Electrothermics

4.3. Basic thermo-inductive technique theory

Flaws have three-dimensional (3D) geometries by their very natures. Modeling a flaw detection method is therefore a 3D problem. Furthermore, this model (for the thermo-inductive technique) is a coupled electromagnetic and thermal problem. Modeling this complex system is generally done by numerical methods, particularly the finite element method.

However, for components with simple geometries (such as rectangular plates and cylindrical tubes) with regular flaws parallel to one of the surfaces, we can find an analytic or semi-analytic solution to the problem. In most cases, these types of solutions only offer very partial indications on the flaw’s presence and its nature. Despite these indications, however, the main advantage of these methods is their capacity to explain physical phenomena simply and comprehensibly. In this spirit, part of this chapter is dedicated to the 1D modeling of flaw detection using the thermo-inductive method.

In this frame of mind, the interaction between thermal waves and the flaw will be tackled to better understand the notion of amplitude contrast and phase shift contrast as the two principal discrimination parameters to detect and analyze flaws. The advantages and complementarity of these two parameters will be analyzed for all the three modes of stimulation (i.e. the pulsated mode, the modulated mode, and the pulsated phase mode).

4.3.1. One-dimensional models for the propagation of the thermal wave in a ...