Effect of overlapping inclusions on effective elastic properties of composites (original) (raw)
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To determine variability in composite properties, the physics of experimental microstructure was first analyzed using image processing techniques. The obtained statistics were used in generation of synthetic microstructures. Synthetic microstructures were rearranged by acceptance rejection criterion to match the statistics of an experimental microstructure. One hundred statistically equivalent realizations of a synthetic microstructure were generated to investigate the effect of microstructural variability on elastic properties. The generated microstructures were converted to finite element models such that each element represents a pixel in the microstructure. Transverse Young's moduli and shear modulus were obtained for each realization. It was observed that there is a minor variation from one realization to another indicating the independence of elastic moduli on fiber spatial locations. This study also shows that the micromechanics model of hexagonal fiber packing can predict the average elastic moduli within 3% error.
International Journal of Solids and Structures, 2015
This work deals with the problem of modeling the effect due to an interphase zone between inclusion and matrix in particulate composites to better estimate the bulk modulus of materials with inclusions. To this end, in this paper the problem of a body containing a hollow or solid spherical inclusion subjected to a spherically symmetric loading is investigated in the framework of the elasticity theory. The interphase zone around the inclusion is modeled by considering the elastic properties varying with the radius moving away from the interface with inclusion and, asymptotically approaching the value of the homogeneous matrix. The explicit solutions are obtained in closed form by using hypergeometric functions and numerical investigations are performed to highlight the localized effects of the graded interphase in the stress transfer between inclusion and matrix. Finally, the exact solutions are used to estimate the effective bulk modulus of a material containing a dispersion of hollow or solid spherical inclusions with graded interphase zone.
International Journal for Multiscale Computational Engineering, 2004
In this work, a 3D finite element model has been developed to compute the macroscopic elastic properties of polymer/clay nanocomposites (PCNs) from the microstructure morphologies and the elastic behaviour of each phase. Microstructural parameters of clay or clay stacks such as elastic properties, aspect ratio, interlayer spacing and clay volume fraction have been taken into account in the proposed models. A parametric study of the effect of these parameters on the macroscopic elastic properties of PCNs has been carefully investigated. The results show that the macroscopic rigidity of PCNs materials depends not only on the clay volume fraction but also on the dispersion state of clay platelets in the polymer matrix. An exfoliated structure may improve the macroscopic rigidity of PCNs much more efficiently than intercalated ones, particularly at high volume fraction of clays. The key role of interphase on the mechanical properties enhancement of PCNs has also been demonstrated. In addition, the partially exfoliated morphology, in which individual clay layers and intercalated blocks are simultaneously present in the polymer matrix, has been studied. The last morphology is commonly encountered in PCN processing, especially when high clay content is used. The comparison with the experimental and theoretical results extracted from the literature has been performed.
Particle shape influence on elastic-plastic behaviour of particle-reinforced composites
Archives of materials science and engineering, 2014
Particle-reinforced composite materials very often provide unique and versatile properties. Modelling and prediction of effective heterogeneous material behaviour is a complex problem. However it is possible to estimate an influence of microstructure properties on effective macro material properties. Mentioned multi-scale approach can lead to better understanding of particle-reinforced composite behaviour. The paper is focused on prediction of an influence of particle shape on effective elastic properties, yield stress and stress distribution in particle-reinforced metal matrix composites. Design/methodology/approach: This research is based on usage of homogenization procedure connected with volume averaging of stress and strain values in RVE (Representative Volume Element). To create the RVE geometry Digimat-FE software is applied. Finite element method is applied to solve boundary value problem, in particular a commercial MSC.Marc software is used. Findings: Cylindrical particles provide the highest stiffness and yield stress while the lowest values of stiffness and yield stress are connected with spherical particles. On the other hand stress distribution in spherical particles is more uniform than in cylindrical and prismatic ones, which are more prone to an occurrence of stress concentration. Research limitations/implications: During this study simple, idealised geometries of the inclusions are considered, in particular sphere, prism and cylinder ones. Moreover, uniform size and uniform spatial distribution of the inclusions are taken into account. However in further work presented methodology can be applied to analysis of RVE that maps the real microstructure. Practical implications: Presented methodology can deal with an analysis of composite material with any inclusion shape. Predicting an effective composite material properties by analysis of material properties at microstructure level leads to better understanding and control of particle-reinforced composite materials behaviour. Originality/value: The paper in details presents in details an investigation of influence of inclusion shape on effective elastic-plastic material properties. In addition it describes the differences between stress distributions in composites with various inclusion shapes.
