Bhushan, B. “Nanomechanical Properties of Solid Surfaces and Thin Films”
Handbook of Micro/Nanotribology.
Ed. Bharat Bhushan
Boca Raton: CRC Press LLC, 1999
© 1999 by CRC Press LLC© 1999 by CRC Press LLC

10

Nanomechanical
Properties of Solid

Surfaces and Thin Films

Bharat Bhushan

10.1 Introduction
10.2 Nanoindentation Hardness Measurement
Apparatuses

Commercial Nanoindentation Hardness Apparatuses with
Imaging of Indents after Unloading • Prototype Depth-
Sensing Nanoindentation Hardness Apparatuses •
Commercial Depth-Sensing Nanoindentation Hardness
Apparatus and Its Modifications

10.3 Analysis of Indentation Data

Hardness • Modulus of Elasticity • Determination of Load

10.7 Other Applications of Nanoindentation
Techniques

Time-Dependent Viscoelastic/Plastic Properties •
Nanofracture Toughness • Nanofatigue

10.8 Closure
References

© 1999 by CRC Press LLC

10.1 Introduction

Mechanical properties of the solid surfaces and surface thin films are of interest as the mechanical
properties affect the tribological performance of surfaces. Among the mechanical properties of interest,
one or more of which can be obtained using commercial and specialized hardness testers, are elastic–plas-
tic deformation behavior, hardness, Young’s modulus of elasticity, scratch resistance, film-substrate adhe-
sion, residual stresses, time-dependent creep and relaxation properties, fracture toughness, and fatigue.
Hardness measurements can assess structural heterogeneities on and underneath the surface such as
diffusion gradients, precipitate, presence of buried layers, grain boundaries, and modification of surface
composition.
Hardness implies the resistance to local deformation. For example, with materials that go through
plastic deformation, a hard indenter is pressed into the surface and the size of the permanent (or plastic)
indentation formed for a given load is a measure of hardness. With rubberlike materials (which do not
go through plastic deformation), an indenter is pressed into the material and how far it sinks under load
is measured. With brittle materials (which do not go through plastic deformation), hardness is measured
by scratching it by a harder material. Hardness signifies different things to different people, for instance,
resistance to penetration to a metallurgist, resistance to scratching to a mineralogist, and resistance to
cutting to a machinist, but all are related to the plastic flow stress of material.
Hardness measurements usually fall into three main categories: scratch hardness, rebound or dynamic

material which forms a permanent (plastic) indentation in the surface of the material to be examined.
The hardness number (GPa or kg/mm

2

), equivalent to the average pressure under the indenter, is
calculated as the applied normal load divided by either the curved (surface) area (Brinell, Rockwell, and
Vickers hardness numbers) or the projected area (Knoop and Berkovich hardness numbers) of the contact
between the indenter and the material being tested, under load (Lysaght, 1949; Berkovich, 1951; Tabor,

© 1999 by CRC Press LLC

1951, 1970; Mott, 1957; O’Neill, 1967; Westbrook and Conrad, 1973; Anonymous, 1979; Johnson, 1985;
Blau and Lawn, 1986; Bhushan and Gupta, 1997).
Macrohardness tests are widely used because of availability of inexpensive testers, simplicity of mea-
surement, portability, and direct correlation of the hardness with service performance. For applications
with ultrasmall loads (few mN to nN) being applied at the interface, nanomechanical properties of the
skin (as thin as a monolayer) of a solid surface or a surface film are of interest. Furthermore, ultrathin
films as thin as a monolayer are used for micromechanical applications and their mechanical properties
are of interest. Hardness tests can be performed on a small amount (few mg) of material and with the
state-of-the-art equipment it is possible to measure hardness of the few surface layers on the sample
surface.
In a conventional indentation hardness test, the contact area is determined by measuring the inden-
tation size by a microscope after the sample is unloaded. At least, for metals, there is a little change in
the size of the indentation on unloading so that the conventional hardness test is essentially a test of
hardness under load, although it is subject to some error due to varying elastic contraction of the
indentation (Stilwell and Tabor, 1961). More recently, in depth-sensing indentation hardness tests, the
contact area is determined by measuring the indentation depth during the loading/unloading cycle
(Pethica et al., 1983; Blau and Lawn, 1986; Wu et al., 1988; Bravman et al., 1989; Doerner et al., 1990;
Nix et al., 1992; Pharr and Oliver, 1992; Oliver and Pharr, 1992; Nastasi et al., 1993; Townsend et al.,

eliminated. It is therefore generally accepted that the depth of indentation should never exceed 30% of
the film thickness (Anonymous, 1979). The minimum load for most commercial microindentation testers

