Nanoindentation
Lecture 1
Basic Principle
Do Kyung Kim
Department of Materials Science and
Engineering
KAIST
Indentation test (Hardness test)
• Hardness – resistance to penetration of a hard indenter
Hardness
• Hardness is a measure of a material’s resistance to surface
penetration by an indenter with a force applied to it.
• Hardness
– Brinell, 10 mm indenter, 3000 kg Load F /surface area of
indentation A
– Vickers, diamond pyramid indentation
• Microhardness
– Vickers microindentation : size of pyramid comparable to
microstructural features. You can use to assess relative
hardness of various phases or microconstituents.
• Nanoindentation
Microhardness - Vickers and Knoop
Microindentation
• Mechanical property
measurement in micro-scale
(Micro-indentation)
Optical micrograph of a Vickers
indentation (9.8 N) in soda-lime glass
including impression, radial cracking,
and medial cracking fringes.
– To study the mechanical
behavior of different
orientations, we need
single crystals.
– For a bulk sample, it is
hard to get a nano-scale
response from different
grains.
– Very little information on
the elastic-plastic
transition.
Nanoindentation
• Nanoindentation is called as,
– The depth sensing indentation
– The instrumented indentation
• Nanoindentation method gained popularity with the
development of,
– Machines that can record small load and displacement
with high accuracy and precision
– Analytical models by which the load-displacement data
can be used to determine modulus, hardness and other
mechanical properties.
Micro vs Nano Indentation
•
Microindentation
•
Nanoindentation
A prescribed load appled to an indenter in
contact with a specimen and the load is
then removed and the area of the residual
impression is measured. The load divided
by the by the area is called the hardness.
A prescribed load is appled to an indenter
in contact with a specimen. As the load is
applied, the depth of penetration is
measured. The area of contact at full load
is determined by the depth of the
impression and the known angle or radius
of the indenter. The hardness is found by
dividing the load by the area of contact.
Shape of the unloading curve provides a
measure of elastic modulus.
Basic Hertz’s elastic solution (1890s)
Schematics of indenter tips
Vickers
Berkovich
Knoop
Conical
Rockwell
Spherical
4-sided indenters
3-sided indenters
Cone indenters
Indenter geometry
Effective
cone angle
(a)
Intercept
factor
Geometry
correction
factor (b)
Indenter type
Projected area
Semi angle
(q)
Sphere
A  p2Rhp
N/A
N/A
0.75
1
Berkovich
A = 3hp2tan2q
65.3 
70.2996 
0.75
1.034
Vickers
A = 4hp2tan2q
68 
70.32 
0.75
1.012
Knoop
A = 2hp2tanq1tanq2
q1=86.25 
q2=65 
77.64 
0.75
1.012
Cube Corner
A = 3hp2tan2q
35.26 
42.28 
0.75
1.034
Cone
A = php2tan2a
a
a
0.72
1
Stress field under indenter - contact field
Boussinesq fields (point load)
Hertzian fields (spherical indenter)
Brian Lawn, Fracture of Brittle Solids, 1993, Cambridge Press
Anthony Fischer-Cripp, Intro Contact Mechanics, 2000, Springer
Sharp indenter (Berkovich)
• Advantage
– Sharp and well-defined
tip geometry
– Well-defined plastic
deformation into the
surface
– Good for measuring
modulus and hardness
values
• Disadvantage
– Elastic-plastic transition
is not clear.
Blunt indenter - spherical tip
• Advantage
– Extended elastic-plastic
deformation
– Load displacement results
can be converted to
indentation stress-strain
curve.
– Useful in determination of
yield point
• Disadvantage
– Tip geometry is not very
sharp and the spherical
surface is not always
perfect.
Data Ananlysis
•
•
•
•
P : applied load
h : indenter displacement
hr : plastic deformation after load removal
he : surface displacement at the contact perimeter
Analytical Model – Basic Concept
•
Nearly all of the elements of this analysis were first developed by workers at the
Baikov Institute of Metallurgy in Moscow during the 1970's (for a review see Bulychev
and Alekhin). The basic assumptions of this approach are
– Deformation upon unloading is purely elastic
– The compliance of the sample and of the indenter tip can be
combined as springs in series
– The contact can be modeled using an analytical model for
contact between a rigid indenter of defined shape with a
homogeneous isotropic elastic half space using
•
where S is the contact stiffness and A the contact area. This relation was presented
by Sneddon. Later, Pharr, Oliver and Brotzen where able to show that the equation is
a robust equation which applies to tips with a wide range of shapes.
Analytical Model – Doerner-Nix Model
Doerner, Nix, J Mater Res, 1986
Analytical Model – Field and Swain
• They treated the indentation as a reloading of a preformed
impression with depth hf into reconformation with the
indenter.
Field, Swain, J Mater Res, 1993
Analytical Model – Oliver and Pharr
Oliver & Pharr, J Mater Res, 1992
Continuous Stiffness Measurement (CSM)
• The nanoindentation system
applies a load to the indenter
tip to force the tip into the
surface while simultaneously
superimposing an oscillating
force with a force amplitude
generally several orders of
magnitude smaller than the
nominal load.
• It provides accurate
measurements of contact
stiffness at all depth.
• The stiffness values enable us
to calculate the contact radius
at any depth more precisely.
Oliver, Pharr, Nix, J Mater Res, 2004
Analysis result
• Reduced modulus
1
E
• Stiffness
• Contact area
*
dP

