Effective Properties Of Composites Research Articles

Effective elastic properties of composites with randomly distributed thin rigid fibres

The aim of the work is to analyse the effective elastic properties of composites with randomly distributed thin rigid fibres. The matrix is linear-elastic, homogenous and isotropic, and the fibres are perfectly connected to the matrix. Two-dimensional models of composites are analysed using the boundary element method (BEM). The method requires division of fibres and external boundaries of the plate into boundary elements. The boundary quantities are interpolated using quadratic shape functions. The direct solutions are: displacements and tractions along the external boundaries, displacements of fibres and interaction forces between the fibres and the matrix. Three numerical examples are presented in the paper: a single fibre in a circular disc, uniformly distributed parallel fibres and randomly distributed and oriented fibres in a square plate. The influence of distribution and orientation of fibres on effective Young’s moduli, Poisson’s ratios and Kirchhoff’s moduli is analysed. The examples demonstrate the accuracy and efficiency of the method.

New insights into the synergistic influence of voids and interphase characteristics on effective properties of unidirectional composites

Micro-voids are common imperfections generated during manufacturing or prolonged service of composites. The present paper emphasizes on the effect of not only matrix-pores, but also the interphase-defects on the effective stiffness of unidirectional fiber-reinforced composites (UFRCs). To this aim, a hierarchical modeling of porous UFRCs is established, in which an interphase model is incorporated to characterize the linkage among the fiber content, the content and properties of the interphase, as well as the trait of the interphase-pores. An effective and easy-to-implement two-step homogenization scheme, based on Mori-Tanaka method and Huang’s bridging method, is developed for the effective properties of such porous UFRCs. Comparison studies against available experimental data are conducted to demonstrate the validity of the proposed model. Afterwards, detailed parametric analyses are performed, and new insights into the effect of pores on UFRCs are provided, which may have important implications in the further manufacturing and defects speculation of composites.

Effective transport properties for periodic multiphase fiber-reinforced composites with complex constituents and parallelogram unit cells

The two-scale asymptotic homogenization method is used to find closed-form formulas for effective properties of periodic multi-phase fiber-reinforced composites where constituents have complex-valued transport properties and parallelogram unit cells. An antiplane problem relevant to linear elasticity is formulated in the frame of transport properties. The application of the method leads to the need of solving some local problems whose solution is found using potential theory and shear effective coefficients are explicitly obtained for n-phase fiber-reinforced composites. Simple formulae are explicitly given for three- and four-phase fiber-reinforced composites. The broad applicability, accuracy and generality of this model is determined through comparison with other methods reported in the literature in relation to shear elastic moduli and several transport problems of multi-phase fiber-reinforced composites in their realm, such as conductivity in a biological context and permittivity leading to gain and loss enhancement of dielectrics. Also, the example of gain enhancement of inertial mass density is looked into. Good agreement with other theoretical approaches is obtained. The formulas may be useful as benchmarks for checking experimental and numerical results.

Buckling and free vibration analyses of pultruded GFRP laminated composites: Experimental, numerical and analytical investigations

Two of the most important of the loads exposed to the structures whose construction material is pultruded GFRP are buckling and vibration loads. Therefore, it is crucial to determine the behavior of this material against buckling and vibration loads considering the fiber and layer configurations. Pursuant to this goal, comprehensive experimental, numerical and analytical studies have been undertaken. An exact analytical solution based on first order shear deformation plate theory was used for the solution of stability and vibration problems. The virtual displacement principle was utilized herein to derive governing differential equations. Effective material properties of pultruded GFRP composites were obtained by using the mixture rule model. The laminated plate was assumed to be a plate strip in cylindrical bending. The solutions were obtained with an infinite series. On the other hand, a numerical study was conducted by a finite element software, ABAQUS. Burn-out and mechanical tests were performed to determine the mechanical properties of the obtained pultruded GFRP composite specimens. The buckling and modal analysis for natural frequencies tests were utilized to investigate the performance of pultruded GFRP specimens. The experimental findings were compared with the calculated analytical and numerical results, and good conformance was obtained. Macro and micro mechanical damage analyzes were performed to better understand the behavior of the pultruded GFRP composite specimens.

