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Signed effective stress

Signed effective stress

Signed effective stress

(OP)
Hi,

I'm developing an in house code for analysing polymers.  The algorithm I'm using to check when failure will occur is temperature dependent, so we need a formula for calculating how much the temperature will rise due to stress cycling.  I've found the formula

Temp=TempAmbient+Psi*(EffectiveStress)^2/(CyclePeriod)^2

Which is fine for uniaxial stress states, but complex stress states can exist in the polymer.  The effective stress needs to be capable of representing compressive stress (so that a stress that has a high amplitude but zero mean increases the temperature more than one that has low amplitude and high mean), so the Von Mises isn't suitable.  I was considering the hydrostatic stress (Sigma 1+Sigma 2+Sigma 3).  Any thoughts on this?

Thanks for your help.

RE: Signed effective stress

why not just principal stress ?  max major, min minor

RE: Signed effective stress

I'm not sure I've understood the basis of your proposed equation, but a few thoughts:

- The energy (per unit volume) dissipated per cycle is the area enclosed by the stress-strain curve (or effective stress-strain) nearly all of which is dissipated as heat.  
- Specific to your question maybe an effective stress range would be appropriate, i.e., subtract the stress components at stress state B from stress state A and find the Von Mises stress of the differences.  
- I'm not a polymer guy but I do not think the hydrostatic part of the stress is appropriate.  

RE: Signed effective stress

(OP)
Thanks, I've actually decided to use the signed von mises stress (I found it on the fatigue part of the Ansys website).  In Excel code:

SignedVM=if(abs(Sig1)>abs(Sig3),sign(Sig1),sign(Sig3))*VM

You're right about the energy in the stress strain curve, the original formula in my first post is derived from a formula from the energy not retained which uses the "loss compliance" of the polymer.  Psi in the equation above is a catch all value that accounts for the  thermal conductivity, loss compliance etc.

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