MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 137

procedure is violated, and different analyses must be employed. Time-
dependent deformation appears most readily in nanoindentation data as
increasing creep displacement at fixed load; in some cases, further
forward displacement can be seen during unloading, a feature that has
been termed a “nose” in the curve. 24 When experiments are conducted in
displacement control instead of load control, the time-dependence is seen
as load relaxation at fixed depth, and no “nose” is present in the data.
Related to the existence of time-dependent deformation observed at fixed
load or displacement, there are clear differences observed in the load-
displacement response of time-dependent materials when probed at
different load- or displacement- rates.
In this section, two mechanisms of time-dependent deformation will
be explored, viscoelasticity and poroelasticity. Empirical viscoelastic
approaches will be presented first, addressing both linear and nonlinear
viscoelasticity. Mechanism-driven poroelastic approaches will then be
considered, in which the time-dependent deformation is explicitly
associated with fluid flow through a porous elastic network.
6.1. Viscoelastic contact
There are two limits to the elastic modulus in all materials, the adiabatic
modulus and the isothermal modulus. In relatively time-independent
materials, the two limits are comparable and are typically the difference
is not easily noted in routine mechanical testing experiments. In time-
dependent materials, the two limits can be widely divergent and the
region of transition between the limits can be complicated. As it is
experimentally impossible to measure mechanical properties either
infinitely quickly or infinitely slowly, the apparent elastic modulus of a
viscoelastic material changes with time over reasonable experimental
time-frames. A full physical and mechanistic model for viscoelastic
behavior remains elusive; for engineering practice, it is common to fit the
elastic modulus-time responses to empirical functions based on simple
mathematical constructs such as an exponential decay or a power-law
decay in time.