# Von Mises stress Vs Principle stress

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1. Jan 15, 2015

### Saumya Kar

Hello Folks,

May be I am bring up the old topic again., but I've lost enough sleep over this topic. I understand that we use Von-Mises criteria for ductile material failure by comparing to yield limit and max principal stress is used to check failure for brittle materials. My question is bit more basic in nature.

By principal stress do we mean perpendicular stress acting on X, Y & Z planes ? Or it is combination of all three components ? Do we also consider shear stress ζx, ζy & ζz in calculating principal stress ?

Is Von-Mises stress a real stress value, or its kind of an index which is calculated to check for failure criteria ?
If yes, what is the physical significance of Von-Mises stress ?
Is it only used as a pass fail criteria to understand if the component will pass or fail or we can extract additional information (such as fatigue life) ? How ?
Is Damage factor (calculated from FEA) related to Von-Mises stress ? How ?

I might be asking basic questions (and a lot of them), but need to sort things out once and for all.

Regards
Saumya

2. Jan 15, 2015

### timthereaper

1. Principal stresses are the stresses normal to planes where there is no shear stress acting in that plane. Cauchy says that the stress vector is equal to the product of the stress tensor and the normal to the plane ($\mathbf{T} = \mathbf{\sigma}\cdot\mathbf{n}$).. The stress tensor is where we get our notions of $\sigma_{11}$ and so on. If a stress vector isn't parallel with a normal to an arbitrary plane, we call the component in the direction of the normal the "normal stress" and the component of the vector in the plane a "shear stress". So mathematically, there are 3 planes in a material where the stress vectors and the normal vectors are the same, so in those directions there is no shear stress. Those planes are called principal planes and the stress vectors are called principal stresses.
2. We use the term "Von Mises stress", but what we're really saying is that we want to use the von Mises yield criterion to determine yielding (sometimes this is used for failure). The von Mises criterion just uses the principal stresses to compute an equivalent tensile stress in the material so we can do a simple comparison with the tension allowable for the material. Physically, it says that when the stress is up above some critical value, there's enough strain energy in the material to make it yield. This is called the "maximum distortion strain energy criterion". Typically, using von Mises is a pass/fail check.
3. Fatigue life isn't determined by von Mises. Typically, fatigue is caused by cyclic loading well below the ultimate tensile stress limit (UTS) and von Mises is used for stresses close to the UTS.
4. Not sure what you mean by damage factor. I know of a lot of types of damage, so you might need to be more specific there.

Wikipedia is your friend. A lot more information is there in those specific articles. Check it out if you want to know more about anything I've talked about.

-Tim

3. Jan 15, 2015

### Saumya Kar

Thanks a lot Tim,

This really helped.

For damage factor, I was referring to fatigue life analysis where for the design to be safe, damage factor needs to be below 1. I am not sure if it is referred with any other name.

Regards
Saumya