Mesoscale computational modeling of concrete-like particle-reinforced composites with non-convex aggregates

This paper presents a novel mesoscale finite element model for predicting the effective mechanical properties of concrete-like particle-reinforced composites with concave aggregates. In the mesoscale model, unit cells (UC) with randomly distributed non-convex particles and period boundaries are generated through computationally efficient algorithms to represent the periodic microstructures of concrete composites. Numerical homogenization is performed to calculate the effective mechanical parameters based on an unsorted node set technique. The results predicted by the proposed model show good agreement with the experimental measurements. The parametric study also indicates that UC models with periodic placement of particles at the boarders yield higher elastic modulus compared with those without periodic boundary particle placement, and the influence of boarder particles on homogenized material properties decreases as the UC size increases. Moreover, computational studies show that the elastic moduli of composites consisting of concavity particles are larger than those with the round and smooth particles given the same particle volume fraction. The proposed mesoscale modeling approach can serve as an easy and fast tool in assisting the design and optimization of strong, light-weight and reliable particle-reinforced composites.

A numerical study of the meso-structure variability in the compaction process of prepreg platelet molded composites

Compaction deformations in a thermoplastic composite system molded from chopped prepreg platelets were analyzed to obtain statistical distributions of local distortions that define the final consolidated meso-structure. This study provides an insight into and allows quantification of the intrinsic geometric variability of the composite meso-structure that controls the variability of the effective composite mechanical properties. A two-phase viscoelastic finite element model was utilized to treat the behavior of molten prepreg platelets, which were assumed to be incompressible and inextensible in the fiber direction during processing. A two-step simulation procedure with discretely modeled platelets and platelet-to-platelet contacts is proposed. The analysis begins with a drop simulation of the uncontrolled material deposition followed by a 3D finite element analysis of the preform compaction and bulk material flow. The proposed model provides a method for generating a composite meso-structure ab initio starting from a statistical sampling of the initial conditions for platelet deposition. The predicted platelet thickness distribution, intra-platelet fiber waviness and out-of-plane platelet undulations were found to be in good agreement with experimental measurements. An estimate of the volume of resin pockets was inferred from the compaction simulation.

Effective Electromagnetic Properties of Woven Fiber Composites for Shielding Applications

Composite materials reinforced with woven conductive fibers can be good candidates for electromagnetic shielding applications. Their light weight provides an important advantage over metallic alloys classically used in the automotive and aircraft industries. However, numerical modeling of composite-based large-scale structures, such as shielding enclosures, is rendered almost impossible by the heterogeneities at the microscopic scale. This problem is commonly addressed using electromagnetic homogenization methods. In this paper, we propose a homogenization technique based on finite element computations and inverse problem solving for estimating the effective properties of woven composites. The effect of electrical contacts between the fibers is also studied and its influence on the global behavior of the material is analyzed. The results are then shown to diverge from those obtained using analytical mixing rules over the frequency range of 1-40 GHz. Thus the suitability of these homogenization methods is discussed with respect to the studied frequency range and the nature of the microstructure.

Thermally induced postbuckling of higher order shear deformable CNT-reinforced composite flat and cylindrical panels resting on elastic foundations with elastically restrained edges

In spite of considerable importance in engineering practice, especially in aerospace structures, thermal postbuckling behavior of nanocomposite curved panels has received little attention. This article aims to analyze different situations of postbuckling response of carbon nanotube (CNT) reinforced composite flat and cylindrical panels exposed to uniform temperature rise. CNTs are embedded into isotropic matrix through functionally graded distributions. The properties of constitutive materials are assumed to be temperature dependent and effective properties of CNT-reinforced composite are estimated according to an extended rule of mixture. Governing equations of thick panels are established within the framework of higher order shear deformation theory taking into account geometrical nonlinearity, initial imperfection, panel-foundation interaction, and elasticity of tangential constraints of boundary edges. Analytical solutions for simply supported panels are assumed and Galerkin method is adopted to derive nonlinear load-deflection relations from which temperature-deflection equilibrium paths are traced through an iteration algorithm. The study reveals that combined effects of curvature of panel, tangential constraints of edges, and initial geometrical imperfection can lead to the change in type of buckling response. Numerical analyses also indicate different influences on the postbuckling behavior of thermally loaded nanocomposite panels.

