Application of 3D heat diffusion to detect embedded 3D empty cracks

Abstract

This paper presents a 3D boundary element model (BEM), formulated in the frequency domain, to simulate heat diffusion by conduction in the vicinity of 3D cracks. The model intends to contribute to the interpretation of infrared thermography (IRT) data results and to explore the features of this non-destructive testing technique (NDT) when it is used to detect and characterize defects. The defect is assumed to be a null thickness crack embedded in an unbounded medium. The crack does not allow diffusion of energy, therefore null heat fluxes are prescribed along its boundary. The BEM is written in terms of normal-derivative integral equations (TBEM) in order to handle null thickness defects. The resulting hypersingular integrals are solved analytically.

The applicability of the proposed methodology to defect detection tests is studied once the TBEM results have been verified by means of known analytical solutions. Heat diffusion generated by a 3D point heat source placed in the vicinity of a crack is modeled. The resulting thermal waves phase is compared with that obtained when the defect is absent, so as to understand the influence of crack characteristics on the IRT data results analysis, especially on the phase-contrast images. Parameters such as the size of the crack, its shape, its position (buried depth and inclination) and its distance from the heat source are analyzed. Some conclusions are drawn on the effects of varying those parameters.