 𝑑𝑚(𝑐) = min {1, max{𝑑𝑚(𝑐) , 𝑑𝑚(𝑐)

(19)

which indicates that the total damage variable is the maximum value for tensile and compressive damage. In addition, damage variable is limited as the following equation due to irreversibility. 𝑑𝑚(𝑐) = max{𝑑𝑚(𝑐) (𝑗)}

(20)

where j denotes the analysis increment step.

4.3 Interlaminar damage model Delamination between plies with different fiber angle is simulated by means of inserted cohesive element[66-69]. The delamination damage in cohesive element can be divided into two procedures: damage initiation and damage evolution. Damage initiation can be performed through stress and strain criteria, meanwhile, damage evolution can be modeled based on energy or effective displacement. The interface behavior is elastic linear before damage initiation occurred. The three components of traction stress vector can be expressed as: 𝐾𝑛𝑛 𝑡𝑛 𝒕 = { 𝑡𝑠 } = [ 𝑡𝑡

𝐾𝑠𝑠

𝛿𝑛 ] { 𝛿𝑠 } 𝐾𝑡𝑡 𝛿𝑡

(21)

where t and 𝛿 are traction stress and separation displacement vector consisting of the normal and two shear components, respectively. 𝐾𝑖𝑖 (𝑖 = 𝑛, 𝑠, 𝑙) is separation stiffness. In mixed-mode loading conditions, damage initiation and evolution are determined by damage modes I, II and III. Fig. 10 illustrates a typical mixed-mode response including failure mechanism in cohesive elements.

Fig. 10 Illustration of bilinear mixed-mode response in cohesive elements In present research, stress-based quadratic damage initiation criterion is used as follows: {

〈𝑡𝑛 〉 2 𝑡𝑠 2 𝑡𝑡 2 } +{ } +{ } = 1 𝑁 𝑆 𝑇

(22)

where 𝑡𝑛 , 𝑡𝑠 and 𝑡𝑡 are the traction force in normal and shear direction, respectively. The N, S, T are

the corresponding strength under crack mode I, II and III. Stiffness degradation is introduced into simulation to present the damage of interface. A linear softening formula is chosen to predict damage propagation. Thus, the damage variable 𝑑𝑑𝑒𝑙 is defined as: 𝑑𝑑𝑒𝑙 =

f (𝛿 max 0) 𝛿𝑚 − 𝛿𝑚 𝑚 max (𝛿 f − 𝛿 0 ) 𝛿𝑚 𝑚 𝑚

(23)

f 0 where 𝛿𝑚 and 𝛿𝑚 are the effective displacements corresponding to damage initiation and ultimate max failure. 𝛿𝑚 refers to the maximum value of the effective displacement during the loading history. The

effective displacements can be given by: 2 𝛿𝑚 = √〈𝛿𝑛 〉2 + 𝛿𝑠2 + 𝛿𝑡2 = √〈𝛿𝑛 〉2 + 𝛿𝑠ℎ𝑒𝑎𝑟

(24)

For an opening crack of which the normal displacement 𝛿𝑛 > 0, the mode mix ratio 𝛽 is defined as: 𝛽=

𝛿𝑠ℎ𝑒𝑎𝑟 𝛿𝑛

(25)

obviously, the pure mode I and shear mode are particular cases for 𝛽 = 0 and 𝛽 → ∞, respectively. The components of displacement of damage initiation for the onset of softening in pure mode I, II and III are given as: 𝛿𝑛0 =

𝑁 , 𝐾𝑛𝑛

𝛿𝑠0 =

𝑆 , 𝐾𝑠𝑠

𝛿𝑡0 =

𝑇 𝐾𝑡𝑡

(26)

Substituting eqs.(21, 24-26) into eqs(22), the effective displacement corresponding to damage initiation in mixed loading can be obtained as:

