Deformation Modes of the Graded Closed-Cell Foam under Impact Loading Jiang-long WANG, Xin LI and Gen-wei WANG*

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1 2016 International Conference on Applied Mechanics, Electronics and Mechatronics Engineering (AMEME 2016) ISBN: Deformation Modes of the Graded Closed-Cell Foam under Impact Loading Jiang-long WANG, Xin LI and Gen-wei WANG* Shanxi Key Laboratory of Material Strength & Structural impact, College of Mechanics, Taiyuan University of Technology, Taiyuan, China *Corresponding author Keywords: Graded foam, Deformation mode, Impact loading. Abstract. Compression properties and deformation modes of closed-cell foam are investigated at different impact velocity. The contrast of deformation modes indicates that both uniform and negative graded foam have quasi-static mode, transitional mode and impact mode. On the contrary, the positive graded foam only has one mode; the local deformation propagates from impact end towards supported end. Introduction Aluminum alloy foam is widely used as a buffer to protect objects in transportation industry and aerospace industry. It attracted many researchers interest. Ruan et al. [1] investigated the deformation mode and plateau stress of hexagonal aluminum honeycombs and found that the honeycomb performs X, V and I shaped deformation modes under different impact velocity. Ajdari et al. [2] studied the influence of degrees of irregular shape on foam cell. Song et al. [3] found that the inertia effect has an obvious influence at the impact side, but it is insensitive at stationary side. Hangai et al. [4] found that the Quasi-static nominal stress-strain curve of density graded foam no longer have a platform. Graded foam can be divided into discontinuous density gradient and continuous density gradient foam. Some researchers [5, 6] investigated the dynamical behavior of discontinuous gradient models, but few researches think about the dynamic properties of the 3D continuous density gradient foam. In this paper, we construct two kinds of 3D Voronoi random models of foam: uniform and gradient. Three impact velocities of 30 m/s, 80 m/s, 200 m/s are applied in the numerical simulation. The advantages of uniform and graded foam are discussed respectively. Methodology 3D random Voronoi Technique 3D Voronoi models are created by randomly placing a set of N nuclei inside a cubic region. In order to avoid generating very small cells, the distance of each nucleus is larger than a smallest distance which defined as d min 1 6 V0 3 dmin (1 k) d0 (1 k) ( ) (1) 2 2N where k is the irregularity of porous material, and its value ranges from zero to one [7]. d 0 is the distance of any two adjacent nuclei in a regular tetrakaidecahedron foam model whose volume is V 0. Finite Element Models Uniform and graded 3D Voronoi models are generated, whose size are mm 3, as shown in Fig. 1. The irregularities k of models is 0.2. The cell number of the uniform model is about 760, while the other is about 800. Both cell walls of models have a uniform thickness r, which is about

2 0.05 mm. The bilinear strain-hardening model material was employed for the Voronoi models. The parameters of the materials are listed in Table 1. Material Young s Modulus ( GPa ) Table 1. The parameters of base material. Yield Stress ( MPa ) Poisson s Ratio Density ( g/cm 3 ) aluminum The density gradient γ is defined as d ( x) 0 d( x) L (2) where γ is a dimensionless parameter, and ρ 0 is average density of the porous material. A positive density gradient (γ is greater than zero) which means the density gradually decreases along the crushing direction. The density gradient γ of the 3D Voronoi gradient model is The relative density ρ is Figure 1. Uniform foam (left) and graded foam (right). The models are sandwiched between a fixed rigid solid (supported end) and a moving rigid solid (impact end). The mass of both impact and supported end is about 11.2 kg. The impact and supported solids are defined as rigid solids. An explicit dynamic finite element analysis is conducted in ABAQUS. The FE models are meshed by using shell elements S3R and S4R. Through a mesh sensitivity study, the characteristic length of shell element size is about 0.3 mm. The automatic surface to surface contact is defined and the dynamic friction coefficient is about 0.2. Results and Discussion The deformation modes of foam usually can be divided into three kinds of modes: namely quasi-static mode, transitional mode and shock mode. For uniform model, the deformation mode at 30 m/s is shown in Fig. 2a. The deformation mode is almost same as quasi-static loading, which is defined as quasi-static mode. With the increase of impact velocity, local deformation band firstly began to appear at impact end because of the inertial effect, while the supported end keep static. This deformation mode is defined as transitional mode. The deformation mode at 80 m/s is shown in Fig. 2b. When the impact velocity reaches 200 m/s, local deformation band firstly appears at impact end, and propagates towards the supported end

3 layer by layer. Under this loading condition, there only exists local deformation. This mode is called impact mode and shown in Fig. 2c. Figure 2. Deformation mode of uniform foam (γ =0). The deformation modes of negative graded foam are shown in Fig. 3. At low impact velocity of 30 m/s, the local density plays an important role in deformation mode. The local deformation band propagates from support end (low density) towards impact end (high density). With the increase of impact velocity (v=80 m/s), the impact end generates local deformation firstly. After that, the local deformation appears in the support end and propagates towards the impact end. This mode is called transitional mode. When the velocity is high, the local deformation band firstly show up at impact end, then propagates towards support end layer by layer. This kind of mode is called impact mode.

4 Figure 3. Deformation modes of negative graded foam (γ = -0.32). Figure 4. Deformation modes of positive foam (γ = 0.32). The deformation mode of positive graded foam is single, comparing with uniform and negative gradient foam. At any velocities, only deformation mode I can be observed. The deformation modes of positive graded model are shown in Fig. 4.

5 Summary The uniform, positive and negative density graded models established by 3D Voronoi technique have been simulated to investigate the dynamic compression behavior of the foam. The influences of impact velocity are studied. The contrast of deformation mode indicates that the uniform and negative foam both has quasi-static mode, transitional mode and impact mode. On the contrary, the positive foam only has only one mode. In this situation, the local deformation propagates from impact end towards supported end. Acknowledgements This research was financially supported by the National Natural Science Foundation of China (No ), Shanxi Scholarship Council of China (No ) and Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province (No ). References [1] D Ruan, G Lu, B Wang, et al. In-plane dynamic crushing of honeycombs a finite element study, Int. J. Impact Eng., 28 (2003) [2] A Ajdari, S Babaee, A Vaziri, Mechanical properties and energy absorption of heterogeneous and functionally graded cellular structures, Procedia Eng., 10 (2011) [3] Y Song, Z Wang, L Zhao, et al. Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model, Mater. Design., 31 (2010) [4] Y Hangai, N Kubota, T Utsunomiya, et al. Drop weight impact behavior of functionally graded aluminum foam consisting of A1050 and A6061 aluminum alloys, Mat. Sci. Eng. A-Struct., 639 (2015) [5] Fan J, Zhang J, Wang Z, et al. Dynamic crushing behavior of random and functionally graded metal hollow sphere foams, Mat. Sci. Eng A-Struct., 561 (2013) [6] J Zhang, H Wei, Z Wang, et al. Dynamic crushing of uniform and density graded cellular structures based on the circle arc model, Lat. Am. J. Solids Stru. 12 (2015) [7] H X Zhu, A H Windle. Effects of cell irregularity on the high strain compression of open-cell foams, Acta Mater., 50 (2002)