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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

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Strength of Materials Aims and scope

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 α and β 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.

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Abbreviations

H :

- height of the cone form

R :

- half of diameter of the sharp cone indenter

F :

- load applied to the indenter

S :

- the projected surface of the print

α, β :

- coefficients of the area low mixture model

r :

- diameter of the composite projected surface (measured by experiments)

r ∗ :

- diameter of the projected surface of the substrate

e :

- film thickness

h :

- depth of the imprint

H con :

- hardness of the massif materiel of the cone indenter

H c :

- composite hardness

H f :

- hardness of the film

H s :

- hardness of the substrate

S c :

- surface of the composite imprint project

S f :

- surface of the film imprint project

S s :

- surface of the substrate imprint project

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Acknowledgment

The authors gratefully acknowledge the supports from the general directorate of Scientific Research and Technological Development (DGRSDT).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Technology, Mohamed Boudiaf University, M’sila, Algeria

    A. Boudilmi & M. Slamani

  2. Nonmetallic Materials Laboratory, Institute of Optics and Precision Mechanics, Ferhat Abbas University of Sétif 1, Sétif, Algeria

    A. Boudilmi & K. Loucif

  3. Laboratory of Materials and Mechanics of Structures, Mohamed Boudiaf University of M’sila, M’sila, Algeria

    M. Slamani, M. Titoum & K. Bouchareb

Authors
  1. A. Boudilmi
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  2. K. Loucif
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  4. M. Titoum
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Correspondence to A. Boudilmi.

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Translated from Problemy Mitsnosti, No. 4, p. 118, July-August, 2023

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Boudilmi, A., Loucif, K., Slamani, M. et al. 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 Mater 55, 800–813 (2023). https://doi.org/10.1007/s11223-023-00571-y

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