0 𝛿𝑚

1 + 𝛽2 𝛿𝑛0 𝛿𝑠0√ 0 2 = (𝛿𝑠 ) + (𝛽𝛿𝑛0 )2

𝛿𝑛 > 0

0 𝛿𝑠ℎ𝑒𝑎𝑟

{

(27)

𝛿𝑛 ≤ 0

The damage propagation in mixed loading conditions is usually predicted through fracture toughness and energy release rate. The power law mixed-mode relationship criterion was adopted to control delamination propagation at present: 𝐺𝑛 2 𝐺𝑠 2 𝐺𝑡 2 { 𝑐} + { 𝑐 } + { 𝑐 } = 1 𝐺𝐼 𝐺𝐼𝐼 𝐺𝐼𝐼𝐼

(28)

𝑐 where 𝐺𝐼𝑐 , 𝐺𝐼𝐼𝑐 and 𝐺𝐼𝐼𝐼 are the fracture toughness of mode I, II and III, respectively, as: 𝑓

𝐺𝐼𝑐

𝛿𝑛

𝑓

= ∫ 𝑡𝑛 𝑑𝛿𝑛 ,

𝐺𝐼𝐼𝑐

𝑓

𝛿𝑠

= ∫ 𝑡𝑠 𝑑𝛿𝑠 ,

0

𝑐 𝐺𝐼𝐼𝐼

𝛿𝑡

= ∫ 𝑡𝑡 𝑑𝛿𝑡

0

(29)

0

The effective displacement corresponding to ultimate failure can be expressed as: 𝛼 −1/𝛼

𝛼

2(1 + 𝛽2 ) 1 𝛽2 [( 𝑐 ) + ( 𝑐 ) ] 𝑓 𝐾 𝐺𝐼 𝐺𝐼𝐼 𝛿𝑚 = {

2 √(𝛿𝑠𝑓 )

+

𝑓 2 (𝛿𝑡 )

𝛿𝑛 > 0 (30) 𝛿𝑛 ≤ 0

5 The Finite Element model The 3D finite element model is carried out through ABAQUS/Explicit package for the 150mm×100mm composite sandwich panel. The intralaminar damage of composite facesheet is

implemented by VUMAT subroutine. The organizational chart of VUMAT is presented in Fig. 11

Fig. 11 The organizational chart of VUMAT The geometry of plate including the size of facesheet and detailed honeycomb cell walls, material, stacking sequence and boundary conditions are defined to represent the actual experimental setup consistently. The full model is shown in Fig. 12

Fig. 12. The model of sandwich panel with fixture and impactor. 5.1 Element type and mesh size Three-dimensional solid 8-node linear solid brick elements with reduced integration C3D8R were used for CFRP facesheet for its lower computationally expensive and avoiding to shear locking. In order to present the mechanical behavior and damage distribution, each layer in facesheet with the stacking sequence of [+45/0/-45/90]s has one element along thickness direction. As mentioned above, detailed cell of honeycomb was considered in this research. As a result, honeycomb cell walls were meshed employing 4-node shell elements with reduced integration S4R due to the thin thickness. With consideration of delamination of composite facesheet, cohesive element which is widely used to simulate interface crack is used between plies in facesheet. Hamitouche[69] investigated the delamination of composite laminates by cohesive element and focused on the stability and convergency through introducing viscosity into constitutive equations. According to researches[70], interfaces prone to delamination are the plies with larger difference between fiber angles. Therefore, cohesive element COH3D8 were inserted at the laminate facesheet interfaces between layers with different fiber

orientations to present delamination initiation and propagation with the aforementioned damage criteria. The impactor and fixtures are regarded as completely elastic material. Different mesh sizes were used so as to reduce the computational time. As shown in Fig. 13, in the central region with 40mm×40mm, in the impacted zone, a refined mesh was used for accuracy. And coarser elements were employed in other regions away from center. Identically, for the honeycomb core, a mesh size of 0.3 mm along cell wall width has been determined in central region and coarser elements were used in distant regions.

