Nanoindentation Lecture 1 Basic Principle

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NanoindentationLecture 1 Basic Principle

• Do Kyung Kim
• Department of Materials Science and Engineering
• KAIST

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Indentation test (Hardness test)

• Hardness resistance to penetration of a hard
  indenter

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Hardness

• Hardness is a measure of a materials 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

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Microhardness - Vickers and Knoop
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Microindentation

• Mechanical property measurement in
  micro-scale(Micro-indentation)
• 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.

Optical micrograph of a Vickersindentation (9.8
N) in soda-lime glassincluding impression,
radial cracking,and medial cracking fringes.
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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.

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Micro vs Nano Indentation

• MicroindentationA 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.
• NanoindentationA 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.

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Basic Hertzs elastic solution (1890s)
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Schematics of indenter tips
Vickers
Berkovich
Knoop
Conical
Rockwell
Spherical
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4-sided indenters
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3-sided indenters
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Cone indenters
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Indenter geometry
Indenter type Projected area Semi angle (q) Effective cone angle (a) Intercept factor Geometry correction factor (b)
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 q186.25 ? q265 ? 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
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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
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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.

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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.

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Data Ananlysis

• P applied load
• h indenter displacement
• hr plastic deformation after load removal
• he surface displacement at the contact perimeter

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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.

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Analytical Model Doerner-Nix Model
Doerner, Nix, J Mater Res, 1986
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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
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Analytical Model Oliver and Pharr
Oliver Pharr, J Mater Res, 1992
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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
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Analysis result
E modulus of specimen E modulus of indenter

• Reduced modulus

• Stiffness

• Contact area

for Berkovich indenter

• Hardness

• Elastic modulus

for Berkovich indenter
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One of the most cited paper in Materials Science
No of citation Nov 2003 - 1520, Nov 2005 - 2436
Nov 28, 2006
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Material response
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Nanoindenter tips
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Berkovich indenter
b
Projected area
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Berkovich vs Vickers indenter

• Berkovich projected area

• Vickers projected area

• Face angle of Berkovich indenter 65. 3 ?
• Same projected area-to-depth ratio as Vickers
  indenter
• Equivalent semi-angle for conical indenter 70.3
  ?

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Commercial machines

• MTS_Nano-Indenter XP

• CSIRO_UMIS
• (Ultra-Micro-Indentation System)

• CSM_NHT
• (Nano-Hardness Tester)

• Hysitron_Triboscope

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Commercial machine implementation

• MTS_Nano-Indenter

• CSIRO_UMIS

• Inductive force generation system
• Displacement measured by capacitance gage

• Load via leaf springs by expansion of load
  actuator
• Deflection measured using a force LVDT

• Hysitron_TriboScope

• CSM_NHT

• Two perpendicular transducer systems
• Displacement of center plate capacitively
  measured

• Force applied by an electromagnetic actuator
• Displacement measured via a capacitive system

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Force actuation

• Electromagnetic actuation

• Electrostatic actuation

• most common means
• long displacement range wide load range
• Large and heavy due to permanent magnet

• Electrostatic force btwn 3-plate transducer
  applied
• Small size (tenths of mm) good temperature
  stability
• Limited load(tenths of mN) displacement(tenths
  of mN)

• Spring-based force actuation

• Piezo/spring actuation

• Tip attached to end of cantilever
• Sample attached to piezoelectric actuator
• Displacement of laser determine displacement

• 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

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Displacement measurement

• Differential capacitor

• Optical lever method

• Photodiode measures lateral displacement
• Popular method in cantilever based system
• Detection of deflection lt 1 Å

• Measure the difference btwn C1 and C2 due to ?
• High precision(resolution lt 1 Å) small size
• Relatively small displacement range

• Linear Variable Differential Transducer (LVDT)

• Laser interferometer

• AC voltage proportional to relative displacement
• High signal to noise ratio and low output
  impedance
• lower resolution compared to capacitor gage

• Beam intensity depends on path difference
• Sensitivity lt 1 Å used in hostile environment
• Fabry-Perot system used for displacement
  detection

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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

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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.

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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 load-displacement data
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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 Youngs modulus
  and hardness are assumed to be depth-independent

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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
load-displacement data.
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Real tip shape

• Deviation from perfect shape

Sphero-Conical tips
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Area function calibration

• Ideal tip geometry yields the following
  area-to-depth ratioA 24.5 hc2
• Real tips are not perfect!
• CalibrationUse material with known elastic
  properties (typically fused silica) and determine
  its area as a function of contact

• New area functionA C1hc2 C2hc C3hc1/2
  C4hc1/4 C5hc1/8

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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

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Pile-up and Sinking-in
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Phase transition measurement

• Nanoindentation on silicon and Raman analysis

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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

• It can be done by experiments at different
  loading rate or by studying the holding segment
  of a nanoindentation.

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Fracture toughness measurement
Combining of Laugier proposed toughness model and
Ouchterlonys 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
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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.

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Nanomechanical testing

• Common Applications
• 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

• Tests
• Nanohardness/Elastic modulus
• Continuous Stiffness Measurements
• Acoustic Emmisions
• Properties at Various Temperature
• Friction Coefficient
• Wear Tests
• Adhesion
• NanoScratch Resistance
• Fracture Toughness
• Delamination