Effective Mechanical Properties Of Composites Research Articles

Average Eshelby tensor of an arbitrarily shaped inclusion from convexity to non-convexity: Effective elastic properties of composites

The effective mechanical properties of composites are strongly influenced by the morphology, volume fraction, and properties of the inclusion phase. Extensive theoretical models for the evaluation of effective properties are mainly based on the continuum micromechanics derived from the well-known Eshelby’s solution of an ellipsoidal inclusion problem, which are subjected to the limitations on the Eshelby tensor for a non-ellipsoidal inclusion. This work devises a three-step method to derive the average Eshelby tensor of an arbitrarily shaped inclusion from convexity to non-convexity in an elastic field. The proposed three-step method is user-friendly and avoids the singularity that arises from solving the complicated integrals for an arbitrarily shaped inclusion. The calculated average Eshelby tensors of inclusions with different morphologies, including Platonic solids, superballs, superellipsoids, doughnuts, helices, and non-convex particles, are thereafter compared against the existing data reported in the literature, in order to verify the reliability of the present method. Moreover, we also incorporate the proposed method into a micromechanical model to predict the effective elastic moduli of two-phase composites, in which congruent non-ellipsoidal inclusions of a specific volume fraction are randomly distributed in a homogeneous matrix. Comparisons with the direct finite element method (FEM) simulations indicate that the developed micromechanical model is a reliable means to evaluate the elastic properties of composites. The proposed average Eshelby tensor of an arbitrarily shaped inclusion can also be generalized to the theoretical predictions of the effective transport properties of composites with inclusions of diverse types and shapes, such as particles, rocks, granules, pores, fibers, and cracks.

Determination of the mechanical properties of 3d-printed polymer products by methods of structural mechanics

Mathematical models of stress-strain state (SSS) for modeling tests of polymer composite samples obtained by fused deposition modeling (FDM) in approximations of isotropic and orthotropic media are formulated. An algorithm for solving the inverse SSS problem to determine the effective mechanical properties in the orthotropic approximation of composite products printed by the FDM method has been developed. Numerical models have been developed to solve inverse SSS problems to determine the effective orthotropic mechanical properties of composite products with different degrees of reinforcement, obtained using additive technologies based on the FDM method. The grid convergence of the developed numerical models by the method of double recalculation is investigated. It is established that the used mesh of geometric models of product samples leads to errors in determining the vector of the modulus of elasticity in the range of 0–3.19%, and the vector of the shear modulus does not exceed 0.05–0.2%. Numerical experiments to determine the effective mechanical properties of samples of composite polymeric materials in the approximation of orthotropic homogeneous medium were performed. The obtained results are compared with the data of calculations by analytical dependences to determine the effective mechanical properties of composite materials. It is shown that the results of numerical studies agree satisfactorily with the corresponding data obtained from analytical dependences in the range of 0.081–5.696%. It is established that all three components of the vectors of modulus of elasticity and shear increase with the degree of reinforcement. The largest increase is observed for the components of vectors and , which is due to the reinforcement in the direction , and the difference between the values ​​of the components of vectors and and and is due to the cross-sectional asymmetry of the strand. Dependences for operative prediction of effective orthotropic mechanical properties of composites based on PLA + KEVLAR 29 within the limits of change in the volume fraction of reinforcing fibers up to 5% are obtained. To develop new composite materials with predetermined properties, it is not necessary to perform multivariate, rather complex and cumbersome numerical experiments in solving the inverse SSS problem.

Study of complex morphology of agglomerations formed by graphite nanoinclusions and its effect on the mechanical properties of the composite materials

The effective mechanical properties of composites are affected by the distribution and formation of agglomerations of graphite nanoparticles in a polyester resin matrix. The samples were made varying the volume concentration of inclusions and their maximum tensile strength and morphology of agglomerations were measured. The morphology of agglomerations was analyzed by measuring their average area, fractal dimension and lacunarity from the micrographs. A predictive model of the effective mechanical properties based on the rule-of-mixtures (ROM) was proposed, the parameters related to the complex microstructure were incorporated into the ROM model. This modified model proved to be a good tool for describing the effect of inclusions on effective mechanical properties by changing their volume concentration. Also, a statistical model based on multiple linear regression of observable variables was proposed, which is better for predicting the effective mechanical property.

Analytical modeling of low velocity impact on carbon nanotube-reinforced composite (CNTRC) plates

ABSTRACTIn this paper, a new analytical model for behavior of carbon nanotubes reinforced composite plates under low velocity impact has been presented. Nanotubes aligned, straight and randomly oriented are distributed on rectangular simply supported composite plate. The Mori–Tanaka model is used to obtain effective mechanical properties of composites reinforced with nanotubes consisting of aligned, straight and randomly oriented carbon nanotubes embedded in a polymer matrix. The analytical model based on the first-order shear deformation theory and spring-mass model. The results of analytical model are compared with the results of low velocity impact on fiber-reinforced polymer composites. The results show that the deflection and energy absorption of plate in a randomly oriented distribution is more than aligned straight of carbon nanotubes in the composite layers.