Fig. 13. The description of full finite element model The mesh convergence test was performed to determine element size in the central region. Fig. 14 shows the four mesh models with element sizes 2.0mm×2.0mm, 1.25mm×1.25mm, 0.75mm×0.75mm and 0.5mm×0.5mm. The FE model for mesh convergence test was implemented under 6J impact energy with material damage model. Fig. 15 indicates the maximum contact force with different mesh sizes. It is demonstrated that the maximum force decreased with smaller mesh size and was eventually converged for the size of 0.5mm×0.5mm. Therefore, the refined mesh size 0.5mm×0.5mm was used in the central region.

Fig. 14 FE models with four mesh sizes.

Fig. 15 Maximum contact force in terms of the mesh size

The FE model of honeycomb includes the cell walls and conventional shell element with reduced integration was used to obtain the detailed deformation. Many researchers have developed the finite element model to simulate the out-of-plane compressive and shear response[71,72]. In actual, Nomex honeycomb cell walls consist of orthotropic ductile aramid paper layer in the center and isotropic brittle phenolic resin coated on surface. Distinct approaches including single isotropic layer[73], single orthotropic layer[74] and multi layers[15] can be found in papers to model the cell walls of Nomex honeycomb. In this paper, the single isotropic layer model with elastic-perfect plastic behavior will be used for cell walls due to its simplicity and capability of representing the mechanical behavior well[75]. The chosen elastic modulus in finite element model is E=5GPa and the yielding stress of plasticity is 105MPa. The parameters have been validated through comparison of flatwise compressive strength of simulation and experiment. In addition, the damage of honeycomb core is also considered. After yielding of the cell walls, the ductile damage criterion is used for the damage prediction. Actually, the cell walls under tension loading featured by more brittle failure comparing to compression. Thus, it is assumed that the compression damage can hardly occur. The equivalent plastic strain predicting the damage onset of cell walls under uniaxial and shear are set as 0.05 and 0.1, respectively. Following damage initiation, the degradation of stress and stiffness control the damage evolution. The debonding between facesheet and core is actually an important failure mode for sandwich structures. Shah et al[54] studied the strain energy release rate of the facesheet foam-core interface with several approaches. In this paper, the debonding is simulated by inserting cohesive element between facesheet and honeycomb core. The cohesive elements were connected with facesheet and honeycomb core with kinematic tie constrain. 5.2 Boundary conditions As shown in Fig. 13, fixture with cutout is also modeled in this simulation in order to obtain more accurate boundary conditions consistent with experiment. All the nodes attached to the bottom surface of fixture is fixed in all three degrees. The impactor is assigned a predefined initial velocity according experimental values in vertical direction without other movements. The general contact algorithm in ABAQUS/Explicit is implemented in this model. The contact includes normal and tangential behavior based on penalty formulation. In this paper, friction coefficient of 0.3 was used for simplicity. 5.3 Material properties The Puck progressive damage model discussed in Section 4 was implemented via VUMAT user subroutine for the laminate facesheet. The elements stiffness was degraded during loading process. As is well-know, the stiffness degradation in local impact region can result in excessive element distortion which leads to convergence problems during solutions. Therefore, a maximum value of 0.999 for damage variable was set to avoid infinitesimal stiffness. In addition, element would be deleted when fiber tension damage d1 reach to critical value. It is in accordance with the physical phenomena that composite material will loss loading capacity with fiber breakage. The material properties are listed in Table 2. Table 2 Material parameters of the T300/epoxy unidirectional laminate Layer properties Modulus(GPa)

E11=140; E22=E33=9GPa; G12=G13=4.6; G23=3.2;

Poisson’s ratio

υ12=υ13= 0.32; υ23=0.38

Strength(MPa)

Xt=1760; Xc=1100; Yt=51; Yc=130; S12=S13=S23=70 2

Fracture toughness(kJ/m )

Gft=91.6; Gfc=79.9; Gmt=0.22; Gm12=Gm23=0.92

Interface properties Strength(MPa)

