TSOM Webinar on Instrumented Indentation.
Dr. Ilja Hermann 11-19-2015
• Motivation
• Theory of instrumented-indentation
• Experimental aspects
• NanoForce
• Application examples
Outline
Motivation
Why do we need mechanical properties ?
November 19, 2015 3
Mechanical
Properties
Failure Analysis Virtual Tests
Materials design Tribology
Wear
Understand and prevent irreversible deformation
November 19, 2015 4
Motivation
Fundamentals of mechanical properties
Stress and Strain :
A
F=σ
Normal
Stress
l
l∆=ε
Normal
Strain
A
F=τ
Shear
Stress
tanγ =∆x
h
Shear
Strain
...++= mnklijklmnklijklij SS εεεσ
Constitutive Equation :
November 19, 2015 5
Motivation
Measuring mechanical properties
Test & specimen:
• Uniaxial tension/compression
• Bending
• Acoustic wave
=> Mechanical properties on macroscopic scale
Hooke:
11
12
ε
εν −=
11
11
ε
σ=E
klijklij S εσ =
homogenious, isotropic:
Properties:
• E, ν, K, G,
• Y0, KI
November 19, 2015 6
Motivation
Hardness test
28544.1
d
FHV =
[Applied load] = kgf
[Diagonal] = mm
VICKERS-
Hardness
number
23
32
21
015.0
c
F
H
E
l
aKI
=Fracture-
Toughness
F…Applied load (N)H…Hardness (Gpa)
E…Young’s Modulus (Gpa)c,a,l…distances from img (m)
Pros:
• Simple application
• Small specimen
• Easy to scale
Cons:
• HV difficult co-relate to physical properties
• Scaling limited by imaging resolution
• No elastic properties
Concept: 1. Apply load.
2. Analysis of residual imprint after load removal
November 19, 2015 7
Motivation
Instrumented indentation
Concept: 1. Accurate measurement of compliance curve
2. Elastic analysis of tri-axial stress-state in contact
Nano-indentation
Elastic-plastic
Typical load: ~10 mN
Typical depth: ~100 nm
Property access: E, H, Y, KI, σRep(εRep)
=>Mechanical properties on mesoscopic scale
November 19, 2015 8
Theory of Nano-indentation
Fundamentals of contact mechanics
p(r,φ)
σi, εi
∫∫−
= φφπ
νdrdrp
Euz ),(
12
Point-contact solution
Superposition
Obtaining contact stress field and surface deformation
σ, ε = ?
November 19, 2015 9
Theory of Nano-indentation
Elastic surface deformation
Contact
Geometry
Pressure
distribution
Mean pressure Surface
Deflection (r=0)
Surface
Deflection (r=a)
Flat Punch Sneddon:
Sphere
(Hertz)
Cone
(Sneddon) ( ) 21
2
tan2
1
−=
α
νπ
rE
Fh
21
2
2
12
3
−−=
a
r
pm
zσ
r
a
pm
z 1cosh
−−=σ
21
2
2
12
1−
−−=
a
r
pm
zσ ( )F
aEh
r2
12ν−
=
32
4
3
=
RE
Fh
r he = εF
S
pm = HB =4Er
3π
a
R
f (r) = Brn
ε = m 1−1
π
Γm
(2m − 2)
Γm
(2m −1)
with
November 19, 2015 10
Theory of Nano-indentation
Hertzian contact stress
( ) ( ) ( ) ( )( )222222*6
2
1zyxzxyzzxxyyzzyyxxMisesvon
τττσσσσσσσ +++−+−+−=
Prin
cip
al s
tre
ss σ
1
(a.u
.)
Vo
n M
ise
s S
tre
ss
(a.u
.)
