Ultrasonic backscattering in duplex microstructures: Theory and application to titanium alloys

A theory is presented for the ultrasonic backscattering in duplex microstructures. Assuming single scattering described by the Born approximation, we consider a microstructure consisting of macrograins containing colonies with crystallographically related orientations. General results are presented for the backscattering coefficient, assuming that all variants occur with equal probability. These are then applied to the particular case of titanium alloys, in which the macrograins are taken to be prior beta grains and the colonies are assumed to be alpha phase produced by a martensitic transformation. Numerical results illustrate the effects of ultrasonic frequency, colony size and ellipticity, and macrograin size and ellipticity on the backscattering.