1
2

1'
E
 2E
2
E: modulus of specimen
E’: modulus of indenter
E'
A
*
dh
p
2
A  3 3 h p tan 65 . 3  24 . 5 h p
• Hardness
H 
• Elastic modulus
E 
2
for Berkovich indenter
P
24 . 5 h p
*
2
dP
1
2
1
dh 2 h p b
p
24 . 5
b  1 . 034 for Berkovich indenter
One of the most cited paper in Materials Science
Nov 28, 2006
No of citation
Nov 2003 - 1520, Nov 2005 - 2436
Material response
Nanoindenter tips
Berkovich indenter
l
tan 60 
o
a/2
b
l
3
a
2
A proj 
al
3

2
cos 65 . 27
2
a
4
o
h

b
Projected area
h
a cos 65 . 3
o
2 3 sin 65 . 3
a

o
2 3 tan 65 . 3
a  2 3 h tan 65 . 3
o
o
A proj  3 3 h tan 65 . 3  24 . 56 h
2
2
o
2
Berkovich vs Vickers indenter
• Berkovich projected area
A proj  3 3 h tan 65 . 3  24 . 56 h
2
2
o
• Vickers projected area
2
A proj  4 h tan
2
2
68  24 . 504 h
o
2
• Face angle of Berkovich indenter: 65. 3 
• Same projected area-to-depth ratio as Vickers indenter
• Equivalent semi-angle for conical indenter: 70.3 
A  p h p tan a
2
2
Commercial machines
• MTS_Nano-Indenter XP
• CSIRO_UMIS
• Hysitron_Triboscope
• CSM_NHT
•(Ultra-Micro-Indentation System)
•(Nano-Hardness Tester)
Commercial machine implementation
• MTS_Nano-Indenter
• Inductive force generation system
• Displacement measured by capacitance gage
• Hysitron_TriboScope
• Two perpendicular transducer systems
• Displacement of center plate capacitively measured
• CSIRO_UMIS
• Load via leaf springs by expansion of load actuator
• Deflection measured using a force LVDT
• CSM_NHT
• Force applied by an electromagnetic actuator
• Displacement measured via a capacitive system
Force actuation
• Electromagnetic actuation
• most common means
• long displacement range & wide load range
• Large and heavy due to permanent magnet
• Spring-based force actuation
• Tip attached to end of cantilever &
• Sample attached to piezoelectric actuator
• Displacement of laser determine displacement
• Electrostatic actuation
• Electrostatic force btwn 3-plate transducer applied
• Small size (tenths of mm) & good temperature stability
• Limited load(tenths of mN) & displacement(tenths of mN)
• Piezo/spring actuation
• Tip on leaf springs are displaced by piezoelectric actuator
• Force resolution is very high ( pN range),
• As resolution goes up, range goes down & Tip rotation
Displacement measurement
• Differential capacitor
C 
• Optical lever method
  0  A
d
• Measure the difference btwn C1 and C2 due to 
• High precision(resolution < 1 Å) & small size
• Relatively small displacement range
• Linear Variable Differential
Transducer (LVDT)
• AC voltage proportional to relative displacement
• High signal to noise ratio and low output impedance
• lower resolution compared to capacitor gage
• Photodiode measures lateral displacement
• Popular method in cantilever based system
• Detection of deflection < 1 Å
• Laser interferometer
• Beam intensity depends on path difference
• Sensitivity < 1 Å & used in hostile environment
• Fabry-Perot system used for displacement detection
Factor affecting nanoindentation
• Thermal Drift
• Initial penetration depth
• Instrument compliance
• Indenter geometry
• Piling-up and sinking-in
• Indentation size effect
• Surface roughness
• Tip rounding
• Residual stress
• Specimen preparation
Thermal drift
• Drift can be due to vibration or a thermal drift
• Thermal drift can be due to
– Different thermal expansion in the machine
– Heat generation in the electronic devices
• Drift might have parallel and/or a perpendicular component
to the indenter axis
• Thermal drift is especially important when studying time
varying phenomena like creep.
Thermal drift calibration
