Unconventional flash technique for the identification of multilayer thermal diffusivity tensors

https://doi.org/10.1016/j.ijthermalsci.2020.106430Get rights and content

Abstract

This paper presents a novel non-intrusive technique for the thermal characterization of opaque multilayer materials that consists in the simultaneous estimation of the thermal diffusivities tensors of each constituting layers that may be isotropic or orthotropic. The present identification method is based on the resolution of an inverse heat conduction problem consisting in the minimization of the least square objective function constructed with the temperature measurements and the prediction of a pseudo-analytical model. The pseudo-analytical model relies on the quadrupoles formalism that proves its capability to treat multi-layered materials and to mimic the experimental method investigated in this work. This latter, inspired from the flash method, relies on a unique and non-intrusive experiment, in terms of excitation and measurements. One of the sample surfaces is locally and shortly heated by means of a CO2 laser, while the resulting transient temperature field is continuously recorded during the cooling period by an IR camera. The minimization procedure invokes a PSO algorithm that has been proved to be convenient for such complex problems that deal with a non-linearity and a large number of unknown parameters, including those related to the excitation. The overall identification method is validated using an isotropic opaque monolayer material of known properties. The identification method is then performed on an actual two layers sample. The accuracy and robustness is discussed depending on the face of excitation and measurement leading to two distinct experimental configurations. A strong emphasis is placed on the sensitivity analysis in order to test the feasibility of the estimation for both configurations.

Introduction

The use of sophisticated materials, i.e. anisotropic, non-homogeneous or multilayered materials, has been remarkably increased in the past decade, especially for machinery, equipment manufacturing and structures. In modern engineering application, multilayer materials have drawn significant attention due to its additional benefits of combining various thermal, mechanical and physical properties of different materials. These layered structures are increasingly used in many industries (e.g. civil, mechanical, chemical, automobile), and have a wide range of application in aerospace and automotive ships and vehicles. This observation drove researches in many scientific and industrial fields to characterize such complex materials.

In thermal sciences, the knowledge of properties, especially the diffusivities, allows the evaluation of the manufactured materials quality and the control of their behavior during processes. In this context, most authors have been interested in the characterization of 1D thermal diffusivity or conductivity of thin films [[1], [2], [3]] or coatings [[4], [5], [6], [7], [8], [9], [10], [11], [12]] on substrates. Such type of layer being increasingly used for mechanical protection (i.e. erosion or oxidation prevention), thermal protection or optical properties improvement reasons. One of the distinctive features is the difficulty, or impossibility in most situations, to obtain these coatings or thin films separately from their substrates. To avoid any destructive delamination or structure modification during the estimation process, a strong emphasis should be placed on direct and simultaneous thermal characterization of all the layers that constitute the sample. Some works attempted to estimate the diffusivities of coatings without any knowledge of the substrate parameters, using two steps estimation technique and by working at very short time, which limites the strategy to relatively thick coatings [13].

Very few research work are focused on the thermal characterization of multilayers structure. Among those research works, some attempted to reach the one-dimensional thermal diffusivity of one isotropic layer present in two or three layered system composed by isotropic layers [[14], [15], [16], [17], [18]].

Some works are based on a two steps measurement strategy (e.g. substrate alone and substrate recovered by the thermal barrier coating in Ref. [19]) or a three steps measurement strategy (e.g. at three different frequencies in Ref. [20]).

It is important to note that, any estimation strategy involving more than one step, for example [21] where the in-plane and in-depth thermal conductivity of a sample are estimated successively by the hot wire and the hot strip methods, may propagate errors throughout the various stages of estimation. In most previously cited works, the identification of the thermal properties of one layer requires the knowledge of its all other thermal properties and the properties of the remaining layer(s). Thus, any error in these properties are propagated through the model and results in an inaccuracy of the required estimation.

