Strain hardening ratio

[Sh3das]

Hello friends,

I have a question and I will so appreciate if you can help me to figure it out.
I want to define material by defining stress-strain curve for ASTM992. In some finite element program I saw they used bilinear stress strain curve which strain hardening is 0.02E.
but according to this formula which is make sense:
strain hardening modulus = Ultimate Strength - Yield Strength/((Elongation at 2 in)/100 - yield strain)
For A50
yield strain=50/29000=0.00172 and elongation at 2 in for A572 grade50 = 0.21
Therefore:
Strain hardening ratio modulus=(65-50)/(0.21-0.00172)=0.002 which is not equal to 0.02.

I am really confused, because I got very different results with 0.002 and 0.02, and I do not which one is really correct. I will so appreciate if anybody can help me to figure it out.

Thanks,

 

[realtime2]

It seems that the formula is something like (y2-y1)/(x2-x1) = slope
where x1,y1 is the yield point and x2,y2 is the ultimate (true stress or engr. stress?)

The problem may be that "%Elongation 2 in" means total elongation of tensile test
using a 2 inch gauge length.
Probably a better estimate for x2 would be: what is the strain at the ultimate stress?

However if the elongation is "uniform elongation" then that would be the Engineering
strain at ultimate Engineering stress.

Unfortunately for most plastic FEA models you are probably suppose to use True stress
rather than Engineering stress ? also the True strain rather than the Engr. strain.


Best method is to plot the engr. stress srain curve AND the true stress strain curve
and measure the slope of the strain hardening region using which ever co-ordinate system the FEA
program requires..