. .. Results,

. .. , Degenerated case: coating on substrate characterization

. .. Conclusion, 164 d'acquisition de la camera thermique, ce temps n'est connu qu'à une image d'acquisition prêt. Compte tenu des matériaux modérément diffusifs étudiés ici, cette hypothèse n'a que peu d'influence. Pour envisager l'étude de materiaux plus diffusifs, il conviendrait de travailler avec des fréquences d'acquisition plus élevées et d'envisager une correction de l'origine des temps de mesure

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. .. , Some industrial applications of the handled complex materials, p.12

]. .. ,

]. .. ,

, Application of the phosphor coating on the surface of the engine piston, p.14

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, Application of the phosphor coating for a 2D temperature measurement at the inlet and exhaust valves surfaces

, Classification and panorama of thermal characterisation methods in unsteady state

, Classification of unsteady thermal caracterization methods as given by Degiovanni [19] and Rodiet

. .. , Inverse problem principle and main sections (steps), p.45

, Experimental setup representing the front face flash method and including the main devices involved in the measurement procedure : the sample, CO 2 laser and IR camera

.. .. Samples,

, Some devices/tools of the experimental setup

, Front and (b) Back infrared camera faces

, Miscellaneous items used for the materials densities measurement, p.52

C. Calorimeter, C80 by Setaram©

, Data acquisition and treatments software

, Calibration of the data (correspondence or correlation pixel/mm) using a graduated scale

, Framing of the measurements exploitation windows (cropping of the pictures or images), the red square bounds the region that will exported for treatments and involved in the identification method

, LIST OF FIGURES 2.14 The global classifications of commonly-used optimization methods, p.64

. .. , 15 3D test functions applied for the optimization algorithms, p.66

, Sensitivities evolution of linearly independent parameters problems (i.e. wellposed problems))[231]

, Sensitivities evolution of linearly dependent parameters problems (i.e. ill-posed problems) [231]

, Principe du problème inverse et description des étapes

, Physical configuration, mathematical modelling and boundary conditions in the real domain

, 2 Physical configuration, mathematical modelling and boundary conditions in the xy-Fourier and t-Laplace domains

, Front and rear face normalized harmonics for both models: "model" representing the direct correlation found in the literature and presented in 3.9, and "quad" representing the one developed using quadrupoles formalism

, PSO particles evolution during the optimization process, applied for the characterization of the CFRP material

, Experimental temperature fields on the exposed surface (z = 0), and temperature profiles at the boundaries (x = 0, x = l x , y = 0 and y = l y ), just after the excitation and at the exploitation limit, for the orthotropic CFRP studied material, p.100

.. .. Samples, 101 3.8 Normalized harmonics temporal evolution for experimental (dotted or normal lines) and inversely estimated data (symbols)

. .. , and the composite -CFRP (black; pentagram) -samples, p.103

. .. , 106 3.11 Sensitivities of the entire harmonics modes used for identification of the polyamide three main thermal diffusivities

, Sensitivities of the entire harmonics modes used for identification of the composite three main thermal diffusivities

, Sensitivities of the front face first harmonics representing the mean fields ? 0,0 , to the in-depth diffusivies a z and the total amount of heat Q absorbed at the surface of both samples, with their ratio in order to detect the decorrelation between both parameters

, Evolution of the first 4 harmonics, according to the value of the overall heat coefficient h

, Time evolution of the relative absolute deviation (error in %) between the front face normalized harmonics with an overall heat transfer h = 0 W · m ?2 · K ?1 and those with h = 10 W · m ?2 · K ?1

. .. , surface of polyamide sample, reconstructed from estimated parameters (left figure), and experimentally measured (right figure)

. .. Experimental-setup-overview,

. .. , 123 3.20 Comparison between experimental and estimated normalized harmonics evolution using impulse (circle) and pulse (star) type excitation for the polyamide material

, Calculation time relative to both the pseudo-analytical and numerical simulations according to the excitation duration time ? ex , with the average quadratic error between the two signals, p.130

