ROUND ROBIN TEST ON ELASTIC PROPERTIES OF PORO- AND VISCOELASTIC MATERIALS FOR VIBRO-

ACOUSTIC APPLICATIONS

P. Bonfiglio, F . Pompoli, K. V. Horoshenkov, M.I.B.S.A . Rahim, L. Jaouen, J. Rodenas, F.-X. Bécot, E.

Gourdon, D. Jaeger, V. Kursch, M. Tarello, N. B. Roozen, C. Glorieux, F. Ferrian, P. Leroy, S. Berger, F.

Briatico Vangosa, N. Dauchez, F. Foucart, L. Lei, K. Carillo, F. Sgard, O. Doutres, R. Panneton, K. Verdiere,

C. Bertolini, R. Bär, J.-P. Groby, A. Geslain, N. Poulain, L. Rouleau, A. Guinault, H. Ahmadi, C. Forge

Outline •  General motivations and aim of the research •  Participants •  Tested materials •  Measurement methods •  Results •  Conclusions

•  At the present, NO unique standards exist!!!

•  Each lab and/or research center is using elastic data in several applications (quality control, numerical simulations, validation of theoretical models)

•  Still some open issues (Viscoelasticity, Temperature effect, etc…)

•  The aim of the proposed Round Robin Test (RRT) was to investigate the state of the art

about the viscoelastic characterization of poroelastic materials for vibro-acoustic

applications.

•  The idea was to test the same materials in different labs. Each participant applied any

arbitrary technique to measure viscoelastic properties (Young’s moduli, shear moduli,

Poisson’s ratio, loss factor, etc…) , in any possible frequency and temperature ranges.

•  The main goal was to collect information on the dispersion of the results for a given

material. The additional goal was to involve participants both from academicals

institutions and from companies

General motivations and aim of the research

Several inter-laboratory studies to understand the dispersion in the acoustical (surface impedance, sound absorption coefficient, characteristic impedance and complex wavenumber) and related non-acoustical parameters (airflow resistivity, open porosity, tortuosity and characteristic lengths) of porous media. 1. K.V. Horoshenkov et al. , “Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests)”, J. Acoust. Soc. Am. 122 (1), (2007).

2. F. Pompoli et al, How reproducible is the acoustical characterization of porous media? J. Acoust. Soc. Am. 141 (2) 945-955, (2017).

3. M. Garai, F. Pompoli, “A European Inter-Laboratory Test of Airflow Resistivity Measurements”, Acustica united with Acta Acustica 89 pp. 471-478 (2003).

The inter-laboratory studies on the viscoelastic properties of porous media are much more scarce L. Jaouen, A. Renault, M. Deverge, Elastic and damping characterizations of acoustical porous materials: Available experimental methods and applications to a melamine foam,

Applied Acoustics 69–12 1129–1140 (2008).

Review of existing methods and application to a melamine foam

General motivations and aim of the research

Participants

Italy UK France

Canada

France

Germany France

France

Belgium Switzerland Italy

Canada

France

Italy

Material A: homogenous, nearly isotropic and relatively low dependency of its viscoelastic properties on temperature and frequency.

Materials B and C: anisotropic structure (due to their oriented fiber structure)

Material D:closed cell foam material with a strong viscoelastic behaviour.

Material E:high density, strong viscoelastic behaviour, and it is not homogenous (due to rubber reconstitution process)

Tested materials

# Material Nominal thickness [mm] Nominal density [kg/m3] Kindly provided by:

A Melamine foam 25 10

B Glass wool 50 80

C Felt 20 40

D K-FLEX ST 25 48

E K-FLEX K-FONIK OPEN CELL 240 25 240

1.  Quasi-static longitudinal method

2.  Resonant method Transmissibility based method

3.  Dynamic mechanical analysis and TTS principle

4.  Lamb and Surface wave method

5.  Transfer function/ transfer matrix method

Measurement methods

low frequency quasi-static

methods

dynamic methods

1,3

2

1

2

3 4

5 4

Quasi-static longitudinal methods

Measurement methods

Partner 3 Frequency range: 20-45 Hz Size of sample(mm): 22. 5 (R)

S. Sahraoui, E. Mariez, M. Etchessahar, Mechanical testing of polymeric foams at low frequency, Polymer Testing 20 93–96 (2001).

