Calculate the bulk modulus of an alloy body if its modulus of elasticity is found to be 180 Gpa. Consider that the Poisson's ratio of tested material is 0.25.

Concept :

The relation between E, K, and μ

E = 2G (1 + μ)

E = 3K (1 - 2μ)

\({\rm{E}} = \frac{{9{\rm{K}}}}{{3{\rm{K}} + {\rm{G}}}}\)

Where,

E = Young's Modulus of Rigidity = Stress / strain

G = Shear Modulus or Modulus of rigidity = Shear stress / Shear strain

μ = Poisson’s ratio = - lateral strain / longitudinal strain

K = Bulk Modulus of elasticity = Volumetric stress / Volumetric strain

Calculation:

Given, E = 180 GPa, μ = 0.25

E = 3K (1 - 2μ)

180 = 3 × K (1 - 2 × 0.25)

∴ K =  120 GPa.