Vertical Cracks Excited in Lock-in Vibrothermography Experiments: Identification of Open and Inhomogeneous Heat Fluxes.

Lock-in vibrothermography has proven to be very useful to characterizing kissing cracks producing ideal, homogeneous, and compact heat sources. Here, we approach real situations by addressing the characterization of non-compact (strip-shaped) heat sources produced by open cracks and inhomogeneous fluxes. We propose combining lock-in vibrothermography data at several modulation frequencies in order to gather penetration and precision data. The approach consists in inverting surface temperature amplitude and phase data by means of a least-squares minimization algorithm without previous knowledge of the geometry of the heat source, only assuming knowledge of the vertical plane where it is confined. We propose a methodology to solve this ill-posed inverse problem by including in the objective function penalty terms based on the expected properties of the solution. These terms are described in a comprehensive and intuitive manner. Inversions of synthetic data show that the geometry of non-compact heat sources is identified correctly and that the contours are rounded due to the penalization. Inhomogeneous smoothly varying fluxes are also qualitatively retrieved, but steep variations of the flux are hard to recover. These findings are confirmed by inversions of experimental data taken on calibrated samples. The proposed methodology is capable of identifying heat sources generated in lock-in vibrothermography experiments.

Sizing the Depth and Width of Narrow Cracks in Real Parts by Laser-Spot Lock-In Thermography.

We present a complete characterization of the width and depth of a very narrow fatigue crack developed in an Al-alloy dog bone plate using laser-spot lock-in thermography. Unlike visible micrographs, which show many surface scratches, the thermographic image clearly identifies the presence of a single crack about 1.5 mm long. Once detected, we focus a modulated laser beam close to the crack and we record the temperature amplitude. By fitting the numerical model to the temperature profile across the crack, we obtain both the width and depth simultaneously, at the location of the laser spot. Repeating the process for different positions of the laser spot along the crack length, we obtain the distribution of the crack width and depth. We show that the crack has an almost constant depth (0.7 mm) and width (1.5 µm) along 0.7 mm and features a fast reduction in both quantities until the crack vanishes. The results prove the ability of laser-spot lock-in thermography to fully characterize quantitatively narrow cracks, even below 1 µm.

Generalizing the flash technique in the front-face configuration to measure the thermal diffusivity of semitransparent solids.

In this work, we have extended the front-face flash method to retrieve simultaneously the thermal diffusivity and the optical absorption coefficient of semitransparent plates. A complete theoretical model that allows calculating the front surface temperature rise of the sample has been developed. It takes into consideration additional effects, such as multiple reflections of the heating light beam inside the sample, heat losses by convection and radiation, transparency of the sample to infrared wavelengths, and heating pulse duration. Measurements performed on calibrated solids, covering a wide range of absorption coefficients (from transparent to opaque) and thermal diffusivities, validate the proposed method.

Thermal diffusivity of nonflat plates using the flash method.

The flash method is the standard technique to measure the thermal diffusivity of solid samples. It consists of heating the front surface of an opaque sample by a brief light pulse and detecting the temperature evolution at its rear surface. The thermal diffusivity is obtained by measuring the time corresponding to the half maximum of the temperature rise, which only depends on the sample thickness and thermal diffusivity through a simple formula. Up to now, the flash method has been restricted to flat samples. In this work, we extend the flash method to measure the thermal diffusivity of nonflat samples. In particular, we focus on plates with cylindrical and spherical shapes. The theoretical model indicates that the same expression for flat samples can also be applied to cylindrical and spherical plates, except for extremely curved samples. Accordingly, a curvature limit for the application of the expression for flat samples is established. Flash measurements on lead foils of cylindrical shape confirm the validity of the model.

Thermal diffusivity measurements of thin plates and filaments using lock-in thermography.

Photothermal radiometry has been widely used to measure the thermal diffusivity of bulk materials. In the case of thin plates and filaments, a one-dimensional heat propagation model including heat losses has been developed, predicting that the thermal diffusivity can be obtained by recording both the surface temperature amplitude and phase profile slopes ("slope method"). However, this method has given highly overestimated values of the thermal diffusivity of poor-conducting films and filaments. In this paper we analyze the effect of the experimental factors affecting the thermal diffusivity measurements of thin plates and filaments using infrared thermography, in order to establish the experimental conditions needed to obtain accurate and reliable values of the diffusivity of any kind of material using the slope method. We present the calculations of the surface temperature of thin isotropic and anisotropic plates heated by a modulated and tightly focused laser beam, showing that the slope method is also valid for this kind of pointlike heating. Special attention is paid to the effect of surface heat losses (convective and radiative) on the diffusivity measurements of small-dimension and poor-conducting materials. Lock-in thermography measurements performed in the best experimental conditions on a wide set of samples of different thermal properties (thin isotropic and anisotropic plates and filaments) confirm the validity of the slope method to measure accurately the thermal diffusivity of samples of these shapes.