Elastic wave scattering by shelled spherical scatterers in a focused field

Embrittlement of many important metal alloys has been related to the accumulation of undesirable materials at grain boundaries, a condition which may be detectable through measurement of ultrasonic scattering from the material’s microstructure. Grains with decorated grain boundaries are modeled as shelled microspheres embedded in an isotropic elastic host, and a practical means of predicting scattering from these particles is developed. The incident field often used for measuring backscattered grain noise is focused; both plane and focused incident fields are treated. Theoretical predictions of scattering from isolated scatterers are compared with experimental measurements on metal microspheres embedded in plastic to validate the computational procedure, then predictions of scattering from similar spherical structures embedded in a metal host are presented. In the former case theoretical predictions are found consistent with observations, although differences between shelled and nonshelled scatterers are obscured by the great contrast between host and scatterer. In the latter case, where host and core are quite similar, even thin shells can produce scattering readily distinguishable from the weak scattering in polycrystals that may be due to locally inhomogeneous properties. Results of this study can be used to calculate a backscattering coefficient for calculations of grain noise in metals containing, or composed of, numerous shelled scatterers.