N=30; S=T=70 2

Fracture toughness(kJ/m )

GIc=0.22; GIIc=GIIIc=0.92

6. Simulation results and discussion 6.1 Impact response The simulation results of thick core specimen under three impact energy levels are shown to validate the prediction. Fig. 16a and b illustrate the comparison of the impact dynamic response and energy absorption of simulation results and experiment under 3J impact. In general, the trend of contact force history of simulated and experimental results has closed correlation. The maximum contact force and impact duration of numerical result are consistent with experiments. Furthermore, it can be seen in Fig.

16b, the trend of real-time energy absorption of simulation and experiment are almost the same. The predicted final absorbed energy is slightly lower than experiment.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 16. Comparison between simulation and experiment results under three impact energy levels The contact force history and energy absorption curve under impact energy of 6J are plotted in Fig. 16c and d. The reasonable results of prediction are achieved due to the correlation with experiment plot for contact force history. We can find the load drop from both the simulated and experimental results.

Correspondingly, the predicted absorbed energy versus time curves are compared with those of experiment illustrated in Fig. 16d and f. As expected, the simulation result is coincided with experiment plot at loading stage before the maximum real-time absorbed energy. The initial kinetic energy of impactor is absorbed mainly through the material damage and plastic deformation. The simulations underestimate absorbed energy under 6J and 10J impact. The reason might be that the material model of cell walls of honeycomb cannot be completely accurate to describe the characters. The honeycomb core can absorb energy due to its large irreversible deformation during impact. The cell wall is not isotropic due to the orthotropic ductile aramid paper layer in the center. Although published literatures proposed that elastic-perfect plastic behavior can represent the mechanical behavior well, discrepancy is unavoidable. In addition, this difference will influence the damage degree of facesheet due to the interaction of facesheet and core damage behavior. As we can see, the load drop occurs twice under 10J impact and the simulation cannot capture the second load drop. 6.2 Visible damage The visible damage of simulation results is also validated. Fig. 17 shows the fiber breakage on surface of upper facesheet from FE model and experiments. We can observe similar failure modes and visible fiber breakage appeared under large impact energy.

Experiment

Simulation

(a)

(b)

(c)

Fig. 17. Visible fiber breakage of facesheet: (a)3J; (b) 6J; (c) 10J 6.3 Internal damage Predicted delamination of facesheet under three impact level are shown in Fig. 18. The delamination area under 3J impact is almost the same with experiment. Meanwhile, the FE model underestimates the total projected delamination area under larger impact energy. The simulation captures the delamination area precisely in the elliptical region under impactor. However, the delamination of bottom interface of facesheet cannot been represented in FE results. The discrepancy might be due to the parameters used in damage criterion of the interface in the simulation cannot perfectly agree with truth material.

Fig. 18. Comparison between predicted and experimental delamination of facesheet

Fig. 19 indicates predicted interface damage and debonding between facesheet and core. The distribution of facesheet/core interface damage is consistent of the regular hexagon of honeycomb cells. It is reasonable due to the connection between facesheet and honeycomb core. The complete debonding only occurs in the central of damage region along several cell walls, as shown in Fig. 19.

Fig. 19. Predicted facesheet/core interface damage and debonding 6.4 Damage characterization The material damage initiation and evolution during impact can be obtained from simulation. The typical predicted intralaminar damage of upper facesheet under 6J impact is demonstrated in Fig. 20. As we can see, at the initial stage, slight matrix damage appears without fiber damage. At about 1ms, the bending deformation becomes larger causing the growth of matrix tensile damage whereas no fiber can be observed. With the increase of impact process, the area of matrix tension damage and delamination continue to increase and facesheet/core interface damage also appears. Meanwhile, slight fiber damage appeared at the bottom plies of top facesheet. After that, the contact force reached its peak of about 2.6kN. An amount of matrix damage can be noted and fiber damage barely changed at that time. After the peak force, fiber breakage occurred on the surface of facesheet resulting in noticeable load drop. In addition, extensive matrix damage is observed and spread toward around especially on the back side of the facesheet. During the impact process, tensile damage was dominated for both matrix and fiber. The delamination and debonding between facesheet and core can also be predicted in simulation. The delamination in facesheet spread rapidly before the maximum contact force, especially before the fiber breakage. Meanwhile, damage also occurs in facesheet/core interface and extends during loading