A Mori–Tanaka Based Micromechanical Model for Predicting the Effective Electroelastic Properties of Orthotropic Piezoelectric Composites with Spherical Inclusions

Piezoelectric nanocomposites consisting of an orthotropic piezo-active polymer matrix and with piezo-ceramic nanoparticles as reinforcement are potential candidates as materials for structural components of the next-generation energy-harvesting micro-devices that are compatible with flexible electronics. Prediction of effective electroelastic properties of such piezoelectric composites is an essential step towards design and development of such energy-harvesting micro/nano-structures. This paper proposes a micromechanical model for determination of effective elastic, piezoelectric and dielectric properties of unidirectional piezoelectric polymer composites having spherical type inclusions embedded in an orthotropic matrix. The model is based on Mori–Tanaka’s mean field homogenization scheme and involves the determination of piezoelectric Eshelby tensors. As an example, the effective electromechanical properties of PVDF (polyvinylidene fluoride)/PZT 7A (lead zirconate titanate) composite were determined using the micromechanical model and the results were validated with a finite element model and with experimental data available in literature. The results demonstrate that the micromechanics model developed here successfully predicts the effective electroelastic properties of piezoelectric orthotropic composite at low volume fractions of the reinforcement.

Evolution of the effective elastic properties of metal matrix composites during the synthesis

We propose a simple analytical model to evaluate changes in the overall elastic properties of metal matrix composites during the manufacturing process. The problem is solved in several steps. First, the moving boundary problem on formation and growth of the transient layer between the matrix and inhomogeneities is solved analytically in quasi-stationary approximation. This solution is used to estimate changes in phase concentrations during the synthesis and to calculate effective properties of the representative inhomogeneous inclusion (of variable size) consisting of the core inhomogeneity and growing transit layer. At the last stage, variation of the effective properties of a composite with varying concentrations of phases during the synthesis is evaluated using micromechanical homogenization schemes. The approach is illustrated on example of Al/W composite when Al5W phase is formed.

Three-dimensional image-based numerical homogenisation using octree meshes

The determination of effective material properties of composites based on a three-dimensional representative volume element (RVE) is considered in this paper. The material variation in the RVE is defined based on the colour intensity in each voxel of an image which can be obtained from imaging techniques such as X-ray computed tomography (XCT) scans. The RVE is converted into a numerical model using hierarchical meshing based on octree decompositions. Each octree cell in the mesh is modelled as a scaled boundary polyhedral element, which only requires a surface discretisation on the polyhedron’s boundary. The problem of hanging (incompatible) nodes – typically encountered when using the finite element method in conjunction with octree meshes – is circumvented by employing special transition elements. Two different types of boundary conditions (BCs) are used to obtain the homogenised material properties of various samples. The numerical results confirm that periodic BCs provide a better agreement with previously published results. The reason is attributed to the fact that the model based on the periodic BCs is not over-constrained as is the case for uniform displacement BCs.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

Effective predictions of heterogeneous flexoelectric multilayered composite with generalized periodicity

In this work, the general mathematical statements for flexoelectric heterogeneous equilibrium boundary value problems are reported. A methodology to find the local problems and the effective properties of flexoelectric composites with generalized periodicity is presented, using the two-scales asymptotic homogenization method. The statement of the homogenized boundary values problem is given. A procedure to solve the local problems of stratified multilayered composites with complex geometry and perfect contact at the interface is proposed. Consequently, the analytical expressions of the effective coefficients are obtained. The piezoelectric limit case for rectangular bi-laminated composites is validated. Finally, numerical analysis to illustrate the behavior of the effective properties for rectangular and wavy flexoelectric bi-layered structures are shown.

