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 ð5 mmÞ 3 at resolutions down to 7 mm. 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 E=E s Z ðr=r s Þ 2 give a good Downloaded from correlation. Assuming a constant Poisson's ratio n leads to reasonable agreement. The best correlation for n is given by assuming a slight variation in n 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.

Calculating structural and geometrical parameters by laboratory measurements and X-ray microtomography: a comparative study applied to a limestone sample before and after a dissolution experiment

“…It might be interesting to simulate drainage and imbition experiments using the XMT images as previously done by Knackstedt et al (2006) and Prodanovic et al (2010) in order to compare the laboratory RET measurements in a further study. To summarize, one should note that the pore-size distribution obtained by the retention curves indicates the capillary pressure needed to extract a specific fluid volume, but without any information about the amount of pores containing this fluid volume and the respective pore diameters.…”

“…Only one similar study was done by Lamande et al (2013) on soil material using a medical scanner with a large pixel size (0.6 mm). Nevertheless, op.…”

“…3-D data provides access to some very important geometric and topological characteristics such as size, shape, orientation distribution of individual features and that of their local neighbourhoods, connectivity between features and network, composition, etc. Computational techniques have progressed to the point where material properties such as conductivity (Arns et al, 2001), diffusivity (Schwartz et al, 1994;Knackstedt et al, 2006;Promentilla et al, 2009;Gouze and Luquot, 2011), permeability (Martys et al, 1999;Arns et al, 2004;Arns et al, 2005a;Arns et al, 2005b), pore-size distribution (Dunsmuir et al, 1991;Prodanovic et al, 2010;Garing et al, 2014;Luquot et al, 2014a) and linear elasticity (Roberts and Garboczi, 2000;Arns et al, 2002;Knackstedt et al, 2006) can be calculated on large threedimensional digitized grids (over 10 9 voxels). More details on this technique, acquisition and data computing step can be found in Taina et al (2008); Cnudde and Boone (2013) and Wildenschild and Sheppard (2013).…”

3D mapping of anisotropic ferroelectric/dielectric composites

“…11,12 Another probe for ferroelectric anisotropy is the piezoelectric resonance that is less sensitive to all spurious free charges that could always be accumulated at the ferroelectric/dielectric interfaces and that could contribute to the depolarization currents. For the piezoelectric experiments, the parallel sample was a bar 5.59 × 1.48 × 0.82 mm 3 and the perpendicular sample a Plate 2.28 × 1.33 × 0.53 mm 3 . In both cases, an electric field of 7.3 kV cm −1 was applied on cooling and the piezoelectric resonance was recorded at fixed temperature while heating.…”

“…In the field of functional materials, XCMT has been mainly used for fluid flow in porous media, 1 for the in situ control of sintering 2 and for mechanical properties. 3 In the first two cases, the resulting 3D map is the starting point for the implementation of fluid dynamics equations. 4 In the third, large-scale elastic excitations are usually considered.…”