© 1999 by CRC Press LLC

available is about 10 mN. Loads on the order of 50 µN to 1 mN are desirable if the indentation depths
are to remain few tens of a nanometer. In this case, the indentation size sometimes reaches the resolution
limit of a light microscope, and it is almost impossible to find such a small imprint if the measurement
is made with a microscope after the indentation load has been removed. Hence, either the indentation
apparatuses are placed

in situ

and a scanning electron microscope (SEM) or

in situ

indentation depth
measurements are made. The latter measurements, in addition, would offer the advantages to observe
the penetration process itself. In viscoelastic/visoplastic materials, since indentation size changes with
time,

in situ

measurements of the indentation size are particularly useful, which can, in addition, provide
more complete creep and relaxation data of the materials.
In this chapter, we will review various prototype and commercial nanoindentation hardness test
apparatuses and associated scratch capabilities for measurements of mechanical properties of surface
layers of bulk materials and extremely thin films (submicron in thickness). A commercial depth-sensing
nanohardness test apparatus will be described in detail followed by data analysis and use of nanohardness


mounted on a double-leaf spring cantilever and is moved against the sample by an electromagnetic system
to attain the required indentation load, which is measured by strain gauges mounted on the leaf springs,
Figure 10.3 (Bangert et al., 1981; Bangert and Wagendristel, 1986). Tilting the stage with respect to the
electron beam allows observation of the tip during the indentation process. The indentation cycle is fully
programmable and is controlled by the strain gauge signal. The motion of the indenter, perpendicular
to the surface, is performed by increasing the coil current until a signal from the strain gauges is detected.
Further, an increase of the current up to a certain gauge signal leads to the desired indentation force
ranging from 50 µN to 20 mN. After the required load has been reached and the dwell time has elapsed,
the sample is unloaded, and the indentation diagonal is measured by an SEM.

FIGURE 10.2

Schematic of the microindentation hardness
apparatus for use in a light optical microscope. (From Pulker,
H.K. and Salzmann, K., 1986,

SPIE Thin Film Technol.

652,
139–144. With permission.)

FIGURE 10.3

Schematic of the nanoindentation hardness apparatus for use in an SEM by Anton Parr K.G., Graz,
Austria. (From Bangert, H. et al., 1981,

Colloid Polym. Sci.

259, 238–242. With permission.)

FIGURE 10.4

Schematic of a modified commercial microhardness test apparatus for load-penetration depth mea-
surements. (From Pharr, G.M. and Cook, R.F., 1990,

J. Mater. Res.

5, 847–851. With permission.)

© 1999 by CRC Press LLC

load cell. The specimen was attached to the center of this mount with the displacement gauges flanking
it on either side. The gauges sensed the motion of a thin aluminum wing rigidly attached to the base of
the moving diamond and its mount. The outputs from the displacement gauges were averaged so as to
negate any displacements caused by bending in the system. The load and displacement outputs were
measured using a storage oscilloscope.
In a typical experiment, the load and displacement signals were recorded as a function of time, with
the load–displacement curve derived subsequently from these data. This modified apparatus can only be
used for loads as low as about 100 mN, making it useful for only microhardness measurements.

