High-Throughput Nanoindentation for Statistical and Spatial Property Determination
High-Throughput Nanoindentation for Statistical and Spatial Property Determination
0 1.-Bruker Nano Surfaces , Eden Prairie, MN, USA. 2.-Bruker Nano Surfaces, Aachen, Germany. 3.-
Standard nanoindentation tests are ''high throughput'' compared to nearly all other mechanical tests, such as tension or compression. However, the typical rates of tens of tests per hour can be significantly improved. These higher testing rates enable otherwise impractical studies requiring several thousands of indents, such as high-resolution property mapping and detailed statistical studies. However, care must be taken to avoid systematic errors in the measurement, including choosing of the indentation depth/spacing to avoid overlap of plastic zones, pileup, and influence of neighboring microstructural features in the material being tested. Furthermore, since fast loading rates are required, the strain rate sensitivity must also be considered. A review of these effects is given, with the emphasis placed on making complimentary standard nanoindentation measurements to address these issues. Experimental applications of the technique, including mapping of welds, microstructures, and composites with varying length scales, along with studying the effect of surface roughness on nominally homogeneous specimens, will be presented.
ERIC D. HINTSALA,1 UDE HANGEN,2 and DOUGLAS D. STAUFFER
Nanoindentation has been proven to be a
powerful tool for exploring mechanical behavior at
smalllength scales. This is due to the technique being
highly localized and only semi-destructive, while
simultaneously allowing extraction of a diverse set
of properties including elastic, plastic, and fracture.
In addition, the sample preparation requirements
are significantly less stringent than most other
mechanical testing techniques, and the procedures
are well established.1–5 However, standard
nanoindentation testing requires several minutes per test
for tasks such as locating suitable areas, the sample
approach, drift correction, and retraction of the tip.
This makes certain applications, such as property
mapping by indentation grids6,7 or generation of
statistical data sets, extremely time consuming and,
in some cases, too slow to be practical. Various
technologies have been developed in recent years
that have greatly accelerated nanoindentation
testing, with state-of-the-art speeds of up to 6 indents/
second representing at least two orders of
magnitude improvement over standard quasi-static
testing. This means that 10,000 indent maps can
be completed in less than an hour—for perspective,
this would generate a property map of
100 9 100 lm with 1-lm spacing. The speeds,
resolution, scan size, and sample preparation
requirements are comparable to a variety of SEM mapping
techniques, such as electron backscatter diffraction
(EBSD) and energy dispersive spectrometry (EDS).
The fact that they also give highly complementary
information means that correlated surveying of
microstructural features for their crystallographic,
chemical and mechanical properties provides
researchers with a powerful tool. Besides this,
statistical indentation techniques allow users to
quickly determine parameters of significance,
screen materials, and identify more global trends
from highly localized nanoindentation tests.8 In
addition, statistical data sets help combat factors
producing data outliers, such as surface
roughness,9–12 which are a hindrance to accurate
nanoindentation testing. Lastly, these techniques can also
be applied to systems with environmental control,
such as heating, controlled humidity, or even
submerged specimens, providing additional variables to
explore. To date, hardness mapping has been
utilized to explore spatial variations in a variety of
materials including cement pastes,13 concrete,14
tooth enamel,15 metal matrix composites,6,7,15,16
intermetallics,17 metal alloys,6,18,19 and wood
However, properly conducting high-speed
nanoindentation and interpreting its results requires one
to consider various factors, such as indentation
spacing, strain rate effects, and indentation depth.
In addition, it can currently only be applied to
measuring hardness and elastic modulus because of
the restrictions on load function choice. Thus,
highspeed indentation is not a replacement for standard
indentation techniques. Rather, the approach that
is advocated is that of a complementary technique
for standard indentation, where the standard
testing protocol allows one to assess indentation size
effects,21–23 rate dependence,24 and spacing effects.
Here, we will review these key concepts first before
presenting example application data emphasizing
EXPERIMENTAL CONSIDERATIONS FOR
To produce high-quality property maps,
consideration of the stress field underneath the indenter tip
is critical. Not only is there potential for the damage
zones from individual tests to overlap and
invalidate the results, but the ‘‘resolution’’ of the
nanoindentation test is relevant when testing near
boundaries of features, such as grain and phase
boundaries, weld zones, composite interfaces, and
material gradients, for damage or composition. The
indenter resolution needs to be carefully defined, as
the stress field occurs in three dimensions and
consists of separately sized elastic and plastic zones.
A second consideration involves the necessity of
high loading rates, which may induce strain rate
sensitivity changes in the measured hardness. Both
subjects will be covered in the following two
sections, ‘‘Indentation Spacing and Resolution’’ and
‘‘Strain Rate Sensitivity’’.
