Structural Investigation of Size Effects in Plasticity using Indentation ...

1 Introduction
changes with the depth of penetration. One type of indenter, which meets this geometric
similarity, is the Vickers indenter. 5,6 Consequently, Meyer analysis of Vickers
hardness data should yield a constant Meyer index of 2. In the following many studies
were performed using the Vickers hardness test and it was found that the Vickers
hardness as well is load-dependent, especially at low loads. 6–9
In the following, great efforts were made to explain the observed behavior. Generally,
two sets of explanations can be distinguished. The first set concerns experimental
errors, 10 resulting from the resolution of the objective lens, 11,12 the geometry
of the indenter, 13 friction between indenter and specimen 13–15 and errors associated
with sample preparation. 7,8,16,17 The second set 1,18 is directly related to the intrinsic
structural factors of the tested materials, including e.g. indentation elastic
recovery 14,19–25 and work hardening during indentation. 1 The conclusion was, that
load-dependent hardness is a genuine effect and is not caused by instrumental errors
or the presence of a surface layer. A more detailed review on the early work of
load-dependent hardness can be found in the work of Mott. 1
One of the first systematic investigations on load-dependency of hardness, was
performed by Upit and Varchenya 26–29 on various single crystalline materials, using
a low-load microhardness testing device. Upit and Varchenya found that the
increase in hardness with decreasing load, is associated with a corresponding reduction
of the size of dislocation assemblies, surrounding the indentations. They
called the observed variation of hardness with load, “size effect”. However, the term
“indentation size effect” (ISE) was accepted years later. At the same time, Gane
and Cox 30,31 performed indentation experiments on single crystalline gold. Gane
and Cox found, that hardness could be increased by a factor of three when decreasing
the contact diameter down to 200 nm. They suggested, that the increase must
have some fundamental origins, connected to dislocation processes occurring in the
stressed volume around the indenter.
More than one decade later, the development of instrumented nanoindentation
techniques rekindled the interest in the phenomenon of load-dependent hardness.
Instrumented indentation technique was used by Pethica et al. 32 to perform hardness
tests on nickel, gold and silicon using indenter penetration depths as low as
20 nm. The indenter penetration was monitored continuously during loading and
unloading, while the areas of the indents were determined by means of a scanning
electron microscope (SEM). 33 For every material under examination a pronounced
indentation size effect was found, especially for depths less than 100 nm. Pethica et
al. explained the indentation size effect by local extreme work hardening, since all
glide planes are active and intersecting in regions less than 100 nm across. 32
Further improvement of instrumented nanoindentation technique was achieved
by the work of Doerner and Nix 34 as well as Oliver and Pharr. 35 The enhanced
technique made the determination of mechanical properties from load-displacement
curves possible, even when the indentations were too small to be imaged conveniently.
Driven by the growing interest in the deformation of small material volumes
caused by the development of thin films and the increased use of nanostructured materials,
load and displacement sensing indentation became a major tool to investigate
2