Mathematically Simulated Elastic Characteristics of the Composite Reinforced by Spherical Inclusions

Abstract

Composite materials are widely used in engineering, especially in constructions working under simultaneous intensive mechanical and thermal loads. In the industry the main requirements for materials are restrictions on the elastic characteristics, such as bulk modulus and shear modulus. Composite materials consist of a base material, a so-called binder (matrix), and reinforcing inclusions. The composite matrix defines a method for the composite manufacturing and must meet a set of operational and technological requirements. The most commonly used types are a metal matrix and a polymer one, because of the relative ease of manufacture, good wettability, and chemical resistance. Reinforcing inclusions can be of different nature (boron, crystalline, etc.) and shape (spherical, lamellar, fiber). Lately, active researches have been conducted with the nanostructural elements (fullerenes, single-walled and multi-walled carbon nanotubes (SWCNTs and MWCNTs) plates, nanoclusters) used as the filler. There are various ways of modeling the elastic properties of the composites. The most common are numerical methods using a finite element method and analytical methods. In simulation of composite characteristics, in addition to the properties of its components, a reinforcing structure plays an important role. The paper considers an obtained isotropic composite with a metal matrix reinforced by the spherical nanoclusters of randomly oriented SWNTs with a reinforcement scheme similar to the cubic crystal lattice. Numerical modeling and analytical methods were used. For the numerical solution two types of periodic structure of the material were obtained: a cube with eight parts of the ball in the corners of a cube and a sphere in the center. For each of the periodic cells a representative volume is selected in which, using the kinematic and force boundary conditions, have been implemented two types of stress-strain state, namely stretching along one axis and shear. For numerical implementation was used a ANSYS software complex coupled with a specially designed software module that allows creating tensors of elastic coefficient and pliability of the composite, as well as averaging its elastic characteristics to have values of bulk and shear moduli of the material. The results of numerical simulations have been compared with the analytical estimates obtained by the self-consistent method and the dual formulation of the elasticity problem in a heterogeneous solid. It is found that in numerical implementation a choice of the composite periodic cell has a significant impact on the values of the shear modulus as opposed to the bulk modulus of elasticity. It is also shown that the numerical simulation results are between the estimates obtained using the analytical models. These results allow predicting the elastic properties of composites, reinforced by spherical inclusions, including advanced materials, i.e. nanocomposites reinforced by spherical nanoclusters of randomly oriented SWCNTs. The paper is done within the framework of implementing basic part of the Governmental task of the Ministry of Education and Science of the Russian Federation (Project 9.7784.2017/БЧ).