Tensile stress Von Mises stress
Hertzian cone fracture Residual imprint by sub-surface plasticity
Related material failure modes
November 19, 2015 11
Theory of Nano-indentation
Elastic-plastic indentation
σ = σ i +σ R
a
R= cos(α)
Ideal cone/Pyramid: elastic-plastic transition occurs instantly
≥ 0.07
> 0.5
Stress field during unloading altered by elastic constraint plastic zone
November 19, 2015 12
Theory of instrumented-indentation
Oliver & Pharr method
c
pA
FH =
S
Fhhc ε−= max
81
44
1
32
1
2
1
1
2
0)( cccccccc hahahahahachAA +++++==
SA
Ec
r2β
π=
1
0)(
max
−−== m
F
hhmadh
dFS
−−
−=
Ei
i
Er
pEp
ν
ν
211
21
Contact stiffness:
Contact depth:
Tip calibration:
Reduced modulus:
Indentation modulus:
Indentation hardness:
Ei, νi…elastic indenter properties νp..Poisson ratio of specimen
Ai, m, a, h0…fit parameters ; ε, β…contact model parameters (Sneddon, Oliver&Pharr resp.)
hc
= hmax
−εF
Sf(r)=Brn
r
“Effective indenter”F = a(h − h
0)
mFitting unloading curve:
November 19, 2015
Quasi-Static vs. Dynamic indentation
Oliver&Pharr:
cA
FH =
hc = hmax
−εF
S
Ac = Ac (hc )
maxFdh
dFS =
SA
Ec
r2β
π=
)cos(2 0
0' φβ
π
h
F
AE
c
r =
Dynamic indentation
)sin(2 0
0'' φβ
π
h
F
AE
c
r =
tieFtKh
dt
tdhD
dt
thdm
ω02
2
)()()(
=−−
)(
0)(φω += ti
ehth
02
2
=−∂
∂− i
j
iji Fxdt
udm
σ
klijklij S εσ =
Co
nta
ct m
ech
anic
s
Oscill
ato
r th
eo
ry
Missing
Contact
mechanics !
cA
FH =
Theory of instrumented-indentation
November 19, 2015 14
Experimental aspects
Typical test setup
Calibrations:
• Tip-shape
• Load frame compliance
• in-line tool offsets
Specimen requirements:
• Roughness
• Flatness
• Mounting stiffness
November 19, 2015 15
Experimental aspects
High-level corrections during raw-data post-processing
• Thermal drift
• Frame Compliance:
• Zero-Point correction:
i
frameS
Fh =∆
tt
hh
imedriftholdt
th∆
∆=∆
"
zerozero hh =∆
""" zero
iimedriftholdt
framethzero hS
Ft
t
hhhhhhh −
−
∆
∆−=∆−∆−∆−=
Depth at intersect of loading curve and
abscissa. HERTZian contact fit with fit
parameter A and the zero offset h”zero
Treated as superposition of
HOOKEian compliances for
load frame deformation small
compared to contact
2
3
"""")()( zerohhAhF −=
...111
++=cir SSS
First order estimate from drift during the unloading hold
time. Validity assumes linear-elastic bahaviour ,
stationary drift, and a total drift << hmax, ∆hcreep, ∆hhystersis
etc.
Metrology chain corrections at a glance: Contact model…
November 19, 2015 16
NanoForce
November 19, 2015 17
NanoForce
System overview
• Electromagnetic actuator (indentation loads between 0.2 uN and 45 mN) • Three-plate capacitor (indentation depth up to 40 um)• Load control • Depth- and strain-rate control by S/W feedback control• Berkovich tip is included; misc. different indenter geometries optional; easy switch • In-line microscope with coaxial turret optics and AFM are standard• Automatic multi-specimen handling (magnetic, vacuum, mech. clamp mounting)
Coaxial optical lenses and AFM
Thermal/Acoustic/Seismic hood
Internal (3-plate) capacitance sensor housing
Microscope for inspection pre- and pre- and post-test
Actuator housing
Quantitative property assessment: HIT, EIT, E’ , E”, Y, KIC, σRep(εRep), FCrit., topography
November 19, 2015 18
Loading profile
Experimental aspects
Controlled channels:
• Force (H/W)
• Displacement (S/W FBC)
• Strain (S/W FBC)
Profile element types:
• Constant
• Increasing/decreasing
