The influence of surface coatings on the differences between numerical and experimental results for samples subject to a pulse thermography examination

This paper presents the analysis of the influence that black surface paint layers have on the differences in the results obtained from numerical modelling and those obtained experimentally. Surface paints are commonly used for the purposes of pulse experiments in order to increase the sample surface emissivity and help enhance the signal obtained. The paper argues that it is important to include these paint layers in the numerical analysis either directly, as additional material layer, or alternatively, to estimate their influence and take it into account when comparing the corresponding results. Infrared thermography is a method of non-contact surface temperature measurement. The measurement principle is based on the radiation law, which puts into relation the energy radiated from the object’s surface and its surface temperature. Two different surfaces do not necessarily radiate the same amount of energy when they are at the same temperature. The amount of energy emitted depends also on the object surface emissivity, a coefficient ranging from 0 to 1 and putting into relation the energy emitted from the real object surface at a given temperature and the energy that the ideal blackbody surface would emit at the same temperature. The higher the surface emissivity, the closer the real object surface to the ideal blackbody surface and the higher the quantity of energy emitted at a given temperature. In non-destructive testing, more often than not, surface characteristics of materials that are subject to pulse thermography (or other IR thermography) testing procedures, have poor surface emissivity properties. In the case of different metals, such as aluminium and steel, emissivity values range from 0.1 to 0.4 [1]. Knowing already that the thermal signal has a relatively low signal to noise ratio (SNR), especially when the temperatures obtained are not much higher with respect to room temperature, different strategies of signal enhancement are commonly used [2]. High emissivity surface paints (�>0.95) are applied on tested sample surfaces prior to experiment in order to increase the signal that is emitted from the sample surface and captured by the IR camera. Those layers of paint are often neglected when thermal contrast analysis is made, assuming therefore that their influence on the experimental results is negligible. An experiment, in which a metal flat-bottom hole sample plate was tested, revealed large differences when the results were compared between the black-painted region and a small region where the surface black paint fell off over the time. This observation encouraged further research which was directed towards a Plexiglass model. It was expected that Plexiglass was to be easier to work with due to its lower conductivity and, therefore, to the slower rate at which the changes in the sample appear during the experiment, thus making it easier to see the differences. As a result of that research, this article demonstrates to what extent the surface paints can influence the maximum thermal contrast as well as the time of its appearance and why they should not be neglected completely when numerical models are compared to the corresponding experimental sample. 2. Relevant literature overview In an attempt to develop a method that would enable the quantitative subsurface defect characterisation based upon the maximum thermal contrast, many authors have used the theoretical models of heat transfer applied to the given sample tested via pulse thermography inspection procedure. In such a way, they were able to determine the theoretical thermal contrasts which then could be compared to those obtained by experiments for corresponding defects. Different approaches were adopted depending on the model assumptions with respect to the model geometry (1D, 2D or 3D), to the heat transfer mechanisms included, as well as to the mathematical method used to obtain the solution of the problem previously defined. Some models included development of analytical models assuming the sample to be a semi-infinite body subject to a short Dirac pulse of high intensity and with boundary conditions defined to be adiabatic, so that no heat was exchanged between the object and its environment after the heat pulse was completed. [3,4,5] Others treated the models of delaminations between the two material layers and used integral methods (Fourier, Laplace …) in order to obtain the solution of the inverse problem in the explicit form in the transformed time-space domain. [6, 7, 8, 9] Application of the finite difference method as well as the finite element method was also reported in several articles, treating the problem of heat transfer in tested samples. It was found useful to turn to these mathematical tools especially in cases where modelling of complex samples was needed and in those cases where boundary conditions included heat transfer by radiation and where some properties of the materials used in modelling were temperature dependant [10, 11,