This study is a mathematical and geometric proof of the expression of the micro- and nanohardness
of thin coating resulting from the indentation of a needle form of a cone tip. It is geometric and
mathematical modeling of the indentation of the monolayer solid material, where approaches to the
coefficients of the model of surfaces mixture are presented. Firstly, formulations of hardness
indentations of the composite and the substrate of the mono-layer-coated material have been
established. Then, the hardness formula of the thin film of the coating material was derived from the
additive law of mixtures. The project imprint result from the indentation of the cone tip on a plane
surface is considered as a disk form and the coefficients ߙ and ߚ are ratios of circle surfaces. The
hardness of the composite and the substrate of the coating material are expressed as functions of the
imprint projected dimensions and the applied load. The contribution of the film to the composite
hardness is determined by the model of the surfaces – low mixture of the area – low mixture model.
Finally, the expression of the hardness film becomes a function of the composite hardness, the indenter
dimension, the imprint dimension, and the film thickness.
Citation
Mohamed SLAMANI ,
Aissa BOUDILMI ,
Messaoud TITOUM ,
KHALED Bouchareb ,
K. Loucif, , (2023-10-13), NEW METHOD FOR THE MICRO- AND NANOHARDNESS MEASUREMENT OF THIN FILM OF MONOLAYER SOLID BY THE INDENTATION OF A SHARP NEEDLE OF A CONE TIP, Strength of Materials,
Vol:55, Issue:4, pages:800-813, Springer
