MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 127

3.3 . Sharp elastic contact

Most commonly a sharp indenter tip—either a cone or a three-sided
pyramid—is used in nanoindentation. The three-sided pyramid, called a
“Berkovich” tip, was designed to mimic the relationship between
indentation depth and projected contact area as is found for a Vickers
pyramid—the four-sided pyramid most commonly used in classic
microindentation hardness experiments. The full elastic solution for
conical indentation is 9 :

= π

tan ψ E

P

) h 2

(5-8)

2 γ

2

(1 − ν

2

for a conical indenter with included half-angle and where is = /2.

4. Elastic-Plastic Contact

The standard metric for evaluating the extent of plastic deformation in an
indentation test is by the “hardness” which is representative of the
resistance to plastic deformation, and can be related to a metal's yield
stress. In microindentation, the residual indentation impression is
measured with an optical microscope, and the hardness—a representative
contact stress—is computed as the ratio of indentation load to projected
area 10 :

P max
2 b 2

P max
π a 2

H = = (5-9)

where b is half the length of the impression diagonal for a Vickers four-
sided pyramid, or a is the effective contact radius for a circular
impression. In soft metals, the bulk of indentation deformation is plastic,
not elastic. In ceramics there is a more even balance of elastic and
plastic deformations 11 while in polymers and elastomers there may be
little or no plastic deformation. In the case of an absence of plastic
deformation, the “hardness” can still be computed as the mean contact
stress, although obviously there is no residual impression to measure and
the contact radius at maximum load must be inferred from a calibration
function.