Simulation Analysis of Effect of Porosity on Compression Behaviorand Energy Absorption Properties of Aluminum Foam Sandwich Panels

Renjun Dou1, Xinna Zhang2, Qingxian Hao1, Yan Ju1 and Yuebo Hu1,+

1Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology,Kunming 650500, Yunnan, China2Faculty of Electrical Engineering, Kunming Metallurgy College, Kunming Yunnan 650033, China

According to the microstructure characteristics of sandwich (AFS) panels, two-dimensional random models of AFS panels with differentporosities were created by C++ and ANSYS/LS-DYNA software in this paper. The main purpose of the current paper is investigating andanalyzing the effects of porosity on the compression behaviors and energy absorption capacities of AFS panels under the same compressiveloading on base of established random models. It was found that there were obvious three stages in the stress-strain curves of AFS panels,namely elastic region, collapse region and densification region. In addition, the results also confirmed that porosity had apparent effect on thecompressive capacities and energy absorption capacities of AFS panels. Furthermore, through comparison and analysis, the simulation results inthis work were basically consistent with the previous theoretical results and experimental results. [doi:10.2320/matertrans.M2015310]

(Received August 3, 2015; Accepted October 21, 2015; Published December 25, 2015)

Keywords: simulation, compression, energy absorption, sandwich panels, compressive capacity, energy absorption capacity

1. Introduction

Sandwich (AFS) panels, including aluminum foam coreand metallic face sheets which attach firmly to the core, notonly have some common properties of aluminum foam, butalso have higher apparent elastic modulus, strength andrigidity in the actual applications.1) All of these make AFSpanels develop into novel structural and functional materialswhich have been used in a variety of applications such asaerospace, shipbuilding, electronics, automobile sectors,construction fields, and so on.2,3)

In recent years, the study on AFS panels has been attractingconsiderable attention. Yang et al.4) discussed deformationbehaviors and mechanical properties of AFS panels duringstatic three-point bending test and pointed out that open-cellAFS panels had higher bending strengths than closed-cellAFS panels, and the later had higher energy absorptioncapacity than the former ones. The study on processing andpore structure of AFS panels was conducted by Wang et al.5)

The research results showed that the microstructure of porewall varied at different stages, and the foaming process ofAFS panels was composed of three different stages, namelypore forming, pore growing and pore cracking. Zen et al.6)

investigated simulation analysis of dynamic response for AFSpanels under moving load and found that the AFS panel withhexagonal honeycomb core was superior to others, and theAFS panel with solid metal core was the worst to resist thedestruction under moving load.

As new cushion materials and energy absorption materials,AFS panels have broad application prospects. However, asfar as we known, the numerical simulation study on the effectof porosity on the compression behaviors and energyabsorption properties of AFS panels is few. So, in this paper,two-dimensional random models for AFS panels withdifferent porosities were created by C++ and ANSYS/LS-DYNA software, and the related properties were studiedbased on the established simulation models of AFS panels.

2. Modeling and Simulating

Geometry, material and contact nonlinear problems can besimulated by using ANSYS/LS-DYNA software, especiallyfor the analysis of dynamic problems associated with largedeformation, low and high velocity impact, ballistic pene-tration and wave propagation, and so on.7) Therefore, it isvery suitable to analyze compression behavior by usingANSYS/LS-DYNA software for AFS panels with differentporosities.

Due to the simple geometry shapes and the easy dividingof meshes, two-dimensional random models can be usedbetter in some studies compared with three-dimensionalmodels and have a lot of applications in Ref. 8) andRef. 9). In this work, two-dimensional random models ofAFS panels are generated by using C++ and ANSYS/LS-DYNA software to study the compression behavior andenergy absorption properties for AFS panels with differentporosities. The modeling processes of AFS panels have beenillustrated in details in our previous work.10) The models ofAFS panels obtained are based on a highly porous aluminumfoam core (70mm width, 15mm thickness) and twoaluminium sheets (70mm width, 1mm thickness). Accordingto Ref. 11), the cell size varies from 1 to 5mm for all themodels of AFS panels. Aluminum foam core contain a largeamount of holes and the porosity has important influence onthe performances of foam materials. Based on above reasons,four porosities (40%, 50%, 60% and 70%) are chosen toanalyze the influence of the porosity on compressionbehavior and energy absorption properties of AFS panels.Aluminium sheets used is LY8 and the main compositions ofaluminum foam core are shown in Table 1.12) The models forAFS panels with different porosities in the simulation areshown in Fig. 1. Based on performance characteristic of AFSpanels, the classical bilinear isotropic hardening model isused, which uses two slopes (elastic and plastic) to representthe stress-strain behavior of AFS panels. The materialparameters of the models for AFS panels used are shownin Table 2.12,13)+Corresponding author, E-mail: huyb@kmust.edu.cn

