  A general second order attenuation (SOA) model is proposed to predict the
elastic wave attenuation and phase velocity dispersion in heterogeneous
polycrystalline media. It is valid for statistically isotropic aggregates with
triclinic crystals of equiaxed shape and is equivalent to well-known
Stanke&Kino model when applied to cubic polycrystals. Moreover, an
approximation form of the general SOA model is obtained to improve
computational efficiency but retain adequate accuracy. Further comparison
between the SOA model and the approximated second order attenuation (ASOA)
model indicates the ASOA model has reasonable agreement with the SOA model both
on attenuation and phase velocity. Additional computational examples show the
ASOA model has better performance than Karal&Keller model. Thus, this
theoretical study provides effective approaches for modeling of acoustic
attenuation in heterogeneous polycrystalline materials for whole frequency
range, including the Rayleigh region, the stochastic region and the geometric
region. It will shed light on the practical development of ultrasonic
characterization of polycrystalline metals.