Indentation Spacing and Resolution
When mapping surface properties, the in-plane
spatial resolution is of primary concern; however,
defining this requires consideration of the full
threedimensional shape of the indentation stress field or
the volume of material being tested. Since the stress
field decays continuously as a function of distance
from the contact zone, boundaries can only be
defined by a specific stress or strain value. The
most important is the subdivision into a purely
elastic25 and an elastic–plastic zone with the
boundary set by the yield criterion of the material,26 as
illustrated in Fig. 1. Thus, the entire elastic zone
contributes to the modulus measurement, while
only the elastic–plastic zone contributes to the
hardness, H, measurement. In terms of a more
practical definition for defining the indentation
resolution, one can define an acceptable relative
change of properties in proximity to a feature,
such as a microstructural boundary or a previous
Some indenters have a geometry that can be
described as self-similar, which is simply a tip shape
with a constant ratio of the contact area to depth
versus load. This property is maintained by common
pyramidal indenters, including Berkovich and cube
corners, as well as conical tips, and implies that the
measured properties will not change as a function of
indentation load. Notably, spherical tips are an
exception. Thus, for a self-similar indenter,
allimportant geometrical parameters can be expressed
as a function of the contact radius, a. The contact
radius is defined as the radius of a circle of
estimated equivalent area to that of the actual
contact, thus allowing pyramidal probes to be
described by the same parameter as spherical and
Regarding issues with indent-to-indent spacing,
there are several effects. If the second indent
overlaps with the residual impression or pileup
from the previous, this clearly invalidates the
semiinfinite half-space assumption and the actual
contact radius will deviate significantly from the
assumed value. Subtler is the overlap of plastic
zones, which extend further in the sub-surface of
the testing plane. The residual plastic zone could be
considered cold-worked, thereby elevated hardness,
but the exact interaction of plastically nucleated
defects could also produce a softening effect by
providing dislocation sources. The radius of the
plastic zone, Rp, in relationship to the contact radius
is material specific because of differences in
plasticity mechanisms. For metals, this ratio can range
from 3a to 6a.27–29 For a sharp Berkovich tip with
50-nm radius of curvature, reliable hardness
measurements can be achieved at a depth of at least
15 nm as shown in Fig. 1 (note that the modulus
was constant for the three tips over the entire depth
range). This corresponds to a maximum contact
radius of 57 nm, thus requiring a 315-nm indent
spacing for a soft metal with Rp 6a. This situation
improves for a cube corner that has a steeper
contact radius to a depth ratio of 0.7 compared to
3.5 for a Berkovich. Since these tips are self-similar,
the plastic zone size is proportional to the contact
radius and is reduced by approximately a factor of 5
as well. As previously discussed, the exact plastic
zone size is specific to a given tip-material-depth
combination, so experimental evaluation is required
to determine this size precisely. This can be
illustrated by two case studies: (
) the influence of one
indentation on its neighbor and (
) the influence of
interfaces in the proximity of an indent.
To illustrate this effect, the indent spacing, d, was
varied on an Al sample as tested with a Berkovich tip,
as shown in Fig. 2a. Interestingly, reducing d results
in a corresponding decrease in hardness rather than
an increase as would be expected for work hardening.
Additionally, no effect on modulus would be expected
from plastic zone overlap. Therefore, the effect on
modulus at the smaller values of d indicates the
invalidation of the area function due to pileup. This
pileup-affected zone begins at d = 750 nm, slightly
less than the recommended distance of 5.6 times the
contact radius, or 840 nm for a maximum
displacement of 50 nm. Clearly, a trade-off occurs between
lateral resolution and hardness measurement
accuracy, as using a sharper tip at smaller depths gives a
reduced elastic–plastic zone. An additional tradeoff
can be made by sacrificing the hardness
measurement altogether and limiting testing to a purely
elastic regime. The absence of a plastic zone and
residual displacement and thus no pileup in a purely
elastic indent allow for the contact radii to overlap
between individual indents.