Materials Transactions, Vol. 57, No. 1 (2016) pp. 33 to 36©2015 The Japan Institute of Metals and Materials

During the finite element analysis, according to structuralfeatures of the models of AFS panels, the free meshing isused. The reasons lie in the fact that it applies to irregular faceand body and the element shapes are not required. BecauseAFS panels have complex cell structures and cells contacteach other in the compression process, the single surfacecontact is defined in this work. In order to simulate the loadand boundary conditions, in the normal direction to the facesheets, the loading is conducted by the pressure head whichmoves down at a high rate (15m/s). The bottom face of themodel is restrained in all the directions. The Model loadingand constraint diagram is shown in Fig. 2.

3. Results and Discussions

Under the same compressive loading, compressive stress-strain curves for AFS panels with different porosities areshown in Fig. 3. As seen from Fig. 3, all of them consist ofthree stages, namely elastic region, collapse region anddensification region. From 0 to about 0.0035, the stress-strain

curves of AFS panels are in the elastic region. In the angle ofmicroscopic, the distances between atoms change when AFSpanels bear external force, and the resistance between atomsis produced to balance external force. So, as long as latticestructures are not broken, the stress-strain curves of AFSpanels are in the elastic region, where the deformations ofAFS panels are recoverable.14) From 0.0035 to about 0.5, thestress-strain curves of AFS panels are in the collapse region.Aluminum foam core contains a large amount of cells,providing enough space to be occupied during the process ofcompression, which brings about a long platform in thecollapse region, as showed in Fig. 3. Moreover, from Fig. 3,it can be seen that the stress has a slow increase as thecompression continues. The maximum mechanism may bethat the stress concentration and yielding of cell walls resultin the cells to be broken and present a wide range of structurecollapses, but the required stress changes little when eachlayer of cells are crushed in the region.15) Furthermore, fromFig. 3, it can be observed that the stress-strain curves of AFSpanels have a little fluctuation. The reason is that the highstress is produced near the stress-bearing surface under a highcompression rate. As shown in Fig. 4, based on existingstress concentration, high stress can make thin cell walls nearthe stress-bearing surface produce the bends and thedestruction, which causes the stress reducing. Moreover,after the cell walls contact with each other, hardened layersare gradually formed which are derived from the localdensification under the high compression rate. The hardened

(a) (b)

(c) (d)

Fig. 1 The geometric models of AFS panels; (a) model for porosity of40%, (b) model for porosity of 50%, (c) model for porosity of 60%,(d) model for porosity of 70%.

Table 2 Material properties of the models for AFS panels.12,13)

Component Aluminum foam core Aluminum sheets

Density, µ/kg·m¹3 650 2700

Poisson ratio, v 0.3 0.31

Young’s modulus, E/MPa 1150 71000

Yield strength, ·/MPa 20 110

Tangent modulus, T/MPa 10 600

Fig. 2 Model loading and constraint diagram.

Fig. 3 Stress-strain curves for AFS panels with different porosities.

(a) (b)

(c) (d)

(e) (f)

Fig. 4 Deformation process of AFS panels with the porosity 60%.

Table 1 Main compositions of aluminum foam core.12)

Compositions Al Fe Si Cu Zn MgOther

compositions

Content (%) ²99.7 ¯0.20 ¯0.10 ¯0.01 ¯0.03 ¯0.02 ¯0.03

R. Dou, X. Zhang, Q. Hao, Y. Ju and Y. Hu34

layers generated can lead to the compressive capacity to beimproved and the stress rises again until new bend anddestruction are formed in other weak layers.16) Therefore,the stress-strain curves of AFS panels show a fluctuationphenomenon, as shown in Fig. 3. With the increase of thetime, the fluctuation is not obvious since the stress transmitsto the distance and the localization of AFS panels is weaker.Besides, as shown in Fig. 4(d), the model is obviouslydivided into two obvious districts, where elastic and plasticdeformation is generated, respectively. In addition, fromFig. 4, the plasticity is expanding in the whole compressionprocess. The cell walls begin to plastic flow in the transversedirection after the plastic strain in the loading directionreaches a very high level. Finally, the elastic deformationdisappears and the model is basically dense.16) From 0.5 toabout 0.7, the stress-strain curves of AFS panels are in thedensification region, where all the cells are almost crushedand the cell walls are contact with each other on base ofplenty of collapse and destruction. Due to further hardeningof AFS panels originated from the integral densification andthe rapid increase of the resistance of the matrix, the stresshas a distinct increase with the increase of the strain in thecompression process, as showed in Fig. 3.

