Calculation of Young's modulus

[briancanadien]

Hi,

I'm trying to measure the Young's modulus as per ASTM standard 638 for reinforced plastics. I have in Instron Machine with Axial extensometer returning load and strain values.

The standard says the following with regards to the calculation of Elastic (Young's) Modulus:

Calculate the modulus of elasticity by extending the initial linear portion of the load extension curve and dividing the difference in stress corresponding to any segment of section on this straight line by the corresponding difference in strain.

The problem is the initial portion of the curve is non-linear. Long story, but my area of interest of from 0 to 2000 micro strain (ue). When I do least squares best fit on 250 to 2500 ue I get a reasonable fit to the line. When I include 0 to 250 ue, the initial curved area of the line makes my line of best fit poor. At least I think it's poor. Any suggestions on how to proceed? Can I justify truncating the first 250 ue response because because of measurement error at low loading? The attached graph shows a sample plot of Stress vs. strain from 0 to 2500 ue.

Thanks for your input.

briancanadien

 

[SWComposites]

Your "best fit" line does not seem to be a good fit to the curve; how did you generate it?

Why don't you just draw a line from (0,0) to (2500ue,stress)?

And there does not appear to be a classical "toe" at the start of the curve that would be attributed to test fixture/instrumentation displacement

 

[SWComposites]

edit: Why don't you just draw a line from (0,0) to (2000ue,stress)?

 

[briancanadien]

The graph I attached as the best fit to 5000 ue by least squares. Above 2000 ue I get a different failure mode I don't care about so I've started to truncate to 2000 ue. I've attached another graph with the best fit by least squares to 2000 ue; one line is the best fit and one line is best fit with y intercept equal to zero. I put a smidge of preload on to eliminate the toe from the graph.

I'm testing seven different materials for micro-cracks so I started my testing with my worst performing material. That material is showing a lot of variation in Elastic Modulus and a somewhat non linear strain repsonse. When I test my best performing material, I'm getting little variation and an excellent fit by least squares--especially when I don't use from 0 to 250 ue to calculate the line of best fit. I think the poor fit on the worst performing material is probably why it's the worst performing material.

I think I'll just go with not using 0-250ue for line of best fit for determining the Elastic Modulus. Any other comments would be appreciated.

briancanadien

 

[briancanadien]

Drawing a straight line between 0 and 2000 ue is not what the standard says to do. The standard says to extend the initial linear portion of the line. That statement is open to interpretation. What if the initial portion of the line is not linear? I don't believe I would have this non linearity issue if I were testing 1020 steel. I've done some background checking and composite materials can have a non linear response in pull testing.

I think least squares from 250 to 2000 ue should be fine.

 

[Compositepro]

In my experience secant modulus is usually used for composites. This would be a line drawn though the 25% and 75% load points (for example) on the curve. This has the most practical usefulness.

 

[briancanadien]

Compositepro,

I like your suggestion. Can you provide a reference for your suggestion, or is it just based on your experience?

briancanadien

 

[Compositepro]

Secant modulus is defined in D638 but the definition is very flexible and allows you to define what is most suitable. For highly linear materials secant modulus will be the same as Young's modulus. For non-linear materials the secant modulus will be exactly correct at one point, and basically be the average modulus over the specified range of strain (where you specify the range).

 

[SWComposites]

Typically one would use a secant modulus over the typically strain range to be experienced by the structure. The strain range may be much less than the tested range for the specimen, so 25%-75% of max load may not (and likely is not) appropriate.

And trying to detect micro-cracking (unless it is very severe) by modulus measurement is likely a futile exercise; the measurement error is probably larger than what you are trying to detect. Incremental loading (loading up to a series of strain levels, unloading, and x-raying or edge polishing and photoing) will probably work better.

 

[briancanadien]

I'm not trying to detect the fracture during the test. I have failing stain (Weibull Beta & Eta) for seven different laminates under monotonic spherical bend. The testing is extremely expensive so I'm trying to correlate the B0.1 lives to the base material properties in order to evaluate different vendor materials more efficiently. My materials have Young's modulus ranging from 15 to 28 GPa as determined by the Secant method. The lower Young's modulus in general are performing better, but it's not giving me the whole picture. I'm probably going to do some micro-indentation hardness on the resin rich layer on the outer layer of the laminate to see if that tells me anything else. Any other suggestions would be appreciated. Thanks for your help.

briancanadien

 

[SWComposites]

Huh?

you state you are using ASTM D638 which is a tensile test, then state you have failure strain under bending? and how are you doing "spherical" bending? do you mean cylindrical (2D) bending, or some sort of 3D bending?

you first talk about static tensile and bending tests, then mention "lives" meaning presumably a fatigue type test; confusing.

what is your specific measure of "performance" that you are trying to evaluate?

I can't see how a hardness test would be useful, but perhaps you could describe all of your testing and performance measurements.