Elastic Constants Of Composites Research Articles

Modeling elastic properties of biocomposites using various analytical models and ansys material designer

A major focus of emerging research is the design and development of new materials for future industries in order to replace older ones in an environment-friendly way. Composite material is one of them, especially biocomposites. Over the past few decades, there is a lot of advancement in developing composite materials. We can see the applications of composite materials are increasing day by day in aerospace, automotive, medical, and construction field. Generally, the properties of unidirectional composites are evaluated by analytical methods or by Finite element Method. We present here a study of the properties of unidirectional biocomposite by using Ansys Material Designer and compare them with analytical methods including Rule of mixtures (ROM), Modified Rule of mixtures (MROM), Halpin-Tsai, Chamis, and Elasticity Approach models. The use of finite element analysis requires rigorous analysis of representative volume element (RVE), results strongly depend on the loading and boundary conditions we applied. So it is a cumbersome task to find out the elastic constants of composites. Hence, we used Ansys material designer, which is the easiest and quickest way of modeling composites. It is also possible to model various RVEs like square, hexagonal, and diamond. The results obtained by analytical methods and Ansys material designer are compared through graphs and the explanation is provided for each deviation in the properties. The results show great accuracy as compared with analytical methods. Only the Transverse elastic modulus (E22) and in-plane shear modulus (G12) show slight variation in properties. As we got accurate results, we also proposed properties for Random unidirectional, Woven, and Chopped fiber composites also by using Ansys material designer.

A re-formulation of the Mori–Tanaka method for predicting material properties of fiber-reinforced polymers/composites

In this investigation, a re-formulation has been developed to investigate the effect of fiber aspect ratio on the effective elastic moduli of fiber-reinforced polymers/composites. The matrix and inclusions are considered as isotropic materials. The five independent elastic constants are derived based on a modified Mori–Tanaka theory. The relationship between composite elastic constants and inclusion aspect ratio is also established. Three types of composites containing unidirectional aligned fiber and two-dimensional and three-dimensional random orientated inclusions are explicitly analyzed. Moreover, three extreme cases involving long fibers, spheres, and thin discs are taken into account. It is found that the longitudinal elastic properties are very sensitive to fiber-like inclusions, whereas the transverse elastic properties are closely related to disc-like inclusions.

A robust Bézier based solution for nonlinear vibration and post-buckling of random checkerboard graphene nano-platelets reinforced composite beams

In the present study, an accurate Bézier based multi-step method is developed and implemented to find the nonlinear vibration and post-buckling configurations of Euler-Bernoulli composite beams reinforced with graphene nano-platelets (GnP). The GnP is assumed to be randomly and uniformly dispersed in the composite mix-proportion, with a random checkerboard configuration. Therefore, a probabilistic model together with an efficient simulation technique is proposed to find the effective moduli of a matrix reinforced GnP. It is worth noting that the presented micro-mechanics model found by the employed Monte-Carlo simulation matches exactly the experimental data and predicts the composite elastic constants more accurate than that found from other common methods, including the Halpin-Tsai theory. Also, for mathematical simplification, the composite beam in-plane inertia is neglected. The presented multi-step method is based on Burnstein polynomial basis functions while shows interesting potential to provide robust solutions for various initial and boundary value problems. It is found that adding a relatively low content of GnP would drastically increase the composite elastic constants, particularly in the transverse direction to fiber. In addition, the numerical results are compared with those provided by exact analytical solutions, where the stability of results suggests the effectiveness of the presented methodology.

Strategies for modelling and optimization of bi-stable composite laminates actuated by embedded Shape Memory Alloy wires

Shape-adaptive or morphing capability is regarded as significant to increase aerodynamic performance of airfoils employed in aerospace, wind turbines or race cars, while at the same time reducing the number of moving parts. The inherent bistable behavior of asymmetric cross-ply composites makes them as a suitable candidate for morphing applications with a small energy input, and an efficient way to switch between the two equilibrium configurations is given by embedded shape memory alloy (SMA) wires. However, when a bi-stable composite plate is integrated with SMA wires (Shape Memory Alloy Composite, SMAC), the identification of design parameters, namely laminate size and layup, composite elastic constants, SMA wires number and thermomechanical behavior, SMAC manufacturing cycle, is not straightforward. The present work described the strategies developed by the authors to model and optimize a SMAC subjected to bi-stability and post-manufacturing deflection requirements.