10.2.2.2 AERE Harwell/Micro Materials Design

Newey et al. (1982) developed an apparatus capable of continuously monitoring the penetration depth
as the load is applied, Figure 10.5. The test sample I is mounted on a piezoelectric barrel transducer J,
their horizontal position being controlled by a micrometer movement K. A high-voltage supply is
connected to the transducer J by means of a commutator arrangement. The indenter assembly C is made
from folded tantalum foil to give a light structure, and is fitted with tungsten pivots seated in jeweled
bearings D, from which it is suspended. Force is applied electrostatically by increasing the potential on
the two plates B; force plate A is part of indenter assembly C and is kept at ground potential. The resulting
force causes A to move into B and indenter F to move toward the specimen. The indentation depth is

indentation force can be varied from 10 µN to 5 mN. Indenter (1) is clamped to the holder (2) and can
easily be exchanged. The indenter holder (2) supported on an air bearing can be moved virtually
frictionlessly along a horizontal shaft (3). Two stops (4 and 5) attached to the shaft limit the movement
of the holder. The shaft is supported by a linear drive mechanism (6) making use of friction wheels and
guide rollers. The apparatus is equipped with two inductive displacement transducers (7 and 8) which
measure the displacement of the indenter with respect to the shaft and of the shaft with respect to the
surroundings, respectively. The signal from transducer 8 is automatically corrected for changes in the
ambient temperature during an experiment. This is done by the application of a temperature-sensing
element mounted on transducer 8. The indenter force is adjusted by means of an electromagnetic system.
A coil (9) is attached to the indenter holder and can move in the annular gap of an electromagnet (10),
which is mounted on the shaft. The sample holder (11) can be moved in two directions perpendicular
to the axis of the shaft (3). Samples are held by using an accessory (12) which is held by suction to the
sample holder. (Also see Wierenga and van der Linden, 1986.)
For an indentation experiment, the indenter is first brought into contact with the sample. For this
purpose, transducer 7 is adjusted to give a zero signal when the stylus holder is somewhere between stops
4 and 5. By switching on the motor of the linear drive mechanism, the shaft and indenter are moved
toward the sample. After the indenter has touched the sample surface, movement of the shaft is auto-
matically halted when the signal from transducer 7 equals zero. The starting position for an indentation
experiment is achieved by moving the sample a short distance sideways at a minimum indenter force. If
the indenter force is increased, the signal from transducer 7 is kept to zero with the control system by
moving the shaft. Thus, the penetration depth can be determined with transducer 8, which measures the
displacement of the shaft with respect to the frame.

FIGURE 10.6

Schematic of a depth-sensing nanoindentation hardness apparatus by Philips Laboratory, Eindhoven,
The Netherlands: (1) indenter, (2) indenter holder, (3) central shaft, (4) and (5) stops, (6) linear drive mechanism,
(7) and (8) displacement transducers, (9) coil, (10) electromagnet, (11) sample holder, (12) accessory for holding
the sample (From Wierenga, P.E. and van der Linden, J. H. M., 1986, in


pass through a beam expander to enlarge the beam circle diameter. Three of the outer beams strike the
indenter mirror and the other three pass through holes in the indenter mirror and stage and strike the
sample mirror. Because of the large beam circle diameter, the beams avoid striking the central obstruc-
tions, the sample, and the indenter. The light reflected from both mirrors then returns to the interfer-
ometer. Thus, the positions of the sample and indenter mirrors are continuously monitored by comparing
the relative phases of the light beams returning from the mirrors to the central reference beam. The
computer subtracts the positions of the two mirrors to determine the resulting indentation depth and
multiplies the indenter mirror position and the spring constant of the indenter parallel spring guide to
determine the indentation load.
To initiate a test, the actuator slowly raises the sample toward the indenter until motion is registered
by the interferometer, implying that contact has been made between the sample and the indenter. The
control loop then takes over and performs the chosen test — it either keeps the load constant and
measures the penetration depth as a function of time or it keeps the depth constant and measures the
load as a function of time.

10.2.2.5 NEC, Kawasaki Design

Tsukamoto et al. (1987) and Yanagisawa and Motomura (1987, 1989) developed a nanoindentation
hardness apparatus. NEC Corp., Kawasaki 216, Japan is attempting to commercialize it, although it is
not popular, Figure 10.8. It consists of three parts: an indenter actuator, a load detector, and a displace-
ment sensor. Indenter (1) with a diamond tip is attached to stylus (2) which is clamped on holder (3).
The holder is attached to a piezoelectric actuator (4), which drives the holder up and down controlled
by a personal computer (5) through an amplifier (6), a regulated power source (7), and an interface (8).
Indentation load is detected by a digital electrobalance (9) with a 1-µN resolution at loads of up to
300 mN. The output signal is fed to the

X

-axis of an



FIGURE 10.7

Schematic of a depth-sensing nanoindentation hardness apparatus by IBM Corporation, Tucson, and University of Arizona, Tucson,
AZ. (From Bhushan, B. et al., 1988,

ASME J. Tribol.

