Mohrs Circle, Von Mises and Minimum Yield Strength Help!by Mairi Tags: mohrs circle, von mises, yield strength 

#1
Nov2112, 11:14 AM

P: 5

Hi
Wasn't sure where to post this, hope it's ok in here! I've gotten myself very confused as to how to find the minimum yield strength for an element. I have used Mohrs circle to find sigma1 and sigma2, then plugged that into the von mises equation to find sigmavon = 636.8MPa. The textbook gives me the answer of minimum yield strength of 660.4MPa, but how do I get to that? I've checked and double checked my sigma1 and 2 answers (610.2 and 50.2)and I think they are correct. Not sure where to go from here and neither lecture slides nor textbook are helping much! Thanks! 



#2
Nov2112, 12:53 PM

P: 5,462

Hello mairi, welcome to Physics Forums.
What values of sigmax and sigmay (and tau if they exist) did you start with? 



#3
Nov2112, 04:42 PM

P: 5

Woops might have been an idea to state that in the first place! Sigmax was 560MPa, sigmay 0MPa and tauxy was 175MPa.




#4
Nov2112, 07:54 PM

P: 5,462

Mohrs Circle, Von Mises and Minimum Yield Strength Help!
Well I agree with your figures for both the Mohr circle and by direct calculation.
Incidentally you do not need a Mohr circle for the stress state indicated. If σ_{y} = 0 then Von Mises can be written [tex]Y = \sqrt {\sigma _x^2 + 3\tau _{xy}^2} [/tex] as an alternative to the formula using σ_{1 }and σ_{2} So I would be interested if you have a reference or could post more of this book. 



#5
Nov2212, 02:48 PM

P: 5,462

Are you sure you haven;t got the Tresca and Von Mises ctiteria mixed up?
The formula for the Tresca max stress is [tex]Y = \sqrt {\sigma _x^2 + 4\tau _{xy}^2} [/tex] or the max difference of principel stresses. Either way that works out to the 660.4 MPa in your book. 



#6
Nov2312, 04:44 AM

P: 5

You're absolutely right, I didn't register that the question was asking me for the maxshearstress theory not maxdistortion energy! Silly mistake!
But thank you :D 



#7
Nov2312, 05:37 AM

P: 5,462

They are actually both shear stress theories, but offer different estimates of the maximum shear stress encountered, given a particular state of stress at some point.
The Tresca method estimates the actual max stress as being (slightly) higher than does the Von Mises theory. Are you comfortable with how this leads to the the conclusion that Tresca is more conservative or that the failure envelope is smaller? 



#8
Nov2412, 05:22 AM

P: 5

Yes that makes sense. Thank you!



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