To validate the performance of inspection techniques, probability of detection (POD) studies are performed. The preparation of POD samples with real fatigue cracks and the process to acquire a statistically significant number of measurements is often very time consuming and expensive, providing a significant burden for the validation of new inspection techniques.

Model-Assisted Probability of Detection

Nondestructive evaluation (NDE) is to materials and structures what CAT scanning is to the human body—an attempt to look inside without opening up the body. As in CAT scanning, modern NDE requires sophisticated mathematical software to perform its function. This is especially true with regard to quantitative NDE, wherein we attempt to quantify defects, that is, determine their size, location, even shape, rather than just to detect their presence. Low-frequency electromagnetic methods using eddy-currents are a traditional mode of doing NDE (approximately 35% of NDE uses eddy-currents, depending upon the specific application), but the technology still suffers from a lack of algorithms and software to allow its full potential to be realized. The electromagnetics code, VIC-3D ®, was developed to alleviate that problem, and in this book we apply VIC-3D ®to solve forward and inverse problems in eddy-current NDE.

Overview of Methods of Computational Electromagnetics

In the last chapter, we developed a volume-integral approach to the analysis of printed-circuit probes. Such probes are finding increased use in planar and conformable arrays, because of their small size and the ability to be manufactured in various shapes. Arrays are typically composed of a set of transmitter coils and receiver coils, which allows a variety of multiplexing schemes to generate responses with given features (see [96]). For example, one can generate a two-dimensional “scan” with a suitable array, without moving it. This can be very effective when doing voxel-based inversions, as will be discussed in a later volume of this work.

Planar and Conforming Arrays of Probes

In this chapter, we describe the mathematical development of a general axisymmetric model for VIC-3D®. This model is capable of analyzing tubes with tube supports and roll-expanded transition zones. Features such as magnetite and sludge,are included, and materials may be either ferromagnetic or nonmagnetic. The model described in this chapter will include only differential (or absolute) bobbin coils.

Multilayered Media with Cylindrical Geometries

The preceding chapters of this book dealt largely with problems in which the host material and any anomalies were pure electrical conductors. The presence of magnetic permeabilities was merely an interesting side effect to the creation of the VIC-3D ® model and its solution. There are, of course, many problems in which magnetic permeability is present with electrical conductivity and must be accounted for, not only in creating the model but also in understanding the physics of the solution and its effect on the NDE process. In this chapter we consider magnetic effects in heat-exchanger tubes, focusing later on ferritic tubes, which are becoming of increasing importance in the nuclear power industry.

Coupled Problems in Heat-Exchanger Tubes

Techniques are described for numerical modeling of through-the-earth communication. The basic problem considered is evaluation of the field at a surface or airborne station due to an antenna buried in the earth. Equations are given for the field of a point source in a homogeneous or stratified earth. These expressions involve infinite integrals over wave number, sometimes known as Sommerfield integrals. Numerical techniques used for evaluating these integrals are outlined. The problem of determining the current on a real antenna in the earth, including the effect of insulation, is considered. Results are included for the fields of a point source in homogeneous and stratified earths and the field of a finite insulated dipole. The results are for electromagnetic propagation in the ELF-VLF range, but the codes also can address propagation problems at higher frequencies.

R.J. Lytle

Papers

Numerical modeling of subsurface communication