Dyneema Thermal Expansion - Enough to Break Things?

[markxengineerin]

Dyneema, Aluminum, and Stainless steel all expand as temperature increases and contract as temperature decreases.

This is wrong, as you would learn if you read the thread.... See post #26 for the best example.

[markxengineerin]

@BjarneK

Aluminium has a coefficient of thermal expansion of about 13 ppm / deg C and for dyneema it is about -12 ppm / deg C.

I think you may have mixed english and metric units
Aluminum should be in the low 20's for metric units of meters/meter deg C. This would correspond to the Dyneema number of 12.


I made a spreadsheet to also include the effects of the mast stiffness, and 4 shrouds (for now) instead of just one, and I'm getting some scary values. I still need to include the different shroud angles and lengths, for now they are all parallel and equal to mast length.
Can someone check my work? I imagine I must have an error somewhere.

This site won't allow an Excel file to be attached, but happy to email it to anyone interested.

Edit: that last result is in pounds

[wholybee]

I had been considering that I might switch to dyneema the next time I replace my rigging. This thread makes me question that.

[RaymondR]

Alloy disk with a rubber disk underneath the mast foot should solve it??

[Lee Jerry]

Originally Posted by markxengineerin

I made a spreadsheet to also include the effects of the mast stiffness, and 4 shrouds (for now) instead of just one, and I'm getting some scary values. I still need to include the different shroud angles and lengths, for now they are all parallel and equal to mast length.
Can someone check my work? I imagine I must have an error somewhere.

This site won't allow an Excel file to be attached, but happy to email it to anyone interested.

Edit: that last result is in pounds

Here are some comments:

You have the area of the shrouds wrong - you forgot to divide by 4 since it is diameter.

I think the modulus of the dyneema is too high. That is the modulus for the bare stands / material, but the constructed rope will be less, and at low loads (definitely <10% and probably <15%) will be significantly less. This is indicated by the higher stretch at lower loads. We can discuss further, if desired. So a more appropriate value is probably more like 60-70 GPa (assuming initial tension <15%, which I think it should be).

Why 4 shrouds? Do you mean 2 shrouds plus fore and aft stays? Or is it 4 lowers looking at only part of the mast? Not sure why this (the number of shrouds) even matters though, at least the way I look at / calculate it.

I also don't see why you need the mast stiffness. This may be the same answer as the number of shrouds. What are you using for Eq 8.3? (I might be able to deduce it, but it's easier to just ask.)

[markxengineerin]

Thanks for taking a look. Here are the formulas I used, which were developed for analyzing the change in pre-load on a bolted joint when the temperature of the joint changes. I think the mast/dyneema situation is basically the same.


I think I have the area right- 11mm shroud gives an area of 95.03mm^2. I am including 4 "lines" for now, so maybe that's where you noticed a factor of 4? Yes, referring to 2 shrouds plus fore and aft stays. My boat also has lowers, but leaving them out for now, will plan to include later.

The number of shrouds matters because it increases the effective stiffness of the dyneema. If there was an infinite cross section of dyneema, the aluminum mast would see an infinite resistance to the growth it desires when temperature increases. The result is, more shrouds = more change in tension for a given change in temperature.

Yes, same logic behind why the mast stiffness (axial) matters.

[markxengineerin]

Alloy disk with a rubber disk underneath the mast foot should solve it??

I want to think about the side effects of this one some more after sleeping, brain fried for today, interesting idea though.

[Lee Jerry]

Originally Posted by Lee Jerry

I think the modulus of the dyneema is too high. That is the modulus for the bare stands / material, but the constructed rope will be less, and at low loads (definitely <10% and probably <15%) will be significantly less. This is indicated by the higher stretch at lower loads. We can discuss further, if desired. So a more appropriate value is probably more like 60-70 GPa (assuming initial tension <15%, which I think it should be).

Also, FWIW, I think BjarneK made the same "mistake" w.r.t. modulus of dyneema (if we agree it should be lower), but it is offset by the lower mast elongation he used, and therefore his results / conclusion are in the generally right ballpark.

[markxengineerin]

That is the modulus for the bare stands / material, but the constructed rope will be less, and at low loads (definitely <10% and probably <15%) will be significantly less. This is indicated by the higher stretch at lower loads. We can discuss further, if desired. So a more appropriate value is probably more like 60-70 GPa (assuming initial tension <15%, which I think it should be).

I don't know where the Dyneema modulus I used came from originally, I trace it back to the Rigging Doctor, but, not the most reliable source. I agree with your logic but would be great to find some test data for constructed rope's young's modulus vs. load and vs. temperature, both sure to affect these calculations.

[Lee Jerry]

Originally Posted by markxengineerin

Thanks for taking a look. Here are the formulas I used, which were developed for analyzing the change in pre-load on a bolted joint when the temperature of the joint changes. I think the mast/dyneema situation is basically the same.


I think I have the area right- 11mm shroud gives an area of 95.03mm^2. I am including 4 "lines" for now, so maybe that's where you noticed a factor of 4? Yes, referring to 2 shrouds plus fore and aft stays. My boat also has lowers, but leaving them out for now, will plan to include later.

The number of shrouds matters because it increases the effective stiffness of the dyneema. If there was an infinite cross section of dyneema, the aluminum mast would see an infinite resistance to the growth it desires when temperature increases. The result is, more shrouds = more change in tension for a given change in temperature.

