Ultralight Cellular Materials
Nature discovered and evolved low density cellular materials soon after on earth life began. Today tall trees could not support the bending loads applied by strong winds and our bones would not be able to support our weight were it not for low density (very light) cellular materials configures as the cores of columns and beams with strong (denser) outer surfaces. Figure 1 shows examples of the structure of a Hornbill beak and an avian wing bone which demonstrate how well nature exploits these clever design practices to create structures that can support high bending loads at minimal weight – all from materials that can be synthesized "in vitro".
Figure 1: Cross sections of (top) the beak of a Hornbill and (bottom) an avian wing bone.
With far superior synthetic materials now available from which to make cellular material, materials scientists and mechanical engineers are beginning to fabricate cellular solids that rival those of nature. For example, aerospace engineers have exploited honeycomb cellular materials like those shown in Figure 2 made from Nomex (an aramid molecule closely related to that used in kevlar armor). Our group specializes in designing, making, and understanding the performance of cellular structures made from high strength materials. We focus upon those with lattice topologies, Figure 3. These have a unit cell which can be translated in 3D to fill space and are more efficient at supporting stress than foams.
Figure 2: Examples of honeycomb cellular materials and some of the applications in which they are used.
Figure 3: Examples of the topologies of a variety of cellular lattices configured as the cores of sandwich panel structures.
Figure 4 shows three examples of lattice structures based upon a tetrahedral (three sided) arrangement of inclined trusses as well as others with pyramidal (four sided) and 3D kagome structures (where six trusses meet at a node). These structures pick-up applied stresses and efficiently resolve them onto the trusses whose in-plane displacement is restrained by interlayers of planar trusses.
Figure 4: Examples of lattice truss structures than be multilayered to fill 3D space.
Photographs of several structures made in our laboratory are shown in Figure 5. They include a 6061 T6 aluminum octet truss structure and a high thermal conductivity copper 3D kagome structure (configured as the core of a sandwich panel). The aluminum octet truss was made using a layered manufacturing technique and a brazing process that formed strong nodes by transiently melting an Al-Si alloy foil. The copper structure fabrication is an early example of rapid prototyping. Using a 3D additive manufacturing method, we first fabricated a plastic version of the structure. We then used that to make an investment casting from a Cu-2% alloy.
Figure 5: Photographs of lattice structures based upon (a) tetrahedral trusses and (b) 3D Kagome trusses.
An example of a carbon fiber reinforced polymer (CFRP) lattice is shown in Figure 6. This used a "snap-fit" assembly technique to make the trusses from a [0/90] CFRP laminate. We ensured that half the fibers were always oriented along the trusses to maximize both their elastic stiffness and compressive/tension strength.
Figure 6: Example of a CFRP lattice structure.
The mechanical properties of lattice materials are governed, in part, by those of the material from which it is made. The topology of the structure and the fraction of the unit cell occupied by material (the relative density of the cellular structure) also contribute to the cellular materials mechanical properties. Some of the strongest (but most expensive) cellular materials we have fabricated were made from 150 μm diameter silicon carbide fibers that were coated with a titanium alloy to enable diffusion bonding of a diamond collinear titanium matrix composite (TMC) lattice, Figure 7.
Figure 7: (Left) a cross section of a titanium alloy coated silicon carbide fiber and (right) diamond cell lattice structures made from them.
By using materials with a high elastic stiffness and low density, it is possible to make very light, yet stiff materials and structures, as are shown in the material property chart of Figure 8. The highest “specific” stiffness (modulus divided by density) materials are those to the upper left of the property chart. The chart shows that cellular materials made from CFRP, light metals, and titanium matrix composites are approaching the theoretical limits of elastic modulus at low density.
Figure 8: Material property chart comparing the Young’s modulus and density of engineering materials with polymer and metal foams and various lattices made from CFRP, aluminum alloys and titanium matrix composites. Aerospace designers seek light stiff materials for their applications (materials to the upper left of the chart).
To create strong (as well as stiff) cellular materials requires the use of materials and topologies that delay the onset of failure modes such as truss elastic or plastic buckling, and plastic yielding of metals, or buckling, delamination and fiber microbuckling in fibrous composites. Figure 9 shows several examples of light cellular lattice materials made by our group that have strengths much higher than conventional foams and natural materials such as wood.
Figure 9: A material property chart comparing the compressive strength and density of engineering materials with polymer and metal foams and various lattices.
Interest today in cellular materials is being driven by new vehicles which need to be lighter than ever (to reduce fuel usage) but are also stiff, strong and capable of absorbing mechanical energy (e.g. during an automobile impact), Figure 10. Our group is at the forefront of efforts to develop material solutions for these applications.
Figure 10: Examples of applications of advanced cellular materials.
The Topological Design of Multifunctional Cellular Metals, A.G. Evans, J.W. Hutchinson, N.A. Fleck, M.F. Ashby, H.N.G. Wadley, Progress in Materials Science, 46, p. 309-327, 2001.
Fabrication and Structural Performance of Periodic Cellular Metal Sandwich Structures, H.N.G. Wadley, N.A. Fleck, A.G. Evans, Composites Science and Technology, 63, p. 2331-2343, 2003.
Measurement and Simulation of the Performance of Lightweight Metallic Sandwich Structures with Tetrahedral Truss Cores, H.J. Rathbun, Z. Wei, M.Y. He, F.W Zok, A.G. Evans, D.J. Sypeck, H.N.G. Wadley, Journal of Applied Mechanics, 71, p. 368-374, 2004.
Multifunctional Periodic Cellular Materials, H.N.G. Wadley, Proc. Roy. Soc. A., 364, p. 31-68, 2006.
Lattice Truss Structures from Expanded Metal Sheet, Gregory W. Kooistra, H.N.G. Wadley, Materials and Design, 28, p. 507-514, 2007.
The Compressive Response of Carbon Fiber Composite Pmyamidal Truss Sandwich Cores, K. Finnegan, G. Kooistra, H.N.G. Wadley, V.S. Deshpande, International Journal of Matierals Research, 98, 2007.
The Compressive and Shear Response of Titanium Matrix Composite Lattice Structures, P. Moongkhamklang, V.S. Deshpande, H.N.G. Wadley, Acta Materialia, 58, p. 2822-2835, 2010.
Hollow Pyramidal Lattice Truss Structures, Douglas T. Queheillalt, Haydn N.G. Wadley, International Journal of Materials Research, 102, p. 389-400, 2011.
Collapse Mechanisms Maps for the Hollow Pyramidal Coare of a Sandwich Panel Under Transverse Shear, S.M. Pingle, N.A. Fleck, V.S. Deshpande, H.N.G. Wadley, International Journal of Solids and Structures, 48, p. 3417-3430, 2011.