Partners 2,8,9

Frequency range (2-9) 10-60 Hz, (8) 20-40 Hz Size of sample(mm): (2) 20 and 50 (R) (8) 44.4 and 29 (R) (9) 15 and 22.25 (R)

C. Langlois, R. Panneton, and N. Atalla. Polynomial relations for quasi-static mechanical characterization of isotropic poroelastic materials. J. Acoust. Soc. Am., 110:3032–3040, (2001)

Partners 6, 10, 12, 13* * TTS principle was applied

Frequency range (6) 20-120 Hz (10) 10-100 Hz (12) 0.1-100 Hz (13) 0.1-10000 Hz Size of sample(mm): (6-10) 22.25 (R) (12) 15 (R) (13) 15 (LS)

S. Sahraoui, E. Mariez, M. Etchessahar, Mechanical testing of polymeric foams at low frequency, Polymer Testing 20 93–96 (2001). C. Langlois, R. Panneton, and N. Atalla. Polynomial relations for quasi-static mechanical characterization of isotropic poroelastic materials. J. Acoust. Soc. Am., 110:3032–3040, (2001)

Resonant method/ Transmissibility based method

Measurement methods

Partners 1,4

Frequency range At resonance frequency Size of sample(mm): (1) 50 (LS) (2) 49 (R)

Not declared / internal protocol

Partners 7,11

Frequency range (7) At resonance frequency (11) 40-500 Hz Size of sample(mm): (7) 50-100 (LS) (11) 450 (R) and circular annular

ISO 18437-5 - Mechanical vibration and shock - Characterization of the dynamic mechanical properties of visco-elastic materials - Part 5: Poisson ratio based on comparison between measurements and finite element analysis (International Organization for Standardization, Geneva 2011). C. Langlois, R. Panneton, and N. Atalla. Polynomial relations for quasi-static mechanical characterization of isotropic poroelastic materials. J. Acoust. Soc. Am., 110:3032–3040, (2001)

Lamb and Surface wave method

Measurement methods

Partner 5 Frequency range 100-1000 Hz Size of sample(cm): 40 x 100

N.B. Roozen, L. Labelle, Q. Leclère, K. Ege, S. Alvarado, Non-contact experimental assessment of apparent dynamic stiffness of constrained-layer damping sandwich plates in a broad frequency range using a Nd:YAG pump laser and a laser Doppler vibrometer, In Journal of Sound and Vibration, Volume 395, pp 90-101 (2017).

Partner 10B

Frequency range: 200-4000 Hz Size of sample(cm): 40 x 100

A. Geslain, S. Raetz, M. Hiraiwa, M. Abi Ghanem, S. P. Wallen, A. Khanolkar, N. Boechler, J. Laurent, C. Prada, A. Duclos, P. Leclaire, and J.-P. Groby, Spatial Laplace transform for complex wavenumber recovery and its application to the analysis of attenuation in acoustic systems, Journal of Applied Physics 120, 135107 (2016).

Shear mechanical analysis

Transfer function/ transfer matrix method

Measurement methods

Partner 14 * TTS principle was applied

Frequency range 0.1 – 5e5 Hz Size of sample(mm): 12 (R)

L. Rouleau, J.-F. Deü, A. Legay and F. Le Lay. Application of the Kramers-Kronig relations to time-temperature superposition for viscoelastic materials. Mechanics of Materials, 65:66-75, 2013

Partner 3B

Frequency range 60 – 1000 Hz Size of sample(mm): 22.5 (R)

P. Bonfiglio, F. Pompoli, K.H. Horoshenkov, M. I. B. S. A. Rahim, A simplified transfer matrix approach for the determination of the complex modulus of viscoelastic materials, Polymer Testing 53 180-187(2016).

Measurement methods

Only 7 partners

carried out Poisson’s ratio tests

Different excitation signals, static load/compression rate,

mounting conditions !!!!

Preliminary tests

Results

0

50

100

150

200

250

300

350

400

A B C D E

Mea

sure

d de

nsity

[kg/

m^3

]Partner 1

Partner 2

Partner 3

Partner 4

Partner 5*

Partner 6

Partner 7

Partner 8

Partner 9

Partner 10*

Partner 11

Partner 12*

Partner 13

Relative standard deviation of density: •  6-7% for materials A, B

and D •  29 % for material C •  17% for material E

Density

Anisotropy

0

1

2

3

4

5

6

7

8

9

10

A B C D E

Ex/

Ez

and

Ey/

Ez

[-]

Material

Ex/EzEy/Ez

•  A, D and E are close to being isotropic

•  significant deviation in the Young’s moduli observed for material B in the direction y and for material C in both in-plane directions.

With respect z direction

Preliminary tests

Results

•  strong dependence of the Young’s modulus, Ε, from the static preload for materials B, C and E,

•  strong dependence of the Poisson’s ratio, ν, for materials B and C.

•  No significant variation as a function of static preload were observed for the loss factor η.