• Calculated (custom)
• Harmonic
Full loading profile:
Sequence of different element types
& control modes
November 19, 2015 19
NanoForce
System data sheet
Indentation head Load Resolution (uN) 0.003
Load noise floor PP (uN) 0.05
max peak load (mN) 45
min peak load (mN) 0.01
min contact force (uN) 0.2
Displacement Resolution (nm) 0.0003
noise floor rms (nm) 0.1
max displacement (um) 40
Dynamics Minimum Force amplitude (uN) 0.025
Maximum Force amplitude (uN) 1900
Bandwidth (Hz) 45-250
Natural frequency oscillator air (Hz) 120
Drift System in contact (ppm/K) 1.54
Pre-test drift threshold (nm/s) 0.01
Indenter options misc., including Berkovich, Cube corner, Vickers, Conical, Flat punch
Specimen holder Automatic ally handled up to 4
max. diameter (mm) 25.4
max. height (mm) 10
min. lateral dimension (mm) 0.001
max diameter on Vacuum chuck (mm) 200
Platform Max. stage travel X (mm) 154
Max. stage travel Y (mm) 110
Max. stage travel X, useable (mm) 64
Max. stage travel Y, useable (mm) 65
Stage resolution XY (um) 0.1
Max. stage travel Z (mm) 23
Max. stage travel Z, useable (mm) 7
Stage resolution Z (nm) 34.6
Frame stiffness (10^6 N/m) 17.9
Imaging Optical objective magnifications 2.5x, 8x, 20x,
max FOV (um) 2241
min FOV (um) 28
Color Yes
Screen Magnification max (x) 7217
Illumination Bright-field std.; Dark-filed optional
NanoLens objective (AFM) standard, topographical imaging
Z range (um) 22
XY range (um) 110
Environment Thermal-, acoustic- and seismic insulation hood included
November 19, 2015 20
Typcial Nanoindentation test
AFM & Optical View (for test positioning ; here post-imaging of surface with 9 indents at different surface locations)
Force-Displacement curves(Indentations at 9 different surface locations)
NanoForce
1. Test positioning
2. Applying the test method (running indent-loading profile and analysis)
3. Post inspection of tested surface area
1.7mm
1.5 um
Indentations
Cube corner into Si (100)
Berkovich into HPFS
How small the testing object can be (indenter tip not to miss target spot…)?
Even after subsequently adding 9 more indents, all tests remain <0.5 um away from target position
Tim
eli
ne
NanoForce
IndentAFM
10-timesExperiment:
After indent #1 After indent #10
Target
=> Nanoforce can perform NI experiments on specimen under 1 um lateral size
ftp://tmtftp.bruker-nano.com/tmt/outgoing/NanoForce/Nano-Dart.m4vVideo:
NanoForce
Instrument calibration
November 19, 2015 23
NanoForce
Frame Compliance Si
i
Experiment
r
HertzModelS
Fh
RE
Fh −=
=
32
,4
3
With:• Tip radius R from AFM (calculations with radius as function of depth (R(h))
• Best Fit for 3 reference materials (Fused Silica, Sapphire (0001) and Si (100))
Extraction of Load-Frame stiffness from HERTZian contact modeling
Best fit: Frame stiffness ~2.5 N/um
(good agreement with 2.2 N/um from elastic-
plastic indentation by load-over-stiffness-square
method (F/S2))
This is what we are after here…
Tip Area-function Ac
NanoForce
Direct tip characterization by NanoLens AFM
( ) 22
2
49.24
2tan
tan3)( hhhA =
=
γ
α α: included face-angle to axis of symmetry : 65.27o
γ: included angle between pyramid base-lines: 60o
h: height of pyramid apex above base
Example: modified Berkovich tip
With:
The perfect one…
Reality check:
Conclusion:
Direct tip characterization if possible with NF . However, there is a quicker, and more accurate way quantify Ac ….
