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Principal stress in plastic region

Principal stress in plastic region

Principal stress in plastic region

Good Morning,
I run a 3D non-linear analysis in Nastan using SOL106.

The volume is modeled with CTETRA elements while CTRIA3 exist on skin.
Part is loaded in traction.

Material used is a steel for which an elasto-plastic curve - like the one shown here below - is used:
Further, MAT1 and MAST1 with PLASTIC option at field 4 is used.

I run 4 analyses:

- @ 50% of load
- @ 100% of load
- @ 150% of load
- @ 2000% of load

At critical site, I extracted Von Mises and Max principal stresses,(sigma1).
Here is what I get when I superpose Von Mises stresses on material curve.

Here is what I get when I superpose principal stresses on material curve.

Could anyone explain why VM stress follows the curce and Principal stress does not, (in plastic region this is evident) ?
Do I need to rotate material properties in principal stress direction in the second graph?

Thank you for you help ans suggestions.

RE: Principal stress in plastic region

are you specifying (or is the FE defining for you) that the failure theory is von Mises stress ?

noting that (however) von Mises is a linear stress failure theory.

the "odd" thing to me is if the part is loaded in simple tension, where are the other principal stresses coming from ? (as von mises is the combination of the three principal stresses).

But that said, von mises is the better failure theory (IMHO) if you have a multi-axis stress field, as a way to account for the interaction between the stresses; in your case you seem to have tension is the other directions (if you had compression then max principal would be less than critical). If you have a uni-axial stress then von mises collapses to max principal.

another day in paradise, or is paradise one day closer ?

RE: Principal stress in plastic region

There are multiple plasticity material models but the most common is von Mises model. It is assumed
that yielding occurs when vm stress exceeds yield strength.


In multiaxial loading conditions it is possible for maximum principal stress to exceed vm stress.

Check also for other principal stresses if they exist because of for example a fixed
boundary condition.

RE: Principal stress in plastic region

I had understood that von Mises is a reasonable predictor of yielding (or the onset of plasticity) in metals, but it's use as an ultimate failure theory (ie von Mises stress = ftu) was convenient (and conservative) but not strictly correct.

another day in paradise, or is paradise one day closer ?

RE: Principal stress in plastic region

My guess is that your solver is using the von Mises stress as the determination of where on the curve the elements are, this is directly enforcing it to stay on the curve. After solving in this manner, you have some sort of multi-axial behavior occurring as stated by others which is changing your Max. Principal Stress to be above the others. Why not take an element or node and look at the shears and normal stresses and plot Mohr's circle? I've done this quite a few times when confused,but it's always pointed me in the right direction and shown me the contributing factors, and once I check the reason for each of the normals and shears, if they seem out of line, I always find what I'm looking for.

RE: Principal stress in plastic region

Hallo Marc
Nicely described question.
I think what is happening, is that although the part is in tension in say the x-dir., there is developing a tensile stress in the perpendicular or y-dir. due to Poisson's ratio (it wants to contract but is restraint from doing so by say a strong shoulder). E.g. a s1=1 plus s2=0.3 would give you a Svm=0.9

RE: Principal stress in plastic region

principle stress is a different animal than von misses stress. principle stress is obtained from the Mohr's circle where von misses takes the average of the square of the principle stresses.

disclaimer: all calculations and comments must be checked by senior engineers before they are taken to be acceptable.

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