Quasi-static Compressive Behavior of U-type Corrugated Cores Sandwich Panels

ZHANG Yan-chang,ZHANG Shi-lian,WANG Zi-li,LIU Kun

(1 School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 20030,China;2 School of Naval Architecture&Ocean Eng.,Jiangsu University of Science and Technology,Zhenjiang 212003,China)

1 Introduction

Metal sandwich panels consist of two face sheets welded with a relatively low-density core structures resulting in good stiffness to weight ratio,which leads to promising design advantages,such as higher stiffness to weight,higher strength to weight ratios,higher pre-manufacturing accuracy,better mechanical properties and substantial energy absorbing capacity[1-5].Sandwich panels in general can be classified as:metallic sandwich panels and composite sandwich panels.For metallic sandwich panels,there are basically two types of panels:panels with metallic face plates and nonmetallic core bonded together such as SPS(Sandwich Panel System)panels,panels with both metallic face plates and core welded together[1].The metal core structure can also possess various topologies:a web,a honeycomb,and a corrugated cellular core.

The impact resistance performance of ship structures subjected to impact loads was of great interests to engineering communities and government agencies.Metal sandwich panels were of potential use in ships structures especially in accidental or terrorist blasts because of substantial energy absorbing capacity.Periodic cellular metals such as corrugated core,honeycombs and lattice truss can absorb considerable energy by plastic deformation in compression.The energy absorption behavior of structures and materials has recently been presented comprehensively in two monographs by Jones and Lu[5-6].The out-of-plane compressive behaviors of honeycomb core structures were investigated by experimental research and FE analysis[11,14-15].Radford,Ferri,Lee and Zhang et al[15-17]have investigated the dynamic response of honeycomb core,folded structure core and the pyramidal truss core via experiments and finite element simulations.Compression tests and finite element analysis were conducted to better understand the behavior of corrugated sandwich cores under out-of-plane compression and assist in the selection of desirable core structures attributes for enhancing the impact resistance of ship structures.

In the present study,the quasi-static compressive response of U-type corrugated core sandwich panel was investigated using numerical simulation and experiment.The objectives of these researches were to verify the finite element modeling of sandwich panel and observe the deformation behavior and energy absorbing capacity under out-of-plane compressive load.

2 Specimen design and fabrication

Uniaxial compression test was designed to measure the crushing force and progressive crushing behavior of sandwich panel under out-of-plane crushing load.The properties of core and face-sheets were mild steel Q235.U-type corrugated cores were examined in this test.Two type core shapes are shown in Fig.1.The thickness of both two face-sheets and core structures was approximately 3.5 mm.Each core structure had a height of 120 mm.Each specimen includes four core units across the width and the length of 200 mm.

Hybrid laser arc welding(HLAW)has many advantages over current conventional welding technologies in steel fabrication.The advantages include an appreciable decrease of heat distortions,high processing speed and a constant good weld quality.HLAW is ideal for connecting the core to the face-sheets.The ship building industry has expected laser welding to provide fabricated components in ship production due to improvements and cost benefits that can be achieved compared to hot rolled stripped-T or split-I stiffeners[18-19].While the highly required assembling tolerances,high investment cost and other factors limit the applications in manufacturing sandwich specimens of this test,the conventional electric welding was utilized for connecting the core and face-sheets.Fig.1(a)shows the assembly process of sandwich panels.The V-type core structures were formed by folding the flat plate with thickness of 3.5mm.The flat plate was cut into eight parts with width of 127 mm which composes the U-type core structures.Two face-sheets were welded with core structures along the edge of core unit.The height of weld leg was not less than 3mm.Photographs of specimens manufactured are shown in Fig.1(b).

Fig.1 Structure diagram and assembly processes of U-type core sandwich panel

3 Quasi-static crushing test

The crushing tests were conducted by an electro-hydraulic servo universal testing machine (YNS1000).This test was designed to measure the crushing force versus displacement and deformation modes of corrugated core structures.The scene of experiment is shown in Fig.2.The specimen was placed on the plate of testing machine coinciding with the axis of actuator.The actuator was positioned above the support block with thickness of 50 mm at the upper face plate of specimen.The pre-compression force of 10kN was loaded in order to flat the sandwich plane and confirm the uniformity of actuator loading.The displacement loading with the speed of 0.16 mm/s giving a nominal strain rate of ε˙=1.4×10-3s-1was applied on the rigid plate.The curve of crushing loads versus compressive displacement was recorded automatically by computer at the frequency of 10 Hz.The deformation figures were taken a photograph in the process of test.