A contribution of the reliability based approach for cylindrical composite of sensitivity analytical design

The present paper focuses on the sensitivity evaluation of analytical design tool of cylindrical composite structures to geometrical and mechanical uncertainties through a reliability approach based on the Monte Carlo method. The present tool design is developed to study the analytical mechanical response of multilayered cylindrical composite structures under pressure and to access strain and stress states. Using the hoop stress for each ply, the Monte Carlo method is used to predict the distribution function of the mechanical response, for random design variables of composite structure. Three random design variables with uncertainties are selected, namely: composite elastic constants, ply angles and finally the mechanical loading (pressure). To ensure accuracy of results, we performed 104 simulations. The results obtained show that the probability of failure increases significantly when all the random variables are considered simultaneously.

Quantification of effects of stochastic feature parameters of yarn on elastic properties of plain-weave composite. Part 1: Theoretical modeling

This paper is a comprehensive theoretical study on the influences of stochastic feature parameters of yarn on elastic properties of plain-weave composite. The compliance (or stiffness) of yarn is obtained by introducing the Taylor expansion of local stochastic variable metric basis and applying orientation averaging method. Volume averaging method is then employed to compute the elastic properties of plain-weave composite. The lower and upper bounds of the impacts of stochastic feature parameters of yarn on elastic constants of the composite can be obtained by utilizing isostress and isostrain conditions. The numerical results show that the elastic constants of plain-weave composite are determined by the comprehensive effect of definite statistics of feature parameters of yarn. Once the statistics of feature parameters of yarn are determined, the influences of stochastic feature parameters of yarn on elastic properties of composite can be quantified.

Micromechanics of Composites Using a Two-Parameter Model and Response Surface Predictions

A novel method involving the use of micromechanical analysis to predict elastic constants of a unidirectional fiber-reinforced composite is proposed. The method revolves around a model called the two-parameter model. The two parameters are obtained by performing one micromechanical analysis of the composite unit cell along one of its transverse directions. The method involves construction of response surfaces that act as surrogate models, for the prediction of the two parameters, corresponding to any fiber-reinforced composite design that uses a transversely isotropic fiber and an isotropic matrix. Using the two parameters, four of the five elastic constants can be computed. The fifth elastic constant, longitudinal shear modulus, is predicted using a separate response surface. The results indicate that the two-parameter model in conjunction with the response surface makes accurate prediction of composite elastic constants.

Buckling Load Design of Long Cross-Ply Laminates of Hybrid Construction with Material Uncertainties

Elastic constants of composites are often determined with some level of uncertainty. In the present study minimum cost design problem for long cross-ply plates of hybrid construction is solved subject to material uncertainties. By using minimum amount of more expensive composite in outer layers and less expensive composite in inner layers, a more efficient and cost-effective design is obtained. The effect of hybridization is studied for uniformly and linearly varying buckling loads.

Parametric constitutive model of plain-weave fabric reinforced composite ply

A computational model that allows to explicitly determine orthotropic elastic constants of plain-weave fabric-reinforced composite ply as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic representative volume element is employed. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.

Probabilistic analysis of the mechanical response of thick composite pipes under internal pressure

In the present work an analytical method is developed to study the mechanical response of thick composite pipes under internal pressure. The present method considers that the surface tension must satisfy, on the interface between two adjacent layers, all the boundary conditions imposed on the radial and hoop stresses, which are computed using a specific model for thick multi-layered composite cylinders suggested by Tsai. This model uses the plane strain states of cylindrical tubes under internal pressure containing a number of cylindrical sub-layers, each of which is cylindrically orthotropic. Such analytical method is considered as simple, fast and precise compared to other analytical and numerical methods. Thereafter, the effects of random design variables on the pipe behavior are quantified by probabilistic analysis. Using these stress components for each ply, the Monte Carlo method is used to predict the distribution function of the mechanical response, in addition to the failure probability. Five random design variables are considered, namely, the composite elastic constants, the ply angles, the inner and outer diameters, thickness and the mechanical loading. The improvement of multi-layered filament-wound composite pipes design based on the probabilistic analysis is also discussed. According to the obtained results, we note that the thickness of the pipe and the internal pressure variation are the principal factors influencing the scatter of stress distribution.