110, 563–571. With permission.)

© 1999 by CRC Press LLC

optical fiber and the mirror is adjusted to a region with linearity by a micrometer (18). A bolt (19) is
loosened in this adjustment and is fastened after the adjustment to make the optical fiber move together
with the indenter. Measurement begins with increasing the voltage applied to the piezoelectric actuator.
After the indenter touches and penetrates the sample (loading process), the voltage applied to the
piezoelectric actuator is reduced (unloading process).

10.2.2.6 Ecole Central of Lyon Design

The surface force apparatus commonly used for molecular rheology of thin lubricant films, was modified
by Loubet et al. (1993) to conduct nanoindentation studies. Figure 10.9 shows the schematic of their
nanoindenter design which uses piezoelectric crystal for indenter motion and two capacitance probes
for measurement of the load and the displacement. The indenter is fixed to the piezoelectric crystal and
the specimen is supported by double-cantilever spring whose stiffness can be adjusted between 4

¥

10



Lubr. Eng.

43, 52–56. With permission.)

© 1999 by CRC Press LLC

signal consists of two ramp reference signal and a sinusoidal signal. Ramp reference signal allows the use
of a constant speed from 50 to 0.005 nm/s (typical speed of 0.5 nm/s). The sinusoidal motion designed
to determine the dynamic behavior of the solids is obtained using a two-phase lock-in analyzer. It is
generally set of about 0.26 nm rms in the frequency range of 0.01 to 500 Hz (typically 38 Hz). The
displacement resolution is 0.015 nm.

10.2.2.7 Cornell University Design

Hannula et al. (1986) developed the nanoindentation apparatus shown in Figure 10.10. It is used to
measure indenter penetration and load as a function of time during loading and unloading cycles. The
apparatus is constructed with two load trains such that both large (up to 50 mm) and small (up to 12 µm)
displacements can be applied accurately and independently to the same specimen. The large displacement
is produced by a moving crosshead. The small displacements are made possible by using a piezoelectric
translator. A load as small as 0.5 mN can be applied.
A specimen is attached to the (moving) crosshead and the diamond tip is attached to a part, which
also serves as a counter plate for two capacitance probes. These probes are used either for controlling
the position of the tip or for measuring the indentation depth. The load cell is placed between the part
and the piezoelectric translator and is used to measure the normal load. The specimen can be aligned
by using an

x

–

Schematic of a depth-sensing nanoindentation hardness apparatus by Ecole Central of Lyon. (From
Loubet, J.L. et al., 1993, in

Mechanical Properties and Deformation of Materials Having Ultra-Fine Microstructures

(M. Nastasi et al., eds.), pp. 429–447. Kluwer Academic, Dordrecht. With permission.)

© 1999 by CRC Press LLC

in controlling the motion of the indenter. The applied load can be calculated using the output voltage
of the load cell capacitance probe (1) and the calibrated load cell spring constant. The total depth
penetrated by the indenter with respect to the sample surface can be obtained either directly from the
sample capacitance gauge (6) or from the difference of the displacement measurements between indenter
gauge (7) and the load cell gauge (1). The load cell has loading ranges from a few tens of micronewtons
to 2 N with a resolution of about 30 µN. Indentations with a depth of as low as 20 nm with a depth
resolution of 1 nm can be made. For hardness measurements, the apparatus is operated in continuous
loading and unloading modes with indenting speeds of 2 to 20 nm s

–1

. A three-sided pyramidal diamond
indenter, known as the Berkovich indenter, is used for measurements.
The PZT stack is driven by a voltage amplifier to follow a predetermined reference pattern and is
monitored by closed-loop servo-circuitry. Either the indenter displacement (IND) output (7) or the
normal load cell (LC) output (1) can be employed as a servo-input signal and in turn different testing
modes can be generated using an IND servo, constant indenter rate testing (typically used in the constant
loading and unloading tests), or constant indenter position (used in the load relaxation tests), or any
programmed displacement pattern for the indenter can be performed. But using an LC servo, constant
loading rate indentation (used in the continuous loading and unloading tests, or constant load inden-
tation (used in the indentation creep test), or cyclic loading (using sawtooth or sinusoidal references, in