Fig.2 Photos of crushing experiment

4 Finite element analysis

4.1 Scheme of numerical simulation

The crush performance of the sandwich panels was analyzed by the numerical simulation with nonlinear finite element code-Abaqus.The hammer was used to strike the sandwich panels with a low velocity to simulate the dynamic progressive buckling behavior,the weight of the hammer is 106kg,and the striking velocity is 0.5 m/s.The material of sandwich panels is the mild steel Q235,with the density ρ=7850 kg/m3,Poisson’s ratio γ=0.3,elastic modulus E=206 GPa.The finite element material model is defined as the true stress-strain relationship.

4.2 Finite element model

The cores,faces and welding seams are simulated as solid elements in finite element mode.There are two elements in the direction of thickness.And the size of the finite element is about 2 mm.The nodes of the lower-face are rigidly fixed,while the upper-face is fixing the moving in the horizontal plane.The adaptive self contact is defined in the cores,while adaptive master-self contact is defined between the cores and faces,where the contact friction coefficient is 0.3.The finite element model is shown as Fig.3.

The plastic deformation is made at the middle of the core plates as initial imperfection in order to obtain the same deformation mode as experimental mode.Taking the deformation mode I for example,the influences of different initial plastic deformation on result of finite element simulation are discussed.

Fig.3 Finite element mode of sandwich panel

5 Results

5.1 Crushing force

Fig.4 Curves of crushing force versus compressive displacement

The crushing force-compression displacement curves of the U-type core sandwich from the experiment are shown in Fig.4,according to the deformation figures(shown as Figs.8-10),the curves can be divided into three phases.The first phase is named as the first peak phase(Phase I).In process of this period,the crushing force increases quickly.When the sandwich cores are crushed,and the crushing force reaches to the first peak.Then,the plastic hinges are generated in the middle of the core structures,and then the crushing force decreases to stability.Fig.7(a)shows that if the two adjacent core structures have the same buckling deformation direction-up or down,they will form a “funnel” type deformation mode(Mode A forms four funnels,Mode B forms one,Mode C forms three).With the increasing of crushing displacement,the connection between the core and the faces forms the line areas of plastic hinges.When the line areas of plastic hinge contact with each other,the deformation becomes to Phase II.Fig.7(b)shows that if the two adjacent core structures have the opposite buckling deformation direction,with the increasing of crushing displacement,the adjacent core structures will not contact with each other,the cores are folded to contact with the faces,then deform to Phase II.In this phase,the three deformation modes caused by the different buckling directions share almost the same mechanical performances of the crushing force,deformation mode and crushing displacement.The second phase is named second peak phase(Phase II),with the increase of the crushing displacement,the adjacent core plates with the “funnel” type deformation begin to contact with each other,the crushing force increases again,and then the second peak generates.After that,the contact of the half core plates buckled and the line areas of plastic hinges take place,then the “diamond”type buckling deformation modes generate.The deformation mode,second peak crushing force and crushing forcedisplacement curve of the four specimen with the deformation mode I are similar,but the crushing force and deformation of the specimen with opposite buckling directions have a great difference.The more of the “funnel”type deformation number,the higher value of the peak crushing force.Mode I with the number of four “funnel” type deformation,the second peak crushing force of which is from 521 kN to 583 kN.Mode II with one “funnel”type deformation,the second peak crushing force of which produces one funnel shape deformation modes is 282 kN,and the value of specimen U3-2 which produces three funnel shape deformation modes is 487 kN.Phase III,the compaction phase,starts when the crushing displacement reaches to about 100 mm,and the maximum compression displacements of different deformation modes are basically the same.

The comparison of crushing load curves between quasi-static test and FE simulations is presented in Fig.5(a),(b)and(c)respectively.Experimental results are in good agreement with finite element numerical results,such as the tendency of curves,the value of peak crushing force and compression displacement,etc.

Fig.5 Comparison between FE and experiment

5.2 Deformation modes

The buckling will occur when the core plate unit is in the lateral pressure.As shown in Fig.6,each core plate has two buckling directions:up or down.According to buckling direction of two adjacent core plates,the deformation of the two adjacent core plates is called deformation mode unit.They are divided into two types.One unit de-formation mode is named as mode I,the two adjacent core plates have the same buckling direction.The two adjacent core plates of this type have two deformation combinations,shown in Fig.6(a).Another unit deformation mode is named as mode II,the two adjacent core plates have the opposite buckling directions.The two adjacent core plates of this type have four deformation combinations,shown in Fig.6(b).With the increase of the compression displacement,the progressive buckling process of the two deformations are shown in Fig.7(a)and(b)respectively.The difference between the two unit deformation modes is whether the two adjacent core plates can contact with each other or not.Before they contact with each other,their peak crushing force and crushing force-displacement curve are basically the same.In the deformation mode I,because the contact constraint is generated from the adjacent core plates,the crushing force increases again,then the second peak crushing force appears.That is the pivotal factor affecting the crushing performance of the sandwich panels.

