Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Multi-Scale Effects in the Strength of Ceramics



Robert F. Cook


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.
Journal of the American Ceramic Society


Ceramic, Strength, Multi-Scale, Indentation


Cook, R. (2015), Multi-Scale Effects in the Strength of Ceramics, Journal of the American Ceramic Society, [online], (Accessed June 22, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 15, 2015, Updated January 27, 2020