Statistical construction of 3-D microstructures from 2-D exemplars collected on oblique sections

Abstract Material internal structure (generally referred as microstructure) is known to play an important role in controlling the properties/performance characteristics of the material. Most commonly employed methods of microstructure characterization result in 2-D (two dimensional) sampling of the inherently 3-D microstructure. This is because the available methods of 3-D characterization incur several orders of magnitude larger time and effort compared to the well-established and validated 2-D characterization protocols. However, if one accepts the fundamental hypothesis that the microstructure in a hierarchical material system need only be quantified rigorously in a statistical framework for establishing the desired correlations with bulk (effective) properties of the material, then it raises the potential of whether or not one can build statistically equivalent 3-D microstructures from the low-cost 2-D exemplars collected from oblique (non-parallel) sections on the sample. This paper develops and discusses a suitable framework to explore such an approach, and demonstrates its viability and utility through selected case studies.