Micromechanical Model for the Orthotropic Elastic Constants of Polyetheretherketone Composites Considering the Orientation Distribution of the Hydroxyapatite Whisker Reinforcements

Hydroxyapatite (HA) whisker reinforced polyetheretherketone (PEEK) composites have been investigated as bioactive materials for load-bearing orthopedic implants with tailored mechanical properties governed by the volume fraction, morphology, and preferred orientation of the HA whisker reinforcements. Therefore, the objective of this study was to establish key structure-property relationships and predictive capabilities for the design of HA whisker reinforced PEEK composites and, more generally, discontinuous short fiber-reinforced composite materials. HA whisker reinforced PEEK composites exhibited anisotropic elastic constants due to a preferred orientation of the HA whiskers induced during compression molding. Experimental measurements for both the preferred orientation of HA whiskers and composite elastic constants were greatest in the flow direction during molding (3-axis, C33), followed by the transverse (2-axis, C22) and pressing (1-axis, C11) directions. Moreover, experimental measurements for the elastic anisotropy and degree of preferred orientation in the same specimen plane were correlated. A micromechanical model accounted for the preferred orientation of HA whiskers using two-dimensional implementations of the measured orientation distribution function (ODF) and was able to more accurately predict the orthotropic elastic constants compared to common, idealized assumptions of randomly oriented or perfectly aligned reinforcements. Model predictions using the 3-2 plane ODF, and the average of the 3-1 and 3-2 plane ODFs, were in close agreement with the corresponding measured elastic constants, exhibiting less than 5% average absolute error. Model predictions for C11 using the 3-1 plane ODF were less accurate, with greater than 10% error. This study demonstrated the ability to accurately predict differences in orthotropic elastic constants due to changes in the reinforcement orientation distribution, which will aid in the design of HA whisker reinforced PEEK composites and, more generally, discontinuous short fiber-reinforced composites.

Parametric constitutive model of uni-directional fiber–matrix composite

A computational model that allows to explicitly determine transversely isotropic elastic constants of uni-directional fiber–matrix composite tow as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic RVE is employed. The technique is enhanced by introduction of averaging procedure over different shapes of the 2D fiber layout pattern in the tow cross-section. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.

Combining self-consistent and numerical methods for the calculation of elastic fields and effective properties of 3D-matrix composites with periodic and random microstructures

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.

Ultrasonic material characterization using large-aperture PVDF receivers

This work describes the use of a large-aperture PVDF receiver in the measurement of liquid density and composite material elastic constants. The density measurement of several liquids is obtained with accuracy of 0.2% using a conventional NDE emitter transducer and a 70-mm-diameter, 52 - μ m P(VDF–TrFE) membrane with gold electrodes. The determination of the elastic constants is based on the phase velocity measurement. Diffraction can lead to errors around 1% in velocity measurement when using alternatively the conventional pair of ultrasonic transducers (1-MHz frequency and 19-mm-diameter) operating in through-transmission mode, separated by a distance of 100 mm. This effect is negligible when using a pair of 10-MHz, 19-mm-diameter transducers. Nevertheless, the dispersion at 10 MHz can result in errors of about 0.5%, when measuring the velocity in composite materials. The use of an 80-mm diameter, 52 - μ m -thick PVDF membrane receiver practically eliminates the diffraction effects in phase velocity measurement. The elastic constants of a carbon fiber reinforced polymer were determined and compared with the values obtained by a tensile test.

Composite Skin Elastic Constants from Monolithic In-plane Specimens and Bonded Out-of-plane Specimens

In this study, a full set of elastic constants (in-plane (IP) and out-of-plane (OOP)) is determined/estimated for two sandwich composite skin laminates. For the out-of-plane properties, compression and shear specimens are cut from the skin laminates and bonded together to avoid making thick laminates. This approach gives a relatively low experimental scatter for the elastic constants indicating that the measurements are not affected by the presence of the thin adhesive layers between the laminates. Finite element calculations are performed to further study the effect of the adhesive layers. It is found that the effect of the adhesive layers is minor in the range of strains used to determine the elastic constants.

