Ultrasonic nonlinearity parameter in precipitate-hardened steels

We have experimentally investigated a series of steel specimens containing copper-rich precipitates. The precipitate microstructure depended on the final aging treatment (time and temperature), which in turn affected the specimen hardness. We performed harmonic generation experiments to determine the nonlinearity ultrasonic parameter β for each specimen and measured the ultrasonic longitudinal velocity and attenuation in separate experiments. β was observed to increase as the hardness increased. In contrast, the longitudinal phase velocity in the same specimens varied only slightly and showed no consistent trend with hardness. Corrections for attenuation were large enough to affect the values of β, but were approximately the same for all specimens. The average lattice strain e in each sample was measured in x-ray diffraction line broadening experiments and increased with hardness. The subsequent correlation between β and e can be understood in terms of a model for harmonic generation by precipitate-pinned...