The Young's modulus for steel is 2x1011 and its rigidity modulus is 8x1010 Nm-2. Find the Poisson's ratio and its bulk modulus.
How is this a challenge?
a google search shows up the simple formula
E=2G(r+1)
2*10^11 = 2*8*10^10(r+1)
1/8 * 10 = r+1
1.25 = r+1
0.25 = r
Also, for Bulk modulus K,
E = 3K(1-2r)
2*10^11 = 3K(1-2*.25)
2*10^11 = 1.5K
K = 1.33*10^11
To find the Poisson's ratio and bulk modulus of a material, we need to use the formulas that relate these parameters to the Young's modulus and rigidity modulus.
1. Poisson's ratio (ν):
Poisson's ratio is defined as the negative ratio of lateral strain (εl) to longitudinal strain (εt). It relates the transverse deformation of a material to its axial deformation.
The formula for Poisson's ratio is:
ν = -εl/εt
To find the Poisson's ratio, we need to know either the longitudinal strain or lateral strain. Since we only have the Young's modulus and rigidity modulus, we cannot directly calculate the Poisson's ratio.
2. Bulk modulus (K):
The bulk modulus relates the volume decrease of a material under uniform pressure to the applied pressure.
The formula for the bulk modulus is:
K = (2/3) * rigidity modulus
Let's calculate the bulk modulus using the given rigidity modulus:
K = (2/3) * rigidity modulus = (2/3) * 8x1010 Nm-2 = 1.333x1011 Nm-2
Note that we cannot determine the Poisson's ratio without additional information, such as the longitudinal or lateral strain.