In the elastic region, the apparent elastic modulus can beobtained from the following formula (1)17)

E ¼ ·=¾ ð1Þwhere E is the apparent elastic modulus, · is the stress, ¾ isthe strain of specimen model. In the top of straight lines, theyield strengths are obtained. The data of the apparent elasticmodulus and yield strengths for AFS panels with differentporosities are shown in Fig. 5. Under compressive loading,the apparent elastic modulus and yield strengths decreaseaccordingly with the increase of the porosities, as shown inFig. 5. The reasons lie in the fact that with the increase of theporosities, the volume fraction of the matrix, wall thicknessand pressed area of aluminum foam core decrease, respec-tively, which lead to compressive capacities of AFS panels toreduce under compressive loading.

During the compression process, a large amount of energyis absorbed by AFS panels with the increase of the strain andenergy absorption capacity is an important aspect to evaluatethe properties of AFS panels. Because face sheets are so thin

and the deformations of face sheets are small, the energy ismainly absorbed by aluminum foam core under compressiveprocess, meaning absorbed energy of aluminum foam core isapproximately equal to one of AFS panels. According to theformula (2),18) absorbed energy of unit volume of aluminumfoam core can be expressed in the compression process.

W ¼Z ¾m

0

·ð¾Þ d¾ ð2Þ

where W is absorbed energy of unit volume of aluminumfoam core, ¾ is the strain, · is the stress, ¾m is arbitrary strain.Seen from formula (2), absorbed energy of unit volume ofaluminum foam core is equal to the areas under stress-straincurves in the same strain. In order to clearly show the changeof energy, by using origin software, the relation curvesbetween the energy and strain for AFS panels with differentporosities are shown in Fig. 6. From the Fig. 6, it can befound that the absorbed energy of AFS panels follows thesame trend, but absorbed energy decreases with the increaseof the porosity for AFS panels with different porosities. Thereasons lie in the fact that AFS panels with smaller porosityhave larger compressive capacities, as mentioned above. So,more energy is needed for AFS panels with smaller porosityin the same amount of compression, as showed in Fig. 6. Inaddition, from Fig. 3, AFS panels with smaller porosity havea higher stress plateau, which also decides the structure canabsorb more energy. It is well known that, a large number ofenergy converts into strain energy of AFS panels because ofthe increase of the strain and deformation of cell walls in thecompression process, implying that absorbed energy in-creases with the increase of the strain for AFS panels withdifferent porosities.

A comparison is conducted between the simulation dataand many study results of Ref. 19­21). It is confirmed thatthe simulation results in this work are in satisfactoryagreement with previous study results, which show thefeasibility of the models used.

4. Conclusion

In this work, AFS panels with different porosities aresimplified into two-dimensional random models using C++software, whose compression behavior and energy absorption

Fig. 5 Yield strengths and apparent elastic modulus for AFS panels withdifferent porosities. Fig. 6 Energy absorption curves for AFS panels with different porosities.

Simulation Analysis of Effect of Porosity on Compression Behavior and Energy Absorption Properties of Aluminum Foam Sandwich Panels 35

characteristic are analyzed by the finite element method. It isfound that the deformation process for AFS panels withdifferent porosities has the “three stage”, namely elasticregion, collapse region and densification region. The reasonsof the fluctuation on the stress-strain curves can be attributeto the local bends and destruction of pore structure and thehardened layers due to the mutual contact of cell walls. Inaddition, the results show, with the increase of the porosity ofAFS panels, the yield strengths and apparent elastic modulusdecrease accordingly, and the porosity of AFS panels issmaller, the ability to absorb energy is bigger. Theseconfirmed that porosity has a strong influence on thecompression and energy absorption properties of AFS Panels.This study will help to offer the theoretical supports in thisresearch field, and it is of great significance for the choices ofcushion materials and energy absorption materials.

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