Determination of the modulation frequency for thermographic non-destructive testing

• Inverse heat conduction in a multi-layer slab with periodic boundary excitation.
• Lumped parameters representation to relate temperature and modulation frequency.
• Modulation frequency determines the temperature amplitude (defect detectability).
• Series solutions provide explicit representations of frequency versus temperature.
• Experimental validation of the predicted range of modulation frequencies.

We propose polynomial solutions of the inverse heat conduction problem to design thermographic non-destructive tests for detecting defects in composite and multi-layer materials. Inverse heat conduction in a multi-layer material slab with periodic temperature excitation is considered, and analytical quadrupole representation is used to derive a lumped parameters formulation. Predictions of the proposed polynomial representations are experimentally validated by detecting machined defects on thermally excited panels. For modulation frequencies outside the predicted detection range, defects appear on thermal images as blurry and unstructured; conversely, for modulation frequencies within the predicted range, defects are correctly represented on thermal images.