R. Celorrio

Simultaneous measurement of thermal diffusivity and optical absorption coefficient using photothermal radiometry. II Multilayered solids

coefficient using photothermal radiometry. II Multilayered solids Agustı́n Salazar, Raquel Fuente, Estibaliz Apiñaniz, Arantza Mendioroz, and R. Celorrio Departamento de Fı́sica Aplicada I, Escuela Técnica Superior de Ingenierı́a, Universidad del Paı́s Vasco, Alameda Urquijo s/n, Bilbao 48013, Spain Departamento de Matemática Aplicada, EINA/IUMA, Universidad de Zaragoza, Campus Rı́o Ebro, Edificio Torres Quevedo, Zaragoza 50018, Spain

Application of the thermal quadrupole method to the propagation of thermal waves in multilayered cylinders

Up to now, research in photothermal techniques has been mainly restricted to samples with flat surfaces. In this work the surface temperature oscillation of multilayered cylindrical samples which are heated by a modulated light beam is calculated by using the quadrupole method. Different illumination geometries have been studied. Moreover, the lack of adherence between layers, as well as heat losses at the surface, has been considered in the model. Following this theoretical approach, photothermal techniques can be used for the quantitative thermophysical characterization of cylindrical samples with continuously varying in-depth thermal conductivity.

Thermal diffusivity of rods, tubes, and spheres by the flash method

The flash method is the most used technique to measure the thermal diffusivity of solid samples. It consists of heating the front face of an opaque slab by a short light pulse and detecting the temperature evolution at its rear surface, from which the thermal diffusivity is obtained. In this paper, we extend the classical flash method to be used with rods, tubes, and spheres. First, the temperature evolution of the back surface of solid cylinders, hollow cylinders, and spheres is calculated. Then, experimental measurements of the thermal diffusivity on a set of stainless steel samples confirm the validity of the method.

On the effective thermal diffusivity of fiber-reinforced composites

Modulated photothermal techniques provide useful methods based on linear relations between measurable quantities to obtain the thermal diffusivity of homogeneous materials. In this letter the applicability of such linear relations in the case of unidirectional fiber-reinforced composites (UFRC) is analyzed. Based on the solution of the propagation of plane thermal waves in a material with aligned buried cylinders, we found that the linear relation valid for homogeneous materials still holds for UFRC. However, its slope does not give the effective thermal diffusivity as derived from the effective thermal conductivity measured by steady-state experiments. Anyway, as the number of cylinder rows increases the thermal diffusivity measured by modulated methods approaches the steady value asymptotically. The model is validated by photothermal measurements performed on calibrated samples.

Characterization of vertical buried defects using lock-in vibrothermography: II. Inverse problem

An inversion procedure is presented to reconstruct buried heat sources (revealing defects) from surface temperature data obtained by multifrequency lock-in vibrothermography. The severe ill-posedness of the problem is overcome by regularizing the minimization of the squared differences between experimental and calculated data. Two regularization functionals, zero-order Tikhonov and total variation, have been tested by inverting synthetic data. For added uniform white noise levels as high as 20%, total variation has proven to give more accurate inversions. This procedure is applied to reconstruct heat sources from experimental lock-in vibrothermographic measurements performed on metallic samples containing calibrated inner heat sources. The results are very promising regarding the characterization of hidden defects using lock-in vibrothermography.

Accurate reconstruction of the thermal conductivity depth profile in case hardened steel

The problem of retrieving a nonhomogeneous thermal conductivity profile from photothermal radiometry data is addressed from the perspective of a stabilized least square fitting algorithm. We have implemented an inversion method with several improvements: (a) a renormalization of the experimental data which removes not only the instrumental factor, but the constants affecting the amplitude and the phase as well, (b) the introduction of a frequency weighting factor in order to balance the contribution of high and low frequencies in the inversion algorithm, (c) the simultaneous fitting of amplitude and phase data, balanced according to their experimental noises, (d) a modified Tikhonov regularization procedure has been introduced to stabilize the inversion, and (e) the Morozov discrepancy principle has been used to stop the iterative process automatically, according to the experimental noise, to avoid “overfitting” of the experimental data. We have tested this improved method by fitting theoretical data gene...

Scattering of cylindrical thermal waves in fiber composites: In-plane thermal diffusivity

In this article, we present a general solution for the ac temperature field of an opaque material containing aligned subsurface cylinders produced by a modulated line illumination parallel to the cylinders. This work completes the case of plane illumination treated in a previous paper [J. M. Terron, A. Salazar, and A. Sanchez-Lavega, J. Appl. Phys. 91, 1087 (2002)]. The model includes the multiple scattering effects suffered by the cylindrical thermal wave, generated by the line heat source, when interacting with the cylinders and with the sample surfaces. Numerical calculations illustrate the effect of buried cylinders on the sample surface temperature. This model is then used to calculate the in-plane effective thermal diffusivity of unidirectionally fiber-reinforced composites. We also calculate the decrease of this effective thermal diffusivity as a consequence of the presence of a thermal resistance between fibers and matrix. Experimental measurements using modulated photothermal techniques on calibr...

Periodic Dirac Delta Distributions in the Boundary Element Method

This paper is concerned with the numerical solution of boundary integral equations on smooth curves of the plane with some numerical methods having in common the use of sets of equally spaced periodic Dirac delta distributions as trial functions. In a functional frame of classical periodic pseudodifferential equations of nonpositive order, delta-spline and delta–delta methods are introduced and analysed with the overall aim of obtaining asymptotic expansions of the error in weak and strong norms. As a byproduct we obtain the convergence of the coefficients associated to the discrete delta approximation to pointwise values of the unknown, as well as superconvergent choices of positions of the delta distributions in relation with the discretization grid. Two numerical examples are explored to show nodal errors and the applicability of Richardson extrapolation.

Design of experiments and energy dissipation analysis for a contact mechanics 3D model of frictional bolted lap joints

Bolted lap joints allow structural assemblies to be made. The answer to requirements, both static and dynamic, depends on the joint behaviour. Bolted joints are a primary source of energy dissipation in dynamic built-up and space structures among others. This paper presents an analysis of a bolted lap joint, subjected to a relative displacement after applying a pre-stress on the bolt in order to characterise the joint behaviour. For this purpose a 3D modelling is made by means of finite elements, using design techniques of experiments (DOE) to fit constitutive contact parameters. The theoretical results relative to elasto-plastic hysteresis cycles of the joint are experimentally validated. Finally, the preload effect and the magnitude of the displacement on the non-linear joint behaviour are analysed to determine equivalent stiffness and dissipated energy in the hysterical loops of the joint.

Vertical cracks characterization using lock-in thermography: II finite cracks

The aim of this work is to characterize vertical cracks of finite size and arbitrary shape using optically excited lock-in thermography. In the first place, we have solved the direct problem, which consists of calculating the surface temperature distribution when the shape, size and width of the vertical crack are known. To do this we have developed a new method based on discontinuous finite elements, which allows one to deal even with very narrow cracks, for which classical finite element methods fail. The surface temperature of steel samples containing semi-infinite cracks and illuminated with a laser beam focused close to the crack has been measured using a lock-in thermography setup. A least square fit of the amplitude and phase of the surface temperature is used to retrieve the width and depth of the semi-infinite crack. A very good agreement between the nominal and retrieved values of both parameters is found, confirming the validity of the model.