Multi‐Scale Effects in the Strength of Ceramics

Multiple length‐scale effects are demonstrated in indentation‐strength measurements of a range of ceramic materials under inert and reactive conditions. Meso‐scale effects associated with flaw disruption by lateral cracking at large indentation loads are shown to increase strengths above the ideal indentation response. Micro‐scale effects associated with toughening by microstructural restraints at small indentation loads are shown to decrease strengths below the ideal response. A combined meso‐micro‐scale analysis is developed that describes ceramic inert strength behaviors over the complete indentation flaw size range. Nano‐scale effects associated with chemical equilibria and crack velocity thresholds are shown to lead to invariant minimum strengths at slow applied stressing rates under reactive conditions. A combined meso‐micro‐nano‐scale analysis is developed that describes the full range of reactive and inert strength behaviors as a function of indentation load and applied stressing rate. Applications of the multi‐scale analysis are demonstrated for materials design, materials selection, toughness determination, crack velocity determination, bond rupture parameter determination, and prediction of reactive strengths. The measurements and analysis provide strong support for the existence of sharp crack tips in ceramics such that the nano‐scale mechanisms of discrete bond rupture are separate from the larger scale crack driving force mechanics characterized by continuum‐based stress‐intensity factors.