Mohrs Circle, Von Mises and Minimum Yield Strength Help

[Mairi]

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 sigma-von = 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!

 

[Studiot]

Hello mairi, welcome to Physics Forums.

What values of sigma-x and sigma-y (and tau if they exist) did you start with?

 

[Mairi]

Woops might have been an idea to state that in the first place! Sigma-x was 560MPa, sigma-y 0MPa and tau-xy was 175MPa.

 

[Studiot]

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

$$Y = \sqrt {\sigma _x^2 + 3\tau _{xy}^2}$$

as an alternative to the formula using σ₁ and σ₂

So I would be interested if you have a reference or could post more of this book.

 

[Studiot]

Are you sure you haven;t got the Tresca and Von Mises ctiteria mixed up?

The formula for the Tresca max stress is


$$Y = \sqrt {\sigma _x^2 + 4\tau _{xy}^2}$$


or the max difference of principel stresses.

Either way that works out to the 660.4 MPa in your book.

 

[Mairi]

You're absolutely right, I didn't register that the question was asking me for the max-shear-stress theory not max-distortion energy! Silly mistake!

But thank you :D

 

[Studiot]

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?

 

[Mairi]

Yes that makes sense. Thank you!