nano indentation (1)

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    NanoindentationBasic Principle

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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 material’s resistance to surfacepenetration by an indenter with a force applied to it.

    • Hardness• Brinell, ! mm indenter, "!!! #$ %oad F &surface area of

    indentation A• 'ic#ers, diamond pyramid indentation

    • icrohardness

    • 'ic#ers microindentation si*e of pyramid comparable tomicrostructural features. +ou can use to assess relatie hardnessof arious phases or microconstituents.

    • Nanoindentation

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    icroindentation

    Optical micrograph of a Vickers

    indentation (9.8 N) in soda-lime glassincluding impression, radial cracking,and medial cracking fringes.

    - Mechanical propertymeasurement in micro-scale(Micro-indentation)

    – To study themechanical behavior ofdierent orientations,we need singlecrystals.

    – For a bul sample, it ishard to get a nano-scale response fromdierent grains.

    – !ery little informationon the elastic-plastictransition.

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    Nanoindentation

    • Nanoindentation /he depth sensin$ indentation  /he instrumented indentation

    • Nanoindentation method $ained popularity with thedeelopment of 

    • achines that can record small load and displacement withhi$h accuracy and precision

    • 0nalytical models by which the load1displacement data can beused to determine modulus, hardness and other mechanicalproperties.

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    icro s Nano Indentation

    • icroindentation0 prescribed load appled to an indenter incontact with a specimen and the load isthen remoed and the area of the residualimpression is measured. /he load diided bythe by the area is called the hardness.

    • Nanoindentation0 prescribed load is appled to an indenter incontact with a specimen. 0s the load isapplied, the depth of penetration ismeasured. /he area of contact at full load isdetermined by the depth of the impressionand the #nown an$le or radius of the

    indenter. /he hardness is found by diidin$the load by the area of contact. 2hape ofthe unloadin$ cure proides a measure ofelastic modulus.

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    2chematics of indenter tips

    Vickers Berkoich !noop "onical #ock$ell %pherical

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    Indenter $eometry

    Indentertype

    Pro3ected area 2emian$le

    (θ)

    45ectiecone an$le(α)

    Intercept factor

    6eometr

    ycorrection factor

    (β)

    2phere 0 ≈ π78hp N&0 N&0 !.9:

    Ber#oich 0 "hp7tan7θ ;:." ° 9!.7;.7:° θ

    7;:°

    99.;= ° !.9: .!7

    @ube @orner 0 "hp7tan7θ ":.7; ° =7.7> ° !.9: .!"=

    @one 0 πhp7tan7α   α α !.97

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    2harp indenter (Ber#oich)- "dvantage

    – #harpt and well-de$ned tip geometry

    – %ell-de$ned plasticdeformation into thesurface

    – &ood for measuringmodulus and hardnessvalues

    - 'isadvantage– lastic-plastic

    transition is not clear.

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    Blunt indenter 1 2pherical- "dvantage

    – tended elastic-plastic deformation

    – *oad displacementresults can beconverted toindentation stress-strain curve.

    – +seful indetermination of yieldpoint

    - 'isadvantage– Tip geometry is not

    very sharp and the

    spherical surface isnot always perfect.

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    Aata 0nanlysis

    • P  applied load

    • h  indenter displacement• hr  plastic deformation after load remoal

    • he  surface displacement at the contact perimeter

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    0nalytical odel – Basic @oncept

    • Nearly all of the elements of this analysis were rst deeloped by wor#ers atthe Bai#o Institute of etallur$y in oscow durin$ the

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    0nalytical odel – Dlier and Pharr

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    @ontinuous 2ti5ness easurement(@2)

    • /he nanoindentation systemapplies a load to theindenter tip to force the tipinto the surface whilesimultaneouslysuperimposin$ an oscillatin$

    force with a force amplitude$enerally seeral orders ofma$nitude smaller than thenominal load.

    • It proides accurate

    measurements of contactsti5ness at all depth.• /he sti5ness alues enable

    us to calculate the contactradius at any depth moreprecisely.

