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The accumulation of dislocations, which are atomic defects in materials subjected to plastic deformation, can cause structural failures. Early detection of such dislocation-related damage is essential to prevent these failures. The acoustic nonlinearity parameter β has been shown to be sensitive to the nonlinearity of dislocation motions, and prior research has shown a relationship between β and dislocation parameters in various damage mechanisms. While most work thus far reports that β generally increases with increased plastic deformation, recent research showed that β can decrease during monotonic tensile loading in stainless steel 316L characterized by in situ nonlinear ultrasonic measurements. The objective of this research is to examine the correlation between the decrease of β with plastic strain as reported in this recent study, and the initial microstructure and strain hardening rate. The initial microstructure, characterized with electron backscatter diffraction (EBSD), shows an increase in dislocation density and a reduction of grain area, which can possibly result in a decrease in β. Further, it is shown that the decrease rate of β monotonically decreases with hardening rate, providing a evidence that the decrease in β may relate to the shift from planar slip to wavy slip. These results help interpret the underlying mechanisms for the decrease in β during tensile loading. 

Abstract Locally resonant materials allow for wave propagation control in the subwavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this article, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e., its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.