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Trinity College Dublin

Foams

Mohammad Saadatfar, Stefan Hutzler and Denis Weaire, School of Physics, Trinity College Dublin

What do aeroplane wings, water filters, car floors and the 2008 Olympic Aquatic Centre have in common? They are all metallic foams in one way or another! Metal foams combine weight and strength advantages over solid metals, making them ideal materials for a variety of industrial applications. For example, planes and cars require lightweight materials that are hard enough to provide structural support but are soft enough to crumple and absorb energy in a crash. They have also found numerous applications in filtering water and other fluids due to their highly porous structure and large surface-to-volume ratio. Or take cases where damping vibration is essential, such as bulkheads and car floors. These novel materials are studied at foam group in TCD in collaboration with Hahn-Meitner-Institute Berlin under a project commissioned by ESA.

Figure 1: Cross-section through an Aluminume foam fabricated by powder metallurgical process [2].

These distinctive properties of metal foams arise largely from the complex structure of the foams rather than the physical properties of the metal they are made of [1]. Linking properties to foam structure will lead to an understanding of how cellular solids can be optimised for given applications. Different manufacturing processes result in different foam structure which in turn results in different physical properties. Metallic foams may be prepared by bubbling gas into molten alloys. An alternative method is based on heating a mixture of metal powder and foaming agent [2]. As the mixture begins to melt, gas is released from the foaming agent which leads to foam formation, in a process similar to baking bread. What remains after cooling is a closed-cell pore structure (see Figure 1). Bubble rearrangement and coalescence complicate the process and result in continuous evolution of the foam’s microstructure due to gas release from the foaming agents and diffusion process.

Figure 2: 3D visualization of a metallic foam sample based on its tomogram. Visualization is primarily used to explore tomograms before carrying out qualitative analyses.

In order to control the foaming process and the properties of the product, one needs to be able to measure bubble size distribution and the thickness of films and struts inside the foam body at different stages of preparation. Other questions that immediately spring to mind are: how well-connected are the foam elements? Is it a single connected labyrinth, or a number of isolated pieces? What are the shapes of the bubbles and films and struts? These questions relate to the connectivity (topology) or shape (geometry) of foams. A qualitative answer to these questions may further our understanding of natural/biological foam-like structures such as trabecular bone which is crucial in understanding osteoporosis.

One of the best ways to answer these questions is to reconstruct or simulate the foam by imaging its inner structure using 3D X-ray Computed Tomography (CT). This non-invasive technique now enables researchers to measure the complex morphology of materials in 3D to a few microns of resolution. Similarly to medical CAT scans, a series of 2D x-ray images of the object are taken at different angles, which are then processed by a computer using well-known reconstruction algorithms [3] to produce a full 3D image of the sample called a tomogram. Based on this virtual foam, a variety of physical properties can be calculated and simulated by solving relevant equations, thereby linking the foam’s complex structure to its physical properties in question. Figure 2 displays a 3D rendering of a tomogram of a metal foam sample prepared in ESA’s microgravity facility.

For example, fluid flow through the pores of a foam sample can be simulated by solving the Navier-Stokes equations using the boundary conditions defined by the tomogram. Likewise, to calculate elastic properties such as how the foam behaves under stress, one can employ a numerical method to minimize the elastic energy. These simulations are demonstrated in Figure 3, which shows a 3D visualization of an open-cell foam sample along with the stress map in the solid phase and fluid streamline in the pore phase [4].

Figure 3: A 500 μm subvolume of an open-cell foam material. (b) The stress fields of the solid phase are overlaid on the foam. The more vivid the red, the larger the stress. (c) In the connected pore space, the liquid stream lines are illustrated [4].

Visualization, 3D image analysis and modeling on these large data sets is computationally intensive. For instance, for simulating the mechanical and fluid properties mentioned above, one needs to assign between 50-150 bytes to each voxel (3D version of 2D pixels). A typical tomogram is comprised of 20483 (8 billion) voxels, therefore at least 20483 x 50 byte ~ 400 giga bytes of memory is required to perform the simulations. Such vast amounts of memory are only accessible through supercomputing facilities such as IITAC.

References:

  1. “The Physics of Foams”, Denis Weaire and Stefan Hutzler. Oxford University Press, 2000.
  2. “A study of aluminium foam formation - kinetics and microstructure” I. Duarte and J. Banhart. 2000. Acta Mater. 48:2349–2362.
  3. “An inversion formula for cone-beam reconstruction” H.K. Tuy,. Siam J. Appl. Math. 43 3 (1983), pp. 546–552.
  4. “Developing a virtual materials laboratory” Arthur Sakellariou, Christoph H. Arns, Adrian P. Sheppard, Rob M. Sok, Holger Averdunk, Ajay Limaye, Anthony C. Jones, Tim J. Senden and Mark A. Knackstedt. Materials Today, Volume 10, Issue 12, December 2007, Pages 44-51

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