# What are the different methods to calculate the Young's modulus of a material?

I would like to know about the different methods to calculate Young's modulus of a material (say aluminum or steel)

I would like to know about the different methods to calculate Young's modulus of a material (say aluminum or steel)

- You can use stress-strain curve already available..

Or

if you willing to perform experiment, you can use a standard test specimen, load it on universal testing machine with graph plotting attachment. You will get Stress-Strain graph and from that you can find out Young's modulus.. - Try ultrasonic pulse echo technique;
- Thanks for the reply..Also, would I get the same modulus value using these methods or what could be the variation/ which is more accurate?
- Most accurate method of Young's module determination is recording of curve "sigma-epsilon" of specially prepared specimen during tension test. Inclination of curve in the elastic region gives E : "sigma = E * epsilon" or "E=sigma/epsilon".

Other methods use calibration based on mechanically determined values of E. - Unfortunately, there are significant differences in the elastic behavior of metals based on their cell structures and binding energies. While steels generally have a rather linear load/deflection or stress/strain up to their yield point, aluminum has an ever-decreasing one in a curved fashion. Therefore, for the latter the datum for "elastic modulus" is somewhat arbitrary. Ultrasonic measurements can be made to deduce an elastic modulus for such alloys, but how they would look actually plotted on a load/deflection or stress/strain plot and how they should be interpreted is another matter. I've never performed a comparison myself, but presumably they correlate fairly well with the standard proportional limit method.
- One can also measure the Young's Modulus by non-destructive method. Excite a specially prepared test specimen by a sound impulse and measure the time-decay of the impulse signal. The modulus is related to the velocity of sound. By a set of calculations one can evaluate the modulus.
- note: when acoustic method is used - speed of sound measurement - density of material is needed. Besides, need to be aware of the type of acoustic wave - usually longitudinal wave is taken, but its amplitude is often small compare to transverse wave.

As to stress-strain experiment - have to conduct it according to ASTM standards (experience from thousands of experiments conducted in dozens of laboratories) - since the obtained value of E depends on the methodology of measurements. - If you do it by stress-strain you need to approach it differently than you would a tensile test.

When I do it I take a few steps.

1. modify extensometer for longer gage length, usually 4" or 5" instead of 2"

2. carefully cycle sample loading. start by loading to 50% of yield, then unload to 20%, then relaod and take measurements. This helps take mechanical slack out of the system and assure cleaner data.

3. take multiple tests (5 is my favorite) and verify data.

As has already been noted some materials have poorly defined stress/strain curves. For these the stress level of interest is important. You may need to focus on a portion of the curve only. - You can measure elastic modulus by nanoindentation technique also.
- Try Resonant Frequency Damping Analyzer;
- If one uses an indentation technique then a finite element (or other discrete forms) may be needed to calculate the material properties especially when boundary conditions are relevant. We have development a FREE online finite element simulation tool called nanoindentation and can be accessed at
- Dear Anurag,

Test methods for Young's modulus usually include four types:

1. static (tensile, torsion, bending test)

2. dynamic (resonant frequency method)

3. wave propagation methods (ultrasonic echo-pulse method)

4. nanoindentation

Each method has its own advantages and disadvantages. Also, the measured Young's modulus values are different, even for the same sample material.

Hope it helps!

Best wishes,

Zhong

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