Detection of inclusions embedded in a polycrystalline medium: A diagrammatic approach

Abstract

Diffuse ultrasonic backscatter techniques are used to evaluate and to quantify polycrystalline microstructure in structural materials including steel, aluminum, and concrete. Modeling of the backscatter received from grain scattering is important for both microstructural characterization and flaw detection. Here, the problem of an inclusion embedded in a polycrystalline background is examined using a diagrammatic approach. Expressions are derived that for the attenuation and diffuse backscatter using a Green’s function approach that incorporates Feynman diagrams for simplicity in the analysis. The resulting equations are solved in the single-scattering limit that couples geometric probabilities and correlation functions such that the impact of the inclusion can be quantified. The effects of frequency, average grain size, polycrystalline properties, inclusion properties and inclusion size are considered. Further work related to inspection with focused beams or immersion type ultrasonic inspections is also presented. This work is anticipated to impact the studies of model-assisted probability and inclusion content quantification in ultrasonic non-destructive evaluation.