Multiscale mechanical properties of shales: grid nanoindentation and statistical analytics

The mechanical properties of shales, a type of heterogeneous and multiphase composite, are of multiscale characteristics in nature. A large number of indentation measurements were performed under the continuous stiffness measurement (CSM) mode on the Longmaxi shale, followed by data segmentation, Gaussian mixture modeling (GMM) deconvolution of segmented datasets, and results re-integration. Accompanying compositional analyses by X-ray powder diffraction and surface imaging were also conducted to assist data interpretation. Results showed that the studied shale consisted of a fine-grained, relatively homogeneous clay matrix with randomly embedded, coarse-grained solid inclusions of up to ~ 100 μm in size. The CSM mode enabled the analysis of phase angle lag, which is an effective indicator for surface roughness. The Young’s moduli of both microscopic constituent phases (e.g., clay matrix, carbonates, quartz, pyrite) and macroscopic bulk shale were precisely determined and, through the probability analysis of the indent locations, the characteristic lengths of the shale’s constituent phases were estimated. The clay matrix and carbonates have relatively large characteristic lengths than quartz and pyrite. The data analytics proposed in this study may provide a feasible framework to assess the multiscale mechanical properties as well as the characteristic lengths of the shale’s constituent phases via a single type of measurement technique on the same piece of sample.