Tip apex radius ~40 nm (Note: that is comparable with a typical
indentation depths and cannot be neglected)
November 19, 201525
Indirect method:
Indentation into material with well-known properties, then reverse contact contact modeling
NanoForce
Force-Displacement curve
(corrected raw-data)
F/S2
Hardness
Modulus
Tip Area-function Ac
This is corrected for Si already…
2
)(2
)(
= c
r
cc hSE
hAβ
π
Typical results – dynamic indentation
E(hc) if were calculated with ideal Ac
November 19, 201526
Typical results - quasi-static indentation:
NanoForce
Force-Displacement curve
(corrected raw-data)Hardness
Modulus
Tip Area-function Ac
E(hc) if were calculated with ideal Ac
November 19, 2015 27
Results on other typical reference materials
HPFS
BK7
NanoForce
Hardness- and Modulus-measurements on for instrument verification and calibration.
HPFS
BK7
…homogenous, isotropic, linear-elastic (with well-known elastic constants),
…surface w/o contamination ; low roughness
…Not any material makes a suitable reference material.
Some key requirements :
November 19, 2015 28
NanoForce
Surface Roughness measurement
HPFS (Fused Silica), Contact, 256pts/ln
Result: RMS ~0.9 nm
Impact on experimental design: => Indentations must be deeper than ~20 nm (>20 x h) to neglect surface micro-structure in contact model
Topographical surface pre-inspection with AFM
NanoForce
Thin film applications
November 19, 2015
Traditional approaches to measure thin-film Hardness
+
=
D
d
hB
s
f
sfH
HHH
1
1
'
[1] H. Buckle, Metallurgical Reviews 4, London, Institute of Metals, (1959) 49
[2] X.Z. Hu and B.R. Lawn: A simple indentation stress–strain relation for contacts with spheres on bilayer structures. Thin Solid Films 322, 225 (1998).
http://www.msel.nist.gov/lawn/Publications/Papers.BRL/PapersBRL.1998/ThinSolidFilms%20322%20225%201998.pdf
10 % rule [1]
Film hardness if data within: hc<0.1d
Film hardness from Interpolation [2]:
Oliver&Pharr:
A
FH =
hc = hmax −εF
S
Ac = Ac (hc )
maxFdh
dFS =
Compound
Hardness !
Example: Hardness
by Indentation into
100 nm DLC
NanoForce
November 19, 2015 31
NanoForce
Cyclic (quasi-static) measurements of thermal-SiO2 on Silicon
Strain-rate controlled indentation with Berkovich tip and 30 partial unloading
cycles, applied to SiO2 of different thickness on Si (100) substrate:
Note:
• Noisy data; property-depth-profile recognize-/quantify- able.
• Modulus shows strong gradient even for the thickest film
• Effective modulus @ ~50 nm depth: 137 Gpa, 110 Gpa, 83 Gpa, 71.8 Gpa (thin=>Bulk)
50 nm
100 nm
300 nm
BulkBulk SiO2:~72 GPa
Bulk Si: ~164 GPa
November 19, 2015 32
NanoForce
Dynamic measurements of thermal-SiO2 film on Silicon
Strain-rate controlled indentation with Berkovich tip and superimposed 2 nm harmonic excitation amplitude @ 120 Hz on various thickness SIO2 on Si (100) on substrate:
50 nm
100 nm
300 nm
Bulk
Bulk SiO2:~72 GPa
Bulk Si: ~164 GPa
Note:
• Dynamic test data are much less noisy!
• Modulus- and hardness- gradients exhibit clear trend
• Effective modulus @ 50 nm depth is still disclosing significant substrate-effect
November 19, 2015 33
NanoForce
Cube Corner
( ) 2
2
2
2tan
tan3 hA
=
γ
α
⋅
=
2tan
2tansin
γβα a
β
α: included face-angle to axis of symmetry : 35.26o
β: included angle between ribs: 90o
γ: included angle between pyramid base-lines: 60o
h: height of pyramid apex above base
With:
November 19, 2015 34
NanoForce
Note:
• With dynamics and sharper (Cube corner) tip the Young’s modulus of SiO2 films can be measured practically independent on thickness down to 50 nm film thickness.
