TSOM Webinar on Instrumented Indentation - Bruker€¢ Motivation • Theory of...

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


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


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



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


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


Experimental aspects

Typical test setup

Calibrations:

• Tip-shape

• Load frame compliance

• in-line tool offsets

Specimen requirements:

• Roughness

• Flatness

• Mounting stiffness



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…


NanoForce


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


Loading profile


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


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


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


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


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


E(hc) if were calculated with ideal Ac


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 :


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


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


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


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:


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


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


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


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


NanoForce

Brittle material characterization


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


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


NanoForce

Characterization of metallic single crystals


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


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


NanoForce

Indentation Creep


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


NanoForce

(Soft) Polymers


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%


NanoForce

Adhesion


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


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


NanoForce

Other misc. applications


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


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


[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

TSOM Webinar on Instrumented Indentation - Bruker€¢ Motivation • Theory of...

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