Dear Arash;

I am dealing with the same issue, according to the instrumented nano-indentation results. I think in is mainly due to the fact that the micro/nano-scale mechanical tests are not sensitive to the crystalline and macro defects in the structure. about the maco-compression test of ceramics and glassy materials, as you know, the results are highly depended on the macro-scale defects, i.e porosity, segregation and inclusions.

It is impossbile to obtain the modulus different in orders merely becuase of defect. You can measure Young's modulus through impulse excitation technique (IET) which is more accurate. I recorded the data of your picture and obtained the Young's modulus is 23.9GPa other than 26.1GPa. Thus, your experiments should be re-examined. You may invite some partners to moniter the experiment processes.

If because of defect, the defect ratio can be estimated as 1-26/170≈85%. It is impossible for a well-made BMG.

I agree with Mr. Jianbiao Wang

The differences between the different methods are due to a scale effect.

This effect does not only consider the presence of defect, but is also influence by the heterogeneity of the structure at the microscopic scales.

The engineers value is the one obtained by macro compression tests.

Glass like concrete have high modulus in compression and the discrepancies in result obtained may not be unconnected with defects are suggested by Wang

Hello Arash,

What is the "micro compression" test ?

Although the magnitude of difference you report is large, differences between those measuring methods could be explained physically.

In my field, provided that measurements are ideals and that the exact same medium has been probed(*), two main physical causes have been shown to induce lower "static" than "ultrasonic" Young's moduli: the frequency and the amplitude of measurement.

Frequency:

if your solid is viscoelastic (e.g. plexiglass) or poroelastic (e.g. fluid-saturated rocks), an increase in elastic moduli is expected as the frequency of measurement increases. Because typical "static" measurement are at low strain rates (frequencies typically of about 1Hz), there could be a difference in frequency of up to six orders of magnitude with ultrasonic measurements.

In our case (of fluid saturated rocks), we did measure values almost three times larger solely due to an increase in measuring frequency.

If your material is measured at high temperatures, viscoelasticity could be a good candidate.

Strain amplitude:

Large dependences could be expected in some cases, and particularly when defects are present. The underlying explanation is simple. Elastic constants/moduli are defined by partial derivatives ('d'). However, what we typically measure in the laboratory are variations ('Delta') of - sometimes - large amplitudes. The approach holds in lab experimental life only if 'd'(l)='Delta'(l), (hence linear elasticity).

In some rocks, in the extreme case, it is considered for instance that dependences to the strain amplitude could appear starting from strains as low as about the micrometer/meter (10-6).

Best,

Lucas

(*) from static measurements, I guess you corrected for the apparatus compliance !? if the apparatus is very compliant and the sample very stiff, the "apparent" strain measured is largely affected by that of the apparatus rather than that of the sample.

(*) from ultrasonic measurements, crystals/defects need to be much smaller than the wavelength probing the medium. At ultrasonic frequencies, and relatively high P-wave velocities, the scale should be in the range of few millimetres. In rocks, for instance, this holds only when crystals size are in the sub-millimetre range.

Hello all,

Thank you for your input. Below, I have provided a brief explanation to your comments.

The Young’s modulus of 26.1±0.54GPa is the averaged number of 8 independent measurements which is slightly different from the slope of a typical stress-strain curve attached to the question.

I have tested 8 specimens, at room temperature, with two different machines, run by two operators, and at two different laboratories. So, I am confident in the validity of measurements.

In the micro compression test, we compress micro pillars with a micron size. I used FIB to make cylindrical pillars with a diameter of 3um and a height of 8um and then compressed them in the nano indentation machine.

Lucas: You are suggesting two sources for the overestimation of E values from ultrasonic measurement. I am not sure if these numbers are off. Basically, Fe-based bulk metallic glasses have a Young’s modulus above 200GPa. Even if frequency and the amplitude of measurement are playing a role, how much would be the percentage of the error that they cause?

This Fe-based bulk metallic glass shows a very strong size-effect (about 200%), meaning that the difference between the yield strength at micro and macro scales are about 200%. It is well-known that the size effect in bulk metallic glasses and their composites is related to a lower density of defects (porosity, cracks with a length below the critical one, and so forth) at micro scale which provides a higher strength. According to the literature, the Young’s modulus is almost independent from the sample size since it is associated with the nature of bonds between constituent elements. This convinces me that such a huge difference between the Young’s modulus values (Macro compression Vs. micro compression/ultrasonic) dose not have much to do with structural defects. Instead, it is related to the compositional fluctuations in the amorphous matrix (or heterogeneity of the structure at the microscopic scales). Devitrification of nano crystals during the sintering process can create regions that are either rich or poor of specific elements which induce microstructural heterogeneity. But if this is the case and the results of macro compression test are affected by microstructural heterogeneities, then how come that ultrasonic measurement is not affected by such heterogeneities? Micro compression test involves a small volume of material that contains much less heterogeneities compared to a bulk sample. Hence, it is expected that results of micro compression test will not be significantly affected. But what about ultrasonic measurements?

My conclusion is that the huge difference in measuring E, originates from microstructural heterogeneities. However, it might not influence all measuring methodologies to the same extent.

Please comment on my comments!

Hello,

I never looked at heterogeneity effects, so I am getting quite interested in following answers.

An additional thought: Could there be some anisotropy in your glass?

If the direction of measurement differs, heterogeneity that induces anisotropy could be a good candidate !?

First, I would argue that - to me - it is not that one measurement "overestimates" the properties. It is simply that different states (or elastic regimes) are measured. Personally, I am equally interested in those regimes.

In my case, of rocks that I chose isotropic and homogenous at the mesoscale (REV), the two physical effects originating from "frequency" and "amplitude" effects are linked to the presence of "defects": micro cracks or open grain contacts.

For the exemple of what I address as "frequency" effect that I studied during my PhD. At low frequency, the sample measured is "relaxed". At high frequency, it is "unrelaxed". In the specific case of a liquid-saturated rocks (i.e. poroelasticity), the macroscopic changes in elastic regimes link to relaxation mechanisms of the fluid pressure in the pore network, i.e.: At low frequency, fluid has time to equilibrate in the network, At high frequency, it has no time to anymore.

In a natural fluid-saturated sandstone, we measured dispersions (D=(Emax-E0)/E0) that could reach above 100% (e.g. squares in Fig.11, Pimienta et al., 2015; Experimental study of Young's modulus dispersion...). It could be more if for instance my solid was made of crystals/minerals of Young's modulus much higher than that of quartz (as is the case in my sandstones).

For the "amplitude" effects, I am currently researching on those to find cases where large differences could be found between dynamic and static measurements :-)

Hoping that it helps,

I think in the study of the young modulus value of a material to any load always has a difference. The question is how big, is it still within tolerance or greater. The problem and need to think about further if the difference is too large.

Hello Arash,

Regarding your stress-strain curve, what is the unit of the strain (1 or percentage)? For Fe-BMG synthesized by SPS, I think it is reasonable that the figure shows 1.1%, if it's 0.11, 11% we say, it's not possible. With a 1.1% strain, the E can be ~ 230 GPa.