process. The shape of region is regular hexagon corresponding to honeycomb. The final facesheet/core debonding is mainly located in the central region.

Matrix damage

Fiber damage

Delamination

Face/Core Debonding

A

B

C

D

E

F

Fig. 20. Numerical damage contours of facesheet for 6J impact energy The honeycomb core can influence the impact procedure including impact response and damage significantly. For global deformation, facesheet support bending loading while honeycomb core transfer shear loading. However, focusing on local deformation, the core as foundations can support the facesheet in which bending and shear as well as membrane stress. The honeycomb core was crushing because of impact loading which will result in the change of supporting stiffness to the facesheet. It is difficult to observe the crushing process during impact whereas that can be obtained and analyzed through numerical

results.

Fig. 21 illustrates the crushing process corresponding to the moment marked in Fig. 20. As mentioned above, the buckling of cell walls initiates at about 0.5ms and the growth rate of impact contact force decrease afterward. These phenomena are observed from both experimental plot and numerical prediction. It can be attributed to matrix damage and honeycomb core crushing. The core crushing spread with the deformation of facesheet during impact.

Fig. 21. Numerically core crushing contours for 6 J impact energy In general, the damage mechanism of intralaminar and interlaminar damage can be investigated through the combined results of experiment and simulation. It can be concluded that the buckling of cell walls and matrix damage occurred firstly followed by delamination propagation immediately. Then, the main damage modes were matrix tensile damage and delamination combined with core crushing. The facesheet/core interface damage also started to initiate around this time. Fiber damage would appear after that and visible fiber breakage lead to the decrease of load capacity presenting obvious load drop. Meanwhile, facesheet/core interface damage extended and debonding occurs in the central region. Core damage also extended under the impact region. Finally, the impactor continues to move downward until the start of rebound. Fig. 22 summarized the damage sequence and failure modes during the impact procedure.

Fig. 22. Damage sequence and failure modes It is concluded directly from FE model that the core crushing initiate firstly. Then fiber damage appears meanwhile matrix damage and delamination still extend continually. Meanwhile facesheet/core damage also extends and debonding appears in the central region. In addition, fiber and matrix damage as well as delamination continue to spread after the load drop almost until unloading stage. Therefore, the matrix damage and core crushing cause the stiffness change after a short period. And the three damage modes especially fiber breakage lead to the load drop of contact force. 6.5 Damage of honeycomb core with different core thickness

Fig. 23 shows the comparison between the simulated and experimental section inspection shape of honeycomb including core crushing after the impact. The results illustrate good agreement of experiment and simulation in both macro and meso-scale. The core crushing appears under the impact region resulting from large local deformation during impact. In addition, it is shown that the cell wall rapture along the width direction due to folding. Simulation result predict the cell wall folding and fracture which are consistent with experiments. Thus, this model can capture core crushing behavior of honeycomb under low-velocity impact.

Fig. 23. Comparison between experiment and simulation

Fig. 24 shows the damage distribution of honeycomb core for specimen with different thickness under peak impact force for 6J impact. As we can see, the damage region for local crushing of both specimens are almost identical. Core shear damage is observed in thinner specimen which is not identical with thicker ones due to larger shear stress in thinner core. Although the FE model can predict the core crushing well, it has not predicted the shear cracking for thinner specimens. The reason can be attributed to the complicated properties of cell walls. As mentioned before, the cell walls consist of orthotropic ductile aramid paper layer in the center and isotropic brittle phenolic resin coated on surface. In addition, the cell walls have different failure modes under tensile and compressive loading. Therefore, it is difficult to present the shear crack through homogeneous model combined with ductile damage criterion. It is expected that the results will be better after introducing more appropriate material models. In order to obtain more accurate prediction and improve the applicability of this study, future work will focus on the constitutive law and damage criteria considering the corresponding failure modes under different stress states.

