Temperature Effects of Elastic Modulus for copper

[FerrariEngineering]

Hello-
I am running a simulation of a simple brazed copper assembly; brazed at 1050°C. I believe the Young's Modulus will drastically change after brazing at this temperature since the annealed state is "dead soft". My analyst colleague is using an annealed value for E of 15E-6 psi, which isn’t much less than cold-drawn. My deflection values are nowhere near the actual measurements I am empirically seeing, and I’m thinking E must be much less. I have located some graphs that do show E decreasing with temperature, but none close to 1050°C. Qualitatively speaking, I can vigorously swing a length of copper annealed at this temperature and see it bend like a noodle, so the E has to be lower. I am comparing to a behavior of something like lead??
Since my simulation model really only requires E in terms of the material properties for deflection, I can’t think what else is causing such a discrepancy?? Other boundary conditions are quite simple.
Anyone have knowledge of material properties for REALLY annealed copper at 1050°C??
Thank you in advance.
Chris

 

[MagBen]

E of cold worked and annealed does not have a big difference. It is unlikely E of annealed Cu lower than 15E+6 psi. I assume you calculated deflection under a load, if the load was too large, it could lead to plastic deformation, and then you should not use E to simulate deflection.

If you bonded Cu with other another material to form a so-called bimetal, due to different thermal expansion coefficient of these two (or more) metals, temperature changes can casue deflection, then you calculate deflection total differently, having more things to be considered.

 

[EdStainless]

If there is deflection then there must be load, what are you using for yield strength at temp?
It is probably something like 100psi, if not lower.
This isn't a modulus issue, it is strength.

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Plymouth Tube

 

[FerrariEngineering]

Thanks for response.
My belief is some analysts (for brazing) are using an incorrect E. I agree the value of E for typically annealed copper (like CF gaskets or home wire) are basically the same at 15E6. But running Cu just below the melting temp, which is common in H2 brazing, the copper become dead soft; easily bendable.
As an extreme, a rubber band has a low E value, so if my copper rod at a furnace-braze condition can be bent magnitudes easier than before braze, wouldn’t the E value decrease?? Running an interpolation of the attached graph indicates a very small E, but who knows if the behavior is linear, hence exploring if some brazing simulation guru has experienced such a requirement??
I’m not sure if some people realize how soft coper can be after brazing. I am evaluating some conditions of a brazed copper assembly pulled under vacuum, and unfortunately, I do not have a lot of real-estate to beef-up the assembly, and my empirical measurements are not jiving with my model using 15E6 for E.
Thx

 

[FerrariEngineering]

Thanks EdStainless.

If I recall, aren’t deflection calculations dependent of E?? Changing the YS will not affect the deflection results, at least not in my simple model. Just looking at simple beam deflection formulas, no strength values, just E….

I am using ~4500 psi for YS which is significantly less than drawn at 30ksi. Value is used by SLAC.

 

[FerrariEngineering]

And I should add I understand this whole E thing is based on Hooke's Law,small delflections and whatnot; the problem is running an FEA model with higher values of E indicate very little deflection, whereas empircal measurements indicate different. So considering if the E value realistically is much less for dead-soft copper, then my first-order simulations may indeed indicate larger displacments, granted maybe large enough requiring some non-linear analysis. My predicament is the E value (if not accurate) is misleading the initial model to be linear.

 

[Compositepro]

Ferrari, I think you are confusing the observed effects caused by yield strength versus modulus. For example, all steels have very similar Young's Modulus. The difference between spring steel and soft bailing wire is the yield strength.

 

[FerrariEngineering]

Would you agree that modulus will decrease with increased temperatures, along with yield strength??

 

[Compositepro]

yes.

 

[FerrariEngineering]

Thanks Compositepro; I really appreciate all the comments.
So I understand a linear FEA model requires only elastic modulus and poisson’s ratio for stress distributions, displacements, etc. And if the stress ends up exceeding the YS of the material then the model is non-linear and additional information is required, especially YS and tangent modulus for the true stress-strain curve. So this is why I am so adamant the E value at elevated temperatures is important to correctly determine if the first-order approach is linear or not. And for brazed copper (at a high temp), the E value is much less. So I thought I had the whole YS vs modulus thing figured out, but maybe I need to re-think it….Thx

 

[EdStainless]

This data does not go hot enough, but take a look.

http://ethesis.nitrkl.ac.in/2054/

from just below RT to 500C there is almost no change in E.
But the yield strength drops 80%.
In order for the E to control defection the stress must be in the elastic region.
In your case the stress just from the weight of the wire it self at high temp exceeds the yield strength of the material.

