Physics question (Young's Modulus)

TheCenturion · 10 Oct 2010 at 13:29

If you know the Young's Modulus of a material, and you know the stress being applied to it, can you work out the amount that it will stretch? Or, if you know the strain, can you work out the stress?

Thanks

gillywibble · 10 Oct 2010 at 13:29

Possibly.

p4radox · 10 Oct 2010 at 13:33

E = stress/strain

Therefore given the modulus and the stress, you can work out the strain. However, to work out the amount that a particular sample will stretch, you need dimensions.

If you know the strain, you can easily work out the stress.

Jonny Wright · 10 Oct 2010 at 13:38

Young's Modulus = Stress/Strain

Strain = Change in Length/Original Length

To answer both your questions:

1) Work out the strain using the first formula.

2) Use that and the original length of the material to work out the change in length.

TheCenturion · 10 Oct 2010 at 13:41

p4radox said:
E = stress/strain

Therefore given the modulus and the stress, you can work out the strain. However, to work out the amount that a particular sample will stretch, you need dimensions.

If you know the strain, you can easily work out the stress.

Thanks, that's what I thought.

I think I should just be able to work it out by rearranging the equation.

If the Young Modulus is 180 GPa, let's say you apply a stress of 60 MPa, then you get:

Strain = 60x10^6/180x10^9 = 3.3r x10^-4 % of strain?

Metatron · 10 Oct 2010 at 13:44

Jonny Wright · 10 Oct 2010 at 13:49

TheCenturion said:
Thanks, that's what I thought.

I think I should just be able to work it out by rearranging the equation.

If the Young Modulus is 180 GPa, let's say you apply a stress of 60 MPa, then you get:

Strain = 60x10^6/180x10^9 = 3.3r x10^-4 % of strain?

Thats what I got, then use Strain = Change In Length/Original Length to get the stretch of the material.

TheCenturion · 10 Oct 2010 at 13:51

Jonny Wright said:
Thats what I got, then use Strain = Change In Length/Original Length to get the stretch of the material.

thanks, but this is theoretical, I don't actually have a sample of said material at hand. However, does that mean that the orignial length will stretch by 3.3rx10^-4 %?

Amleto · 10 Oct 2010 at 15:02

a ratio != %. you need to x100 to use %

TheCenturion · 10 Oct 2010 at 15:05

Ah ****

Rookie errorz, thanks mate

Duff-Man · 10 Oct 2010 at 15:12

Under the assumption of linear elasticity, yes you can, if the problem is just one-dimensional. Linear elasticity is a good assumption for most non-plastic materials undergoing small deformations.

If it's a multi-dimensional problem (i.e. 2D or 3D), then you will need to know Poisson's ratio also.

TheCenturion · 10 Oct 2010 at 15:53

Hang on a second, I think I'm getting a bit confused.

If the Young's Modulus is 180 and the stress applied is 6GPa, then it follows that:

6/180 x100 = 3.333333

But does this mean that when 6GPa is applied to any sample ofthe material, it will stretch by 3.3333%?

p4radox · 10 Oct 2010 at 16:14

Assuming that the units of Young's modulus in this case are also GPa, then yes, that's correct.

/edit: as Duff-man says, this is all assuming one-dimensional deformation.

TheCenturion · 10 Oct 2010 at 16:18

yes, simply linear deformation

flibbage0 · 10 Oct 2010 at 16:44

TheCenturion said:
If you know the Young's Modulus of a material, and you know the stress being applied to it, can you work out the amount that it will stretch? Or, if you know the strain, can you work out the stress?

Thanks

You are already doing Young's modulus!

We didn't start till after January, brings back bad memories.