Fatigue with signed von Mises stress 2

[Joel Lapointe]

I just saw a method for calculating the fatigue with Goodman diagram which involves the equivalent von Mises stress.
Normally, von Mises is only positive. Those 2 methods allows to add a "sing" to the von Mises value.
Method 1:
- Take the diagonal of the constraint tensor : diag([s_ij]) = [S1, S2, S3] the principal stresses.
- By convention, the principal stresses are arranged by order of stress magnitude: S1 the biggest stress, S3 the smallest stress and S2 in between S1 and S3.
- Calculate the trace of the tensor: trace([s_ij]) = S1 + S2 +S3 the sum of the principal stresses.
- Take the sign of the trace. If trace is negative than this is compression state.
- Apply the sign on the von Mises value: (sign trace)*(vonMises value) = signed von mises
- Calculate Sm (averange stress) and Sa (amplitude stress) on the variation of the signed von Mises stresses

Method 2:
- Take S1 and S3 the extrema of principal stresses.
Note: S1 is always S1 > S3 by definition.
- The sign is taken from the highest magnitude between S1 and S3. sign(max(|S1|, |S3|))
- Apply the sign on the von Mises value: (sign trace)*(vonMises value) = signed von mises
- Calculate Sm (average stress) and Sa (amplitude stress) on the variation of the signed von Mises stresses


The problem is that, it can give different signs. This is an example:

The principal stresses are: S1 = 1.2, S2 = -0.8, S3 = -0.9
The 2 methods do not agree.


Here are some literature on the 2 methods.
(Link 1) at page 4
(Link 2) around page 24
(Link 3) section 2.2
(Link 4) section 3.1 (they doesn't seems to take principal stresses, they seems to take Sx, Sy, Sz the normal stresses, why?)


Some body has an idea on which method is the best?

Thank you very much.

 

[SWComposites]

Seems like rubbish. Putting a negative sign on VM stress makes no sense. And further VM is a yield criteria, which doesn’t apply to fatigue. Just use max principal stress for metal fatigue.

 

[TheTick]

I'm glad someone smarter than me said what I was thinking.

 

[Sparweb]

Has anyone ever used complex numbers in stress analysis before?
What would it even mean?

 

[dik]

Rather than think of them as complex, it's time to revert again and call them 'imaginary'...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[rb1957]

where did complex (or imaginary) numbers come from ? I think the OP is thinking if my principal stresses are -ve, how do I get von mises stress to be -ve ? (just take the -ve sqrt ?)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[swimfar]

I agree with the other replies. But just because it's bothering me, I wanted to point out that method 1 is overly complicated. It's effectively just taking the sign of the trace of the stress tensor, which is the same as the sign of the hydrostatic stress. There's no need to have the principal stresses, or worry about what order the three stresses are in.

PS Good job on providing references to your methods, instead of just saying, "I have read..." etc.