nano indentation (1)
TRANSCRIPT
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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
l
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$e
d
AC
⋅⋅
= 0ε ε
- Photodiode measures lateral displacement- Popular method in cantileer based system- Aetection of deKection M &
- 0@ olta$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