Self-Consistency Method to Evaluate a Linear Expansion Thermal Coefficient of Composite with Dispersed Inclusions

• Main Authors: V. S. Zarubin, G. N. Kuvyrkin, I. Yu. Savelieva
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2015-01-01
• Series: Nauka i Obrazovanie
• Subjects: composite; method of self-consistency; two-sided estimates; isotropic spherical inclusion; temperature coefficient of linear expansion
• Online Access: http://technomag.edu.ru/jour/article/view/367

<p>The rational use of composites as structural materials, while perceiving the thermal and mechanical loads, to a large extent determined by their thermoelastic properties. From the presented review of works devoted to the analysis of thermoelastic characteristics of composites, it follows that the problem of estimating these characteristics is important. Among the thermoelastic properties of composites occupies an important place its temperature coefficient of linear expansion.</p><p>Along with fiber composites are widely used in the technique of dispersion hardening composites, in which the role of inclusions carry particles of high-strength and high-modulus materials, including nanostructured elements. Typically, the dispersed particles have similar dimensions in all directions, which allows the shape of the particles in the first approximation the ball.</p><p>In an article for the composite with isotropic spherical inclusions of a plurality of different materials by the self-produced design formulas relating the temperature coefficient of linear expansion with volume concentration of inclusions and their thermoelastic characteristics, as well as the thermoelastic properties of the matrix of the composite. Feature of the method is the self-accountability thermomechanical interaction of a single inclusion or matrix particles with a homogeneous isotropic medium having the desired temperature coefficient of linear expansion. Averaging over the volume of the composite arising from such interaction perturbation strain and stress in the inclusions and the matrix particles and makes it possible to obtain such calculation formulas.</p><p>For the validation of the results of calculations of the temperature coefficient of linear expansion of the composite of this type used two-sided estimates that are based on the dual variational formulation of linear thermoelasticity problem in an inhomogeneous solid containing two alternative functional (such as Lagrange and Castigliano). These functionals on the true distribution of strains and stresses in an inhomogeneous body matching meaningfully reach extremes (minimum and maximum respectively). On the convergence of the distribution of the minimized functional application gives an upper estimate of the desired values of the temperature coefficient of linear expansion of the composite, and maximized use - their lower bound. The difference between these estimates allows to predict the maximum possible error in calculations obtained dependences.</p>