ON THE PROGRESSIVE COLLAPSE OF MICRO LATTICE STRUCTURES R.A.W. Mines, S. McKown, W. Cantwell, S. Tsopanos, W. Brooks, C.J. Sutcliffe Department of Engineering, University of Liverpool, Liverpool, L69 3GH, UK ABSTRACT The progressive collapse behaviours of three micro lattice geometries, for use as core materials in sandwich construction and made from stainless steel using the rapid prototyping method of selective laser melting, are studied experimentally. Blocks of the cellular materials are subject to compression and shear. Both the initiation of crush and the progression of crush are discussed. Physical phenomena such as strut elastic and plastic buckling, as well as strut plastic collapse, are highlighted. These behaviours are benchmarked against the aluminium foam, Alporas. Introduction Foam and honeycomb materials have been used for many years as cores in sandwich construction. Foam materials range from polymeric materials (Divinycell [1], Rohacell [2]), through metals (Alporas aluminium foam [3]), to graphite. Similarly materials for honeycomb can be aluminium (Hexcel) or aramid (Hexcel). The main design variable for these cellular materials is density, but in general the microstructures of these materials are restricted to one, or a few, geometries. More recently, rapid prototyping manufacturing processes, such as selective laser melting, have been developed that allows the realisation of metallic open cellular lattice structures with resolution of 50 micro meters [4]. This process allows the tailoring of cellular architectures. Usually sandwich construction is used in lightweight transport applications. This means that the design of such construction is driven by a variety of application issues, e.g. fatigue, in plane buckling of skins, local loading (connectors), foreign object impact etc. [5]. The application of interest here is foreign object impact. In such a case, the core is subject to multi axial stresses and can suffer progressive damage [6]. Table 1 compares the geometries discussed in this paper. The aluminium foam can be idealized as a truncated octahedron geometry. This has been suggested in the literature [7]. It should be noted that in Alporas closed cell aluminium foam, it can be assumed that the majority of material is concentrated at cell edges, and so a framework model is valid. Obviously, in foams, cell sizes vary by a factor of three. The nomenclature for the lattice structures has been taken from Rehme [8]. f2 refers to two diagonals on a face, fcc refers to face centred, bcc refers to body centred and z refers to vertical struts. Also shown in Table 1 are the densities and cell sizes. The parent material for Alporas is aluminium alloy [3] and the parent material for the lattice structures is 316L stainless steel [4]. Fairly obviously this is not comparing exactly like with like, but the aim here is to identify issues for further study. l refers to low density (large cell size) and h refers to high density (small cell size). It should be mentioned that the manufacturing parameters for the lattice structures need to be optimised before testing and that overall properties can change by a factor of two if this is not done [4]. Experimental tests and results Blocks of cellular material of dimension 25mm cubed were either cut from aluminium foam blocks [3] or manufactured using the selective laser melting method [4]. The blocks were then subject to a number of loading conditions. In the uni-axial compression test, the blocks were placed between two platens in an Instron 50kN servo hydraulic machine and force and deformation recorded. Also, photos were taken of the progressive collapse of the cellular structures. In the shear case, the blocks were bonded to aluminium blocks that were then mounted an Arcan Rig [3]. This rig allows various combinations of tension and shear. Figure 1 shows progressive collapse for compression loading for the micro lattice structures. Photos were not taken for the aluminium foam, but these can be found in the literature [10]. Figure 2 shows the failure modes for pure shear for foam and f2fcc,z-l and h structures. Table 1: Cellular geometries discussed in this paper Cellular Geometry Reference Density Cell 3 (kg/m ) Size (mm) Alporas [3] 200 2-8 f2fcc,z-h [4] 983 1.25 f2fcc,z-l [4] 322 2.5 bcc-h [9] 994 1.5 bcc-l [9] 394 2.5 bcc,z-h [9] 1258 1.5 bcc,z-l [9] 472 2.5 Geometry (a) 7 % strain (b) 16% strain (c) 16% strain Figure 1. Photos of progressive collapse of micro lattice structures: (a) f2fcc,z-l, (b) bcc-l, (c) bcc,z-l (a) (b) (c) (d) Figure 2. Failure modes for pure shear: (a) Alporas foam, (b) f2fcc,z-l and h, (c) detail f2fcc,z-l,(d) bcc-l As far as global stress strain data is concerned, engineering stress strain data was derived for all tests. Data was typical of cellular materials, giving an elastic region (E1,G1) a progressive collapse regime (σ, τ) and a densification regime. Table 2 summarises these data and parameters and Figure 3 gives full stress strain data. Table 2: Global stress strain data Cellular Geometry E1 (GPa) σ (MPa) G1 (GPa) τ (MPa) Alporas [3] 0.70 5.00 0.20 1.00 f2fcc,z-h [4] 1.90 13.50 1.20 6.00 f2fcc,z-l [4] 1.00 5.00 1.20 1.50 bcc-h [9] 0.44 8.00 - - bcc-l [9] 0.05 1.10 0.40 0.6 bcc,z-h [9] 2.70 17.00 - - bcc,z-l [9] 0.45 2.30 - - Discussion of results Discussion is focused on the 2.5mm cell sizes (low density –l), as these are closest in density to the aluminium foam and more complete stress strain data are given for these. Figure 3(1b) and Table 2 shows that the Young’s modulus for f2fcc,z-l is twice that of bcc,z-l. This is due to the fact that there are twice as many diagonal struts for the former case. This is also found in the crush stress, where a factor of 2 is found. Again, this is due to the fact that there are more plastic hinge sites for the f2fcc,z-l case. Figure 1a and 1c show that the mode of failure is similar, viz. buckling of vertical struts causing localisation in block deformation. Progression of collapse is stable, as more shear bands form and coalesce. Figure 3(1a) and Table 2 shows that the Young’s modulus for bcc,z-l is five times the modulus for bcc-l. This shows the effect of the vertical struts. The factor on the crush strength is 2.5. However, Figures 1b and 1c show a change in failure mode. No localisation occurs for the case of no vertical struts. As far as comparison with the aluminium foam is concerned, the bcc-l case is closest to the foam compression modulus and compression crush stress. In the case of the foam, failure is a complex mixture of cell wall buckling and tearing. In terms of the truncated octahedron characterisation (see Table 1), it is proposed that there will be a complex 3D bending and twisting of cell edges as the foam crushes [11]. Figure 2c shows detail of shear failure of f2fcc,z-l case. Cell failure is due to plastic buckling of diagonal elements and plastic hinges at cell corners. This contrasts with the foam, which tears along cell boundaries (see Figure 2a). There is a factor of 2 between f2fcc,z-l and the foam shear crush stress. It should be noted that localisation occurs for bcc-l under shear (see Figure 2(d)). As far as changing the density of the lattice structures is concerned, for compression loading the failure modes stay the same, i.e. localised shear banding for f2fcc,z-l, f2fcc,z-h and overall collapse for bcc-l. However, for shear loading there is a change in failure mode between f2fcc,z-l and f2fcc,z-h. It should be observed that failure modes may be sensitive to edge effects in the blocks under test. 8 Lattice B Lattice C Engineering stress (MPa) 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Engineering strain (1a) f2fcc,z-h f2fcc,z-l (1b) 10 Relative Density 9.8% 8 Relative Density 8.5% 7 6 5 4 3 2 1 0 0.0 0.1 0.2 0.3 0.4 0.5 Engineering strain 0.6 0.7 0.8 (1c) f2fcc,z-h f2fcc,z-l (2a) 1.8 tension experiment 1.6 tension FE 1.4 45deg experiment 45deg FE 1.2 Stress (axial) [Mpa] Engineering stress [MPa 9 shear experiment shear FE 1.0 0.8 0.6 0.4 0.2 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Strain (axial) (2b) 0.07 0.08 0.09 0.10 1.2 1 Stress, MPa 0.8 0.6 0.4 0.2 Compression Shear 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Strain (2c) Figure 3. Stress Strain Data: 1 - Compression: 1a – B/bcc,z-l, C/bcc-l, 1b – f2fcc,z-l and h, 1c – Alporas, 2 - Shear: 2a- f2fcc,z-l and h, 2b- Alporas, 2c – bcc -l General discussion and conclusions Comparing Alporas, f2fcc,z-l, bcc-l, bcc,z-l for the compression case. The f2fcc,z-l structure seems to be more efficient than the bcc,z-l structure for both modulus and crush stress. However, this will only be true for loading in the vertical strut direction. If the material is going to be used as a core material in a sandwich structure (i.e. be subject to multi axial loading), then the bcc-l structure will be less directional. However, localisation under shear occurs for this lattice structure. For lightweight structures, a 2.5mm cell size is more relevant than a 1.25/1.5 mm cell size. However, the higher density lattice may be of use for areas of localised loading. In fact, one of the advantages of the SLM manufacturing process is the ability to realise graded structures, i.e, having the main body of the core as 2.5mm cell size and a 1.5mm cell size for localised loaded area, with a smooth transition between the two [12]. It should be noted that it is possible to realise lattice structures using SLM with other powders, e.g. Aluminium alloy, which would reduce lattice density. The shear loading case has shown the possibility of a change in mode of failure as a result of changing cell size. This shows that using scaling in structural performance from one cell size to another may be problematic. From the above, it can be seen that more research is required to optimise these cellular structures for specific sandwich applications. Acknowledgements The work described in this paper was supported from contracts: EPSRC/EP/C009525/1, EPSRC/EP/009398/1 References 1. Mines, R.A.W., Alias, A., Composites Part A, 33, 11-26, 2002 2. 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Mills, N.J., Zhu, H.X., J. Mech Phys Sol, 47, 669-695, 1999 12. Mines, R.A.W., On the characterisation of cellular materials for sandwich construction, Plenary Lecture ICEM13, (Ed. E. Gdoutos), 2007
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