© 1999 by CRC Press LLC

FIGURE 10.11

(a) Block diagram of a depth-sensing nanoindentation hardness apparatus by IBM Almaden Research Center; (b) schematic
diagram of the indenter assembly and normal load cell assembly: (1) load cell capacitance probe, (2) sample post, (3) Be–Cu diaphragm springs;
(4) sample, (5) indenter, (6) sample capacitance probe, (7) indentation capacitance probe, (8) Be–Cu diaphragm, (9) PZT stack, (10) PZT preload
mechanism, (11) reference plane stage, (12) Z-stage. (From Wu, T.W. et al., 1988,

Thin Solid Films

166, 299–308. With permission.)

© 1999 by CRC Press LLC

In their modified design, a tangential load cell (6, 9) as well as acoustic emission sensor (8) were added.
An additional capacitance probe (TG, 9) was placed to monitor the displacement of the indenter holder,
which is subsequently used to calculate the tangential force that the indenter applies on the sample
surface. The tangential load cell has a loading range of 750 mN with a resolution of about 15 µN. Another
capacitance probe (SD, 16) was added to measure scratch distance.
Figure 10.12b shows schematically the working principle of a nanoscratch test carried out by the
upgraded apparatus (Figure 10.12a). To perform a scratch test, the indenter is first placed about 0.1 µm
away from the sample surface. This step allows a scratch to begin with a zero applied load. Next the
traveling range and speed of the X-translation stage are set usually at 150 µm and 1 µm/s, respectively;
then the motion is started. Finally, the PZT motor is activated to drive the indenter toward the sample
surface at the speed of about 15 nm/s. With this instrument, the following measurements can be made
simultaneously during a scratch test: applied load and tangential load along the scratch length (coefficient
of friction); critical load, i.e., applied normal load corresponding to an event of coating failure during a
scratch process, total depth and plastic depth along the scratch length; the accumulated acoustic emission

–

Z

motorized precision table for positioning and transporting the sample between the optical
microscope and indenter, Figure 10.13a. The loading system used to apply the load to the indenter consists
of a magnet and coil in the indenter head and a high precision current source, Figure 10.13b. A coil is
attached to the top of the indenter (loading) column and is held in a magnetic field. The passage of the
current through the coil is used to raise or lower the column and to apply the required force to make an
indent. The current from the source, after passing through the coil, passes through a precision resistor
across which the voltage is measured and is displayed. During measurement, voltage is controlled by a
computer. Two interchangeable indenter heads are available: the standard head, which features four load
ranges 0 to 4 mN, 0 to 20 mN, 0 to 120 mN, and 0 to 350 mN, and a high-load head, which has a load
range of 0 to 840 mN. The load resolution for the standard head in the most sensitive range is about
±75 nN, while the load resolution for the high load head is ±90 µN.
The displacement-sensing system consists of a special three-plate capacitive displacement sensor, used
to measure the position of the indenter. All three plates are circular disks approximately 1.5 mm thick.
The two outer plates have a diameter of 50 mm, and the inner, moving plate is half that size. The indenter
column is attached to the moving plate. This plate-and-indenter assembly is supported by two leaf springs
cut in such a fashion to have very low stiffness. The motion is damped by airflow around the central

© 1999 by CRC Press LLC

plate of the capacitor, which is attached to the loading column. The load coil is used to raise or lower
the plate and the indenter assembly through its 100-µm travel between the outer plates of the capacitor.
Depth resolution of the systems is about ±0.04 nm. As seen in the plot at the right of Figure 10.13c, a
load voltage of 1.7 V will just lift the indenter off its bottom stop, and 1.8 V suffice to bring it to the top
of its travel. It should be emphasized that only the motion of the indenter column as controlled by the
load coil is used in the actual making of an indent. The voltage output range of the displacement sensing
(capacitance) system is –2.5 to +2.5 V.


