Signed effective stress

[xlxc34]

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.

 

[rb1957]

why not just principal stress ? max major, min minor

 

[TERIO]

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.

 

[xlxc34]

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.