Mechanical Properties

· The longitudinal sound velocity, c_L, is given by: c_L = (E/ρ)^0.5.
· For a shear wave the corresponding sound velocity depends on the shear modulus, G: c_T = (G/ρ)^0.5.
· If the propagation direction, <hkl> is <100> and the material is cubic:
c_L = (C₁₁/ρ)^0.5; and c_T = (C₄₄ / ρ)^0.5
· For n "round trips" of an elastic wave in a sample of length L, with an interval Δt between echoes: c_i = (2nL/n Δt) = (2L/Δt)
· Because time can be measured with high precision, this method provides accurate values for the elastic constants.
· For Aluminum: C₁₁ = 108.2 GPa, C₁₂ = 61.3 GPa, and C₄₄ = 28.5 GPa.
For Iron: C₁₁ = 237 GPa, C₁₂ = 141 GPa, and C₄₄ = 116 GPa.
For Nickel: C₁₁ = 246.5 GPa, C₁₂ = 147.3 GPa, C₄₄ = 124.7 GPa.