Relationship between the anisotropy tensor calculated through global and object measurements in high-resolution X-ray tomography on cellular and composite materials

Structural anisotropy of two-phase materials can be evaluated through global measurements, as volume orientation or mean-intercept length methods do, or through statistics performed on a set of individual measurements. This last procedure is encouraged by recent improvements in the spatial resolution of conventional X-ray tomography. In this paper, the above-described approaches were compared in three case studies: a foam subjected to an in situ compression test, a second foam with a completely different cell morphology and a plastic material reinforced with short fibres. The approach based on the subdivision into distinguishable objects of the considered material phase has proved to be more sensitive in highlighting small deformations in the structure or small irregularities in an otherwise isotropic structure. On the other hand, the other approach is more general and is always usable. The two methods for calculating the fabric tensor tend to converge as the average anisotropy of individual objects in the statistical population increases. The use of Lambert's cylindrical equal-area projection of cell/fibre directions or local volume orientations is suggested, because the density of points is preserved from the sphere to the plane surface. Finally, a quick vector method to evaluate the anisotropy of the directions distribution has been presented, by defining a coherence index of the average direction.