Major Poisson's Ratio Research Articles

Multiscale simulation and theoretical prediction for the elastic properties of unidirectional fiber‐reinforced polymer containing random void defects

AbstractPolymer‐matrix composites are widely used in various industries due to their high specific strength and specific stiffness. However, the void formation is inevitable as a by‐product during manufacturing processes, which may have negative effects on its mechanical properties. The purposes of this paper are to quantitatively evaluate the influence of voids on the anisotropic elastic properties of composites and to provide corresponding theoretical prediction models. Firstly, three‐dimensional representative volume elements (RVE) of fiber‐reinforced composite materials with different fiber contents (36.37%, 45.47%, 50.92%) and different void contents (1%, 3%, 5%, 7%) are established. To obtain the elastic properties in different directions, various periodic boundary conditions are applied to the RVE models and corresponding subroutines are developed by ABAQUS‐PYTHON. Secondly, a series of theoretical models are proposed to quickly predict the anisotropic elastic properties of unidirectional fiber/epoxy composites containing random‐sized void defects, which agree well with the finite element simulation results. Especially, the proposed models have concise expressions, which require only a few parameters to be input, and hence they are convenient for engineering application. Both theoretical and numerical results show that void defects have an obvious influence on the transverse modulus, major Poisson's ratio, and the out‐of‐plane shear modulus. When the void volume reaches 7%, all of the properties mentioned above decrease by more than 10% for the FRPs studied.

In-plane orthotropic property characterization of a polymeric battery separator

The in-plane characterization of an orthotropic porous polymer thin film used as separators in lithium-ion batteries was investigated. The mechanical behavior of an orthotropic material is described by the stress-strain relationships in the principal material directions and shear, and the Poisson's ratios. The measurements of the shear properties and the Poisson's ratio for polymer films with a thickness of tens micrometers has not been well established. In this work, these measurements were attempted for a separator of 25 μm thickness. The mechanical testing was performed with a dynamic mechanical analyzer (DMA). Digital image correlation (DIC) was used for strain measurements. The measured major Poisson's ratio was at a constant value whereas the minor Poisson's ratio increased linearly with strain. The symmetry condition for the elastic orthotropic relation was found to be valid up to 1% strain under transverse tension. The shear properties were measured with an off-axis tensile experiment. The shear modulus determined from the DIC strain measurement agreed well with that from the off-axis modulus and elastic constants. Based on the analogy for anisotropy between the elastic and linear viscoelastic domains, the shear creep response was measured with the off-axis tensile creep experiments. The creep compliances in shear and in the principal material directions were determined. This work laid the foundation for the development of orthotropic elastic and viscoelastic models for battery separators.

Hygrothermal viscoelastic material characterisation of unidirectional continuous carbon-fibre reinforced polyamide 6

This paper presents results of material characterisation experiments on the hygrothermal viscoelastic behaviour of unidirectional laminates of continuous carbon-fibre reinforced polyamide 6. The material behaviour when subjected to the automotive painting process is of interest. Coefficients of thermal- and -moisture expansion were determined from dilatometer experiments and micrometer measurements together with weighing, respectively. Diffusion coefficients were generated from thermogravimetric analysis and fitted with the Arrhenius equation. Dynamic mechanical analysis and digital image correlation of quasi-static tensile tests were performed to obtain a relaxation curve and a major Poisson's ratio, respectively. The Williams-Landel-Ferry equation was fitted to the time shift factors.

Effect of graphene layer thickness on effective modulus of 3D CNT/Graphene nanostructures

Three-dimensional CNT/Graphene nanostructure is consisted of vertically aligned carbon nanotube pillars grown directly on parallel graphene layers. The effect of graphene layer thickness on mechanical properties of the 3D nanostructure is analyzed. Overall, when the graphene layers experience the out-of-plane loading, the effective properties (Young's modulus, shear modulus, and major Poisson's ratio) of the 3D CNT/Graphene structure are significantly dependent upon the thickness of graphene layers. When the graphene layers experience the in-plane loading, the effective properties of the 3D CNT/Graphene structure depend upon the graphene thickness initially and then remain relatively unchanged as the thickness increases. It is found that the optimal performance of the 3D CNT/Graphene structure requires a minimum of thickness for the graphene layers, g/t > 5.

