Abstract
The main objective is to investigate an effect of anisotropic distribution of the reinforcing particles in a cubic representative volume element (RVE) of the carbon–polymer composite including stochastic interphases on its homogenized elastic characteristics. This is done using a probabilistic homogenization technique implemented using a triple approach based on the stochastic perturbation method, Monte Carlo simulation as well as on the semi-analytical approach. On the other hand, the finite element method solution to the uniform deformations of this RVE is carried out in the system ABAQUS. This composite model consists of two neighboring scales–the micro-contact scale relevant to the imperfect interface and the micro-scale—having 27 particles inside a cubic volume of the polymeric matrix. Stochastic interface defects in the form of semi-spheres with Gaussian radius are replaced with the interphase having probabilistically averaged elastic properties, and then such a three-component composite is subjected to computational homogenization on the microscale. The computational experiments described here include FEM error analysis, sensitivity assessment, deterministic results as well as the basic probabilistic moments and coefficients (expectations, deviations, skewness and kurtosis) of all the components of the effective elasticity tensor. They also include quantification of anisotropy of this stiffness tensor using the Zener, Chung–Buessem and the universal anisotropy indexes. A new tensor anisotropy index is proposed that quantifies anisotropy on the basis of all not null tensor coefficients and remains effective also for tensors other than cubic (orthotropic, triclinic and also monoclinic). Some comparison with previous analyses concerning the isotropic case is also included to demonstrate the anisotropy effect as well as the numerical effort to study randomness in composites with anisotropic distribution of reinforcements and inclusions.
Highlights
It is widely known that the interface defects appearing between different phases of composites play a crucial role in reliability, durability and failure of these materials [1,2,3]
5 Conclusions Probabilistic homogenization of the particle-reinforced composite with stochastic interface defects and anisotropic distribution of the particles has been demonstrated in this work by using of three independent stochastic computer techniques
This paper proposes a new measure of anisotropy called the tensorial anisotropy index, which is able to capture the difference in anisotropy caused by spatial placement of its phases and answers the need for anisotropy index effective beyond the cubic tensors (Fig. 15)
Summary
It is widely known that the interface defects appearing between different phases of composites (like a matrix and its reinforcement) play a crucial role in reliability, durability and failure of these materials [1,2,3]. Three concurrent probabilistic methods have been used—Monte Carlo simulation [21], iterative stochastic perturbation technique (called here ISFEM after corresponding FEM implementation) [23] as well as the semi-analytical method [24,25], all based on the finite element method experiments to verify an influence of the interphase with random volume fractions of the defects on the effective characteristics of such a composite We apply for this purpose Gaussian parameter w with the given expectation E[w] and standard deviation σ (w) to compute the first four probabilistic moments and coefficients of the effective tensor and to verify whether it can have Gaussian distribution or not. The entire study is a milestone to carry out reliability assessment of various particle-reinforced materials and structures with the use of a homogenization method, without a need of very precise multi-scale meshing of the composite structural elements
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