Experimental modelling of IR Nonlinear photothermal radiometry in carbon/epoxy composite materials

The potential of thermal nonlinear effects in composite materials was investigated for nondestructive testing. Second harmonic generation in thermal-wave fields has attracted much attention in recent years for the non-destructive evaluation of solid structures. Even though not the only source, the presence of a defect can result in a strong nonlinear signature, which could enhance the detectability of photothermal methods. The following experimental survey trails several theoretical analyses on the subject, mostly for homogeneous isotropic samples. As composite material structures exhibit often thermo-mechanical nonlinearities originating from the polymer matrix, they appeared to be ideal candidates to exploit the potential of nonlinear photothermal radiometry. In this work, a theoretical model that was recently developed is used to estimate the generated overtones that originate from the most common cause of failure of composites, the delamination. Moreover, the theory is experimentally validated using IR photothermal radiometry by modelling the oscillation of the size of the delamination by means of a piezoelectric transducer. Introduction: In principle, nonlinear photothermal radiometry exploits higher harmonic signal generation for nondestructive testing. The temperature field imposed by amplitude modulated laser excitation depends on variations in thermal properties [1-3] as well as the synchronous modification of the boundary conditions [4, 5]. Such effects, which are closely linked with the present of a defect, allow enhancing the contrast of a defected area by detecting the second harmonic temperature signal. The theoretical potential of using nonlinear photothermal radiometry in fibre reinforced composite materials partially emerged as measurements demonstrated recently that the thermal properties exhibit strong dependence on temperature [2, 3]. Nonlinear effects are often present in composites, and originate from the thermomechanical behaviour of the polymer matrix. Numerical analysis using a finite element model of this particular nonlinearity has motivated to perform an experimental examination. When a defect is introduced in an intact sample, spectral analysis shows that the second harmonic of the surface temperature signal is affected much more than the fundamental frequency component. Although the contrast for both signal components follows the same pattern for the fundamental and the second harmonic, the respective relative values are strongly different. This implies in practice a better visibility of the defect. Moreover, delaminations are very often formed in composites due to large interlaminar shear stresses. Modulated laser excitation alters the uniform temperature field to a gradient with higher temperatures near the surface. Therefore, non-uniform thermal expansion results in thermoelastic bending, the modulation of which imposes a vibration of the layer above the delamination [6] at the excitation frequency. The triggered oscillation of the air gap in the delamination entails an alteration of the boundary condition for the heat diffusion problem. This phenomenon was first accredited to explain the strong nonlinearities observed [7]. Later it was shown theoretically that this effect can be really effective [4]. In this work, a theoretical model that was recently developed [12] is validated experimentally. The model was used to estimate the influence of the oscillation of the size of a defect on the photothermal signal and the order of magnitude of the second harmonic that is generated under conditions. To this end, a composite sample was tested in combination with a metallic substrate that was enabled to vibrate independently. Theoretical background: The thermal and the displacement-wave fields in a solid are in general coupled through the equations of thermoelastodynamics [8]. These equations are formulated for a homogeneous anisotropic unbounded medium as follows: