Metal additive manufacturing (AM) has started to overshadow traditional manufacturing practices thanks to its ability to produce complex, high-performance and application-customized components. However, AM process parameters have not been optimized, leading to inconsistencies and imperfections such as cracks and pores in parts, as well as deviations from the original design. Nondestructive evaluation (NDE) methods used for part qualification such as x-ray computed tomography (CT) and conventional ultrasonic testing (UT) have limitations in their abilities. X-ray CT is costly, hazardous, and offers limited resolution for larger components while many UT methods have limited applicability for inspection of parts with complex geometries or rough surfaces. Here, we conduct an integrated numerical and experimental study to investigate the feasibility of resonance ultrasound spectroscopy (RUS) as an alternative NDE method to inspect complex AM lattice structures with a varying number of missing struts. The most encouraging results are obtained when test samples have traction-free boundary conditions. The results of numerical simulations including eigenfrequency and frequency domain analyses are promising, indicating that the pristine and defective lattice samples should theoretically be distinguishable. In addition, given a reference intact sample, characterizing the extent of the defect in terms of the number of missing struts appears feasible. We introduce a similarity metric to compare the spectra after being locally normalized. However, the experimental results are not as conclusive. Although pristine and defective lattices may be distinguished for some cases, the number of missing struts cannot be inferred. The discrepancies between the numerical and experimental results are likely due to our simplified assumptions about material properties in numerical simulations and/or the presence of other unaccounted defects and heterogeneities in test samples.

This paper describes resonant ultrasound spectroscopy (RUS) as a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist. In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3-D laser vibrometer allowing the visualization of most of the modes in the frequency band studied.

Resonant Ultrasound Spectroscopy (RUS) has been used successfully to determine the elastic properties of single crystal and homogeneous materials. We have attempted to answer the following question. Under what conditions is RUS a useful tool for determining the moduli of macroscopic, inhomogeneous samples. We concentrated on identifying a sample geometry that will maximize success with RUS. The work consisted of numerical modeling of sample resonances under varying conditions, and empirical testing of rock samples. Numerical modeling and empirical testing indicate that RUS is a viable technique for characterizing the average isotropic elastic moduli of inhomogeneous materials, although larger RMS errors can be expected than for single crystal materials. Success with RUS can optimized by ensuring that the sample size is large compared to the scale of inhomogeneity and by using a high aspect ratio parallelepiped sample.

All objects exhibit vibrational resonances when mechanically excited. These resonant frequencies are determined by density, geometry, and elastic moduli. Resonant ultrasound spectroscopy (RUS) takes advantage of the known relationship between the parameters. In particular, for a freely suspended object, with three of the four parameters (vibrational spectra, density, geometry, or elastic moduli) known the remaining one can be calculated. From a materials characterization standpoint it is straight-forward to measure density and geometry but less so to measure all the elastic moduli. It has recently become possible to quickly and accurately measure vibrational spectra, and using code written at Los Alamos, calculate all the elastic moduli simultaneously. This is done to an accuracy of better than one percent for compression and 0.1 percent for shear. RUS provides rapid acquisition of materials information here-to-fore obtainable only with difficulty. It will greatly facilitate the use of real materials properties in models and thus make possible more realistic modeling results. The technique is sensitive to phase changes and microstructure. This offers a change to input real data into microstructure and phase change models. It will also enable measurement of moduli at locations in and about a weld thus providing information for a validating coupled thermomechanical calculations.

This first procedural guide to RUS, Resonant Ultrasound Spectroscopy offers a clear step-by-step tutorial, from developing a preliminary set of resonances to final determination of moduli. The book also contains intermediate computer outputs showing where mistakes are made, how to spot them, and how to remeasure to correct problems. Also a complete reference to the language of RUS, this book is full of clear explanations of every variable, concept, and hard-to-find term currently in use.

This book presents the results of two major international research projects on phenomenology, theory and applications of Nonclassical Nonlinearity. It conveys concepts, experimental techniques and applications which were previously found in specialized journals. It also allows for an interdisciplinary audience to better understand the range of practical applications, and is timely and interesting to both researchers and professionals.