A uniform rule between hardness and structure hierarchy of ceramics in both direct and inverse Hall–Petch regimes

Abstract

The MicroStructure Hierarchy Descriptor (μ$\umu$SHD) has built a bridge in linking the structure hierarchy and properties of ceramic materials. Here, a new variable Asc$Asc$, which stands for the average of scales present in a ceramic microstructure, based on the μ$\umu$SHD, is constructed and calibrated. It is found that the Asc$Asc$ is not only related to the size scales, but also the morphological features in microstructures, due to an inheritance from the μ$\umu$SHD. The Asc$Asc$ is positively linear correlated with the average grain size d, but the relationship changes to be nonlinear when the morphology of grains is considered. In the Hall–Petch regime, the Vickers hardness HV of both, ZrO2–SiC composite ceramics and a class of high entropy metallic borides, is found to increase with the decrease of Asc$Asc$ index. For the case study of ZrO2 ceramic, a uniform rule is found to be valid in both the direct and inverse Hall–Petch regimes that the Asc$Asc$ varies in an opposite trend as the HV varies with d.