Hardness-grain-size relations in ceramics

TLDR: In this paper, the Vickers and Knoop hardness (H) was measured at two or more loads in the range of 100-2000 g (most commonly 100 and 500 g) for a variety of dense oxide and non-oxide materials, covering a range of grain sizes (G), including single crystals where possible, were shown to generally be consistent with (often more limited) literature data.

Abstract: Both Vickers and Knoop hardness (H), measured at two or more loads in the range of 100–2000 g (most commonly 100 and 500 g) for a variety of dense oxide and non-oxide materials, covering a range of grain sizes (G), including single crystals where possible, were shown to generally be consistent with (often more limited) literature data. Apparently, conflicting trends of H (1) showing either no G dependence, (2) decreasing from single-crystal or large G values with decreasing G, or (3) having the generally accepted increase with decreasing G are shown to be due to the combination of the limited extent of data and H generally heing determined by two basic trends. These two trends are (a) the normal inverse G (i.e., H–G−1/2) dependence at finer G, (b) a variable G minimum at intermediate G, and (c) H increasing with increasing G at larger G (to. single-crystal values). The H minimum is due to local cracking around the indent (mostly along grain boundaries), generally reaching a maximum effect, e.g., minimum in H, when the indent and grain sizes are similar, and tends to be greater for Vickers vs Knoop indents, higher loads and probably greater grain boundary Impurity, additive contents, and stresses.