MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 128

In elastic-plastic indentation testing, as in metals, ceramics and to
some extent glassy polymers, it is desirable to separate the elastic and
plastic deformation components to allow for calculations of the elastic
modulus as well as the hardness. Key developments in this field were
made by Doerner and Nix 12 prior to the landmark work of Oliver and
Pharr. 1 The Oliver-Pharr procedure is most commonly employed for
conical or pyramidal indentation, although it is occasionally used for
spherical indentation. A second elastic-plastic deconvolution scheme
for spherical indentation is that of Field and Swain, 13 which will be
mentioned briefly. In this section, the mechanisms for measuring elastic
modulus in elastic-plastic materials will be considered, along with
procedures for identifying plastic deformation and for quantifying the
plasticity in terms of hardness.

4.1 . Elastic-plastic spherical contact

In spherical indentation, there is a change in the functional form of the
load-displacement relationship from P ~ h 3/2 to P ~ h when deformation
shifts from elastic to plastic. This change is clearly evident in soft, single
crystal aluminum; nanoindenter data from fused silica glass and
aluminum have been plotted on a log scale along with lines indicating the
two critical functional forms of the load-displacement relationship for
spherical indentation. The aluminum data clearly demonstrates the
transition to P ~ h behavior ( Fig. 5-4 ) while the glass data (the same
response as in Fig. 5-3 ) retains the elastic functional form.
In spherical indentation of elastic-plastic materials, the separation of
elastic and plastic deformation responses is performed utilizing a
procedure that utilizes a modification of the Hertzian elastic expression
( Eq. 5-5 ) based on an assumption of elastic unloading. 13

1/2

3 P 1 1

E = − (5-10)

R

4 h

3/2
e

RR '

where h e is the elastic penetration depth and

11
'

− (5-11)

R R