Study of the Influence of Spherical Inclusions on Mechanical Characteristics
Periódico Tchê Química, 2020
The relevance of the article is due to the stable growth of the composite industry. Due to its high physical and mechanical characteristics, composite materials (CM) play a vital role in many areas of technology, such as aerospace, aviation, automotive, engineering and instrumentation, and the medical industry. When creating materials with the required mechanical and thermal characteristics, various additives and fillers are often used that affect the strength and elasticity of the samples obtained. In this paper, we study the influence of spherical inclusions in epoxy on the mechanical properties of the material. A composite structure of ED-20 epoxy with inclusions in the form of spherical particles of PBS-50 glass was considered. The characteristic particle size was about 50 μm. Within the framework of this study, batches of samples with a specific volumetric inclusion content of 5%, 10%, 15%, and 20% were produced. Each batch consisted of 6 samples of the same type. To check the ...
European Journal of Mechanics - A/Solids, 2012
In many applications elastoplastic composites are used in limited amounts, therefore it is important to have estimates of the size of their representative volume element both for modeling and experimental purposes. In this work the tensile response of particle reinforced random composites is simulated by microstructural finite element models. Several microstructural realizations are considered for each composition and volume, and the scatter in the response is used as representativeness metric. The microstructural morphology is characterized using methods and statistical descriptors that can be employed with micrographs of real materials. Numerical results show that the representative volume element dimensions can be estimated by verifying either the consistency of the stressestrain curve for single microstructural realizations and increasing material volume sizes or the convergence of the response of several microstructural realizations at the same material volume size. The analysis of the stressestrain state at the microstructural level shows that the plastic strain and the hydrostatic pressure in the matrix material depend hyperbolically on the interparticle distance. Microstructural analyses show that the matrix coarseness is correlated to the scatter in the mechanical response and therefore can be used to have approximate estimates of the representative volume element size.
International Journal of Engineering Science, 2011
The work is devoted to the calculation of static elastic fields in 3D-composite materials consisting of a homogeneous host medium (matrix) and an array of isolated heterogeneous inclusions. A self-consistent effective field method allows reducing this problem to the problem for a typical cell of the composite that contains a finite number of the inclusions. The volume integral equations for strain and stress fields in a heterogeneous medium are used. Discretization of these equations is performed by the radial Gaussian functions centered at a system of approximating nodes. Such functions allow calculating the elements of the matrix of the discretized problem in explicit analytical form. For a regular grid of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and matrix-vector products with such matrices may be calculated by the fast fourier transform technique. The latter accelerates significantly the iterative procedure. First, the method is applied to the calculation of elastic fields in a homogeneous medium with a spherical heterogeneous inclusion and then, to composites with periodic and random sets of spherical inclusions. Simple cubic and FCC lattices of the inclusions which material is stiffer or softer than the material of the matrix are considered. The calculations are performed for cells that contain various numbers of the inclusions, and the predicted effective constants of the composites are compared with the numerical solutions of other authors. Finally, a composite material with a random set of spherical inclusions is considered. It is shown that the consideration of a composite cell that contains a dozen of randomly distributed inclusions allows predicting the composite effective elastic constants with sufficient accuracy.
Elastic property of multiphase composites with random microstructures
Journal of Computational Physics, 2009
We propose a computational method with no ad hoc empirical parameters to determine the elastic properties of multiphase composites of complex geometries by numerically solving the stress-strain relationships in heterogeneous materials. First the random microstructure of the multiphase composites is reproduced in our model by the random generation-growth method. Then a high-efficiency lattice Boltzmann method is employed to solve the governing equation on the multiphase microstructures. After validated against a few standard solutions for simple geometries, the present method is used to predict the effective elastic properties of real multiphase composites. The comparisons between the predictions and the existing experimental data have shown that the effects of pores/ voids in composites are not negligible despite their seemingly tiny amounts. Ignorance of such effects will lead to over-predictions of the effective elastic properties compared with the experimental measurements. When the pores are taken into account and treated as a separate phase, the predicted Young's modulus, shear modulus and Poisson's ratio agree well with the available experimental data. The present method provides an alternative tool for analysis, design and optimization of multiphase composite materials. Published by Elsevier Inc.
Statistical model for characterizing random microstructure of inclusion–matrix composites
Journal of Materials Science, 2007
The variation of arrangement of micro-structural entities (i.e. inclusions) influences local properties of composites. Thus, there is a need to classify and quantify different micro-structural arrangements. In other words, it is necessary to identify descriptors that characterize the spatial dispersion of inclusions in random composites. On the other hand, Delaunay triangulation associated with an arbitrary set of points in a plane is unique which makes it a good candidate for generating such descriptors. This paper presents a framework for establishing a methodology for characterizing microstructure morphology in random composites and correlating that to local stress field. More specifically, in this paper we address three main issues: correlating microstructure morphology to local stress fields, effect of clustering of inclusions on statistical descriptors identified in the paper, and effect of number of realizations of statistical volume elements (SVEs) on statistical descriptors.