photoacoustic determination of mechanical properties at...
TRANSCRIPT
Photoacoustic determination of
mechanical properties
at microstructure level
Ludovic Labelle, Bert Roozen,
Christ Glorieux
Laboratory of Acoustics
Soft Matter and Biophysics
Department of Physics and Astronomy, KU Leuven,
Celestijnenlaan 200D, B3001 Heverlee, Belgium
Martino Dossi, Mark Brennan, Koen Kemel, Maarten Moesen,
Jan Vandenbroeck
Huntsman Polyurethanes, Everslaan 45, 3078 Everberg, Sterrebeek
Photoacoustic determination of
mechanical properties
at microstructure level
Ludovic Labelle, Bert Roozen,
Christ Glorieux
Laboratory of Acoustics
Soft Matter and Biophysics
Department of Physics and Astronomy, KU Leuven,
Celestijnenlaan 200D, B3001 Heverlee, Belgium
Martino Dossi, Mark Brennan, Koen Kemel, Maarten Moesen,
Jan Vandenbroeck
Huntsman Polyurethanes, Everslaan 45, 3078 Everberg, Sterrebeek10
-110
010
110
2-120
-100
-80
-60
-40
-20
0
frequency (Hz)
resp
onse
(d
B)
Photoacoustic determination of
mechanical properties
at microstructure level
Ludovic Labelle, Bert Roozen,
Christ Glorieux
Laboratory of Acoustics
Soft Matter and Biophysics
Department of Physics and Astronomy, KU Leuven,
Celestijnenlaan 200D, B3001 Heverlee, Belgium
Martino Dossi, Mark Brennan, Koen Kemel, Maarten Moesen,
Jan Vandenbroeck
Huntsman Polyurethanes, Everslaan 45, 3078 Everberg, Sterrebeek
Studying microscopic elasticity
in poroelastic materialsMotivation:
• Macroscopic elasticity matters in vibration decoupling/damping applications
• Macroscopic elasticity is different from microscopic elasticity: depends on
microscopic elasticity and on frame morphology
• Microscopic elasticity is needed for understanding and tuning macroscopic elasticity
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
Approach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Hooke’s law: 1678: “ ut tensio sic vis”
Studying microscopic elasticity in poroelastic materials
Motivation:
• Macroscopic elasticity matters in vibration decoupling/damping applications
• Macroscopic elasticity depends on microscopic elasticity and on frame morphology
• Microscopic elasticity is needed for understanding and tuning macroscopic elasticity
( )
1 ( )
e M Sk
d
m M S
d
Foam slab: m: mass, S: surface, d: thickness, k: spring constant, M: modulus, :
damping constant
1 2
22
max 24
m
k
m m
Studying microscopic elasticity in poroelastic materials
Motivation:
• Macroscopic elasticity matters in vibration decoupling/damping applications
• Macroscopic elasticity depends on microscopic elasticity and on frame morphology
• Microscopic elasticity is needed for understanding and tuning macroscopic elasticityCompressionShearing
Elasticity of porous materials: static case
Studying microscopic elasticity in poroelastic materials
Motivation:
• Macroscopic elasticity matters in vibration decoupling/damping applications
• Macroscopic elasticity depends on microscopic elasticity and on frame morphology
• Microscopic elasticity is needed for understanding and tuning macroscopic elasticity
3
1 1 0 0
3
0 0
3
Hexagonal lattice:
2
3(3 )
Random lattice:
E =(3 )
With the compliances M and N given by:
4M= , N= , = 1
3 4 3
When the filled volume fraction 0, then
1 1M , N
3 3 3
grid
grid
EM N
M N
M N M
L L t t
Et Et L
EE
L
E
3
random grid E
Studying microscopic elasticity in poroelastic materials
Motivation:
• Macroscopic elasticity matters in vibration decoupling/damping applications
• Macroscopic elasticity depends on microscopic elasticity and on frame morphology
• Microscopic elasticity is needed for understanding and tuning macroscopic elasticity
Chemical reagents (polyurethane)
di/poly-isocyanate
