dynamic nanoindentation characterization: nanodma iii...nanodma iii incorporates a reference...

Dynamic Nanoindentation Characterization: nanoDMA III

Ude Hangen, Ph.D. 2017-11-02

11/02/2017 2 Bruker Confidential

• Elastic-Plastic vs. Viscoelastic Materials Response

• nanoDMA® Technology • Application Examples

• Elastic-Plastic Thin-Hard-Coating PM 2000 alloy

• Viscoelastic 3D-Printed Polylactide Silicone with crosslinking agent Polycarbonate

Outline

nN mN mN N

Load

pN

Dis

pla

cem

ent

nm

m

m

mm

microindenter

AFM

Minimum load ‘pre-load’

nanoindenter

DMA

0 100 200 300 400 500

0

200

400

600

800

1000

Indenta

tion L

oad (

uN

)Indentation Displacement (nm)

0 10 20 30 40 50 60 70

0

200

400

600

800

1000

Load (

µN

)

Time (s)

Load Function

• Materials Properties • Elastic-Plastic Response • Viscoelastic Response

• Easy to identify by quasi-static indentation

Load-Displacement Curve

Al<100> PC

11/02/2017 Bruker Confidential 3

Materials Covered in this Presentation

0 100 200 300 400 500

0

200

400

600

800

1000

Indenta

tion L

oad (

uN


• Materials Properties • Elastic-Plastic Response (Oliver&Pharr) • Viscoelastic Response

• Easy to identify by quasi-static indentation

Hysteresis

Al<100> PC

Elastic and Plastic Deformation

Unloading and Re-Loading Elastic



0 10 20 30 40 50 60 70

0

200

400

600

800

1000

Load (

µN

)

Time (s)

Load Function

Elastic-Plastic Response

• Thin Film Depth Profiling

• High-Temperature Creep testing

of a PM2000 alloy.

Viscoelastic Response

• Investigation of Polylactide Filaments for 3D-printing.

• Comparision of nanoDMA III and Macro DMA tests on silicone with cross linking agent.

• Polycarbonate – Mastercurve.



• Capacitive displacement sensing • Small inertia of moved parts <1 g • Low intrinsic dampening

Indenter

Center Electrode

Outer Electrode

Springs

Outer Electrode

Transducer Stability Specs

• <0.2 nm displacement noise floor

• <100 nN force noise floor

• <0.05 nm/sec thermal drift

*Specs Guaranteed On-Site*

• Load or Displacement Control • 78 kHz Feedback Loop Rate • 38 kHz Data Acquisition Rate • Experimental Noise Floor <100 nN (Digital Controller) • Enhanced Testing Routines • Digital Signal Processor (DSP) + Field Programmable

Gate Array (FPGA) + USB Architecture • Modular Design

Enabling Technology for Ultra-Small Materials Research

11/02/2017 6 Bruker Confidential Bruker Confidential 6

Transducer & Controller Core Technology

Depth, h

Lo

ad

, P

hf

0 0

Contact Area (Ac)

cc hfA

S

Phhc

maxmax

Contact Depth (hc)

m

fhhAP )(

Power-law Fit to Unloading

1

max )(

max

m

f

h

hhmAdh

dPS

Initial Unloading Stiffness


Quasi-Static Nanoindentation

Pmax

hmax hc

Ac

projected contact area (evaluated at maximum load)

c

rA

SE

2

Elastic Modulus (E)

reduced elastic

modulus

cA

PH max

Hardness (H)

s

s

i

ir

E

v

E

vE

221 11

Poisson’s Ratio

Indenter Sample

Sample’s Elastic

Modulus W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564.

Dynamic force superimposed on quasi-static force

Continuously measure properties as a function of contact depth, frequency, and time.


nanoDMA III Overview

• Lock-In Amplifier Frequency Range • Frequency Range for Testing: 0.1 Hz – 300 Hz • Typical Force Amplitude: 0.01 µN to 200 µN • Typical Displacement Amplitude: 0.1 nm to 5 nm

Indenter

Center Electrode

Outer Electrode

Springs

Outer Electrode

11/02/2017 Bruker Confidential

Lock-In Amplifier

Static Force Signal

Oscillating Force (µN, Hz)

Amplitude (nm), Phase (deg)

