Using relation young's elastic constants ,find the theoretical value of poissons ratio
Answers
Answer:
The value of poisons ratio lies in the interval -1 < P < 1/2
Explanation:
Relation between the Young's elastic constant and poisons ratio are as follows:
Where Let Y, K, n and P be the Young's Modulus, Bulk modulus, Modulus of Rigidity and Poisson's Ratio, respectively
Y = 3K ×(1 - 2P) [Standard formula]
Y = 2n× (1 + P) [Standard formula]
Hence, 3K ×(1 - 2P) = 2n× (1 + P).
Now we can consider 2 cases when p is positive and p is negative
CASE:1 p is positive:
If P be +ve, then RHS is always +ve. So LHS must also be +ve. Therefore, 2P < 1 or P <1/2
CASE:2 p is negative:
If P be -ve, then LHS will always be +ve. Therefore, 1+P > 0 or P > -1 .
From the above 2 cases we can conclude that the limiting values of poissons ratio lies between -1 < P < 1/2