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Nanoindentation Lecture 1 Basic Principle

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Title: Nanoindentation Lecture 1 Basic Principle


1
NanoindentationLecture 1 Basic Principle
  • Do Kyung Kim
  • Department of Materials Science and Engineering
  • KAIST

2
Indentation test (Hardness test)
  • Hardness resistance to penetration of a hard
    indenter

3
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

4
(No Transcript)
5
Microhardness - Vickers and Knoop
6
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.
7
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.

8
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.

9
Basic Hertzs elastic solution (1890s)
10
Schematics of indenter tips
Vickers
Berkovich
Knoop
Conical
Rockwell
Spherical
11
4-sided indenters
12
3-sided indenters
13
Cone indenters
14
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
15
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
16
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.

17
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.

18
Data Ananlysis
  • P applied load
  • h indenter displacement
  • hr plastic deformation after load removal
  • he surface displacement at the contact perimeter

19
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.

20
Analytical Model Doerner-Nix Model
Doerner, Nix, J Mater Res, 1986
21
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
22
Analytical Model Oliver and Pharr
Oliver Pharr, J Mater Res, 1992
23
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
24
Analysis result
E modulus of specimen E modulus of indenter
  • Reduced modulus
  • Stiffness
  • Contact area

for Berkovich indenter
  • Hardness
  • Elastic modulus

for Berkovich indenter
25
One of the most cited paper in Materials Science
No of citation Nov 2003 - 1520, Nov 2005 - 2436
Nov 28, 2006
26
Material response
27
Nanoindenter tips
28
Berkovich indenter
b
Projected area
29
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
    ?

30
Commercial machines
  • MTS_Nano-Indenter XP
  • CSIRO_UMIS
  • (Ultra-Micro-Indentation System)
  • CSM_NHT
  • (Nano-Hardness Tester)
  • Hysitron_Triboscope

31
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

32
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

33
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

34
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

35
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.

36
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
37
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

38
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.
39
Real tip shape
  • Deviation from perfect shape

Sphero-Conical tips
40
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

41
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

42
Pile-up and Sinking-in
43
Phase transition measurement
  • Nanoindentation on silicon and Raman analysis

44
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.

45
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
46
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.

47
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
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