Remember, at the melting point the strength is zero.


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Plymouth Tube

 

[metengr]

Back to the OP, Young's Modulus will change as a function of service temperature, for example at RT the value for copper is 18 x 10[sup]6[/sup] psi, while at 700 deg F the modulus is only 14.5 x 10[sup]6[/sup] psi. Once the material is cooled back to RT the Modulus will retain the RT value, as before. The original yield strength will decrease as a function of temperature and but will not revert back to the original RT value because at 1050 deg C you will have grain growth, which would result in lower yield strength at RT.

 

[FerrariEngineering]

Good discussion; thank you all for the comments.
One more response to hopefully wrap this up. I should have mentioned this not a wire or some small piece with clear deformation, but a machined cavity assy which is operated under vacuum; like a copper waveguide. We braze this stuff all the time and usually the cross-section features are large enough to prevent any deflection under vacuum conditions. We confirm this by measuring frequencies which are super sensitive to cavity volume. So there are many cases where a dead-soft copper assy (such as waveguide) is still within the elastic region, agreed??
So, if we also agree my previously mentioned approach to first-order analysis is to first check if the assy is in the elastic region based on E and PR material properties, and then compare the associated stresses (VM in this case I guess) to the YS to determine in the model is non-linear; otherwise the deflections (yes very small) are considered accurate. So since my model using an E of 15E6 resulted with stresses under the YS, which due to the temperature (grain growth per metemgr) is extremely low, I would assume it’s in the elastic region, and hence E is the only mathematical constant that will change stresses, reaction forces, etc in the elastic region. But the actual assembly is displaying larger deflections (and yes perhaps nonlinear), but again measured by frequency shifts.
So since my initial simulation indicated elastic behavior and realizing E does decrease with temperature, and in this case hi-temperature, I was exploring that E for dead-soft copper must be lower, and thinking, much lower than 15E6, and that was my problem. Most graphs only indicate E to specific temps and I’m not sure how linear they remain; for example E for carbon steel exponentially drops at elevated temperatures. So seeing these graphs, I was hopeful that I found the discrepancy and would change my E value to again check for non-linearities.
I did wonder if E returns to RT values during cooling, and one scientist I inquired though not as long as no additional cold-working was present. But he is not a metallurgist, nor am I, so I have learned something from metengr.
So this all points back to why is my model indicating elastic behavior if my E of 15E6 is correct. Either my comparison to the YS I used is incorrect (which I received from SLAC) or my fixture or load boundary condition is incorrect, or ????? If the strength is essentially zero, then an evaluation for any hi-temp brazed copper assy is not in the elastic region, which I’m not sure makes sense to me.
Hopefully this makes sense; final comments welcomed. Thanks for all the consideration. Happy Holidays!

 

[MagBen]

I'm confused. What are you trying to accomplish? Are you interested in E at high temperature (1050C) or RT or else?

At 1050C, E of Cu will decrease to almost half of RT value, and YS is almost zero since the melting point of Cu is only 1085C. At that high temperature, elastic region would be very small.
Is 1050C the brazing temperature or the serving temp? If the former, brazing is supposed to be very local (especially your Cu part is big in size) and has a short period of time. The majority of your Cu part would not be affected mcuh by brazing.
If you are talking about RT properties after brazing, grain size increase could decrease YS, but almost no effect on E as long as the structrure is not changed. Using 15E6 at RT is pretty conservative. Change in YS only affects your elastic region.

@Ed,
A load is not necessary the only source for deflection. when a high expansion metal is bonded with a low expansion metal, temeprature change will cause deflection due to CTE difference. It is not uncommon a Cu layer is bonded intermediatly to adjust resistivity. That was why I asked OP if this was a bimetal application in which the deflection is related to temp change, CTE difference, thickness, ratio of thickness, E etc.

 

[btrueblood]

FE,

Copper has a wide range of yield strength depending on cold work. Dead soft, annealed C100001 copper has a YS of around 10 ksi, and around 40-50 ksi in the hard condition where most machinists like to work with it.

