# Creep rates of steel and wood.

Hello

Is there some data or some formulas to calculate how much does steel wire creep at a constant stress?

If I have, for example, a 1 m steel string with 1 mm diameter under a constant tension of 1000N at a temperature of 20C, how much does it creep or lengthen in a year?

I tried searching the internet for creep rates, but I didn't find anything.

Also, how much does wood creep when I have a pin inside a hole in a wooden block under a constant torque? Lets say the pin has a radius of 5 mm, and a constant 5 newton-metre torque is applied to it, an additional 5 newton-metre is required to break free of static friction caused by the tight hole in the wood that the pin is in and make the steel pin turn.

Is there any way to calculate or estimate these creep rates?

## Answers and Replies

PhanthomJay
Homework Helper
Gold Member
Wiki has a formula which is a function of many variables. You might want to check it out if you dare. Typically, creep is a long term permanent inelastic deformation of a material which becomes a factor at high stress and elevated temperature levels. I would think at 20 degrees C it would be quite small after 1 year. Even after 10 years, my guess is that elongation due to creep even at high temperatures and high stress levels might be in the order of less than 1/10 of a percent of the wire length.

256bits
Gold Member
Calculate the stress on the wire. Look at where you are in the stress strain curve and if it is below the elastic limit there is no permanent deformation of the material. Amorphous solids are more prone to creep such as plasticine, lead and glass,

Wiki has a formula which is a function of many variables. You might want to check it out if you dare. Typically, creep is a long term permanent inelastic deformation of a material which becomes a factor at high stress and elevated temperature levels. I would think at 20 degrees C it would be quite small after 1 year. Even after 10 years, my guess is that elongation due to creep even at high temperatures and high stress levels might be in the order of less than 1/10 of a percent of the wire length.

It is quite small, but I am thinking of a situation where the change in tension can be measured with very high accuracy, as in a musical instrument. As a rough example, in a 1m piano steel wire with 1 mm diameter, a 0,8 mm stretch can change the frequency by almost a semitone, and a semitone is a lot. A semitone is 100 cents, and even a change of a few cents can be noticed if compared to a reference pitch.

I looked at the formula in Wiki, but it wants so many variables and I can't find them.

What I am wondering, is that if such a 1m wire is under a tension of 1000N for 10 years, could it lengthen 0,05 mm, or maybe more? Maybe there is some ballpark data somewhere, if the formula is very hard to calculate accurately? I would like to get just some idea of the rate of creep, also for the pin in the wood example.

I thought all materials creep if they are over 0K and under a constant tension, it can just be very small. Isn't that so, despite the stress being under the elastic limit?

PhanthomJay
Homework Helper
Gold Member
I have a computer program at work that calculates the effect of creep on a wire after I think 10 years, but the program is designed generally for stranded wires of diameters greater than 5 mm and lengths greater than 100 feet. Neverthless, I'll play around with it during my lunch hour on Monday () to see if it gives some clues.

And yes, you are correct that creep occurs even at low temperatures and low elastic stress levels, but is more pronounced at the higher stress levels below yield strength and at higher temperatures.

I don't know much about wood creep... wood is a funny actor and there are inelastic deformations due to all sorts of variables (moisture, shrinkage, decay, etc.) which I'm sure dwarf the effects of creep.

You might want to do the numbers for stress on a 1mm diameter wire under a 1000 N load. I'm not good with SI, but you might find that your stress level is beyond yield in that example.

I would be very interested if you could see what the program says. If you know how it calculates it or what formula it uses, it would be interesting too.

The stress on the wire should be about 1,47 MPa. I didn't find any numbers for the yield strength of piano wire, but the tensile strength should be 2,2-2,48 MPa according to wiki, and 2,6-2,98 MPa according to a website selling piano wire. Looking at the pattern of ratios between yield/tensile strength of other materials based on steel, I would guess the yield strength is about 2 MPa.

AlephZero
Homework Helper
The stress on the wire should be about 1,47 MPa. I didn't find any numbers for the yield strength of piano wire, but the tensile strength should be 2,2-2,48 MPa according to wiki, and 2,6-2,98 MPa according to a website selling piano wire. Looking at the pattern of ratios between yield/tensile strength of other materials based on steel, I would guess the yield strength is about 2 MPa.

I think you mean GPa not MPa. Having the units wrong by a factor of 1000 won't help, even if you find some formulas!

THe rate of creep for piano wire at room temperature will be negligible compared with other factors that change the length or tension, like change in temperature.

In most real pianos the wire is loaded right up to the elastic limit or a bit higher, which means there is some short-term "creep" over the first 10 to 100 hours, but nothing much after that.
Formulas for creep are mostly empirical based on measurements, and people tend to to the measurements for situations where something interesting happens (often at high temperatures) rather than tying up a creep testing machine for 10 years measuring nothing much. There isn't any good way to do creep testing faster that "real time" and stlil get accurate results.

You probably won't find any results for "creep of wood" because the properties are so variable, and over long time periods what happens depends very much on the level and variability of the moisture content. Changes in moisture content cause the wood to swell and shrink which is one reason why piano tuning pins etc tend to work loose over time.

PhanthomJay
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Gold Member
I ran the program for EHS 1/4" steel strand at various high and low stresses , temperatures, and spans. First I ran it 'without creep', and then with 'creep to be considered'. The results for tensions and sags were identical, and the program spits out "Creep is not a factor" in all cases.

Confirming AlephZero's response.

Thank you for the information and running the program.

Yes you are right those should be GPa not MPa. Are you sure the wire is loaded above the elastic limit? The wire needs to be at a constant tension to produce the correct frequency, and if that tension is past the elastic limit, wouldn't that make the wire be unstable and break eventually?

How would the creep of the wood look like microscopically, as the wood swells and contracts? The hole would get slightly tighter and looser, but how would it allow the pin to move, as the hole should swell and contract in all directions the same way, or not? How does the swelling allow the pin to move?

AlephZero
Homework Helper
The wire needs to be at a constant tension to produce the correct frequency, and if that tension is past the elastic limit, wouldn't that make the wire be unstable and break eventually?
Yes the tuning IS unstable in the primary creep phase (for the first few hours) but after that, in practice "eventually" could amount to "in 100 or 1000 years from now", so it doesn't matter much in practice.

Depending on the environment, the wire might fail (or become unuseable even if it didn't actually fail) through corrosion or crack propagation, before creep became significant.

If you try to retune a piano to a different pitch (even by a fraction of a semitone) it won't hold the new pitch after just one tuning. You need to retune it several times over a few days before it settles down, but after that it will be as stable as it was before the pitch was changed.

I thought that the lowering of pitch was caused by the string straightening around the turns and that the coil on the tuning pin tightens. The string is doing slalom around various pins in a piano. Is it actually creep that lowers the pitch? What about the program that said creep is not a factor under various time spans and stresses?

I had thought that the reason why pitch drops when you tune a piano higher, is that once you add tension to one string, it takes tension away from other strings, because the tension is provided by the plate that the strings try to compress and bend. I thought it is like putting two strings on a bow, when you tighten one, the other gets looser. Is this effect actually caused by primary creep?