This thesis demonstrates the practicability of using Resonant Ultrasound Spectroscopy (RUS) in combination with Finite Element Analysis (FEA) to determine the size and location of a defect in a material of known geometry and physical constants. Defects were analyzed by comparing the actual change in frequency spectrum measured by RUS to the change in frequency spectrum calculated using FEA. FEA provides a means of determining acceptance/rejection criteria for Non-Destructive Testing (NDT). If FEA models of the object are analyzed with defects in probable locations; the resulting resonant frequency spectra will match the frequency spectra of actual objects with similar defects. By analyzing many FEA-generated frequency spectra, it is possible to identify patterns in behavior of the resonant frequencies of particular modes based on the nature of the defect (location, size, depth, etc.). Therefore, based on the analysis of sufficient FEA models, it should be possible to determine nature of defects in a particular object from the measured resonant frequency. Experiments were conducted on various materials and geometries comparing resonant frequency spectra measured using RUS to frequency spectra calculated using FEA. Measured frequency spectra matched calculated frequency spectra for steel specimens both before and after introduction of a thin cut. Location and depth of the cut were successfully identified based on comparison of measured to calculated resonant frequencies. However, analysis of steel specimens with thin cracks, and of ceramic specimens with thin cracks, showed significant divergence between measured and calculated frequency spectra. Therefore, it was not possible to predict crack depth or location for these specimens. This thesis demonstrates that RUS in combination with FEA can be used as an NDT method for detection and analysis of cracks in various materials, and for various geometries, but with some limitations. Experimental results verify that cracks can be detected, and their depth and location determined with reasonable accuracy. However, experimental results also indicate that there are limits to the applicability of such a method, the primary one being a lower limit to the size of crack - especially thickness of the crack - for which this method can be applied.

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.

The use of mechanical resonances to test properties of materials is perhaps older than the industrial revolution. Early documented cases of British railroad engineers tapping the wheels of a train and using the sound to detect cracks perhaps mark the first real use of resonances to test the integrity of high-performance alloys. Attempts were made in the following years to understand the resonances of solids mathematically, based on the shape and composition. But Nobel Laureate Lord Rayleigh best summarized the state of affairs in 1894, stating {open_quotes}the problem has, for the most part, resisted attack{close_quotes}. More recently, modern computers and electronics have enabled Anderson and co-workers with their work on minerals, and our work at Los Alamos on new materials and manufactured components to advance the use of resonances to a precision non-destructive testing tool that makes anisotropic modulus measurements, defect detection and geometry error detection routine. The result is that resonances can achieve the highest absolute accuracy for any dynamic modulus measurement technique, can be used on the smallest samples, and can also enable detection of errors in certain classes of precision manufactured components faster and more accurately than any other technique.

The objective of this thesis is to validate Resonant Ultrasound Spectroscopy (RUS) as a non-destructive evaluation tool that can be used to study effects of radiation on the mechanical properties of a material, mainly its elastic constants. RUS involves experimentally measuring the resonant frequencies of a sample and calculating the elastic constants based on these measurements. Finite Element Method (FEM) is used to get the frequencies of the modes of free vibration for the sample model. This result depends on the elastic constant values used in the FEM simulation. Studies were conducted to confirm the accuracy of the FEM model, and determine the right configuration and parameters to use for the simulation. Assuming uniform and isotropic elastic property changes, the effects of radiation damage can be quantified by obtaining a set of matching resonant frequencies between the experimental and FEM simulation results, before and after irradiating the sample. This is done by adjusting the elastic constant values used in the simulation so that the results match with the experimentally obtained resonant frequencies. With powerful enough equipment, even real time monitoring is possible in harsh environments, thus pointing out imminent failure.

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.

Components with defects are identified from the response to strains applied at acoustic and ultrasound frequencies. The relative resonance frequency shift .vertline. DELTA.function./.function.sub.0.vertline., is determined as a function of applied strain amplitude for an acceptable component, where .function.sub.0 is the frequency of the resonance peak at the lowest amplitude of applied strain and .DELTA.function. is the frequency shift of the resonance peak of a selected mode to determine a reference relationship. Then, the relative resonance frequency shift .vertline. DELTA.function./.function.sub.0 is determined as a function of applied strain for a component under test, where fo .function.sub.0 the frequency of the resonance peak at the lowest amplitude of applied strain and .DELTA.function. is the frequency shift of the resonance peak to determine a quality test relationship. The reference relationship is compared with the quality test relationship to determine the presence of defects in the component under test.