Material Models: Piecewise Linear Plasticity

[Ed93]

Hello everyone,

Currently I am investigating the crush behavior of thin walled tubes. Therefore I am doing some analysis with ANSYS/LS-Dyna.
I have a brief question concernen the Material Model 24 (Piecewise Linear Plasticity):

First of all I have obtained a true stress vs. true strain curve for my material (AA6060 T6). Since I have to insert a effective plastic strain vs. effetive stress curve I have transformed it by subtracting true_stress/E. It wasnt excatly 0, thats why I have subtracting the remaining strain as a constant factor from the curve, so that it starts at 0. I hope my method is correct so far. The problem is, that the true stress vs. true strain curve is only defined up to the point of ultimate stress. Does it make sense to assume a perfect plastic behaviour after this point or is it better to extrapolate the remaining curve e.g. with the Voce-Equation? I have compared both results and the results with the voce equation show a way more ductile behavior for some reason.

Does anyone know some advice for me? In papers und in literature the insertion of the material data is not properly explained.


Thanks in advance for your help!

Ed93

 

[NRP99]

Ed93
Don't know much about the Voce-Equation, but logically by extrapolating the curve you are increasing the ultimate point of true stress-true strain curve which is illogical.

After ultimate stress there is constant increase in strain without any increase in stress. So curve should be straight horizontal line depicting perfect plastic behavior.

 

[realtime2]

The ultimate stress (Su) occurs at the point where localized necking
begins. If one places a diametral extensometer at the neck one
could follow the stress and strain beyond Su. It is not often done.

If you are not modeling localized component necking then the Su is
probably the best place to limit the loads or stresses.

If your analysis accounts for component
localized necking then the extrapolation beyond Su
(eu,Su converted to true strain and true stress ) is to the
[pre]

true fracture stress (Fracture load / fracture area Af)
and the
true fracture strain ( ln(Ao/Af) )
where
Ao is original cross section area,
Af is final cross sec. area.
[/pre]

 

[Ed93]

Thank you for your replies!

I will assume a perfect plastic behavior after the Su like you suggested. I have compared both approaches and the extrapolated curve led to worse results. I am not interested in material failure or necking, I am trying to model the crash behavior of a thin walled tube. Mostly I am interested in the amount of energy which can be absorbed and the Force vs Displacement curve.

Many thanks for your helpful advices!

 

[rb1957]

doesn't a true stress correct for necking ? (as opposed to engineering stress, based on the original area)

does the FEA like perfectly plastic material ? I'd've thought that it would ... have a nervous breakdown at the sight of a zero stress/strain slope.

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

 

[Ed93]

Hi rb1957,

what excactly do you mean by your first statement? True stress is based on the actual area, thats why FEA need true stress vs true strain curves.

Yes it does, it is the default. If I define the true stress vs true plastic strain curve up to a certain epsilon value, a perfect plastic beviour after that is assumed automaticly (horizontal line).

 

[nlgyro]

You say you want to model the true stress vs true strain curve for your material which is aluminum.

One of the corner-stones of the theory of plasticity (for metals) is the Drunker's Stability postulates which states that:

"Consider an element initially in some state of stress, to which by an external agency an additional set of stresses is slowly applied and slowly removed. Then,during the application of the added stresses and in a cycle of application-and-removal of the added stresses, the work done by the external agency is non-negative."

In your situation, after UTS, the stress-strain curve has a descending branch which follows a strain-hardening section. In the descending section, the strain increases with decreasing stress. In other words, the additional stress does negative work. The behavior of this kind is called unstable.

The implementation of the theory of plasticity for metals in FE-codes will not support a stress-strain curve that violates the Drunker's postulates.

 

[rb1957]

I was picking up on realtime2's post, which seemed to me to have been met with your original post of "true stress".

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

 

[swimfar]

Yes it does, it is the default. If I define the true stress vs true plastic strain curve up to a certain epsilon value, a perfect plastic beviour after that is assumed automaticly (horizontal line).

This is not what LS-Dyna does. It extrapolates the curve based on the last two points.

 

[Ed93]

This is not what LS-Dyna does. It extrapolates the curve based on the last two points.

Where did you get this information? I could not find it in the manuals. As far as I know LS-Dyna extrapolate only in that way, if there is no true stress for 0 strain defined.

I will test it and define manually the horizontal line to see whether it is extrapolated or a perfect plastic material behavior is assumed. Thanks for the hint anyway!

 

[Ed93]

In your situation, after UTS, the stress-strain curve has a descending branch which follows a strain-hardening section. In the descending section, the strain increases with decreasing stress. In other words, the additional stress does negative work. The behavior of this kind is called unstable.

What do u mean by that? I do not have a descending section in my true stresss/strain curve. Do you mean the engineering stress/strain curve?

 

[nlgyro]

Quoting:

>What do u mean by that? I do not have a descending section in my true stresss/strain curve. Do you mean the engineering stress/strain curve?

No I mean the descending section in your true stress-strain curve for the alum alloy 6060-T6 (see attached picture file)

 

[Ed93]

Ah okay now I know what you mean. My true stress vs strain curve has no descending brach because it is only defined up to UTS.