MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 130

material below the point results in a near-immediate onset of plasticity
and a dominantly plastic overall response. The functional form for elastic
and plastic deformation are both P ~ h 2 under conical or pyramidal
loading, further complicating the distinction ( Fig. 5-5 ) and making it
impossible to separate these deformation components by functional form
in the same manner as for spherical indentation. As mentioned briefly
above ( Eq. 5-9 ), the parameter generically called “hardness” ( H ) is
frequently used to characterize dominantly plastic materials. 10

Figure 5-5. Elastic-plastic indentation responses for a Berkovich on glass demonstrating a
consistent P ~ h 2 response across the entire loading trace. The unloading trace has a
different, and changing, functional form.

The overall scheme for separating elastic and plastic deformations in
the Oliver-Pharr method is based on the assumption that the unloading
response is purely elastic, such that the reduced modulus E R ( Eq. 5-3 ) of
the contact can be related to the unloading stiffness S ( Fig. 5-6 ) via:

S π

E R = (5-12)

2 A c