 

[FerrariEngineering]

@MagBen
See if this helps. I am interested in E at elevated temperatures and here is why. It is common to first run a static linear FEA model to confirm linear elastic region. I think we all agree that E (and PR) are the only material properties used (mathematically) for elastic models. The accompanying stresses are then compared to the YS. If they are greater, then the model is non-linear and a new study is required. And yes, the YS in the annealed condition and will be much lower, thus the comparison for non-linearity is addressed. My initial model indicated elastic behavior using E at 15E6, but empirical measurements proved otherwise. So, I figure two possibilities for the error (excluding model setup); 1) My E value is wrong, or 2) the YS I am comparing the stresses to is too high.
We braze copper assys every day, and I can assure you that post-brazed assemblies will remain elastic under vacuum per specific geometries. So this tells me the YS can’t be zero, very small, but not zero, correct?? So I thought maybe my E value is too high and started to explore temperature effects, and indeed E changes with temperature, but the only data I have is up to a specific temp, and not knowing if the graphs remain linear (unlike carbon steel as I mentioned), I inquired with others if a typical value can be used. Now per this discussion, I am learning that E will return to its original value at RT, which then goes back to why is the model incorrect.
We braze Cu assemblies in a H2 atmosphere furnace braze, so the entire part is annealed; no localized heat. We actually braze at 1030°C; then the assy is cooled back to RT. Service temps vary, but usually nothing above 100-200°C.
So in my case, E of 15E6 is not conservative. I am speaking with some brazing experts, and surprisingly, everyone has a different opinion and I was given a paper from Oak Ridge National Laboratory (1962) that is often referred to (even currently) due to the ambiguity of this topic in the brazing world. Being able to construct a believable FEA model would be very interesting.
Does this help, or am I just adding to the confusion….

 

[MagBen]

Ferrari,
Thanks for explanation. I attached in my previous poster E vs temperature chart from RT to the melting point.

Using one single E for the whole temeprature range is obviously not appropriate.
At RT, YS of course is not close to zero, but at a temperature close to melting point, YS must be very small if not zero.
Again, at RT, 15E6 is conservative, while at high temperature, it is of course overestimated.

P.S. from 0 to YS, the deformation may be elastic, but not necessarily linear, it is safer to say linear at <50% YS.

 

[EdStainless]

So if these are box-like then differential thermal expansion may play a role. As some parts heat faster than others.
Or if not everything is the same alloy you may have the mismatch in TEC driving some distortion.
Also possible that residual stress may be causing some distortion on initial heating.

Maybe you should try cycling a few parts without brazing them and see if they distort.


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Plymouth Tube

 

[FerrariEngineering]

@Ed
These are box-like assys and not completely symmetric, so although the entire assy is copper, I totally agree the thermal expansion along a particular direction will not be exactly the same as another and could cause some residual stress. The braze is implemented in a batch furnace and controlled with TC data, so the temperature ramp is slow and the uniformity is relatively good. The interesting thing is the parts have very little if any deflection out of the furnace; it’s when we pull a vacuum (the load) we see the larger deflection than anticipated. But due to the expansion differences just explained, maybe the higher residual stress areas are adding to the deflection once a load is applied, but nothing without a load. I have had a ceramic-to-copper assy pop itself apart a few days after a braze from residual stress due to the severe CTE mismatch.

I think I can run the deflection simulation with the thermal profile load from the braze run whcih should include those residual stresses. I will try it.

 

[FennLane]

If you have a box like structure how are you measuring deflection to compare to your FEA model?

If your measurements disagree with your model can you state the magnitude of the differences ?

It is much better to look at real numbers

If you are heating the structure to 1030degC I just don't see where the residual stress is coming from.

At these sorts of temperatures if you have any stresses present you could easily be seeing the effect of creep within the structure as you are likely to be seeing some grain boundary sliding or other creep mechanisms starting to operate.

What is not clear to me is if your deformation measurements are made compared to the structure before it was brazed and once it is in service or did you measure it after brazing to establish a new datum.

Depending on the deformation history of the copper and it composition you may be seeing some distortion caused by annealing twins and looking at the structure may help.

I would also say that 15 x 10^6 psi is a little on the low side and in general 17 x 10^6 is the more commonly accepted value.

At 1030degC the bulk modulus of the material will have changed substantially and you could have around 5% of the structure comprising of mobile vacancies (At 7% the material would of course melt) and the stiffness would be very low.

Clearly the modulus would recover upon subsequent cooling.

If you can, however, prove that brazing copper at 1030 deg causes a significant reduction in modulus it would be shattering and stand well accepted Physical Metallurgy on its head.

I don't mean to be sarcastic but it just seems a very, very unlikely hypothesis and I would look very, very carefully at the metrology.