–

Y

–

Z

table whose position relative to
the microscope or the indenter is controlled with a joystick. The spatial resolution of the position of the
table in the

X

–

Y

plane is ±400 nm and its position is observed on the CRT. The specimen holder is a
rectangular metal plate (150

¥

150

¥

28.5 mm) with ten 31.8-mm-diameter holes for mounting of
standard metallographic samples. Samples can also be glued to special metal disks. The three components

volt. The typical value for this constant is 26,876.5 µN/V.
Calibration of the displacement system is carried out by correlating the voltage output of the displace-
ment capacitor with the number of rings generated as the indenter tip is pressed against a lens-and-plate
system designed to produce newton rings. A mirror mounted at the bottom on the indenter tip is pressed
against a partially reflected lens and an He–Ne laser observed during the test on a video camera. The
relationship between displacement voltage and displacement is linear in the range of interest.
Other important calibrations include microscope-to-indenter distance and spring constant of indenter
support springs.

10.2.3.3 The Berkovich Indenter

The main requirements for the indenter are high elastic modulus, no plastic deformation, low friction,
smooth surface, and a well-defined geometry that is capable of making a well-defined indentation
impression. The first four requirements are satisfied by choosing the diamond material for the tip. A
well-defined perfect tip shape is difficult to achieve. Berkovich is a three-sided pyramid and provides a

sharply pointed tip

compared with the Vickers or Knoop indenters, which are four-sided pyramids and
have a slight offset (0.5 to 1 µm) (Tabor, 1970; Bhushan, 1996). Because any three nonparallel planes
intersect at a single point, it is relatively easy to grind a sharp tip on an indenter if Berkovich geometry
is used. However, an indenter with a sharp tip suffers from a finite but an exceptionally difficult-to-
measure tip bluntness. In addition, pointed indenters produce a virtually constant plastic strain impression

TABLE 10.1

Specification of the Commercial Nanoindenter by Nano Instruments, Inc.

Load range
Standard head 0–4 mN

X

- and

Y

-directions
Area examined in a single series of indentations 150

¥

150 mm
Minimum penetration depth ~20 nm
Continuous stiffness option
Frequency range 10–150 Hz
Time constant 0.33 s
Smallest measurable distance 0.1 nm
Scratch and tangential force option
Scratch velocity max. 100 µm/s with 20 points/mm
Tangential displacement range 2 mm
Tangential displacement resolution 400 nm
Tangential load resolution 50 µN
Minimum measurable tangential load 0.5 mN

© 1999 by CRC Press LLC

and there is the additional problem of assessing the elastic modulus from the continuously varying
unloading slope. Spherical indentation overcomes many of the problems associated with pointed indent-
ers. With a spherical indenter, one is able to follow the transition from elastic to plastic behavior and
thereby define the yield stress (Bell et al., 1992). However, a sharper tip is desirable, especially for extremely


is related to the depth

h

as
(10.1a)
The relationship

h

(l

) is dependent on the shape of the indenter. The height of the triangular indent l

is
related to the length of one side of the triangle

a

as
(10.1b)
and
(10.1c)
The projected contact area (

A) for the assumed geometry is given as
(10.2)
The exact shape of the indenter tip needs to be measured for determination of hardness and Young’s
modulus of elasticity. Since the indenter is quite blunt, direct imaging of indentations of small size in

.
l = 0 866. a
h
a
=
1
7 407.
Aa h==0 433 23 76
22
..
© 1999 by CRC Press LLC
© 1999 by CRC Press LLC
approach at a constant loading rate, the indenter is first loaded and unloaded typically three times in
succession at a constant loading rate or displacement rate with each of the unloadings terminated at
about 10 to 20% of the peak loading or displacement, respectively, to assure that contact is maintained
between the specimen and the indenter. In a typical indentation experiment, it is usual to have two hold
segments, the first one at the end of unloading to 10 to 20% after multiple loading/unloading cycles and
the second one at the peak load just before final unloading. The reason for performing multiple loadings
and unloadings is to examine the reversibility of the deformation (hysteresis) and thereby making sure
that the unloading data used for calculation of the modulus of elasticity are mostly elastic. In some
materials, there may be a significant amount of creep during the first unloading; thus, displacement
recovered may not be entirely elastic, and because of this, the use of first unloading curves in the analysis
of elastic properties can sometimes lead to inaccuracies. One way to minimize nonelastic effects is to
include peak load hold periods in the loading sequence to allow time-dependent plastic effects to
diminish. In addition, after multiple loadings, the load is held constant for a period of typically 100 s at
10 to 20% of the peak value while the displacement is carefully monitored to establish the rate of
displacement produced by thermal expansion in the system. To account for thermal drift, the rate of
displacement is measured during the last 80 s of the hold period, and the displacement data are corrected
by assuming that this drift rate is constant throughout the test. Following this hold period, the specimen
is loaded for a final time, with another 100 s hold period inserted at peak load to allow any final time-

