Ultrasonic attenuations and velocities were measured in the cylindrical specimens of Si-Mn steel treated differently as the production process of the helical spring - grinding, quenching, tempering, and shotpeening - by pulse echo method. Ultrasonic wave was generated by conventional piezoelectric transducers and an electromagnetic transducer actuated by electric discharge to study the frequency and the stress amplitude dependence. Attenuation coefficient, α, was found to be dependent on the frequency, f, as α~$f^n$ for all specimens in the frequency range of 2-20 MHz, where the power factor,n was determined to be 1.89 - 2.32. This observation suggested that the attenuation mechanism was dominated by non-scattering terms (~$f^2$) such as magnetomechanical and dislocation damping, not by Rayleigh scattering term (~$f^4$). The attenuation coefficients were also found to be proportional to the stress amplitude, σ, in the range of σ=1-50 bar. The result agreed with the theoretical prediction by magnetomechanical damping ; α- Eσ, where E is the Young's modulus, except for the specimen of grinding in which the scatter was considered to be caused by the coarse microstructure of the specimen. The frequency dependence of longitudinal wave velocity was agreed well with the modified frequency equation by Redwood. The dynamic elastic constants determined by the longitudinal and shear wave velocities agreed with the values measured by static method."