Dynamic measurements of thermal-SiO2 film on Silicon
Strain-rate controlled indentation with Cube corner tip and superimposed 2 nm harmonic excitation amplitude @ 120 Hz on various thickness on Si (100) on substrate:
50 nm
100 nm
300 nm
BulkBulk SiO2:~72 GPa
Bulk Si: ~164 GPa
Depth-profile
converges when
substrate-effect
becomes negligible
November 19, 2015 35
NanoForce
• Hardness-/Modulus coincidence at shallowest depths with sharper tip is independent on
the loading dynamics (completely different models used)
Quasi-static measurements with Cube Corner of thermal-SiO2 film on Silicon
Strain-rate controlled indentation with Berkovich tip and 30 partial unloading cycles, applied to SiO2 of different thickness on Si (100) substrate:
50 nm100 nm
300 nm
Bulk Bulk SiO2:~72 GPa
Bulk Si: ~164 GPa
Depth-profile
converges when
substrate-effect
becomes negligible
Modulus Hardness
November 19, 2015 36
NanoForce
What happens when we change the tip angle ?
Cube corner: sharper tip angle => pile-up, radial fracture
due to buildup of stress-intensity
Cube corner
BerkovichIndentation strain goes up for CC
November 19, 2015
Static vs. instrumented Hardness on metals
Example: Hardness standard reference block 724HV1
Ac,AFM = 1+∆AC
AC
Ac,OP
HV = 725.0 ±11.4( )Kp
mm2 H = 7.11± 0.11( )GPaStatic :
Instrumented : H = 9.82 ± 0.17( )GPa
Poor agreement with traceable Hardness -standard !
Topographical pile-up analysis
Correction:
∆AC
AC
≈ 26% Static
Instrumented
Accurate traditional instrumented tests require correction of pile-up!
-V +V -∆Ac
Apply correction to Vickers imprint into 724 HV1
November 19, 2015
Role of pile-up for a 50 nm Cube corner indent on var. coating thickness
50 nm
100 nm
300 nm
Film thickness Volume analysis of pile-up
NanoForce
Pile-up volume scales approx. inversely-proportional with film thickness. While quasi-static measurements would
become erroneous, dynamic measurements help to minimize this impact from measuring thin-film properties
November 19, 2015 39
NanoForce
Summary – thin films
Accuracy improvement for measurements on a sub-100 nm coatings possible with:
• Noise surpression by superimposed dynamics and low-pass filtering
• Dynamics to take in account for pile-up
• Cube corner tip to reduce the apex radius
November 19, 2015 40
NanoForce
Brittle material characterization
November 19, 2015 41
Fracture toughness
Nano-indentation results
Method inputs:
E…Young’s modulus
H…hardness
P…test load
a, c, l….distances from imageBerkovich [2]:
Cube Corner [1]:
Step 2: Produce a series of indentations at different loads and surface locations
Step 3: Image indents to find critical load for fully developed set of lead corner radial cracks
Step 4: Calculate Fracture toughness :
Step 1: Measure Hardness and Young’s modulus of the specimen
[1] D. S. Harding, W. C. Oliver and G. M. Pharr: Mat. Res. Soc. Symp. Proc., 356, 1995, 663.