The role of sample interfaces, important to
highresolution mapping of compositional and phase
varied materials, is illustrated by mapping with a
metal-ceramic cross-sectional sample. Here, indents
are placed near a material interface in a sample,
specifically, a 750-nm-wide Ti layer sandwiched
between two extremely hard (H 25 GPa) Ti-N
layers. The indenter was carefully placed in the
center of the Ti layer using in situ SPM imaging. A
profile of hardness and modulus as a function of
depth is shown in Fig. 2b, where correct hardness
and reduced modulus values for Ti were only
measured at 15–30-nm depth. At larger depths,
the indentation stress field increasingly interacts
with the TiN layers resulting in increasing modulus
and hardness values. In some mapping scenarios,
the indentation grid is generated with a
predetermined spacing that will place indents at varying
distances from, or on top of, a phase boundary or
interface in the sample. This can produce
measurement errors if plasticity mechanisms are affected by
the presence of the boundary, such as providing
defect sources, sinks, and barriers. These data
points can usually be filtered during analysis by
examining the statistical distribution of measured
properties and removing outliers. These boundary
effects can change the ideal indent spacing for
mapping. Therefore, examining the effect near
sample boundaries to determine the best spacing
value is recommended.
To summarize this section, the achievable limits
of nanoindentation resolution depend strongly on
the tip shape, material being tested, and, crucially,
the deformation regime. Following Jakes et al.,30,31
three dimensionless parameters can be defined that
control indent resolution: the contact area relative
to the distance to a feature, A/d, and two
materialdependent parameters, the ratio E/H and the
Poisson’s ratio. One can define a maximum modulus or
hardness change versus d using these parameters.
Therefore, the smallest achievable d values are
found at the lowest indentation depths in the elastic
regime. However, if hardness measurements are
desired, testing in the elastic–plastic regime is
necessary and a balance between the accuracy of
hardness and lateral resolution must be chosen.
Strain Rate Sensitivity
One of the drawbacks of high-speed
nanoindentation mapping is a loss of flexibility in the load
function, where high loading rates are needed for
increased mapping speed. These high loading rates
can influence the measured hardness, but this
depends again on the material type, tip shape, and
several other variables. The hardness from a
nanoindentation test is strain rate dependent and
fit by a power law relationship by a characterizing
parameter, m @@llnnHe_ , where e_ is the strain rate. The
strain rate for indentation is defined proportionally
as the displacement rate over the total displacement
h_=h or 12 P_=P24 correspondingly for loading rate over
total load for materials that do not have depth
dependence to their response, and for self-similar
indenters. Since this relationship is fit by a power
law, one can describe it as an order of magnitude
effect. As previously discussed, high-speed
nanoindentation techniques can run about two orders of
magnitude faster than standard indentation
techniques. Since typical strain rate sensitivity
parameter m values range from 0.001 to 0.1 in crystalline
materials, this corresponds to a hardness value shift
between 0.4% and 37% compared to standard speed
indentation. However, one must look at the bigger
picture, which is that strain rate sensitivity is
determined by the predominant deformation
mechanism and is strongly affected by variables that aid
or hinder operation of these mechanisms. These
variables most notably include temperature, but
also crystalline orientation and grain size. Special
cases, such as nanocrystalline or ultrafine grain
materials, can possess high strain rate sensitivity
values32 because of the dominance of grain
boundary diffusion mechanisms or, in the case of glasses,
unusual behavior due to shear transformation
zones.33,34 Some literature data are presented in
Table I, which shows how much of a hardness shift
would be expected by increasing the strain rate by
two orders of magnitude as discussed above for some
of the more interesting scenarios.
Thus, the origins of strain rate sensitivity are
complex and require considerations of many
subtleties. However, for several classes of materials the
effect is essentially marginal. The best approach is
to directly measure the strain rate sensitivity for
the materials of interest; these techniques have
recently been reviewed by Maier-Kiener and
Durst.39 As a final point, the role of indentation
depth should be acknowledged, as shallower indents
are typical for indentation mapping and deeper
indents for strain rate sensitivity measurements.
Ideally, this should not affect results but as real tips
are blunt, shallower indents are increasingly
dominated by a spherical-like contact.
Summary and Complimentary
In the absence of sophisticated analysis and/or
modeling, one can simply advocate the approach of
exploring the effects of the parameter space on the
measured properties of interest whenever possible,
specifically, the combination of loading rate,
indentation depth, and indentation spacing. Thus, a
typical complimentary approach to validate a
highspeed indentation map would include:
1. Measurement of depth sensitivity: Depth
profiling is already frequently done to calibrate tip
area functions. A variety of methods can be
used, including a varying depth indent arrays,
partial unload load functions, or dynamic
2. Measurement of spacing sensitivity: With the
depth dependence established, the user can
chose their desired depth for the indentation
map. Next, the spacing effects at that desired
depth can be studied with indent arrays. When
high spatial resolution is unnecessary or
impractical because of the desire to map a larger
area by nanoindentation, conservatively large
spacing could be used freely.
