Engineering-Physical Method for Determining the Thermal Conductivity of Objects with Micrometric Thickness and a Complex Structure
Authors: Kudryakov O. V. , Varavka V. N. , Arefeva L. P. 
Published: June 2023

Introduction. The application of functional coatings on products, the performance properties of which are localized in the surface layer is a trend in modern mechanical engineering and materials science. The issues considered in this regard are relevant, in particular, for thermal-barrier coatings of turbine blades of steam and gas turbine engines. It is worth mentioning the materials that experience significant thermal loads during operation. In this case, the lack of reliable methods for predicting the thermophysical properties of the coating seems to be a problem. The work objective is to create a computational and analytical methodology for determining the thermal conductivity of coatings. This approach is based on experimental data and takes into account structural parameters of the material.

Materials and Methods. The experiments were carried out with the blades of a high-speed gas turbine of a locomotive engine made of heat-resistant chromium-nickel alloy Inconel 713LC. An experimental multiphase coating of the Nb-Ti-Al intermetallic system with a thickness of about 80 microns was applied using vacuum ion-plasma technology. The two-beam scanning electron microscope Zeiss CrossBeam 340 was used in the work. The thermal conductivity of the coatings was determined by an experimental technique based on the measurement of the contact potential difference (CPD). Numerical values of this difference were obtained using a mirror galvanometer with high voltage sensitivity. A special signal amplifier and a USB oscilloscope were used to record the readings.

Results. The calculation apparatus of the thermal conductivity determination technique is based on the experimental values of  ∆φ CPD:

– for the base metal (Inconel 713LC) +846 mkV;

– for the coating Nb-Ti-Al – 90 mkV.

The solution to the problem of the distribution of particles in a force field with a potential difference ∆φ is described by the Boltzmann distribution. Starting from the obtained result, we get:

– CPD at the boundary of the contacting metals;

– energy and thermal conductivity of the Fermi level;

– electron relaxation time.

The multidirectional influence that the dimensional differences of the particles of the second phase have on the effective thermal conductivity is considered. For this case, a dimensionless value of the effective thermal conductivity in the direction of each axis and the effective thermal conductivity of the composite are found. Porosity is taken into account according to the Maxwell – Aiken dependence and introduced into the general calculation system. The thermal conductivity of Nb-Ti-Al is established: λNbTiAl = 4,76 W/m.K. Thus, the thermal barrier coating Nb-Ti-Al fully meets its functional purpose.

Discussion and Conclusion. The method of determining thermal conductivity described in the article is applicable only to conductive consolidated materials or composites with a continuous conductive matrix. The presented work completes the initial stage of creating a computational and analytical model for predicting the thermal conductivity of materials and coatings. The results of testing the model for materials with a complex structure showed its satisfactory accuracy. This indicates the expediency of using the two considered elements of the model. The first one is the instrumental measurement of the CPD. The second one is taking into account the features of the structural and phase state of the material. With the development of the model, it is expected to overcome its weaknesses:

– the impossibility of using non-conductive objects to determine the thermal conductivity;

– a significant decrease in the accuracy of determining thermal conductivity for materials and coatings with a gradient structure.