Abstract
When scanning a specimen using a line heat source at a constant velocity, a temperature change occurs partly due to specular reflection at the defect interface. Assuming that the reflection of a transient thermal response is similar to that of geometrical optics, we performed waveform analysis using an imaging method. Image points are calculated based on differential geometry; this can also be performed for a curved surface using a general equation. A combination of the steepest descent analysis of a moving heat source problem and a convolution technique successfully yielded waveforms comparable to those of experimental temperature responses. We designed and constructed an active thermographic imaging system in which a linearly focused continuous wave laser beam was scanned perpendicular to the beam as it covered the entire surface of specimens with simulated internal defects. The real-time response was recorded as a temperature waveform at each image pixel. Waveforms were calculated for specimens without or with buried cylindrical defects parallel to their surfaces and compared to the experimental data. The theory well-explains the signal generation mechanism, and excellent agreement was obtained in waveforms. Some discrepancy between theory and experiment indicates more complicated problems in heat and mass transfer.
Highlights
Active thermography captures thermal images emitted by solid specimens that have been excited by temporally or spatially varying thermal sources
An analytical solution for a point heat source moving at a constant velocity in one direction was derived by Favro et al
Using a generalized incomplete gamma function,5 Molina-Giraldo et al.6 derived an analytical solution for a moving point source and a numerical solution for a line heat source aligned orthogonally to the specimen surface while moving parallel to it
Summary
Active thermography captures thermal images emitted by solid specimens that have been excited by temporally or spatially varying thermal sources. An analytical solution for a point heat source moving at a constant velocity in one direction was derived by Favro et al.. An analytical solution for a moving point heat source considering heat source distribution was derived by Cline and Anthony for application to laser or electron beam melting. Using a generalized incomplete gamma function, Molina-Giraldo et al. derived an analytical solution for a moving point source and a numerical solution for a line heat source aligned orthogonally to the specimen surface while moving parallel to it. These analyses did not consider temporal behavior in detail.
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