Integral methods and non-destructive testing through stimulated infrared thermography

Integral methods and non-destructive testing through stimulated infrared thermography. integral methods (Fourier, Laplace, Hankel, Mellin,...) constitute classical tools for solving diffusion problems in simple geometries. Recently these methods have been applied to heat transfer in multilayer materials in electronics or in the composite industry. Solution of a multidimensional diffusion problem within a slab that contains one or several defects (delamination, bad sticking, etc.) constitutes an interesting application. These techniques provide a solution of the inverse problem under an explicit form, which brings some advantages when compared to numerical methods (finite elements, finite differences, etc.) low computation time, simple error analysis, filtering. An application to non-destructive testing through active thermography is presented here. It deals with the problem of detecting defects of resistive nature in planar materials and of estimating their characteristics on a quantitative basis. Two inverse methods are presented. The first one is based on a one-dimensional transfer model that is applied locally (Laplace transforms with respect to the time variable), while the second one takes into account the two-dimensional character of the transfer (same time Laplace transformation followed by a Fourier cosine transformation with respect to space). An experiment allows the validation of these two inversion methods.