Elastic analysis of triangular pyramidal indentation by the finite-element method and its application to nano-indentation measurement of glasses

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Abstract
A particular formulation of the three-dimensional finite-element method is established for the elastic analysis of the triangular pyramidal indentation. Numerical analyses are carried out under several conditions to investigate the influences of the elastic properties of the material and the apical angle α of the triangular pyramidal indenter on the loadisplacement (P-h) relationship. The analytical results are expressed by P [dbnd] CE∗ (tan α)h 2, where E∗ is the plane strain modulus of the material and C is a geometrical factor equal to 1·02. The value of C is a factor of 1·60 larger than the theoretical value for a conical indenter, 2/π. The analytical results are evaluated by nano-indentation measurements on five glasses; one is as fused and the others are mechanically surface polished. The experimental geometrical factor obtained on the former glass agrees well with the calculated value, while those on the latter glasses are slightly higher. The experimental P-h curves of the mechanically surface-finished glasses reveal an abnormal surface layer of 20 nm thickness, indicating the occurrence of surface damage.

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