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H ertzian Indentation Stress Field Equations
Author(s) -
Louapre David,
Breder Kristin
Publication year - 2014
Publication title -
international journal of applied ceramic technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.4
H-Index - 57
eISSN - 1744-7402
pISSN - 1546-542X
DOI - 10.1111/ijac.12317
Subject(s) - indentation , consistency (knowledge bases) , stress field , materials science , stress (linguistics) , contact mechanics , brittleness , field (mathematics) , radius , confusion , distribution (mathematics) , mathematical analysis , composite material , structural engineering , geometry , mathematics , finite element method , computer science , engineering , linguistics , philosophy , psychology , computer security , psychoanalysis , pure mathematics
Indentation with hard spherical indenters (so called H ertzian indentation) is a well‐known technique to probe the mechanical properties of ceramics and other brittle materials. Using contact mechanics, it is possible to calculate the stress distribution in the sample and use it to express maximum tensile or compressive stresses as a function of load and contact radius. The equations describing the full stress distribution are not usually mentioned in the literature, and surprisingly most of the classical references disclosing them are either mistaken or incomplete. We recovered the full and detailed equations for the stress field distribution and numerically implemented them using the computer language P ython. We point out the relationships between the different expressions that have been published, check the consistency with existing results, and discuss the sources of confusion.