Fig.6 Deformation modes of two adjacent core plates

Fig.7 Deformation pictures of modes I and II

The deformation mode of the U-type core sandwich specimen is one combination of unit deformation modes I and II,and initial imperfections,manufacturing technologies and other factors have some effects on them.The real deformation modes obtained in the experiment are the combinations of the two deformation modes,such as specimens U1-1,U1-2,U2-1,U2-2,all of them are composed of four units of deformation mode I,which is named as deformation mode A.Specimen U3-1 is composed of one deformation mode I and three deformation mode II,which is named as deformation mode B.U3-2 is composed of three deformation mode I and one deformation mode II,which is named as deformation mode C.

Both of the specimens U1 and U2 have been given initial plastic deformation as initial imperfection,the direction of which is the same as the deformation mode I,then the deformation mode A is obtained from the experiment,shown in Fig.8.As to the specimens of U3-1 and U3-2,which are not given any initial deformation,the deformation modes obtained from the experiment are random,their deformation modes are shown in Fig.9 and Fig.10,and the deformation modes are called Mode B and Mode C respectively.The finite element modeling techniques used in this paper can simulate the deformation mode of the progressive buckling process accurately and clearly.And the calculated results agree well with the experiment results.The results show that the deformation mode can be controlled by applying certain initial plastic deformation.

Fig.8 Deformations of deformation mode A(d=20 mm,40 mm,60 mm)

Fig.9 Deformations of deformation mode B(d=20 mm,40 mm,60 mm)

Fig.10 Deformations of deformation mode C(d=20 mm,40 mm,53 mm)

5.3 Efficiency

Corrugated core structures are designed as energy-absorbing device and the efficiency may be specified in several ways to evaluate the dynamic performance under impact loads.The performance parameters of the specific energy Se,the mean crushing strength σm,and other performance parameters,such as first peak crushing load Fc1,compression displacement δ and relative density ρc,are important to evaluate the capability of corrugated cores as energy absorbing devices.And these crushing performance parameters of U type cores are listed in Tab.1.

Tab.1 Crushing performance parameters of U type cores

The relative error of the performance parameters measured from the test of the four specimens is within 6.5%.The experimental results show that the scheme of crushing experiment is reliable and accurate.Different deformations have a great impact on the crushing mechanics performance.As to the three deformation modes,the specific energy Seand the mean crushing strength of mode A are higher than those of mode B and mode C.The energy absorption of the sandwich cores in deformation mode A is much higher.The first peak crushing force of specimens U3-1 and U3-2 are roughly equal,higher than the other four specimens by 11%～37.6%.The results show that initial deformation has great effects on the peak crushing force,but has little impact on the specific energy,the mean crushing strength and other performance parameters.That can also be obtained from the finite element analysis of model I.

6 Conclusions

The quasi-static out-of-plane compressive behaviors of U-type corrugated core structures have been investigated by experiments and FE simulations.The critical performance parameters such as the deformation modes,curves of crushing force versus displacement are obtained and analyzed.A comprehensive analysis on crushing behavior of core structures is studied when the corrugated core structures are used as energy absorbing devices or protection structures,which include specific energy,mean crushing strength,peak crushing force,manufacturing technology,and so on.The plastic hinge of core plate induced by compression or bend under compression load is the main type of absorbing energy.

The finite element analysis used in this paper can simulate the deformation mode of the crushing process of buckling,crushing force and compression displacement accurately and clearly,and agree well with the experiment results.The finite element analysis considering the initial imperfections can get the same deformation mode to the experiment.That indicates that the reasonable finite element analysis has the reliable accuracy.

The deformation mode of the core plates under lateral crushing force has great effects on the crushing performance.The finite element method and experiment analysis show that the performance of the specific energy and mean crushing strength of mode I are better than those of mode II.The initial imperfection is the key factor to the deformation mode I and mode II,which has great impact on the first peak crushing force,but has little impact on the deformation and crushing force after the first peak crushing force.So the core structures can be designed and manufactured with certain initial deformation to get the deformation mode I in order to increase the mechanical properties of the sandwich core structures.

Whether the two adjacent core plates can contact with each other(effect by the dimension parameters,such as the height of sandwich cores,the angle between the core and the faces,the distance between adjacent core plates)is the key to lead to the deformation mode I or mode II.It is necessary to research on the effects of structure parameters to the crushing performance and optimization study.

Acknowledgements

This work is supported by the national defense priority in advance research project.The authors are grateful to Taixing Jianeng Chemical Container Company Ltd.for manufacturing the specimen and Sheng Chaoming for experiment operation.

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