dynamic nanoindentation characterization: nanodma iii...nanodma iii incorporates a reference...
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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
)Indentation Displacement (nm)
• 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
11/02/2017 Bruker Confidential 4
Materials Covered in this Presentation
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.
11/02/2017 Bruker Confidential 5
Materials Covered in this Presentation
• 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
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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
11/02/2017 Bruker Confidential 7
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.
11/02/2017 Bruker Confidential 8
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
11/02/2017 Bruker Confidential 10
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
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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
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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
11/02/2017 13 Bruker Confidential
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
Bruker Confidential 14
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:
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Bruker Confidential 15
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
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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
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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
Bruker Confidential 18
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
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Bruker Confidential 19
Finding Stress Exponent
U.Hangen et al. AEM (2015).
11/02/2017 20 Bruker Confidential
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
11/02/2017 21 Bruker Confidential
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
11/02/2017 Bruker Confidential 22
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
11/02/2017 Bruker Confidential 23
Depth Profile with Changing Rate
11/02/2017 24 Bruker Confidential
-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
11/02/2017 Bruker Confidential 25
Temperature Dependent Testing
11/02/2017 26 Bruker Confidential
• 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
Bruker Confidential 27
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)
Bruker Confidential 28
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)
11/02/2017 29 Bruker Confidential
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.
11/02/2017 Bruker Confidential 30
nanoDMA III for Viscoelastic Material
11/02/2017 31 Bruker Confidential
-200 0 200 400
0
200
400
600
800
1000
Indenta
tion L
oad (
uN
)Indentation Displacement (nm)
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
11/02/2017 Bruker Confidential 32
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
11/02/2017 Bruker Confidential 33
nanoDMA III - Temperature
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
11/02/2017 Bruker Confidential 34
nanoDMA III Comparison
Polycarbonate Storage and Loss Modulus as a Function of Frequency and Temperature
Frequency: 10-300 Hz; Temperature: 75-175°C
11/02/2017 Bruker Confidential 35
nanoDMA III - Temperature
…Time-Temperature Superposition
Predict viscoelastic properties over a broad frequency range, well outside the experimental range actual measurements can be conducted…
11/02/2017 Bruker Confidential 36
nanoDMA III - Temperature
Combine Frequency Sweeps and Use WLF Equation for a Full Time-Temperature Analysis
log 𝑎𝑇 =−14.34(𝑇 − 150)
49.69 + (𝑇 − 150)
11/02/2017 Bruker Confidential 37
Polycarbonate 150°C Master Curves
11/02/2017 38 Bruker Confidential
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
11/02/2017 39 Bruker Confidential
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