polyol
For validation of tuning attempts and insight:
characterization of final foam properties needed
Physical circumstances during production• temperature
• gas pressure
• surfactant
• surface tension
• viscoelasticity
• vitrification
Morphology and composition of finally formed foam
depend on• timing of cease of chemical reaction
• timing of cease of reaction gas pressure driven foam cell expansion
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Frequency dependent moduli:
relaxation behavior
0
0.5
1
1.5
2
2.5
rea
l(M
)
102
103
104
105
106
107
108
109
1010
0
0.1
0.2
0.3
0.4
0.5
ima
g(M
)
frequency
Temperature dependent
relaxation frequency
3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 510
2
103
104
105
106
107
108
109
1010
1011
1000/T (1/K)
fre
qu
en
cy (
Hz)
Dynamic mechanical analysis
F pSd pS MSk
x xd d d
2
0
MSk m
d
Mass-spring resonance experiment
10-1
100
101
102
-120
-100
-80
-60
-40
-20
0
frequency (Hz)
resp
onse
(d
B)
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Only one frequency at a time and per sample
Limited to low frequencies
photothermal effect
T
z
sinusoidal SAW
gaussian SAW burst SAW
photoacoustic effect
1D, spatially uniform excitation pattern information on impedance:
thermal impedance (thermal effusivity)
& acoustic impedance
2D, non-uniform excitation pattern information on transport properties:
thermal diffusivity/diffusion length
& acoustic velocity and damping/wavelength
Photoacoustic and photothermal phenomena: extracting thermal and elastic information
from spatial and temporal dependence of temperature and displacement
Studying microscopic elasticity in poroelastic materialsApproach:
Challenges:
• Classical methods are limited in frequency range
Approach:
elastic wave propagation analysis
Studying microscopic elasticity in poroelastic materials
x
t
tx
t
Measured signals at different excitation-
detection distances
Mc =
ρ
Studying microscopic elasticity in poroelastic materials
x
t
t
pro
be-p
um
p d
ista
nce
106
107
108
109
2050
2100
2150
2200
frequency (Hz)
ph
ase
ve
locity (
m/s
)
k
2D Fourier transform
c=/k
Fit
real and
imaginary part of
elastic moduli
Approach:
elastic wave propagation dispersion analysis( )
( )
M
c =ρ
Finite size effects, scattering due to mode conversion and reflection
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Wavelength << strut length: ☺
Wavelength ~ strut length:
Wavelength >> strut length:
effective medium behavior
or microscopic behavior?
→ incident mode: A0
→ defect = 0.4L
Aluminium plate L = 1 mm, ω = 2.3 106 rad/s, 1198 basis modes, A0 in
0
0.5
1
0
0.5
1
mm
mm-1 0 1 -1 0 1
Example of interaction of Lamb wave with vertical crack
Studying microscopic elasticity in poroelastic materials
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Examples of scattering at irregularities
Scattering upon
reflection on an
irregular wall
Scattering of a periodic plane
wave in a polycrystal
Studying microscopic elasticity in poroelastic materials
Longitudinal, transverse and Rayleigh waves in homogeneous media: non-dispersive
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
Rayleigh waves: penetration depth < sample thickness non-dispersive
Studying microscopic elasticity in poroelastic materials
https://commons.wikimedia.org/wiki/Category:Beam_vibration_animations
Challenges:
• The elastic moduli are frequency dependent and complex
• Classical methods are limited in frequency range
• The acoustic wavelength at the audio frequencies of interest is much longer than
the pore size
• Guided wave propagation is intrinsically frequency dependent
How to untangle
material dispersion from
guided wave dispersion?
