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We demonstrate an integrated non-destructive inspection methodology that employs the nonlinear ultrasonics-based sideband peak counting (SPC) technique in conjunction with topological acoustics (TA) sensing to comprehensively characterize the acoustic response of steel plates that contain differing levels of damage. By combining the SPC technique and TA, increased sensitivity to defect/damage detection as well as the ability to spatially resolve the presence of defects was successfully established. Towards this end, using a Rockwell hardness indenter, steel plates were subject to one, three and five centrally located indentations respectively. The acoustic response of the plate as a function of number of indentations was examined at a frequency range between 50 kHz and 800 kHz, from which the change in a global geometric phase was valuated. Here, geometric phase is a measure of the topological acoustic field response to the spatial locations of the indentations within the steel plates. The global geometric phase unambiguously showed an increase with increasing number of indentations. In addition, spatial variations in a ‘local’ geometric phase as well as spatial variations in the PC index (SPC-I) were also determined. Spatial variations in both the local geometric phase as well as the SPC-I were particularly significant across the indentations for frequencies below 300 kHz, and by combining the respective spatial variations in the SPC-I and geometric phase, the locations of the indentations were accurately identified. The developed SPC-TA nondestructive method represents a promising technique for detecting and evaluating defects in structural materials. 

evaluated by the sideband peak counting (SPC) nonlinear acoustics method and suitably validated by microfocus X-ray computed tomography (XCT). A wide-band chirp acoustic wave was used to inspect the microstructures of IN718 samples with five distinct process parameters, and the results reveal that the number of sidebands, which result from the non-linearity induced by porosity, is significantly influenced by the distribution and size of pores, in addition to the volume fraction. There was a clear correlation between extent of porosity and the corresponding value of the SPC index. XCT analysis corroborated these findings, providing quantitative insights into the porosity characteristics that affect the ensuing acoustic responses. The findings demonstrated that the porosity with varying sizes and distributions generate different SPC profiles, which were correlated to XCT results to quantitatively assess the size and spatial distributions of the porosity. Fusion of SPC and XCT characterization techniques provides a new strategic approach for non-destructive testing, where the SPC method offers rapid, qualitative evaluation, while XCT provides detailed spatial resolution for defect quantification. The integration of SPC could lead to the development of more cost-effective and advanced quality control protocols, ensuring the reliability of AM-manufactured components regardless of their geometry and composition. 

ABSTRACT The spatial distribution of metals reflects, and can be used to constrain, the processes of chemical enrichment and mixing. Using PHANGS-MUSE optical integral field spectroscopy, we measure the gas-phase oxygen abundances (metallicities) across 7138 H ii regions in a sample of eight nearby disc galaxies. In Paper I, we measure and report linear radial gradients in the metallicities of each galaxy, and qualitatively searched for azimuthal abundance variations. Here, we examine the 2D variation in abundances once the radial gradient is subtracted, Δ(O/H), in order to quantify the homogeneity of the metal distribution and to measure the mixing scale over which H ii region metallicities are correlated. We observe low (0.03–0.05 dex) scatter in Δ(O/H) globally in all galaxies, with significantly lower (0.02–0.03 dex) scatter on small (<600 pc) spatial scales. This is consistent with the measurement uncertainties, and implies the 2D metallicity distribution is highly correlated on scales of ≲600 pc. We compute the two-point correlation function for metals in the disc in order to quantify the scale lengths associated with the observed homogeneity. This mixing scale is observed to correlate better with the local gas velocity dispersion (of both cold and ionized gas) than with the star formation rate. Selecting only H ii regions with enhanced abundances relative to a linear radial gradient, we do not observe increased homogeneity on small scales. This suggests that the observed homogeneity is driven by the mixing introducing material from large scales rather than by pollution from recent and on-going star formation.