Invited Article A Theoretical Model for the Measurement of Fiber Orientation with Thermal Waves

It is an important task of nondestructive testing to determine the fiber orientation of reinforced polymers. One appropriate method, especially for carbon fibers, is phase-sensitive modulated thermography, where images of the phase angle and the amplitude of thermal waves at the surface of the sample are obtained. The anisotropy induced by the fibers results in elliptical contour lines whose direction and excentricity are correlated with the orientation of the fibers and the corresponding degree of thermal anisotropy, respectively. To correctly interpret the measurements one needs a theoretical model. Such a model is developed for layered media with different orientations in different depths. Using a Fourier transform one can reduce the heat conduction in three dimensions to a one-dimensional problem that can be solved analytically. Because the FFT algorithm is used for the numerical evaluation, the calculation of phase and amplitude images is very fast, with the computation time being approximately equal to the measurement time. The comparison with experiments for a test sample shows a good agreement between theory and measurement.