Non-sampling inverse stochastic numerical–experimental identification of random elastic material parameters in composite plates

A non-sampling probability identification method based on the generalized polynomial chaos (gPC) expansion is adopted for estimating random parameters of composite plates form experimental eigenfrequencies. For that, the parameters and the eigenfrequencies are approximated using gPC expansion. Distribution functions of the eigenfrequencies are identified from experimental data employing the Bayesian inference. This identification is then used to construct a vector of random variables and an orthogonal basis for eigenfrequency expansions. The parameters are characterized by the gPC having unknown deterministic coefficients and the same random basis as the eigenfrequencies. The stochastic finite element simulation of the plates bears as the model from which the parameter coefficients are estimated via an inverse problem. The major advantage of the method is using deterministic identification procedure. An application is presented for which samples of orthotropic laminated plates are tested to identify E-moduli, shear modulus and the major Poisson's ratio from measured modal frequencies.

Prediction on macroscopic elastic properties of interphase-contained long-fiber-reinforced composites and multiple nonlinear regression analysis

A convenient method to predict the macroscopic elastic performance of composite containing interphase was developed in this paper based on a new modified random sequential adsorption method and multiple nonlinear regression analysis. First, a three-phase micromechanical model with randomly distributed fibers was established with a new modified random sequential adsorption method named the Moving Window Method. Second, the macroscopic elastic behaviors of T300/914C were predicted based on micromechanical parameters of constituent materials using energy method, and the influence of the randomness of fiber distribution on the prediction was analyzed. Third, the effects of interphase thickness, interphase modulus and Poisson’s ratio on the macroscopic elastic properties of the composite were studied by changing these interphase micromechanical parameters gradually within certain ranges. Finally, the multiple nonlinear regression models that describe the relationship between the macroscopic elastic properties of T300/914C and micromechanical characteristic parameters of the interphase were established using a limited number of data from numerical simulation. Results indicate that the relative errors for the longitudinal modulus and the major Poisson's ratio are within ±1% while for the transverse modulus, shear modulus and Poisson’s ratio at cross section, the relative errors are within 5%.

Generally Cylindrical Orthotropic Constitutive Properties Modeling of Matrix-filled Single-walled Nanotubes: Axial Mechanical Properties

The technology of filling hollow carbon nanotubes with desirable materials has created tremendous interest in recent years. The objective of this study is to introduce analytical solutions for effective longitudinal Young's modulus and major Poisson's ratio of matrix-filled single-walled nanotubes (SWNTs). In this work, both SWNT and its filler material are considered generally cylindrical orthotropic. Analytical solutions are obtained and accordingly reduced to transversely isotropic as well as isotropic cases for both tube and filler materials, and then the results are compared with the existing solutions. For further validation, a 3-D model of a matrix-filled single-walled carbon nanotube (SWCNT) is generated and solved for displacement and strain results numerically, using the finite element method. The finite element numerical analysis is employed to verify the accuracy of the results obtained from the analytical approach for generally cylindrical orthotropic materials. Excellent agreement is achieved between the results obtained from the analytical and numerical methods. Furthermore, a parametric study is also conducted to investigate the effective properties variations of the matrix-filled nanotubes based on the variations of nanotube/filler geometry and material properties.

Transversely isotropic elastic properties of single-walled carbon nanotubes

While it is known that the elastic properties of a single-walled carbon nanotube (SWNT) are transversely isotropic, the closed-form solutions for all five independent elastic moduli have not been solved completely. In this paper, an energy approach in the framework of molecular mechanics is used to evaluate the local and global deformations of a SWNT in a unified manner. This is carried out under four loading conditions: axial tension, torsional moment, in-plane biaxial tension, and in-plane pure shear, respectively, from which the closed-form expressions for the longitudinal Young's modulus, major Poisson's ratio, longitudinal shear, plane strain bulk, and in-plane shear moduli are obtained. It is shown that as the tube diameter increases, the major Poisson's ratio approaches a constant, the longitudinal Young's and shear moduli and the plane strain bulk modulus are inversely proportional to the tube diameter, and the in-plane shear modulus is inversely proportional to the third power of the tube diameter. The dependence of the elastic moduli of a SWNT on the tube diameter and helicity is displayed and discussed.

