Plastic flow on the plastic strain under uniaxial cyclic loading? 2

[mador]

Hello! Everyone,

I have a question in working on the Kinematic Hardening on Plastic Deformation under uniaxial cyclic loading.

My question is:

Since it is in the uniaxial cyclic loading condition, can I have the yield surface as a circle on the biaxial stress plane? I guess not, is that correct? Probably, the yield stress potential is merely a point but not a yield potential surface.

If that is true, then can I apply the plastic flow rule to obtain the plastic strain direction, without a circular yield stress surface but just a yield point under uniaxial cyclic loading condition? As we know, the plastic flow rule is supposed to be on the normal direction to the yield surface.

Thanks for reading the question.
Matt

 

[realtime2]

Hi Mador,

Uniaxial cyclic deformation models can use a one dimensional set of
points rather than the 2 or 3D yield surfaces, yes. As long as you
don't go in other directions(multiaxial) the points, and their movement, are adequate
to describe the yield and, if you have small "interruption" cycles amid
the big ones, the material memory events.
You can define the next yield in terms of either stress or strain or
even nominal load. When one of them "turns around" the others go with
it. The turn around points are stacked just like the yield surfaces.
You need to comply with Masing's rule/hypothesis: the cyclic yields measured from
the turn-around points are double the size of the initial loading yields, and
with material memory you can return to the initial curve/path after a
temporary unloading.

 

[mador]

Realtime2, thanks very much for your response.
I can tell that you are an expert in this deformation theory.
I believe that I would bring you more questions on this topic and hopefully I can have your response then.
Thanks again.