Multi-scale characterization of granular media by in situ laboratory X-ray computed tomography

Abstract

Investigations of biphasic monodisperse soft (rubber) and stiff (glass) particle mixtures under hydrostatic conditions show an interesting behavior with regard to the effective stiffness. P-wave modulus measured by acoustic wave propagation at ultrasonic frequencies showed a significant decline while more soft particles are added, that is, higher rubber volume fractions, due to a change in the microstructure of the granular medium. However, for small volume fractions of soft particles, it could be observed that the P-wave modulus is increasing. This result cannot be explained by classical mixture rules or effective medium theories. For the understanding of those effects, a detailed insight into the microstructure of the granular medium is necessary. To gain this information and link it later back to the measured effective mechanical properties, high-resolution micro X-ray computed tomography ($\mu$XRCT) imaging is a well-established tool. With $\mu$XRCT imaging, the granular microstructure can be visualized in 3D and characterized subsequently. Combining classical effective characterization methods with $\mu$XRCT imaging can help to solve a variety of multi-scale problems. Performing the characterization step in situ, meaning inside the laboratory-based $\mu$XRCT scanner, has the advantage that exactly the same samples are mechanically characterized and visualized. To address the mentioned observation above, we designed a low X-ray absorbing oedometer cell with integrated broadband piezoelectric P-wave transducers which enables this kind of investigation inside a laboratory-based $\mu$XRCT scanner. The focus of this contribution is on the general experimental methodology which can be transferred to other multi-scale problems. It starts with a description of the image acquisition and ends with the post-processing of the in situ acquired image data. To demonstrate this, cylindrical samples consisting of the same monodisperse rubber and glass particle mixtures that were studied before under hydrostatic stress conditions are considered. Selected results are presented to explain the single steps.