Anisotropic properties of tracheal smooth muscle tissue.

The anisotropic (directional-dependent) properties of contracting tracheal smooth muscle tissue are estimated from a computational model based on the experimental data of length-dependent stiffness. The area changes are obtained at different muscle lengths from experiments in which stimulated muscle undergoes unrestricted shortening. Then, through an interative process, the anisotropic properties are estimated by matching the area changes obtained from the finite element analysis to those derived from the experiments. The results obtained indicate that the anisotropy ratio (longitudinal stiffness to transverse stiffness) is about 4 when the smooth muscle undergoes 70% strain shortening, indicating that the transverse stiffness reduces as the longitudinal stiffness increases. It was found through a sensitivity analysis from the simulation model that the longitudinal stiffness and the in-plane shear modulus are not very sensitive as compared to major Poisson's ratio to the area changes of the muscle tissue.

Experimental investigation of Poisson's ratio as a damage parameter for bone fatigue.

The fatigue loading of bone results in the degradation of mechanical properties such as strength and stiffness. Even though several authors have investigated the relationship between the longitudinal modulus and loading cycles, the reduction in Poisson's ratio and its relationship to fatigue loading cycles have not previously been investigated. In this study, the reduction in the major Poisson's ratio and longitudinal modulus for cortical bone specimens as a result of tensile fatigue was experimentally investigated. We compared the results of the major Poisson's ratio reduction to the reduction in longitudinal modulus to determine if there was a relationship between the two. The results showed that the reduction in Poisson's ratio was about 8-22% higher than the reduction in longitudinal modulus, indicating that more microdamage accumulated transversely than longitudinally. Both the longitudinal modulus and major Poisson's ratio decreased in a logarithmic fashion with increasing loading cycles for the bone specimens tested.

Effective elastic moduli of two-phase transversely isotropic composites with aligned clustered fibers

In this paper, we address the issue of the effective elastic moduli of transversely isotropic composites reinforced with aligned clustered continuous fibers. “Clustering” implies that there are portions of the matrix with a dense reinforcement of fibers and other portions with a sparse reinforcement. The clustering effect is characterized by a probability density distribution in “local” fiber volume fractions, obtained from the Dirichlet tessellation of a microstructure. Using a combination of Christensen and Lo's solution of a 3-phase boundary value problem and Hill's self-consistent method, the effective moduli are derived in terms of the probability density distribution function. It is shown that a unimodal distribution (representative of a random microstructure) has a modest effect on the effective moduli whereas a bimodal distribution (representative of a clustered microstructure) has a significant effect over a wide range of inclusion/matrix properties. A parametric study demonstrates that clustering has a significant effect on the shear moduli and the plane strain bulk modulus of the transversely isotropic composite and has a negligible effect on the longitudinal Young's modulus and the major Poisson's ratio. The theory has been compared with the Hashin-Rosen [1] bounds (appropriately modified for the clustered microstructure) and the classical Hashin-Shtrikman [2] bounds, and the theoretical predictions have been found to be bracketed by both bounds. In addition, the plane strain bulk modulus of a sample clustered periodic microstructure is computed by the developed theory and also by the finite element analysis, and the modulus computed by both approaches demonstrates a sensitivity to clustering.

Damage Development and Moduli Reductions in Nicalon—Calcium Aluminosilicate Composites under Static Fatigue and Cyclic Fatigue