Maximum static preload was applied by Partner 4 (~700 Pa, black vertical line)

Influence of static preload/compression rate

0

2

4

6

8

10

0 500 1000 1500 2000 2500E (s

tatic

load

)/E (l

oad=

0) [-

]

Static preload [Pa]

ABCDE

0

2

4

6

8

10

0 500 1000 1500 2000 2500ν(s

tatic

load

)/E (l

oad=

0) [-

]

Static preload [Pa]

ABCDE

0

2

4

6

8

10

0 500 1000 1500 2000 2500η(s

tatic

load

)/E (l

oad=

0) [-

]

Static preload [Pa]

ABCDE

With respect null load condition

Results of viscoelastic parameters: Material A

Results

1.E+04

1.E+05

1.E+06

1 10 100 1000 10000

Rea

l Par

t Com

plex

mod

ulus

[Pa]

Frequency [Hz]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 10 100 1000 10000

Pois

son'

s rat

io [-

]

Frequency [Hz]

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1 10 100 1000 10000

Los

s fac

tor [

-]

Frequency [Hz]

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1 10 100 1000 10000

Rea

l Par

t Com

plex

mod

ulus

[Pa]

Frequency [Hz]

Results of viscoelastic parameters: Material B

Results

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 10 100 1000 10000

Pois

son'

s rat

io [-

]

Frequency [Hz]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1 10 100 1000 10000

Los

s fac

tor [

-]

Frequency [Hz]

Results of viscoelastic parameters: Material D

Results

1.E+04

1.E+05

1.E+06

1.E+07

1 10 100 1000 10000

Rea

l Par

t Com

plex

mod

ulus

[Pa]

Frequency [Hz]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 10 100 1000 10000

Pois

son'

s rat

io [-

]

Frequency [Hz]

0.00

0.10

0.20

0.30

0.40

0.50

0.60

1 10 100 1000 10000

Los

s fac

tor [

-]

Frequency [Hz]

Overall deviations

Two different reasons can affect the overall standard deviation for the storage modulus, (up 2 orders of magnitude)

•  frequency range of investigation; in fact materials D and E show a marked viscoelasticity (that is the storage modulus increases with frequency).

•  effect of data from Partner 5 who appear to overestimate the storage modulus significantly and particularly for materials B and C.

Considerable dispersion in Poisson’s ratio results (for material B Partner 2 measured 0.4)

Results

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

A B C D E

Rea

l Par

t Com

plex

mod

ulus

[Pa]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

A B C D E

Pois

son'

s rat

io [-

]0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

A B C D E

Los

s fac

tor [

-]

Statistical analysis: ISO 5725 parts 1 and 2 The standard refers to the same measurement method!

We limited analyses to frequencies around 50 Hz. Moreover we considered only partners which tested 5 samples for each material

Results

2 2 2= +R L rs s s2

2

2

L

r

R

estimate of the between laboratory varianceestimate of the repeatability varianceestimate of the reproducibility var

sss iance

−

Statistical analysis: ISO 5725 parts 1 and 2 In addition we applied Mandel h (between consistency) and k (within consistency) tests - 5% significance level

Results

Real part of complex modulus

the examination of h and k plot can indicate those laboratories which exhibit inconsistent results.

Statistical analysis: ISO 5725-1 and 5725-2 In addition we applied Mandel h (between consistency) and k (within consistency) tests - 5% significance level

Results

Loss factor

the examination of h and k plot can indicate those laboratories which exhibit inconsistent results.

We applied also Cochran test Results are omitted

•  The inter-laboratory tests on the mechanical properties of 5 types of porous media suggest a poor reproducibility between the 14 participating laboratory partners

•  The results of the error analysis suggest that the maximum relative reproducibility standard deviation in the measurement of the

•  Young’s modulus was around 70% (Material A).

•  Loss factor was around 60%.

•  Significant deviations in Poisson’s ratio measurement

Conclusions

These findings suggest that there is an obvious need for harmonization of the procedures to measure the complex Young’s modulus and Poisson’s ratio of porous media.

This is not an easy task also because

results have to be considered regarding the observed deviation for material production, or from a modeling point of view

Conclusions

- STL of Steel plate (0.7 mm) – Material D– EPDM mass (5 kg/m2 – 2.6 mm)

Lp

LI

Simulations using TMM and results from all laboratories

1.E+04

1.E+05

1.E+06

1.E+07

1 10 100 1000 10000

Rea

l Par

t Com

plex

mod

ulus

[Pa]

Frequency [Hz]

Submitted Nov 28, 2017

Conclusions

This research is based upon work from COST Action DENORMS CA 15125, supported by COST (European Cooperation in Science and Technology).

THANK YOU !!!