Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: Applications to probing nanoelectromechanical properties of materials

Journal Article · Thu Jan 01 04:00:00 EST 2009 · Journal of the Mechanics and Physics of Solids

DOI:https://doi.org/10.1016/j.jmps.2009.01.002· OSTI ID:1030985

Karapetian, E. ^[1]; Kachanov, M. ^[2]; Kalinin, Sergei V ^[3]

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1. Suffolk University, Boston
2. Tifts University, Medford, MA
3. ORNL

Stiffness relations for voltage-dependent contact mechanics of piezoelectric material are derived for an indenter of arbitrary planform under normal force, centrally or non-centrally applied, and electric charge distribution at the base. Relations between indentation depth, indentation force, electric potential and electric charge are explicitly given in terms of indenter s geometry and piezoelectric material constants. The analysis covers indenters with non-flat base approximated by a second-order surface; elliptic paraboloid is considered as an example. In the case of the elliptic non-flat planform, the derived stiffness relations are exact; otherwise, they are approximate and are shown to have good accuracy. The stiffness relations are given in elementary functions and are obtained by utilizing the recently established principle of correspondence between the piezoelectric and purely elastic problems. Besides contributing to extension of Hertzian mechanics to piezoelectric materials, these results are essential for quantitative interpretation of the Scanning Probe Microscopy and piezoelectric nanoindentation data on piezoelectric, ferroelectric, and multiferroic materials.

• Research Organization: Oak Ridge National Laboratory (ORNL); Center for Nanophase Materials Sciences
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1030985
• Journal Information: Journal of the Mechanics and Physics of Solids, Journal Name: Journal of the Mechanics and Physics of Solids Journal Issue: 4 Vol. 57; ISSN 0022-5096; ISSN JMPSA8
• Country of Publication: United States
• Language: English

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