Among research works that deal with simultaneous estimation of two or more layers in a multilayer structure, only few works have tried to estimate the thermal diffusivity of each isotropic layer. Some authors have attempted to develop methods allowing the simultaneous and direct estimation of 2D thermal properties in cylindrical coordinates, of anisotropic coatings deposited on an isotropic substrate, with limited results [22,23].

In this paper a one-step and non-intrusive procedure to directly and simultaneously identify the 3D thermal diffusivity tensor of each isotropic or orthotropic component in the layered material, is investigated. It consists in an inverse problem based on the best fit between the recorded time dependent temperature field on the excited face, and the outputs of a corresponding analy-tical model describing the case of transient heat conduction in a multi-layers system. Analytical approach is still of significant importance because it highlights the dependency of the system thermal behavior on thermal properties of each layer and provides a direct insight into the physical processes. This model, inspired from the thermal quadrupoles [24] method is of great consistency with the conducted experiment that belongs to the classic parker flash method [25] which has been recommended as an ASTM standard (E1461) and extended by various authors for 2D and 3D estimations [[26], [27], [28], [29], [30], [31], [32]]. The present 3D flash technique relies on a front face temperature evolution measurement resulting from a local heating of the sample using an IR camera.

After the validation performed using a material of known properties, the method is applied on a bi-layered reference sample manufactured for this purpose and constituted with an isotropic Polyamide polymer and an orthotropic carbon fibers reinforced polymer (CFRP) composite. The a priori isotropic nature of the polymer leads to what we call the 4diff identification case. The same experiment is performed by considering the Polyamide polymer layer as an orthotropic material, referred to as the 6diff identification case. Both strategies (i.e.4diff and 6diff identification) and both experimental configurations (i.e. faces being excited and measured) are studied by means of a sensitivity analysis in order to explain the differences in the estimation results.

The method proposed in this paper is of great importance, especially for the multi-layer materials that may not be separated or when the layer of interest is not available as a free-standing sample, due to manufacturing process, for instance.

Section snippets

Problem description

The handled problem consists in an inverse heat conduction problem whose objective is to retrieve the thermal diffusivity tensor based on the minimization of the deviation between the output of a mathematical model and experimental measurements. This fit is achieved by means of an optimization algorithm that minimizes a cost function expressing the discrepancy between the two signals, in this case the quadratic error between the model and the experimental outputs. The overall estimation

Overall method validation

A two-layer material is a multilayer material with k=2, on which the identification method proposed in this study is applied. In this case, the thermal diffusivities of both layers, a1=[ax,1,ay,1,az,1] and a2=[ax,2,ay,2,az,2], have to be estimated. Calculation of the front face normalized harmonics can be performed by Eqs. (12), (14) with the coefficient given by Eq. (19).(Am,n(p)Bm,n(p)Cm,n(p)Dm,n(p))=(am,n,1(p)bm,n,1(p)cm,n,1(p)dm,n,1(p))×(1Rc01)×(am,n,2(p)bm,n,2(p)cm,n,2(p)dm,n,2(p))

The

Experimental results and discussion

In this section, a two-layer plane and opaque material is considered, as shown in Fig. 5. It is constituted by an isotropic Polyamide polymer layer laminated on an orthotropic layer of carbon fibers reinforced composite. The orthotropic characteristic of the composite material is resulting from the unidirectional carbon fibers oriented in the y direction. This type of materials is frequently used in hydrogen transportation and storage vessels.

The properties measured for both layers, such as the

Conclusion

The principal features of a novel non-intrusive and one step technique for the thermal characterization of opaque multilayers material is presented in this paper. Each element of the method, which allows the simultaneous estimation of the thermal diffusivity tensors of each constituting layers, is described and discussed. Among these elements, the analytic model and the hypothesis on which it is based as well as the stochastic algorithm used to minimize the discrepancy between the outputs of

Declaration of competing interest

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The Authors thank the European Union and the Nouvelle Aquitaine District for their financial support through the CPER/FEDER 2014–2020 programs.

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