Fig. 24. Core damage distribution of honeycomb core

7 Conclusions In this paper, low-velocity impact tests are implemented on composite sandwich structures using drop weight impact testing machine to study the impact resistance. The dynamic response is recorded. Damage morphology is observed through ultrasonic C-Scan and digital optical microscope. The impact damage with two core thickness under different impact energy levels is investigated. Also, a refined finite element model is developed for thorough and clear understanding of impact behavior. The main

conclusions are listed below: (1) The low-velocity impact can cause different damage modes in sandwich structures. The permanent dent appears under impactor. Fiber and matrix cracking can be observed in composite facesheet. Honeycomb core crushing and cracking also occur under facesheet resulting from local and global deformation. Delamination is detected in damaged facesheets. (2) In small impact energies, there is no visible damage on the facesheet, and the contact force history is in a form sine function. For larger impact energy, the impact region shows apparent indention with fiber breakage and sharply load drop appears in contact force history. The relationship between maximum contact force and impact energy is not linear. Fiber breakage cause the peak force to be constant with the impact energy increasing under larger impact energy. The maximum contact force cannot indicate the damage degree directly under larger impact energy. Meanwhile, the dent depth, delamination area in the facesheet and energy absorbed arise with the impact energy increasing. (3) The deformation behavior during impact of honeycomb for thinner core shows a global pattern, while the thicker one shows a local pattern. The core crushing occurs under facesheet in both core thickness while shear cracking appeared only in thinner specimens. In addition, delamination area increases with the increasing of core thickness. The thickness of honeycomb core has no considerable influence on energy absorption. (4) The refined finite element model can predict dynamic response and material accurately. Good agreement in terms of contact force histories, energy absorption and material damage of the sandwich plate was observed between the experimental data and the numerical results. (5) The simulation relives the damage process of the honeycomb sandwich composite structure subjected to low-velocity impact. It reveals that the honeycomb crushing and matrix damage occur first, then followed by delamination initiation, which induced the stiffness drop. Facesheet/core interface damage also initiates and extends during loading process. The fiber breakage in the facesheet appears lastly. The five types of damage modes interact with each other and result in the drop of contact load between the impactor and the honeycomb sandwich composite structure. Further study needs to focus on the more appropriate constitutive law and damage criteria on cell walls of aramid honeycomb core under different loading conditions. The core shear cracking must be predicted for under various conditions to improve the applicability of this model. Reference [1] Elamin M, Li B, Tan KT. Impact damage of composite sandwich structures in arctic condition. Composite Structures 2018;192:422-33. [2] Zenkert D. The Handbook of Sandwich Construction. 2nd: PEMAS Press,1997. [3] Rong Y, Liu J, Luo W, He W. Effects of geometric configurations of corrugated cores on the local impact and planar compression of sandwich panels. Composites Part B: Engineering 2018;152:32435. [4] Fu K, Wang H, Chang L, Foley M, Friedrich K, Ye L. Low-velocity impact behaviour of a shear thickening fluid (STF) and STF-filled sandwich composite panels. Composites Science and Technology 2018;165:74-83. [5] Farshidi A, Berggreen C, Schäuble R. Numerical fracture analysis and model validation for disbonded honeycomb core sandwich composites. Composite Structures 2019;210:231-8.

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Zhang Xiaoyu: Conceptualization, Methodology, Software, Experiment, Writing Xu Fei: Conceptualization, Methodology, Investigation, Writing, Resources Zang Yuyan: Experiment, Formal analysis Feng Wei: Visualization, Formal analysis