Calculation of Young's modulus
Calculation of Young's modulus
(OP)
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
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





RE: Calculation of Young's modulus
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
RE: Calculation of Young's modulus
RE: Calculation of Young's modulus
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
RE: Calculation of Young's modulus
I think least squares from 250 to 2000 ue should be fine.
RE: Calculation of Young's modulus
RE: Calculation of Young's modulus
I like your suggestion. Can you provide a reference for your suggestion, or is it just based on your experience?
briancanadien
RE: Calculation of Young's modulus
RE: Calculation of Young's modulus
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.
RE: Calculation of Young's modulus
briancanadien
RE: Calculation of Young's modulus
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.