Adam L. Pilchak

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.

Progress in model development for eddy current response in the presence of small conductivity changes

In this paper, an approximation technique for predicting the response of an eddy current coil in the presence of small changes in conductivity is discussed. The small changes in conductivity that are considered in this work are changes in the orientation of single crystals in polycrystalline, anisotropic materials. Data from electron backscatter imaging techniques is presented and used for the analysis. The models were run for the microstructure data and an approximation to the eddy current response is shown. This image is compared with images from actual eddy current probes and the approximations are shown to be relatively accurate compared with a previously presented model.

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.

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.

2D stochastic-integral models for characterizing random grain noise in titanium alloys

We extend our previous work, in which we applied high-dimensional model representation (HDMR) and analysis of variance (ANOVA) concepts to the characterization of a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field. That example was treated as a onedimensional problem, because those were the only data available. In this study, we develop a more rigorous two-dimensional model for characterizing random, anisotropic grain noise in titanium alloys. Such a model is necessary if we are to accurately capture the clumping of crystallites into long chains that appear during the processing of the metal into a finished product. The mathematical model starts with an application of the Karhunen-Loeve (K-L) expansion for the random Euler angles, θ and φ, that characterize the orientation of each crystallite in the sample. The random orientation of each crystallite then defines the stochastic nature of the electrical conduct...

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.