Stress occuring in cooling plastic (settle a debate!)

[DanteBlake]

You have a plastic bar. It has a constant coefficient of linear thermal expansion. The stress-strain curve is non-linear. Now imagine both of these scenarios:

Scenario 1: You heat the plastic bar to 100C. You then fix it at both ends and let it cool to 23C. Let's assume that thermal expansion caused a 1% decrease in length. However, since it was fixed at both ends at 100C, that translates into a 1% strain.

Scenario 2: At 23C, you fix both ends of a plastic bar. You then stretch it to a 1% strain.

Will both scenarios result in the same stress. Or will scenario 1 have a smaller stress due the higher temperatures having a lower modulus. We only care about the end stress at 23C.

 

[Compositepro]

Most plastics will creep quickly at 100C, so it is likely that #1 will end with lower stress.

 

[FeX32]

Assuming it does not creep, and assuming a constant thermal expansion and assuming it is exactly 1% strain after cooling; the stress should be equivalent.

With creep of course the stress changes alleviating scenario 1.


Fe (IronX32)

 

[tienti]

Yes I'd think they have the same strain due to change in length over original length. But creep has an effect

 

[1gibson]

If you remove all the realistic differences in material properties from the equation, then what is there left to debate? 1% = 1% doesn't have much room for interpretation. Or does it....

How are you fixing the ends? With clamps of some sort?

Here is my contribution: If the 1% change in length is for the complete unrestrained bars, and not a description of length between constraints, then the initially HOT specimen has higher strain because it is stretched more between constraints, than the initially COLD specimen. The clamp has a small amount of material on the "outside" of the jaws, and there is more material there for the initially HOT specimen if the clamps are placed at the same distance from the end of each bar. Therefore, less material in between constraints for initially HOT, so it is stretched 1.0001% once it cools.

 

[bobslo]

As 1gibson said:
Theoretically have both cases identical end state!.
But one topic must be pointed out: This is valid only if part can be approximated with a line (beam).

In real world, body have 3-dimensions and temperature expansion works in 3-axis.
Based on that, conclusion is that scenario 1 will produce larger stresses due to additional stresses in other 2-dimensions.

 

[FeX32]

Very good point bobslo. I agree.


Fe (IronX32)

 

[DanteBlake]

I'm not understanding how the other two dimensions come into play. Or why thermal stress is relevant when both bars stress are being measured at the same temperature.

The debate was attempting to answer the following question: When attempting to determine stress at the final RT of 23C ... should you assume the standard 23C modulus for the material or something higher? Like the mid point between 23 and 100 ... 61.5

 

[FeX32]

With no creep the answer has been given, with creep also has been given. Changing Moduls depends on the material, subjected properties etc.


Fe (IronX32)

 

[77JQX]

bobslo, Fex32 - doesn't stretch also work in 3-d, according to the poisson ratio? Not trying to argue - I'm not smart enough for that - but just understand the difference you've explained.

 

[cloa]

Plastics have viscoelastic properties so they tend to stress relax even without creep.

 

[mech2926]

These are my opinions:

In scenario 1, since the bar is 1% longer when you clamp it, it is also 1% wider, so in the end state, scenario 1 is stretched more in the transverse direction at the clamps than scenario 2.

I would use the average thermal expansion coefficient between the two temperatures and the Young's modulus at the final temperature. So if the part is at 23C, then the modulus at 23C applies, regardless of the temperature it was at previously.

I agree with the others that the plastic might relax.

 

[DanteBlake]

This question was actually meant for CAD simulation. So I have the ability to enter a CLTE vs. temperature curve. The problem was which non-linear tensile stress-strain curve to use once the cooling strain was calculated.

So creep is ignored. Also, the bar wouldn't "clamped" at both ends, it would be fixed normal to the direction of 1% strain...leaving the other two directions to allow for free movement.

So it sounds like a halfway tensile stress-strain curve would be wrong.