Static Displacement Signal

Bruker Confidential 9

nanoDMA III Technology

Dynamic Testing

Lock-In Amplifier

Force & Displacement vs. Time

Amplitude & Phase vs. Time

Stiffness vs. Time

CMX Profile: Hardness & Modulus


CMX – Force & Displacement & Stiffness

• DLC coating on high-strength steel

• Image of film edge on substrate

• In-situ SPM Metrology on coating:

• Cross-Section Profile

• Surface Roughness

0 5 10 15 20 25 30

0

50

100

150

200

Heig

ht

(nm

)

Position (µm)

Film Thickness: 135 nm

DLC-Coating: Peak To Valley = 4.5926 nm Average Roughness (Ra) = 0.3858 nm RMS Roughness (Rq) = 0.4599 nm

Steel Substrate: Peak To Valley = 14.8 nm Average Roughness (Ra) = 2.5704 nm RMS Roughness (Rq) = 3.1151 nm


Thin Film Nanoindentation

135 nm DLC

0 20 40 60 80 100 120 140 1600

5

10

15

20

25

Ha

rdn

ess (

GP

a)

Contact Depth (nm)

0 20 40 60 80 100 120 140 160

0

50

100

150

200

250

Re

du

ce

d M

od

ulu

s (

GP

a)

Contact Depth (nm)

Steel Substrate

75 nm DLC 25 nm DLC

• 3 coatings on steel

• Berkovich Indenter

• CMX-depth profile


Thin Film Nanoindentation

• Low Thermal Expansion Design

• Tight Temperature Control

• Uniform Sample Temperature

• Probe Tip Heating in Uniform Environment

• Easy Sample Mounting

• Atmosphere Control

• Fast Warm-up and Stabilization

• Constructed to Handle Temperatures up to ~1000°C; Limitation by Tip Material


xSol High Temperature Stage Nanomechanical Characterization at Temperatures up to 800°C

• Quasi-static load is held constant (in this case 5 mN).

• A relatively small (~1 nm) amplitude sinusoidal force is superimposed at user-specified frequency (in this case 220 Hz).

• Force amplitude, displacement amplitude, and phase shift are measured, allowing contact stiffness to be measured continuously.

11/02/2017


Reference Creep Testing

nanoDMA III incorporates a reference frequency technique for thermal drift correction during the course of an experiment. • Enables the measurement of contact area without relying on the raw

displacement data. The continuously measured stiffness is used to accurately determine contact area and contact depth in-situ.

• In-situ drift compensation during long duration frequency sweeps and creep tests.

Stiffness vs. Depth on FQ

S(Ef*, A(hc))

Calibrated tip area function relates contact depth to contact area:

11/02/2017


Reference Frequency Technique

A(hc) = C1hc 2 + C2hc + C3hc

1/2 + C4hc1/4 + C5hc

1/8 + C6hc1/16

Tensile Testing

𝜀 = ℎ / ℎ

ℎ

ℎ

Indentation Testing

ℎ ℎ

• Uniform Stress • Uniform Strain

• Stress Field • Strain Field

11/02/2017


Converting Depth to Strain Rate

𝜀 = ℎ / ℎ

𝜎 = P/A = H

The mean contact pressure, is the applied force divided by the projected contact area. This is also the definition of hardness.

The strain rate is the indenter velocity divided by the indentation depth. (Pyramidal Indenter)

• Strain rate varies with stress and temperature:

𝜀 = 𝐴𝜎𝑚𝑒−𝑄 𝑅𝑇

m: Stress Exponent Q: Activation Energy T: Temperature

: Stress : Strain R: Gas Constant A: Proportionality Constant

11/02/2017


Steady State Creep

Depth h and velocity are determined from a fit to the creep curve. Pressure equals the hardness value.

ℎ

PM 2000 ODS Alloy: FeCrAl alloy with dispersed oxide nano-particles High creep resistance of dispersion hardened materials • Typical stress exponent m = 20 . . . 200 (creep rate drops fast with stress) • Interaction of dislocation with dispersed oxides:

• Small particles can be passed by climbing • Line energy between particle and dislocation is reduce • Thermal activation and external stress needed

• Mechanism is highly dependent on external stress

Indenter Used: Berkovich – Sapphire Shield Gas: 95%N5%H

U.Hangen et al. AEM (2015). 11/02/2017


Reference Creep Test on PM 2000

Plot ln(𝜀 ) versus ln 𝐻 and slope is

stress exponent ‘m’.

m80: typical for ODS alloys m8: thermal activated dislocation motion

Temp. (C) m

300 78.5

500 15.7

600 8.6

700 8.2

11/02/2017


Finding Stress Exponent

U.Hangen et al. AEM (2015).