3. Measurement of rate sensitivity: Either through
grids with varying indent speed or
characterizing the strain rate sensitivity coefficient.39
There could also be a desire to define the desired
indent spacing first, i.e., resolution of the map, then
what maximum depth can be used needs to be
determined, thereby reversing steps 1 and 2.
APPLICATIONS FOR NANOINDENTATION
In the following, several examples are presented
that highlight the capabilities of state-of-the-art
high-speed nanoindentation. The following
examples were all performed using a Hysitron TI-980
TriboIndenter (Bruker Nano Surfaces, Minneapolis,
MN, USA) operating in Accelerating Property
Mapping (XPM) mode.
Correlated EBSD and Nanoindentation
The most obvious application for such technology
is mapping of small-scale material interfaces as
they cannot be easily evaluated at the bulk scale.
These include welds, especially microscale ones as
produced by laser and resistance techniques,
mapping of phases, and grains in alloys, and evaluation
of composites. In particular, dissimilar material
welds produce complex microstructures42 and can
be better engineered using nanoindentation data to
establish statistically significant variables.43
The scale and resolution of high-speed
indentation can be demonstrated through a correlated
EBSD and nanoindentation map of a 410 stainless
steel, which was laser clad onto a 4140 stainless
steel substrate. The large-scale structure of the
heat-affected zone from the laser cladding process is
shown via a traditional stage automation method in
Fig. 3a. To investigate the transition from the
cladding to the substrate in more detail, a fiduciary
marker was drawn around the interface using
focused ion beam machining to facilitate testing of
the same region by nanoindentation mapping and
EBSD. In this case, a Berkovich tip was used with
400 lN force and an indent spacing of 500 nm. The
nanoindentation mapping shows little difference in
modulus between the cladding and the substrate,
but a substantial change in hardness with 5 GPa
average for the 4140 substrate and 8 GPa
hardness average for the cladding. In the correlated
EBSD boundary map, it appears that the region of
highest hardness corresponds closely with regions of
a high density of high-angle grain boundaries,
marked in blue.
High-Speed Nanoindentation at Elevated and
High-temperature nanoindentation is a growing
field of research for reactors, engines, turbines, and
more. One popular high-temperature material, a
SiC matrix and SiC fiber composite, is evaluated at
high temperature using 5-lm indent spacing, 7-mN
load, and a Berkovich tip. The difference in
hardness between the fibers and the matrix is apparent,
along with a region of low hardness along the
interface (Fig. 4). This is likely due to free volume
along the fiber/matrix interface, reducing the
hardness through decreased material confinement. The
distributions of hardness and modulus at 400 C
show a bimodal distribution, individually
corresponding to the fiber and matrix. As the
temperature is increased to 800 C, the modulus values shift
slightly downward overall, as expected, but
maintains a bimodal distribution. The two
measurements were taken from different regions of the
sample, so the change in total counts for the two
phases is different. More interestingly, the hardness
distribution is observed to shift towards a single
peaked distribution at 800 C.
Cryogenic temperatures are of interest for
materials that are subjected to conditions such as outer
space, arctic or winter environments, and part of
cooling systems. A ubiquitous structural alloy, 1018
steel, was studied from room temperature down to
120 C. A hardness map at 0 C generated with
1lm indent spacing, a peak load of 500 lN, and a
Berkovich tip clearly shows the two-phase ferrite
and pearlite microstructure, which is also reflected
by the hardness distribution as seen in Fig. 5.
Indents into the ferrite phase were done as part of
a decreasing temperature sweep, with the resulting
load displacement curves indicating a
ductile-tobrittle transition at 58 C. Here, homogeneous
dislocation plasticity at the above temperatures
gave way to serrated flow, indicating dislocation
bursts. Since ferrite is BCC, the Peierls’ barrier is
relatively large compared to FCC metals and is thus
reliant on thermal assistance for homogeneous
plasticity. This was also reflected in the hardness,
which increased 44% over the tested temperature
range. This hardening for decreasing temperatures
also relates to the ductile to brittle temperature
transition. This transition is more obvious when
looking at the pop-in behavior of the indentation
curves.44 The room temperature behavior is
primarily a smooth curve or with very short pop-ins to
approximate a predominately smooth curve. As
temperatures decrease, the flow becomes more
stochastic with increasing pop-in size. There seems
to be a transition between the 15 C and 25 C
curves. This DBTT is lower than the 5 C value
typically reported for Charpy impact testing, which
is a much higher strain rate.