Asymptotic and numerical homogenization methods applied to fibrous viscoelastic composites using Prony’s series

The paper focuses on the evaluation of the effective properties of linear viscoelastic composites with a periodic structure, containing long cylindrical fibers of circular cross-section and for two different cell arrangements: square and hexagonal unit cells. For this purpose, we use the two-scale asymptotic homogenization method (AHM) and a numerical homogenization method (NHM). Based on the correspondence principle, the local functions and the relaxation overall properties are obtained in explicit form by the AHM using the Prony series. Additionally, the NHM is established for a three-dimensional representative cell, and the problem is solved under appropriate boundary conditions, by using the Finite Element Method. The numerical results obtained by the AHM and NHM are compared and verified with other theoretical approaches. The comparisons show a good agreement and a benchmark for further experimental and theoretical investigations.

Hierarchical multi-scale models for mechanical response prediction of highly filled elastic–plastic and viscoplastic particulate composites

Though a vast amount of literature can be found on modelling particulate reinforced composites and suspensions, the treatment of such materials at very high volume fractions Vf (>90%), typical of high performance energetic materials, remains a challenge. The latter is due to the very wide particle size distribution needed to reach such a high value of Vf. In order to meet this challenge, multiscale models that can treat the presence of particles at various scales are needed. This study presents a novel hierarchical multiscale method for predicting the effective properties of elasto-viscoplastic polymeric composites at high Vf. Firstly, simulated microstructures with randomly packed spherical inclusions in a polymeric matrix were generated. Homogenised properties predicted using the finite element (FE) method were then iteratively passed in a hierarchical multi-scale manner as modified matrix properties until the desired filler Vf was achieved. The validated hierarchical model was then applied to a real composite with microstructures reconstructed from image scan data, incorporating cohesive elements to predict debonding of the filler particles and subsequent catastrophic failure. The predicted behaviour was compared to data from uniaxial tensile tests. Our method is applicable to the prediction of mechanical behaviour of any highly filled composite with a non-linear matrix, arbitrary particle filler shape and a large particle size distribution, surpassing limitations of traditional analytical models and other published computational models.

Numerical Evaluation of the Thermal Properties of UD-Fibers Reinforced Composites for Different Morphologies

In this paper, the numerical homogenization technique is used to evaluate the representative volume element and to compute the effective transverse thermal properties of unidirectional fibers reinforced composites. Three unit cells are constructed including square, hexagonal and random arrangement. The results obtained by finite element analysis showed the effect of unit cells configurations on the prediction of effective transverse thermal properties of unidirectional fibers composites for a wide range of fiber volume fractions and contrasts of properties. The numerical results are compared to available analytical models in the thermal conductivity of composites and experimental test results from the literature.

Mesh Size Optimization of Unidirectional Fiber-Reinforced Composite Model for Precisely Characterizing the Effective Elastic Property

Structural representative volume unit (RVU) has been extensively used to characterize the real effective elastic properties (EEPs) of fiber-reinforced composites (FRCs). The focus of this study is to optimize the optimum mesh size of a multiscale unidirectional RVU (UD-RVU) model to precisely characterize the EEPs of unidirectional FRCs (UD-FRCs). First, a variety of mechanical properties test experiments are carried out to obtain the real EEPs of UD-FRCs for the preparation of the optimization analysis. Then, a microscopic structural UD-RVU is established according to the fiber distribution of the UD-FRCs, and the corresponding ABAQUS/Python code that is used to characterize the EEPs is developed based on asymptotic homogenization theory. Finally, a complete optimization analysis, which is used for balancing simulation time and characterization accuracy, is performed to obtain the optimum mesh size of the multiscale finite element model. The optimized results reveal that the global mesh size of approximately 0.7 μm is the most optimal mesh, which has high accuracy and high simulation efficiency for characterizing the EEPs of UD-FRCs. The maximum error is close to 4.23% compared with experiments, which has a higher precision than the conventional calculation model, and the characterization model is reported in the literature.

