Knoop Hardness–Apparent Yield Stress Relationship in
Ceramics
Jeffrey J. Swab* and Jerry C. LaSalvia
US Army Research Laboratory, Aberdeen Proving Ground, Maryland, 21005
Andrew A. Wereszczak
Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831
Kevin T. Strong Jr., Dominic Danna, Meredith E. Ragan, and Patrick J. Ritt
Oak Ridge Institute for Science and Education, Oak Ridge, Tennessee, 37831
In Tabor’s classical studies of the deformation of metals, the yield stress (Y) and hardness (H) were shown to be related
according to H/Y 3 for complete or fully plastic deformation. Since then it has been anecdotally shown for ceramics that
this ratio is <3. Interest exists to explore this further so Hertzian indentation was used to measure the apparent yield stress of
numerous ceramics and metals and their results were compared with each material’s load-dependent Knoop hardness. The
evaluated ceramics included standard reference materials for hardness (silicon nitride and tungsten carbide), silicon carbide,
alumina, and glass. Several steel compositions were also tested for comparison. Knoop hardness measurements at 19.6 N (i.e.,
toward “complete or fully plastic deformation”), showed that 2 < H/Y < 3 for the metals and 0.8 < H/Y < 1.8 for the
glasses and ceramics. Being that H/Y 6¼ 3 for the ceramics indicates that Tabor’s analysis is either not applicable to ceramics
or that full plastic deformation is not achieved with a Knoop indentation or both.
Introduction
Many models used to simulate and predict the bal-
listic performance of candidate armor ceramics incorpo-
rate yield stress (Y) as an input parameter since it is a
*jeffrey.j.swab.civ@mail.mil
© 2011 The American Ceramic Society and Wiley Periodicals, Inc.
Int. J. Appl. Ceram. Technol., 1–6 (2011)
DOI:10.1111/j.1744-7402.2011.00686.x