Indenter displacement vs time
during a period of constant
load. The measured drift rate
is used to correct the load
displacement data.
Application of thermal
drift correction to the
indentation loaddisplacement data
Machine compliance
• Displacement arising from the compliance of the testing
machine must be subtracted from the load-displacement
data
• The machine compliance includes compliances in the
sample and tip mounting and may vary from test to test
• It is feasible to identify the machine compliance by the
direct measurement of contact area of various indents in a
known material
• Anther way is to derive the machine compliance as the
intercept of 1/total contact stiffness vs 1/ sqrt(maximum
load) plot, if the Young’s modulus and hardness are
assumed to be depth-independent
Machine compliance calibration
Usually done by manufacturer
using materials with known
properties (aluminum for large
penetration depths, fused
silica for smaller depth).
Using an accurate value
of machine stiffness is
very important for large
contacts, where it can
significantly affect the
measured loaddisplacement data.
Real tip shape
• Deviation from perfect shape
Sphero-Conical tips
Area function calibration
• Ideal tip geometry yields
the following area-todepth ratio:
A = 24.5 hc2
• Real tips are not perfect!
• Calibration
Use material with known elastic
properties (typically fused silica)
and determine its area as a
function of contact
• New area function
A = C1hc2 + C2hc + C3hc1/2 + C4hc1/4 + C5hc1/8 + …
Surface roughness
•
•
•
As sample roughness does have a significant effect on the measured
mechanical properties, one could either try to incorporate a model to
account for the roughness or try to use large indentation depths at which
the influence of the surface roughness is negligible.
A model to account for roughness effects on the measured hardness is
proposed by Bobji and Biswas.
Nevertheless it should be noticed that any model will only be able to
account for surface roughnesses which are on lateral dimensions
significantly smaller compared to the geometry of the indent
Pile-up and Sinking-in
Phase transition measurement
• Nanoindentation on silicon and Raman analysis
Creep measurement
• Plastic deformation in all
materials is time and
temperature dependent
• Important parameter to
determine is the strain rate
sensitivity
• The average strain rate can
be given by
 ind 
1 dh c
h c dt
• It can be done by experiments at different loading rate
or by studying the holding segment of a
nanoindentation.
Fracture toughness measurement
Combining of Laugier proposed toughness
model and Ouchterlony’s radial cracking
modification factors, fracture toughness
can be determined.
Fracture toughness expression
Kc = 1.073 xv (a/l)1/2 (E/H)2/3 P / c3/2
High temperature measurement
Nanindentation with or
without calibration
• Temperature match btw. indenter and sample is
important for precision test.
• Prior depth calibration and post thermal drift correct are
necessary.
Nanomechanical testing
• Tests
– Nanohardness/Elastic
modulus
– Continuous Stiffness
Measurements
– Acoustic Emmisions
– Properties at Various
Temperature
– Friction Coefficient
– Wear Tests
– Adhesion
– NanoScratch Resistance
– Fracture Toughness
– Delamination
• Common Applications
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Fracture Analysis
Anti-Wear Films
Lubricant Effect
Paints and Coatings
Nanomachining
Bio-materials
Metal-Matrix Composites
Diamond Like Carbon
Coatings
Semiconductors
Polymers
Thin Films Testing and
Development
Property/Processing
Relationships