Modeling of elastic behavior of multicomponent composite materials based on approximate solution of stochastic boundary value problems

This work is devoted to development and application of the statistical mechanics approaches to studying microstructural behavior of multi-component composites. The object of the study is heterogeneous materials consisting of more than two components. The aim is to develop analytical tools for the analysis of the microstructural stress and strain fields in multicomponent media taking into account geometrical and mechanical properties of components and basied on calculation of the statistical characteristics of the local fields of stress and strain in components. Research of the microstructure behavior of components of composites is based on the concept of representative volume elements. It is assumed that the components are homogeneous and isotropic. Information about the internal morphology of the representative volume is formalized by means of correlation functions of various orders. Characteristics of the deformation processes are the statistical moments (statistics) of stress and strain fields in the components of the material. Analytical expressions for the statistical characteristics of the local stress and strain fields are obtained using the solution of the boundary problem of elasticity theory in a stochastic formulation. The boundary value problem is solved using the Green's functions method for the elastic medium. The developed analytical model takes into account both the geometrical parameters of the microstructure and mechanical properties of components. For the first time expressions for the moments of the first and second order of local stress fields for the multicomponent materials were derived. Case studies of composites with titanium (Ti) matrix reinforced with randomly distributed particles of silicon carbide (SiC) were investigated. Analysis of the influence of microstructural parameters on the behavior of each phase separately was performed. Numerical results for the statistics of stress and strain fields are presented.