indent. When contact occurs, the indenter is pushed upward, tripping the Z-motor interrupts and
stopping the Z-motor of the table. The table is then moved downward at slow speed for 15 s before being
moved in the X, Y plane until the point on the sample halfway between the initial surface-finding indent
and the location of the first indent is under the indenter. The table is now raised once more, but at slow
speed until contact with the specimen is made once more. This second contact gives the best estimate
of the surface elevation that can be obtained by moving the table alone.
FIGURE 10.15 Different segments of a typical constant-loading indentation experiment.
TABLE 10.2 Examples of Two Typical Indentation Experiments
Segments
a
Rate Maximum Value
(a) Constant Loading Experiment
Approach 10 nm/s —
Loading at constant loading rate 12 mN/s 120 mN
Unloading at constant unloading rate 12 mN/s 10–20% of 120 mN
Multiple loading/unloading cycles
(typically three times)
•
•
Hold for 100 s Data rate 1/s 100 points
Loading at constant loading rate 12 mN/s 120 mN
Hold for 100 s Data rate 1/s 100 points
Unloading at constant unloading rate 12 mN/s 0 mN
(b) Constant Displacement Experiment
Approach 10 nm/s —
Loading at constant displacement rate 20 nm/s 200 nm
Unloading at constant displacement rate 20 nm/s 10–20% of 200 nm
(typically three times)
•
•

identifies the sample surface to within 0.1 to 0.2 nm. However, for very soft materials such as many
polymers or for other approach rates and stiffness-factor increases, the user may find it advisable to plot
the approach segment data and, if necessary, change the algorithm used to define the precise point of
contact with the sample surface.
Once surface contact is established, the other segments of the indentation process are carried out as
prescribed in the programmed indentation experiment. The final segment always involves load removal.
When the voltage on the indenter coil passes the displacement voltage at which the surface was detected
in the approach portion of the cycle, the current through the coil is fixed while the raw data are recorded
on the hard disk, and plotted on the computer monitor. The indenter is then raised well away from the
surface in preparation for moving the sample to the position of the next indent. For subsequent indents
in a given series of indents, the initial estimate of surface position used is that found in making the
previous indent.
For each indentation step, load voltages, displacement (penetration depth or indentation depth)
voltages, and real time are recorded in separate files. These raw voltage data are converted to load vs.
displacement data by using load and displacement calibration constants. From the displacement data,
the contact depth is calculated for calculations of the hardness. The slope of the unloading curve is used
to calculate the modulus of elasticity.
10.2.3.5 Acoustic Emission Measurements during Indentation
AE measurement is a very sensitive technique to monitor cracking of the surfaces and subsurfaces. The
nucleation and growth of cracks result in a sudden release of energy within a solid; then some of the
energy is dissipated in the form of elastic waves. These waves are generated by sudden changes in stress
and in displacement that accompany the deformation. If the release of energy is sufficiently large and
rapid, then elastic waves in the ultrasonic frequency regime (AE) will be generated and these can be
detected using PZTs via expansion and compression of the PZT crystals (Yeack-Scranton, 1986; Scruby,
1987; Bhushan, 1996).
Weihs et al. (1992) used an AE sensor to detect cracking during indentation tests using the nanoin-
denter. The energy dissipated during crack growth can be estimated by the rise time of the AE signal.
They mounted a commercial transducer with W-impregnated epoxy backing for damping underneath