Unidirectional and cross‐ply Nicalon fiber‐reinforced calcium aluminosilicate (CAS) glass‐ceramic composite specimens were subjected to tension–tension cyclic fatigue and static fatigue loadings. Microcrack densities, longitudinal Young's modulus, and major Poisson's ratio were measured at regular intervals of load cycles and load time. The matrix crack (0° plies) density and transverse crack (90° plies) density increased gradually with fatigue cycles and load time. The crack growth is environmentally driven and depends on the maximum load and time. Young's modulus and Poisson's ratio decreased gradually with fatigue cycles and load time. The saturation crack densities under fatigue loadings were found to be comparable to those under monotonic loading. A matrix crack growth limit strain exists, below which matrix cracks do not grow significantly under fatigue loading. This limit coincides with the matrix crack initiation strain. Linear correlations between crack density and moduli reductions obtained from quasi‐static data can predict the moduli reductions under cyclic loading, using experimentally measured crack densities. A logarithmic correlation can predict the Young's modulus reduction in a limited stress range. A fatigue crack growth model is proposed to explain the presence of two distinct regimes of crack growth and Young's modulus reduction.

Elastic constants of orthotropic composite materials using plate resonance frequencies, classical lamination theory and an optimized three-mode rayleigh formulation

This paper shows how the four independent elastic constants (longitudinal and transverse Young's moduli, in-plane shear modulus and major Poisson's ratio) of an orthotropic material may be extracted from the modal resonance data of a freely-supported rectangular thin plate made from the material, using the classical lamination theory and an optimized three-mode Rayleigh formulation with a suitably formed least-squares objective function. Results are obtained for orthotropy ratios of unity (aluminum), about three (unidirectional E-glass/vinylester) and about 13 (graphite/epoxy), and plate aspect ratios of unity and about two. The results suggest that the method proposed has potential for rapid characterization of elastic properties of advanced composites.

Characterization and modeling of microcracking and elastic moduli changes in nicalon/cas composites

The damage progression in silicon carbide fiber (Nicalon) reinforced calcium alumino-silicate (CAS) glass-ceramic composites subjected to monotonic uniaxial tensile loading has been studied. A unidirectional composite and three cross-ply laminates were investigated. Microcrack densities were recorded at regular intervals of applied stress. Young's modulus and the major Poisson's ratio were also measured at the corresponding stress levels. Both longitudinal and transverse stress/strain relations show significant nonlinearity with the onset and development of damage. Matrix microcracking in a direction perpendicular to the applied load reaches a critial level, and the Young's modulus and Poisson's ratio start decreasing. On further loading, cracking increases and reaches a saturation level. A shear lag model was used to predict the variation of Young's modulus with applied stress based upon the experimentally measured crack densities. Model predictions suggest that at the saturation of matrix cracking, load transfer from the fibre to the matrix occurs only through frictional stresses. In the cross-ply laminates the two major modes of damage are transverse cracking in the 90° plies and matrix cracking in the 0° plies. The initiation strain and saturation density of transverse cracks increase as the 90° layer thickness decreases. The initiation strain and the saturation density of matrix cracks in the 0° plies of the cross-ply laminates are comparable to those of matrix cracks in the unidirectional composite. A shear lag model was adapted to calculate the reduced Young's modulus of the cracked 90° plies. The shear lag model for the unidirectional composite was used to calculate the reduced Young's modulus of the 0° plies. The reduced moduli of both 0° and 90° plies were input to the rule of mixtures for predicting the Young's moduli of the cross-ply laminates. Here again, model predictions suggest thay at the saturation of matrix cracking, load transfer from the fiber to the matrix occurs only through frictional stresses.

Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties

A microporous, anisotropic form of expanded polytetrafluoroethylene has been found to have a large negative major Poisson's ratio. The value of Poisson's ratio varies with tensile strain and can attain values as large as -12. The microporous structure of the material is described and the mechanisms that lead to this large negative Poisson's ratio are identified. Micro-rotational degrees of freedom are observed, suggesting that a micropolar elasticity theory may be required to describe the mechanical properties.

Compressive Fatigue and Static Properties of a Unidirectional Graphite/Epoxy Composite

Static and fatigue properties of a unidirectional graphite/epoxy composite were determined experimentally under compressive loading. A programable data acquisition system was used to record axial and bending strains and load. When the moduli are calculated from the average axial values, they are shown to be insensitive to the magnitude of bending. When under compressive load, a (±45)s, angle-ply specimen is shown to be suitable for obtaining axial shear properties of a unidirectional lamina. Axial, transverse, and shear moduli as well as major Poisson's ratio and the corresponding strength values are obtained for quasi-static conditions. Under fatigue conditions, life expectancy is the highest for axial loading, next for transverse loading, and least for axial shear loading.

