# Young's modulus and temperature

## Main Question or Discussion Point

Hi,
I'm doing an IB extended essay in physics (like a 4000 word investigation) and I'm looking to do it on Young's modulus- in particular perhaps how temperature effects it. Is this legit? Like does temperature have a significant effect, in such a way that if young's modulus decreased with temperature then from a stress/strain curve you could see that less stress would be needed to cause the same amount of strain- therefore making things weaker in hotter climates? Really unsure. Also would it make more sense to go down the route of young's modulus and thermal expansion using those formulas, although I do need to carry out an experiment as a part of the investigation so I'm not sure what I'd do for that. I was thinking of an experiment use Searle's apparatus if the school has it or just clamping a steel wire to a desk with a pulley and weight to measure stress/strain then draw a graph to get a gradient of young's modulus. Also, I wanna link this experiment to the real world as i'm interested in construction- in particular I can see this being relevant to bridges- so if I got young's modulus experimentally from a steel wire it can be applied to a massive steel rod used to build things too right? (Just checking)(We haven't actually been taught any of this which is why some bits are confusing me a bit)
And help/more ideas would be massively welcomed,
Thanks! :]

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AlephZero
Homework Helper
Young's modulus is temperature dependent. Here are some graphs for metals.

If you want to do an experiment to measure the change in Young's modulus with temperature, that is not easy to do with metals because the changes are small for temperatures that are easy to work with (e.g. between 0 C and 100 C)

Plastics and similar materials can show much bigger changes at lower temperatures, for example

Graphs from
http://www.engineeringtoolbox.com/young-modulus-d_773.html
http://www.ptonline.com/columns/the-effects-of-temperature

Philip Wood
Gold Member
I'm afraid the chances of an experimental investigation of the change in YM with temperature in an ordinary school or undergraduate Physics lab don't look too promising to me. According to the wonderful graphs posted by Aleph Zero, the percentage change in YM for steel is only about 3% over 100°C, and it's pretty hard even to measure the YM to a better uncertainty than 3% using simple apparatus. If I wanted to detect a thermal effect, I'd try passing a current through the loaded wire in order to to heat it. Even then I'd have to distinguish between extension of the wire due to thermal expansion, and extension due to change of the YM. [I presume that to first order these effects can be treated separately.]

sophiecentaur
Gold Member
I'm afraid the chances of an experimental investigation of the change in YM with temperature in an ordinary school or undergraduate Physics lab don't look too promising to me. According to the wonderful graphs posted by Aleph Zero, the percentage change in YM for steel is only about 3% over 100°C, and it's pretty hard even to measure the YM to a better uncertainty than 3% using simple apparatus. If I wanted to detect a thermal effect, I'd try passing a current through the loaded wire in order to to heat it. Even then I'd have to distinguish between extension of the wire due to thermal expansion, and extension due to change of the YM. [I presume that to first order these effects can be treated separately.]
I agree. Unless you have specialist equipment and some significant technician help (or bags of practical experience, yourself), I reckon you will find it very hard to get results.
If you are interested in Materials, would you, perhaps, find it interesting to look at strengths of different structures (i.e.various shapes, sizes of beams or rods) and relate measurements to theory? I am not an ME but there is a lot of information available (I found some good links when looking into a loft extension for my house and also some useful basics in the local University Library).

AlephZero
Homework Helper
the percentage change in YM for steel is only about 3% over 100°C, and it's pretty hard even to measure the YM to a better uncertainty than 3% using simple apparatus. If I wanted to detect a thermal effect, I'd try passing a current through the loaded wire in order to to heat it.
I agree. Unless you have specialist equipment and some significant technician help (or bags of practical experience, yourself), I reckon you will find it very hard to get results.
You don't need complicated apparatus to measure E accurately enough, but you won't succeed by hanging weights from wires. A better way is to measure the vibration frequency of a bar of matieral with accurately known dimensions, suspended so it can vibrate freely/ For exmple you could hang it from two flexible supports are at the nodal points along the beam where it doesn't move when it vibrates.

Very high temperatures are a problem, because most "simple" measurement transducers like an accelerometer or a strain gauge will only survive up to about 150C or 200C maximum. But the good news is you don't need an accurately calibrated transducer with a linear response, because the only thing you need to measure is frequency. You could use very simple non-contact measurement techniques, like just recording the sound of the vibration with a microphone (shielded from the high temperature of course).

A random idea - you could probably measure the frequency change of the metal bars in a wind chime, over a temperature range from about 0 to 100 C ....

sophiecentaur
Gold Member
Cool idea to measure speed of sound. You would need to compensate for density, too. But not a problem.

AlephZero
Homework Helper
Cool idea to measure speed of sound.
In case that causes any confusion, the vibration frequency of a wind chime does not depend on the speed of sound in the air. The vibrations are bending of the metal tube itself.

Actually, to get the "best" sound it helps to design the tube so its bending frequency is close to the resonant frequency of the air inside, but the vibration of the tube is what controls the frequency, not the air.