Domain of Testing Strain Rate Frequency Temperature

Constant Strain Rate Testing x

Indentation Creep Testing x

Creep and Recovery Testing x x

nanoDMA III Testing x x

nanoDMA III Testing + xSol x x x

Viscoelastic Matter

0 50 100 150 200 250 300 350 400

0

2000

4000

6000

8000

Load (

µN

)Time(s)

• Viscoelastic Response • Time Dependent Deformation • Hardness depends on strain rate Experimental: • A constant strain rate is achieved by

exponential loading. • T = 23°C • Force Amplitude/Quasi-static Force <<1 • Dynamic Frequency 110 Hz • Small displacement amplitude of 1-2 nm


0.5 1/s 0.1 1/s

0.05 1/s 0.01 1/s

Polylactide Characterization

0 100 200 300 400 500 600 700 800 900 1000

0.2

0.3

0.4

0.5 Strain rate 0.01

Strain rate 0.1

Hard

ne

ss (

GP

a)

Contact Depth (nm)

0 100 200 300 400 500 600 700 800 900 1000

5

6

7

8 Strain rate 0.01

Strain rate 0.1

Red

uce

d M

odu

lus (

GP

a)

Contact Depth (nm)

• Viscoelastic Response

• Time Dependent Deformation

• Reduced modulus is strain rate independent

• Hardness (stress under indenter) relates to a strain rate


Depth Profile

0 100 200 300 400 500 600 700 800 900 1000

0.2

0.3

0.4

0.5 Strain rate 0.01

Strain rate 0.1

Strain rate jump 0.1-0.01-0.1

Hard

ne

ss (

GP

a)

Contact Depth (nm)

0 100 200 300 400 500 600 700 800 900 1000

5

6

7

8 Strain rate 0.01

Strain rate 0.1

Strain rate jump 0.1-0.01-0.1R

ed

uce

d M

odu

lus (

GP

a)

Contact Depth (nm)

• A load function with combined strain rate segments results in the respective hardness readings.

0 50 100 150 200 250 300 350 400

0

2000

4000

6000

8000

Forc

e (

µN

)

Time (s)

Technique proposed by: V. Maier et al., J. Mater. Res., (2011).

0.1 1/s 0.01 1/s

Strain Rate Jumping


Depth Profile with Changing Rate


-2.0 -1.8 -1.6 -1.4 -1.2 -1.0

-12

-10

-8

-6

-4

-2

0 Creep Test 1h

Creep Test 1h

Creep Test 1h

Strain rate 0.01

Strain rate 0.05

Strain rate 0.1

strain rate 0.5

ln (

str

ain

ra

te)

ln (H)

• High Strain Rates: Constant strain rate testing; 0.01 / 0.05 / 0.1 / 0.5 1/s (left) • Low Strain Rates: 1 hour reference creep experiment

Strain Rate Spectrum

• Temperature range for 3D printed parts

• Polylactide is thermoplastic

• What is the glass transition temperature Tg about?

• Structural changes • Mechanical changes

As 3D-printed Deformed at T>Tg


Temperature Dependent Testing


• Low Thermal Expansion Design

• Tight Temperature Control

• Uniform Sample Temperature

• Probe Tip Heating in Uniform Environment

• Interfaces with all testing modes:

• Quasi-static Testing

• nanoDMA III Testing

• Scratch Testing

• In-situ SPM imaging

xSol Sample Heating Solution

Creep

-300 -200 -100 0 100 200 300 400

0

200

400

Indenta

tion L

oad (

uN

)

Indentation Displacement (nm)

Recovery

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

0

50

100

150

200

250

300

350

Ind

en

tatio

n D

isp

lace

me

nt

(nm

)

Time (s)

Creep Displacement

Recovery Displacement

Controlled Loading Step 500 µN/0.1s

Controlled Un-Loading Step Response 400 µN/0.1s

Viscoelastic behavior tested between 23°C and 100°C:

• Creep response to a fast loading step • Sample recovery after fast unloading

11/02/2017


Quasi-static Indentation

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105

0.00

0.02

0.04

Ha

rdn

ess (

Gp

a)

