Photoacoustic determination of mechanical properties at...

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

Christ Glorieux

Jan Vandenbroeck

Huntsman Polyurethanes, Everslaan 45, 3078 Everberg, Sterrebeek10

frequency (Hz)

Christ Glorieux

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 depends on microscopic elasticity and on frame morphology

e M Sk

Foam slab: m: mass, S: surface, d: thickness, k: spring constant, M: modulus, :

damping constant

max 24

Motivation:

• Microscopic elasticity is needed for understanding and tuning macroscopic elasticityCompressionShearing

Elasticity of porous materials: static case

Motivation:

1 1 0 0

Hexagonal lattice:

Random lattice:

E =(3 )

With the compliances M and N given by:

4M= , N= , = 1

When the filled volume fraction 0, then

1 1M , N

L L t t

Et Et L

random grid E

Motivation:

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 pore size

Frequency dependent moduli:

relaxation behavior

frequency

Temperature dependent

relaxation frequency

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 510

1000/T (1/K)

Dynamic mechanical analysis

F pSd pS MSk

x xd d d

Mass-spring resonance experiment

frequency (Hz)

Challenges:

the pore size

Only one frequency at a time and per sample

Limited to low frequencies

photothermal effect

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:

Approach:

elastic wave propagation analysis

Measured signals at different excitation-

detection distances

frequency (Hz)

locity (

2D Fourier transform

real and

imaginary part of

elastic moduli

Approach:

elastic wave propagation dispersion analysis( )

Finite size effects, scattering due to mode conversion and reflection

Challenges:

the pore size

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

mm-1 0 1 -1 0 1

Example of interaction of Lamb wave with vertical crack

Challenges:

the pore size

Examples of scattering at irregularities

Scattering upon

reflection on an

irregular wall

Scattering of a periodic plane

wave in a polycrystal

Longitudinal, transverse and Rayleigh waves in homogeneous media: non-dispersive

Challenges:

the pore size

Rayleigh waves: penetration depth < sample thickness non-dispersive

https://commons.wikimedia.org/wiki/Category:Beam_vibration_animations

Challenges:

the pore size

How to untangle

material dispersion from

guided wave dispersion?

Waves in beams, plates, struts, membranes: wavelength > thickness dispersive + multi-mode

frequency (Hz)

locity (

2D Fourier transform

real and

imaginary part of

elastic moduli

Challenge: Guided wave propagation is intrinsically frequency dependent

Ideal world scenario of extraction of elastic modulus from wave propagation

characteristics

Real world scenario: combined dispersion due to guided wave character and

material relaxation

Dispersion due to

material relaxationDispersion due to

Lamb wave character

Dispersion due to

material relaxation

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

Approach:

2 2 22

1 1 1 11

( , ) is to be found in experimentally inaccessible

( , )1 is known from experiment in feasib

le , range(

relaxation

exp is known by extrapolating VFT law

from fit of B and T in experimentally acces

and E are known from experim

sed , rang

2 0 1 0

1 2 2 2 0 1 0 2

Scaling of relaxation frequency:

y accessed

( ) ( )exp

Scaling of frequency:

, rang

relaxation relaxation

B BT T

T T T T

i i B B E

T T T T T T

2 0 1 0

, )1 exp

Substitution of relaxation behavior into scaled frequency term:

( ,( ,

1 )1( p) 1 ex

relaxation

T E B B

E T T T T

EE T E

i E T E B

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:

▪ 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

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

Young’s modulus

(+ Poisson’s ratio)

by curve fitting

Approach:

ps laser excitation

Ywire, piezo-needle = (4.5 ± 0.1) GPaYwire,ps = (2.92 ± 0.07) GPaYwire,ns = (3.61 ± 0.07) GPa

Approach:

Poisson ratio: 0.4 fixed or fitted with large uncertaintynylon=1200kg/m3 dnylon=150micron

0, 0 2

TA f T

TS f T

c fdv c

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:

DMA measurement 25Hz +TT extrapolation for nylon fiber

Photoacoustically excited guided waves along a 2D foam-like polyamide grid

Photo of sample Digitized image of sample

for programming xy-scanning

Photoacoustically excited guided waves along a regular polyamide 2D grid

15mm 7.5mm

scanning direction scanning direction scanning direction

scannin

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)

For comparison/calibration: single strut

Cubic grid 7.5mm

Cubic grid 7.5mmComparison between

• experimental

• FEM-simulated dispersion curve

Effects of mode

conversion at strut

crossings

~ phononic

bandgaps

Cubic grid 7.5mm Cubic grid 7.5mm

Orthorombic grid AR 2:1

scanning along slow period

Orthorombic grid AR 2:1

scanning along short period

Photoacoustically excited guided waves along a random polyamide 2D grid

Photo of sample

Sample

Young’s

modulus

Poisson’s

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 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

R.B. Bergmann et al., Solar Energy

Materials & Solar Cells 74 (2002) 213–

5 micron

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

THANK YOU FOR YOUR ATTENTION

Christ.Glorieux@kuleuven.be

Acknowledgments:

H2020-MSCA-RISE-2015 No. 690970

COST Action CA15125

Photoacoustic determination of mechanical properties at...

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