Waves in beams, plates, struts, membranes: wavelength > thickness dispersive + multi-mode
x
t
t
pro
be-p
um
p d
ista
nce
106
107
108
109
2050
2100
2150
2200
frequency (Hz)
ph
ase
ve
locity (
m/s
)
k
2D Fourier transform
c=/k
Fit
real and
imaginary part of
elastic moduli
Challenge: Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Ideal world scenario of extraction of elastic modulus from wave propagation
characteristics
Challenge: Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Real world scenario: combined dispersion due to guided wave character and
material relaxation
Dispersion due to
material relaxationDispersion due to
Lamb wave character
S0
A0
Dispersion due to
material relaxation
Challenge: Guided wave propagation is intrinsically frequency dependent
Studying microscopic elasticity in poroelastic materials
Real world scenario: combined dispersion due to guided wave character and
material relaxation
Combined dispersion due to Lamb
wave character and material relaxation
Dispersion due to
Lamb wave character
Challenging to unravel
dispersion due to material
relaxation
from total dispersion
(guided wave & relaxation)
Strategy:
▪ Investigate influence of fiber cross section by simulations
Challenge: complex morphology of struts and membranes
Studying microscopic elasticity in poroelastic materials
Approach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Studying microscopic elasticity in poroelastic materials
1
2 2 22
1
1 1 1 11
1
2
2
( , ) is to be found in experimentally inaccessible
( , )1 is known from experiment in feasib
,T
( )
le , range(
ra g
(
)
n e
1)
relaxation
r
relax
elaxa
ation
tion
E T E
EE T
i TT
E
i
E
T
T
1 0
0 2 2
exp is known by extrapolating VFT law
from fit of B and T in experimentally acces
and E are known from experim
sed , rang
ll
e
enta
B
T
E
T
T
1 2
2 0 1 0
1 1
2 2
2 1
1 2 2 2 0 1 0 2
Scaling of relaxation frequency:
y accessed
( ) ( )exp
Scaling of frequency:
(exp
, rang
( ) )
e
(
relaxation relaxation
relaxation relaxation
B BT T
T T T T
i i B B E
T T T T T T
T
1
2 2
2 0 1 0
1 11
1
2 2
2 2
1
1
, )1 exp
Substitution of relaxation behavior into scaled frequency term:
( ,( ,
)
1 )1( p) 1 ex
relaxation
EE
T E B B
E T T T T
EE T E
i E T E B
TT E
0 1 0
B
T T T
http://www.open.edu/openlearn/science-maths-technology/science/chemistry/introduction-polymers/content-section-5.3.1
modulus M(t,T1)
shift factor t(T2/T1) (e.g. Williams-Landel-FerryWilliams-Landel-Ferry (WLF) relation)
modulus M(tt,T2)
Approach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Studying microscopic elasticity in poroelastic materials
Approach:
▪ Local excitation: small source, short wavelength ,
high frequency fexc
▪ Local detection:
▪ vibrometer probe spot size <<
▪ Local guided wave velocity and damping
local real and imaginary part of elastic modulus
Validation step: piezoelectrically and photoacoustically
excited guided waves along a nylon wire
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Approach:
▪ Local excitation: small source, short wavelength ,
high frequency fexc
▪ Local detection:
▪ vibrometer probe spot size <<
▪ Local guided wave velocity and damping
local real and imaginary part of elastic modulus
Validation step: piezoelectrically and photoacoustically
excited guided waves along a nylon wire
Studying microscopic elasticity in poroelastic materials
Young’s modulus
(+ Poisson’s ratio)
by curve fitting
Approach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Validation step: piezoelectrically and photoacoustically
excited guided waves along a nylon wire
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Validation step: piezoelectrically and photoacoustically
excited guided waves along a nylon wire
Studying microscopic elasticity in poroelastic materials
ps laser excitation
Ywire, piezo-needle = (4.5 ± 0.1) GPaYwire,ps = (2.92 ± 0.07) GPaYwire,ns = (3.61 ± 0.07) GPa