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    0nalysis result

    - Hardness

    '

    '111  22

    *  E  E  E 

    υ υ    −+

    −=

     p

     A E 

    dh

    dP    *2=

    2225.243.65tan33  p p   hh A   ==

    5.24

    1

    2

    1*   π 

    β  phdh

    dP  E   =

    25.24  ph

     P 

     H  =

    - 4lastic modulus

    - @ontact area

    - 2ti5ness

    - 8educed modulus

    034.1=β  for Ber#oich indenter

    4 modulus of specimen4’ modulus of indenter

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    aterial response

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    0nalytical odel 1 4/@

    • 4lasto1plastic materials

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    Ber#oich indenter

    Pro3ected area

    222

    2

    56.243.65tan33

    3.65tan32

    3.65tan323.65sin32

    3.65cos

    27.65cos

    4

    3

    2

    2

    3

    2/

    60tan

    hh A

    ha

    aah

    b

    h

    aal 

     A

    al 

    a

    o

     proj

    o

    oo

    o

    o

     proj

    o

    ==

    =

    ==

    =

    ==

    =

    =

    b

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    Ber#oich s 'ic#ers indenter

    - Face an$le of Ber#oich indenter ;:. " °

    - 2ame pro3ected area1to1depth ratio as 'ic#ers indenter

    - 4Euialent semi1an$le for conical indenter 9!." ° α π    22

    tan ph A =

    22256.243.65tan33   hh A

      o

     proj   ==222

    504.2468tan4   hh A   o proj   ==

    - erovich proected area - !icers proected area

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    @ommercial machines- /2GNano1Indenter

    P

    - @2GNH/-(Nano1Hardness /ester)

    - HysitronG/riboscope

    - @2I8DGI2

    -(ltra1icro1Indentation2ystem)

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    @ommercial machineimplementation

    - MT#/ano-0ndenter - 1#023+M0#

    - 4ysitronTribo#cope - 1#M/4T

    - Inductie force $eneration system- Aisplacement measured by capacitance $a$e

    - /wo perpendicular transducer systems- Aisplacement of center plate capacitiely measured

    - %oad ia leaf sprin$s by eJpansion of load act- AeKection measured usin$ a force %'A/

    - Force applied by an electroma$netic actuator- Aisplacement measured ia a capacitie syst

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    Force actuation- lectromagneticactuation

    - lectrostaticactuation

    - #pring-based forceactuation

    - 5ie6o7springactuation

    - most common means- lon$ displacement ran$e L wide load ran$e- %ar$e and heay due to permanent ma$net

    - 4lectrostatic force btwn "1plate transducer applied- 2mall si*e (tenths of mm) L $ood temperature stab- %imited load(tenths of mN) L displacement(tenths

    - /ip attached to end of cantileer L

    - 2ample attached to pie*oelectric actuator- Aisplacement of laser determine displacement

    - /ip on leaf sprin$s are displaced by pie*oelectric ac

    - Force resolution is ery hi$h ( pN ran$e),- 0s resolution $oes up, ran$e $oes down L /ip rotati

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    Aisplacement measurement- 'ierential capacitor - 3ptical lever method

    - *inear !ariable'ierential Transducer

    (*!'T)

    - *aser interferometer

    - easure the di5erence btwn @ and @7 due to ∆ - Hi$h precision(resolution M ) L small si*e- 8elatiely small displacement ran$e

     AC 

      ⋅⋅

    =  0ε ε 

    - Photodiode measures lateral displacement- Popular method in cantileer based system- Aetection of deKection M  & 

    - 0@ olta$e proportional to relatie displacement

    - Hi$h si$nal to noise ratio and low output impedance- lower resolution compared to capacitor $a$e

    - Beam intensity depends on path di5erence

    - 2ensitiity M L used in hostile enironment- Fabry1Perot system used for displacement dete

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    Factor a5ectin$ nanoindentation• /hermal Arift

    • Initial penetration depth

    • Instrument compliance

    • Indenter $eometry

    • Pilin$1up and sin#in$1in

    • Indentation si*e e5ect

    • 2urface rou$hness

    • /ip roundin$

    • 8esidual stress

    • 2pecimen preparation

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     /hermal drift

    • Arift can be due to ibration or a thermal drift

    • /hermal drift can be due to•

    Ai5erent thermal eJpansion in the machine• Heat $eneration in the electronic deices

    • Arift mi$ht hae parallel and&or a perpendicularcomponent to the indenter aJis

    • /hermal drift is especially important when studyin$time aryin$ phenomena li#e creep.