High-speed nanoindentation techniques provide
an advantage when operating at extreme
nonambient temperatures through reduced contact
time, which reduces tip wear, and the relative effect
of drift. Tip-sample thermal equilibrium is one of
the largest challenges to extreme temperature
testing as it produces drift when they are brought
into contact. The cryo and high-temperature stage
in this article utilizes a multi-element heating
microchamber45 that exposes the tip and sample to
the same environment. However, it has been
shown46,47 that thermal stabilization in vacuum is
more time consuming and difficult. Reducing the
typical time in contact from 20 s to 0.2 s reduces the
effect of drift on the measurement by two orders of
magnitude. This reduced time in contact also
significantly reduces tip wear, a major issue of high
temperature testing.48 The tip sample contact can
be modeled as a high-pressure diffusion couple in
thermodynamic software such as Thermal Calc.
Simply reducing the time in contact has a dramatic
impact on the number of indentations that can be
performed with a given tip/sample combination.
Generation and Utilization of Large Data Sets
In contrast to the heterogeneous samples tested
thus far, nanoindentation is often performed on
samples that are relatively homogeneous, such as
foils, thin films on substrates, and the substrates
themselves. Even a layered sample with large
dimensions in the sample plane can be considered locally
homogeneous. In these cases, statistics allow for
generation of large data sets where the precise values
can be determined, with data histograms allowing for
the identification of statistical outliers. This can be
compared to the number of tests run in a typical
nanoindentation study, where n £ 10 in many cases.
A simple experiment can be done looking at the
statistical distribution of hardness and modulus
comparing vibratory polished (100) aluminum and
aluminum polished with 600 grit paper. Arrays of
nine indents, 3 9 3 with 15-um spacing between
indents, are placed in a larger 5 9 5 array (Fig. 6).
The total number of indents is now n = 225 for
each sample, which is a factor of a 20 times larger
number of tests than for most nanoindention
studies. The pileup corrected modulus and hardness
histograms (Fig. 7) show both an increase in
hardness for the roughened/work-hardened sample and
a corresponding increase in the spread of the data.
Combining both statistical analysis and mapping
compared against high-speed nanoindentation for a
railway weld joint in a railway steel can be
compared to traditional Vickers microhardness
testing.49–51 Here, 196 indent grids produced by
high-speed nanoindentation with 5-mN load and a
Berkovich indenter are compared against a single
Vickers indent in a line scan starting in the weld
joint and moving progressively through the
heataffected zone, using an empirical relationship to
compare hardness.52 The grid of nanoindentations
fit into approximately the same area as the single
microhardness test (Fig. 8). In this case, a variety of
microstructures are encountered, from martensitic
rich regions near the weld joint progressively into
bainite and finally ferrite. It can be observed that
although the hardness versus distance curves are
comparable between the average value of the
highspeed nanoindentation grids and microindentation,
the grids feature scatter bands due to the varying
microstructure. For instance, the spread is
increased near the weld joint, as the martensite
clustered into islands around the grain boundaries,
where as bainite and ferrite represent better
dispersed microstructures. In these regions, a
researcher could consider moving to more of a
mapping rather than statistical sampling type of
CONCLUSIONS AND OUTLOOK
Overall, high-speed indentation techniques are
relatively underused given they possess many
potential applications. Property mapping, especially
when used in conjunction with correlated
techniques characterizing the structure, provide
detailed information on small-scale regions of
significant industrial importance that are not easily
tested on the bulk scale, such as welds, fine grain
and phase structures, composites and interfaces,
and more. Statistical distributions can be generated
simultaneously, which offer a variety of useful
information. However, these techniques do not
replace standard nanoindentation techniques, as
the influence of the indentation size effect from
depth, strain rate sensitivity, and spacing should be
studied in conjunction.
Looking forward, there are many relatively
unexplored applications for these techniques. Though
there are a multitude of material microstructures to
potentially map and model, it is the authors’ opinion
that sophisticated analysis of ‘‘big data’’ sets,
through techniques like machine learning,
represent one the biggest frontiers in materials science.
The theme of bridging length scales and producing
cohesive understanding of bulk mechanical
behavior based on nanoscale measurements is very
attractive and may lead to future breakthroughs in
materials design and fine-tuning of their
performance. As a rapid and highly localized mechanical
measurement tool, high-speed nanoindentation
mapping should play an important role in this
The authors gratefully acknowledge assistance
from Richard Nay, Jared Risan, Robert Dietrich,
Anqi Qiu, and Benjamin Stadnick with the
specimen testing and Daniel Sorensen with sample
This article is distributed under the terms of the
Creative Commons Attribution 4.0 International
which permits unrestricted use, distribution, and
reproduction in any medium, provided you give
appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons
license, and indicate if changes were made.
Funding was provided by Bruker Nano Surfaces.
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