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A Theoretical Study of Indentation with an Oblate Spheroid Shape

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Abstract

In this study, firstly we introduced general mathematical concepts related to the geometrical form of ellipse and ellipsoid. Secondly, the hardness was calculated when we used an indenter having a geometrical shape of an oblate spheroid; the mathematical expressions of static hardness were determined as functions of the applied load, the radius or the depth of the imprint area. The general static hardness formula was expressed considering the projected and the real area imprint of the oblate spheroid indenter. Thirdly mathematical assumptions were introduced in order to simplify the mirohardness and nanohardness formulas when we used the real imprint area. Finally we did a comparative study between the oblate spheroid and the spherical indenters.

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Abbreviations

A, B, C :

Semi-axes of an ellipsoid

R, C :

Semi-axes of the oblate spheroid

D :

Diameter of the spherical indenter

d :

Diameter of the projected imprint area

H ac :

Static hardness of oblate spheroid indenter (case of projected imprint area)

H ar :

Static hardness of oblate spheroid indenter (case of real imprint area)

H m :

Microhardness

H n :

Nanohardness

F a :

Applied load on the oblate spheroid indenter

F S :

Applied load on the sphere indenter

S :

The projected imprint area

r :

Radius of the imprint projected area

h a :

Imprint depth of the oblate spheroid indenter

h S :

Imprint depth of the sphere indenter

S a :

Real imprint area of the oblate spheroid indenter

S S :

Real imprint area of the sphere indenter

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Authors and Affiliations

  1. Département de génie mécanique, Faculté de technologie, Université de M’sila, M’sila, Algeria

    A. Boudilmi

  2. Laboratoire des matériaux non métalliques, Institut d’optique et mécanique de précision, Université ferhat abbas, Sétif1, Algeria

    A. Boudilmi & K. Loucif

Authors
  1. A. Boudilmi
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  2. K. Loucif
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Correspondence to A. Boudilmi.

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Boudilmi, A., Loucif, K. A Theoretical Study of Indentation with an Oblate Spheroid Shape. Trans Indian Inst Met 70, 1527–1531 (2017). https://doi.org/10.1007/s12666-016-0949-x

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