Pulsed thermography in the evaluation of an aircraft composite using 3D thermal quadrupoles and mathematical perturbations

Abstract

This paper is devoted to the characterization of a subsurface flaw within an anisotropic medium during a nondestructive evaluation test using stimulated infrared thermography. A typical illustration is a delamination within a stratified composite material. The originality of the current study consists of providing simple analytical solutions to evaluate the depth and the volume of the flaw in a three-dimensional heat transfer configuration. The volume of the flaw is defined as the product of its lateral extent by its thickness. If the thermal contact resistance of the flaw is known, its lateral extent can be derived from the volume expression. The method proposed here consists of applying first a Laplace transform on the time variable t, then a Fourier transform on the space variables, x and y. The numerical or semi-analytical true solution of integral equations generated by this problem may be very time-consuming, especially in a three-dimensional configuration. We therefore suggest a modelling reduction using the analytical perturbation method written only at its first order. It is however assumed that flaw thermal resistance is small compared to the whole thermal resistance of the material under investigation. The perturbation formalism leads to the construction of approximate analytical solutions that are very convenient for quantitative inversion. The validity of this method has been analysed through a real nondestructive test performed on a calibrated carbon-epoxy laminate of known characteristics.