A new model to predict effective elastic constants of composites with spherical fillers

In this study, a new model to predict the effective elastic constants of composites with spherical fillers is proposed. The original Eshelby model is extended to a finite filler volume fraction without using Mori-Tanaka’s mean field approach. When single filler is embedded in the matrix, the effective elastic constants of the composite are computed. The composite is in turn considered as a new matrix, where new single filler is again embedded in the matrix. The predicted results by the present model with a series of embedding procedures are compared with those by Mori-Tanaka, self-consistent, and generalized self-consistent models. It is revealed through parametric studies such as stiffness ratio of the filler to the matrix and filler volume fraction that the present model gives more accurate predictions than Mori-Tanaka model without using the complicated numerical scheme used in self-consistent and generalized self-consistent models.

Genetic algorithm reconstruction of orthotropic composite plate elastic constants from a single non-symmetric plane ultrasonic velocity data

This paper reports a Genetic Algorithm (GA) based reconstruction procedure to determine the elastic constants of an orthotropic plate from ultrasonic velocity data. Phase velocity measurements are carried out using ultrasonic back-reflection technique on laminated unidirectional graphite–epoxy (0) 16 and quasi-isotropic graphite–epoxy (+45, −45, 0, 90) 7s fiber reinforced composite plates. A forward model to generate the slowness curves from elastic constants has been used to verify the quality of the reconstruction. The sensitivity of the chosen GA parameters is studied. As expected, out of 9 orthotropic elastic constants to be determined, the C 23 and C 44 found to be insensitive. The GA based reconstruction using data obtained from multiple planes were evaluated and it is shown that the single plane reconstruction at a non-symmetric plane was sufficient for the computation of the seven elastic constants.

Predicting Elastic Constants of 2D-Braided Fiber Rigid and Elastomeric–Polymeric Matrix Composites

In a previous work, an analytical model based on Classical Laminate Plate Theory (CLPT) was developed to predict the braid elastic constants (Ex, Ey, Gxy and xy) of closed-mesh 2Dbraided fiber composite. In this work, the sensitivity of the braid elastic constants to composite constituent elastic constants was evaluated. The torsion of thin-walled tubes was used to experimentally obtain the braid shear modulus. The results predicted by the model are in good agreement with other models and with experimental results for Ex and Gxy of Kevlar 49 fiber-braided tubes with both rigid epoxy and elastomeric polyurethane resin matrices.

Probabilistic deformation and strength prediction for a filament wound pressure vessel

In this study; probabilistic analysis and experimental tests are conducted to predict the probabilistic deformation and strength of composite pressure vessels subjected to inner pressure loading. A computer code was utilized for the progressive failure analysis and probabilistic strength analysis with the Edgeworth expansion method and the Monte-Carlo method. The effects of design random variables on the structural behavior of the composite pressure vessel were quantified by probabilistic analysis. Three design random variables with uncertainties were selected: (1) composite elastic constants; (2) lamina strength; and (3) the thickness of the helical and hoop layer. The accuracy of probabilistic analysis was verified by comparing the predicted results with the experimental hoop strain or with the burst pressure obtained by a hydro-test with ten composite pressure vessels. The improvement of the structural design based on the probabilistic analysis is also discussed. The sensitivities of each response to the design random variables were evaluated and conclusions are drawn concerning the relative importance of these variables in the design problem.

Fiber packing and elastic properties of a transversely random unidirectional glass/epoxy composite

Image analysis was used to characterize the microstructure of a unidirectional glass/epoxy composite which was found to be transversely randomly packed. Starting from a measured distribution of fiber diameter, a Monte Carlo procedure was employed to generate periodic computer models with unit cells comprising of random dispersion of a hundred non-overlapping parallel fibers of different diameter. The morphology generated in this way showed excellent agreement with that of the actual composite studied. An ultrasonic velocity method was used to measure a complete set of composite elastic constants and those of the epoxy matrix. On the basis of periodic three-dimensional meshes, the composite elastic constants of the Monte Carlo models were calculated numerically. Numerical and measured elastic constants were in good agreement. It was shown numerically that the randomness of the composite microstructure had a significant influence on the transverse composite elastic constants while the effect of fiber diameter distribution was small and unimportant. The predictive potential of the Halpin-Tsai and some other models commonly employed for predicting the elastic behavior of unidirectional composites was also assessed.