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     /hermal drift calibration

    'ndenter displacement s timeduring a period of constantload. he measured drift rateis used to correct the loaddisplacement data.

     pplication of thermaldrift correction to theindentation load-displacement data

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    achine compliance

    • Aisplacement arisin$ from the compliance of the testin$machine must be subtracted from the load1displacement data

    • /he machine compliance includes compliances in the sample

    and tip mountin$ and may ary from test to test

    • It is feasible to identify the machine compliance by the directmeasurement of contact area of arious indents in a #nownmaterial

    • 0nther way is to derie the machine compliance as theintercept of &total contact sti5ness s & sErt(maJimum load)plot, if the +oun$’s modulus and hardness are assumed to bedepth1independent

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    achine compliance calibration

    *suall+ done + manufacturerusing materials $ith kno$nproperties (aluminum for largepenetration depths, fusedsilica for smaller depth).

    *sing an accurate alueof machine stiffness iser+ important for largecontacts, $here it cansignificantl+ affect themeasured load-

    displacement data.

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    8eal tip shape

    • Aeiation from perfect shape

    %phero-"onical tips

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    0rea function calibration• Ideal tip $eometry yields

    the followin$ area1to1depth ratio

    0 7=.: hc7

    • 8eal tips are not perfectO

    • @alibrationse material with #nown elasticproperties (typically fused silica)

    and determine its area as afunction of contact

    - /ew area function

    " 8 19hc: ; 1:hc ; 1hc

    97? ; @

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    2urface rou$hness

    • 0s sample rou$hness does hae a si$nicant e5ect on themeasured mechanical properties, one could either try to incorporatea model to account for the rou$hness or try to use lar$e indentationdepths at which the inKuence of the surface rou$hness is ne$li$ible.

    • 0 model to account for rou$hness e5ects on the measured hardnessis proposed by Bob3i and Biswas.• Neertheless it should be noticed that any model will only be able

    to account for surface rou$hnesses which are on lateral dimensionssi$nicantly smaller compared to the $eometry of the indent

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    Pile1up and 2in#in$1in

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    Phase transition measurement• Nanoindentation on silicon and 8aman analysis

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    @reep measurement

    dt 

    dh

    h

    c

    c

    ind 

    1=ε 

    - 5lastic deformation inall materials is time andtemperature dependent

    - 0mportant parameter todetermine is the strain

    rate sensitivity

    - The average strain ratecan be given by

    - 0t can be done by eperiments at dierentloading rate or by studying the holding segment

    of a nanoindentation.

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    Fracture tou$hness measurement

    "omining of augier proposed toughnessmodel and Ouchterlon+s radial cracking

    modification factors, fracture toughnesscan e determined.

    Fracture toughness expression

    K c = /.012 x  (a/l)1/2  (E/H)2/3 P / c 3/2 

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    Fati$ue measurement• Nanoscale fati$ue has not

    been studied eJtensielybecause of lac# ofinstruments.

    • @2 can proides sinusoidalforce cycles at hi$hfreEuencies.

    • @han$e in contact sti5nesscan $ie us fati$ue behaioras contact sti5ness issensitie to dama$eformation.

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    Hi$h temperature measurement

    Nanindentation with or

    without calibration

    - Temperature match btw. indenter and sample isimportant for precision test.

    - 5rior depth calibration and post thermal drift

    correct are necessary.

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    Nanomechanical testin$

    • /ests• Nanohardness&4lastic

    modulus• @ontinuous 2ti5ness

    easurements• 0coustic 4mmisions• Properties at 'arious

     /emperature• Friction @oecient• Qear /ests• 0dhesion• Nano2cratch 8esistance• Fracture /ou$hness

    • Aelamination

    - 1ommon

    "pplications– Fracture "nalysis– "nti-%ear Films– *ubricant ect– 5aints and 1oatings– /anomachining– io-materials– Metal-Matri

    1omposites

    – 'iamond *ie 1arbon1oatings

    – #emiconductors– 5olymers– Thin Films Testing and

    'evelopment

    – 5roperty75rocessing2elationships