Elastic Moduli Of Particulate Composites Research Articles

N-Phase micromechanical framework for the conductivity and elastic modulus of particulate composites: Design to microencapsulated phase change materials (MPCMs)-cementitious composites

The smart design of microencapsulated phase change materials (MPCMs) in cementitious composites requires an explicit understanding of effects of soft microcapsule particles, stiff aggregates and their surrounding weak interfaces on the physico-mechanical properties of particulate composites. This paper devises a n-phase micromechanical framework to predict the effective thermal conductivity and elastic modulus of multicomponent particulate composites that consist in stiff and soft anisotropic-shaped inclusions, their surrounding weak interfaces and matrix. In this micromechanical model, the volume fraction of weak interfaces treated as the interphase model is quantified and incorporated into the n-phase differential effective medium model. It is found that the structural configuration of interfaces has a significant effect on the effective physico-mechanical properties of particulate composites. The micromechanical model leads to predictions of the effective conductivity and elastic modulus of multicomponent particulate composites to a good accuracy by comparing with available experimental data for regular concrete, quartz mortar and MPCMs-cementitious composites. By utilizing the micromechanical model, the authors further develop a theoretical design rule for the robust overall performance of MPCMs-cementitious composites with the better thermal resistance and elastic modulus. These results can also be used to design other multiphase particulate composites and porous media with the cherry-pit structure.

Analytical effective elastic properties of particulate composites with soft interfaces around anisotropic particles

Understanding the effects of interfacial properties on effective elastic properties is of great importance in materials science and engineering. In this work, we propose a theoretical framework to predict the effective moduli of three-phase heterogeneous particulate composites containing spheroidal particles, soft interfaces, and a homogeneous matrix. We first derive the effective moduli of two-phase representative volume elements (RVEs) with matrix and spheroidal inclusions using the variational principle. Subsequently, an analytical model considering the volume fraction of soft interfaces around spheroidal particles is presented. The effective moduli of such three-phase particulate composites are eventually derived by the generalized self-consistent scheme. These theoretical schemes are compared with experimental studies, numerical simulations, and theoretical approximations reported in the literature to verify their validity. We further investigate the dependence of the effective elastic modulus on the interfacial properties and the geometric characteristics of anisotropic particles based on the proposed theoretical framework. Results show that the interfacial volume fraction and the effective elastic modulus of particulate composites are strongly dependent on the aspect ratio, geometric size factor, volume fraction, and particle size distribution of ellipsoidal particles.

Size-dependent effective elastic moduli of particulate composites with interfacial displacement and traction discontinuities

This work aims at estimating the size-dependent effective elastic moduli of particulate composites in which both the interfacial displacement and traction discontinuities occur. To this end, the interfacial discontinuity relations derived from the replacement of a thin uniform interphase layer between two dissimilar materials by an imperfect interface are reformulated so as to considerably simplify the characteristic expressions of a general elastic imperfect model which is adopted in the present work and include the widely used Gurtin–Murdoch and spring-layer interface models as particular cases. The elastic fields in an infinite body made of a matrix containing an imperfectly bonded spherical particle and subjected to arbitrary remote uniform strain boundary conditions are then provided in an exact, coordinate-free and compact way. With the aid of these results, the elastic properties of a perfectly bonded spherical particle energetically equivalent to an imperfectly bonded one in an infinite matrix are determined. The estimates for the effective bulk and shear moduli of isotropic particulate composites are finally obtained by using the generalized self-consistent scheme and discussed through numerical examples.

Evaluation of the effective elastic moduli of particulate composites based on Maxwell’s concept of equivalent inhomogeneity: microstructure-induced anisotropy

Maxwell’s concept of equivalent inhomogeneity is employed for evaluating the effective elastic properties of macroscopically anisotropic particulate composites with isotropic phases. The effective anisotropic elastic properties of the material are obtained by comparing the far-field solutions for the problem of a finite cluster of isotropic particles embedded in an infinite isotropic matrix with those for the problem of a single anisotropic equivalent inhomogeneity embedded in the same matrix. The former solutions precisely account for the interactions between all particles in the cluster and for their geometrical arrangement. Illustrative examples involving periodic (simple cubic) and random composites suggest that the approach provides accurate estimates of their effective elastic moduli.