Annular Coated Inclusion model and applications for polymer nanocomposites – Part II: Cylindrical inclusions

This work provides an analytical solution for the unknown components of the dilute strain concentration tensors for coated cylindrical inclusions, which can be directly implemented into traditional micromechanical models to predict the effective mechanical properties of composites with coated cylindrical/fibrous inclusions. Comparison of the predictions of the proposed model with predictions based on the standard Mori-Tanaka (MT) approach shows that differences between the models are largest when the annular interphase region is softer than the matrix material. A two-dimensional finite element (FE) analysis is then used to benchmark the transversely isotropic composite behavior captured in the proposed model. Using standard orientational averaging approaches, the effective moduli of composites with randomly oriented cylindrical inclusions are predicted and compared to experimental results for polymer nanocomposites described in the literature, providing insight into the utility of the approach. In addition, by providing an analytical solution to the dilute strain concentration tensor, the proposed methodology would allow one to connect the average stress and strain fields in the constituent phases to known macroscopic fields. The proposed model may be particularly useful as a guide to evaluate the impact of various strategies that seek to tailor the properties of the interphase region in nanocomposite materials.

Representative volume element for composites reinforced by spatially randomly distributed discontinuous fibers and its applications

Combining with the random sequential absorption (RSA) algorithms, the method entitled Fiber Growth Method is presented for generating the representative volume element (RVE) with the spatially randomly distributed discontinuous fibers and with a relatively high fiber volume fraction (∼25%). The formulation of the Axes Distance Method for checking the overlapping of fibers in the RVEs is discussed. Within the framework of elasticity, the generated RVEs are analyzed to obtain the effective mechanical properties of composites reinforced by spatially randomly distributed discontinuous fibers using the numerical homogenization technique based on the finite element analysis (FEA). The validation is performed by comparing the Bulk modulus and Shear modulus predicted by the FEA against those obtained from the traditional equations based on the Halpin–Tsai estimation. FEA results show that due to the spatial random distribution of fibers, composites behaves homogeneously isotropic at the macroscopic scale. Bulk moduli and Shear moduli of composites increase with the fiber volume fraction increasing while the Poisson’s ratios of composites decrease.

A Closed-Form Solution of Effective Young's Modulus for Composites Including Multi-Shape Inclusions Using Improved Mori-Tanaka Model

In this paper, an improved model is proposed by combining Mori-Tanaka method with Eshelbys equivalent inclusion concept to derive a closed-form solution of the effective Young's modulusE11for hybrid composites reinforced with multi-shapes inclusions. When only the fiber-like inclusions are considered in the model, the results are consistent with those from Tandons unidirectional aligned composites based on Mori-Tanaka theory. For composites reinforced with fiber-like and spherical inclusions, the homogenization theory is employed to verify the effects of the proposed model. The influence of volume fraction and Youngs modulus of each phase on effective Youngs modulusE11is investigated, and the results show thatE11is sensitive to the inclusion shapes, and the model is practicable to predict the effective mechanical properties of composites reinforced by several inclusions with different shapes.

Effective Mechanical Properties for Composites with Three-Phase Randomly Distributed Aggregates Predicted by Multi-Step Mori-Tanaka Method

Multi-step Mori-Tanaka method (MMT) is applied to the estimation of the effective mechanical properties for composites with three-phase randomly distributed aggregates in this paper. The Multi-phase Homogenization Theory (MHT) which is based on mathematical homogenization method and is employed to verify the results of MMT method. Results show that MMT method is reasonable and practicable to predict the effective mechanical properties of composites with several phases, and the Young’s moduli and Poisson’s ratios of each phase may have some effects on the effective mechanical properties of multi-phase composites.

On the mechanical properties of alumina–epoxy composites with an interpenetrating network structure

Methods of predicting effective mechanical properties of composites with an interpenetrating network structure are currently not well understood, particularly for cases in which the constituent materials have widely differing properties. Alumina–epoxy composites with an interpenetrating composite structure have been produced via an infiltration process and the elastic properties were measured via the impulse excitation technique. A strong dependence of properties on composition and processing was observed. Properties were compared with several mixing law predictions made using compositional data obtained from microstructural analysis. The effective medium approximation (EMA) was shown to predict properties adequately, whilst others models proved inappropriate.

The Macro-Microscopic Numerical Simulation of the Mechanical Behavior of CFCC with Matrix Anisotropic Damage by Homogenization Method

Abstract In this paper, a damage constitutive model based on a micro-mechanical approach is established and used to predict the macro-microscopic elastic-brittle mechanical behavior of continuous fiber reinforced ceramic matrix composites (CFCC). Anisotropic damage is applied to describe the matrix phase damage which reflects all types of damage such as nucleation and coalescence of voids and micro-cracks that the matrix material undergoes. The asymptotic expansion homogenization method is used to obtain the effective mechanical properties of composites and to derive the homogenized damage elastic concentration factor and the gross stiffness matrix of unidirectional and cross-ply laminate composite materials. Internal variables are introduced to describe the evolution of the damage state and the degradation of the material stiffness. Using the proposed theory, the unidirectional composite and the cross-ply laminate composites with /03/90/03/, /03/902/03/, and /03/903/03/ stacking sequences are analyzed, and the numerical results are consistent with those of the experiments.

Effective Mechanical Properties of Composites at Finite Deformations

A new representation theorem for the deformation gradient rate in the presence of cracks and kinematic constraints is presented. This representation theorem uses an extension of the concept of transformation strains to finite deformations. Based on the representation theorem the overall concentration factor was decomposed into contributions from the opening and sliding of cracks and from material nonhomogeneities. Also, inelastic deformations at the microscale were related to those at the macroscale through elastic concentration factors, where it was found that some of the elastic deformation at the microscale may contribute to the macroscale inelastic deformations.