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What mean mid principal stress?
in practice?
Here are my thoughts on this.
For a 3d model the stress has 6 components.
Principal space is just a rotation of the coordinate system for stress and still has all 6 d.o.f. of stress.
Various failure theories use the 3D stress state, either generically or in principal space.
For example Von Mises has a general formula and a principal space formula.
See summary table https://en.wikipedia.org/wiki/Von_Mises_yield_criterion
The principal space formula uses the Mid Principal stress.
Also I find this a good reference. (also in textbook form) It has nice 3D plots showing failure envelopes in 3D principal stress space.
https://www.failurecriteria.com
I believe the Mid Principal communicates hydro-static stress as well.
I think in practice mid principal is rarely used by itself but it is available for the fully defined 3D state of stress.
Maybe one could generate or use failure theories different than the built-in CREO failure theories.