Elastic and transport properties of cellular solids derived from three-dimensional tomographic images

Abstract

We describe a three-dimensional imaging and analysis study of eight industrial cellular foam morphologies. The foam morphologies were generated by differing industrial processing methods. Tomograms are acquired on an X-ray micro-computed tomography facility at scales of approximately equal to Graphic at resolutions down to 7 μm. The image quality is sufficient in all cases to measure local structure and connectivity of the foamed material, and the field of view large enough to calculate a range of material properties. Phase separation into solid and porous components is straightforward.

Three-dimensional structural characteristics are measured directly on the porous and solid phases of the images. A number of morphological parameters are obtained, including pore volume-to-surface-area ratio, connectivity, the pore and solid phase size distributions defined by maximal sphere openings and chord length measurements. We further calculate the pore size distribution associated with capillary pressure via simulating of mercury drainage on the digital images.

The binarized microstructures are used as a basis for calculations of transport properties (fluid permeability, diffusivity and thermal conductivity) and elastic moduli. From the data, we generate property–porosity relationships for the range of foam morphologies imaged and quantitatively analyse the effects of porosity and microstructure on the resultant properties of the foams.

We compare our numerical data to commonly used theoretical and empirical property–porosity relationships. For thermal conductivity, we find that the numerical results agree extremely well with an empirical expression based on experimental data of various foams. The upper Hashin–Shtrikman bound also provides an excellent prediction of the data across all densities. From simulation of the diffusivity, we can define the tortuosity of the pore space within the cellular solid. We find that different processing methods lead to strong variations in the tortuosity of the pore space of the foams. For elastic properties, our results show that for the Young modulus, E, both the differential effective medium theory and the classical correlation Graphic give a good correlation. Assuming a constant Poisson's ratio Graphic leads to reasonable agreement. The best correlation for Graphic is given by assuming a slight variation in Graphic as a linear function of porosity. The permeability of the foams varies over three orders of magnitude. Correlations for permeability based on the classical Kozeny–Carman equation lead to reasonable agreement, except at the lowest porosities. Permeability estimations based on mercury porosimetry give excellent agreement for all foams.