| Abstract
| - In nondestructive micro-characterization, elastic constants are generally expressed in terms of velocities of longitudinal waves, V L, and transverse waves, V T. However, it is often difficult to determine these velocities by a single measurement. In this context, we propose the derivation of new expressions according to only one parameter: V L, V T or Rayleigh velocity, V R. Thus, by using Viktorov formula and certain acceptable physically approximations, deduced, for any material of density ρ the following relations: E = 0.757 $\rho {{\rm V}_{\rm L}}^{2}$, E = 2.586 $\rho {{\rm V}_{\rm T}}^{2}$, E = 2.99 $\rho {{\rm V}_{\rm R}}^{2}$, G = 0.293 $\rho {{\rm V}_{\rm L}}^{2}$ and G = 1.156 $\rho {{\rm V}_{\rm R}}^{2}$.The validity of these relations is put into evidence for a large number of materials (Al, Cd, Fe, Mg, Mo, Ti, W, Pt, Ni, etc) characterized by fast, medium or slow velocities. Excellent precisions of 0.007 % and 0.009 % were obtained respectively for G = f(V $_{\rm L})$ with Mo and for E = f(V $_{\rm T})$ with Fe. These very encouraging results find their applications in acoustic microscopy into which only one surface mode often dominates the acoustic materials signatures, V(z).
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