Young’s modulus is a mechanical property that indicates the tensile stiffness of a solid material. It is named after 18th-century physicist Thomas Young. Young’s modulus is the ratio of longitudinal stress and longitudinal strain of a solid mater. It is often called 'longitudinal modulus of elasticity' and sometimes only ‘Young Modulus’. For materials having a length greater than its width or thickness, young’s modulus is concerned there. Sometimes, it is denoted with E, sometimes with Y. We used ‘Y’ in this post.
If a solid material’s cross-sectional area, say A, is being pulled with a force of F at both ends, then the solid material may stretch a bit or in a good amount. If we say the initial length Li and the new length ‘L’, then the increased length is (L-Li). This is happened due to stress. Learn more about stress and strain from the linked article.
Now, we got the increased length. We will find strain from the ratio of the increased length and the initial length.
Strain`=\frac{IncreasedL}{InitialL}`
As we put the force towards length, the strain we got is longitudinal strain. Now we need longitudinal stress that is the cause of the strain we found. Stress is the force we applied per cross-sectional area. We have force, F and we have the area of the material, A. Therefore, stress is `\frac FA`.
By now, we have got the longitudinal stress and strain both. So if we find stress per unit strain, then we will get Young’s modulus. So here we go.
`Young` `Modu``lus=``\frac{STRESS}{STRAIN}=``\frac{\frac FA}{\frac lL}``=\frac{FL}{Al}`
Look at an example to be clearer about this concept. If we give 200N force as stress and the strain we get is 5, then the modulus is (200/5)=40.
Now, if you have stress and strain, you can find out Young’s modulus easily. Again, if you have area, force, initial length and new length, you can find the modulus. If you have the diameter or radius, you can find out the area and use that area to find out the modulus. You can find it in some other ways too.
We have made a tool that will give you Young’s modulus after calculating the data that you have. It can calculate directly from stress and strain, it can calculate from the force, area, initial length, new length, or increased length. If you have Bulk modulus and Poisson’s ratio, it will give you Young’s modulus. It can calculate this modulus from Modulus of Rigidity as well.
1. Find Young's Modulus using Longitudinal Stress and Strain
`Y=``\frac{STRESS}{STRAIN}`
2. Find Young's Modulus using applied Force, Length and Cross-sectional Area
`Y=``\frac{\frac FA}{\frac lL}``=\frac{FL}{Al}`
Here, L is the initial length and l is the increased length. If you have the new length you can find the increased one easily by subtracting.
3. Find Young's Modulus using Bulk Modulus, Poisson's ratio and Rigidity Modulus
If you have any two of those data, you can easily find out Young's Modulus using the equations mentioned below.
Using Bulk Modulus and Poisson's ratio
`Y=``(3\times Bu``l``k``)\times(1-2\times Poissons)`
Using Poisson's ratio and Modulus of Rigidity
Say, `A=``(Poissons\times1)+1`
`Y=``2\times A\times Rigidity` `Modu``lus`
Using Bulk Modulus and Modulus of Rigidity
Say, `A=(9\times Bu``l``k` `Modu``lus\timesRigidity` `Modu``lus)`
Say, `B=``(3\times Bu``l``k)+(Rigidity\times1)`
So, `Y=\frac{A}{B}`