Comment on "Buckling of Composite Plates with a Free Edge in Edgewise Bending and Compression"

T ABLE 2 of Ref. 1 presented buckling loads for a laminated rectangular plate with two loaded edges simply supported, one side free and the opposite side either simply supported or clamped, for linearly varying edge loads. Since the analysis of Ref. 1 is based on classical plate theory, it is of interest to compare those results with buckling loads that include the effect of transverse shear deformations. Such buckling loads have been presented for plates with uniformly loaded edges. These were calculated using the shell-of-revolution program FASOR by considering the plate as part of a cylinder of very large radius. The circumferential direction of the cylindrical model corresponds to the longitudinal (loaded) direction of the plate, and the axial length of the cylinder equals the plate width b. The plate buckling load is obtained by minimizing the model buckling load with respect to the circumferential wave number N subject to the condition N=nirR/a, where n is the number of longitudinal half-waves of the plate buckle, R is the radius of the cylindrical model, and a is the length of the plate. This procedure is also applicable to plates with linearly varying edge loading. The dimensions of the laminated plate analyzed in Ref. 1 are 0 = 254 mm (10 in.) and 6 = 50.8 mm (2 in.). It is made of 0.127-mm (0.005-in.)-thick tape with the following insurface elastic properties: EX/E2 = 10.05, G12/E2 = Q.349, Hi =0.34, and E2 = 13.03 GPa (1.89x 10 psi), where 1 and 2 signify directions parallel and transverse, respectively, to the fibers and /*, is the major Poisson's ratio. The laminate definition is [±453/03]5 (erroneously reported as [±453 / 03/903]5in Ref. 1), thus giving a laminate thickness /z = 2.286 mm (0.090 in.) Neglecting the small anisotropic effect, this laminate has the bending stiffness matrix given by Eq. (25) of Ref. 1. Since the values of the transverse shear moduli G13 and G23 are unavailable, it is assumed that G13 = G23 = G12. (For typical unidirectional laminae, G23<G12 .) Again neglecting the small anisotropic effect, FASOR gives the transverse shear stiffness matrix [K] =8.951 x 10 N/m (5.112xl0 Ib/in.) [/], where [/] is the 2 x 2 unit matrix. Table 1 compares the classical plate theory results of Ref. 1 with the transverse shear deformation theory results Simply supported

Strain Rate, Temperature, and Humidity Influences on Strength and Moduli of a Graphite/Epoxy Composite

Results of an experimental study of the influence of strain rate, temperature, and humidity on the mechanical behavior of a graphite/epoxy fiber composite are presented. Three principal strengths (longitudinal, transverse, and shear) and four basic moduli (longitudinal, transverse, axial shear, and major Poisson's ratio) of a unidirectional graphite/epoxy (T300/5208) composite were studied as functions of strain rate, temperature, and humidity. Each test was performed at a constant tensile strain rate in an environmental chamber providing simultaneous temperature and humidity control. Before being tested, specimens were given a moisture preconditioning treatment at 60°C. Values for the matrix-dominated moduli and strength were significantly influenced by both environmental and rate parameters, whereas the fiber-dominated moduli were not. However, the longitudinal strength was significantly influenced by temperature and moisture content. A qualitative explanation for these observations is presented.

Evaluation of elastic moduli of composite materials by linear programming

A method of applying linear programming to evaluate the elastic moduli of unidirectionally fiber-reinforced composite materials is presented. Based on the theory of elasticity, the stresses and displacements of the fiber and of the resin are expressed in terms of harmonic series. The coefficients of the series are determined by the simplex algorithm to minimize the deviations which occur when the stresses and displacements are matched at the fiberresin interface and at the outer boundary of the representative element of the composite. By applying the energy principle, the Young's modulus in the fiber direction and the major Poisson's ratio of the E-glass/resin composite are found to be in good agreement with existing results, while the gap of the bounds for its bulk modulus is considerably narrowed in comparison to earlier results.