Mathematical Modelling of Transient Thermography and Defect Sizing

The principle employed to obtain an image of a sub-surface defect by transient thermography is deceptively simple. A surface is heated by powerful flash lamps and subsequent thermal transients are recorded by an infrared camera. Defects cause perturbations in heat flow which are revealed by the camera. Whilst there is now a considerable body of practical experience of the application of the technique, there is rather less precise quantitative information about the image formation process that could lead to reliable defect sizing. In earlier papers [1,2] one of the authors considered circular air gap defects by treating them as buried uniformly heated disks. The thermal edge-effect occurring at the tip of a perfect crack-like defect was dealt with analytically by adapting the well established Wiener-Hopf [3] solution for the scattering of light or sound from the edge of a semi-infinite half-plane. The problem was solved in the frequency-domain, i.e. to obtain a thermal wave solution, and then a time-domain solution was obtained by a suitable transformation. The analysis showed an edge-effect amounting to a decay in temperature contrast over a distance of about a thermal diffusion length from the edge of the crack. A crucial feature of the edge-effect was the decay of thermal contrast to zero at the crack tip. This, and the edge-effect as a whole, is caused by the flow of heat around the crack tip from the hot upper surface of the crack to the cold under surface. The symmetry of this process ensures that there is no net flux increase for material in front of the crack tip