Investigating the elastic behavior of carbon nanocone reinforced nanocomposites

This paper deals with the evaluation of the effective mechanical properties of carbon nanocone centered composites using a 3D nanoscale representative volume element based on continuum mechanics. For extracting the effective material constants, the authors have taken the basis of theories of elasticity. The results constituting the effective Young's modulus of the composite and Poisson's ratio for different parameters stated above have been presented and validated with rule of mixtures. It can be clearly visualized from the results that the load-carrying capacities of carbon nanocones in the representative volume elements are quite significant and the same has been demonstrated with subsequent cases. Simulation-based modeling can show a considerable part in the improvement of carbon nanocone-based composites by providing results that help in appreciative of the performance of composites. Moreover, for a volume fraction of the CNC as 2.33% in a cylindrical representative volume element and a 19.2° apex angle of the cone, the stiffness of the composite can increase as many as 4.9 times of the matrix. Similarly for hexagonal and square, the increase is in terms of 4.3 and 3.01 times respectively. Cylindrical representative volume element is the best as it provides the maximum reinforcement in terms of effective Young's modulus of the composite. Carbon nanocone-based composites provide results that help in understanding the elastic behavior of composites.

The effect of micromechanics models on mechanical property predictions for short fiber composites

The Tandon-Weng (T-W), the Halpin-Tsai (H-T) micromechanical models and a novel numerical implementation of asymptotic homogenization method (NIAH) for determining the stiffness of unidirectional orientation short fiber composites are compared. Based on rigorous mathematical theory, NIAH can be easily implemented using commercial software as a black box as representative volume approaches. Representative volume element (RVE) models were generated using random sequential adsorption technique (RSA) based on the optimal Latin hypercube sampling method. For arbitrary fiber orientation, the NIAH approach was compared with orientation averaging with the T-W and the H-T micromechanical models. Agreement between the three approaches in predicting the effective properties of short fiber composites was found to be excellent. Finally, the results calculated with the three approaches were compared with experimental values. It is shown that the three approaches in this paper are in quite good agreement with measured values. However, for random oriented short fiber composites with fiber length and fiber diameter distribution, the NIAH method still can provide calculated results with sufficient prediction accuracy, and the other two methods are not any more effective.

Conversion efficiency and effective properties of particulate-reinforced thermoelectric composites

It is well known that nanoparticles have the ability to enhance the performance of thermoelectric materials. A comprehensive analytical model exploring the mechanism by which this enhancement takes place remains largely absent from the literature. We address this deficiency by introducing a simple model of a nanoparticle as a circular nanoinhomogeneity and analyze its effect on thermal–electric conversion efficiency and the effective properties of thermoelectric composites. Taking interface phonon scattering into consideration, the effective material parameters around a nanoinhomogeneity are derived explicitly, while the effective properties and optimal conversion efficiency are discussed in detail via numerical analysis. Our results show that the nanoinhomogeneity equally effects both the figure of merit and the conversion efficiency. A carefully selected inhomogeneity not only improves the thermoelectric power factor but also suppresses the effective thermal conductivity, and thus greatly improves the optimal conversion efficiency. Specifically, a nanoinhomogeneity with higher electric and thermal conductivities generates a higher thermoelectric figure of merit regardless of the magnitude of its Seebeck coefficient. Noting that the thermoelectric performance improved by the presence of the inhomogeneity is restricted by the intensity of interface phonon scattering, we further calculate the expressions for the effective figure of merit in certain extreme cases. Furthermore, we see that a smaller inhomogeneity has a stronger ability to improve the conversion efficiency for a given doping proportion, mainly because the interface phonon scattering of the smaller inhomogeneity has a relatively greater effect on thermal conduction.