One of the important directions in investigation of reliability of composite structures is in developing of multi-scale approaches. Many modern mathematical models for composite materials allow not only operate with effective characteristics, but also take into account properties of their heterogeneous structure and allow to describe behavior of each distinct phase during deformation. This is important for prediction of fracture mechanisms of composites and estimation of reliability of constructions in specific loading conditions. The aim of this research is to develop new theoretical models and simulation tools for analysis of stress fields in phases of composites with complex stochastic geometry and for prediction of behavior of considered materials during deformation processes.
Polydisperse composites with randomly distributed ellipsoidal and spherical inclusions were considered. For such non-periodic randomly reinforced composites, stochastic methods based on random functions theory are used [1]. According to such methods, deformation processes are described with multipoint statistical moments of stochastic stress and strain fields in phases of composites. These moments have been determined analytically from solution of stochastic boundary value problems or with finite-elements analysis based on statistical properties of the microstructure. In this work the new solutions of boundary value problems in elastic and elastoplastic cases with the Green’s functions method were used.
Though there are many approaches for simulation of microstructures composites have emerged [2], the question of description of component interaction at a micro-scale is open. Statistical information about geometry of microscopic structure of materials is characterized with high-order multipoint correlation functions using the concept of a Representative Volume Element (RVE). The functions up to fifth order have been built for synthesized 3D RVE models. The structural function of damageability was introduced to describe failure parameters on a micro-scale.
New analytical expressions for failure probability and statistical characteristics in phases of composites were derived. The computation results for parameters of deformation and failure process in components were calculated for composites with different types of structural parameters and properties in some specific cases of RVE loading.
The work was carried out at Perm National Research Polytechnic University with support of the Government of Russian Federation (The decree № 220 on April 9, 2010) under the Contract № 14.В25.310006, on June 24, 2013.
References
[1] V. Buryachenko, Micromechanics of Heterogeneous Materials, 1st ed., Springer, New York, (2007)
[2] M.M. Kaminski, Computational Mechanics of Composite Materials, Springer, (2005)