Measurement of the thermal radial diffusivity of anisotropic materials by the converging thermal wave technique

Abstract

Thermal non-destructive testing techniques are increasingly being used for testing and characterizing various materials. The technique we discuss here is quite appropriate for laminated materials, which are often highly anisotropic, with a thermal radial diffusivity a r (parallel with the laminae) that is very different from the thermal normal diffusivity a z (normal to the sheets). The radial diffusivity a r is measured using a method proposed by Cielo et al. A pulsed laser heats the sample through an axicon (lens of conical cross-section), so that the heated surface is annular. The surface temperature is monitored by an IR detector focused on the center of the annulus. From the experimental temperature-time history θ exp(t) of this point, one can plot an apparent radial diffusivity vs. time curve, under the assumptions that: (1) the medium is either semi-infinite, or extremely thin or translucent; (2) there are no convection heat losses at the surface of the medium; (3) the energy deposit on the medium is of short duration in comparison with the characteristic radial diffusion time. This apparent radial diffusivity curve can be obtained either by direct inversion of the experimental thermogram θ exp(t) using the mathematical expression of the theoretical thermogram θ th(t) , or by a technique using its logarithmic derivative with respect to time. In the case of a semi-infinite medium, these two methods are compared here from the point of view of the error in the evaluation of a r while assuming an absolute error in the temperature (due to the noise of the experiment). Then the general case of the sample of finite thickness with heat losses at its surface is studied numerically. Firstly the errors in the calculation of a r are evaluated with the two methods, then mathematical corrections are proposed to reduce the effects of finite thickness and heat losses in the experimental thermogram. Finally, several sources of error in the evaluation of a r are presented and studied numerically, namely the non-zero width of the annulus, the offset and the radial extent of the detection area respectively.