Matthew R. Cherry

Focusing of longitudinal ultrasonic waves in air with an aperiodic flat lens.

Modeling and experimental results of an ultrasonic aperiodic flat lens for use in air are presented. Predictive modeling of the lens is performed using a hybrid genetic-greedy algorithm constrained to a linear structure. The optimized design parameters are used to fabricate a lens. A method combining a fiber-disk arrangement and scanning laser vibrometer measurements is developed to characterize the acoustic field distribution generated by the lens. The focal spot size is determined to be 0.88 of the incident wavelength of 80-90 kHz at a distance of 2.5 mm from the lens. Theoretically computed field distributions, optimized frequency of operation, and spatial resolution focal length are compared with experimental measurements. The differences between experimental measurements and the theoretical computations are analyzed. The theoretical calculation of the focal spot diameter is 1.7 mm which is 48% of the experimental measurement at a frequency of 80-90 kHz. This work illustrates the capabilities of a hybrid algorithm approach to design of flat acoustic lenses to operate in air with a resolution of greater than the incident wavelength and the challenges of characterizing acoustic field distribution in air.

Demonstration of model-assisted probability of detection evaluation methodology for eddy current nondestructive evaluation

A model-assisted POD (MAPOD) evaluation approach is explored for the eddy current inspection of fatigue cracks in titanium. Experimental results are presented comparing crack and EDM notch responses and different eddy current measurement systems. The MAPOD evaluation process is performed using a simulated case study, highlighting the benefit of leveraging better models to mitigate variation in the model fit and minimize test sample requirements. The benefit of validating NDE techniques that use inverse methods to estimate uncontrolled measurement conditions is also studied.

Characterization of microstructure with low frequency electromagnetic techniques

Abstract : A new computational method for characterizing the relationship between surface crystallography and electrical conductivity in anisotropic materials with low frequency electromagnetic techniques is presented. The method is discussed from the standpoint of characterizing the orientation of a single grain, as well as characterizing statistical information about grain ensembles in the microstructure. Large-area electron backscatter diffraction (EBSD) data was obtained and used in conjunction with a synthetic aperture approach to simulate the eddy current response of beta annealed Ti-6Al-4V. Experimental eddy current results are compared to the computed eddy current approximations based on electron backscatter diffraction (EBSD) data, demonstrating good agreement. The detectability of notches in the presence of noise from microstructure is analyzed with the described simulation method and advantages and limitations of this method are discussed relative to other NDE techniques for such analysis.

A synthetic aperture routine to approximate Rayleigh surface wave imaging scans over anisotropic media

A method for determining the effective Rayleigh surface wave (RSW) velocity under the probe during a RSW imaging experiment was developed. The synthetic aperture routine can take in polycrystalline data with arbitrary c-axis orientation for each crystal and calculate the total effect that the crystals below the probe has on the response. It relies on calculation of RSW velocity in arbitrary directions for hexagonal crystals by applying numerical methods to the general theory described by several groups using the Stroh formalism. In this paper, the method will be summarized and example will be shown that demonstrate the feasibility of the routine for approximating scans over the surface of samples. Application of the method in the context of material characterization will be discussed.

Broadband aperiodic air coupled ultrasonic lens

This paper demonstrates the possibility of subwavelength, defined as less than the incident wavelength, broadband focusing in an aperiodic air coupled ultrasonic lens. A near field probe is used to detect well defined resonances from 75 to 125 kHz. The spatial resolution at each of the resonant frequencies is determined and demonstrated to be smaller than the wavelength of the ultrasonicwaves. The strongest resonance is observed at 82.9 kHz with a focal spot size of 3.12 mm. The subwavelength spatial resolution of the lens structures at the resonances is attributed to the near field scattering of the acoustic waves.

Forward propagation of parametric uncertainties through models of NDE inspection scenarios

Forward uncertainty propagation has been a topic of interest to NDE researchers for several years. To this point, the purpose has been to gain an understanding of the uncertainties that can be seen in signals from NDE sensors given uncertainties in the geometric and material parameters of the problem. However, a complex analysis of an inspection scenario with high variability has not been performed. Furthermore, these methods have not seen direct practical application in the areas of model assisted probability of detection or inverse problems. In this paper, uncertainty due to spatial heterogeneity in material systems that undergo NDE inspection will be discussed. Propagation of this uncertainty through forward models of inspection scenarios will be outlined and the mechanisms for representing the spatial heterogeneity will be explained in detail. Examples will be provided that illustrate the effect of high variability in uncertainty propagation in the context of forward modeling.

Experimental eddy current measurements of flawed edges compared with results from probabilistic numerical models

Abstract : Eddy current detection of flaws in edges presents challenges in experimental procedures during benchmark studies in the laboratory for model validation as well as practical implementation of a real world detection system. These difficulties result in distortions to the signal that mask the effects from the flawed region itself. Rather than attempting to perfect the experimental setup, we propose to make the numerical models more robust by incorporating randomness in the experimental procedure with uncertainty quantification methods. We present the motivation for the specific method chosen, the probabilistic collocation method (PCM), and the mathematical development behind the method, and then present the results from numerical simulations with a validation measure.

Modeling of the Change of Impedance of an Eddy Current Probe Due to Small Changes in Host Conductivity

Two different approximation techniques for predicting the response of an eddy current coil in the presence of small changes in conductivity were developed. The small changes in conductivity are the result of changes in the orientation of individual anisotropic crystals in a polycrystalline aggregate. Orientation information from electron backscatter diffraction was imported directly into the modeling domain and the simulations were run to map orientations into an approximated eddy current response. These approximated responses were compared with experimental data obtained with commercially available eddy current equipment, and the approximations were found to be in good agreement with experiment. Further verification was performed with other existing numerical and analytical models to demonstrate the accuracy of the approximations made in deriving the eddy current response. This paper shows these results and demonstrates the viability of using low-fidelity approximations in predicting the eddy current response when the change in conductivity is low.

Role of interface conditions in low frequency electromagnetic testing of multilayer structures

When developing simulations of NDE testing methods it is imperative to use an accurate physical representation. Many inaccuracies in simulations can be traced to faulty or incomplete assumptions made for specific problem geometries, parameter constraints, or boundary conditions. An example of this is the assumed eddy current flaw response in layered media. A critical assumption often made is that when the plates are in contact, they are in electrical contact and behave as a single conductor. The purpose of this study is to dissect this assumption and propose alternate representations of the problem. A series of experiments were conducted alongside numerical models to provide evidence of the inadequacy of the assumption. Simulations were also used to predict the effects of varying interface conditions on eddy current signals due to surface cracks in sub-layer metals.

Characterization of a random anisotropic conductivity field with Karhunen-Loeve methods

Abstract : While parametric uncertainty quantification for NDE models has been addressed in recent years, the problem of stochastic field parameters such as spatially distributed electrical conductivity has only been investigated minimally in the last year. In that work, the authors treated the field as a one-dimensional random process and Karhunen-Loeve methods were used to discretize this process to make it amenable to UQ methods such as ANOVA expansions. In the present work, we will treat the field as a two-dimensional random process, and the eigenvalues and eigenfunctions of the integral operator will be determined via Galerkin methods. The Karhunen-Loeve methods is extended to two dimensions and implemented to represent this process. Several different choices for basis functions will be discussed, as well as convergence criteria for each. The methods are applied to correlation functions collected over electron backscatter data from highly micro textured Ti-7Al.