Characterization of interfacial stress transfer ability of particulate cellulose composite materials

Composites with cellulose reinforcements are steadily gaining increased use. The stress transfer ability between reinforcement and polymer matrix has a strong influence on mechanical properties like strength and fracture toughness. This work presents a method to assess the stress transfer ability between cellulose and polymer matrix from a model material with cellulose spheres embedded in a polymer matrix. Such a material show smaller variability compared with composites based on natural cellulose fibres, and is less cumbersome than single fibre tests with regard to interfacial characterization. Measured elastic moduli of particulate composites is compared with predicted values from a micromechanical model based on a composite sphere assembly in a self-consistent scheme with only a spring constant of an imperfect interface as fitting parameter expressed in Pa/m. This interface parameter is identified through inverse modelling and used to quantify stress-transfer ability of cellulose/polylactide and cellulose/polystyrene composite interfaces. A higher degree of interfacial interaction was found for the former. This ranking was corroborated by adhesive force measurements using a micrometre sized cellulose sphere attached to the end of a cantilever in an atomic force microscope. With the model microstructure of a cellulose-sphere composite, an interfacial efficiency parameter can be backed out from stiffness measurements to be used in e.g. ranking of different fibre surface treatments and choice of matrix in the development of stronger natural-fibre composites.

Estimation of Elastic Moduli of Particulate Composites by New Models and Comparison with Moduli Measured by Tension, Dynamic, and Ultrasonic Tests

The elastic constants of particulate composites are evaluated employing a theoretical cube-within-cube formation. Two new models of four and five components, respectively, formed by geometrical combination of three-component models existing in the literature, are used as Representative Volume Elements. Using the governing stress and strain equations of the proposed models, two new equations providing the static elastic and shear moduli of particulate composites are formulated. In order to obtain the dynamic elastic and shear moduli, the correspondence principle was applied successively to components connected in series and/or in parallel. The results estimated by the proposed models were compared with values evaluated from existing formulae in the literature, as well as with values obtained by tensile, dynamic, and ultrasonic experiments in epoxy/iron particulate composites. They were found to be close to values obtained by static and dynamic measurements and enough lower compared with values obtained from ultrasonic experiments. The latter is attributed to the high frequency of ultrasonics. Since measurements from ultrasonic's and from dynamic experiments depend on the frequency, the modulus of elasticity estimated by ultrasonic's is compared with that (storage modulus) estimated by dynamic experiments.

Geometrical Correction to the Elastic Stiffness of Particulate Composites

A geometrical correction to previous models for the elastic modulus of particulate composites is proposed in this article in a closed-form analytical expression. By comparing the geometrically corrected models (which adopt spherical particulates) to previous models (which employ cubic particulates) a set of correction factors and functions are extracted. The correction factors modify the influence of filler volume fraction while the correction functions describe the effect of filler—matrix boundary shape to the overall composite modulus. With the aid of geometrical correction, the validity, or otherwise, of earlier models are discussed with reference to previous experimental data and are elucidated through their representative volume element’s assumed boundary conditions. These correction parameters allow the practitioner to easily incorporate geometrical correction to previously known models.

An engineering approach for evaluating effective elastic moduli of particulate composites

A simple approach to compute the effective elastic moduli of two-phase particulate composites is proposed. Using the three-phase spherical model, the effective bulk modulus is computed, and the Poisson's ratio is obtained using rule of mixtures. The computed effective elastic moduli compare favorably with other computational models and with experimental data.

Elastic moduli of particulate composites with graded filler‐matrix interfaces

AbstractThe elastic response of plane‐array models of composites reinforced by particles or aligned fibers having graded interfaces with the matrix is analyzed. Such microstructure is representative of a new class of polymer matrix composite materials in which the filler is nanometer‐sized. In such materials, the polymer chains in the matrix are preferentially oriented close to the interface with the relatively rigid fillers, this leading to a graded interfacial layer about each inclusion. The composite elastic moduli are determined based on the properties and geometry of the interfacial graded layer as well as on the moduli of the filler and the matrix, and the volume fraction of filler. Conversion curves are constructed allowing for an equivalence to be established between the present case and that of similar composites without graded interfaces. Based on these conversion curves, standard homogenization algorithms can be applied to determine the overall elastic properties of such composite. The fillers are considered to be stiffer than the matrix, both rigid and of finite stiffness. Results for both sliding and bonded interfaces are presented. The effect of anisotropic material properties in the graded region on the composite moduli is also investigated. The results of the model are compared with published experimental data.

The elastic moduli of particulate‐filled polymers

AbstractThe static and dynamic elastic moduli of particulate composites, consisting of two phases, one of which has isotropic–elastic and the other linear viscoelastic properties, were studied. For this purpose a model defining the approximate equations for determining the elastic modulus of a composite from the properties of the constituent materials was used. Classical theory of elasticity was applied to this simplified model of a composite‐unit cell. The following assumptions are made: (i) filler particles are spherical; (ii) fillers are completely dispersed; and (iii) the volume fraction of fillers is sufficiently small, so that any interaction among fillers may be neglected. A class of iron‐filled epoxy composites was subjected to tests in order to compare the theoretical values with the experimental results. The elastic modulus calculated by the expression derived in this study seems to corroborate with the experimental results fairly well. Finally, by applying the correspondence principle to this expression, theoretical relationships for the dynamic storage and loss moduli were also derived.