[2] R. Dukino and M.V. Swain, J. Am. Ceram. Soc. 75 12, 1992, 3299
November 19, 2015 42
Fracture toughness
Nano-indentation results
Method Inputs:
E…Young’s modulus
H…hardness
P…test load
c….distance from image
Cube Corner:
HPFSBK7
BK7 glass is ~ twice as tough as synthetic Silica
November 19, 2015 43
NanoForce
Characterization of metallic single crystals
November 19, 2015 44
NanoForce
• Initial elastic-plastic transition can be observed at ~20uN
• Perfect elastic partial unloading cycles (no hysteresis)
• Pop-ins appear associated to the beginning / end of a partial unloading cycle
Quasi-static indentation with multiple-partial unloading
Modified Berkovich tip on Aluminum (110) single crystal
Fkrit
November 19, 2015 45
NanoForce
Dynamic indentation on single crystals:
Cu (110)Cu (111)
• The (111) orientation appears stiffer than the (110) orientation
• The (111) orientation exhibits pop-in events at approx. 10 uN load
Fcrit
Cube Corner tip on Copper (110) and (111) orientations
November 19, 2015 46
NanoForce
Indentation Creep
November 19, 2015 47
NanoForce
• Indentation Creep found to be CIT~6%
• Most significant contributor to depth-increase during peak-load-hold time are
pop-in events (Plastic flow/ dislocation mobility)
Quasi-static indentation with multiple-partial unloading and CREEP
Cube corner on Aluminum (110) single crystal
OM AFM
CREEP @ Pmax
Pop-in @ constant load
November 19, 2015 48
NanoForce
(Soft) Polymers
November 19, 2015 49
NanoForce
(soft) Polymers
Quasi-static indentation on PDMS with cube corner tip(…very sharp on very soft…)
EIT=(5.4+-0.2) Mpa
HIT=(1.07+-0.08) Mpa
EIT=(2.55+-0.53) Mpa
HIT=(0.36+-0.02) Mpa
CIT=(52+-9) %
CIT=(33.7+-2.6) %
• Repeatable raw-data due to precise load-control below 10 uN• Both PDMS-blends clearly distiguished at hand of raw-curves (F(h), h(t))• Resultant YOUNG’s modulus is in line with expectations (3.5 Mpa & 2.5 MPa resp. for PeakForce QNM)• Indentation creep exceeds 30%
November 19, 2015 50
NanoForce
Adhesion
November 19, 2015 51
NanoForce
Adhesion
Quasi-static indentation on PDMS with 50 um conical tip
Obtain quantitative data : • DMT modulus , starting @ ~1 Mpa• Adhesion • Energy dissipation• Surface deformation
Adhesionrindenter PRdEP += 3
3
4
Tip-stiction forces was measured @ approach (and pull-off) down to 2.5 um radius
Contact model with stiction (DMT)
Nano-Indenter gives
insights into new more
complex contact physics:
R=50um
R=5 um
R=2.5 um
November 19, 2015 52
NanoForce
Scratch
NanoForce
Scratch
Mixed loading profile: Dynamic indentation combined with Creep and scratch
=> Conical tip R=2.5 um on AR glass coating on float glass
20 x OM
Fcrit~42mN
50 x OM
Note:
Coating starts
chipping here
250 x OM (50 x opt & 5 x digital)
PreIMG PostIMG
• Single test method run tests to measure E’, E”, H, CIT and Scratch resistance
November 19, 2015 54
NanoForce
Other misc. applications
November 19, 2015 55
NanoForce
Precision of head mount and Indenter tip mounting
Cube Corner tip => Berkovich tip
Berkovich Tip => Conical tip
• mod. Berkovich
• Cube Corner
• Vickers
• Conical R=Var
• Flat Punch R=Var
• …
NanoForce tip shape options:
Requires remove/reinstall tip
Experiment: Measure remaining pos. accuracy after tip change
Quiz:
What if re-cal is skipped?:
Pos error ~7 um
Pos error ~5 um
Answer:
No big problem: pos accuracy remain better 10 um !(…and is this is not enough – best accuracy is just s fe clicks away (no new indent required)
and re-calibrate inline offset
November 19, 2015 56
NanoForce
Optical Microscope
• FOV All pixels
• Resolution ~500nm opt; ~1.6 nm AFM scanner
• >3000x total magnification + digital zoom
• Bright-field illumination;
• Optional: Extra objectives & Dark-field
5x
2.5x
8x
10x
20x
AFM
optional
Standard
DF
BF
Silicon or smooth, reflective
surfaces in Bright-field…
Skin or rough, absorbing surfaces:
Dark-field…
Vs. dark-field…
2.5x
2.5x50x
November 19, 2015 57
[Diagonal] = mm
28544.1
d
FHV =
[Applied load] = kgf
Concept: 1. Apply load
2. Analysis of residual imprint after load removal
Direct method…. -difficult to co-relate to physical properties
-No elastic properties
+
(static load) (OM image)
Ca
lcu
late
nu
mb
er
Static Apply static concept with NanoForce
NanoForce
Hardness measurement with Sharp (cone/pyramid) - the traditional way
2. Direct measurement of actual- or projected contact area Ac by AFM…3. Calculate Hardness4. Convert to other hardness scales.
1. Apply loading profile