Through dispersion measurements. Have you studied Biot's theory ad its subsequent modifications?

Please develop.

I have no idea. I wish to buy a commercial device, I can't build something special.

Please let me know.

Alain

@ Alain

What kind of porous medium you interested? Can you give some examples?

Foams for thermal insulation, among other rigid cellular monoliths for which mechanical tests by compression are majorly done. As doing tensile or shear tests are almost impossible with such fragile and leightweight materials, I was looking for a method able to give access to shear modulus and Poisson ration by an indirect way. I therefore thought about acoustic methods. I know that it is possible on wood, which is another porous material, but is absorbs much less the acoustic waves, so that such measurements become possible below 100 kHz.

Alain

Ultrasound has often been employed in studying the elastic properties of porous medium. I will add some references soon.

In the case of open-cell foam, filling with fluid of similar sound velocity can help in acoustic methods.

In common case, X-ray tomography is universal method http://iccm-central.org/Proceedings/ICCM17proceedings/Themes/Applications/SANDWICH%20STRUCTURES/INT%20-%20SANDWICH%20STRUCTURES/IB6.1%20Schlimper.pdf

@ Andrei

I knew of X-rays, but I did not recommend it as I guess it is much expensive than ultrasound based systems. Also X -ray system is more suitable for materials with very minute spacing. Also, I guess more research work has been done using acoustic waves.

Dear Alain,

I guess that you should be able to excite the resonant frequencies of the samples. The resonant modes are related to the elastic constants so such tests may fulfill your needs. In addition, you will be able to draw conclusions about the acoustic attenuation, energy losses and viscoelasticity. There exist different test configurations, that basically differ in how the resonant frequencies are excited. For instance with a hammer blow, or with an ultrasonic sweep over the resonant frequency of interest (using an ultrasonic transducer). The ASTM E2001 and ASTM E1876 can be a good benchmark for these tests:

• ASTM E2001 Standard Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic.
• ASTM E1876 Standard Test Method for Dynamic Young's Modulus , Shear Modulus , and Poisson's Ratio by Impulse Excitation of Vibration

I bet that there are a bunch of works reporting this kind of tests in porous materials.

Regards,

Dear Jesus,

The technique you are talking about consists in hitting one corner of the material with a little hammer, recording the sound obtained and making calculations based on it.

Unfortunately, for porous materials such as mines, the shock produces no sound at all, as all the energy is absorbed (or the material is damaged, depending on the cases ...). From where my trials to find a technique investigating the mechanical properties by measuring the wave velocity in transmission between 2 transducers. But even the latter technique seems virtually impossible with so attenuating materials.

Thanks anyway

Alain

Dear Alain,

I agree  with Andrei. To my exlerience the only reliable method is CTI/segmentation/meshing/FEM. Provided of course the suitable accuracy in each step. Once you have a realistic mesh you can perform a linear elastic compression and measure E. With other methods, you know better than me, one has to make  always some compromise.

Alberto

Well, I tried to provide a general view. Of course, the most simple case consists of an impact. But you can use too an ultrasonic configuration (emitter-receiver). Perhaps, it will be needed high-power amplifiers to ensure the wave propagation through the material. This technique is referred as Resonant Ultrasound Spectroscopy (RUS). If these options seem not possible, I still think you should be able to excite the resonant frequencies, or in any case adapt a resonant vibration test to derive the elastic properties. I found this paper

• Renault, A., Jouen, L.,  Sgard, F. Characterization of elastic parameters of acoustical porous materials from beam bending vibrations. J Sound and Vibration 330 (2011) 1950-1963.

In such paper they mentioned the standard

• ASTM-E756-98 Standard Test Method for Measuring Vibration-Damping Properties of Materials

A different test that I think you can use is the Kolsky bar or Hopkinson bar. One example applied to a polypropylene foam:

• Bouix, R., Viot P., Lataillade J-L. Polypropylene foam behaviour under dynamic loadings: Strain rate, density and microstructure effects. International Journal of Impact Engineering,  2009, 36, pp.329-342.

I didn't ask. Are you able to produce different shapes in your samples, or in constrast, you have a preset shape that you cannot modify?

Regards

Thanks you all.

Let me remember that I have a budget for buying the relevant device. I have no workshop to develop my own devices and methods. If you are aware of commercial apparatuses adapted to absorbing porous materials (hence not for metals, for which ultrasounds techniques work very well), please let me know.

Alain

using AFM, the high resolution one. or the AFM equipped with the acoustic tip.

https://www.researchgate.net/publication/282981783_Ultrasonic_structural_probing_of_products_based_on_materials_with_a_complex_structure_by_analyzing_the_statistical_characteristics_of_the_structural_noise

Article Ultrasonic structural probing of products based on materials...

For highly porous and rigid materials, the methods based on resonance frequencies (ASTM-E1876 and E1875) are the most accurate choice because they see the specimen as a whole. If you use pulse-echo, you should ensure the wave length is long enough to do not have reflections on the pores. See the video from the link for more information about how the technique from the ASTM-E1876 works (Impulse Excitation Technique).

https://youtu.be/zaoWAKXoSYc

Dear Alain,

Kindly have a look at this paper. 

http://dx.doi.org/10.1016/j.engstruct.2012.10.027

This paper deals with ultrasonic pulse echo measurement in porous materials.You can buy similar equipment's as shown in the paper start the measurements straight away.

Dear All,

I finally found the solution: the quasi-static mechanical analyser QMA-X from Mecanum. It uses a non-destructive method for determining elastic modulus and Poisson ratio of very weak, highly porous, materials. The very low frequency that it is used allows doing this kind of measurement for highly attenuating materials. Moreover, it complies with the ISO 18437-5 standard.

Have a look at the flyer, here attached.

Alain

Dear Alain,

we use the Buzz-o-sonic method reliable and successful on porous foams. This method follows ASTM E1876 and C1259.

Best Tobias