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Task 1 Final Report, Theoretical/Mathematical Modeling of Ultrasonic Wave Propagation in Anisotropic Polycrystalline Stainless Steels

One of the tasks of the U.S. Nuclear Regulatory Commission-sponsored project titled "Reliability of Nondestructive Examination (NDE) for Nuclear Power Plant (NPP) Inservice Examination (ISI)" is to provide collaborative assistance to Commissariat a l’Energie Atomique (CEA) in France through theoretical predictions of ultrasonic scattering by grains of cast stainless steels (CASS) components. More specifically, a mathematical treatment of ultrasonic scattering in media having duplex micro¬structure is sought because cast stainless steel components often contains larger-scale macrograins that are composed of sub-grains/colonies. In this report, we present formal mathematical theories for ultrasonic wave propagation in polycrystalline aggregates having both simple (composed of grains only) and complex microstructures (having macrograins and sub-grains/colonies). Computations based on these theories are then carried out for ultrasonic backscatter power, attenuation due to scattering, and phase velocity dispersions. Specifically, numerical results are presented for backscatter coefficient for plane longitudinal wave propagating in duplex steel containing macrograins and colonies. Furthermore, the expected propagation characteristics (attenuation coefficient and phase velocity) are computed and described in this report for plane longitudinal waves propagating in (1) steels composed of randomly oriented grains, (2) [001] aligned grains encountered in austenitic stainless steel welds and casts, and (3) duplex steels.