, Reduced sensitivities of the front first four even normalized harmonics to the composite diffusivities (a x , a y , a z ), as a function of the laser pulse duration time (0.1, 10 and 30 s)

, as a function of the laser pulse duration time (0.1, 10 and 30 s)

, General principle of the identification procedure consisting in finding the set of parameter ? minimizing the differences between the synthetic projected data ? exp and the inverse projected model output ? mod

. .. , Raw and filtered experimental signals revealing the noise level, p.133

. .. Level, 134 3.29 Front face normalized harmonics evolution related to synthetic experimental data (raw data and noisy data simulated by FlexPDE) and reconstructed data by means of estimated parameters, for Q=10J and ? ex = 10 s

, Rear face normalized harmonics evolution related to synthetic experimental data (raw data and noisy data simulated by FlexPDE) and reconstructed data by means of estimated parameters, for Q=10J and ? ex = 10 s

, Multi-layer material subjected to a short and non-uniform laser excitation at the front face, with a continuous measurement of the corresponding temperature recording via an IR camera

. .. , Subdivision principle for the multilayers model validation, p.157

, Front and rear normalized harmonics using the monolayer and three-layers models, applied on the PA monolayer material fictitiously divided into three layers

, The difference in the main field ? 0,0 obtained using monolayer (Mono) model and that obtained using bilayer (Bi) model , with an illustration of ENH limitation, applied for both configurations

, 186 4.28 The both numerically tested and compared experimental configurations, dedicated to the thermal characterization of the TPT coating, vol.2

. .. , The evolution of normalized harmonics ? 2,2 reduced sensitivities to the in-depth thermal diffusivities of both layers, and for both configurations (a) and (b), p.191

. Tpt-coating-over and . .. Hdpe,

, Parameters and values used in the PSO algorithm

, 1 PSO specifications, and stopping criteria selected for the estimation procedure, p.98

, 2 Comparison of the diffusivity values estimated by the Direct and Simultaneous Estimation using Harmonics (DSEH), with the values obtained by the Estimation using the Normalization of Harmonics method (ENH) and the Multiple Steps Estimation using Harmonics (MSEH)

, Comparison of the diffusivity and energy Q (J) values estimated by the Direct and Simultaneous Estimation using Harmonics (DSEH), with the values obtained by the Estimation using Normalization of Harmonics method (ENH) and the Multiple Steps Estimation using Harmonics (MSEH)

, energy Q estimation results as a function of the excitation spatial form

, Comparison of the results between the one-step (non-predefined) and two-step methods

, Comparison of estimation results between other more accurate alternative strategies, and those of the current method

, Comparison of estimation results between other tested cases, and those of the current method

, Values of the identified thermal diffusivities for the polyamide and CFRP using two possible shapes of thermal excitation

, 128 3.10 Front and rear maximum temperature evolution (in ? C) at the center of the material, for different laser pulse durations ? ex and amount of the heat subjected on the surface of the material Q (J), Values of the parameters required for the numerical and analytical simulations and the sensitivity analysis

. .. , 134 3.12 Estimation results using synthetic measurements where Q is already known (Q = 0.71 J ), and excitation shape is predefined

E. E. Rassy, Y. Billaud, and D. Saury, Under-review) E. El Rassy, Y. Billaud, and D. Saury, Simultaneous identification method of multilayers thermal diffusivity tensors using unconventional flash technique, Measurement, vol.135, pp.199-212, 2019.

E. E. Rassy, Y. Billaud, and D. Saury, Flash method experimental design for the thermal characterization of an orthotropic material. Peer-Reviewed Conference Papers

E. E. Rassy, Y. Billaud, and D. Saury, Estimation directe de propriétés thermophysiques de matériaux orthotropes

E. E. Rassy, Y. Billaud, and D. Saury, Best strategy to simultaneously estimate the thermal diffusivities of orthotropic composite medium embedded in two-layer materials, pp.4-14

E. E. Rassy, Y. Billaud, and D. Saury, Etude de faisabilité de la caractérisation thermique d'un matériau bicouche constitué d'un revêtement ou d'un film mince déposé sur un substrat, Nantes, 2019.