Approach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Poisson ratio: 0.4 fixed or fitted with large uncertaintynylon=1200kg/m3 dnylon=150micron
1/42
0, 0 2
1/22
0, 0 2
21
3
2 1
TA f T
L
TS f T
L
c fdv c
c
cv c
c
Validation step: piezoelectrically and photoacoustically
excited guided waves along a nylon wire
Studying microscopic elasticity in poroelastic materials
Ywire, piezo-needle = (4.5 ± 0.1) GPaYwire,ps = (2.92 ± 0.07) GPaYwire,ns = (3.61 ± 0.07) GPaYwire,DMA,TT = (5 ± 1) GPa
Approach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
DMA measurement 25Hz +TT extrapolation for nylon fiber
Photoacoustically excited guided waves along a 2D foam-like polyamide grid
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Photo of sample Digitized image of sample
for programming xy-scanning
Photoacoustically excited guided waves along a regular polyamide 2D grid
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
15mm 7.5mm
15
mm
7.5
mm
15mm
7.5
mm
scanning direction scanning direction scanning direction
scannin
g d
irection
Cubic/orthorhombic grids/lattices with Slenderness/unit cell Aspect Ratio (AR) 1:1 and 2:1
and different unit cell dimensions (15mm and 7.5mm)
AR
1:1
AR
1:1
AR
2:1
Photoacoustically excited guided waves along a regular polyamide 2D grid
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
For comparison/calibration: single strut
Cubic grid 7.5mm
Photoacoustically excited guided waves along a regular polyamide 2D grid
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Cubic grid 7.5mmComparison between
• experimental
• FEM-simulated dispersion curve
Effects of mode
conversion at strut
crossings
~ phononic
bandgaps
Photoacoustically excited guided waves along a regular polyamide 2D grid
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Cubic grid 7.5mm Cubic grid 7.5mm
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Orthorombic grid AR 2:1
scanning along slow period
Orthorombic grid AR 2:1
scanning along short period
Photoacoustically excited guided waves along a regular polyamide 2D grid
Photoacoustically excited guided waves along a random polyamide 2D grid
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Photo of sample
Sample
Young’s
modulus
(GPa)
Poisson’s
ratio
Random 2.00 ± 0.05 0.33 ± 0.02
3D 1:1 2.01 ± 0.02 < 0.35
3D 1:2 1.50 ± 0.02 < 0.35
For comparison: single strut:
Example of fitting analysis
Studying microscopic elasticity in poroelastic materialsApproach:
• Time-temperature superposition principle
• Guided acoustic wave dispersion analysis
Studying microscopic elasticity
in poroelastic materialsIntermediate summary:
• With photoacoustic excitation, a wide frequency range is accessible
• Preliminary results on simplified model system:
• cm size struts
• periodical and random network structure
• non-relaxing temperature range: frequency independent material behavior
• Single strut-like dispersion can be obtained from strut embedded in porous frame
• Elastic properties of single struts can be extracted but large fitting covariance,
mainly on Poisson’s ratio
Future work:
• Experiments in temperature range where material’s behavior is frequency dependent
• Exploit time-temperature superposition to extrapolate high frequency results to audio
frequency results
• Experiments on real foams with (sub-)mm size struts
• Investigation of in-plane grid elasticity
• Full-field vibrometry for simultaneous assessment of macro- and microscopic
dynamics
Nanoporous silicon
Nanoporous silicon
R.B. Bergmann et al., Solar Energy
Materials & Solar Cells 74 (2002) 213–
218
5 micron
100 200 300 400 500 600 700 800 900 1000
100
200
300
400
500
600
700
800
900
1000
Heterodyne diffraction method
Fast and sensitive displacement detection
Characterization of porous silicon
c' = (c11-c12)/2 = 27.5 ± 0.25 GPa
c44 = 40.1 ± 0.1 GPa
Characterization of porous silicon
Characterization of porous silicon
THANK YOU FOR YOUR ATTENTION
Acknowledgments:
H2020-MSCA-RISE-2015 No. 690970
COST Action CA15125