Yes, same logic behind why the mast stiffness (axial) matters.

That's a nice application that I hadn't thought of. I can match your numbers exactly.

Note that your numbers are ~30% LESS than my simpler analysis when using 110 GPa modulus for dyneema. Your numbers are ~30% MORE than my simpler analysis with 60 GPa modulus. In either case, if the initial load in the shrouds are in the 10-15% range, then the change is only ~10% of that preload (~1% of breaking strength). That seems perfectly acceptable to me.

[BjarneK]

Originally Posted by markxengineerin

@BjarneK

I think you may have mixed english and metric units
Aluminum should be in the low 20's for metric units of meters/meter deg C.

Good catch, thank you.

[s/v Jedi]

Originally Posted by OneBoatman

The coefficients of thermal expansion for the materials you are discussing are pretty much of a similar magnitude. Dyneema, Aluminum, and Stainless steel all expand as temperature increases and contract as temperature decreases. They are not all dead equal, but they move similarly. Your rig will do it's job if tuned properly and not require re-tuning to prevent damage because your mast get shorter and so do the shrouds, change of less than .2 inches over a length of ~50 ft. is not enough to cause you a problem. You might want to re-check your tune if you are sailing from the Caribbean up through the Northwest Passage.

You missed the “minus sign” in the numbers. Dyneema shrinks when temperature increases, i.e. the opposite of what you state.

[markxengineerin]

The equivalent stretch chart published for Colligo says that 11mm dyneema replaces -10 Navtec rod. -10 Navtec rod has a diameter of 0.250". Modulus for steel is 199GPa. With some algebra, this indicates that the modulus of Dyneema is ~66GPa, probably not an exact number, but should be in the ballpark, and presumably at the stresses and temperatures relevant to a sailboat rig.

If I update with 66GPa I get the following scenario- my shrouds tensioned at 80F will lose 1100 pounds of tension, or roughly 75%, at 32F.



Where is the error? I still cannot believe this is the case, but if Lee Jerry has got the same numbers, it is becoming concerning. I have been constantly re-tensioning my dyneema rig for the past 6 months, and not enough data yet to separate creep from thermal effects. But it has needed a lot of adjustment to keep constant tension, one way or the other.

[OneBoatman]

I stand corrected Dyneema does have a negative Cte whereas SS and aluminum have positive Cte thus I believe it is post #6 that does well to put things in perspective. This results in a greater change than one would think. So over say a 15M shroud the net change for converting an aluminum mast from standard 1 x 19 wire depending on just how much shorter the mast is than any stays switched out for Dyneema, the maximum change treating them as equal in length would be [[.oooo23 - (-.000012)] x 16.7 Deg K] x 15M x 39.37 in/M = 0.34". So, more likely nearer a net change of a quarter of an inch for a 15 M stay. If you tuned too close to the breaking strength of any of your critical fittings at low temperature, you could experience a failure when the temperature rises 30 degrees F as in the example. However, it would be quite unusual for one to tune their rigging so tight as to approach the failure point of their critical components. Working loads are typically engineered nearer 50% of break. But many boats were designed pre-Dyneema. Weak chain plates may show themselves to be exactly that. After all, even the engineers Maxi racers which quite frequently test the limits of many components, do not want their skippers experiencing dismasting. It should not be overlooked that a quarter of an inch change over 15 M is significant considering the range of adjustment in your turnbuckles and the effect it has on the tension in your rigging even if not resulting in a failure. Manufacturers are looking at techniques which include both formulation and pre-stretching that improve predicatability near the temperatures we use them.

[Lee Jerry]

Originally Posted by markxengineerin

The equivalent stretch chart published for Colligo says that 11mm dyneema replaces -10 Navtec rod. -10 Navtec rod has a diameter of 0.250". Modulus for steel is 199GPa. With some algebra, this indicates that the modulus of Dyneema is ~66GPa, probably not an exact number, but should be in the ballpark, and presumably at the stresses and temperatures relevant to a sailboat rig.

If I update with 66GPa I get the following scenario- my shrouds tensioned at 80F will lose 1100 pounds of tension, or roughly 75%, at 32F.

Where are you sailing? What type of sailing - racing v cruising? 26 degC is a large temp range for “in season.” A better baseline might be 60 degF, with a more balanced range. Or I would think for cruising, changing once between winter and summer (and then back) would be adequate, providing a smaller seasonal range - maybe 75 degF summer and 40 degF winter (of course depending on where you are).

What are you tuning your rig to? Breaking strength for 11mm is about 34,800 lb (15,800 kg). So 10% would be ~3500 lb and thus 1100 lb would be ~1/3. 15% would be ~5200 lb, and 1100 lb becomes ~20%. Again, these numbers go (way) down for a smaller temp range and closer to median baseline.

Where is the error? I still cannot believe this is the case, but if Lee Jerry has got the same numbers, it is becoming concerning. I have been constantly re-tensioning my dyneema rig for the past 6 months, and not enough data yet to separate creep from thermal effects. But it has needed a lot of adjustment to keep constant tension, one way or the other.

Are you just tightening or both tightening and loosening?

To answer the OP, I don’t think you should be breaking anything. The rig going slack (-ish) might be a bigger concern. But only if actually sailing in that condition (i.e. cold), not sitting at the dock waiting for better weather.