Alternative Methods for Accurately Calculating Elastic Modulus?

[Chris Brown]

I'm attempting to calculate the elastic modulus of some steel samples throught tensile testing. Unfortunately I've come across the common problem of finding a value that is 2 to 3 times lower than the expected value (due to innacurate displacement measurements). Can anyone suggest another method of accurately calculating this value? I'm currently searching for appropriate spring theory formulae whereby the elastic modulus can be calculated from bending the sample around a cylinder of known radius.

 

[Gokul43201]

Can you provide details of your measurement? Are you following the appropriate ASTM Test specs?

Flexural modulus can differ from the elastic modulus in tension, by as much as 20% (from what I've noticed among a small number of cases).

http://www.astm.org/cgi-bin/SoftCart.exe/STORE/filtrexx40.cgi?U+mystore+kcok8713+-L+STEEL:YOUNGS:MODULUS:TEST+/usr6/htdocs/astm.org/DATABASE.CART/REDLINE_PAGES/E855.htm

The simplistic calculation described below should get you pretty close:
http://www.engineersedge.com/strength_of_materials.htm

 

[Chris Brown]

Calculating Youngs Modulus

Thanks for the reply. I'm not familiar with the ASTM test specs. Here's some of the data for one of the tests

Mild Steel sample:
Displacement (mm) / Load (kN)
0 / 0
0.5/ 1.125
1/ 1.88
1.5/ 1.91
2/ 2
2.5/ 2.08
3/ 2.125
3.5/ 2.21
4/ 2.23
4.5/ 2.25
5/ 2.26
5.5/ 2.27
6/ 2.28
6.5/ 2.28
7/ 2.28
7.5/ 2.27
8/ 2.265
8.5/ 2.255
9/ 2.25
9.5/ 2.2
10/ 2.18
10.5/ 1.66

 

[PerennialII]

...yeah, hate when system compliances cause trouble and/or when material behaves in a nonlinear manner "when it should not" [if these happen to be your problems] . Usually the estimation is most inaccurate near the origin and at near yield, one very simple method have seen used to decrease the sensitivity is that first you compute E on the basis of force and displacement at origin & near yield strength, then you do the rest of the analysis as a function of the points of evaluation so that in the end you end up with a contracted range of force & displacement (nearly a single point) at about half yield strength (so 1st calculation of E is done at [0, yield] - stress, next at [0+small number, yield-small number], ...). And with any luck you'll have a somewhat convergent value for E. When using tensile data to determine E have seen people use such & similar methods to rid themselves of the inaccuracies, or at least improve their results (surprisingly it helps a bit).

 

[AlephZero]

That looks like a believable yield curve - but if you want to find the elastic modulus, you have only got one point (disp = 0.5 load = 1.25) that might be in the elastic range, or might not. So it's not surprising your answer isn't as you expect.

Estimate the strain and load at the yield point, then measure a reasonable number of points (e.g. 10 or 20) with loads and strains below that value.

 

[FredGarvin]

The first thing I always check now is the extensometer (that has bitten me in the past). If you have any take-up that will throw off the initial part of your plot. Like Perennial said, system compliances...

Also, I think Aleph has a good point about your methodology for the test. If you are simply calculating the elastic modulus, why bother taking the part to yield? Estimate what the yield point would be and then work below that in the linear range.