Dear Khalid, Young's modulus, E, can be calculated by dividing the tensile stress by the extensional strain in the elastic portion of the stress–strain curve. You can get it with a help of nanoindentation. Also you can use wave propagation methods (ultrasonic echo-pulse method), static (tensile, torsion, bending test) and dynamic (resonant frequency method) methods.

possible ASTM procedures to follow are these:

C1198 (continuous) or

C1259 (impulse)

From the mass density and two sound velocities (longitudinal and transversal) you can calculate all elastic moduli and Poisson's ratio of the ceramics. A flat plate of 5-15 mm thickness is fine. You need a ultrasonic pulse generator and sensors plus an oscilloscope to perform the sound velocity measurements.

For ceramics materials the direct and well-known static mechanical bending test is preferable. Then you can compare results (module elasticity) of bending test with data obtained by dynamic (f.e. sound) method or by indentation mentioned above and obtained on the same samples (prizmatic plates or rodes)

Dear Khalid：

The elastic modulus  can also be measured by the impulse excitation technique. In this method, the sample is given a mechanical impulse and the vibration is detected by a microphone, then analyzed with the resonance frequency and damping

analyzer, which is a standard testing method for dynamic Young’s modulus,

shear modulus, and Poisson’s ratio by sonic resonance. The

Young’s modulus was calculated from the flexural resonate

frequency, fF, according to ASTM E1876-9727. 

I have several paper on measuring the Young's modulus of ceramics. Hope they are useful to you. 

you can obtain young modulus by three or four bending test

its the most right value than other methods like grindosonic or ultrason

However, in practice for some ceramic materials, including zirconia, static Young's modulus is not independent on stress magnitude (non-linear elasticity)... This is because of "crack containing" microstructure... Plus the anisotropic factor, which is always inherent to any ceramics prepared by pressing-sintering or hot-pressing procedures... So, you have to be ready to face a lot of troubles on your way of obtaining true results...

we have an instrument based on the impulse excitation technique (see ASTM E1876 and C1259) - contact me for more details if you are interested  or visit our website

For materials with high modulus of elasticity (Young's Modulus) like zirconia, the methods based on resonance frequencies (ASTM-E1876 and E1875) are the most practical and accurate choice because of the low stress and strain involved, specially the Impulse Excitation Technique (ASTM-E1876). See the video from the link for more information about how the IET works.

https://youtu.be/zaoWAKXoSYc

Yes, I agree that the Impulse Excitation Technique is a good way to go (ASTM E1876 and C1259...) - see www.buzzmac.com

Paul

-------

Dr. Paul Bosomworth

President/CEO

BuzzMac International LLC

Ph (US): 414-352-5419

Ph (UK): 020-7193-5249

FAX (US): 253-540-9798

Erik Carton :

Dear Dr. Erik,

Thank you for your suggested method. I would like to know which standard or article that explain this technique?

Thank you for your help.

Hanh

Dear Hahn,

I am sure there must be standards for determining elastic moduli using ultrasonic techniques. But it is rather simple in principle: You need to accurately determine the material thickness H (the thicker the better). Then you apply a ultrasonic transducer on one of the free surfaces (using a coupling agent in between). The transducer can both emit and receive ultrasonic pulses which travel with the speed of sound through the thickness and reflect from the opposite free surface.

The time between the emitted pulse and its reflection (dt) took the elastic wave to travel twice through the sample. Hence: C = 2H/dt

Depending on the wave the transducer emits (longitudinal or transversal waves), you can determine the longitudinal and transversal sound velocity of the material.

Together with the mass density (rho) of the material you can calculate the elastic properties (E, G, K and Poisson's ratio).

What you need is two types of transducers, two coupling agents and an oscilloscope to measure dt.

We use NASA's method for material properties. I don't know their method number, but a 1 page full explanation is attached with all the formulas