Cross-scale characterization of the elasticity of shales: Statistical nanoindentation and data analytics

Shales are a class of multiscale, multiphase, hybrid inorganic-organic composite materials exhibiting both frictional and cohesive behavior, and it is very challenging to characterize and interpret their complex mechanical properties. A statistical nanoindentation approach with pertinent viable data analytics was developed to probe the mechanical properties of shales across different length scales. Grid nanoindentation experiments with continuous stiffness measurement performed on shales to relatively large depths of 6–8 µm obtained massive data, which were processed by the new data analytics: segmentation at selected depths of a great number (e.g., >500) of continuous Young's modulus versus indentation depth curves obtained from unknown constituent phases yielded multiple discretized sub-datasets that were processed to extract individual phases' elastic moduli at respective segmentation depths via probability density function (PDF)-based deconvolution; these depth-dependent Young's moduli of each phase were then fitted by a newly proposed surround effect model, leading to determination of the properties of both individual phases at the nano/micro-scales (i.e., virtually infinitesimal depths) and the bulk rock at the macroscale (i.e., ~10–100 µm depths). A significant advantage of this massive data-based indentation approach is that the mechanical properties of composite materials such as shales can be probed across different scales by a single measurement technique. In addition, a new criterion, termed Bin Size Index, was formulated for selecting depth-dependent, rational, optimized bin sizes for PDF construction. For the studied shales, results show that five mechanically-distinct phases are discerned, including a virtual interface phase between hard and soft constituents accounting for a majority of indents. Coincidently, the Young's modulus of the bulk rock is nearly the same as that of the interface phase, suggesting that the macroscopic properties of similar composites may be estimated from measurements on the interface of two phases with contrasting mechanical properties. Finally, this approach can guide the selection of appropriate indentation depths to probe the mechanical properties of both highly heterogeneous bulk materials at the macroscale and their individual constituent phases at the nano/micro-scale.