Download - Moduli of Elasticity
How to differentiate Young’s modulus, spring constant, biaxial
modulus, and bulk modulus?
1) Young’s modulus: The modulus corresponding to axial loading.
Material shape: axial or 1-D.
Young’s modulus is usually obtained from tensile test.
The loading, hence stress and strain, is axial in the tensile test.
2) Spring constant: The stiffness of a spring during deflection loading.
Material shape: beam, 1-D.
2.1 The beam is axial, so does stress and strain.
à Young’s modulus is used to calculate spring constant:
3) Biaxial modulus: The modulus corresponding to biaxial loading.
Material shape: thin film, sheet. 2-D.
3.1 What is biaxial loading? à.
3.2 Biaxial modulus is:
Why? You have to know the definition of Poisson Ratio and derive generalized Hook’s
law.
Therefore,
Now, use what we have learned in 2.1 you will get.
1 (1 )xx xxEε ν σ= − ##
Finally, you get the biaxial modulus is xx and yy direction.
4) Bulk modulus: the volume change due to pressure loading.
Material shape: rigid bulk, 3-D.
4.1 Definition:
4.2 The relationship with Young’s modulus.
3(1 2 )E
Kν
=−
You can also use generalized Hook’s law to derive it. How?
Hint: (1 3 ), ....o xxV V ε ε ε∆ = − = = , clear enough?
4.3 Need more details, check this link:
http://scienceworld.wolfram.com/physics/BulkModulus.html