Temperature (degC)

Hardness

20 30 40 50 60 70 80 90 100 110

0

10

20

30

40

50

60

Creep rate

Cre

ep

ra

te (

nm

/s)

Temperature (degC)

0

10

20

30

40

50

60

Recovery rate

Re

co

very

ra

te (

nm

)

Creep Rate = Creep displacement / Holding time (10s) Recovery Rate = Recovery displacement / Holding time (10s)


Creep and Recovery Analysis

-100

-50

0

50

100

150

200

0 200 400 600 800 1000 1200 1400

Ph

as

e s

hif

t,

the

ta

F requency, rad /s

0

50

100

150

200

Dy

na

mic

C

om

plia

nc

e,

m/N

(a)

(b)


m mass of the indenter 350 mg

Ci system damping coeff. 0.01 Ns/m

Cs specimen damping coeff. ?

Ki spring constant 300 N/m

Ks contact stiffness ?

222 si

o

o

CCmk

FX

2

1tan

mk

CCsi

Amplitude

Phase

5.2422 ** hE

AEKs

is KKk

Contact stiffness

Contact stiffness Loss ss CK ''

• Experimental - Model fit R=0.9999

Frequency, rad/s

Ph

ase S

hif

t,

deg

Dyn

am

ic

Co

mp

lia

nc

e, m

/N Ki Ci

Ks Cs

tFo sinm

S.A. Syed Asif, K.J. Wahl and R.J. Colton Rev. Sci. Instrum. 70 (1999) 2408; J. Mater. Res. 15 (2000) 546.

Dynamic Model

Dynamic Measurement of Hardness, Reduced Modulus, Storage Modulus, Loss Modulus, Tan Delta

Kelvin Voigt Model

Typical displacement amplitude: 0.1 – 5 nm

The contact area is assumed to stay constant

during the load cycle. No opening and closing

at the edge of the contact area.

Asif et al., J. Appl. Phys. 90 (2001) 1192.


nanoDMA III for Viscoelastic Material

-200 0 200 400

0

200

400

600

800

1000

Indenta

tion L

oad (

uN


xSol Stage for Temperature Control:

• nanoDMA III testing between 23°C and 100°C

• 5 indentations per temperature

• Displacement amplitude 1 nm

• Dynamic test at 10 Hz at max load


nanoDMA III - Temperature

20 30 40 50 60 70 80 90 100 110

0

1

2

3

4

5

6

Modulu

s (

GP

a)

Temperature (degC)

Storage Modulus

Loss Modulus

0.0

0.1

0.2

0.3

Tan Delta

Tan D

elta

xSol Stage for Temperature Control:

• E’, E” and tan(delta) are averaged

• E’ drop from 23°C to 100°C

• Tan(delta) peak at approx. 80°C



Samples and Macro DMA testing courtesy of Donna Ebenstein, Department of Biomedical Engineering, Bucknell University.

Comparison of nanoDMA III and macro DMA storage modulus and tan delta for 4 silicone samples with varying amounts of crosslinking agent


nanoDMA III Comparison

Polycarbonate Storage and Loss Modulus as a Function of Frequency and Temperature

Frequency: 10-300 Hz; Temperature: 75-175°C



…Time-Temperature Superposition

Predict viscoelastic properties over a broad frequency range, well outside the experimental range actual measurements can be conducted…



Combine Frequency Sweeps and Use WLF Equation for a Full Time-Temperature Analysis

log 𝑎𝑇 =−14.34(𝑇 − 150)

49.69 + (𝑇 − 150)


Polycarbonate 150°C Master Curves


Bruker’s improved nanoscale dynamic mechanical testing enables:

• A truly continuous measurement of x (x = hardness, storage modulus, loss modulus, complex modulus, tan-delta, etc.) as a function of contact depth, frequency, and time.

• Application and testing accuracy across a wide range of materials—from hydrogels to ultra-hard coating.

• Drift correction allows for long-duration frequency sweeps and creep tests to be reliably performed.

• Overcomes the inaccuracies of stiffness measurements on viscoelastic materials when employing quasi-static indentation. Measurements of E’, E” and tan delta comparable to measurements at larger length scales.

Conclusions


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dynamic nanoindentation characterization: nanodma iii...nanodma iii incorporates a reference...

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